Finite Group Databasebeta

← C2×#22614068 #33253573

Subgroups — C2×#22614068 #33253573

Order 18688.

2942 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D73C211yesmaximal, characteristic
2#22614068C2116yesmaximal, direct product factor
3C2×#17988526C211yesmaximal, characteristic, complemented
4C2×#17988520C211yesmaximal, characteristic, complemented
5C2×#17988518C211yesmaximal, characteristic, complemented
6C2×#17988517C211yesmaximal, characteristic, complemented
7C2×#17988482C211yesmaximal, characteristic, complemented
8C2×#17988473C211yesmaximal, characteristic, complemented
9C2×#17988471C211yesmaximal, characteristic, complemented
10C2×#17988458C211yesmaximal, characteristic
11C2×#17988458C211yesmaximal, characteristic
12C2×#17988458C211yesmaximal, characteristic
13C2×#17988458C211yesmaximal, characteristic
14C2×#17988444C211yesmaximal, characteristic
15C2×C4×#11924005C211yesmaximal, characteristic
16C22×#125×C73C211yesmaximal, characteristic, complemented
17C23×C4×D73C2211yescharacteristic
18C23×C4×D73C2211yescharacteristic
19C23×C4×D73C2211yescharacteristic
20C22×C4⋊Dic73C2211yescharacteristic
21C22×C4⋊Dic73C2211yescharacteristic
22C22×#11924007C2211yescharacteristic
23C22×#11924007C2211yescharacteristic
24C22×#11924007C2211yescharacteristic
25C22×#11924007C2211yescharacteristic
26C22×#11924007C2211yescharacteristic
27C22×#11924007C2211yescharacteristic
28C2×C4⋊C4×D73—28no—
29C2×C4⋊C4×D73C2218yes—
30C22×#11924005C2211yescharacteristic
31C22×#11924005C2211yescharacteristic
32C22×#11924005C2211yescharacteristic
33C22×#11924005C2211yescharacteristic
34C22×C4×Dic73C2211yescharacteristic
35#17988526C2218yescomplemented
36#17988520C2218yescomplemented
37#17988518C2218yescomplemented
38#17988517C2218yescomplemented
39#17988482C2218yescomplemented
40#17988473C2218yescomplemented
41#17988471C2218yescomplemented
42#17988458C2218yes—
43#17988458C2218yes—
44#17988458C2218yes—
45#17988458C2218yes—
46#17988444C2218yes—
47C4×#11924005C2218yes—
48C2×#14556498C2211yescharacteristic
49C2×#14556498C2211yescharacteristic
50C2×#14556498C2211yescharacteristic
51C2×#14556498C2211yescharacteristic
52C2×#14556498C2211yescharacteristic
53C2×#14556498C2211yescharacteristic
54C2×#14556498C2211yescharacteristic
55C2×#14556498C2211yescharacteristic
56C2×#14556498C2211yescharacteristic
57C2×#14556498C2211yescharacteristic
58C2×#14556498C2211yescharacteristic
59C2×#14556498C2211yescharacteristic
60C2×#125×C73—28no—
61C2×#125×C73C2218yescomplemented
62C22×C4⋊C4×C73C2211yescharacteristic
63C22×C4⋊C4×C73C2211yescharacteristic
64C22×C4⋊C4×C73C2211yescharacteristic
65C22×C4⋊C4×C73C2211yescharacteristic
66C22×C4⋊C4×C73C2211yescharacteristic
67C22×C4⋊C4×C73C2211yescharacteristic
68C22×C42×C73C2211yescharacteristic
69C24×D73C2311yescharacteristic
70C23×Dic73C2311yescharacteristic
71C23×Dic73C2311yescharacteristic
72C23×Dic73C2311yescharacteristic
73C23×Dic73C2311yescharacteristic
74C23×Dic73C2311yescharacteristic
75C23×Dic73C2311yescharacteristic
76C23×Dic73C2311yescharacteristic
77C22×C4×D73—24no—
78C22×C4×D73—24no—
79C22×C4×D73—24no—
80C22×C4×D73—24no—
81C22×C4×D73—24no—
82C22×C4×D73—24no—
83C22×C4×D73—24no—
84C22×C4×D73—42no—
85C22×C4×D73—42no—
86C22×C4×D73C2314yes—
87C22×C4×D73C2314yes—
88C22×C4×D73C2314yes—
89C2×C4⋊Dic73—24no—
90C2×C4⋊Dic73—42no—
91C2×C4⋊Dic73C2314yes—
92C2×C4⋊Dic73C2314yes—
93C2×#11924007—24no—
94C2×#11924007—24no—
95C2×#11924007—24no—
96C2×#11924007—24no—
97C2×#11924007—42no—
98C2×#11924007—42no—
99C2×#11924007C2314yes—
100C2×#11924007C2314yes—
101C2×#11924007C2314yes—
102C2×#11924007C2314yes—
103C2×#11924007C2314yes—
104C2×#11924007C2314yes—
105C4⋊C4×D73—232no—
106C2×#11924005—24no—
107C2×#11924005—24no—
108C2×#11924005—24no—
109C2×#11924005Q818yes—
110C2×#11924005C2314yes—
111C2×#11924005C2314yes—
112C2×#11924005C2314yes—
113C2×#11924005C2314yes—
114C2×C4×Dic73—42no—
115C2×C4×Dic73C2314yes—
116#14556498C2314yes—
117#14556498C2314yes—
118#14556498C2314yes—
119#14556498C2314yes—
120#14556498C2314yes—
121#14556498C2314yes—
122#14556498C2314yes—
123#14556498C2314yes—
124#14556498C2314yes—
125#14556498C2314yes—
126#14556498C2314yes—
127#14556498C2314yes—
128C23×C4×C73C2311yescharacteristic
129C23×C4×C73C2311yescharacteristic
130C23×C4×C73C2311yescharacteristic
131C23×C4×C73C2311yescharacteristic
132C23×C4×C73C2311yescharacteristic
133C23×C4×C73C2311yescharacteristic
134C23×C4×C73C2311yescharacteristic
135#125×C73—232no—
136C2×C4⋊C4×C73—24no—
137C2×C4⋊C4×C73—24no—
138C2×C4⋊C4×C73—24no—
139C2×C4⋊C4×C73—24no—
140C2×C4⋊C4×C73—24no—
141C2×C4⋊C4×C73D418yes—
142C2×C4⋊C4×C73C2314yes—
143C2×C4⋊C4×C73C2314yes—
144C2×C4⋊C4×C73C2314yes—
145C2×C4⋊C4×C73C2314yes—
146C2×C4⋊C4×C73C2314yes—
147C2×C4⋊C4×C73C2314yes—
148C2×C42×C73—24no—
149C2×C42×C73C2314yes—
150C23×D73—22no—
151C23×D73—22no—
152C23×D73—22no—
153C23×D73—22no—
154C23×D73C2×Q814yes—
155C23×D73#4114yes—
156C23×D73#4114yes—
157C23×D73C2412yes—
158C22×Dic73—22no—
159C22×Dic73—22no—
160C22×Dic73—22no—
161C22×Dic73—22no—
162C22×Dic73—22no—
163C22×Dic73—22no—
164C22×Dic73—22no—
165C22×Dic73—22no—
166C22×Dic73—22no—
167C22×Dic73—22no—
168C22×Dic73—22no—
169C22×Dic73—22no—
170C22×Dic73—22no—
171C22×Dic73—22no—
172C22×Dic73—22no—
173C22×Dic73—22no—
174C22×Dic73—22no—
175C22×Dic73—22no—
176C22×Dic73—22no—
177C22×Dic73C2×Q814yes—
178C22×Dic73#4114yes—
179C22×Dic73C2412yes—
180C22×Dic73C2412yes—
181C22×Dic73C2412yes—
182C22×Dic73C2412yes—
183C22×Dic73C2412yes—
184C22×Dic73C2412yes—
185C22×Dic73C2412yes—
186C2×C4×D73—232no—
187C2×C4×D73—28no—
188C2×C4×D73—28no—
189C2×C4×D73—28no—
190C2×C4×D73—28no—
191C2×C4×D73—28no—
192C2×C4×D73—28no—
193C2×C4×D73—28no—
194C2×C4×D73—44no—
195C2×C4×D73—44no—
196C2×C4×D73—416no—
197C2×C4×D73—416no—
198C4⋊Dic73—28no—
199C4⋊Dic73—44no—
200#11924007—28no—
201#11924007—28no—
202#11924007—28no—
203#11924007—28no—
204#11924007—44no—
205#11924007—44no—
206#11924005—28no—
207#11924005—28no—
208#11924005—28no—
209#11924005C2×Q8116yes—
210C4×Dic73—44no—
211C24×C73C2411yescharacteristic
212C22×C4×C73—22no—
213C22×C4×C73—22no—
214C22×C4×C73—22no—
215C22×C4×C73—22no—
216C22×C4×C73—22no—
217C22×C4×C73—22no—
218C22×C4×C73—22no—
219C22×C4×C73—22no—
220C22×C4×C73—22no—
221C22×C4×C73—22no—
222C22×C4×C73—22no—
223C22×C4×C73—22no—
224C22×C4×C73—22no—
225C22×C4×C73—22no—
226C22×C4×C73—22no—
227C22×C4×C73—22no—
228C22×C4×C73—22no—
229C22×C4×C73C2×D414yes—
230C22×C4×C73C2×D414yes—
231C22×C4×C73C2×D414yes—
232C22×C4×C73C2×Q814yes—
233C22×C4×C73C2412yes—
234C22×C4×C73C2412yes—
235C22×C4×C73C2412yes—
236C22×C4×C73C2412yes—
237C22×C4×C73C2412yes—
238C22×C4×C73C2412yes—
239C22×C4×C73C2412yes—
240C4⋊C4×C73—28no—
241C4⋊C4×C73—28no—
242C4⋊C4×C73—28no—
243C4⋊C4×C73—28no—
244C4⋊C4×C73—28no—
245C4⋊C4×C73C2×D4116yes—
246C42×C73—28no—
247C23×C73C22×D412yes—
248C23×C73C22×Q812yes—
249C23×C73C2×#4112yes—
250C23×C73C2×#4112yes—
251C23×C73C2×#4112yes—
252C23×C73H(5,𝔽2)12yes—
253C23×C732−1+412yes—
254C23×C73C2511yescharacteristic
255C22×D73—28no—
256C22×D73—28no—
257C22×D73—28no—
258C22×D73—28no—
259C22×D73—28no—
260C22×D73—28no—
261C22×D73—22no—
262C22×D73—22no—
263C22×D73—22no—
264C22×D73—22no—
265C22×D73#125116yescomplemented
266C22×D73C22×Q814yes—
267C22×D73C2×#4114yes—
268C22×D73C2×#4114yes—
269C2×C4×C73—28no—
270C2×C4×C73—28no—
271C2×C4×C73—28no—
272C2×C4×C73—28no—
273C2×C4×C73—22no—
274C2×C4×C73—22no—
275C2×C4×C73—22no—
276C2×C4×C73—22no—
277C2×C4×C73—22no—
278C2×C4×C73—22no—
279C2×C4×C73—22no—
280C2×C4×C73—22no—
281C2×C4×C73—22no—
282C2×C4×C73—22no—
283C2×C4×C73—22no—
284C2×C4×C73—22no—
285C2×C4×C73—22no—
286C2×C4×C73—22no—
287C2×C4×C73—22no—
288C2×C4×C73—22no—
289C2×C4×C73—22no—
290C2×C4×C73—44no—
291C2×C4×C73—44no—
292C2×C4×C73—44no—
293C2×C4×C73C22×D414yes—
294C2×C4×C73C22×D414yes—
295C2×C4×C73C22×D414yes—
296C2×C4×C73C22×Q814yes—
297C2×Dic73—28no—
298C2×Dic73—28no—
299C2×Dic73—22no—
300C2×Dic73—22no—
301C2×Dic73—22no—
302C2×Dic73—22no—
303C2×Dic73—22no—
304C2×Dic73—22no—
305C2×Dic73—22no—
306C2×Dic73—22no—
307C2×Dic73—22no—
308C2×Dic73—22no—
309C2×Dic73—22no—
310C2×Dic73—22no—
311C2×Dic73—22no—
312C2×Dic73—22no—
313C2×Dic73—22no—
314C2×Dic73—22no—
315C2×Dic73—22no—
316C2×Dic73—22no—
317C2×Dic73—22no—
318C2×Dic73—44no—
319C2×Dic73—44no—
320C2×Dic73—44no—
321C2×Dic73—44no—
322C2×Dic73—44no—
323C2×Dic73C22×Q814yes—
324C2×Dic73C2×#4114yes—
325C4×D73—232no—
326C4×D73—416no—
327C4×D73—416no—
328C22×C73#52514yes—
329C22×C73C2×#12514yes—
330C22×C73#53914yes—
331C22×C73#54614yes—
332C22×C73D4×Q814yes—
333C22×C73#55214yes—
334C22×C73#55414yes—
335C22×C73C23×D411yescharacteristic
336C22×C73C23×Q811yescharacteristic
337C22×C73C22×#4111yescharacteristic
338C22×C73C22×#4111yescharacteristic
339C22×C73C22×#4111yescharacteristic
340C22×C73C2×H(5,𝔽2)11yescharacteristic
341C22×C73C2×2−1+411yescharacteristic
342C2×D73—24no—
343C2×D73—24no—
344C2×D73—24no—
345C2×D73—24no—
346C2×D73—24no—
347C2×D73—24no—
348C2×D73—232no—
349C2×D73C2×#12518yescomplemented
350C4×C73—24no—
351C4×C73—24no—
352C4×C73—24no—
353C4×C73—24no—
354C4×C73—42no—
355C4×C73—42no—
356C4×C73—42no—
357Dic73—24no—
358Dic73—24no—
359Dic73—42no—
360Dic73—42no—
361Dic73—42no—
362Dic73—42no—
363Dic73—42no—
364C2×#2473—731nomaximal, Sylow
365C2×C73#247318yescomplemented
366C2×C73C2×#52511yescharacteristic
367C2×C73C22×#12511yescharacteristic
368C2×C73C2×#53911yescharacteristic
369C2×C73C2×#54611yescharacteristic
370C2×C73C2×D4×Q811yescharacteristic
371C2×C73C2×#55211yescharacteristic
372C2×C73C2×#55411yescharacteristic
373D73—28no—
374C22×#125D7311yescharacteristic, complemented
375C23×C4⋊C4—731no—
376#2473—7316no—
377C2×#400—731no—
378C2×#398—731no—
379C2×#398—731no—
380C2×#398—731no—
381C2×#389—731no—
382C2×#387—731no—
383C2×#387—731no—
384C2×#385—731no—
385C2×#385—731no—
386C2×#385—731no—
387C2×#385—731no—
388C2×#380—731no—
389C2×C4×C22⋊C4—731no—
390C73C2×#247311yescharacteristic, complemented, Sylow
391C24×C4—731no—
392C24×C4—731no—
393C24×C4—731no—
394C2×#125—28no—
395C2×#125C2×D7318yescomplemented
396C22×C4⋊C4—731no—
397C22×C4⋊C4—731no—
398C22×C4⋊C4—731no—
399C22×C4⋊C4—731no—
400C22×C4⋊C4—731no—
401C22×C4⋊C4—731no—
402C22×C4⋊C4—731no—
403C22×C4⋊C4—731no—
404C22×C4⋊C4—738no—
405C22×C4⋊C4—1468no—
406C22×C4⋊C4C2×D7311yescharacteristic
407C22×C4⋊C4C2×D7311yescharacteristic
408C22×C4⋊C4C2×D7311yescharacteristic
409C22×C4⋊C4C2×D7311yescharacteristic
410C22×C4⋊C4C2×D7311yescharacteristic
411C22×C4⋊C4C2×D7311yescharacteristic
412C22×C22⋊C4—731no—
413C22×C22⋊C4—731no—
414C22×C22⋊C4—731no—
415C22×C22⋊C4—731no—
416C22×C42—731no—
417C22×C42C2×D7311yescharacteristic
418#400—738no—
419#398—738no—
420#398—738no—
421#398—738no—
422#389—738no—
423#387—738no—
424#387—738no—
425#385—738no—
426#385—738no—
427#385—738no—
428#385—738no—
429#380—738no—
430C4×C22⋊C4—738no—
431C2×#95—731no—
432C2×#95—731no—
433C2×#95—731no—
434C2×#95—731no—
435C2×#95—731no—
436C2×#95—731no—
437C2×#95—731no—
438C2×#95—731no—
439C2×#95—731no—
440C2×#95—731no—
441C2×#95—731no—
442C2×#95—731no—
443C25—731no—
444C23×C4—2922no—
445C23×C4—2922no—
446C23×C4—734no—
447C23×C4—734no—
448C23×C4—731no—
449C23×C4—731no—
450C23×C4—731no—
451C23×C4—731no—
452C23×C4—731no—
453C23×C4—731no—
454C23×C4—731no—
455C23×C4—734no—
456C23×C4—1464no—
457C23×C4—1464no—
458C23×C4—1464no—
459C23×C4—1464no—
460C23×C4—1464no—
461C23×C4—1464no—
462C23×C4—1464no—
463C23×C4C22×D7311yescharacteristic
464C23×C4C22×D7311yescharacteristic
465C23×C4C22×D7311yescharacteristic
466C23×C4C22×D7311yescharacteristic
467C23×C4C22×D7311yescharacteristic
468C23×C4C22×D7311yescharacteristic
469C23×C4C22×D7311yescharacteristic
470#125—232no—
471C2×C4⋊C4—24no—
472C2×C4⋊C4—24no—
473C2×C4⋊C4—24no—
474C2×C4⋊C4—24no—
475C2×C4⋊C4—24no—
476C2×C4⋊C4—2922no—
477C2×C4⋊C4—2922no—
478C2×C4⋊C4—2922no—
479C2×C4⋊C4—734no—
480C2×C4⋊C4—734no—
481C2×C4⋊C4—734no—
482C2×C4⋊C4—734no—
483C2×C4⋊C4—734no—
484C2×C4⋊C4—734no—
485C2×C4⋊C4—734no—
486C2×C4⋊C4—734no—
487C2×C4⋊C4—1464no—
488C2×C4⋊C4—1464no—
489C2×C4⋊C4—1464no—
490C2×C4⋊C4—1464no—
491C2×C4⋊C4—1464no—
492C2×C4⋊C4—14632no—
493C2×C4⋊C4C22⋊D7318yes—
494C2×C4⋊C4C22×D7314yes—
495C2×C4⋊C4C22×D7314yes—
496C2×C4⋊C4C22×D7314yes—
497C2×C4⋊C4C22×D7314yes—
498C2×C4⋊C4C22×D7314yes—
499C2×C4⋊C4C22×D7314yes—
500C2×C22⋊C4—738no—
501C2×C22⋊C4—734no—
502C2×C22⋊C4—734no—
503C2×C22⋊C4—734no—
504C2×C22⋊C4—734no—
505C2×C22⋊C4—1464no—
506C2×C22⋊C4—1464no—
507C2×C22⋊C4—1464no—
508C2×C42—24no—
509C2×C42—2922no—
510C2×C42—734no—
511C2×C42C22×D7314yes—
512#95—734no—
513#95—734no—
514#95—734no—
515#95—734no—
516#95—734no—
517#95—734no—
518#95—734no—
519#95—734no—
520#95—734no—
521#95—734no—
522#95—734no—
523#95—734no—
524C24—734no—
525C24—734no—
526C24—734no—
527C24—732no—
528C24—1462no—
529C24—1462no—
530C24—1462no—
531C24—1462no—
532C24C23×D7311yescharacteristic
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—29216no—
551C22×C4—29216no—
552C22×C4—2924no—
553C22×C4—2924no—
554C22×C4—734no—
555C22×C4—734no—
556C22×C4—732no—
557C22×C4—732no—
558C22×C4—732no—
559C22×C4—732no—
560C22×C4—732no—
561C22×C4—732no—
562C22×C4—732no—
563C22×C4—1468no—
564C22×C4—1468no—
565C22×C4—1468no—
566C22×C4—1468no—
567C22×C4—14632no—
568C22×C4—1462no—
569C22×C4—1462no—
570C22×C4—1462no—
571C22×C4—1462no—
572C22×C4—1462no—
573C22×C4—1462no—
574C22×C4—1462no—
575C22×C4—1462no—
576C22×C4—1462no—
577C22×C4—1462no—
578C22×C4—1462no—
579C22×C4—1462no—
580C22×C4—1462no—
581C22×C4—1462no—
582C22×C4—1462no—
583C22×C4—1468no—
584C22×C4—1468no—
585C22×C4—1462no—
586C22×C4—1462no—
587C22×C4—1462no—
588C22×C4—1462no—
589C22×C4—1468no—
590C22×C4C2×C22⋊D7314yes—
591C22×C4C2×C22⋊D7314yes—
592C22×C4C2×C22⋊D7314yes—
593C22×C4Q8×D7314yes—
594C22×C4C23×D7312yes—
595C22×C4C23×D7312yes—
596C22×C4C23×D7312yes—
597C22×C4C23×D7312yes—
598C22×C4C23×D7312yes—
599C22×C4C23×D7312yes—
600C22×C4C23×D7312yes—
601C4⋊C4—28no—
602C4⋊C4—28no—
603C4⋊C4—28no—
604C4⋊C4—28no—
605C4⋊C4—28no—
606C4⋊C4—2924no—
607C4⋊C4—2924no—
608C4⋊C4—2924no—
609C4⋊C4—1468no—
610C4⋊C4—1468no—
611C4⋊C4—1468no—
612C4⋊C4—1468no—
613C4⋊C4—1468no—
614C4⋊C4C2×C22⋊D73116yes—
615C22⋊C4—7316no—
616C22⋊C4—1468no—
617C22⋊C4—1468no—
618C22⋊C4—1468no—
619C42—28no—
620C42—2924no—
621C23—734no—
622C23—734no—
623C23—734no—
624C23—7316no—
625C23—1462no—
626C23—1462no—
627C23—1462no—
628C23—1462no—
629C23—1468no—
630C23—1468no—
631C23—1468no—
632C23—1468no—
633C23—1468no—
634C23—1468no—
635C23C22×C22⋊D7312yes—
636C23C2×Q8×D7312yes—
637C23#41×D7312yes—
638C23#41×D7312yes—
639C23#41×D7312yes—
640C23#1455663712yes—
641C23#1455663912yes—
642C23C24×D7311yescharacteristic
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—28no—
652C2×C4—28no—
653C2×C4—28no—
654C2×C4—28no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—44no—
665C2×C4—44no—
666C2×C4—44no—
667C2×C4—29216no—
668C2×C4—29216no—
669C2×C4—2924no—
670C2×C4—2924no—
671C2×C4—2924no—
672C2×C4—2924no—
673C2×C4—2924no—
674C2×C4—734no—
675C2×C4—734no—
676C2×C4—14632no—
677C2×C4—1462no—
678C2×C4—1462no—
679C2×C4—1462no—
680C2×C4—1462no—
681C2×C4—1462no—
682C2×C4—1462no—
683C2×C4—1462no—
684C2×C4—1462no—
685C2×C4—1462no—
686C2×C4—1462no—
687C2×C4—1462no—
688C2×C4—1462no—
689C2×C4—1462no—
690C2×C4—1462no—
691C2×C4—1462no—
692C2×C4—1462no—
693C2×C4—1462no—
694C2×C4—1462no—
695C2×C4—1462no—
696C2×C4—1468no—
697C2×C4—1468no—
698C2×C4C22×C22⋊D7314yes—
699C2×C4C22×C22⋊D7314yes—
700C2×C4C22×C22⋊D7314yes—
701C2×C4C2×Q8×D7314yes—
702C22—738no—
703C22—1464no—
704C22—14632no—
705C22—1464no—
706C22—1464no—
707C22—1464no—
708C22—1464no—
709C22—1464no—
710C22#1798909414yes—
711C22#125×D7314yes—
712C22#1798918514yes—
713C22#1798922514yes—
714C22Q8×C22⋊D7314yes—
715C22#1798926914yes—
716C22#1798929314yes—
717C22C23×C22⋊D7311yescharacteristic
718C22C22×Q8×D7311yescharacteristic
719C22C2×#41×D7311yescharacteristic
720C22C2×#41×D7311yescharacteristic
721C22C2×#41×D7311yescharacteristic
722C22C2×#1455663711yescharacteristic
723C22C2×#1455663911yescharacteristic
724C4—24no—
725C4—24no—
726C4—24no—
727C4—24no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—2922no—
732C4—2922no—
733C4—2922no—
734C4—2922no—
735C4—2922no—
736C4—1464no—
737C4—1464no—
738C2—1468no—
739C2#2261406818yesdirect product factor
740C2C2×#1798909411yescharacteristic
741C2C2×#125×D7311yescharacteristic
742C2C2×#1798918511yescharacteristic
743C2C2×#1798922511yescharacteristic
744C2C2×Q8×C22⋊D7311yescharacteristic
745C2C2×#1798926911yescharacteristic
746C2C2×#1798929311yescharacteristic
subgroupG/H
centerC24C23×D73
commutator, cosocleC23×C73C25
FrattiniC23C24×D73
FittingC22×#125×C73C2
socleC24×C73C24
prime radicalC24×D73C23
hypercenterC22×#125D73
hypocenterC73C2×#2473
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C24 ◁ C22×#125

Complements

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

NH ≅ G/Ntype
2. #22614068C2direct (N × H)
3. C2×#17988526C2semidirect
4. C2×#17988520C2semidirect
5. C2×#17988518C2semidirect
6. C2×#17988517C2semidirect
7. C2×#17988482C2semidirect
8. C2×#17988473C2semidirect
9. C2×#17988471C2semidirect
16. C22×#125×C73C2semidirect
35. #17988526C22semidirect
36. #17988520C22semidirect
37. #17988518C22semidirect
38. #17988517C22semidirect
39. #17988482C22semidirect
40. #17988473C22semidirect
41. #17988471C22semidirect
61. C2×#125×C73C22semidirect
265. C22×D73#125semidirect
349. C2×D73C2×#125semidirect
365. C2×C73#2473semidirect
374. C22×#125D73semidirect
390. C73C2×#2473semidirect
395. C2×#125C2×D73semidirect
739. C2#22614068direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D732
#226140682
C2×#179885262
C2×#179885202
C2×#179885182
C2×#179885172
C2×#179884822
C2×#179884732
C2×#179884712
C2×#179884582
C2×#179884442
C2×C4×#119240052
C22×#125×C732
C2×#247373