Finite Group Databasebeta

← C2×#22622201 #33962855

Subgroups — C2×#22622201 #33962855

Order 18688.

2114 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989277C211yesmaximal, characteristic, complemented
2C2×#17989246C211yesmaximal, characteristic
3#22622201C2116yesmaximal, direct product factor
4C2×#17988942C211yesmaximal, characteristic, complemented
5C2×#17988923C211yesmaximal, characteristic, complemented
6C2×#17988912C211yesmaximal, characteristic, complemented
7C2×#17988895C211yesmaximal, characteristic, complemented
8C2×#17988845C211yesmaximal, characteristic, complemented
9C2×#17988833C211yesmaximal, characteristic, complemented
10C2×#17988810C211yesmaximal, characteristic, complemented
11C2×#17988751C211yesmaximal, characteristic, complemented
12C2×#17988745C211yesmaximal, characteristic, complemented
13C2×C4×Dic292C211yesmaximal, characteristic, complemented
14C2×#17988589C211yesmaximal, characteristic, complemented
15C2×#17988597C211yesmaximal, characteristic, complemented
16C2×#436×C73C211yesmaximal, characteristic, complemented
17C22×#11924028C2211yescharacteristic
18C23×Dic146C2211yescharacteristic
19C22×Dic292C2211yescharacteristic
20C22×Dic292C2211yescharacteristic
21C22×#11924017C2211yescharacteristic
22#17989277—24no—
23#17989277C2218yescomplemented
24#17989246—24no—
25#17989246C2218yes—
26C2×#14556584—21no—
27C2×#14556583C2211yescharacteristic
28C2×#14556581—21no—
29C2×#14556579C2211yescharacteristic
30C2×#14556577—21no—
31C2×#14556572—21no—
32C2×#14556570C2211yescharacteristic
33C2×#14556570C2211yescharacteristic
34C2×#14556570C2211yescharacteristic
35C2×#14556569—21no—
36C2×#14556565C2211yescharacteristic
37C2×#14556563—21no—
38C2×C4×Dic146C2211yescharacteristic
39C2×C4×Dic146C2211yescharacteristic
40C2×#14556551—21no—
41C2×#14556550C2211yescharacteristic
42C2×#14556547—21no—
43C22×C4⋊Dic73C2211yescharacteristic
44#17988942C2218yescomplemented
45#17988923C2218yescomplemented
46#17988912C2218yescomplemented
47#17988895C2218yescomplemented
48#17988845C2218yescomplemented
49#17988833C2218yescomplemented
50#17988810C2218yescomplemented
51#17988751C2218yescomplemented
52#17988745C2218yescomplemented
53C4×Dic292C2218yescomplemented
54C2×#14556525C2211yescharacteristic
55C2×#14556525C2211yescharacteristic
56C2×#14556523C2211yescharacteristic
57#17988597C2218yescomplemented
58#17988589C2218yescomplemented
59C2×#14556516C2211yescharacteristic
60C2×#14556516C2211yescharacteristic
61C2×#14556516C2211yescharacteristic
62C2×#14556516C2211yescharacteristic
63C2×#14556516C2211yescharacteristic
64C2×#14556516C2211yescharacteristic
65C2×#14556516C2211yescharacteristic
66C2×#14556513C2211yescharacteristic
67C2×#14556513C2211yescharacteristic
68C2×#14556513C2211yescharacteristic
69C22×M16×C73C2211yescharacteristic
70C22×M16×C73C2211yescharacteristic
71C2×C4×D4×C73C2211yescharacteristic
72#436×C73C2218yescomplemented
73C2×C4⋊C8×C73C2211yescharacteristic
74C2×C22⋊C8×C73C2211yescharacteristic
75C2×C22⋊C8×C73C2211yescharacteristic
76C2×C4×C8×C73C2211yescharacteristic
77C2×#11924028—24no—
78C2×#11924028—22no—
79C2×#11924028—42no—
80C2×#11924028C2314yes—
81C22×Dic146—24no—
82C22×Dic146—22no—
83C22×Dic146—21no—
84C22×Dic146—42no—
85C22×Dic146C2311yescharacteristic
86C22×Dic146C2311yescharacteristic
87C22×Dic146C2314yes—
88C22×Dic146C2311yescharacteristic
89C22×D292C2311yescharacteristic
90C22×C22⋊D73—21no—
91C22×C22⋊D73—21no—
92C23×Dic73—21no—
93C23×Dic73—21no—
94C22×C4×D73—21no—
95C2×Dic292—24no—
96C2×Dic292—42no—
97C2×Dic292C2314yes—
98C2×Dic292C2314yes—
99C2×#11924017—42no—
100C2×#11924017C2314yes—
101#14556584—28no—
102#14556583—22no—
103#14556583C2314yes—
104#14556581—28no—
105#14556579—22no—
106#14556579C2314yes—
107#14556577—28no—
108#14556572—28no—
109#14556570—22no—
110#14556570—22no—
111#14556570—22no—
112#14556570C2314yes—
113#14556570C2314yes—
114#14556570C2314yes—
115#14556569—28no—
116#14556565—22no—
117#14556565C2314yes—
118#14556563—28no—
119C4×Dic146—22no—
120C4×Dic146—22no—
121C4×Dic146C2314yes—
122C4×Dic146C2314yes—
123#14556551—28no—
124#14556550—22no—
125#14556550C2314yes—
126#14556547—28no—
127C2×C4⋊Dic73—22no—
128C2×C4⋊Dic73—21no—
129C2×C4⋊Dic73C2311yescharacteristic
130C2×C4⋊Dic73C2311yescharacteristic
131C2×C4⋊Dic73C2311yescharacteristic
132C2×C4⋊Dic73C2311yescharacteristic
133C2×C4⋊Dic73C2314yes—
134C2×#11924007—21no—
135C2×#11924007—21no—
136C2×#11924007—21no—
137C2×#11924007—21no—
138C2×#11924007—21no—
139C2×#11924007—21no—
140C2×#11924007—21no—
141C2×C22⋊Dic73—21no—
142C2×C22⋊Dic73—21no—
143C2×C22⋊Dic73—21no—
144C2×C22⋊Dic73—21no—
145C2×#11924005—21no—
146C2×#11924005—21no—
147C2×#11924005—21no—
148C2×C4×Dic73—21no—
149C2×C4×Dic73—21no—
150C2×C4×Dic73—21no—
151#14556525C2314yes—
152#14556525C2314yes—
153#14556523C2314yes—
154#14556516C2314yes—
155#14556516C2314yes—
156#14556516C2314yes—
157#14556516C2314yes—
158#14556516C2314yes—
159#14556516C2314yes—
160#14556516C2314yes—
161#14556513C2314yes—
162#14556513C2314yes—
163#14556513C2314yes—
164C22×D4×C73D411yescharacteristic
165C23×C4×C73C2311yescharacteristic
166C23×C4×C73C2311yescharacteristic
167C2×M16×C73—42no—
168C2×M16×C73—42no—
169C2×M16×C73C2314yes—
170C2×M16×C73C2314yes—
171C22×C8×C73C2311yescharacteristic
172C22×C8×C73C2311yescharacteristic
173C22×C8×C73C2311yescharacteristic
174C22×C8×C73C2311yescharacteristic
175C4×D4×C73D414yes—
176C4×D4×C73C2314yes—
177C2×C4⋊C4×C73D411yescharacteristic
178C2×C22⋊C4×C73D411yescharacteristic
179C2×C22⋊C4×C73D411yescharacteristic
180C2×C42×C73C2311yescharacteristic
181C4⋊C8×C73C2314yes—
182C22⋊C8×C73C2314yes—
183C22⋊C8×C73C2314yes—
184C4×C8×C73C2314yes—
185C23×D73—21no—
186#11924028—28no—
187#11924028—44no—
188#11924028—48no—
189C2×Dic146—21no—
190C2×Dic146—22no—
191C2×Dic146—22no—
192C2×Dic146—22no—
193C2×Dic146—22no—
194C2×Dic146—22no—
195C2×Dic146—28no—
196C2×Dic146—21no—
197C2×Dic146—24no—
198C2×Dic146—21no—
199C2×Dic146—44no—
200C2×Dic146—48no—
201C2×Dic146—44no—
202C2×Dic146#4114yes—
203C2×Dic146C2412yes—
204C2×Dic146C2412yes—
205C2×Dic146C2412yes—
206C2×D292—22no—
207C2×D292—22no—
208C2×D292—21no—
209C2×D292C2412yes—
210C2×C22⋊D73—24no—
211C2×C22⋊D73—24no—
212C2×C22⋊D73—44no—
213C2×C22⋊D73—44no—
214C22×Dic73—21no—
215C22×Dic73—21no—
216C22×Dic73—21no—
217C22×Dic73—21no—
218C22×Dic73—21no—
219C22×Dic73—21no—
220C22×Dic73—21no—
221C22×Dic73—24no—
222C22×Dic73—24no—
223C22×Dic73—44no—
224C22×Dic73—44no—
225C2×C4×D73—24no—
226C2×C4×D73—44no—
227Dic292—28no—
228Dic292—44no—
229#11924017—44no—
230C4⋊Dic73—21no—
231C4⋊Dic73—21no—
232C4⋊Dic73—24no—
233C4⋊Dic73—21no—
234C4⋊Dic73—21no—
235C4⋊Dic73C2412yes—
236C4⋊Dic73C2412yes—
237C4⋊Dic73C2412yes—
238C4⋊Dic73C2412yes—
239#11924007—24no—
240#11924007—24no—
241#11924007—24no—
242#11924007—24no—
243#11924007—24no—
244#11924007—24no—
245#11924007—24no—
246C22⋊Dic73—24no—
247C22⋊Dic73—24no—
248C22⋊Dic73—24no—
249C22⋊Dic73—24no—
250#11924005—24no—
251#11924005—24no—
252#11924005—24no—
253C4×Dic73—24no—
254C4×Dic73—24no—
255C4×Dic73—24no—
256C24×C73C2×D411yescharacteristic
257C24×C73C2×D411yescharacteristic
258C2×D4×C73—42no—
259C2×D4×C73C2×D414yes—
260C22×C4×C73—22no—
261C22×C4×C73—22no—
262C22×C4×C73—22no—
263C22×C4×C73—22no—
264C22×C4×C73C2×D411yescharacteristic
265C22×C4×C73C2×D411yescharacteristic
266C22×C4×C73C2×D411yescharacteristic
267C22×C4×C73C2×D411yescharacteristic
268C22×C4×C73C2×D412yes—
269C22×C4×C73C2×D412yes—
270C22×C4×C73C2412yes—
271C22×C4×C73C2412yes—
272C22×C4×C73C2411yescharacteristic
273M16×C73—44no—
274M16×C73—44no—
275C2×C8×C73—22no—
276C2×C8×C73—22no—
277C2×C8×C73—22no—
278C2×C8×C73—22no—
279C2×C8×C73C2412yes—
280C2×C8×C73C2412yes—
281C2×C8×C73C2412yes—
282C2×C8×C73C2412yes—
283C4⋊C4×C73C2×D414yes—
284C22⋊C4×C73C2×D414yes—
285C22⋊C4×C73C2×D414yes—
286C42×C73C2×D412yes—
287C42×C73C2412yes—
288C23×C73—22no—
289C23×C73—22no—
290C23×C73—22no—
291C23×C73—22no—
292C23×C73—22no—
293C23×C73—22no—
294C23×C73C22×D412yes—
295C23×C73C22×D412yes—
296C23×C73C22×D411yescharacteristic
297C22×D73—22no—
298C22×D73—42no—
299C22×D73—42no—
300C22×D73—42no—
301D4×C73—44no—
302C2×C4×C73—22no—
303C2×C4×C73—22no—
304C2×C4×C73—22no—
305C2×C4×C73—22no—
306C2×C4×C73—24no—
307C2×C4×C73—24no—
308C2×C4×C73—22no—
309C2×C4×C73—22no—
310C2×C4×C73—22no—
311C2×C4×C73—22no—
312C2×C4×C73C22×D412yes—
313C2×C4×C73C22×D412yes—
314C2×C4×C73C22×D412yes—
315C2×C4×C73C22×D412yes—
316C2×C4×C73C22×D411yescharacteristic
317C2×C4×C73C2×#4112yes—
318C2×C4×C73H(5,𝔽2)12yes—
319C2×C4×C73C2511yescharacteristic
320C22⋊D73—48no—
321C22⋊D73—48no—
322C2×Dic73—24no—
323C2×Dic73—22no—
324C2×Dic73—22no—
325C2×Dic73—22no—
326C2×Dic73—22no—
327C2×Dic73—22no—
328C2×Dic73—22no—
329C2×Dic73—22no—
330C2×Dic73—48no—
331C2×Dic73—48no—
332C2×Dic73—42no—
333C2×Dic73—42no—
334C2×Dic73—42no—
335C2×Dic73—42no—
336C2×Dic73—42no—
337C2×Dic73—42no—
338D292—22no—
339D292—22no—
340D292—42no—
341C4×D73—48no—
342Dic146—24no—
343Dic146—22no—
344Dic146—22no—
345Dic146—22no—
346Dic146—22no—
347Dic146—22no—
348Dic146—48no—
349Dic146—42no—
350Dic146—42no—
351Dic146C2×#4114yes—
352C8×C73—22no—
353C8×C73—22no—
354C8×C73—22no—
355C8×C73—22no—
356C22×C73—22no—
357C22×C73—22no—
358C22×C73—22no—
359C22×C73—22no—
360C22×C73—22no—
361C22×C73—22no—
362C22×C73—44no—
363C22×C73—44no—
364C22×C73#54612yes—
365C22×C73#57512yes—
366C22×C73#57812yes—
367C22×C73C23×D411yescharacteristic
368C2×D73—42no—
369C2×D73—42no—
370C2×D73—42no—
371C2×D73—84no—
372C4×C73—22no—
373C4×C73—22no—
374C4×C73—22no—
375C4×C73—22no—
376C4×C73#54612yes—
377C4×C73C22×#4111yescharacteristic
378C4×C73C2×H(5,𝔽2)11yescharacteristic
379Dic73—24no—
380Dic73—42no—
381Dic73—42no—
382Dic73—42no—
383Dic73—42no—
384Dic73—42no—
385Dic73—42no—
386C2×#3327—731nomaximal, Sylow
387C2×C73—42no—
388C2×C73—42no—
389C2×C73#332714yescomplemented
390C2×C73C2×#54611yescharacteristic
391C2×C73C2×#57511yescharacteristic
392C2×C73C2×#57811yescharacteristic
393D73—82no—
394C2×#552—731no—
395C2×#548—731no—
396#3327—7316no—
397C2×#488—731no—
398C2×#484—731no—
399C2×#482—731no—
400C2×#479—731no—
401C2×#470—731no—
402C2×#468—731no—
403C2×#464—731no—
404C2×#452—731no—
405C2×#451—731no—
406C2×C4×Q16—731no—
407C2×#436D7311yescharacteristic, complemented
408C2×#417—731no—
409C2×#419—731no—
410C73C2×#332711yescharacteristic, complemented, Sylow
411C22×#41—731no—
412C23×Q8—731no—
413C22×Q16—731no—
414C22×Q16—731no—
415C22×SD16—731no—
416C22×M16C2×D7311yescharacteristic
417C22×M16C2×D7311yescharacteristic
418#552—738no—
419#552—1464no—
420#548—738no—
421#548—1464no—
422C2×#126—1461no—
423C2×#125—731no—
424C2×#125—1461no—
425C2×#124—731no—
426C2×#124—1461no—
427C2×#123—1461no—
428C2×C22⋊Q8—731no—
429C2×C22⋊Q8—731no—
430C2×C22⋊Q8—731no—
431C2×C22⋊Q8—1461no—
432C2×#121—731no—
433C2×#121—1461no—
434C2×C4×Q8—731no—
435C2×C4×Q8—731no—
436C2×C4×D4—1461no—
437C2×C4×D4C2×D7311yescharacteristic
438C2×#117—731no—
439C2×#117—1461no—
440C22×C4⋊C4—731no—
441#488—738no—
442#484—738no—
443#482—738no—
444#479—738no—
445#470—738no—
446#468—738no—
447#464—738no—
448#452—738no—
449#451—738no—
450C4×Q16—738no—
451#436C2×D7318yescomplemented
452C2×#107—731no—
453C2×#107—731no—
454C2×#106—731no—
455C2×C4⋊C8C2×D7311yescharacteristic
456#419—738no—
457#417—738no—
458C2×#103—731no—
459C2×#103—731no—
460C2×#103—731no—
461C2×#103—731no—
462C2×#103—731no—
463C2×#103—731no—
464C2×#103—731no—
465C2×#102—731no—
466C2×#102—731no—
467C2×#102—731no—
468C2×C22⋊C8C2×D7311yescharacteristic
469C2×C22⋊C8C2×D7311yescharacteristic
470C2×C4×C8C2×D7311yescharacteristic
471C2×#41—2922no—
472C2×#41—734no—
473C2×#41—1464no—
474C2×#41—1462no—
475C22×Q8—2922no—
476C22×Q8—734no—
477C22×Q8—731no—
478C22×Q8—731no—
479C22×Q8—731no—
480C22×Q8—1464no—
481C22×Q8—1461no—
482C22×Q8—1462no—
483C22×D4—731no—
484C22×D4—1461no—
485C22×D4—1461no—
486C22×D4D29211yescharacteristic
487C23×C4—1461no—
488C23×C4—1461no—
489C23×C4—1461no—
490C23×C4C22×D7311yescharacteristic
491C23×C4C22×D7311yescharacteristic
492C2×Q16—2922no—
493C2×Q16—734no—
494C2×Q16—734no—
495C2×Q16—1464no—
496C2×SD16—2922no—
497C2×SD16—734no—
498C2×M16—42no—
499C2×M16—42no—
500C2×M16C22×D7314yes—
501C2×M16C22×D7314yes—
502C22×C8C22×D7311yescharacteristic
503C22×C8C22×D7311yescharacteristic
504C22×C8C22×D7311yescharacteristic
505C22×C8C22×D7311yescharacteristic
506#126—1468no—
507#125—734no—
508#125—1468no—
509#125—1462no—
510#124—734no—
511#124—1468no—
512#124—1462no—
513#123—1468no—
514C22⋊Q8—734no—
515C22⋊Q8—734no—
516C22⋊Q8—734no—
517C22⋊Q8—1462no—
518C22⋊Q8—1462no—
519C22⋊Q8—1462no—
520C22⋊Q8—1468no—
521#121—734no—
522#121—1468no—
523#121—1462no—
524C4×Q8—734no—
525C4×Q8—734no—
526C4×Q8—1462no—
527C4×Q8—1462no—
528C4×D4—1468no—
529C4×D4D29214yes—
530C4×D4C22×D7314yes—
531#117—734no—
532#117—1462no—
533#117—1468no—
534C2×C4⋊C4—731no—
535C2×C4⋊C4—731no—
536C2×C4⋊C4—734no—
537C2×C4⋊C4—731no—
538C2×C4⋊C4—731no—
539C2×C4⋊C4—1461no—
540C2×C4⋊C4—1462no—
541C2×C4⋊C4—1461no—
542C2×C4⋊C4—1461no—
543C2×C4⋊C4—1461no—
544C2×C4⋊C4—1461no—
545C2×C4⋊C4—1461no—
546C2×C4⋊C4—1461no—
547C2×C4⋊C4—1461no—
548C2×C4⋊C4D29211yescharacteristic
549C2×C22⋊C4—1461no—
550C2×C22⋊C4—1461no—
551C2×C22⋊C4—1461no—
552C2×C22⋊C4—1461no—
553C2×C22⋊C4—1461no—
554C2×C22⋊C4—1461no—
555C2×C22⋊C4—1461no—
556C2×C22⋊C4D29211yescharacteristic
557C2×C22⋊C4D29211yescharacteristic
558C2×C42—1461no—
559C2×C42—1461no—
560C2×C42—1461no—
561C2×C42C22×D7311yescharacteristic
562#107—734no—
563#107—734no—
564#106—734no—
565C4⋊C8C22×D7314yes—
566#103—734no—
567#103—734no—
568#103—734no—
569#103—734no—
570#103—734no—
571#103—734no—
572#103—734no—
573#102—734no—
574#102—734no—
575#102—734no—
576C22⋊C8C22×D7314yes—
577C22⋊C8C22×D7314yes—
578C4×C8C22×D7314yes—
579C24—1461no—
580C24C2×D29211yescharacteristic
581C24C2×D29211yescharacteristic
582#41—2928no—
583#41—2924no—
584#41—1468no—
585C2×Q8—2928no—
586C2×Q8—2924no—
587C2×Q8—2924no—
588C2×Q8—734no—
589C2×Q8—732no—
590C2×Q8—732no—
591C2×Q8—732no—
592C2×Q8—1468no—
593C2×Q8—1462no—
594C2×Q8—1462no—
595C2×Q8—1462no—
596C2×Q8—1462no—
597C2×Q8—1461no—
598C2×Q8—1461no—
599C2×Q8—1464no—
600C2×Q8—1461no—
601C2×Q8—1462no—
602C2×D4—42no—
603C2×D4—2924no—
604C2×D4—2924no—
605C2×D4—732no—
606C2×D4—1464no—
607C2×D4—1464no—
608C2×D4—1461no—
609C2×D4—1462no—
610C2×D4—1462no—
611C2×D4C2×D29214yes—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—2924no—
617C22×C4—2924no—
618C22×C4—2924no—
619C22×C4—1464no—
620C22×C4—1464no—
621C22×C4—1461no—
622C22×C4—1461no—
623C22×C4—1461no—
624C22×C4—1461no—
625C22×C4—1461no—
626C22×C4—1461no—
627C22×C4—1464no—
628C22×C4—1461no—
629C22×C4C2×D29212yes—
630C22×C4C2×D29212yes—
631C22×C4C2×D29211yescharacteristic
632C22×C4C2×D29211yescharacteristic
633C22×C4C2×D29211yescharacteristic
634C22×C4C2×D29211yescharacteristic
635C22×C4C23×D7312yes—
636C22×C4C23×D7312yes—
637C22×C4C23×D7311yescharacteristic
638Q16—2924no—
639Q16—1468no—
640SD16—2924no—
641M16—44no—
642M16—44no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—22no—
646C2×C8—22no—
647C2×C8C23×D7312yes—
648C2×C8C23×D7312yes—
649C2×C8C23×D7312yes—
650C2×C8C23×D7312yes—
651C4⋊C4—732no—
652C4⋊C4—732no—
653C4⋊C4—732no—
654C4⋊C4—732no—
655C4⋊C4—1464no—
656C4⋊C4—1464no—
657C4⋊C4—1464no—
658C4⋊C4—1464no—
659C4⋊C4—1464no—
660C4⋊C4—1464no—
661C4⋊C4—1464no—
662C4⋊C4—1461no—
663C4⋊C4—1461no—
664C4⋊C4—1464no—
665C4⋊C4—1461no—
666C4⋊C4—1461no—
667C4⋊C4C2×D29214yes—
668C22⋊C4—1464no—
669C22⋊C4—1464no—
670C22⋊C4—1464no—
671C22⋊C4—1464no—
672C22⋊C4—1464no—
673C22⋊C4—1464no—
674C22⋊C4—1464no—
675C22⋊C4C2×D29214yes—
676C22⋊C4C2×D29214yes—
677C42—1464no—
678C42—1464no—
679C42—1464no—
680C42C2×D29212yes—
681C42C23×D7312yes—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—2922no—
689C23—2922no—
690C23—2922no—
691C23—1462no—
692C23C22×D29212yes—
693C23C22×D29212yes—
694C23C22×D29211yescharacteristic
695Q8—2928no—
696Q8—2922no—
697Q8—2922no—
698Q8—734no—
699Q8—1462no—
700Q8—1462no—
701Q8—1462no—
702Q8—1462no—
703Q8—1462no—
704Q8—1464no—
705D4—44no—
706D4—2928no—
707D4—2928no—
708D4—2922no—
709D4—1462no—
710D4—1462no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—2928no—
722C2×C4—2928no—
723C2×C4—2922no—
724C2×C4—2922no—
725C2×C4—2922no—
726C2×C4—2922no—
727C2×C4—2922no—
728C2×C4—2922no—
729C2×C4—2928no—
730C2×C4—1462no—
731C2×C4—1462no—
732C2×C4—1462no—
733C2×C4—1462no—
734C2×C4—1462no—
735C2×C4—1462no—
736C2×C4—1462no—
737C2×C4—1464no—
738C2×C4C22×D29212yes—
739C2×C4C22×D29212yes—
740C2×C4C22×D29212yes—
741C2×C4C22×D29212yes—
742C2×C4C22×D29211yescharacteristic
743C2×C4#41×D7312yes—
744C2×C4#1455663612yes—
745C2×C4C24×D7311yescharacteristic
746C8—22no—
747C8—22no—
748C8—22no—
749C8—22no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—44no—
757C22—44no—
758C22—2922no—
759C22—2922no—
760C22—2922no—
761C22—5844no—
762C22#1798923212yes—
763C22#1798938712yes—
764C22#1798940412yes—
765C22C23×D29211yescharacteristic
766C4—22no—
767C4—22no—
768C4—22no—
769C4—22no—
770C4—2922no—
771C4—2922no—
772C4—2922no—
773C4—2922no—
774C4—2922no—
775C4—2922no—
776C4—1464no—
777C4#1798923212yes—
778C4C2×#41×D7311yescharacteristic
779C4C2×#1455663611yescharacteristic
780C2—42no—
781C2—42no—
782C2—5842no—
783C2#2262220114yesdirect product factor
784C2C2×#1798923211yescharacteristic
785C2C2×#1798938711yescharacteristic
786C2C2×#1798940411yescharacteristic
subgroupG/H
centerC23C22×D292
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#436×C73C2
socleC23×C73C22×D4
prime radicalC2×#17989246C2
hypercenterC2×#436D73
hypocenterC73C2×#3327
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#436

Complements

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

NH ≅ G/Ntype
1. C2×#17989277C2semidirect
3. #22622201C2direct (N × H)
4. C2×#17988942C2semidirect
5. C2×#17988923C2semidirect
6. C2×#17988912C2semidirect
7. C2×#17988895C2semidirect
8. C2×#17988845C2semidirect
9. C2×#17988833C2semidirect
10. C2×#17988810C2semidirect
11. C2×#17988751C2semidirect
12. C2×#17988745C2semidirect
13. C2×C4×Dic292C2semidirect
14. C2×#17988589C2semidirect
15. C2×#17988597C2semidirect
16. C2×#436×C73C2semidirect
23. #17989277C22semidirect
44. #17988942C22semidirect
45. #17988923C22semidirect
46. #17988912C22semidirect
47. #17988895C22semidirect
48. #17988845C22semidirect
49. #17988833C22semidirect
50. #17988810C22semidirect
51. #17988751C22semidirect
52. #17988745C22semidirect
53. C4×Dic292C22semidirect
57. #17988597C22semidirect
58. #17988589C22semidirect
72. #436×C73C22semidirect
389. C2×C73#3327semidirect
407. C2×#436D73semidirect
410. C73C2×#3327semidirect
451. #436C2×D73semidirect
783. C2#22622201direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179892772
C2×#179892462
#226222012
C2×#179889422
C2×#179889232
C2×#179889122
C2×#179888952
C2×#179888452
C2×#179888332
C2×#179888102
C2×#179887512
C2×#179887452
C2×C4×Dic2922
C2×#179885892
C2×#179885972
C2×#436×C732
C2×#332773