Finite Group Databasebeta

← C2×#22620000 #33954055

Subgroups — C2×#22620000 #33954055

Order 18688.

2170 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989141C211yesmaximal, characteristic, complemented
2C2×C4×#11924029C211yesmaximal, characteristic
3#22620000C2116yesmaximal, direct product factor
4C2×#17988930C211yesmaximal, characteristic, complemented
5C2×#17988926C211yesmaximal, characteristic, complemented
6C2×#17988870C211yesmaximal, characteristic, complemented
7C2×#17988866C211yesmaximal, characteristic, complemented
8C2×#17988795C211yesmaximal, characteristic, complemented
9C2×#17988791C211yesmaximal, characteristic, complemented
10C2×#17988752C211yesmaximal, characteristic
11C2×#17988748C211yesmaximal, characteristic
12C2×C4×#11924018C211yesmaximal, characteristic, complemented
13C2×C4×#11924017C211yesmaximal, characteristic, complemented
14C2×C4×#11924015C211yesmaximal, characteristic, complemented
15C2×#17988638C211yesmaximal, characteristic, complemented
16C2×C4×Q16×C73C211yesmaximal, characteristic, complemented
17C22×#11924029C2211yescharacteristic
18C22×#11924018C2211yescharacteristic
19C22×#11924017C2211yescharacteristic
20C22×#11924015C2211yescharacteristic
21#17989141—24no—
22#17989141C2218yescomplemented
23C2×#14556590C2211yescharacteristic
24C2×#14556589C2211yescharacteristic
25C2×#14556581—21no—
26C2×#14556571C2211yescharacteristic
27C2×#14556569—21no—
28C2×#14556567C2211yescharacteristic
29C4×#11924029—24no—
30C4×#11924029C2218yes—
31C2×Q8×Dic73C2211yescharacteristic
32C2×C4×Dic146—21no—
33C2×C4×Dic146C2211yescharacteristic
34C2×C4×D292—21no—
35C2×C4×D292C2211yescharacteristic
36C2×#14556553—21no—
37C2×#14556553C2211yescharacteristic
38C2×#14556549—21no—
39C2×#14556549C2211yescharacteristic
40C2×#14556548—21no—
41C2×C42×D73—21no—
42C2×C42×D73C2211yescharacteristic
43#17988930C2218yescomplemented
44#17988926C2218yescomplemented
45#17988870C2218yescomplemented
46#17988866C2218yescomplemented
47#17988795C2218yescomplemented
48#17988791C2218yescomplemented
49#17988752C2218yes—
50#17988748C2218yes—
51C4×#11924018C2218yescomplemented
52C4×#11924017C2218yescomplemented
53C4×#11924015C2218yescomplemented
54#17988638C2218yescomplemented
55C2×#14556524C2211yescharacteristic
56C2×#14556523C2211yescharacteristic
57C2×#14556522C2211yescharacteristic
58C2×#14556520C2211yescharacteristic
59C2×#14556520C2211yescharacteristic
60C2×#14556516C2211yescharacteristic
61C2×#14556515C2211yescharacteristic
62C2×#14556515C2211yescharacteristic
63C2×#14556514C2211yescharacteristic
64C2×#14556513C2211yescharacteristic
65C2×#14556511C2211yescharacteristic
66C2×#14556503C2211yescharacteristic
67C2×#14556503C2211yescharacteristic
68C2×C4×#10596831C2211yescharacteristic
69C22×Q16×C73C2211yescharacteristic
70C2×C4×Q8×C73C2211yescharacteristic
71C2×C4×Q8×C73C2211yescharacteristic
72C4×Q16×C73C2218yescomplemented
73C2×#107×C73C2211yescharacteristic
74C2×#103×C73C2211yescharacteristic
75C2×#103×C73C2211yescharacteristic
76C2×C4×C8×C73C2211yescharacteristic
77C2×#11924029—24no—
78C2×#11924029—22no—
79C2×#11924029—24no—
80C2×#11924029C2314yes—
81C22×Dic146—21no—
82C22×Dic146C2311yescharacteristic
83C22×D292—21no—
84C22×D292C2311yescharacteristic
85C22×C4×D73—21no—
86C22×C4×D73—21no—
87C22×C4×D73—21no—
88C22×C4×D73D411yescharacteristic
89C22×C4×D73D411yescharacteristic
90C22×C4×D73C2311yescharacteristic
91C2×#11924018—24no—
92C2×#11924018C2314yes—
93C2×#11924017—24no—
94C2×#11924017C2314yes—
95C2×#11924015—24no—
96C2×#11924015C2314yes—
97C22×#10596831C2311yescharacteristic
98C22×#10596831C2311yescharacteristic
99#14556590—22no—
100#14556590C2314yes—
101#14556589—22no—
102#14556589C2314yes—
103#14556581—28no—
104#14556571—22no—
105#14556571C2314yes—
106#14556569—28no—
107#14556567—22no—
108#14556567C2314yes—
109Q8×Dic73—22no—
110Q8×Dic73C2314yes—
111C4×Dic146—28no—
112C4×Dic146—22no—
113C4×Dic146C2314yes—
114C4×D292—28no—
115C4×D292—22no—
116C4×D292C2314yes—
117#14556553—28no—
118#14556553—22no—
119#14556553C2314yes—
120#14556549—22no—
121#14556549—28no—
122#14556549C2314yes—
123#14556548—28no—
124C2×C4⋊Dic73—21no—
125C2×C4⋊Dic73—21no—
126C2×C4⋊Dic73C2311yescharacteristic
127C2×C4⋊Dic73C2311yescharacteristic
128C2×#11924007—21no—
129C2×#11924007—21no—
130C2×#11924007—21no—
131C2×#11924007—21no—
132C2×#11924007—21no—
133C2×#11924005—21no—
134C2×#11924005—21no—
135C2×#11924005—21no—
136C2×#11924005—21no—
137C2×#11924005—21no—
138C2×C4×Dic73—21no—
139C2×C4×Dic73—21no—
140C2×C4×Dic73—21no—
141C2×C4×Dic73D411yescharacteristic
142C2×C4×Dic73D411yescharacteristic
143C2×C4×Dic73C2311yescharacteristic
144C42×D73—28no—
145C42×D73D414yes—
146C42×D73C2314yes—
147#14556524C2314yes—
148#14556523C2314yes—
149#14556522C2314yes—
150#14556520C2314yes—
151#14556520C2314yes—
152#14556516C2314yes—
153#14556515C2314yes—
154#14556515C2314yes—
155#14556514C2314yes—
156#14556513C2314yes—
157#14556511C2314yes—
158#14556503C2314yes—
159#14556503C2314yes—
160C4×#10596831C2314yes—
161C22×Q8×C73C2311yescharacteristic
162C22×Q8×C73C2311yescharacteristic
163C2×Q16×C73—24no—
164C2×Q16×C73C2314yes—
165C22×C8×C73C2311yescharacteristic
166C22×C8×C73C2311yescharacteristic
167C4×Q8×C73—22no—
168C4×Q8×C73—22no—
169C4×Q8×C73C2314yes—
170C4×Q8×C73C2314yes—
171C2×C4⋊C4×C73—21no—
172C2×C4⋊C4×C73—21no—
173C2×C4⋊C4×C73C2311yescharacteristic
174C2×C4⋊C4×C73C2311yescharacteristic
175C2×C42×C73—21no—
176C2×C42×C73—21no—
177C2×C42×C73C2311yescharacteristic
178#107×C73C2314yes—
179#103×C73C2314yes—
180#103×C73C2314yes—
181C4×C8×C73C2314yes—
182C23×D73—21no—
183C23×D73C2×D411yescharacteristic
184#11924029—216no—
185#11924029—28no—
186#11924029—28no—
187C2×Dic146—22no—
188C2×Dic146—22no—
189C2×Dic146—21no—
190C2×Dic146—24no—
191C2×Dic146—44no—
192C2×Dic146C2412yes—
193C2×D292—28no—
194C2×D292—24no—
195C2×D292—21no—
196C2×D292—22no—
197C2×D292#4114yes—
198C2×D292C2412yes—
199C22×Dic73—21no—
200C22×Dic73—21no—
201C22×Dic73—21no—
202C22×Dic73C2×D411yescharacteristic
203C22×Dic73C2×D411yescharacteristic
204C22×Dic73C2×D411yescharacteristic
205C2×C4×D73—28no—
206C2×C4×D73—24no—
207C2×C4×D73—22no—
208C2×C4×D73—22no—
209C2×C4×D73—24no—
210C2×C4×D73—24no—
211C2×C4×D73—24no—
212C2×C4×D73—24no—
213C2×C4×D73—44no—
214C2×C4×D73—44no—
215C2×C4×D73C2×D412yes—
216C2×C4×D73C2×D414yes—
217C2×C4×D73C2×D414yes—
218C2×C4×D73C2412yes—
219#11924018—28no—
220#11924017—28no—
221#11924015—28no—
222C2×#10596831—22no—
223C2×#10596831—22no—
224C2×#10596831C2412yes—
225C2×#10596831C2412yes—
226C4⋊Dic73—21no—
227C4⋊Dic73—21no—
228C4⋊Dic73—24no—
229C4⋊Dic73—24no—
230C4⋊Dic73C2412yes—
231C4⋊Dic73C2412yes—
232#11924007—24no—
233#11924007—24no—
234#11924007—24no—
235#11924007—24no—
236#11924007—24no—
237#11924005—24no—
238#11924005—24no—
239#11924005—24no—
240#11924005—24no—
241#11924005—24no—
242C4×Dic73—24no—
243C4×Dic73—24no—
244C4×Dic73—24no—
245C4×Dic73C2×D414yes—
246C4×Dic73C2×D412yes—
247C4×Dic73C2×D414yes—
248C4×Dic73C2412yes—
249C2×Q8×C73—21no—
250C2×Q8×C73—21no—
251C2×Q8×C73—22no—
252C2×Q8×C73—22no—
253C2×Q8×C73—22no—
254C2×Q8×C73#4114yes—
255C2×Q8×C73C2412yes—
256C2×Q8×C73C2412yes—
257C22×C4×C73—21no—
258C22×C4×C73—21no—
259C22×C4×C73—21no—
260C22×C4×C73—21no—
261C22×C4×C73C2×D411yescharacteristic
262C22×C4×C73C2×D411yescharacteristic
263C22×C4×C73C2411yescharacteristic
264Q16×C73—28no—
265C2×C8×C73—22no—
266C2×C8×C73—22no—
267C2×C8×C73C2412yes—
268C2×C8×C73C2412yes—
269C4⋊C4×C73—24no—
270C4⋊C4×C73—24no—
271C4⋊C4×C73—21no—
272C4⋊C4×C73—21no—
273C4⋊C4×C73C2412yes—
274C4⋊C4×C73C2412yes—
275C42×C73—24no—
276C42×C73—24no—
277C42×C73C2×D412yes—
278C42×C73C2412yes—
279C23×C73C22×D411yescharacteristic
280C22×D73—22no—
281C22×D73—24no—
282C22×D73—22no—
283C22×D73—22no—
284C22×D73—22no—
285C22×D73—42no—
286C22×D73—42no—
287C22×D73C22×D412yes—
288Q8×C73—24no—
289Q8×C73—22no—
290Q8×C73—22no—
291Q8×C73—22no—
292Q8×C73—42no—
293Q8×C73C2×#4114yes—
294C2×C4×C73—24no—
295C2×C4×C73—22no—
296C2×C4×C73—22no—
297C2×C4×C73—22no—
298C2×C4×C73—22no—
299C2×C4×C73—22no—
300C2×C4×C73—42no—
301C2×C4×C73—42no—
302C2×C4×C73—42no—
303C2×C4×C73#13714yes—
304C2×C4×C73C22×D412yes—
305C2×C4×C73C22×D411yescharacteristic
306C2×C4×C73C22×D412yes—
307C2×C4×C73C2×#4112yes—
308C2×C4×C73C2×#4112yes—
309C2×C4×C73C2511yescharacteristic
310C2×Dic73—22no—
311C2×Dic73—22no—
312C2×Dic73—22no—
313C2×Dic73—22no—
314C2×Dic73—22no—
315C2×Dic73—42no—
316C2×Dic73—42no—
317C2×Dic73—42no—
318C2×Dic73#13514yes—
319C2×Dic73C22×D412yes—
320C2×Dic73C22×D412yes—
321C2×Dic73C22×D412yes—
322D292—216no—
323D292—24no—
324D292—22no—
325D292C2×#4114yes—
326C4×D73—216no—
327C4×D73—24no—
328C4×D73—28no—
329C4×D73—22no—
330C4×D73—22no—
331C4×D73—28no—
332C4×D73—48no—
333C4×D73—48no—
334Dic146—22no—
335Dic146—22no—
336Dic146—42no—
337Dic146—48no—
338C8×C73—22no—
339C8×C73—22no—
340#10596831—22no—
341#10596831—22no—
342C22×C73#52512yes—
343C22×C73C2×#13512yes—
344C22×C73C2×#13712yes—
345C22×C73C23×D411yescharacteristic
346C2×D73—22no—
347C2×D73—24no—
348C2×D73—22no—
349C2×D73—22no—
350C2×D73—44no—
351C2×D73—48no—
352C2×D73—42no—
353C2×D73—42no—
354C4×C73—24no—
355C4×C73—22no—
356C4×C73—42no—
357C4×C73—42no—
358C4×C73—42no—
359C4×C73#52512yes—
360C4×C73C2×#13714yes—
361C4×C73C22×#4111yescharacteristic
362C4×C73C22×#4111yescharacteristic
363Dic73—22no—
364Dic73—22no—
365Dic73—42no—
366Dic73—42no—
367Dic73—42no—
368Dic73C2×#13514yes—
369C2×#3107—731nomaximal, Sylow
370C2×C73#310714yescomplemented
371C2×C73C2×#52511yescharacteristic
372C2×C73C22×#13511yescharacteristic
373C2×C73C22×#13711yescharacteristic
374D73—42no—
375D73—44no—
376C2×#533—731no—
377C2×C4×#41—731no—
378#3107—7316no—
379C2×#485—731no—
380C2×#485—731no—
381C2×#475—731no—
382C2×#474—731no—
383C2×#462—731no—
384C2×#461—731no—
385C2×#452—731no—
386C2×#452—731no—
387C2×C4×Q16—731no—
388C2×C4×Q16D7311yescharacteristic, complemented
389C2×C4×SD16—731no—
390C2×C4×SD16—731no—
391C2×#431—731no—
392C73C2×#310711yescharacteristic, complemented, Sylow
393C22×#41—731no—
394C22×Q16—731no—
395C22×Q16C2×D7311yescharacteristic
396C22×SD16—731no—
397C22×SD16—731no—
398#533—738no—
399#533—1464no—
400C2×C4⋊Q8—731no—
401C2×C4⋊Q8—731no—
402C2×#125—1461no—
403C2×C22⋊Q8—731no—
404C2×C22⋊Q8—731no—
405C2×C22⋊Q8—1461no—
406C4×#41—738no—
407C4×#41—1464no—
408C2×C4×Q8—731no—
409C2×C4×Q8—731no—
410C2×C4×Q8—1461no—
411C2×C4×Q8C2×D7311yescharacteristic
412C2×C4×Q8C2×D7311yescharacteristic
413C2×C4×D4—731no—
414C2×C4×D4—731no—
415C2×C4×D4—1461no—
416C2×C4×D4—1461no—
417C2×#117—731no—
418C2×#117—1461no—
419C2×#117—1461no—
420C22×C42—731no—
421C22×C42—1461no—
422#485—738no—
423#485—738no—
424#475—738no—
425#474—738no—
426#462—738no—
427#461—738no—
428#452—738no—
429#452—738no—
430C4×Q16—738no—
431C4×Q16C2×D7318yescomplemented
432C4×SD16—738no—
433C4×SD16—738no—
434#431—738no—
435C2×#107—731no—
436C2×#107C2×D7311yescharacteristic
437C2×#106—731no—
438C2×#106—731no—
439C2×C4⋊C8—731no—
440C2×C4⋊C8—731no—
441C2×#103—731no—
442C2×#103—731no—
443C2×#103—731no—
444C2×#103—731no—
445C2×#103C2×D7311yescharacteristic
446C2×#103C2×D7311yescharacteristic
447C2×#102—731no—
448C2×#102—731no—
449C2×C22⋊C8—731no—
450C2×C22⋊C8—731no—
451C2×C4×C8—731no—
452C2×C4×C8C2×D7311yescharacteristic
453C2×#41—734no—
454C2×#41—1462no—
455C2×#41—1464no—
456C2×#41—1464no—
457C22×Q8—731no—
458C22×Q8—1461no—
459C22×Q8C22×D7311yescharacteristic
460C22×Q8C22×D7311yescharacteristic
461C22×D4—731no—
462C22×D4—1461no—
463C23×C4—731no—
464C23×C4—731no—
465C23×C4—731no—
466C23×C4—1461no—
467C23×C4—1461no—
468C23×C4—1461no—
469C2×Q16—24no—
470C2×Q16—734no—
471C2×Q16—1464no—
472C2×Q16C22×D7314yes—
473C2×SD16—734no—
474C2×SD16—734no—
475C2×SD16—1464no—
476C2×SD16—1464no—
477C22×C8—731no—
478C22×C8—731no—
479C22×C8C22×D7311yescharacteristic
480C22×C8C22×D7311yescharacteristic
481C4⋊Q8—734no—
482C4⋊Q8—734no—
483C4⋊Q8—1462no—
484C4⋊Q8—1462no—
485#125—1468no—
486C22⋊Q8—734no—
487C22⋊Q8—734no—
488C22⋊Q8—1462no—
489C22⋊Q8—1468no—
490C22⋊Q8—1462no—
491C4×Q8—22no—
492C4×Q8—22no—
493C4×Q8—734no—
494C4×Q8—734no—
495C4×Q8—1468no—
496C4×Q8—1462no—
497C4×Q8—1462no—
498C4×Q8C22×D7314yes—
499C4×Q8C22×D7314yes—
500C4×D4—734no—
501C4×D4—734no—
502C4×D4—1468no—
503C4×D4—1462no—
504C4×D4—1468no—
505C4×D4—1462no—
506#117—734no—
507#117—1468no—
508#117—1468no—
509#117—1462no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—731no—
513C2×C4⋊C4—731no—
514C2×C4⋊C4—1461no—
515C2×C4⋊C4—1461no—
516C2×C4⋊C4—1461no—
517C2×C4⋊C4—1461no—
518C2×C4⋊C4—1461no—
519C2×C4⋊C4—1461no—
520C2×C4⋊C4—1461no—
521C2×C4⋊C4C22×D7311yescharacteristic
522C2×C4⋊C4C22×D7311yescharacteristic
523C2×C22⋊C4—1461no—
524C2×C22⋊C4—1461no—
525C2×C22⋊C4—1461no—
526C2×C22⋊C4—1461no—
527C2×C22⋊C4—1461no—
528C2×C42—21no—
529C2×C42—21no—
530C2×C42—731no—
531C2×C42—731no—
532C2×C42—731no—
533C2×C42—734no—
534C2×C42—734no—
535C2×C42—1468no—
536C2×C42—1461no—
537C2×C42—1461no—
538C2×C42—1461no—
539C2×C42C22×D7311yescharacteristic
540#107—734no—
541#107C22×D7314yes—
542#106—734no—
543#106—734no—
544C4⋊C8—734no—
545C4⋊C8—734no—
546#103—734no—
547#103—734no—
548#103—734no—
549#103—734no—
550#103C22×D7314yes—
551#103C22×D7314yes—
552#102—734no—
553#102—734no—
554C22⋊C8—734no—
555C22⋊C8—734no—
556C4×C8—734no—
557C4×C8C22×D7314yes—
558C24—731no—
559C24—1461no—
560#41—1468no—
561#41—14616no—
562#41—1468no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—22no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—2924no—
569C2×Q8—732no—
570C2×Q8—1464no—
571C2×Q8—1462no—
572C2×Q8—1462no—
573C2×Q8—1461no—
574C2×Q8#1192402814yes—
575C2×Q8C23×D7312yes—
576C2×Q8C23×D7312yes—
577C2×D4—734no—
578C2×D4—732no—
579C2×D4—1464no—
580C2×D4—1468no—
581C2×D4—1461no—
582C2×D4—1462no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—2924no—
588C22×C4—2924no—
589C22×C4—731no—
590C22×C4—731no—
591C22×C4—731no—
592C22×C4—734no—
593C22×C4—732no—
594C22×C4—734no—
595C22×C4—732no—
596C22×C4—1464no—
597C22×C4—1464no—
598C22×C4—1464no—
599C22×C4—1468no—
600C22×C4—1461no—
601C22×C4—1461no—
602C22×C4—1461no—
603C22×C4—1464no—
604C22×C4—1464no—
605C22×C4—1462no—
606C22×C4—1462no—
607C22×C4D4×D7311yescharacteristic
608C22×C4D4×D7311yescharacteristic
609C22×C4C23×D7311yescharacteristic
610Q16—28no—
611Q16—1468no—
612SD16—1468no—
613SD16—1468no—
614C2×C8—22no—
615C2×C8—22no—
616C2×C8—732no—
617C2×C8—732no—
618C2×C8—1462no—
619C2×C8—1462no—
620C2×C8C23×D7312yes—
621C2×C8C23×D7312yes—
622C4⋊C4—24no—
623C4⋊C4—24no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—732no—
627C4⋊C4—732no—
628C4⋊C4—1464no—
629C4⋊C4—1464no—
630C4⋊C4—1464no—
631C4⋊C4—1464no—
632C4⋊C4—1464no—
633C4⋊C4—1464no—
634C4⋊C4—1464no—
635C4⋊C4—1461no—
636C4⋊C4—1461no—
637C4⋊C4C23×D7312yes—
638C4⋊C4C23×D7312yes—
639C22⋊C4—1464no—
640C22⋊C4—1464no—
641C22⋊C4—1464no—
642C22⋊C4—1464no—
643C22⋊C4—1464no—
644C42—24no—
645C42—24no—
646C42—734no—
647C42—734no—
648C42—732no—
649C42—732no—
650C42—1464no—
651C42—1464no—
652C42—1464no—
653C42D4×D7312yes—
654C42C23×D7312yes—
655C23—2922no—
656C23—2922no—
657C23—732no—
658C23—1462no—
659C23—1462no—
660C23—1464no—
661C23—1462no—
662C23—1462no—
663C23C2×D4×D7311yescharacteristic
664Q8—22no—
665Q8—24no—
666Q8—22no—
667Q8—22no—
668Q8—42no—
669Q8—2928no—
670Q8—2922no—
671Q8—1462no—
672Q8—1462no—
673Q8C2×#1192402814yes—
674D4—734no—
675D4—14616no—
676D4—1462no—
677D4—1464no—
678C2×C4—22no—
679C2×C4—24no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—2928no—
688C2×C4—2922no—
689C2×C4—2922no—
690C2×C4—2922no—
691C2×C4—2928no—
692C2×C4—732no—
693C2×C4—734no—
694C2×C4—732no—
695C2×C4—732no—
696C2×C4—1468no—
697C2×C4—14616no—
698C2×C4—1462no—
699C2×C4—1462no—
700C2×C4—1462no—
701C2×C4—1462no—
702C2×C4—1462no—
703C2×C4—1468no—
704C2×C4—1462no—
705C2×C4—1462no—
706C2×C4—1464no—
707C2×C4#1455662314yes—
708C2×C4C2×D4×D7312yes—
709C2×C4C2×D4×D7312yes—
710C2×C4C2×D4×D7311yescharacteristic
711C2×C4#41×D7312yes—
712C2×C4C2×#1192402812yes—
713C2×C4C24×D7311yescharacteristic
714C8—22no—
715C8—22no—
716C8—1462no—
717C8—1462no—
718C22—2928no—
719C22—2924no—
720C22—2922no—
721C22—2922no—
722C22—1462no—
723C22—1462no—
724C22—1464no—
725C22—1462no—
726C22#1798909612yes—
727C22#135×D7312yes—
728C22C2×#1455662312yes—
729C22C22×D4×D7311yescharacteristic
730C4—22no—
731C4—24no—
732C4—42no—
733C4—42no—
734C4—42no—
735C4—2922no—
736C4—2922no—
737C4—2922no—
738C4—734no—
739C4—1462no—
740C4—1462no—
741C4#1798909612yes—
742C4C2×#1455662314yes—
743C4C2×#41×D7311yescharacteristic
744C4C22×#1192402811yescharacteristic
745C2—2924no—
746C2—2922no—
747C2#2262000014yesdirect product factor
748C2C2×#1798909611yescharacteristic
749C2C2×#135×D7311yescharacteristic
750C2C22×#1455662311yescharacteristic
subgroupG/H
centerC22×C4D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×C4×Q16×C73C2
socleC23×C73C22×D4
prime radicalC22×#11924029C22
hypercenterC2×C4×Q16D73
hypocenterC73C2×#3107
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
1. C2×#17989141C2semidirect
3. #22620000C2direct (N × H)
4. C2×#17988930C2semidirect
5. C2×#17988926C2semidirect
6. C2×#17988870C2semidirect
7. C2×#17988866C2semidirect
8. C2×#17988795C2semidirect
9. C2×#17988791C2semidirect
12. C2×C4×#11924018C2semidirect
13. C2×C4×#11924017C2semidirect
14. C2×C4×#11924015C2semidirect
15. C2×#17988638C2semidirect
16. C2×C4×Q16×C73C2semidirect
22. #17989141C22semidirect
43. #17988930C22semidirect
44. #17988926C22semidirect
45. #17988870C22semidirect
46. #17988866C22semidirect
47. #17988795C22semidirect
48. #17988791C22semidirect
51. C4×#11924018C22semidirect
52. C4×#11924017C22semidirect
53. C4×#11924015C22semidirect
54. #17988638C22semidirect
72. C4×Q16×C73C22semidirect
370. C2×C73#3107semidirect
388. C2×C4×Q16D73semidirect
392. C73C2×#3107semidirect
431. C4×Q16C2×D73semidirect
747. C2#22620000direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179891412
C2×C4×#119240292
#226200002
C2×#179889302
C2×#179889262
C2×#179888702
C2×#179888662
C2×#179887952
C2×#179887912
C2×#179887522
C2×#179887482
C2×C4×#119240182
C2×C4×#119240172
C2×C4×#119240152
C2×#179886382
C2×C4×Q16×C732
C2×#310773