Finite Group Databasebeta

← C73×#15316 #32924720

Subgroups — C73×#15316 #32924720

Order 18688.

2442 conjugacy classes of subgroups.

The subgroup lattice has 1352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#121×C73C211yesmaximal, characteristic
2C2×#396×C73C211yesmaximal, characteristic, complemented
3C2×#394×C73C211yesmaximal, characteristic, complemented
4C2×#394×C73C211yesmaximal, characteristic, complemented
5C2×#394×C73C211yesmaximal, characteristic, complemented
6C2×#390×C73C211yesmaximal, characteristic, complemented
7C2×#389×C73C211yesmaximal, characteristic, complemented
8C2×#385×C73C211yesmaximal, characteristic, complemented
9C73×#1441C211yesmaximal, characteristic, complemented
10C73×#1439C211yesmaximal, characteristic, complemented
11C73×#1439C211yesmaximal, characteristic, complemented
12C73×#1438C211yesmaximal, characteristic, complemented
13C73×#1438C211yesmaximal, characteristic, complemented
14C73×#1437C211yesmaximal, characteristic, complemented
15C73×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C73C2211yescharacteristic
17C23×D4×C73C2211yescharacteristic
18C23×D4×C73C2211yescharacteristic
19C24×C4×C73C2211yescharacteristic
20C2×#121×C73—24no—
21C2×#121×C73—24no—
22C2×#121×C73—24no—
23C22×C4⋊C4×C73C2211yescharacteristic
24C22×C4⋊C4×C73C2211yescharacteristic
25C22×C4⋊C4×C73C2211yescharacteristic
26C22×C4⋊C4×C73C2211yescharacteristic
27C22×C4⋊C4×C73C2211yescharacteristic
28C22×C4⋊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
42C22×C22⋊C4×C73C2211yescharacteristic
43C22×C42×C73C2211yescharacteristic
44#396×C73—24no—
45#394×C73—24no—
46#394×C73—24no—
47#394×C73—24no—
48#390×C73—24no—
49#389×C73—24no—
50#385×C73—24no—
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
64C22×D4×C73—22no—
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—41no—
79C22×D4×C73—41no—
80C22×D4×C73—41no—
81C22×D4×C73—41no—
82C22×D4×C73—41no—
83C22×D4×C73—41no—
84C22×D4×C73D414yes—
85C23×C4×C73—22no—
86C23×C4×C73—22no—
87C23×C4×C73—22no—
88C23×C4×C73—22no—
89C23×C4×C73—22no—
90C23×C4×C73—41no—
91C23×C4×C73—41no—
92C23×C4×C73C2311yescharacteristic
93C23×C4×C73C2311yescharacteristic
94C23×C4×C73C2311yescharacteristic
95C23×C4×C73C2311yescharacteristic
96C23×C4×C73C2311yescharacteristic
97C23×C4×C73C2311yescharacteristic
98C23×C4×C73C2311yescharacteristic
99C23×C4×C73C2311yescharacteristic
100C23×C4×C73C2311yescharacteristic
101C23×C4×C73C2311yescharacteristic
102C23×C4×C73C2311yescharacteristic
103C23×C4×C73C2311yescharacteristic
104#121×C73—232no—
105C2×C4⋊C4×C73—22no—
106C2×C4⋊C4×C73—22no—
107C2×C4⋊C4×C73—22no—
108C2×C4⋊C4×C73—22no—
109C2×C4⋊C4×C73—22no—
110C2×C4⋊C4×C73—22no—
111C2×C4⋊C4×C73—22no—
112C2×C4⋊C4×C73—22no—
113C2×C4⋊C4×C73—22no—
114C2×C4⋊C4×C73—22no—
115C2×C4⋊C4×C73—22no—
116C2×C4⋊C4×C73—22no—
117C2×C4⋊C4×C73—22no—
118C2×C4⋊C4×C73—41no—
119C2×C4⋊C4×C73—41no—
120C2×C4⋊C4×C73—41no—
121C2×C4⋊C4×C73D414yes—
122C2×C4⋊C4×C73D414yescomplemented
123C2×C22⋊C4×C73—22no—
124C2×C22⋊C4×C73—22no—
125C2×C22⋊C4×C73—22no—
126C2×C22⋊C4×C73—22no—
127C2×C22⋊C4×C73—22no—
128C2×C22⋊C4×C73—22no—
129C2×C22⋊C4×C73—22no—
130C2×C22⋊C4×C73—22no—
131C2×C22⋊C4×C73—22no—
132C2×C22⋊C4×C73—22no—
133C2×C22⋊C4×C73—22no—
134C2×C22⋊C4×C73—22no—
135C2×C22⋊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—41no—
154C2×C22⋊C4×C73—41no—
155C2×C22⋊C4×C73—41no—
156C2×C22⋊C4×C73—41no—
157C2×C22⋊C4×C73—41no—
158C2×C22⋊C4×C73—41no—
159C2×C22⋊C4×C73—41no—
160C2×C22⋊C4×C73—41no—
161C2×C22⋊C4×C73—41no—
162C2×C22⋊C4×C73—41no—
163C2×C22⋊C4×C73D414yes—
164C2×C22⋊C4×C73D414yescomplemented
165C2×C42×C73—22no—
166C2×C42×C73—22no—
167C2×C42×C73—41no—
168#95×C73—22no—
169#95×C73—22no—
170#95×C73—22no—
171#95×C73—22no—
172#95×C73—22no—
173#95×C73—22no—
174#95×C73—22no—
175#95×C73—22no—
176#95×C73—41no—
177#95×C73—41no—
178C24×C73—21no—
179C24×C73—21no—
180C24×C73—21no—
181C24×C73—21no—
182C24×C73—21no—
183C24×C73—21no—
184C24×C73—21no—
185C24×C73—21no—
186C24×C73—21no—
187C24×C73—21no—
188C24×C73—21no—
189C24×C73—21no—
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×C73C2×D412yes—
219C24×C73C2×D412yes—
220C24×C73C2×D412yes—
221C24×C73C2×D412yes—
222C24×C73#4112yes—
223C24×C73C2411yescharacteristic
224C2×D4×C73—28no—
225C2×D4×C73—28no—
226C2×D4×C73—28no—
227C2×D4×C73—28no—
228C2×D4×C73—44no—
229C2×D4×C73—44no—
230C2×D4×C73—44no—
231C2×D4×C73—44no—
232C2×D4×C73—44no—
233C2×D4×C73—44no—
234C2×D4×C73—44no—
235C2×D4×C73—44no—
236C2×D4×C73—44no—
237C2×D4×C73—44no—
238C2×D4×C73—44no—
239C2×D4×C73—44no—
240C2×D4×C73—44no—
241C2×D4×C73—44no—
242C2×D4×C73—44no—
243C2×D4×C73—44no—
244C2×D4×C73—44no—
245C22×C4×C73—21no—
246C22×C4×C73—21no—
247C22×C4×C73—21no—
248C22×C4×C73—21no—
249C22×C4×C73—21no—
250C22×C4×C73—21no—
251C22×C4×C73—21no—
252C22×C4×C73—21no—
253C22×C4×C73—21no—
254C22×C4×C73—21no—
255C22×C4×C73—21no—
256C22×C4×C73—21no—
257C22×C4×C73—28no—
258C22×C4×C73—21no—
259C22×C4×C73—21no—
260C22×C4×C73—21no—
261C22×C4×C73—21no—
262C22×C4×C73—21no—
263C22×C4×C73—21no—
264C22×C4×C73—21no—
265C22×C4×C73—21no—
266C22×C4×C73—21no—
267C22×C4×C73—21no—
268C22×C4×C73—21no—
269C22×C4×C73—21no—
270C22×C4×C73—21no—
271C22×C4×C73—21no—
272C22×C4×C73—21no—
273C22×C4×C73—21no—
274C22×C4×C73—21no—
275C22×C4×C73—21no—
276C22×C4×C73—21no—
277C22×C4×C73—21no—
278C22×C4×C73—21no—
279C22×C4×C73—21no—
280C22×C4×C73—21no—
281C22×C4×C73—21no—
282C22×C4×C73—21no—
283C22×C4×C73—21no—
284C22×C4×C73—21no—
285C22×C4×C73—21no—
286C22×C4×C73—21no—
287C22×C4×C73—21no—
288C22×C4×C73—21no—
289C22×C4×C73—21no—
290C22×C4×C73—21no—
291C22×C4×C73—21no—
292C22×C4×C73—21no—
293C22×C4×C73—21no—
294C22×C4×C73—21no—
295C22×C4×C73—21no—
296C22×C4×C73—21no—
297C22×C4×C73—21no—
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—44no—
317C22×C4×C73—44no—
318C22×C4×C73—44no—
319C22×C4×C73—44no—
320C22×C4×C73—44no—
321C22×C4×C73—44no—
322C22×C4×C73C2×D412yes—
323C22×C4×C73C2×D412yes—
324C22×C4×C73C2×D412yes—
325C22×C4×C73C2×D412yes—
326C22×C4×C73C2×D412yes—
327C22×C4×C73C2×D412yes—
328C22×C4×C73C2×D412yes—
329C22×C4×C73C2×D412yes—
330C22×C4×C73C2×D412yes—
331C22×C4×C73C2×D412yes—
332C22×C4×C73C2×D412yes—
333C22×C4×C73#4112yes—
334C22×C4×C73#4112yes—
335C22×C4×C73#4112yes—
336C4⋊C4×C73—28no—
337C4⋊C4×C73—28no—
338C4⋊C4×C73—44no—
339C4⋊C4×C73—44no—
340C4⋊C4×C73—44no—
341C4⋊C4×C73—44no—
342C22⋊C4×C73—28no—
343C22⋊C4×C73—28no—
344C22⋊C4×C73—28no—
345C22⋊C4×C73—44no—
346C22⋊C4×C73—44no—
347C22⋊C4×C73—44no—
348C22⋊C4×C73—44no—
349C22⋊C4×C73—44no—
350C22⋊C4×C73—44no—
351C22⋊C4×C73—44no—
352C22⋊C4×C73—44no—
353C22⋊C4×C73—44no—
354C22⋊C4×C73—44no—
355C22⋊C4×C73—44no—
356C42×C73—44no—
357C23×C73—22no—
358C23×C73—22no—
359C23×C73—22no—
360C23×C73—22no—
361C23×C73—22no—
362C23×C73—22no—
363C23×C73—22no—
364C23×C73—22no—
365C23×C73—22no—
366C23×C73—22no—
367C23×C73—22no—
368C23×C73—22no—
369C23×C73—22no—
370C23×C73—22no—
371C23×C73—22no—
372C23×C73—22no—
373C23×C73—22no—
374C23×C73—22no—
375C23×C73—22no—
376C23×C73—22no—
377C23×C73—22no—
378C23×C73—22no—
379C23×C73—22no—
380C23×C73—22no—
381C23×C73—22no—
382C23×C73—22no—
383C23×C73—22no—
384C23×C73—22no—
385C23×C73—22no—
386C23×C73—22no—
387C23×C73—22no—
388C23×C73—22no—
389C23×C73—41no—
390C23×C73—41no—
391C23×C73—41no—
392C23×C73—41no—
393C23×C73—41no—
394C23×C73—41no—
395C23×C73—41no—
396C23×C73—41no—
397C23×C73—41no—
398C23×C73—41no—
399C23×C73—41no—
400C23×C73—41no—
401C23×C73—41no—
402C23×C73—41no—
403C23×C73—41no—
404C23×C73—41no—
405C23×C73—41no—
406C23×C73—41no—
407C23×C73—41no—
408C23×C73—41no—
409C23×C73—41no—
410C23×C73—41no—
411C23×C73—41no—
412C23×C73—41no—
413C23×C73—41no—
414C23×C73—41no—
415C23×C73—41no—
416C23×C73—41no—
417C23×C73—41no—
418C23×C73—41no—
419C23×C73—41no—
420C23×C73—41no—
421C23×C73—41no—
422C23×C73—41no—
423C23×C73—41no—
424C23×C73—41no—
425C23×C73—41no—
426C23×C73—41no—
427C23×C73—41no—
428C23×C73—41no—
429C23×C73—41no—
430C23×C73—41no—
431C23×C73—41no—
432C23×C73—41no—
433C23×C73—41no—
434C23×C73—41no—
435C23×C73—41no—
436C23×C73—41no—
437C23×C73—41no—
438C23×C73—41no—
439C23×C73—41no—
440C23×C73—41no—
441C23×C73—41no—
442C23×C73—41no—
443C23×C73—41no—
444C23×C73—41no—
445C23×C73—41no—
446C23×C73—41no—
447C23×C73—41no—
448C23×C73—41no—
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#12114yes—
462C23×C73C22×D411yescharacteristic
463C23×C73C22×D411yescharacteristic
464C23×C73C22×D411yescharacteristic
465C23×C73C22×D411yescharacteristic
466C23×C73C22×D411yescharacteristic
467C23×C73C2×#4111yescharacteristic
468C23×C73C2×#4111yescharacteristic
469C23×C73C2×#4111yescharacteristic
470C23×C73C2×#4111yescharacteristic
471C23×C73H(5,𝔽2)11yescharacteristic
472C23×C73H(5,𝔽2)11yescharacteristic
473C23×C73H(5,𝔽2)11yescharacteristic
474C23×C73H(5,𝔽2)11yescharacteristic
475C23×C732−1+411yescharacteristic
476C23×C732−1+411yescharacteristic
477D4×C73—416no—
478D4×C73—416no—
479D4×C73—416no—
480C2×C4×C73—22no—
481C2×C4×C73—22no—
482C2×C4×C73—22no—
483C2×C4×C73—22no—
484C2×C4×C73—22no—
485C2×C4×C73—22no—
486C2×C4×C73—22no—
487C2×C4×C73—22no—
488C2×C4×C73—22no—
489C2×C4×C73—22no—
490C2×C4×C73—22no—
491C2×C4×C73—22no—
492C2×C4×C73—22no—
493C2×C4×C73—22no—
494C2×C4×C73—22no—
495C2×C4×C73—22no—
496C2×C4×C73—22no—
497C2×C4×C73—22no—
498C2×C4×C73—22no—
499C2×C4×C73—22no—
500C2×C4×C73—22no—
501C2×C4×C73—22no—
502C2×C4×C73—22no—
503C2×C4×C73—22no—
504C2×C4×C73—22no—
505C2×C4×C73—22no—
506C2×C4×C73—22no—
507C2×C4×C73—22no—
508C2×C4×C73—22no—
509C2×C4×C73—22no—
510C2×C4×C73—22no—
511C2×C4×C73—22no—
512C2×C4×C73—22no—
513C2×C4×C73—416no—
514C2×C4×C73—41no—
515C2×C4×C73—41no—
516C2×C4×C73—41no—
517C2×C4×C73—41no—
518C2×C4×C73—41no—
519C2×C4×C73—41no—
520C2×C4×C73—41no—
521C2×C4×C73—41no—
522C2×C4×C73—41no—
523C2×C4×C73—41no—
524C2×C4×C73—41no—
525C2×C4×C73—41no—
526C2×C4×C73—41no—
527C2×C4×C73—41no—
528C2×C4×C73—41no—
529C2×C4×C73—41no—
530C2×C4×C73—41no—
531C2×C4×C73—41no—
532C2×C4×C73—41no—
533C2×C4×C73—41no—
534C2×C4×C73—41no—
535C2×C4×C73—41no—
536C2×C4×C73—41no—
537C2×C4×C73—41no—
538C2×C4×C73—41no—
539C2×C4×C73—41no—
540C2×C4×C73—41no—
541C2×C4×C73—41no—
542C2×C4×C73—41no—
543C2×C4×C73—41no—
544C2×C4×C73—41no—
545C2×C4×C73—41no—
546C2×C4×C73—41no—
547C2×C4×C73—41no—
548C2×C4×C73—41no—
549C2×C4×C73—41no—
550C2×C4×C73—41no—
551C2×C4×C73—41no—
552C2×C4×C73—41no—
553C2×C4×C73—41no—
554C2×C4×C73—41no—
555C2×C4×C73—41no—
556C2×C4×C73—41no—
557C2×C4×C73—41no—
558C2×C4×C73—41no—
559C2×C4×C73—41no—
560C2×C4×C73—41no—
561C2×C4×C73—41no—
562C2×C4×C73#12014yes—
563C2×C4×C73#12114yes—
564C2×C4×C73#12114yescomplemented
565C22×C73—24no—
566C22×C73—24no—
567C22×C73—24no—
568C22×C73—42no—
569C22×C73—42no—
570C22×C73—42no—
571C22×C73—42no—
572C22×C73—42no—
573C22×C73—42no—
574C22×C73—42no—
575C22×C73—42no—
576C22×C73—42no—
577C22×C73—42no—
578C22×C73—42no—
579C22×C73—42no—
580C22×C73—42no—
581C22×C73—42no—
582C22×C73—42no—
583C22×C73—42no—
584C22×C73—42no—
585C22×C73—42no—
586C22×C73—42no—
587C22×C73—42no—
588C22×C73—42no—
589C22×C73—42no—
590C22×C73—42no—
591C22×C73—42no—
592C22×C73—42no—
593C22×C73—42no—
594C22×C73—81no—
595C22×C73—81no—
596C22×C73—81no—
597C22×C73—81no—
598C22×C73—81no—
599C22×C73—81no—
600C22×C73—81no—
601C22×C73—81no—
602C22×C73—81no—
603C22×C73—81no—
604C22×C73—81no—
605C22×C73—81no—
606C22×C73—81no—
607C22×C73—81no—
608C22×C73—81no—
609C22×C73—81no—
610C22×C73C2×#12011yescharacteristic
611C22×C73C2×#12111yescharacteristic
612C22×C73C2×#12111yescharacteristic
613C22×C73C2×#12111yescharacteristic
614C22×C73#52911yescharacteristic
615C22×C73#53211yescharacteristic
616C22×C73#53411yescharacteristic
617C22×C73#53511yescharacteristic
618C22×C73#53611yescharacteristic
619C22×C73#53711yescharacteristic
620C22×C73#53711yescharacteristic
621C22×C73#53811yescharacteristic
622C22×C73#53911yescharacteristic
623C22×C73#54011yescharacteristic
624C22×C73#54211yescharacteristic
625C22×C73D4211yescharacteristic
626C22×C73D4211yescharacteristic
627C22×C73D4211yescharacteristic
628C22×C73D4211yescharacteristic
629C22×C73#54611yescharacteristic
630C22×C73#54611yescharacteristic
631C22×C73#54611yescharacteristic
632C22×C73#54611yescharacteristic
633C22×C73#54611yescharacteristic
634C22×C73#54711yescharacteristic
635C22×C73#54711yescharacteristic
636C22×C73#54711yescharacteristic
637C22×C73#54811yescharacteristic
638C22×C73#54811yescharacteristic
639C22×C73#54811yescharacteristic
640C22×C73#55011yescharacteristic
641C22×C73#55311yescharacteristic
642C22×C73#55311yescharacteristic
643C22×C73#56211yescharacteristic
644C22×C73#56211yescharacteristic
645C4×C73—24no—
646C4×C73—24no—
647C4×C73—24no—
648C4×C73—42no—
649C4×C73—42no—
650C4×C73—42no—
651C4×C73—42no—
652C4×C73—42no—
653C4×C73—81no—
654C4×C73—81no—
655C4×C73—81no—
656C4×C73—81no—
657#15316C7311yesmaximal, characteristic, direct product factor, Sylow
658C2×C73—44no—
659C2×C73—82no—
660C2×C73—82no—
661C2×C73#240811yescharacteristic
662C2×C73#241011yescharacteristic
663C2×C73#241611yescharacteristic
664C2×C73#241611yescharacteristic
665C2×C73#242511yescharacteristic
666C2×C73#242611yescharacteristic
667C2×C73#242811yescharacteristic
668C2×C73#243211yescharacteristic
669C2×C73#255911yescharacteristic
670C2×C73#267211yescharacteristic
671C2×C73#267611yescharacteristic
672C2×C73#268111yescharacteristic
673C2×C73#268211yescharacteristic
674C2×C73#270111yescharacteristic
675C2×C73#271111yescharacteristic
676C22×#121C2×C7311yescharacteristic
677C2×#396C2×C7311yescharacteristic, complemented
678C2×#394C2×C7311yescharacteristic, complemented
679C2×#394C2×C7311yescharacteristic, complemented
680C2×#394C2×C7311yescharacteristic, complemented
681C2×#390C2×C7311yescharacteristic, complemented
682C2×#389C2×C7311yescharacteristic, complemented
683C2×#385C2×C7311yescharacteristic, complemented
684#1441C2×C7311yescharacteristic, complemented
685#1439C2×C7311yescharacteristic, complemented
686#1439C2×C7311yescharacteristic, complemented
687#1438C2×C7311yescharacteristic, complemented
688#1438C2×C7311yescharacteristic, complemented
689#1437C2×C7311yescharacteristic, complemented
690C22⋊#95C2×C7311yescharacteristic, complemented
691C73#1531611yescharacteristic, direct product factor, Sylow
692C23×D4C22×C7311yescharacteristic
693C23×D4C22×C7311yescharacteristic
694C23×D4C22×C7311yescharacteristic
695C24×C4C22×C7311yescharacteristic
696C2×#121—24no—
697C2×#121—24no—
698C2×#121—24no—
699C22×C4⋊C4C22×C7311yescharacteristic
700C22×C4⋊C4C22×C7311yescharacteristic
701C22×C4⋊C4C22×C7311yescharacteristic
702C22×C4⋊C4C22×C7311yescharacteristic
703C22×C4⋊C4C22×C7311yescharacteristic
704C22×C4⋊C4C22×C7311yescharacteristic
705C22×C22⋊C4C22×C7311yescharacteristic
706C22×C22⋊C4C22×C7311yescharacteristic
707C22×C22⋊C4C22×C7311yescharacteristic
708C22×C22⋊C4C22×C7311yescharacteristic
709C22×C22⋊C4C22×C7311yescharacteristic
710C22×C22⋊C4C22×C7311yescharacteristic
711C22×C22⋊C4C22×C7311yescharacteristic
712C22×C22⋊C4C22×C7311yescharacteristic
713C22×C22⋊C4C22×C7311yescharacteristic
714C22×C22⋊C4C22×C7311yescharacteristic
715C22×C22⋊C4C22×C7311yescharacteristic
716C22×C22⋊C4C22×C7311yescharacteristic
717C22×C22⋊C4C22×C7311yescharacteristic
718C22×C22⋊C4C22×C7311yescharacteristic
719C22×C42C22×C7311yescharacteristic
720#396—24no—
721#394—24no—
722#394—24no—
723#394—24no—
724#390—24no—
725#389—24no—
726#385—24no—
727C2×#95C22×C7311yescharacteristic
728C2×#95C22×C7311yescharacteristic
729C2×#95C22×C7311yescharacteristic
730C2×#95C22×C7311yescharacteristic
731C2×#95C22×C7311yescharacteristic
732C2×#95C22×C7311yescharacteristic
733C2×#95C22×C7311yescharacteristic
734C2×#95C22×C7311yescharacteristic
735C2×#95C22×C7311yescharacteristic
736C2×#95C22×C7311yescharacteristic
737C25C23×C7311yescharacteristic
738C25C23×C7311yescharacteristic
739C25C23×C7311yescharacteristic
740C22×D4—22no—
741C22×D4—22no—
742C22×D4—22no—
743C22×D4—22no—
744C22×D4—22no—
745C22×D4—22no—
746C22×D4—22no—
747C22×D4—22no—
748C22×D4—22no—
749C22×D4—22no—
750C22×D4—22no—
751C22×D4—22no—
752C22×D4—22no—
753C22×D4—22no—
754C22×D4—41no—
755C22×D4—41no—
756C22×D4—41no—
757C22×D4—41no—
758C22×D4—41no—
759C22×D4—41no—
760C22×D4D4×C7314yes—
761C23×C4—22no—
762C23×C4—22no—
763C23×C4—22no—
764C23×C4—22no—
765C23×C4—22no—
766C23×C4—41no—
767C23×C4—41no—
768C23×C4C23×C7311yescharacteristic
769C23×C4C23×C7311yescharacteristic
770C23×C4C23×C7311yescharacteristic
771C23×C4C23×C7311yescharacteristic
772C23×C4C23×C7311yescharacteristic
773C23×C4C23×C7311yescharacteristic
774C23×C4C23×C7311yescharacteristic
775C23×C4C23×C7311yescharacteristic
776C23×C4C23×C7311yescharacteristic
777C23×C4C23×C7311yescharacteristic
778C23×C4C23×C7311yescharacteristic
779C23×C4C23×C7311yescharacteristic
780#121—232no—
781C2×C4⋊C4—22no—
782C2×C4⋊C4—22no—
783C2×C4⋊C4—22no—
784C2×C4⋊C4—22no—
785C2×C4⋊C4—22no—
786C2×C4⋊C4—22no—
787C2×C4⋊C4—22no—
788C2×C4⋊C4—22no—
789C2×C4⋊C4—22no—
790C2×C4⋊C4—22no—
791C2×C4⋊C4—22no—
792C2×C4⋊C4—22no—
793C2×C4⋊C4—22no—
794C2×C4⋊C4—41no—
795C2×C4⋊C4—41no—
796C2×C4⋊C4—41no—
797C2×C4⋊C4D4×C7314yes—
798C2×C4⋊C4D4×C7314yescomplemented
799C2×C22⋊C4—22no—
800C2×C22⋊C4—22no—
801C2×C22⋊C4—22no—
802C2×C22⋊C4—22no—
803C2×C22⋊C4—22no—
804C2×C22⋊C4—22no—
805C2×C22⋊C4—22no—
806C2×C22⋊C4—22no—
807C2×C22⋊C4—22no—
808C2×C22⋊C4—22no—
809C2×C22⋊C4—22no—
810C2×C22⋊C4—22no—
811C2×C22⋊C4—22no—
812C2×C22⋊C4—22no—
813C2×C22⋊C4—22no—
814C2×C22⋊C4—22no—
815C2×C22⋊C4—22no—
816C2×C22⋊C4—22no—
817C2×C22⋊C4—22no—
818C2×C22⋊C4—22no—
819C2×C22⋊C4—22no—
820C2×C22⋊C4—22no—
821C2×C22⋊C4—22no—
822C2×C22⋊C4—22no—
823C2×C22⋊C4—22no—
824C2×C22⋊C4—22no—
825C2×C22⋊C4—22no—
826C2×C22⋊C4—22no—
827C2×C22⋊C4—22no—
828C2×C22⋊C4—22no—
829C2×C22⋊C4—41no—
830C2×C22⋊C4—41no—
831C2×C22⋊C4—41no—
832C2×C22⋊C4—41no—
833C2×C22⋊C4—41no—
834C2×C22⋊C4—41no—
835C2×C22⋊C4—41no—
836C2×C22⋊C4—41no—
837C2×C22⋊C4—41no—
838C2×C22⋊C4—41no—
839C2×C22⋊C4D4×C7314yes—
840C2×C22⋊C4D4×C7314yescomplemented
841C2×C42—22no—
842C2×C42—22no—
843C2×C42—41no—
844#95—22no—
845#95—22no—
846#95—22no—
847#95—22no—
848#95—22no—
849#95—22no—
850#95—22no—
851#95—22no—
852#95—41no—
853#95—41no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24—21no—
875C24—21no—
876C24—21no—
877C24—21no—
878C24—21no—
879C24—21no—
880C24—21no—
881C24—21no—
882C24—21no—
883C24—21no—
884C24—21no—
885C24—21no—
886C24—21no—
887C24—21no—
888C24—21no—
889C24—21no—
890C24—21no—
891C24—21no—
892C24—21no—
893C24—21no—
894C24C2×D4×C7312yes—
895C24C2×D4×C7312yes—
896C24C2×D4×C7312yes—
897C24C2×D4×C7312yes—
898C24#41×C7312yes—
899C24C24×C7311yescharacteristic
900C2×D4—28no—
901C2×D4—28no—
902C2×D4—28no—
903C2×D4—28no—
904C2×D4—44no—
905C2×D4—44no—
906C2×D4—44no—
907C2×D4—44no—
908C2×D4—44no—
909C2×D4—44no—
910C2×D4—44no—
911C2×D4—44no—
912C2×D4—44no—
913C2×D4—44no—
914C2×D4—44no—
915C2×D4—44no—
916C2×D4—44no—
917C2×D4—44no—
918C2×D4—44no—
919C2×D4—44no—
920C2×D4—44no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—28no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—21no—
978C22×C4—21no—
979C22×C4—21no—
980C22×C4—21no—
981C22×C4—21no—
982C22×C4—21no—
983C22×C4—21no—
984C22×C4—21no—
985C22×C4—21no—
986C22×C4—21no—
987C22×C4—21no—
988C22×C4—21no—
989C22×C4—21no—
990C22×C4—21no—
991C22×C4—21no—
992C22×C4—44no—
993C22×C4—44no—
994C22×C4—44no—
995C22×C4—44no—
996C22×C4—44no—
997C22×C4—44no—
998C22×C4C2×D4×C7312yes—
999C22×C4C2×D4×C7312yes—
1000C22×C4C2×D4×C7312yes—
1001C22×C4C2×D4×C7312yes—
1002C22×C4C2×D4×C7312yes—
1003C22×C4C2×D4×C7312yes—
1004C22×C4C2×D4×C7312yes—
1005C22×C4C2×D4×C7312yes—
1006C22×C4C2×D4×C7312yes—
1007C22×C4C2×D4×C7312yes—
1008C22×C4C2×D4×C7312yes—
1009C22×C4#41×C7312yes—
1010C22×C4#41×C7312yes—
1011C22×C4#41×C7312yes—
1012C4⋊C4—28no—
1013C4⋊C4—28no—
1014C4⋊C4—44no—
1015C4⋊C4—44no—
1016C4⋊C4—44no—
1017C4⋊C4—44no—
1018C22⋊C4—28no—
1019C22⋊C4—28no—
1020C22⋊C4—28no—
1021C22⋊C4—44no—
1022C22⋊C4—44no—
1023C22⋊C4—44no—
1024C22⋊C4—44no—
1025C22⋊C4—44no—
1026C22⋊C4—44no—
1027C22⋊C4—44no—
1028C22⋊C4—44no—
1029C22⋊C4—44no—
1030C22⋊C4—44no—
1031C22⋊C4—44no—
1032C42—44no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23#121×C7314yes—
1138C23C22×D4×C7311yescharacteristic
1139C23C22×D4×C7311yescharacteristic
1140C23C22×D4×C7311yescharacteristic
1141C23C22×D4×C7311yescharacteristic
1142C23C22×D4×C7311yescharacteristic
1143C23C2×#41×C7311yescharacteristic
1144C23C2×#41×C7311yescharacteristic
1145C23C2×#41×C7311yescharacteristic
1146C23C2×#41×C7311yescharacteristic
1147C23H(5,𝔽2)×C7311yescharacteristic
1148C23H(5,𝔽2)×C7311yescharacteristic
1149C23H(5,𝔽2)×C7311yescharacteristic
1150C23H(5,𝔽2)×C7311yescharacteristic
1151C232−1+4×C7311yescharacteristic
1152C232−1+4×C7311yescharacteristic
1153D4—416no—
1154D4—416no—
1155D4—416no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—416no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4#120×C7314yes—
1239C2×C4#121×C7314yes—
1240C2×C4#121×C7314yescomplemented
1241C22—24no—
1242C22—24no—
1243C22—24no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22C2×#120×C7311yescharacteristic
1287C22C2×#121×C7311yescharacteristic
1288C22C2×#121×C7311yescharacteristic
1289C22C2×#121×C7311yescharacteristic
1290C22#529×C7311yescharacteristic
1291C22#532×C7311yescharacteristic
1292C22#534×C7311yescharacteristic
1293C22#535×C7311yescharacteristic
1294C22#536×C7311yescharacteristic
1295C22#537×C7311yescharacteristic
1296C22#537×C7311yescharacteristic
1297C22#538×C7311yescharacteristic
1298C22#539×C7311yescharacteristic
1299C22#540×C7311yescharacteristic
1300C22#542×C7311yescharacteristic
1301C22D42×C7311yescharacteristic
1302C22D42×C7311yescharacteristic
1303C22D42×C7311yescharacteristic
1304C22D42×C7311yescharacteristic
1305C22#546×C7311yescharacteristic
1306C22#546×C7311yescharacteristic
1307C22#546×C7311yescharacteristic
1308C22#546×C7311yescharacteristic
1309C22#546×C7311yescharacteristic
1310C22#547×C7311yescharacteristic
1311C22#547×C7311yescharacteristic
1312C22#547×C7311yescharacteristic
1313C22#548×C7311yescharacteristic
1314C22#548×C7311yescharacteristic
1315C22#548×C7311yescharacteristic
1316C22#550×C7311yescharacteristic
1317C22#553×C7311yescharacteristic
1318C22#553×C7311yescharacteristic
1319C22#562×C7311yescharacteristic
1320C22#562×C7311yescharacteristic
1321C4—24no—
1322C4—24no—
1323C4—24no—
1324C4—42no—
1325C4—42no—
1326C4—42no—
1327C4—42no—
1328C4—42no—
1329C4—81no—
1330C4—81no—
1331C4—81no—
1332C4—81no—
1333C2—44no—
1334C2—82no—
1335C2—82no—
1336C2C73×#240811yescharacteristic
1337C2C73×#241011yescharacteristic
1338C2C73×#241611yescharacteristic
1339C2C73×#241611yescharacteristic
1340C2C73×#242511yescharacteristic
1341C2C73×#242611yescharacteristic
1342C2C73×#242811yescharacteristic
1343C2C73×#243211yescharacteristic
1344C2C73×#255911yescharacteristic
1345C2C73×#267211yescharacteristic
1346C2C73×#267611yescharacteristic
1347C2C73×#268111yescharacteristic
1348C2C73×#268211yescharacteristic
1349C2C73×#270111yescharacteristic
1350C2C73×#271111yescharacteristic
subgroupG/H
center, socleC24×C73C24
commutator, Frattini, cosocleC24C24×C73
prime radicalC22×#121×C73C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C73 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#396×C73C2semidirect
3. C2×#394×C73C2semidirect
4. C2×#394×C73C2semidirect
5. C2×#394×C73C2semidirect
6. C2×#390×C73C2semidirect
7. C2×#389×C73C2semidirect
8. C2×#385×C73C2semidirect
9. C73×#1441C2semidirect
10. C73×#1439C2semidirect
11. C73×#1439C2semidirect
12. C73×#1438C2semidirect
13. C73×#1438C2semidirect
14. C73×#1437C2semidirect
15. C73×C22⋊#95C2semidirect
122. C2×C4⋊C4×C73D4semidirect
164. C2×C22⋊C4×C73D4semidirect
564. C2×C4×C73#121semidirect
657. #15316C73direct (N × H)
677. C2×#396C2×C73semidirect
678. C2×#394C2×C73semidirect
679. C2×#394C2×C73semidirect
680. C2×#394C2×C73semidirect
681. C2×#390C2×C73semidirect
682. C2×#389C2×C73semidirect
683. C2×#385C2×C73semidirect
684. #1441C2×C73semidirect
685. #1439C2×C73semidirect
686. #1439C2×C73semidirect
687. #1438C2×C73semidirect
688. #1438C2×C73semidirect
689. #1437C2×C73semidirect
690. C22⋊#95C2×C73semidirect
691. C73#15316direct (N × H)
798. C2×C4⋊C4D4×C73semidirect
840. C2×C22⋊C4D4×C73semidirect
1240. C2×C4#121×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×#396×C732
C2×#394×C732
C2×#390×C732
C2×#389×C732
C2×#385×C732
C73×#14412
C73×#14392
C73×#14382
C73×#14372
C73×C22⋊#952
#1531673