Finite Group Databasebeta

← C2×#22622312 #33964433

Subgroups — C2×#22622312 #33964433

Order 18688.

1930 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989283C211yesmaximal, characteristic
2C2×#17989277C211yesmaximal, characteristic, complemented
3#22622312C2116yesmaximal, direct product factor
4C2×#17988989C211yesmaximal, characteristic, complemented
5C2×#17988923C211yesmaximal, characteristic, complemented
6C2×#17988929C211yesmaximal, characteristic, complemented
7C2×#17988912C211yesmaximal, characteristic, complemented
8C2×#17988901C211yesmaximal, characteristic, complemented
9C2×#17988895C211yesmaximal, characteristic, complemented
10C2×#17988888C211yesmaximal, characteristic, complemented
11C2×#17988816C211yesmaximal, characteristic, complemented
12C2×#17988816C211yesmaximal, characteristic, complemented
13C2×C4×#11924017C211yesmaximal, characteristic, complemented
14C2×#17988625C211yesmaximal, characteristic, complemented
15C22×#14556523C211yesmaximal, characteristic, complemented
16C2×C8×D4×C73C211yesmaximal, characteristic, complemented
17C22×#11924017C2211yescharacteristic
18#17989283—24no—
19#17989283C2218yes—
20#17989277—24no—
21#17989277C2218yescomplemented
22C2×#14556586—21no—
23C2×#14556584—21no—
24C2×#14556583C2211yescharacteristic
25C2×#14556583C2211yescharacteristic
26C2×#14556581—21no—
27C2×#14556573—21no—
28C2×#14556572—21no—
29C2×#14556570C2211yescharacteristic
30C2×#14556570C2211yescharacteristic
31C2×#14556565C2211yescharacteristic
32C2×#14556565C2211yescharacteristic
33C2×#14556563—21no—
34C2×C4×Dic146C2211yescharacteristic
35C2×C4×D292C2211yescharacteristic
36C2×#14556551—21no—
37C2×#14556550C2211yescharacteristic
38C2×#14556550C2211yescharacteristic
39C2×#14556547—21no—
40C22×C4⋊Dic73C2211yescharacteristic
41C22×C4⋊Dic73C2211yescharacteristic
42#17988989C2218yescomplemented
43#17988929C2218yescomplemented
44#17988923C2218yescomplemented
45#17988912C2218yescomplemented
46#17988901C2218yescomplemented
47#17988895C2218yescomplemented
48#17988888C2218yescomplemented
49#17988816C2218yescomplemented
50#17988816C2218yescomplemented
51C4×#11924017C2218yescomplemented
52#17988625C2218yescomplemented
53C2×#14556525C2211yescharacteristic
54C2×#14556525C2211yescharacteristic
55C2×#14556525C2211yescharacteristic
56C2×#14556525C2211yescharacteristic
57C2×#14556523C2211yescharacteristic
58C2×#14556523C2211yescharacteristic
59C2×#14556523C2211yescharacteristic
60C2×#14556523C2211yescharacteristic
61C2×#14556523C2211yescharacteristic
62C2×#14556523C2218yescomplemented
63C2×#14556516C2211yescharacteristic
64C2×#14556516C2211yescharacteristic
65C2×#14556516C2211yescharacteristic
66C2×#14556513C2211yescharacteristic
67C2×#14556513C2211yescharacteristic
68C2×#14556513C2211yescharacteristic
69C23×C8×C73C2211yescharacteristic
70C23×C8×C73C2211yescharacteristic
71C2×C4×D4×C73C2211yescharacteristic
72C8×D4×C73C2218yescomplemented
73C2×C4⋊C8×C73C2211yescharacteristic
74C2×C22⋊C8×C73C2211yescharacteristic
75C2×C22⋊C8×C73C2211yescharacteristic
76C2×C4×C8×C73C2211yescharacteristic
77C22×Dic146C2311yescharacteristic
78C22×D292C2311yescharacteristic
79C22×C22⋊D73—21no—
80C22×C22⋊D73—21no—
81C23×Dic73—21no—
82C23×Dic73—21no—
83C22×C4×D73—21no—
84C2×#11924017—24no—
85C2×#11924017C2314yes—
86#14556586—28no—
87#14556584—28no—
88#14556583—22no—
89#14556583—22no—
90#14556583C2314yes—
91#14556583C2314yes—
92#14556581—28no—
93#14556573—28no—
94#14556572—28no—
95#14556570—22no—
96#14556570—22no—
97#14556570C2314yes—
98#14556570C2314yes—
99#14556565—22no—
100#14556565—22no—
101#14556565C2314yes—
102#14556565C2314yes—
103#14556563—28no—
104C4×Dic146—22no—
105C4×Dic146C2314yes—
106C4×D292—22no—
107C4×D292C2314yes—
108#14556551—28no—
109#14556550—22no—
110#14556550—22no—
111#14556550C2314yes—
112#14556550C2314yes—
113#14556547—28no—
114C2×C4⋊Dic73—22no—
115C2×C4⋊Dic73—22no—
116C2×C4⋊Dic73—21no—
117C2×C4⋊Dic73—21no—
118C2×C4⋊Dic73C2311yescharacteristic
119C2×C4⋊Dic73C2311yescharacteristic
120C2×C4⋊Dic73C2311yescharacteristic
121C2×C4⋊Dic73C2311yescharacteristic
122C2×C4⋊Dic73C2311yescharacteristic
123C2×C4⋊Dic73C2311yescharacteristic
124C2×C4⋊Dic73C2314yes—
125C2×C4⋊Dic73C2314yes—
126C2×#11924007—21no—
127C2×#11924007—21no—
128C2×#11924007—21no—
129C2×#11924007—21no—
130C2×#11924007—21no—
131C2×#11924007—21no—
132C2×#11924007—21no—
133C2×C22⋊Dic73—21no—
134C2×C22⋊Dic73—21no—
135C2×C22⋊Dic73—21no—
136C2×C22⋊Dic73—21no—
137C2×#11924005—21no—
138C2×#11924005—21no—
139C2×#11924005—21no—
140C2×C4×Dic73—21no—
141C2×C4×Dic73—21no—
142C2×C4×Dic73—21no—
143#14556525C2314yes—
144#14556525C2314yes—
145#14556525C2314yes—
146#14556525C2314yes—
147#14556523C2314yes—
148#14556523C2314yes—
149#14556523C2314yes—
150#14556523C2314yes—
151#14556523C2314yes—
152#14556516C2314yes—
153#14556516C2314yes—
154#14556516C2314yes—
155#14556513C2314yes—
156#14556513C2314yes—
157#14556513C2314yes—
158C22×D4×C73D411yescharacteristic
159C23×C4×C73C2311yescharacteristic
160C23×C4×C73C2311yescharacteristic
161C22×C8×C73—24no—
162C22×C8×C73—24no—
163C22×C8×C73C2311yescharacteristic
164C22×C8×C73C2314yes—
165C22×C8×C73C2311yescharacteristic
166C22×C8×C73C2311yescharacteristic
167C22×C8×C73C2314yes—
168C22×C8×C73C2311yescharacteristic
169C4×D4×C73D414yes—
170C4×D4×C73C2314yes—
171C2×C4⋊C4×C73D411yescharacteristic
172C2×C22⋊C4×C73D411yescharacteristic
173C2×C22⋊C4×C73D411yescharacteristic
174C2×C42×C73C2311yescharacteristic
175C4⋊C8×C73C2314yes—
176C22⋊C8×C73C2314yes—
177C22⋊C8×C73C2314yes—
178C4×C8×C73C2314yes—
179C23×D73—21no—
180C2×Dic146—22no—
181C2×Dic146—22no—
182C2×Dic146—21no—
183C2×Dic146C2412yes—
184C2×D292—22no—
185C2×D292—22no—
186C2×D292—21no—
187C2×D292C2412yes—
188C2×C22⋊D73—24no—
189C2×C22⋊D73—24no—
190C2×C22⋊D73—44no—
191C2×C22⋊D73—82no—
192C22×Dic73—21no—
193C22×Dic73—21no—
194C22×Dic73—21no—
195C22×Dic73—21no—
196C22×Dic73—21no—
197C22×Dic73—21no—
198C22×Dic73—21no—
199C22×Dic73—24no—
200C22×Dic73—24no—
201C22×Dic73—44no—
202C22×Dic73—82no—
203C2×C4×D73—24no—
204C2×C4×D73—82no—
205#11924017—28no—
206C4⋊Dic73—21no—
207C4⋊Dic73—21no—
208C4⋊Dic73—21no—
209C4⋊Dic73—21no—
210C4⋊Dic73—24no—
211C4⋊Dic73—24no—
212C4⋊Dic73—21no—
213C4⋊Dic73—21no—
214C4⋊Dic73C2412yes—
215C4⋊Dic73C2412yes—
216C4⋊Dic73C2412yes—
217C4⋊Dic73C2412yes—
218C4⋊Dic73C2412yes—
219C4⋊Dic73C2412yes—
220#11924007—24no—
221#11924007—24no—
222#11924007—24no—
223#11924007—24no—
224#11924007—24no—
225#11924007—24no—
226#11924007—24no—
227C22⋊Dic73—24no—
228C22⋊Dic73—24no—
229C22⋊Dic73—24no—
230C22⋊Dic73—24no—
231#11924005—24no—
232#11924005—24no—
233#11924005—24no—
234C4×Dic73—24no—
235C4×Dic73—24no—
236C4×Dic73—24no—
237C24×C73C2×D411yescharacteristic
238C24×C73C2×D411yescharacteristic
239C2×D4×C73—24no—
240C2×D4×C73C2×D414yes—
241C22×C4×C73—22no—
242C22×C4×C73—22no—
243C22×C4×C73—22no—
244C22×C4×C73—22no—
245C22×C4×C73C2×D411yescharacteristic
246C22×C4×C73C2×D411yescharacteristic
247C22×C4×C73C2×D411yescharacteristic
248C22×C4×C73C2×D411yescharacteristic
249C22×C4×C73C2×D412yes—
250C22×C4×C73C2×D412yes—
251C22×C4×C73C2412yes—
252C22×C4×C73C2412yes—
253C22×C4×C73C2411yescharacteristic
254C2×C8×C73—22no—
255C2×C8×C73—22no—
256C2×C8×C73—22no—
257C2×C8×C73—28no—
258C2×C8×C73—28no—
259C2×C8×C73#4114yes—
260C2×C8×C73C2412yes—
261C2×C8×C73C2412yes—
262C2×C8×C73C2412yes—
263C2×C8×C73C2412yes—
264C4⋊C4×C73C2×D414yes—
265C22⋊C4×C73C2×D414yes—
266C22⋊C4×C73C2×D414yes—
267C42×C73C2×D412yes—
268C42×C73C2412yes—
269C23×C73—22no—
270C23×C73—22no—
271C23×C73—22no—
272C23×C73—22no—
273C23×C73—22no—
274C23×C73#13514yes—
275C23×C73C22×D412yes—
276C23×C73C22×D412yes—
277C23×C73C22×D411yescharacteristic
278C22×D73—22no—
279C22×D73—42no—
280C22×D73—42no—
281C22×D73—42no—
282D4×C73—28no—
283C2×C4×C73—22no—
284C2×C4×C73—22no—
285C2×C4×C73—22no—
286C2×C4×C73—22no—
287C2×C4×C73—24no—
288C2×C4×C73—24no—
289C2×C4×C73—22no—
290C2×C4×C73—22no—
291C2×C4×C73—22no—
292C2×C4×C73—22no—
293C2×C4×C73C22×D412yes—
294C2×C4×C73C22×D412yes—
295C2×C4×C73C22×D412yes—
296C2×C4×C73C22×D412yes—
297C2×C4×C73C22×D411yescharacteristic
298C2×C4×C73C2×#4112yes—
299C2×C4×C732−1+412yes—
300C2×C4×C73C2511yescharacteristic
301C22⋊D73—48no—
302C22⋊D73—84no—
303C2×Dic73—22no—
304C2×Dic73—22no—
305C2×Dic73—22no—
306C2×Dic73—22no—
307C2×Dic73—22no—
308C2×Dic73—22no—
309C2×Dic73—22no—
310C2×Dic73—42no—
311C2×Dic73—48no—
312C2×Dic73—42no—
313C2×Dic73—42no—
314C2×Dic73—42no—
315C2×Dic73—42no—
316C2×Dic73—42no—
317C2×Dic73—42no—
318C2×Dic73—84no—
319D292—22no—
320D292—22no—
321D292—42no—
322C4×D73—84no—
323Dic146—22no—
324Dic146—22no—
325Dic146—42no—
326C8×C73—22no—
327C8×C73—22no—
328C8×C73—22no—
329C8×C73C2×#4114yes—
330C22×C73—28no—
331C22×C73—22no—
332C22×C73—22no—
333C22×C73—22no—
334C22×C73—22no—
335C22×C73—22no—
336C22×C73—44no—
337C22×C73#54712yes—
338C22×C73C2×#13514yes—
339C22×C73C2×#13512yes—
340C22×C73#57712yes—
341C22×C73C23×D411yescharacteristic
342C2×D73—42no—
343C2×D73—42no—
344C2×D73—42no—
345C2×D73—84no—
346C4×C73—22no—
347C4×C73—22no—
348C4×C73—22no—
349C4×C73—22no—
350C4×C73#54712yes—
351C4×C73C22×#4111yescharacteristic
352C4×C73C2×2−1+411yescharacteristic
353Dic73—42no—
354Dic73—42no—
355Dic73—42no—
356Dic73—42no—
357Dic73—42no—
358Dic73—42no—
359Dic73—42no—
360C2×#3337—731nomaximal, Sylow
361C2×C73—24no—
362C2×C73—42no—
363C2×C73#333714yescomplemented
364C2×C73C2×#54711yescharacteristic
365C2×C73C22×#13511yescharacteristic
366C2×C73C2×#57711yescharacteristic
367D73—82no—
368C2×#553—731no—
369C2×#552—731no—
370#3337—7316no—
371C2×#499—731no—
372C2×#484—731no—
373C2×#485—731no—
374C2×#482—731no—
375C2×#480—731no—
376C2×#479—731no—
377C2×#478—731no—
378C2×#465—731no—
379C2×#465—731no—
380C2×C4×SD16—731no—
381C2×C8×D4D7311yescharacteristic, complemented
382C2×#427—731no—
383C22×#106—731no—
384C73C2×#333711yescharacteristic, complemented, Sylow
385C22×SD16—731no—
386C23×C8C2×D7311yescharacteristic
387C23×C8C2×D7311yescharacteristic
388#553—738no—
389#553—1464no—
390#552—738no—
391#552—1464no—
392C2×#126—1461no—
393C2×#126—1461no—
394C2×#125—731no—
395C2×#125—731no—
396C2×#125—1461no—
397C2×#123—1461no—
398C2×#123—1461no—
399C2×C22⋊Q8—731no—
400C2×C22⋊Q8—731no—
401C2×#121—731no—
402C2×#121—731no—
403C2×#121—1461no—
404C2×C4×Q8—731no—
405C2×C4×D4—731no—
406C2×C4×D4—1461no—
407C2×C4×D4C2×D7311yescharacteristic
408C2×#117—731no—
409C2×#117—731no—
410C2×#117—1461no—
411C22×C4⋊C4—731no—
412C22×C4⋊C4—731no—
413#499—738no—
414#485—738no—
415#484—738no—
416#482—738no—
417#480—738no—
418#479—738no—
419#478—738no—
420#465—738no—
421#465—738no—
422C4×SD16—738no—
423C8×D4C2×D7318yescomplemented
424#427—738no—
425C2×#107—731no—
426C2×#107—731no—
427C2×#107—731no—
428C2×#107—731no—
429C2×#106—731no—
430C2×#106—731no—
431C2×#106—738no—
432C2×#106—731no—
433C2×#106—731no—
434C2×#106—731no—
435C2×C4⋊C8C2×D7311yescharacteristic
436C2×#103—731no—
437C2×#103—731no—
438C2×#103—731no—
439C2×#102—731no—
440C2×#102—731no—
441C2×#102—731no—
442C2×C22⋊C8C2×D7311yescharacteristic
443C2×C22⋊C8C2×D7311yescharacteristic
444C2×C4×C8C2×D7311yescharacteristic
445C22×Q8—731no—
446C22×D4—731no—
447C22×D4—1461no—
448C22×D4—1461no—
449C22×D4D29211yescharacteristic
450C23×C4—1461no—
451C23×C4—1461no—
452C23×C4—1461no—
453C23×C4C22×D7311yescharacteristic
454C23×C4C22×D7311yescharacteristic
455C2×SD16—734no—
456C2×SD16—1464no—
457C22×C8—24no—
458C22×C8—24no—
459C22×C8C22×D7311yescharacteristic
460C22×C8C22×D7311yescharacteristic
461C22×C8C22×D7314yes—
462C22×C8C22×D7314yes—
463C22×C8C22×D7311yescharacteristic
464C22×C8C22×D7311yescharacteristic
465#126—1468no—
466#126—1468no—
467#125—734no—
468#125—734no—
469#125—1468no—
470#125—1462no—
471#125—1462no—
472#123—1468no—
473#123—1468no—
474C22⋊Q8—734no—
475C22⋊Q8—734no—
476C22⋊Q8—1462no—
477C22⋊Q8—1462no—
478#121—734no—
479#121—734no—
480#121—1468no—
481#121—1462no—
482#121—1462no—
483C4×Q8—734no—
484C4×Q8—1462no—
485C4×D4—734no—
486C4×D4—1468no—
487C4×D4—1462no—
488C4×D4D29214yes—
489C4×D4C22×D7314yes—
490#117—734no—
491#117—734no—
492#117—1462no—
493#117—1462no—
494#117—1468no—
495C2×C4⋊C4—731no—
496C2×C4⋊C4—731no—
497C2×C4⋊C4—731no—
498C2×C4⋊C4—731no—
499C2×C4⋊C4—734no—
500C2×C4⋊C4—734no—
501C2×C4⋊C4—731no—
502C2×C4⋊C4—731no—
503C2×C4⋊C4—1461no—
504C2×C4⋊C4—1461no—
505C2×C4⋊C4—1462no—
506C2×C4⋊C4—1462no—
507C2×C4⋊C4—1461no—
508C2×C4⋊C4—1461no—
509C2×C4⋊C4—1461no—
510C2×C4⋊C4—1461no—
511C2×C4⋊C4—1461no—
512C2×C4⋊C4—1461no—
513C2×C4⋊C4—1461no—
514C2×C4⋊C4D29211yescharacteristic
515C2×C22⋊C4—1461no—
516C2×C22⋊C4—1461no—
517C2×C22⋊C4—1461no—
518C2×C22⋊C4—1461no—
519C2×C22⋊C4—1461no—
520C2×C22⋊C4—1461no—
521C2×C22⋊C4—1461no—
522C2×C22⋊C4D29211yescharacteristic
523C2×C22⋊C4D29211yescharacteristic
524C2×C42—1461no—
525C2×C42—1461no—
526C2×C42—1461no—
527C2×C42C22×D7311yescharacteristic
528#107—734no—
529#107—734no—
530#107—734no—
531#107—734no—
532#106—734no—
533#106—734no—
534#106—734no—
535#106—734no—
536#106—734no—
537C4⋊C8C22×D7314yes—
538#103—734no—
539#103—734no—
540#103—734no—
541#102—734no—
542#102—734no—
543#102—734no—
544C22⋊C8C22×D7314yes—
545C22⋊C8C22×D7314yes—
546C4×C8C22×D7314yes—
547C24—1461no—
548C24C2×D29211yescharacteristic
549C24C2×D29211yescharacteristic
550C2×Q8—732no—
551C2×Q8—1462no—
552C2×Q8—1462no—
553C2×Q8—1461no—
554C2×D4—24no—
555C2×D4—2924no—
556C2×D4—5842no—
557C2×D4—732no—
558C2×D4—1464no—
559C2×D4—1464no—
560C2×D4—1461no—
561C2×D4—1462no—
562C2×D4—1462no—
563C2×D4C2×D29214yes—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—2924no—
569C22×C4—5842no—
570C22×C4—5842no—
571C22×C4—1464no—
572C22×C4—1461no—
573C22×C4—1461no—
574C22×C4—1461no—
575C22×C4—1461no—
576C22×C4—1461no—
577C22×C4—1461no—
578C22×C4—1461no—
579C22×C4—1464no—
580C22×C4—1464no—
581C22×C4C2×D29212yes—
582C22×C4C2×D29212yes—
583C22×C4C2×D29211yescharacteristic
584C22×C4C2×D29211yescharacteristic
585C22×C4C2×D29211yescharacteristic
586C22×C4C2×D29211yescharacteristic
587C22×C4C23×D7312yes—
588C22×C4C23×D7312yes—
589C22×C4C23×D7311yescharacteristic
590SD16—1468no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—22no—
594C2×C8—28no—
595C2×C8—28no—
596C2×C8#1192402714yes—
597C2×C8C23×D7312yes—
598C2×C8C23×D7312yes—
599C2×C8C23×D7312yes—
600C2×C8C23×D7312yes—
601C4⋊C4—732no—
602C4⋊C4—732no—
603C4⋊C4—732no—
604C4⋊C4—732no—
605C4⋊C4—732no—
606C4⋊C4—732no—
607C4⋊C4—1464no—
608C4⋊C4—1464no—
609C4⋊C4—1464no—
610C4⋊C4—1464no—
611C4⋊C4—1464no—
612C4⋊C4—1464no—
613C4⋊C4—1464no—
614C4⋊C4—1461no—
615C4⋊C4—1461no—
616C4⋊C4—1461no—
617C4⋊C4—1461no—
618C4⋊C4—1464no—
619C4⋊C4—1464no—
620C4⋊C4—1461no—
621C4⋊C4—1461no—
622C4⋊C4C2×D29214yes—
623C22⋊C4—1464no—
624C22⋊C4—1464no—
625C22⋊C4—1464no—
626C22⋊C4—1464no—
627C22⋊C4—1464no—
628C22⋊C4—1464no—
629C22⋊C4—1464no—
630C22⋊C4C2×D29214yes—
631C22⋊C4C2×D29214yes—
632C42—1464no—
633C42—1464no—
634C42—1464no—
635C42C2×D29212yes—
636C42C23×D7312yes—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—2922no—
643C23—2922no—
644C23—2922no—
645C23—1462no—
646C23#1455661314yes—
647C23C22×D29212yes—
648C23C22×D29212yes—
649C23C22×D29211yescharacteristic
650Q8—2922no—
651Q8—1462no—
652Q8—1462no—
653D4—28no—
654D4—2928no—
655D4—2922no—
656D4—5844no—
657D4—1462no—
658D4—1462no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—2922no—
670C2×C4—2922no—
671C2×C4—2922no—
672C2×C4—2922no—
673C2×C4—2928no—
674C2×C4—2922no—
675C2×C4—2922no—
676C2×C4—2922no—
677C2×C4—5844no—
678C2×C4—5844no—
679C2×C4—1462no—
680C2×C4—1462no—
681C2×C4—1462no—
682C2×C4—1462no—
683C2×C4—1462no—
684C2×C4—1462no—
685C2×C4—1462no—
686C2×C4C22×D29212yes—
687C2×C4C22×D29212yes—
688C2×C4C22×D29212yes—
689C2×C4C22×D29212yes—
690C2×C4C22×D29211yescharacteristic
691C2×C4C2×#1192402712yes—
692C2×C4#1455663812yes—
693C2×C4C24×D7311yescharacteristic
694C8—22no—
695C8—22no—
696C8—22no—
697C8C2×#1192402714yes—
698C22—28no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—44no—
705C22—2922no—
706C22—2922no—
707C22—2922no—
708C22—5844no—
709C22#1798924112yes—
710C22C2×#1455661314yes—
711C22C2×#1455661312yes—
712C22#1798939912yes—
713C22C23×D29211yescharacteristic
714C4—22no—
715C4—22no—
716C4—22no—
717C4—22no—
718C4—2922no—
719C4—2922no—
720C4—2922no—
721C4—2922no—
722C4—2922no—
723C4—2922no—
724C4—2922no—
725C4#1798924112yes—
726C4C22×#1192402711yescharacteristic
727C4C2×#1455663811yescharacteristic
728C2—24no—
729C2—42no—
730C2—5842no—
731C2#2262231214yesdirect product factor
732C2C2×#1798924111yescharacteristic
733C2C22×#1455661311yescharacteristic
734C2C2×#1798939911yescharacteristic
subgroupG/H
centerC23C22×D292
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×C8×D4×C73C2
socleC23×C73C22×D4
prime radicalC2×#17989283C2
hypercenterC2×C8×D4D73
hypocenterC73C2×#3337
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×C8×D4

Complements

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

NH ≅ G/Ntype
2. C2×#17989277C2semidirect
3. #22622312C2direct (N × H)
4. C2×#17988989C2semidirect
5. C2×#17988923C2semidirect
6. C2×#17988929C2semidirect
7. C2×#17988912C2semidirect
8. C2×#17988901C2semidirect
9. C2×#17988895C2semidirect
10. C2×#17988888C2semidirect
11. C2×#17988816C2semidirect
12. C2×#17988816C2semidirect
13. C2×C4×#11924017C2semidirect
14. C2×#17988625C2semidirect
15. C22×#14556523C2semidirect
16. C2×C8×D4×C73C2semidirect
21. #17989277C22semidirect
42. #17988989C22semidirect
43. #17988929C22semidirect
44. #17988923C22semidirect
45. #17988912C22semidirect
46. #17988901C22semidirect
47. #17988895C22semidirect
48. #17988888C22semidirect
49. #17988816C22semidirect
50. #17988816C22semidirect
51. C4×#11924017C22semidirect
52. #17988625C22semidirect
62. C2×#14556523C22semidirect
72. C8×D4×C73C22semidirect
363. C2×C73#3337semidirect
381. C2×C8×D4D73semidirect
384. C73C2×#3337semidirect
423. C8×D4C2×D73semidirect
731. C2#22622312direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179892832
C2×#179892772
#226223122
C2×#179889892
C2×#179889232
C2×#179889292
C2×#179889122
C2×#179889012
C2×#179888952
C2×#179888882
C2×#179888162
C2×C4×#119240172
C2×#179886252
C22×#145565232
C2×C8×D4×C732
C2×#333773