Finite Group Databasebeta

← C2×#22620132 #33954233

Subgroups — C2×#22620132 #33954233

Order 18688.

2198 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989192C211yesmaximal, characteristic, complemented
2C2×#17989067C211yesmaximal, characteristic, complemented
3#22620132C2116yesmaximal, direct product factor
4C2×#17988906C211yesmaximal, characteristic, complemented
5C2×#17988901C211yesmaximal, characteristic, complemented
6C2×#17988895C211yesmaximal, characteristic, complemented
7C2×#17988888C211yesmaximal, characteristic, complemented
8C2×#17988788C211yesmaximal, characteristic, complemented
9C2×#17988783C211yesmaximal, characteristic, complemented
10C2×#17988734C211yesmaximal, characteristic, complemented
11C2×#17988734C211yesmaximal, characteristic, complemented
12C2×#17988700C211yesmaximal, characteristic, complemented
13C2×#17988689C211yesmaximal, characteristic, complemented
14C2×C4×#11924017C211yesmaximal, characteristic, complemented
15C2×C4×D584C211yesmaximal, characteristic, complemented
16C2×#433×C73C211yesmaximal, characteristic, complemented
17C22×#11924028C2211yescharacteristic
18C22×#11924017C2211yescharacteristic
19C22×#11924017C2211yescharacteristic
20C22×D584C2211yescharacteristic
21C22×D584C2211yescharacteristic
22#17989192—24no—
23#17989192C2218yescomplemented
24C2×#14556588C2211yescharacteristic
25C2×#14556583C2211yescharacteristic
26C2×#14556576—21no—
27C2×#14556576—21no—
28C2×#14556565C2211yescharacteristic
29C2×#14556565C2211yescharacteristic
30C2×#14556564—21no—
31C2×#14556564—21no—
32#17989067—24no—
33#17989067C2218yescomplemented
34C2×C4×Dic146C2211yescharacteristic
35C2×C4×Dic146C2211yescharacteristic
36C2×C4×D292C2211yescharacteristic
37C2×C4×D292C2211yescharacteristic
38C2×C4×D292C2211yescharacteristic
39C2×C4×D292C2211yescharacteristic
40C2×#14556551—21no—
41C2×#14556551—21no—
42C2×#14556549—21no—
43C22×C4⋊Dic73C2211yescharacteristic
44C2×C4⋊C4×D73—21no—
45#17988906C2218yescomplemented
46#17988901C2218yescomplemented
47#17988895C2218yescomplemented
48#17988888C2218yescomplemented
49#17988788C2218yescomplemented
50#17988783C2218yescomplemented
51#17988734C2218yescomplemented
52#17988734C2218yescomplemented
53#17988700C2218yescomplemented
54#17988689C2218yescomplemented
55C4×#11924017C2218yescomplemented
56C4×D584C2218yescomplemented
57C2×#14556525C2211yescharacteristic
58C2×#14556525C2211yescharacteristic
59C2×#14556523C2211yescharacteristic
60C2×#14556523C2211yescharacteristic
61C2×#14556516C2211yescharacteristic
62C2×#14556516C2211yescharacteristic
63C2×#14556513C2211yescharacteristic
64C2×#14556513C2211yescharacteristic
65C2×#14556513C2211yescharacteristic
66C2×#14556513C2211yescharacteristic
67C2×#14556513C2211yescharacteristic
68C2×#14556513C2211yescharacteristic
69C2×#117×C73C2211yescharacteristic
70#433×C73C2218yescomplemented
71C2×C4⋊C8×C73C2211yescharacteristic
72C2×C4⋊C8×C73C2211yescharacteristic
73C2×C22⋊C8×C73C2211yescharacteristic
74C2×C22⋊C8×C73C2211yescharacteristic
75C2×#97×C73C2211yescharacteristic
76C2×C4×C8×C73C2211yescharacteristic
77C2×#11924028—24no—
78C2×#11924028—24no—
79C2×#11924028—22no—
80C2×#11924028C2314yes—
81C22×Dic146C2311yescharacteristic
82C22×D292—21no—
83C22×D292—21no—
84C22×D292C2311yescharacteristic
85C22×D292C2311yescharacteristic
86C22×D292C2311yescharacteristic
87C22×C22⋊D73—21no—
88C22×C22⋊D73—21no—
89C22×C22⋊D73—21no—
90C23×Dic73—21no—
91C22×C4×D73—21no—
92C22×C4×D73—21no—
93C22×C4×D73—21no—
94C22×C4×D73—21no—
95C22×C4×D73—21no—
96C2×#11924017—24no—
97C2×#11924017—24no—
98C2×#11924017C2314yes—
99C2×#11924017C2314yes—
100C2×D584—24no—
101C2×D584—24no—
102C2×D584C2314yes—
103C2×D584C2314yes—
104#14556588—22no—
105#14556588C2314yes—
106#14556583—22no—
107#14556583C2314yes—
108#14556576—28no—
109#14556576—28no—
110#14556565—22no—
111#14556565—22no—
112#14556565C2314yes—
113#14556565C2314yes—
114#14556564—28no—
115#14556564—28no—
116C4×Dic146—22no—
117C4×Dic146—22no—
118C4×Dic146C2314yes—
119C4×Dic146C2314yes—
120C4×D292—22no—
121C4×D292—22no—
122C4×D292—22no—
123C4×D292—22no—
124C4×D292C2314yes—
125C4×D292C2314yes—
126C4×D292C2314yes—
127C4×D292C2314yes—
128#14556551—28no—
129#14556551—28no—
130#14556549—28no—
131C2×C4⋊Dic73—21no—
132C2×C4⋊Dic73—22no—
133C2×C4⋊Dic73C2311yescharacteristic
134C2×C4⋊Dic73C2311yescharacteristic
135C2×C4⋊Dic73C2311yescharacteristic
136C2×C4⋊Dic73C2311yescharacteristic
137C2×C4⋊Dic73C2314yes—
138C2×#11924007—21no—
139C2×#11924007—21no—
140C2×#11924007—21no—
141C2×#11924007—21no—
142C4⋊C4×D73—28no—
143C2×#11924005—21no—
144C2×#11924005—21no—
145C2×#11924005—21no—
146C2×#11924005—21no—
147C2×#11924005—21no—
148C2×#11924005—21no—
149C2×C4×Dic73—21no—
150C2×C4×Dic73—21no—
151#14556525C2314yes—
152#14556525C2314yes—
153#14556523C2314yes—
154#14556523C2314yes—
155#14556516C2314yes—
156#14556516C2314yes—
157#14556513C2314yes—
158#14556513C2314yes—
159#14556513C2314yes—
160#14556513C2314yes—
161#14556513C2314yes—
162#14556513C2314yes—
163C23×C4×C73C2311yescharacteristic
164C22×C8×C73C2311yescharacteristic
165C22×C8×C73C2311yescharacteristic
166C22×C8×C73C2311yescharacteristic
167C22×C8×C73C2311yescharacteristic
168#117×C73D414yes—
169#117×C73C2314yes—
170C2×C4⋊C4×C73D411yescharacteristic
171C2×C4⋊C4×C73D411yescharacteristic
172C2×C22⋊C4×C73D411yescharacteristic
173C2×C22⋊C4×C73D411yescharacteristic
174C2×C42×C73C2311yescharacteristic
175C2×C42×C73C2311yescharacteristic
176C4⋊C8×C73C2314yes—
177C4⋊C8×C73C2314yes—
178C22⋊C8×C73C2314yes—
179C22⋊C8×C73C2314yes—
180#97×C73C2314yes—
181C4×C8×C73C2314yes—
182C23×D73—21no—
183C23×D73—21no—
184C23×D73—21no—
185#11924028—216no—
186#11924028—28no—
187#11924028—28no—
188C2×Dic146—21no—
189C2×Dic146—22no—
190C2×Dic146#4114yes—
191C2×Dic146C2412yes—
192C2×D292—21no—
193C2×D292—22no—
194C2×D292—22no—
195C2×D292—22no—
196C2×D292—22no—
197C2×D292—22no—
198C2×D292—21no—
199C2×D292—21no—
200C2×D292—24no—
201C2×D292—24no—
202C2×D292—82no—
203C2×D292—82no—
204C2×D292#4114yes—
205C2×D292C2412yes—
206C2×D292C2412yes—
207C2×D292C2412yes—
208C2×C22⋊D73—28no—
209C2×C22⋊D73—24no—
210C2×C22⋊D73—24no—
211C2×C22⋊D73—24no—
212C2×C22⋊D73—82no—
213C2×C22⋊D73—82no—
214C22×Dic73—21no—
215C22×Dic73—21no—
216C22×Dic73—21no—
217C22×Dic73—21no—
218C22×Dic73—21no—
219C22×Dic73—24no—
220C22×Dic73—82no—
221C2×C4×D73—28no—
222C2×C4×D73—24no—
223C2×C4×D73—24no—
224C2×C4×D73—24no—
225C2×C4×D73—24no—
226C2×C4×D73—24no—
227C2×C4×D73—82no—
228C2×C4×D73—82no—
229C2×C4×D73—82no—
230C2×C4×D73—82no—
231#11924017—28no—
232#11924017—28no—
233D584—28no—
234D584—28no—
235C4⋊Dic73—24no—
236C4⋊Dic73—21no—
237C4⋊Dic73—21no—
238C4⋊Dic73—21no—
239C4⋊Dic73—21no—
240C4⋊Dic73C2412yes—
241C4⋊Dic73C2412yes—
242C4⋊Dic73C2412yes—
243C4⋊Dic73C2412yes—
244#11924007—24no—
245#11924007—24no—
246#11924007—24no—
247#11924007—24no—
248#11924005—24no—
249#11924005—24no—
250#11924005—24no—
251#11924005—24no—
252#11924005—24no—
253#11924005—24no—
254C4×Dic73—24no—
255C4×Dic73—24no—
256C24×C73C2×D411yescharacteristic
257C22×C4×C73—22no—
258C22×C4×C73—22no—
259C22×C4×C73C2×D411yescharacteristic
260C22×C4×C73C2×D411yescharacteristic
261C22×C4×C73C2×D411yescharacteristic
262C22×C4×C73C2×D411yescharacteristic
263C22×C4×C73C2×D411yescharacteristic
264C22×C4×C73C2×D412yes—
265C22×C4×C73C2412yes—
266C22×C4×C73C2411yescharacteristic
267C2×C8×C73—22no—
268C2×C8×C73—22no—
269C2×C8×C73—22no—
270C2×C8×C73—22no—
271C2×C8×C73C2412yes—
272C2×C8×C73C2412yes—
273C2×C8×C73C2412yes—
274C2×C8×C73C2412yes—
275C4⋊C4×C73C2×D414yes—
276C4⋊C4×C73C2×D414yes—
277C22⋊C4×C73C2×D414yes—
278C22⋊C4×C73C2×D414yes—
279C42×C73C2×D412yes—
280C42×C73C2×D412yes—
281C42×C73C2412yes—
282C42×C73C2412yes—
283C23×C73—22no—
284C23×C73—22no—
285C23×C73—22no—
286C23×C73C22×D412yes—
287C23×C73C22×D411yescharacteristic
288C22×D73—24no—
289C22×D73—22no—
290C22×D73—22no—
291C22×D73—22no—
292C22×D73—42no—
293C22×D73—42no—
294C22×D73—42no—
295C22×D73—42no—
296C22×D73—42no—
297C22×D73—42no—
298C22×D73—42no—
299C22×D73—42no—
300C2×C4×C73—22no—
301C2×C4×C73—22no—
302C2×C4×C73—22no—
303C2×C4×C73—22no—
304C2×C4×C73—22no—
305C2×C4×C73—24no—
306C2×C4×C73—22no—
307C2×C4×C73—22no—
308C2×C4×C73C22×D412yes—
309C2×C4×C73C22×D412yes—
310C2×C4×C73C22×D412yes—
311C2×C4×C73C22×D412yes—
312C2×C4×C73C22×D412yes—
313C2×C4×C73C22×D411yescharacteristic
314C2×C4×C73C2×#4112yes—
315C2×C4×C73C2×#4112yes—
316C2×C4×C73C2511yescharacteristic
317C22⋊D73—216no—
318C22⋊D73—84no—
319C22⋊D73—84no—
320C2×Dic73—24no—
321C2×Dic73—22no—
322C2×Dic73—22no—
323C2×Dic73—22no—
324C2×Dic73—22no—
325C2×Dic73—22no—
326C2×Dic73—42no—
327C2×Dic73—42no—
328C2×Dic73—42no—
329C2×Dic73—42no—
330C2×Dic73—84no—
331D292—24no—
332D292—22no—
333D292—22no—
334D292—22no—
335D292—22no—
336D292—22no—
337D292—42no—
338D292—42no—
339D292—84no—
340D292—84no—
341D292C2×#4114yes—
342C4×D73—216no—
343C4×D73—84no—
344C4×D73—84no—
345C4×D73—84no—
346C4×D73—84no—
347Dic146—24no—
348Dic146—22no—
349Dic146C2×#4114yes—
350C8×C73—22no—
351C8×C73—22no—
352C8×C73—22no—
353C8×C73—22no—
354C22×C73—22no—
355C22×C73—22no—
356C22×C73—22no—
357C22×C73—44no—
358C22×C73#52512yes—
359C22×C73#57612yes—
360C22×C73#57712yes—
361C22×C73C23×D411yescharacteristic
362C2×D73—24no—
363C2×D73—48no—
364C2×D73—42no—
365C2×D73—42no—
366C2×D73—42no—
367C2×D73—42no—
368C2×D73—42no—
369C2×D73—42no—
370C2×D73—42no—
371C2×D73—42no—
372C2×D73—84no—
373C2×D73—84no—
374C4×C73—22no—
375C4×C73—22no—
376C4×C73—22no—
377C4×C73—22no—
378C4×C73—22no—
379C4×C73#52512yes—
380C4×C73C22×#4111yescharacteristic
381C4×C73C22×#4111yescharacteristic
382Dic73—24no—
383Dic73—42no—
384Dic73—42no—
385Dic73—42no—
386Dic73—42no—
387C2×#3119—731nomaximal, Sylow
388C2×C73—42no—
389C2×C73#311914yescomplemented
390C2×C73C2×#52511yescharacteristic
391C2×C73C2×#57611yescharacteristic
392C2×C73C2×#57711yescharacteristic
393D73—44no—
394D73—82no—
395D73—82no—
396C2×#540—731no—
397C2×#520—731no—
398#3119—7316no—
399C2×#481—731no—
400C2×#480—731no—
401C2×#479—731no—
402C2×#478—731no—
403C2×#460—731no—
404C2×#459—731no—
405C2×#449—731no—
406C2×#449—731no—
407C2×#442—731no—
408C2×#440—731no—
409C2×C4×SD16—731no—
410C2×C4×D8—731no—
411C2×#433D7311yescharacteristic, complemented
412C73C2×#311911yescharacteristic, complemented, Sylow
413C22×#41—731no—
414C22×SD16—731no—
415C22×SD16—731no—
416C22×D8—731no—
417C22×D8—731no—
418#540—738no—
419#540—1464no—
420C2×#127—731no—
421C2×#125—731no—
422C2×#123—1461no—
423C2×#123—1461no—
424C2×#121—731no—
425C2×#121—731no—
426C2×#121—1461no—
427C2×#121—1461no—
428#520—738no—
429#520—1464no—
430C2×C4×Q8—731no—
431C2×C4×Q8—731no—
432C2×C4×D4—731no—
433C2×C4×D4—731no—
434C2×C4×D4—731no—
435C2×C4×D4—731no—
436C2×C4×D4—1461no—
437C2×C4×D4—1461no—
438C2×#117—1461no—
439C2×#117C2×D7311yescharacteristic
440C22×C4⋊C4—731no—
441C22×C4⋊C4—1461no—
442#481—738no—
443#480—738no—
444#479—738no—
445#478—738no—
446#460—738no—
447#459—738no—
448#449—738no—
449#449—738no—
450#442—738no—
451#440—738no—
452C4×SD16—738no—
453C4×D8—738no—
454#433C2×D7318yescomplemented
455C2×#107—731no—
456C2×#107—731no—
457C2×#106—731no—
458C2×#106—731no—
459C2×C4⋊C8C2×D7311yescharacteristic
460C2×C4⋊C8C2×D7311yescharacteristic
461C2×#103—731no—
462C2×#103—731no—
463C2×#102—731no—
464C2×#102—731no—
465C2×#102—731no—
466C2×#102—731no—
467C2×#102—731no—
468C2×#102—731no—
469C2×C22⋊C8C2×D7311yescharacteristic
470C2×C22⋊C8C2×D7311yescharacteristic
471C2×#97C2×D7311yescharacteristic
472C2×C4×C8C2×D7311yescharacteristic
473C2×#41—734no—
474C2×#41—1464no—
475C2×#41—1464no—
476C2×#41—1462no—
477C22×Q8—731no—
478C22×D4—731no—
479C22×D4—731no—
480C22×D4—731no—
481C22×D4—1461no—
482C22×D4—1461no—
483C22×D4—1461no—
484C22×D4—1461no—
485C22×D4—1461no—
486C23×C4—1461no—
487C23×C4—1461no—
488C23×C4—1461no—
489C23×C4—1461no—
490C23×C4—1461no—
491C23×C4—1461no—
492C23×C4C22×D7311yescharacteristic
493C2×SD16—734no—
494C2×SD16—734no—
495C2×SD16—1464no—
496C2×SD16—1464no—
497C2×D8—734no—
498C2×D8—734no—
499C2×D8—1464no—
500C2×D8—1464no—
501C22×C8C22×D7311yescharacteristic
502C22×C8C22×D7311yescharacteristic
503C22×C8C22×D7311yescharacteristic
504C22×C8C22×D7311yescharacteristic
505#127—734no—
506#127—1462no—
507#125—734no—
508#125—1462no—
509#123—1468no—
510#123—1468no—
511#121—734no—
512#121—734no—
513#121—1462no—
514#121—1462no—
515#121—1468no—
516#121—1468no—
517C4×Q8—734no—
518C4×Q8—734no—
519C4×Q8—1462no—
520C4×Q8—1462no—
521C4×D4—734no—
522C4×D4—734no—
523C4×D4—734no—
524C4×D4—734no—
525C4×D4—1468no—
526C4×D4—1468no—
527C4×D4—1462no—
528C4×D4—1462no—
529C4×D4—1462no—
530C4×D4—1462no—
531#117—1468no—
532#117D29214yes—
533#117C22×D7314yes—
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—1468no—
546C2×C4⋊C4D29211yescharacteristic
547C2×C4⋊C4D29211yescharacteristic
548C2×C22⋊C4—1461no—
549C2×C22⋊C4—1461no—
550C2×C22⋊C4—1461no—
551C2×C22⋊C4—1461no—
552C2×C22⋊C4—1461no—
553C2×C22⋊C4—1461no—
554C2×C22⋊C4D29211yescharacteristic
555C2×C22⋊C4D29211yescharacteristic
556C2×C42—1461no—
557C2×C42—1461no—
558C2×C42C22×D7311yescharacteristic
559C2×C42C22×D7311yescharacteristic
560#107—734no—
561#107—734no—
562#106—734no—
563#106—734no—
564C4⋊C8C22×D7314yes—
565C4⋊C8C22×D7314yes—
566#103—734no—
567#103—734no—
568#102—734no—
569#102—734no—
570#102—734no—
571#102—734no—
572#102—734no—
573#102—734no—
574C22⋊C8C22×D7314yes—
575C22⋊C8C22×D7314yes—
576#97C22×D7314yes—
577C4×C8C22×D7314yes—
578C24—1461no—
579C24—1461no—
580C24—1461no—
581C24C2×D29211yescharacteristic
582#41—1468no—
583#41—1468no—
584#41—14616no—
585C2×Q8—734no—
586C2×Q8—732no—
587C2×Q8—1461no—
588C2×Q8—1462no—
589C2×D4—5842no—
590C2×D4—5842no—
591C2×D4—5842no—
592C2×D4—5842no—
593C2×D4—734no—
594C2×D4—732no—
595C2×D4—732no—
596C2×D4—732no—
597C2×D4—1464no—
598C2×D4—1464no—
599C2×D4—1468no—
600C2×D4—1464no—
601C2×D4—1461no—
602C2×D4—1461no—
603C2×D4—1464no—
604C2×D4—1464no—
605C2×D4—1461no—
606C2×D4—1462no—
607C2×D4—1462no—
608C2×D4—1462no—
609C2×D4—1462no—
610C2×D4—1462no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—5842no—
614C22×C4—5842no—
615C22×C4—5842no—
616C22×C4—5842no—
617C22×C4—5842no—
618C22×C4—1468no—
619C22×C4—1461no—
620C22×C4—1461no—
621C22×C4—1461no—
622C22×C4—1461no—
623C22×C4—1464no—
624C22×C4—1464no—
625C22×C4—1464no—
626C22×C4—1464no—
627C22×C4—1464no—
628C22×C4—1461no—
629C22×C4—1464no—
630C22×C4C2×D29212yes—
631C22×C4C2×D29211yescharacteristic
632C22×C4C2×D29211yescharacteristic
633C22×C4C2×D29211yescharacteristic
634C22×C4C2×D29211yescharacteristic
635C22×C4C2×D29211yescharacteristic
636C22×C4C23×D7312yes—
637C22×C4C23×D7311yescharacteristic
638SD16—1468no—
639SD16—1468no—
640D8—1468no—
641D8—1468no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—22no—
646C2×C8C23×D7312yes—
647C2×C8C23×D7312yes—
648C2×C8C23×D7312yes—
649C2×C8C23×D7312yes—
650C4⋊C4—732no—
651C4⋊C4—732no—
652C4⋊C4—732no—
653C4⋊C4—732no—
654C4⋊C4—1464no—
655C4⋊C4—1464no—
656C4⋊C4—1464no—
657C4⋊C4—1464no—
658C4⋊C4—1464no—
659C4⋊C4—1461no—
660C4⋊C4—1461no—
661C4⋊C4—1461no—
662C4⋊C4—1461no—
663C4⋊C4C2×D29214yes—
664C4⋊C4C2×D29214yes—
665C22⋊C4—1464no—
666C22⋊C4—1464no—
667C22⋊C4—1464no—
668C22⋊C4—1464no—
669C22⋊C4—1464no—
670C22⋊C4—1464no—
671C22⋊C4C2×D29214yes—
672C22⋊C4C2×D29214yes—
673C42—1464no—
674C42—1464no—
675C42C2×D29212yes—
676C42C2×D29212yes—
677C42C23×D7312yes—
678C42C23×D7312yes—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—2922no—
683C23—2922no—
684C23—2922no—
685C23—2922no—
686C23—2922no—
687C23—2922no—
688C23—2922no—
689C23—2922no—
690C23—1462no—
691C23—1462no—
692C23—1462no—
693C23—1464no—
694C23C22×D29212yes—
695C23C22×D29211yescharacteristic
696Q8—734no—
697Q8—1462no—
698Q8—1464no—
699D4—2922no—
700D4—2922no—
701D4—5844no—
702D4—5844no—
703D4—5844no—
704D4—5844no—
705D4—734no—
706D4—14616no—
707D4—1462no—
708D4—1462no—
709D4—1462no—
710D4—1462no—
711D4—1462no—
712D4—1464no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—2922no—
722C2×C4—2922no—
723C2×C4—2922no—
724C2×C4—2922no—
725C2×C4—5844no—
726C2×C4—5844no—
727C2×C4—5844no—
728C2×C4—5844no—
729C2×C4—5844no—
730C2×C4—14616no—
731C2×C4—1462no—
732C2×C4—1462no—
733C2×C4—1462no—
734C2×C4—1462no—
735C2×C4—1462no—
736C2×C4—1464no—
737C2×C4C22×D29212yes—
738C2×C4C22×D29212yes—
739C2×C4C22×D29212yes—
740C2×C4C22×D29212yes—
741C2×C4C22×D29212yes—
742C2×C4C22×D29211yescharacteristic
743C2×C4#41×D7312yes—
744C2×C4#41×D7312yes—
745C2×C4C24×D7311yescharacteristic
746C8—22no—
747C8—22no—
748C8—22no—
749C8—22no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—44no—
754C22—2922no—
755C22—2922no—
756C22—2928no—
757C22—2922no—
758C22—2922no—
759C22—2922no—
760C22—2922no—
761C22—2922no—
762C22—2922no—
763C22—5844no—
764C22—5844no—
765C22—1464no—
766C22#1798909912yes—
767C22#1798939212yes—
768C22#1798939912yes—
769C22C23×D29211yescharacteristic
770C4—22no—
771C4—22no—
772C4—22no—
773C4—22no—
774C4—22no—
775C4—2922no—
776C4—2922no—
777C4—2922no—
778C4—2922no—
779C4—1464no—
780C4#1798909912yes—
781C4C2×#41×D7311yescharacteristic
782C4C2×#41×D7311yescharacteristic
783C2—42no—
784C2—2924no—
785C2—5842no—
786C2—5842no—
787C2#2262013214yesdirect product factor
788C2C2×#1798909911yescharacteristic
789C2C2×#1798939211yescharacteristic
790C2C2×#1798939911yescharacteristic
subgroupG/H
centerC23C22×D292
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#433×C73C2
socleC23×C73C22×D4
hypercenterC2×#433D73
hypocenterC73C2×#3119
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
1. C2×#17989192C2semidirect
2. C2×#17989067C2semidirect
3. #22620132C2direct (N × H)
4. C2×#17988906C2semidirect
5. C2×#17988901C2semidirect
6. C2×#17988895C2semidirect
7. C2×#17988888C2semidirect
8. C2×#17988788C2semidirect
9. C2×#17988783C2semidirect
10. C2×#17988734C2semidirect
11. C2×#17988734C2semidirect
12. C2×#17988700C2semidirect
13. C2×#17988689C2semidirect
14. C2×C4×#11924017C2semidirect
15. C2×C4×D584C2semidirect
16. C2×#433×C73C2semidirect
23. #17989192C22semidirect
33. #17989067C22semidirect
45. #17988906C22semidirect
46. #17988901C22semidirect
47. #17988895C22semidirect
48. #17988888C22semidirect
49. #17988788C22semidirect
50. #17988783C22semidirect
51. #17988734C22semidirect
52. #17988734C22semidirect
53. #17988700C22semidirect
54. #17988689C22semidirect
55. C4×#11924017C22semidirect
56. C4×D584C22semidirect
70. #433×C73C22semidirect
389. C2×C73#3119semidirect
411. C2×#433D73semidirect
412. C73C2×#3119semidirect
454. #433C2×D73semidirect
787. C2#22620132direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179891922
C2×#179890672
#226201322
C2×#179889062
C2×#179889012
C2×#179888952
C2×#179888882
C2×#179887882
C2×#179887832
C2×#179887342
C2×#179887002
C2×#179886892
C2×C4×#119240172
C2×C4×D5842
C2×#433×C732
C2×#311973