Finite Group Databasebeta

← C73×#15273 #32924677

Subgroups — C73×#15273 #32924677

Order 18688.

2946 conjugacy classes of subgroups.

The subgroup lattice has 1530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#121×C73C211yesmaximal, characteristic, complemented
2C2×#392×C73C211yesmaximal, characteristic, complemented
3C2×#392×C73C211yesmaximal, characteristic, complemented
4C2×#392×C73C211yesmaximal, characteristic, complemented
5C2×#386×C73C211yesmaximal, characteristic, complemented
6C2×#386×C73C211yesmaximal, characteristic, complemented
7C2×#386×C73C211yesmaximal, characteristic, complemented
8C2×#386×C73C211yesmaximal, characteristic, complemented
9C73×#1442C211yesmaximal, characteristic, complemented
10C73×#1440C211yesmaximal, characteristic, complemented
11C73×#1440C211yesmaximal, characteristic, complemented
12C73×#1439C211yesmaximal, characteristic, complemented
13C73×#1438C211yesmaximal, characteristic, complemented
14C73×#1438C211yesmaximal, characteristic, complemented
15C73×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C73C2211yescharacteristic
17C23×D4×C73C2211yescharacteristic
18C23×D4×C73C2211yescharacteristic
19C23×D4×C73C2211yescharacteristic
20C23×D4×C73C2211yescharacteristic
21C23×D4×C73C2211yescharacteristic
22C24×C4×C73C2211yescharacteristic
23C24×C4×C73C2211yescharacteristic
24C2×#121×C73—24no—
25C2×#121×C73—24no—
26C2×#121×C73—24no—
27C22×C4⋊C4×C73C2211yescharacteristic
28C22×C22⋊C4×C73C2211yescharacteristic
29C22×C22⋊C4×C73C2211yescharacteristic
30C22×C22⋊C4×C73C2211yescharacteristic
31C22×C22⋊C4×C73C2211yescharacteristic
32C22×C22⋊C4×C73C2211yescharacteristic
33C22×C22⋊C4×C73C2211yescharacteristic
34C22×C22⋊C4×C73C2211yescharacteristic
35C22×C22⋊C4×C73C2211yescharacteristic
36C22×C22⋊C4×C73C2211yescharacteristic
37C22×C22⋊C4×C73C2211yescharacteristic
38C22×C22⋊C4×C73C2211yescharacteristic
39C22×C22⋊C4×C73C2211yescharacteristic
40C22×C22⋊C4×C73C2211yescharacteristic
41C22×C22⋊C4×C73C2211yescharacteristic
42#392×C73—24no—
43#392×C73—24no—
44#392×C73—24no—
45#386×C73—24no—
46#386×C73—24no—
47#386×C73—24no—
48#386×C73—24no—
49C2×#95×C73C2211yescharacteristic
50C2×#95×C73C2211yescharacteristic
51C2×#95×C73C2211yescharacteristic
52C2×#95×C73C2211yescharacteristic
53C2×#95×C73C2211yescharacteristic
54C2×#95×C73C2211yescharacteristic
55C2×#95×C73C2211yescharacteristic
56C2×#95×C73C2211yescharacteristic
57C2×#95×C73C2211yescharacteristic
58C2×#95×C73C2211yescharacteristic
59C2×#95×C73C2211yescharacteristic
60C2×#95×C73C2211yescharacteristic
61C25×C73C2311yescharacteristic
62C25×C73C2311yescharacteristic
63C25×C73C2311yescharacteristic
64C25×C73C2311yescharacteristic
65C22×D4×C73—22no—
66C22×D4×C73—22no—
67C22×D4×C73—22no—
68C22×D4×C73—22no—
69C22×D4×C73—22no—
70C22×D4×C73—22no—
71C22×D4×C73—22no—
72C22×D4×C73—22no—
73C22×D4×C73—22no—
74C22×D4×C73—22no—
75C22×D4×C73—22no—
76C22×D4×C73—22no—
77C22×D4×C73—22no—
78C22×D4×C73—22no—
79C22×D4×C73—22no—
80C22×D4×C73—22no—
81C22×D4×C73—22no—
82C22×D4×C73—22no—
83C22×D4×C73—22no—
84C22×D4×C73—22no—
85C22×D4×C73—22no—
86C22×D4×C73—22no—
87C22×D4×C73—22no—
88C22×D4×C73—22no—
89C22×D4×C73—22no—
90C22×D4×C73—22no—
91C22×D4×C73—41no—
92C22×D4×C73—41no—
93C22×D4×C73—41no—
94C22×D4×C73—41no—
95C22×D4×C73—41no—
96C22×D4×C73—41no—
97C22×D4×C73—41no—
98C22×D4×C73—41no—
99C22×D4×C73—41no—
100C22×D4×C73—41no—
101C22×D4×C73—41no—
102C22×D4×C73—41no—
103C22×D4×C73—41no—
104C22×D4×C73—41no—
105C22×D4×C73D414yescomplemented
106C22×D4×C73D414yescomplemented
107C23×C4×C73—22no—
108C23×C4×C73—22no—
109C23×C4×C73—22no—
110C23×C4×C73—22no—
111C23×C4×C73—22no—
112C23×C4×C73—22no—
113C23×C4×C73—22no—
114C23×C4×C73—22no—
115C23×C4×C73—41no—
116C23×C4×C73—41no—
117C23×C4×C73—41no—
118C23×C4×C73—41no—
119C23×C4×C73—41no—
120C23×C4×C73—41no—
121C23×C4×C73C2311yescharacteristic
122C23×C4×C73C2311yescharacteristic
123C23×C4×C73C2311yescharacteristic
124C23×C4×C73C2311yescharacteristic
125C23×C4×C73C2311yescharacteristic
126C23×C4×C73C2311yescharacteristic
127C23×C4×C73C2311yescharacteristic
128C23×C4×C73C2311yescharacteristic
129C23×C4×C73C2311yescharacteristic
130C23×C4×C73C2311yescharacteristic
131C23×C4×C73C2311yescharacteristic
132#121×C73—232no—
133C2×C4⋊C4×C73—22no—
134C2×C4⋊C4×C73—22no—
135C2×C4⋊C4×C73—22no—
136C2×C22⋊C4×C73—22no—
137C2×C22⋊C4×C73—22no—
138C2×C22⋊C4×C73—22no—
139C2×C22⋊C4×C73—22no—
140C2×C22⋊C4×C73—22no—
141C2×C22⋊C4×C73—22no—
142C2×C22⋊C4×C73—22no—
143C2×C22⋊C4×C73—22no—
144C2×C22⋊C4×C73—22no—
145C2×C22⋊C4×C73—22no—
146C2×C22⋊C4×C73—22no—
147C2×C22⋊C4×C73—22no—
148C2×C22⋊C4×C73—22no—
149C2×C22⋊C4×C73—22no—
150C2×C22⋊C4×C73—22no—
151C2×C22⋊C4×C73—22no—
152C2×C22⋊C4×C73—22no—
153C2×C22⋊C4×C73—22no—
154C2×C22⋊C4×C73—22no—
155C2×C22⋊C4×C73—22no—
156C2×C22⋊C4×C73—22no—
157C2×C22⋊C4×C73—22no—
158C2×C22⋊C4×C73—22no—
159C2×C22⋊C4×C73—22no—
160C2×C22⋊C4×C73—22no—
161C2×C22⋊C4×C73—22no—
162C2×C22⋊C4×C73—41no—
163C2×C22⋊C4×C73—41no—
164C2×C22⋊C4×C73—41no—
165C2×C22⋊C4×C73—41no—
166C2×C22⋊C4×C73—41no—
167C2×C22⋊C4×C73—41no—
168C2×C22⋊C4×C73—41no—
169C2×C22⋊C4×C73—41no—
170C2×C22⋊C4×C73—41no—
171C2×C22⋊C4×C73—41no—
172C2×C22⋊C4×C73—41no—
173C2×C22⋊C4×C73—41no—
174C2×C22⋊C4×C73—41no—
175C2×C22⋊C4×C73—41no—
176C2×C22⋊C4×C73D414yescomplemented
177C2×C22⋊C4×C73D414yescomplemented
178#95×C73—22no—
179#95×C73—22no—
180#95×C73—22no—
181#95×C73—22no—
182#95×C73—22no—
183#95×C73—22no—
184#95×C73—22no—
185#95×C73—22no—
186#95×C73—22no—
187#95×C73—41no—
188#95×C73—41no—
189#95×C73D414yescomplemented
190C24×C73—21no—
191C24×C73—21no—
192C24×C73—21no—
193C24×C73—21no—
194C24×C73—21no—
195C24×C73—21no—
196C24×C73—21no—
197C24×C73—21no—
198C24×C73—21no—
199C24×C73—21no—
200C24×C73—21no—
201C24×C73—21no—
202C24×C73—21no—
203C24×C73—21no—
204C24×C73—21no—
205C24×C73—21no—
206C24×C73—21no—
207C24×C73—21no—
208C24×C73—21no—
209C24×C73—21no—
210C24×C73—21no—
211C24×C73—21no—
212C24×C73—21no—
213C24×C73—21no—
214C24×C73—21no—
215C24×C73—21no—
216C24×C73—21no—
217C24×C73—21no—
218C24×C73—21no—
219C24×C73—21no—
220C24×C73—21no—
221C24×C73—21no—
222C24×C73—21no—
223C24×C73—21no—
224C24×C73—21no—
225C24×C73—21no—
226C24×C73—21no—
227C24×C73—21no—
228C24×C73—21no—
229C24×C73—21no—
230C24×C73—21no—
231C24×C73—21no—
232C24×C73—21no—
233C24×C73—21no—
234C24×C73—21no—
235C24×C73—21no—
236C24×C73—21no—
237C24×C73—21no—
238C24×C73—21no—
239C24×C73—21no—
240C24×C73—21no—
241C24×C73—21no—
242C24×C73C2×D412yes—
243C24×C73C2×D412yes—
244C24×C73C2×D412yes—
245C24×C73C2×D412yes—
246C24×C73C2×D412yes—
247C24×C73C2×D412yes—
248C24×C73#4112yes—
249C24×C73#4112yes—
250C24×C73C2411yescharacteristic
251C2×D4×C73—28no—
252C2×D4×C73—28no—
253C2×D4×C73—28no—
254C2×D4×C73—28no—
255C2×D4×C73—28no—
256C2×D4×C73—28no—
257C2×D4×C73—28no—
258C2×D4×C73—44no—
259C2×D4×C73—44no—
260C2×D4×C73—44no—
261C2×D4×C73—44no—
262C2×D4×C73—44no—
263C2×D4×C73—44no—
264C2×D4×C73—44no—
265C2×D4×C73—44no—
266C2×D4×C73—44no—
267C2×D4×C73—44no—
268C2×D4×C73—44no—
269C2×D4×C73—44no—
270C2×D4×C73—44no—
271C2×D4×C73—44no—
272C2×D4×C73—44no—
273C2×D4×C73—44no—
274C2×D4×C73—44no—
275C2×D4×C73—44no—
276C2×D4×C73—44no—
277C2×D4×C73—44no—
278C2×D4×C73—44no—
279C2×D4×C73—44no—
280C2×D4×C73—44no—
281C2×D4×C73—44no—
282C2×D4×C73—44no—
283C2×D4×C73—44no—
284C2×D4×C73—44no—
285C2×D4×C73—44no—
286C2×D4×C73—44no—
287C2×D4×C73—44no—
288C2×D4×C73—44no—
289C2×D4×C73—44no—
290C2×D4×C73—44no—
291C2×D4×C73—44no—
292C2×D4×C73—44no—
293C22×C4×C73—21no—
294C22×C4×C73—21no—
295C22×C4×C73—21no—
296C22×C4×C73—21no—
297C22×C4×C73—28no—
298C22×C4×C73—21no—
299C22×C4×C73—21no—
300C22×C4×C73—21no—
301C22×C4×C73—21no—
302C22×C4×C73—21no—
303C22×C4×C73—21no—
304C22×C4×C73—21no—
305C22×C4×C73—21no—
306C22×C4×C73—21no—
307C22×C4×C73—21no—
308C22×C4×C73—21no—
309C22×C4×C73—21no—
310C22×C4×C73—21no—
311C22×C4×C73—21no—
312C22×C4×C73—21no—
313C22×C4×C73—21no—
314C22×C4×C73—21no—
315C22×C4×C73—21no—
316C22×C4×C73—21no—
317C22×C4×C73—21no—
318C22×C4×C73—21no—
319C22×C4×C73—21no—
320C22×C4×C73—21no—
321C22×C4×C73—21no—
322C22×C4×C73—21no—
323C22×C4×C73—21no—
324C22×C4×C73—21no—
325C22×C4×C73—21no—
326C22×C4×C73—21no—
327C22×C4×C73—21no—
328C22×C4×C73—21no—
329C22×C4×C73—21no—
330C22×C4×C73—21no—
331C22×C4×C73—21no—
332C22×C4×C73—21no—
333C22×C4×C73—21no—
334C22×C4×C73—21no—
335C22×C4×C73—21no—
336C22×C4×C73—21no—
337C22×C4×C73—21no—
338C22×C4×C73—21no—
339C22×C4×C73—21no—
340C22×C4×C73—21no—
341C22×C4×C73—21no—
342C22×C4×C73—21no—
343C22×C4×C73—21no—
344C22×C4×C73—21no—
345C22×C4×C73—21no—
346C22×C4×C73—21no—
347C22×C4×C73—21no—
348C22×C4×C73—21no—
349C22×C4×C73—21no—
350C22×C4×C73—21no—
351C22×C4×C73—21no—
352C22×C4×C73—21no—
353C22×C4×C73—21no—
354C22×C4×C73—21no—
355C22×C4×C73—21no—
356C22×C4×C73—21no—
357C22×C4×C73—21no—
358C22×C4×C73—21no—
359C22×C4×C73—21no—
360C22×C4×C73—44no—
361C22×C4×C73—44no—
362C22×C4×C73—44no—
363C22×C4×C73—44no—
364C22×C4×C73—44no—
365C22×C4×C73—44no—
366C22×C4×C73—44no—
367C22×C4×C73—44no—
368C22×C4×C73—44no—
369C22×C4×C73—44no—
370C22×C4×C73—44no—
371C22×C4×C73—44no—
372C22×C4×C73—44no—
373C22×C4×C73C2×D412yes—
374C22×C4×C73C2×D412yes—
375C22×C4×C73C2×D412yes—
376C22×C4×C73C2×D412yes—
377C22×C4×C73C2×D412yes—
378C22×C4×C73C2×D412yes—
379C22×C4×C73C2×D412yes—
380C22×C4×C73C2×D412yes—
381C22×C4×C73C2×D412yes—
382C22×C4×C73#4112yes—
383C22×C4×C73#4112yes—
384C4⋊C4×C73—28no—
385C22⋊C4×C73—28no—
386C22⋊C4×C73—28no—
387C22⋊C4×C73—44no—
388C22⋊C4×C73—44no—
389C22⋊C4×C73—44no—
390C22⋊C4×C73—44no—
391C22⋊C4×C73—44no—
392C22⋊C4×C73—44no—
393C22⋊C4×C73—44no—
394C22⋊C4×C73—44no—
395C22⋊C4×C73—44no—
396C22⋊C4×C73—44no—
397C22⋊C4×C73—44no—
398C22⋊C4×C73—44no—
399C23×C73—22no—
400C23×C73—22no—
401C23×C73—22no—
402C23×C73—22no—
403C23×C73—22no—
404C23×C73—22no—
405C23×C73—22no—
406C23×C73—22no—
407C23×C73—22no—
408C23×C73—22no—
409C23×C73—22no—
410C23×C73—22no—
411C23×C73—22no—
412C23×C73—22no—
413C23×C73—22no—
414C23×C73—22no—
415C23×C73—22no—
416C23×C73—22no—
417C23×C73—22no—
418C23×C73—22no—
419C23×C73—22no—
420C23×C73—22no—
421C23×C73—22no—
422C23×C73—22no—
423C23×C73—22no—
424C23×C73—22no—
425C23×C73—22no—
426C23×C73—22no—
427C23×C73—22no—
428C23×C73—22no—
429C23×C73—22no—
430C23×C73—22no—
431C23×C73—22no—
432C23×C73—22no—
433C23×C73—22no—
434C23×C73—22no—
435C23×C73—22no—
436C23×C73—22no—
437C23×C73—22no—
438C23×C73—22no—
439C23×C73—22no—
440C23×C73—22no—
441C23×C73—22no—
442C23×C73—22no—
443C23×C73—22no—
444C23×C73—22no—
445C23×C73—22no—
446C23×C73—22no—
447C23×C73—22no—
448C23×C73—22no—
449C23×C73—41no—
450C23×C73—41no—
451C23×C73—41no—
452C23×C73—41no—
453C23×C73—41no—
454C23×C73—41no—
455C23×C73—41no—
456C23×C73—41no—
457C23×C73—41no—
458C23×C73—41no—
459C23×C73—41no—
460C23×C73—41no—
461C23×C73—41no—
462C23×C73—41no—
463C23×C73—41no—
464C23×C73—41no—
465C23×C73—41no—
466C23×C73—41no—
467C23×C73—41no—
468C23×C73—41no—
469C23×C73—41no—
470C23×C73—41no—
471C23×C73—41no—
472C23×C73—41no—
473C23×C73—41no—
474C23×C73—41no—
475C23×C73—41no—
476C23×C73—41no—
477C23×C73—41no—
478C23×C73—41no—
479C23×C73—41no—
480C23×C73—41no—
481C23×C73—41no—
482C23×C73—41no—
483C23×C73—41no—
484C23×C73—41no—
485C23×C73—41no—
486C23×C73—41no—
487C23×C73—41no—
488C23×C73—41no—
489C23×C73—41no—
490C23×C73—41no—
491C23×C73—41no—
492C23×C73—41no—
493C23×C73—41no—
494C23×C73—41no—
495C23×C73—41no—
496C23×C73—41no—
497C23×C73—41no—
498C23×C73—41no—
499C23×C73—41no—
500C23×C73—41no—
501C23×C73—41no—
502C23×C73—41no—
503C23×C73—41no—
504C23×C73—41no—
505C23×C73—41no—
506C23×C73—41no—
507C23×C73—41no—
508C23×C73—41no—
509C23×C73—41no—
510C23×C73—41no—
511C23×C73—41no—
512C23×C73—41no—
513C23×C73—41no—
514C23×C73—41no—
515C23×C73—41no—
516C23×C73—41no—
517C23×C73—41no—
518C23×C73—41no—
519C23×C73—41no—
520C23×C73—41no—
521C23×C73—41no—
522C23×C73—41no—
523C23×C73—41no—
524C23×C73—41no—
525C23×C73—41no—
526C23×C73—41no—
527C23×C73—41no—
528C23×C73—41no—
529C23×C73—41no—
530C23×C73—41no—
531C23×C73—41no—
532C23×C73—41no—
533C23×C73—41no—
534C23×C73—41no—
535C23×C73—41no—
536C23×C73—41no—
537C23×C73#12014yes—
538C23×C73#12114yes—
539C23×C73C22×D411yescharacteristic
540C23×C73C22×D411yescharacteristic
541C23×C73C22×D411yescharacteristic
542C23×C73C22×D411yescharacteristic
543C23×C73C22×D411yescharacteristic
544C23×C73C2×#4111yescharacteristic
545C23×C73C2×#4111yescharacteristic
546C23×C73C2×#4111yescharacteristic
547C23×C73C2×#4111yescharacteristic
548C23×C73H(5,𝔽2)11yescharacteristic
549C23×C73H(5,𝔽2)11yescharacteristic
550C23×C73H(5,𝔽2)11yescharacteristic
551C23×C73H(5,𝔽2)11yescharacteristic
552C23×C73H(5,𝔽2)11yescharacteristic
553C23×C73H(5,𝔽2)11yescharacteristic
554D4×C73—416no—
555D4×C73—416no—
556D4×C73—416no—
557D4×C73—416no—
558D4×C73—416no—
559D4×C73—416no—
560C2×C4×C73—22no—
561C2×C4×C73—22no—
562C2×C4×C73—22no—
563C2×C4×C73—22no—
564C2×C4×C73—22no—
565C2×C4×C73—22no—
566C2×C4×C73—22no—
567C2×C4×C73—22no—
568C2×C4×C73—22no—
569C2×C4×C73—22no—
570C2×C4×C73—22no—
571C2×C4×C73—22no—
572C2×C4×C73—22no—
573C2×C4×C73—22no—
574C2×C4×C73—22no—
575C2×C4×C73—22no—
576C2×C4×C73—22no—
577C2×C4×C73—22no—
578C2×C4×C73—22no—
579C2×C4×C73—22no—
580C2×C4×C73—22no—
581C2×C4×C73—22no—
582C2×C4×C73—22no—
583C2×C4×C73—22no—
584C2×C4×C73—22no—
585C2×C4×C73—22no—
586C2×C4×C73—22no—
587C2×C4×C73—22no—
588C2×C4×C73—22no—
589C2×C4×C73—22no—
590C2×C4×C73—416no—
591C2×C4×C73—416no—
592C2×C4×C73—41no—
593C2×C4×C73—41no—
594C2×C4×C73—41no—
595C2×C4×C73—41no—
596C2×C4×C73—41no—
597C2×C4×C73—41no—
598C2×C4×C73—41no—
599C2×C4×C73—41no—
600C2×C4×C73—41no—
601C2×C4×C73—41no—
602C2×C4×C73—41no—
603C2×C4×C73—41no—
604C2×C4×C73—41no—
605C2×C4×C73—41no—
606C2×C4×C73—41no—
607C2×C4×C73—41no—
608C2×C4×C73—41no—
609C2×C4×C73—41no—
610C2×C4×C73—41no—
611C2×C4×C73—41no—
612C2×C4×C73—41no—
613C2×C4×C73—41no—
614C2×C4×C73—41no—
615C2×C4×C73—41no—
616C2×C4×C73—41no—
617C2×C4×C73—41no—
618C2×C4×C73—41no—
619C2×C4×C73—41no—
620C2×C4×C73—41no—
621C2×C4×C73—41no—
622C2×C4×C73—41no—
623C2×C4×C73—41no—
624C2×C4×C73—41no—
625C2×C4×C73—41no—
626C2×C4×C73—41no—
627C2×C4×C73—41no—
628C2×C4×C73—41no—
629C2×C4×C73—41no—
630C2×C4×C73—41no—
631C2×C4×C73—41no—
632C2×C4×C73—41no—
633C2×C4×C73—41no—
634C2×C4×C73—41no—
635C2×C4×C73—41no—
636C2×C4×C73—41no—
637C2×C4×C73—41no—
638C2×C4×C73#12114yes—
639C22×C73—24no—
640C22×C73—24no—
641C22×C73—24no—
642C22×C73—24no—
643C22×C73—24no—
644C22×C73—24no—
645C22×C73—42no—
646C22×C73—42no—
647C22×C73—42no—
648C22×C73—42no—
649C22×C73—42no—
650C22×C73—42no—
651C22×C73—42no—
652C22×C73—42no—
653C22×C73—42no—
654C22×C73—42no—
655C22×C73—42no—
656C22×C73—42no—
657C22×C73—42no—
658C22×C73—42no—
659C22×C73—42no—
660C22×C73—42no—
661C22×C73—42no—
662C22×C73—42no—
663C22×C73—42no—
664C22×C73—42no—
665C22×C73—42no—
666C22×C73—42no—
667C22×C73—42no—
668C22×C73—42no—
669C22×C73—42no—
670C22×C73—42no—
671C22×C73—42no—
672C22×C73—42no—
673C22×C73—42no—
674C22×C73—42no—
675C22×C73—42no—
676C22×C73—42no—
677C22×C73—42no—
678C22×C73—42no—
679C22×C73—42no—
680C22×C73—42no—
681C22×C73—42no—
682C22×C73—42no—
683C22×C73—81no—
684C22×C73—81no—
685C22×C73—81no—
686C22×C73—81no—
687C22×C73—81no—
688C22×C73—81no—
689C22×C73—81no—
690C22×C73—81no—
691C22×C73—81no—
692C22×C73—81no—
693C22×C73—81no—
694C22×C73—81no—
695C22×C73—81no—
696C22×C73—81no—
697C22×C73—81no—
698C22×C73—81no—
699C22×C73C2×#12011yescharacteristic
700C22×C73C2×#12111yescharacteristic
701C22×C73C2×#12111yescharacteristic
702C22×C73#52511yescharacteristic
703C22×C73#52511yescharacteristic
704C22×C73#53211yescharacteristic
705C22×C73#53411yescharacteristic
706C22×C73#53411yescharacteristic
707C22×C73#53411yescharacteristic
708C22×C73#53511yescharacteristic
709C22×C73#53511yescharacteristic
710C22×C73#53811yescharacteristic
711C22×C73#53811yescharacteristic
712C22×C73#54011yescharacteristic
713C22×C73#54011yescharacteristic
714C22×C73D4211yescharacteristic
715C22×C73D4211yescharacteristic
716C22×C73D4211yescharacteristic
717C22×C73D4211yescharacteristic
718C22×C73D4211yescharacteristic
719C22×C73#54611yescharacteristic
720C22×C73#54611yescharacteristic
721C22×C73#54611yescharacteristic
722C22×C73#54611yescharacteristic
723C22×C73#54611yescharacteristic
724C22×C73#54611yescharacteristic
725C22×C73#54611yescharacteristic
726C22×C73#54611yescharacteristic
727C22×C73#54611yescharacteristic
728C22×C73#55011yescharacteristic
729C22×C73#55311yescharacteristic
730C22×C73#55311yescharacteristic
731C22×C73#55311yescharacteristic
732C22×C73#56011yescharacteristic
733C22×C73#56011yescharacteristic
734C4×C73—24no—
735C4×C73—42no—
736C4×C73—42no—
737C4×C73—42no—
738C4×C73—42no—
739C4×C73—42no—
740C4×C73—42no—
741C4×C73—42no—
742C4×C73—42no—
743C4×C73—81no—
744C4×C73—81no—
745#15273C7311yesmaximal, characteristic, direct product factor, Sylow
746C2×C73—44no—
747C2×C73—44no—
748C2×C73—82no—
749C2×C73—82no—
750C2×C73#240411yescharacteristic
751C2×C73#241011yescharacteristic
752C2×C73#241011yescharacteristic
753C2×C73#242411yescharacteristic
754C2×C73#242811yescharacteristic
755C2×C73#245611yescharacteristic
756C2×C73#246411yescharacteristic
757C2×C73#253511yescharacteristic
758C2×C73#254311yescharacteristic
759C2×C73#266811yescharacteristic
760C2×C73#266911yescharacteristic
761C2×C73#267311yescharacteristic
762C2×C73#268811yescharacteristic
763C2×C73#268811yescharacteristic
764C2×C73#270311yescharacteristic
765C22×#121C2×C7311yescharacteristic, complemented
766C2×#392C2×C7311yescharacteristic, complemented
767C2×#392C2×C7311yescharacteristic, complemented
768C2×#392C2×C7311yescharacteristic, complemented
769C2×#386C2×C7311yescharacteristic, complemented
770C2×#386C2×C7311yescharacteristic, complemented
771C2×#386C2×C7311yescharacteristic, complemented
772C2×#386C2×C7311yescharacteristic, complemented
773#1442C2×C7311yescharacteristic, complemented
774#1440C2×C7311yescharacteristic, complemented
775#1440C2×C7311yescharacteristic, complemented
776#1439C2×C7311yescharacteristic, complemented
777#1438C2×C7311yescharacteristic, complemented
778#1438C2×C7311yescharacteristic, complemented
779C22⋊#95C2×C7311yescharacteristic, complemented
780C73#1527311yescharacteristic, direct product factor, Sylow
781C23×D4C22×C7311yescharacteristic
782C23×D4C22×C7311yescharacteristic
783C23×D4C22×C7311yescharacteristic
784C23×D4C22×C7311yescharacteristic
785C23×D4C22×C7311yescharacteristic
786C23×D4C22×C7311yescharacteristic
787C24×C4C22×C7311yescharacteristic
788C24×C4C22×C7311yescharacteristic
789C2×#121—24no—
790C2×#121—24no—
791C2×#121—24no—
792C22×C4⋊C4C22×C7311yescharacteristic
793C22×C22⋊C4C22×C7311yescharacteristic
794C22×C22⋊C4C22×C7311yescharacteristic
795C22×C22⋊C4C22×C7311yescharacteristic
796C22×C22⋊C4C22×C7311yescharacteristic
797C22×C22⋊C4C22×C7311yescharacteristic
798C22×C22⋊C4C22×C7311yescharacteristic
799C22×C22⋊C4C22×C7311yescharacteristic
800C22×C22⋊C4C22×C7311yescharacteristic
801C22×C22⋊C4C22×C7311yescharacteristic
802C22×C22⋊C4C22×C7311yescharacteristic
803C22×C22⋊C4C22×C7311yescharacteristic
804C22×C22⋊C4C22×C7311yescharacteristic
805C22×C22⋊C4C22×C7311yescharacteristic
806C22×C22⋊C4C22×C7311yescharacteristic
807#392—24no—
808#392—24no—
809#392—24no—
810#386—24no—
811#386—24no—
812#386—24no—
813#386—24no—
814C2×#95C22×C7311yescharacteristic
815C2×#95C22×C7311yescharacteristic
816C2×#95C22×C7311yescharacteristic
817C2×#95C22×C7311yescharacteristic
818C2×#95C22×C7311yescharacteristic
819C2×#95C22×C7311yescharacteristic
820C2×#95C22×C7311yescharacteristic
821C2×#95C22×C7311yescharacteristic
822C2×#95C22×C7311yescharacteristic
823C2×#95C22×C7311yescharacteristic
824C2×#95C22×C7311yescharacteristic
825C2×#95C22×C7311yescharacteristic
826C25C23×C7311yescharacteristic
827C25C23×C7311yescharacteristic
828C25C23×C7311yescharacteristic
829C25C23×C7311yescharacteristic
830C22×D4—22no—
831C22×D4—22no—
832C22×D4—22no—
833C22×D4—22no—
834C22×D4—22no—
835C22×D4—22no—
836C22×D4—22no—
837C22×D4—22no—
838C22×D4—22no—
839C22×D4—22no—
840C22×D4—22no—
841C22×D4—22no—
842C22×D4—22no—
843C22×D4—22no—
844C22×D4—22no—
845C22×D4—22no—
846C22×D4—22no—
847C22×D4—22no—
848C22×D4—22no—
849C22×D4—22no—
850C22×D4—22no—
851C22×D4—22no—
852C22×D4—22no—
853C22×D4—22no—
854C22×D4—22no—
855C22×D4—22no—
856C22×D4—41no—
857C22×D4—41no—
858C22×D4—41no—
859C22×D4—41no—
860C22×D4—41no—
861C22×D4—41no—
862C22×D4—41no—
863C22×D4—41no—
864C22×D4—41no—
865C22×D4—41no—
866C22×D4—41no—
867C22×D4—41no—
868C22×D4—41no—
869C22×D4—41no—
870C22×D4D4×C7314yescomplemented
871C22×D4D4×C7314yescomplemented
872C23×C4—22no—
873C23×C4—22no—
874C23×C4—22no—
875C23×C4—22no—
876C23×C4—22no—
877C23×C4—22no—
878C23×C4—22no—
879C23×C4—22no—
880C23×C4—41no—
881C23×C4—41no—
882C23×C4—41no—
883C23×C4—41no—
884C23×C4—41no—
885C23×C4—41no—
886C23×C4C23×C7311yescharacteristic
887C23×C4C23×C7311yescharacteristic
888C23×C4C23×C7311yescharacteristic
889C23×C4C23×C7311yescharacteristic
890C23×C4C23×C7311yescharacteristic
891C23×C4C23×C7311yescharacteristic
892C23×C4C23×C7311yescharacteristic
893C23×C4C23×C7311yescharacteristic
894C23×C4C23×C7311yescharacteristic
895C23×C4C23×C7311yescharacteristic
896C23×C4C23×C7311yescharacteristic
897#121—232no—
898C2×C4⋊C4—22no—
899C2×C4⋊C4—22no—
900C2×C4⋊C4—22no—
901C2×C22⋊C4—22no—
902C2×C22⋊C4—22no—
903C2×C22⋊C4—22no—
904C2×C22⋊C4—22no—
905C2×C22⋊C4—22no—
906C2×C22⋊C4—22no—
907C2×C22⋊C4—22no—
908C2×C22⋊C4—22no—
909C2×C22⋊C4—22no—
910C2×C22⋊C4—22no—
911C2×C22⋊C4—22no—
912C2×C22⋊C4—22no—
913C2×C22⋊C4—22no—
914C2×C22⋊C4—22no—
915C2×C22⋊C4—22no—
916C2×C22⋊C4—22no—
917C2×C22⋊C4—22no—
918C2×C22⋊C4—22no—
919C2×C22⋊C4—22no—
920C2×C22⋊C4—22no—
921C2×C22⋊C4—22no—
922C2×C22⋊C4—22no—
923C2×C22⋊C4—22no—
924C2×C22⋊C4—22no—
925C2×C22⋊C4—22no—
926C2×C22⋊C4—22no—
927C2×C22⋊C4—41no—
928C2×C22⋊C4—41no—
929C2×C22⋊C4—41no—
930C2×C22⋊C4—41no—
931C2×C22⋊C4—41no—
932C2×C22⋊C4—41no—
933C2×C22⋊C4—41no—
934C2×C22⋊C4—41no—
935C2×C22⋊C4—41no—
936C2×C22⋊C4—41no—
937C2×C22⋊C4—41no—
938C2×C22⋊C4—41no—
939C2×C22⋊C4—41no—
940C2×C22⋊C4—41no—
941C2×C22⋊C4D4×C7314yescomplemented
942C2×C22⋊C4D4×C7314yescomplemented
943#95—22no—
944#95—22no—
945#95—22no—
946#95—22no—
947#95—22no—
948#95—22no—
949#95—22no—
950#95—22no—
951#95—22no—
952#95—41no—
953#95—41no—
954#95D4×C7314yescomplemented
955C24—21no—
956C24—21no—
957C24—21no—
958C24—21no—
959C24—21no—
960C24—21no—
961C24—21no—
962C24—21no—
963C24—21no—
964C24—21no—
965C24—21no—
966C24—21no—
967C24—21no—
968C24—21no—
969C24—21no—
970C24—21no—
971C24—21no—
972C24—21no—
973C24—21no—
974C24—21no—
975C24—21no—
976C24—21no—
977C24—21no—
978C24—21no—
979C24—21no—
980C24—21no—
981C24—21no—
982C24—21no—
983C24—21no—
984C24—21no—
985C24—21no—
986C24—21no—
987C24—21no—
988C24—21no—
989C24—21no—
990C24—21no—
991C24—21no—
992C24—21no—
993C24—21no—
994C24—21no—
995C24—21no—
996C24—21no—
997C24—21no—
998C24—21no—
999C24—21no—
1000C24—21no—
1001C24—21no—
1002C24—21no—
1003C24—21no—
1004C24—21no—
1005C24—21no—
1006C24—21no—
1007C24C2×D4×C7312yes—
1008C24C2×D4×C7312yes—
1009C24C2×D4×C7312yes—
1010C24C2×D4×C7312yes—
1011C24C2×D4×C7312yes—
1012C24C2×D4×C7312yes—
1013C24#41×C7312yes—
1014C24#41×C7312yes—
1015C24C24×C7311yescharacteristic
1016C2×D4—28no—
1017C2×D4—28no—
1018C2×D4—28no—
1019C2×D4—28no—
1020C2×D4—28no—
1021C2×D4—28no—
1022C2×D4—28no—
1023C2×D4—44no—
1024C2×D4—44no—
1025C2×D4—44no—
1026C2×D4—44no—
1027C2×D4—44no—
1028C2×D4—44no—
1029C2×D4—44no—
1030C2×D4—44no—
1031C2×D4—44no—
1032C2×D4—44no—
1033C2×D4—44no—
1034C2×D4—44no—
1035C2×D4—44no—
1036C2×D4—44no—
1037C2×D4—44no—
1038C2×D4—44no—
1039C2×D4—44no—
1040C2×D4—44no—
1041C2×D4—44no—
1042C2×D4—44no—
1043C2×D4—44no—
1044C2×D4—44no—
1045C2×D4—44no—
1046C2×D4—44no—
1047C2×D4—44no—
1048C2×D4—44no—
1049C2×D4—44no—
1050C2×D4—44no—
1051C2×D4—44no—
1052C2×D4—44no—
1053C2×D4—44no—
1054C2×D4—44no—
1055C2×D4—44no—
1056C2×D4—44no—
1057C2×D4—44no—
1058C22×C4—21no—
1059C22×C4—21no—
1060C22×C4—21no—
1061C22×C4—21no—
1062C22×C4—28no—
1063C22×C4—21no—
1064C22×C4—21no—
1065C22×C4—21no—
1066C22×C4—21no—
1067C22×C4—21no—
1068C22×C4—21no—
1069C22×C4—21no—
1070C22×C4—21no—
1071C22×C4—21no—
1072C22×C4—21no—
1073C22×C4—21no—
1074C22×C4—21no—
1075C22×C4—21no—
1076C22×C4—21no—
1077C22×C4—21no—
1078C22×C4—21no—
1079C22×C4—21no—
1080C22×C4—21no—
1081C22×C4—21no—
1082C22×C4—21no—
1083C22×C4—21no—
1084C22×C4—21no—
1085C22×C4—21no—
1086C22×C4—21no—
1087C22×C4—21no—
1088C22×C4—21no—
1089C22×C4—21no—
1090C22×C4—21no—
1091C22×C4—21no—
1092C22×C4—21no—
1093C22×C4—21no—
1094C22×C4—21no—
1095C22×C4—21no—
1096C22×C4—21no—
1097C22×C4—21no—
1098C22×C4—21no—
1099C22×C4—21no—
1100C22×C4—21no—
1101C22×C4—21no—
1102C22×C4—21no—
1103C22×C4—21no—
1104C22×C4—21no—
1105C22×C4—21no—
1106C22×C4—21no—
1107C22×C4—21no—
1108C22×C4—21no—
1109C22×C4—21no—
1110C22×C4—21no—
1111C22×C4—21no—
1112C22×C4—21no—
1113C22×C4—21no—
1114C22×C4—21no—
1115C22×C4—21no—
1116C22×C4—21no—
1117C22×C4—21no—
1118C22×C4—21no—
1119C22×C4—21no—
1120C22×C4—21no—
1121C22×C4—21no—
1122C22×C4—21no—
1123C22×C4—21no—
1124C22×C4—21no—
1125C22×C4—44no—
1126C22×C4—44no—
1127C22×C4—44no—
1128C22×C4—44no—
1129C22×C4—44no—
1130C22×C4—44no—
1131C22×C4—44no—
1132C22×C4—44no—
1133C22×C4—44no—
1134C22×C4—44no—
1135C22×C4—44no—
1136C22×C4—44no—
1137C22×C4—44no—
1138C22×C4C2×D4×C7312yes—
1139C22×C4C2×D4×C7312yes—
1140C22×C4C2×D4×C7312yes—
1141C22×C4C2×D4×C7312yes—
1142C22×C4C2×D4×C7312yes—
1143C22×C4C2×D4×C7312yes—
1144C22×C4C2×D4×C7312yes—
1145C22×C4C2×D4×C7312yes—
1146C22×C4C2×D4×C7312yes—
1147C22×C4#41×C7312yes—
1148C22×C4#41×C7312yes—
1149C4⋊C4—28no—
1150C22⋊C4—28no—
1151C22⋊C4—28no—
1152C22⋊C4—44no—
1153C22⋊C4—44no—
1154C22⋊C4—44no—
1155C22⋊C4—44no—
1156C22⋊C4—44no—
1157C22⋊C4—44no—
1158C22⋊C4—44no—
1159C22⋊C4—44no—
1160C22⋊C4—44no—
1161C22⋊C4—44no—
1162C22⋊C4—44no—
1163C22⋊C4—44no—
1164C23—22no—
1165C23—22no—
1166C23—22no—
1167C23—22no—
1168C23—22no—
1169C23—22no—
1170C23—22no—
1171C23—22no—
1172C23—22no—
1173C23—22no—
1174C23—22no—
1175C23—22no—
1176C23—22no—
1177C23—22no—
1178C23—22no—
1179C23—22no—
1180C23—22no—
1181C23—22no—
1182C23—22no—
1183C23—22no—
1184C23—22no—
1185C23—22no—
1186C23—22no—
1187C23—22no—
1188C23—22no—
1189C23—22no—
1190C23—22no—
1191C23—22no—
1192C23—22no—
1193C23—22no—
1194C23—22no—
1195C23—22no—
1196C23—22no—
1197C23—22no—
1198C23—22no—
1199C23—22no—
1200C23—22no—
1201C23—22no—
1202C23—22no—
1203C23—22no—
1204C23—22no—
1205C23—22no—
1206C23—22no—
1207C23—22no—
1208C23—22no—
1209C23—22no—
1210C23—22no—
1211C23—22no—
1212C23—22no—
1213C23—22no—
1214C23—41no—
1215C23—41no—
1216C23—41no—
1217C23—41no—
1218C23—41no—
1219C23—41no—
1220C23—41no—
1221C23—41no—
1222C23—41no—
1223C23—41no—
1224C23—41no—
1225C23—41no—
1226C23—41no—
1227C23—41no—
1228C23—41no—
1229C23—41no—
1230C23—41no—
1231C23—41no—
1232C23—41no—
1233C23—41no—
1234C23—41no—
1235C23—41no—
1236C23—41no—
1237C23—41no—
1238C23—41no—
1239C23—41no—
1240C23—41no—
1241C23—41no—
1242C23—41no—
1243C23—41no—
1244C23—41no—
1245C23—41no—
1246C23—41no—
1247C23—41no—
1248C23—41no—
1249C23—41no—
1250C23—41no—
1251C23—41no—
1252C23—41no—
1253C23—41no—
1254C23—41no—
1255C23—41no—
1256C23—41no—
1257C23—41no—
1258C23—41no—
1259C23—41no—
1260C23—41no—
1261C23—41no—
1262C23—41no—
1263C23—41no—
1264C23—41no—
1265C23—41no—
1266C23—41no—
1267C23—41no—
1268C23—41no—
1269C23—41no—
1270C23—41no—
1271C23—41no—
1272C23—41no—
1273C23—41no—
1274C23—41no—
1275C23—41no—
1276C23—41no—
1277C23—41no—
1278C23—41no—
1279C23—41no—
1280C23—41no—
1281C23—41no—
1282C23—41no—
1283C23—41no—
1284C23—41no—
1285C23—41no—
1286C23—41no—
1287C23—41no—
1288C23—41no—
1289C23—41no—
1290C23—41no—
1291C23—41no—
1292C23—41no—
1293C23—41no—
1294C23—41no—
1295C23—41no—
1296C23—41no—
1297C23—41no—
1298C23—41no—
1299C23—41no—
1300C23—41no—
1301C23—41no—
1302C23#120×C7314yes—
1303C23#121×C7314yes—
1304C23C22×D4×C7311yescharacteristic
1305C23C22×D4×C7311yescharacteristic
1306C23C22×D4×C7311yescharacteristic
1307C23C22×D4×C7311yescharacteristic
1308C23C22×D4×C7311yescharacteristic
1309C23C2×#41×C7311yescharacteristic
1310C23C2×#41×C7311yescharacteristic
1311C23C2×#41×C7311yescharacteristic
1312C23C2×#41×C7311yescharacteristic
1313C23H(5,𝔽2)×C7311yescharacteristic
1314C23H(5,𝔽2)×C7311yescharacteristic
1315C23H(5,𝔽2)×C7311yescharacteristic
1316C23H(5,𝔽2)×C7311yescharacteristic
1317C23H(5,𝔽2)×C7311yescharacteristic
1318C23H(5,𝔽2)×C7311yescharacteristic
1319D4—416no—
1320D4—416no—
1321D4—416no—
1322D4—416no—
1323D4—416no—
1324D4—416no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—416no—
1356C2×C4—416no—
1357C2×C4—41no—
1358C2×C4—41no—
1359C2×C4—41no—
1360C2×C4—41no—
1361C2×C4—41no—
1362C2×C4—41no—
1363C2×C4—41no—
1364C2×C4—41no—
1365C2×C4—41no—
1366C2×C4—41no—
1367C2×C4—41no—
1368C2×C4—41no—
1369C2×C4—41no—
1370C2×C4—41no—
1371C2×C4—41no—
1372C2×C4—41no—
1373C2×C4—41no—
1374C2×C4—41no—
1375C2×C4—41no—
1376C2×C4—41no—
1377C2×C4—41no—
1378C2×C4—41no—
1379C2×C4—41no—
1380C2×C4—41no—
1381C2×C4—41no—
1382C2×C4—41no—
1383C2×C4—41no—
1384C2×C4—41no—
1385C2×C4—41no—
1386C2×C4—41no—
1387C2×C4—41no—
1388C2×C4—41no—
1389C2×C4—41no—
1390C2×C4—41no—
1391C2×C4—41no—
1392C2×C4—41no—
1393C2×C4—41no—
1394C2×C4—41no—
1395C2×C4—41no—
1396C2×C4—41no—
1397C2×C4—41no—
1398C2×C4—41no—
1399C2×C4—41no—
1400C2×C4—41no—
1401C2×C4—41no—
1402C2×C4—41no—
1403C2×C4#121×C7314yes—
1404C22—24no—
1405C22—24no—
1406C22—24no—
1407C22—24no—
1408C22—24no—
1409C22—24no—
1410C22—42no—
1411C22—42no—
1412C22—42no—
1413C22—42no—
1414C22—42no—
1415C22—42no—
1416C22—42no—
1417C22—42no—
1418C22—42no—
1419C22—42no—
1420C22—42no—
1421C22—42no—
1422C22—42no—
1423C22—42no—
1424C22—42no—
1425C22—42no—
1426C22—42no—
1427C22—42no—
1428C22—42no—
1429C22—42no—
1430C22—42no—
1431C22—42no—
1432C22—42no—
1433C22—42no—
1434C22—42no—
1435C22—42no—
1436C22—42no—
1437C22—42no—
1438C22—42no—
1439C22—42no—
1440C22—42no—
1441C22—42no—
1442C22—42no—
1443C22—42no—
1444C22—42no—
1445C22—42no—
1446C22—42no—
1447C22—42no—
1448C22—81no—
1449C22—81no—
1450C22—81no—
1451C22—81no—
1452C22—81no—
1453C22—81no—
1454C22—81no—
1455C22—81no—
1456C22—81no—
1457C22—81no—
1458C22—81no—
1459C22—81no—
1460C22—81no—
1461C22—81no—
1462C22—81no—
1463C22—81no—
1464C22C2×#120×C7311yescharacteristic
1465C22C2×#121×C7311yescharacteristic
1466C22C2×#121×C7311yescharacteristic
1467C22#525×C7311yescharacteristic
1468C22#525×C7311yescharacteristic
1469C22#532×C7311yescharacteristic
1470C22#534×C7311yescharacteristic
1471C22#534×C7311yescharacteristic
1472C22#534×C7311yescharacteristic
1473C22#535×C7311yescharacteristic
1474C22#535×C7311yescharacteristic
1475C22#538×C7311yescharacteristic
1476C22#538×C7311yescharacteristic
1477C22#540×C7311yescharacteristic
1478C22#540×C7311yescharacteristic
1479C22D42×C7311yescharacteristic
1480C22D42×C7311yescharacteristic
1481C22D42×C7311yescharacteristic
1482C22D42×C7311yescharacteristic
1483C22D42×C7311yescharacteristic
1484C22#546×C7311yescharacteristic
1485C22#546×C7311yescharacteristic
1486C22#546×C7311yescharacteristic
1487C22#546×C7311yescharacteristic
1488C22#546×C7311yescharacteristic
1489C22#546×C7311yescharacteristic
1490C22#546×C7311yescharacteristic
1491C22#546×C7311yescharacteristic
1492C22#546×C7311yescharacteristic
1493C22#550×C7311yescharacteristic
1494C22#553×C7311yescharacteristic
1495C22#553×C7311yescharacteristic
1496C22#553×C7311yescharacteristic
1497C22#560×C7311yescharacteristic
1498C22#560×C7311yescharacteristic
1499C4—24no—
1500C4—42no—
1501C4—42no—
1502C4—42no—
1503C4—42no—
1504C4—42no—
1505C4—42no—
1506C4—42no—
1507C4—42no—
1508C4—81no—
1509C4—81no—
1510C2—44no—
1511C2—44no—
1512C2—82no—
1513C2—82no—
1514C2C73×#240411yescharacteristic
1515C2C73×#241011yescharacteristic
1516C2C73×#241011yescharacteristic
1517C2C73×#242411yescharacteristic
1518C2C73×#242811yescharacteristic
1519C2C73×#245611yescharacteristic
1520C2C73×#246411yescharacteristic
1521C2C73×#253511yescharacteristic
1522C2C73×#254311yescharacteristic
1523C2C73×#266811yescharacteristic
1524C2C73×#266911yescharacteristic
1525C2C73×#267311yescharacteristic
1526C2C73×#268811yescharacteristic
1527C2C73×#268811yescharacteristic
1528C2C73×#270311yescharacteristic
subgroupG/H
center, socleC24×C73C24
commutator, Frattini, cosocleC24C24×C73
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C73 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×#121×C73C2semidirect
2. C2×#392×C73C2semidirect
3. C2×#392×C73C2semidirect
4. C2×#392×C73C2semidirect
5. C2×#386×C73C2semidirect
6. C2×#386×C73C2semidirect
7. C2×#386×C73C2semidirect
8. C2×#386×C73C2semidirect
9. C73×#1442C2semidirect
10. C73×#1440C2semidirect
11. C73×#1440C2semidirect
12. C73×#1439C2semidirect
13. C73×#1438C2semidirect
14. C73×#1438C2semidirect
15. C73×C22⋊#95C2semidirect
105. C22×D4×C73D4semidirect
106. C22×D4×C73D4semidirect
176. C2×C22⋊C4×C73D4semidirect
177. C2×C22⋊C4×C73D4semidirect
189. #95×C73D4semidirect
745. #15273C73direct (N × H)
765. C22×#121C2×C73semidirect
766. C2×#392C2×C73semidirect
767. C2×#392C2×C73semidirect
768. C2×#392C2×C73semidirect
769. C2×#386C2×C73semidirect
770. C2×#386C2×C73semidirect
771. C2×#386C2×C73semidirect
772. C2×#386C2×C73semidirect
773. #1442C2×C73semidirect
774. #1440C2×C73semidirect
775. #1440C2×C73semidirect
776. #1439C2×C73semidirect
777. #1438C2×C73semidirect
778. #1438C2×C73semidirect
779. C22⋊#95C2×C73semidirect
780. C73#15273direct (N × H)
870. C22×D4D4×C73semidirect
871. C22×D4D4×C73semidirect
941. C2×C22⋊C4D4×C73semidirect
942. C2×C22⋊C4D4×C73semidirect
954. #95D4×C73semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#121×C732
C2×#392×C732
C2×#386×C732
C73×#14422
C73×#14402
C73×#14392
C73×#14382
C73×C22⋊#952
#1527373