Finite Group Databasebeta

← C73×#14519 #32923923

Subgroups — C73×#14519 #32923923

Order 18688.

2390 conjugacy classes of subgroups.

The subgroup lattice has 1342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#392×C73C211yesmaximal, characteristic
2C2×#390×C73C211yesmaximal, characteristic, complemented
3C2×#386×C73C211yesmaximal, characteristic, complemented
4C2×#386×C73C211yesmaximal, characteristic, complemented
5C2×#386×C73C211yesmaximal, characteristic, complemented
6C2×#386×C73C211yesmaximal, characteristic, complemented
7C2×#385×C73C211yesmaximal, characteristic, complemented
8C73×#1442C211yesmaximal, characteristic, complemented
9C73×#1440C211yesmaximal, characteristic, complemented
10C73×#1439C211yesmaximal, characteristic, complemented
11C73×#1439C211yesmaximal, characteristic, complemented
12C73×#1438C211yesmaximal, characteristic, complemented
13C73×#1437C211yesmaximal, characteristic, complemented
14C73×#1434C211yesmaximal, characteristic, complemented
15C73×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C73C2211yescharacteristic
17C23×D4×C73C2211yescharacteristic
18C23×D4×C73C2211yescharacteristic
19C24×C4×C73C2211yescharacteristic
20C24×C4×C73C2211yescharacteristic
21C22×C4⋊C4×C73C2211yescharacteristic
22C22×C4⋊C4×C73C2211yescharacteristic
23C22×C22⋊C4×C73C2211yescharacteristic
24C22×C22⋊C4×C73C2211yescharacteristic
25C22×C22⋊C4×C73C2211yescharacteristic
26C22×C22⋊C4×C73C2211yescharacteristic
27C22×C22⋊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×C42×C73C2211yescharacteristic
37#392×C73C418yescomplemented
38#390×C73—24no—
39#386×C73—24no—
40#386×C73—24no—
41#386×C73—24no—
42#386×C73—24no—
43#385×C73—24no—
44C2×#95×C73C2211yescharacteristic
45C2×#95×C73C2211yescharacteristic
46C2×#95×C73C2211yescharacteristic
47C2×#95×C73C2211yescharacteristic
48C2×#95×C73C2211yescharacteristic
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
58C25×C73C2311yescharacteristic
59C25×C73C2311yescharacteristic
60C25×C73C2311yescharacteristic
61C22×D4×C73—22no—
62C22×D4×C73—22no—
63C22×D4×C73—22no—
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—41no—
72C22×D4×C73—41no—
73C22×D4×C73—41no—
74C22×D4×C73—41no—
75C22×D4×C73—41no—
76C22×D4×C73—41no—
77C22×D4×C73—41no—
78C22×D4×C73—41no—
79C22×D4×C73C2×C414yes—
80C22×D4×C73C2×C414yescomplemented
81C22×D4×C73C2×C414yescomplemented
82C23×C4×C73—22no—
83C23×C4×C73—22no—
84C23×C4×C73—22no—
85C23×C4×C73—22no—
86C23×C4×C73—22no—
87C23×C4×C73—22no—
88C23×C4×C73—41no—
89C23×C4×C73—41no—
90C23×C4×C73—41no—
91C23×C4×C73—41no—
92C23×C4×C73—41no—
93C23×C4×C73—41no—
94C23×C4×C73—41no—
95C23×C4×C73—41no—
96C23×C4×C73C2311yescharacteristic
97C23×C4×C73C2311yescharacteristic
98C23×C4×C73C2311yescharacteristic
99C23×C4×C73C2311yescharacteristic
100C23×C4×C73C2311yescharacteristic
101C23×C4×C73C2311yescharacteristic
102C23×C4×C73C2311yescharacteristic
103C23×C4×C73C2311yescharacteristic
104C23×C4×C73C2311yescharacteristic
105C23×C4×C73C2311yescharacteristic
106C23×C4×C73C2311yescharacteristic
107C23×C4×C73C2311yescharacteristic
108C2×C4⋊C4×C73—22no—
109C2×C4⋊C4×C73—22no—
110C2×C4⋊C4×C73—22no—
111C2×C4⋊C4×C73—41no—
112C2×C4⋊C4×C73—41no—
113C2×C4⋊C4×C73—41no—
114C2×C22⋊C4×C73—22no—
115C2×C22⋊C4×C73—22no—
116C2×C22⋊C4×C73—22no—
117C2×C22⋊C4×C73—22no—
118C2×C22⋊C4×C73—22no—
119C2×C22⋊C4×C73—22no—
120C2×C22⋊C4×C73—22no—
121C2×C22⋊C4×C73—22no—
122C2×C22⋊C4×C73—22no—
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—41no—
131C2×C22⋊C4×C73—41no—
132C2×C22⋊C4×C73—41no—
133C2×C22⋊C4×C73—41no—
134C2×C22⋊C4×C73—41no—
135C2×C22⋊C4×C73—41no—
136C2×C22⋊C4×C73—41no—
137C2×C22⋊C4×C73—41no—
138C2×C22⋊C4×C73—41no—
139C2×C22⋊C4×C73—41no—
140C2×C22⋊C4×C73—41no—
141C2×C22⋊C4×C73—41no—
142C2×C22⋊C4×C73—41no—
143C2×C22⋊C4×C73—41no—
144C2×C22⋊C4×C73—41no—
145C2×C22⋊C4×C73—41no—
146C2×C22⋊C4×C73—41no—
147C2×C22⋊C4×C73—41no—
148C2×C22⋊C4×C73C2×C414yescomplemented
149C2×C22⋊C4×C73C2×C414yescomplemented
150C2×C22⋊C4×C73C2×C414yescomplemented
151C2×C22⋊C4×C73D414yescomplemented
152C2×C22⋊C4×C73D414yescomplemented
153C2×C42×C73—22no—
154C2×C42×C73—22no—
155C2×C42×C73—41no—
156#95×C73—22no—
157#95×C73—22no—
158#95×C73—22no—
159#95×C73—22no—
160#95×C73—22no—
161#95×C73—22no—
162#95×C73—22no—
163#95×C73—22no—
164#95×C73—41no—
165#95×C73—41no—
166#95×C73—41no—
167#95×C73—41no—
168#95×C73C2×C414yescomplemented
169#95×C73D414yescomplemented
170C24×C73—21no—
171C24×C73—21no—
172C24×C73—21no—
173C24×C73—21no—
174C24×C73—21no—
175C24×C73—21no—
176C24×C73—21no—
177C24×C73—21no—
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×C73C22×C412yes—
209C24×C73C22×C412yes—
210C24×C73C22×C412yes—
211C24×C73C2×D412yes—
212C24×C73C2×D412yes—
213C24×C73#4112yes—
214C24×C73#4112yes—
215C24×C73C2411yescharacteristic
216C2×D4×C73—28no—
217C2×D4×C73—28no—
218C2×D4×C73—28no—
219C2×D4×C73—28no—
220C2×D4×C73—28no—
221C2×D4×C73—44no—
222C2×D4×C73—44no—
223C2×D4×C73—44no—
224C2×D4×C73—44no—
225C2×D4×C73—44no—
226C2×D4×C73—44no—
227C2×D4×C73—44no—
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—
237C22×C4×C73—21no—
238C22×C4×C73—21no—
239C22×C4×C73—21no—
240C22×C4×C73—21no—
241C22×C4×C73—21no—
242C22×C4×C73—21no—
243C22×C4×C73—21no—
244C22×C4×C73—21no—
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—21no—
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—44no—
310C22×C4×C73—44no—
311C22×C4×C73—44no—
312C22×C4×C73—44no—
313C22×C4×C73—44no—
314C22×C4×C73—44no—
315C22×C4×C73—44no—
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×C73—44no—
323C22×C4×C73C22×C412yes—
324C22×C4×C73C22×C412yes—
325C22×C4×C73C22×C412yes—
326C22×C4×C73C22×C412yes—
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×C73C2×D412yes—
334C22×C4×C73#4112yes—
335C4⋊C4×C73—44no—
336C4⋊C4×C73—44no—
337C22⋊C4×C73—28no—
338C22⋊C4×C73—44no—
339C22⋊C4×C73—44no—
340C22⋊C4×C73—44no—
341C22⋊C4×C73—44no—
342C22⋊C4×C73—44no—
343C22⋊C4×C73—44no—
344C22⋊C4×C73—44no—
345C22⋊C4×C73—44no—
346C22⋊C4×C73—44no—
347C22⋊C4×C73—44no—
348C22⋊C4×C73—44no—
349C22⋊C4×C73—44no—
350C42×C73—44no—
351C23×C73—22no—
352C23×C73—22no—
353C23×C73—22no—
354C23×C73—22no—
355C23×C73—22no—
356C23×C73—22no—
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—22no—
390C23×C73—22no—
391C23×C73—22no—
392C23×C73—22no—
393C23×C73—22no—
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×C73C4×D414yes—
455C23×C73C4×D414yes—
456C23×C73C23×C411yescharacteristic
457C23×C73C22×D411yescharacteristic
458C23×C73C22×D411yescharacteristic
459C23×C73C22×D411yescharacteristic
460C23×C73C2×#4111yescharacteristic
461C23×C73C2×#4111yescharacteristic
462C23×C73C2×#4111yescharacteristic
463C23×C73H(5,𝔽2)11yescharacteristic
464C23×C73H(5,𝔽2)11yescharacteristic
465C23×C73H(5,𝔽2)11yescharacteristic
466C23×C73H(5,𝔽2)11yescharacteristic
467C23×C73H(5,𝔽2)11yescharacteristic
468C23×C73H(5,𝔽2)11yescharacteristic
469C23×C73H(5,𝔽2)11yescharacteristic
470C23×C732−1+411yescharacteristic
471D4×C73—416no—
472D4×C73—416no—
473D4×C73—416no—
474C2×C4×C73—22no—
475C2×C4×C73—22no—
476C2×C4×C73—22no—
477C2×C4×C73—22no—
478C2×C4×C73—22no—
479C2×C4×C73—22no—
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—416no—
508C2×C4×C73—416no—
509C2×C4×C73—41no—
510C2×C4×C73—41no—
511C2×C4×C73—41no—
512C2×C4×C73—41no—
513C2×C4×C73—41no—
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×C73C4×D414yes—
560C22×C73—24no—
561C22×C73—24no—
562C22×C73—24no—
563C22×C73—24no—
564C22×C73—24no—
565C22×C73—24no—
566C22×C73—42no—
567C22×C73—42no—
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—42no—
595C22×C73—42no—
596C22×C73—42no—
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×C73C2×C4×D411yescharacteristic
606C22×C73C2×C4×D411yescharacteristic
607C22×C73C2×C4×D411yescharacteristic
608C22×C73#51811yescharacteristic
609C22×C73#51811yescharacteristic
610C22×C73#51811yescharacteristic
611C22×C73#52011yescharacteristic
612C22×C73#53411yescharacteristic
613C22×C73#53411yescharacteristic
614C22×C73#53511yescharacteristic
615C22×C73#53511yescharacteristic
616C22×C73#53511yescharacteristic
617C22×C73#53711yescharacteristic
618C22×C73#53811yescharacteristic
619C22×C73#53811yescharacteristic
620C22×C73#53811yescharacteristic
621C22×C73#53911yescharacteristic
622C22×C73#54011yescharacteristic
623C22×C73#54011yescharacteristic
624C22×C73D4211yescharacteristic
625C22×C73D4211yescharacteristic
626C22×C73D4211yescharacteristic
627C22×C73#54611yescharacteristic
628C22×C73#54611yescharacteristic
629C22×C73#54611yescharacteristic
630C22×C73#54611yescharacteristic
631C22×C73#54711yescharacteristic
632C22×C73#54811yescharacteristic
633C22×C73#55111yescharacteristic
634C22×C73#55111yescharacteristic
635C22×C73#55311yescharacteristic
636C22×C73#56011yescharacteristic
637C22×C73#56011yescharacteristic
638C22×C73#56211yescharacteristic
639C22×C73#56211yescharacteristic
640C4×C73—24no—
641C4×C73—42no—
642C4×C73—42no—
643C4×C73—42no—
644C4×C73—42no—
645C4×C73—42no—
646C4×C73—42no—
647C4×C73—42no—
648C4×C73—42no—
649C4×C73—42no—
650C4×C73—81no—
651C4×C73—81no—
652#14519C7311yesmaximal, characteristic, direct product factor, Sylow
653C2×C73—44no—
654C2×C73—44no—
655C2×C73—82no—
656C2×C73#232111yescharacteristic
657C2×C73#232511yescharacteristic
658C2×C73#232811yescharacteristic
659C2×C73#235811yescharacteristic
660C2×C73#235811yescharacteristic
661C2×C73#236111yescharacteristic
662C2×C73#237711yescharacteristic
663C2×C73#266911yescharacteristic
664C2×C73#267111yescharacteristic
665C2×C73#267611yescharacteristic
666C2×C73#267811yescharacteristic
667C2×C73#268811yescharacteristic
668C2×C73#269611yescharacteristic
669C2×C73#270611yescharacteristic
670C2×C73#274911yescharacteristic
671C2×#392C2×C7311yescharacteristic
672C2×#390C2×C7311yescharacteristic, complemented
673C2×#386C2×C7311yescharacteristic, complemented
674C2×#386C2×C7311yescharacteristic, complemented
675C2×#386C2×C7311yescharacteristic, complemented
676C2×#386C2×C7311yescharacteristic, complemented
677C2×#385C2×C7311yescharacteristic, complemented
678#1442C2×C7311yescharacteristic, complemented
679#1440C2×C7311yescharacteristic, complemented
680#1439C2×C7311yescharacteristic, complemented
681#1439C2×C7311yescharacteristic, complemented
682#1438C2×C7311yescharacteristic, complemented
683#1437C2×C7311yescharacteristic, complemented
684#1434C2×C7311yescharacteristic, complemented
685C22⋊#95C2×C7311yescharacteristic, complemented
686C73#1451911yescharacteristic, direct product factor, Sylow
687C23×D4C22×C7311yescharacteristic
688C23×D4C22×C7311yescharacteristic
689C23×D4C22×C7311yescharacteristic
690C24×C4C22×C7311yescharacteristic
691C24×C4C22×C7311yescharacteristic
692C22×C4⋊C4C22×C7311yescharacteristic
693C22×C4⋊C4C22×C7311yescharacteristic
694C22×C22⋊C4C22×C7311yescharacteristic
695C22×C22⋊C4C22×C7311yescharacteristic
696C22×C22⋊C4C22×C7311yescharacteristic
697C22×C22⋊C4C22×C7311yescharacteristic
698C22×C22⋊C4C22×C7311yescharacteristic
699C22×C22⋊C4C22×C7311yescharacteristic
700C22×C22⋊C4C22×C7311yescharacteristic
701C22×C22⋊C4C22×C7311yescharacteristic
702C22×C22⋊C4C22×C7311yescharacteristic
703C22×C22⋊C4C22×C7311yescharacteristic
704C22×C22⋊C4C22×C7311yescharacteristic
705C22×C22⋊C4C22×C7311yescharacteristic
706C22×C22⋊C4C22×C7311yescharacteristic
707C22×C42C22×C7311yescharacteristic
708#392C4×C7318yescomplemented
709#390—24no—
710#386—24no—
711#386—24no—
712#386—24no—
713#386—24no—
714#385—24no—
715C2×#95C22×C7311yescharacteristic
716C2×#95C22×C7311yescharacteristic
717C2×#95C22×C7311yescharacteristic
718C2×#95C22×C7311yescharacteristic
719C2×#95C22×C7311yescharacteristic
720C2×#95C22×C7311yescharacteristic
721C2×#95C22×C7311yescharacteristic
722C2×#95C22×C7311yescharacteristic
723C2×#95C22×C7311yescharacteristic
724C2×#95C22×C7311yescharacteristic
725C2×#95C22×C7311yescharacteristic
726C2×#95C22×C7311yescharacteristic
727C2×#95C22×C7311yescharacteristic
728C2×#95C22×C7311yescharacteristic
729C25C23×C7311yescharacteristic
730C25C23×C7311yescharacteristic
731C25C23×C7311yescharacteristic
732C22×D4—22no—
733C22×D4—22no—
734C22×D4—22no—
735C22×D4—22no—
736C22×D4—22no—
737C22×D4—22no—
738C22×D4—22no—
739C22×D4—22no—
740C22×D4—22no—
741C22×D4—22no—
742C22×D4—41no—
743C22×D4—41no—
744C22×D4—41no—
745C22×D4—41no—
746C22×D4—41no—
747C22×D4—41no—
748C22×D4—41no—
749C22×D4—41no—
750C22×D4C2×C4×C7314yes—
751C22×D4C2×C4×C7314yescomplemented
752C22×D4C2×C4×C7314yescomplemented
753C23×C4—22no—
754C23×C4—22no—
755C23×C4—22no—
756C23×C4—22no—
757C23×C4—22no—
758C23×C4—22no—
759C23×C4—41no—
760C23×C4—41no—
761C23×C4—41no—
762C23×C4—41no—
763C23×C4—41no—
764C23×C4—41no—
765C23×C4—41no—
766C23×C4—41no—
767C23×C4C23×C7311yescharacteristic
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
779C2×C4⋊C4—22no—
780C2×C4⋊C4—22no—
781C2×C4⋊C4—22no—
782C2×C4⋊C4—41no—
783C2×C4⋊C4—41no—
784C2×C4⋊C4—41no—
785C2×C22⋊C4—22no—
786C2×C22⋊C4—22no—
787C2×C22⋊C4—22no—
788C2×C22⋊C4—22no—
789C2×C22⋊C4—22no—
790C2×C22⋊C4—22no—
791C2×C22⋊C4—22no—
792C2×C22⋊C4—22no—
793C2×C22⋊C4—22no—
794C2×C22⋊C4—22no—
795C2×C22⋊C4—22no—
796C2×C22⋊C4—22no—
797C2×C22⋊C4—22no—
798C2×C22⋊C4—22no—
799C2×C22⋊C4—22no—
800C2×C22⋊C4—22no—
801C2×C22⋊C4—41no—
802C2×C22⋊C4—41no—
803C2×C22⋊C4—41no—
804C2×C22⋊C4—41no—
805C2×C22⋊C4—41no—
806C2×C22⋊C4—41no—
807C2×C22⋊C4—41no—
808C2×C22⋊C4—41no—
809C2×C22⋊C4—41no—
810C2×C22⋊C4—41no—
811C2×C22⋊C4—41no—
812C2×C22⋊C4—41no—
813C2×C22⋊C4—41no—
814C2×C22⋊C4—41no—
815C2×C22⋊C4—41no—
816C2×C22⋊C4—41no—
817C2×C22⋊C4—41no—
818C2×C22⋊C4—41no—
819C2×C22⋊C4C2×C4×C7314yescomplemented
820C2×C22⋊C4C2×C4×C7314yescomplemented
821C2×C22⋊C4C2×C4×C7314yescomplemented
822C2×C22⋊C4D4×C7314yescomplemented
823C2×C22⋊C4D4×C7314yescomplemented
824C2×C42—22no—
825C2×C42—22no—
826C2×C42—41no—
827#95—22no—
828#95—22no—
829#95—22no—
830#95—22no—
831#95—22no—
832#95—22no—
833#95—22no—
834#95—22no—
835#95—41no—
836#95—41no—
837#95—41no—
838#95—41no—
839#95C2×C4×C7314yescomplemented
840#95D4×C7314yescomplemented
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
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—
879C24C22×C4×C7312yes—
880C24C22×C4×C7312yes—
881C24C22×C4×C7312yes—
882C24C2×D4×C7312yes—
883C24C2×D4×C7312yes—
884C24#41×C7312yes—
885C24#41×C7312yes—
886C24C24×C7311yescharacteristic
887C2×D4—28no—
888C2×D4—28no—
889C2×D4—28no—
890C2×D4—28no—
891C2×D4—28no—
892C2×D4—44no—
893C2×D4—44no—
894C2×D4—44no—
895C2×D4—44no—
896C2×D4—44no—
897C2×D4—44no—
898C2×D4—44no—
899C2×D4—44no—
900C2×D4—44no—
901C2×D4—44no—
902C2×D4—44no—
903C2×D4—44no—
904C2×D4—44no—
905C2×D4—44no—
906C2×D4—44no—
907C2×D4—44no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
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—21no—
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—44no—
981C22×C4—44no—
982C22×C4—44no—
983C22×C4—44no—
984C22×C4—44no—
985C22×C4—44no—
986C22×C4—44no—
987C22×C4—44no—
988C22×C4—44no—
989C22×C4—44no—
990C22×C4—44no—
991C22×C4—44no—
992C22×C4—44no—
993C22×C4—44no—
994C22×C4C22×C4×C7312yes—
995C22×C4C22×C4×C7312yes—
996C22×C4C22×C4×C7312yes—
997C22×C4C22×C4×C7312yes—
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×C4#41×C7312yes—
1006C4⋊C4—44no—
1007C4⋊C4—44no—
1008C22⋊C4—28no—
1009C22⋊C4—44no—
1010C22⋊C4—44no—
1011C22⋊C4—44no—
1012C22⋊C4—44no—
1013C22⋊C4—44no—
1014C22⋊C4—44no—
1015C22⋊C4—44no—
1016C22⋊C4—44no—
1017C22⋊C4—44no—
1018C22⋊C4—44no—
1019C22⋊C4—44no—
1020C22⋊C4—44no—
1021C42—44no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
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—
1125C23C4×D4×C7314yes—
1126C23C4×D4×C7314yes—
1127C23C23×C4×C7311yescharacteristic
1128C23C22×D4×C7311yescharacteristic
1129C23C22×D4×C7311yescharacteristic
1130C23C22×D4×C7311yescharacteristic
1131C23C2×#41×C7311yescharacteristic
1132C23C2×#41×C7311yescharacteristic
1133C23C2×#41×C7311yescharacteristic
1134C23H(5,𝔽2)×C7311yescharacteristic
1135C23H(5,𝔽2)×C7311yescharacteristic
1136C23H(5,𝔽2)×C7311yescharacteristic
1137C23H(5,𝔽2)×C7311yescharacteristic
1138C23H(5,𝔽2)×C7311yescharacteristic
1139C23H(5,𝔽2)×C7311yescharacteristic
1140C23H(5,𝔽2)×C7311yescharacteristic
1141C232−1+4×C7311yescharacteristic
1142D4—416no—
1143D4—416no—
1144D4—416no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
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—416no—
1179C2×C4—416no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
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×C4C4×D4×C7314yes—
1231C22—24no—
1232C22—24no—
1233C22—24no—
1234C22—24no—
1235C22—24no—
1236C22—24no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
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—81no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22C2×C4×D4×C7311yescharacteristic
1277C22C2×C4×D4×C7311yescharacteristic
1278C22C2×C4×D4×C7311yescharacteristic
1279C22#518×C7311yescharacteristic
1280C22#518×C7311yescharacteristic
1281C22#518×C7311yescharacteristic
1282C22#520×C7311yescharacteristic
1283C22#534×C7311yescharacteristic
1284C22#534×C7311yescharacteristic
1285C22#535×C7311yescharacteristic
1286C22#535×C7311yescharacteristic
1287C22#535×C7311yescharacteristic
1288C22#537×C7311yescharacteristic
1289C22#538×C7311yescharacteristic
1290C22#538×C7311yescharacteristic
1291C22#538×C7311yescharacteristic
1292C22#539×C7311yescharacteristic
1293C22#540×C7311yescharacteristic
1294C22#540×C7311yescharacteristic
1295C22D42×C7311yescharacteristic
1296C22D42×C7311yescharacteristic
1297C22D42×C7311yescharacteristic
1298C22#546×C7311yescharacteristic
1299C22#546×C7311yescharacteristic
1300C22#546×C7311yescharacteristic
1301C22#546×C7311yescharacteristic
1302C22#547×C7311yescharacteristic
1303C22#548×C7311yescharacteristic
1304C22#551×C7311yescharacteristic
1305C22#551×C7311yescharacteristic
1306C22#553×C7311yescharacteristic
1307C22#560×C7311yescharacteristic
1308C22#560×C7311yescharacteristic
1309C22#562×C7311yescharacteristic
1310C22#562×C7311yescharacteristic
1311C4—24no—
1312C4—42no—
1313C4—42no—
1314C4—42no—
1315C4—42no—
1316C4—42no—
1317C4—42no—
1318C4—42no—
1319C4—42no—
1320C4—42no—
1321C4—81no—
1322C4—81no—
1323C2—44no—
1324C2—44no—
1325C2—82no—
1326C2C73×#232111yescharacteristic
1327C2C73×#232511yescharacteristic
1328C2C73×#232811yescharacteristic
1329C2C73×#235811yescharacteristic
1330C2C73×#235811yescharacteristic
1331C2C73×#236111yescharacteristic
1332C2C73×#237711yescharacteristic
1333C2C73×#266911yescharacteristic
1334C2C73×#267111yescharacteristic
1335C2C73×#267611yescharacteristic
1336C2C73×#267811yescharacteristic
1337C2C73×#268811yescharacteristic
1338C2C73×#269611yescharacteristic
1339C2C73×#270611yescharacteristic
1340C2C73×#274911yescharacteristic
subgroupG/H
center, socleC24×C73C24
commutatorC23C23×C4×C73
Frattini, cosocleC24C24×C73
prime radicalC2×#392×C73C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C73 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#390×C73C2semidirect
3. C2×#386×C73C2semidirect
4. C2×#386×C73C2semidirect
5. C2×#386×C73C2semidirect
6. C2×#386×C73C2semidirect
7. C2×#385×C73C2semidirect
8. C73×#1442C2semidirect
9. C73×#1440C2semidirect
10. C73×#1439C2semidirect
11. C73×#1439C2semidirect
12. C73×#1438C2semidirect
13. C73×#1437C2semidirect
14. C73×#1434C2semidirect
15. C73×C22⋊#95C2semidirect
37. #392×C73C4semidirect
80. C22×D4×C73C2×C4semidirect
81. C22×D4×C73C2×C4semidirect
148. C2×C22⋊C4×C73C2×C4semidirect
149. C2×C22⋊C4×C73C2×C4semidirect
150. C2×C22⋊C4×C73C2×C4semidirect
151. C2×C22⋊C4×C73D4semidirect
152. C2×C22⋊C4×C73D4semidirect
168. #95×C73C2×C4semidirect
169. #95×C73D4semidirect
652. #14519C73direct (N × H)
672. C2×#390C2×C73semidirect
673. C2×#386C2×C73semidirect
674. C2×#386C2×C73semidirect
675. C2×#386C2×C73semidirect
676. C2×#386C2×C73semidirect
677. C2×#385C2×C73semidirect
678. #1442C2×C73semidirect
679. #1440C2×C73semidirect
680. #1439C2×C73semidirect
681. #1439C2×C73semidirect
682. #1438C2×C73semidirect
683. #1437C2×C73semidirect
684. #1434C2×C73semidirect
685. C22⋊#95C2×C73semidirect
686. C73#14519direct (N × H)
708. #392C4×C73semidirect
751. C22×D4C2×C4×C73semidirect
752. C22×D4C2×C4×C73semidirect
819. C2×C22⋊C4C2×C4×C73semidirect
820. C2×C22⋊C4C2×C4×C73semidirect
821. C2×C22⋊C4C2×C4×C73semidirect
822. C2×C22⋊C4D4×C73semidirect
823. C2×C22⋊C4D4×C73semidirect
839. #95C2×C4×C73semidirect
840. #95D4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#392×C732
C2×#390×C732
C2×#386×C732
C2×#385×C732
C73×#14422
C73×#14402
C73×#14392
C73×#14382
C73×#14372
C73×#14342
C73×C22⋊#952
#1451973