Finite Group Databasebeta

← C2×#22610404 #33087841

Subgroups — C2×#22610404 #33087841

Order 18688.

1654 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556621C211yesmaximal, characteristic
2C2×#17988604C211yesmaximal, characteristic
3C2×#17988597C211yesmaximal, characteristic, complemented
4C22×#14556509C211yesmaximal, characteristic, complemented
5#22610404C218yesmaximal, direct product factor
6C2×#17988359C211yesmaximal, characteristic, complemented
7C2×#17988345C211yesmaximal, characteristic, complemented
8C2×#568×C73C211yesmaximal, characteristic
9C23×Dic146C2211yescharacteristic
10C2×#14556621—22no—
11C2×#14556621—22no—
12C2×#14556621—22no—
13C2×#14556621—22no—
14C2×#14556621C414yescomplemented
15C2×#14556621C2214yes—
16C22×#11924018C412yescomplemented
17C22×#11924016C412yescomplemented
18C22×#11924012C2211yescharacteristic
19C22×#11924012C2211yescharacteristic
20C2×#14556550C2211yescharacteristic
21#17988604—22no—
22#17988604C2214yes—
23C2×#14556518—22no—
24#17988597—22no—
25#17988597C2214yescomplemented
26C2×#14556516—22no—
27C2×#14556509—22no—
28C2×#14556509—22no—
29C2×#14556509C2214yescomplemented
30#17988359C2214yescomplemented
31#17988345C2214yescomplemented
32C22×#41×C73C2211yescharacteristic
33#568×C73—22no—
34#568×C73—22no—
35#568×C73—22no—
36#568×C73C2214yes—
37C2×#131×C73—22no—
38C2×#131×C73—22no—
39C22×M16×C73—22no—
40C22×M16×C73C2211yescharacteristic
41C22×M16×C73C2211yescharacteristic
42C22×Dic146—21no—
43C22×Dic146—21no—
44C22×Dic146—21no—
45C22×Dic146—21no—
46C22×Dic146—21no—
47C22×Dic146—21no—
48C22×Dic146—21no—
49C22×Dic146—21no—
50C22×Dic146—21no—
51C22×Dic146—21no—
52C22×Dic146—21no—
53C22×Dic146C2×C412yes—
54C22×Dic146C2×C412yes—
55C22×Dic146C2312yes—
56C23×Dic73—21no—
57#14556621—28no—
58#14556621—28no—
59#14556621—28no—
60#14556621—28no—
61C2×#11924018—24no—
62C2×#11924018—24no—
63C2×#11924018C2×C418yescomplemented
64C2×#11924016—24no—
65C2×#11924016—24no—
66C2×#11924016C2×C418yescomplemented
67C2×#11924012—21no—
68C2×#11924012—21no—
69C2×#11924012—21no—
70C2×#11924012—21no—
71C2×#11924012—21no—
72C2×#11924012—21no—
73C2×#11924012—21no—
74C2×#11924012—21no—
75C2×#11924012—21no—
76C2×#11924012C2×C412yes—
77C2×#11924012C2312yes—
78C2×#11924012C2312yes—
79C22×#10596831—21no—
80C22×#10596831C2×C412yes—
81#14556550—21no—
82#14556550—21no—
83#14556550—21no—
84#14556550C2312yes—
85C2×C4⋊Dic73—21no—
86C2×C22⋊Dic73—21no—
87C2×C4×Dic73—21no—
88#14556518—28no—
89#14556516—28no—
90#14556509—28no—
91C2×#41×C73—21no—
92C2×#41×C73—21no—
93C2×#41×C73—21no—
94C2×#41×C73—21no—
95C2×#41×C73—21no—
96C2×#41×C73—21no—
97C2×#41×C73C2×C412yes—
98C2×#41×C73D412yes—
99C2×#41×C73D412yes—
100C2×#41×C73D412yes—
101C2×#41×C73D412yes—
102C2×#41×C73C2312yes—
103C22×Q8×C73C2×C411yescharacteristic
104C22×D4×C73—21no—
105C22×D4×C73C2×C411yescharacteristic
106C23×C4×C73—21no—
107C23×C4×C73C2311yescharacteristic
108#131×C73—28no—
109#131×C73—28no—
110#131×C73—28no—
111#131×C73—28no—
112C2×M16×C73—24no—
113C2×M16×C73—28no—
114C2×M16×C73—21no—
115C2×M16×C73—21no—
116C2×M16×C73—21no—
117C2×M16×C73—21no—
118C2×M16×C73—21no—
119C2×M16×C73—21no—
120C2×M16×C73—21no—
121C2×M16×C73—28no—
122C2×M16×C73D412yes—
123C2×M16×C73D412yes—
124C2×M16×C73D412yes—
125C2×M16×C73C2312yes—
126C2×M16×C73C2312yes—
127C22×C8×C73—24no—
128C22×C8×C73—21no—
129C22×C8×C73D412yes—
130C2×Dic146—22no—
131C2×Dic146—22no—
132C2×Dic146—22no—
133C2×Dic146—22no—
134C2×Dic146—22no—
135C2×Dic146—22no—
136C2×Dic146—22no—
137C2×Dic146—22no—
138C2×Dic146—22no—
139C2×Dic146—22no—
140C2×Dic146—22no—
141C2×Dic146—22no—
142C2×Dic146—22no—
143C2×Dic146—22no—
144C2×Dic146—22no—
145C2×Dic146—41no—
146C2×Dic146—41no—
147C2×Dic146—41no—
148C2×Dic146—41no—
149C2×Dic146—41no—
150C2×Dic146—41no—
151C2×Dic146—41no—
152C2×Dic146—41no—
153C2×Dic146—41no—
154C2×Dic146—41no—
155C2×Dic146—41no—
156C2×Dic146—41no—
157C2×Dic146C22×C414yes—
158C22×Dic73—22no—
159C22×Dic73—22no—
160C22×Dic73—22no—
161C22×Dic73—41no—
162C22×Dic73—41no—
163C22×Dic73—41no—
164C22×Dic73—41no—
165C22×Dic73—41no—
166#11924018—216no—
167#11924016—216no—
168#11924012—22no—
169#11924012—22no—
170#11924012—22no—
171#11924012—22no—
172#11924012—22no—
173#11924012—22no—
174#11924012—41no—
175#11924012—41no—
176C2×#10596831—22no—
177C2×#10596831—22no—
178C2×#10596831—22no—
179C2×#10596831—41no—
180C2×#10596831—41no—
181C2×#10596831C22×C414yes—
182C4⋊Dic73—22no—
183C4⋊Dic73—41no—
184C22⋊Dic73—22no—
185C22⋊Dic73—41no—
186C4×Dic73—22no—
187C4×Dic73—41no—
188C24×C73—21no—
189C24×C73#4111yescharacteristic
190#41×C73—22no—
191#41×C73—22no—
192#41×C73—22no—
193#41×C73—22no—
194#41×C73—22no—
195#41×C73—22no—
196#41×C73—22no—
197#41×C73—22no—
198#41×C73—22no—
199#41×C73—22no—
200#41×C73—22no—
201#41×C73—22no—
202#41×C73C22⋊C414yes—
203#41×C73C22⋊C414yes—
204#41×C73C2×D414yes—
205#41×C73C2×D414yes—
206C2×Q8×C73—21no—
207C2×Q8×C73—21no—
208C2×Q8×C73—21no—
209C2×Q8×C73C22⋊C412yes—
210C2×Q8×C73C22⋊C412yes—
211C2×Q8×C73C22×C412yes—
212C2×D4×C73—22no—
213C2×D4×C73—22no—
214C2×D4×C73—22no—
215C2×D4×C73—22no—
216C2×D4×C73—22no—
217C2×D4×C73—22no—
218C2×D4×C73—21no—
219C2×D4×C73—21no—
220C2×D4×C73—21no—
221C2×D4×C73C22⋊C412yes—
222C2×D4×C73C22⋊C412yes—
223C2×D4×C73C22×C412yes—
224C22×C4×C73—21no—
225C22×C4×C73—22no—
226C22×C4×C73—22no—
227C22×C4×C73—22no—
228C22×C4×C73—22no—
229C22×C4×C73—22no—
230C22×C4×C73—22no—
231C22×C4×C73C22×C411yescharacteristic
232C22×C4×C73C22×C411yescharacteristic
233C22×C4×C73C2×D411yescharacteristic
234C22×C4×C73C2×D411yescharacteristic
235C22×C4×C73C2×D411yescharacteristic
236C22×C4×C73C2×D411yescharacteristic
237C22×C4×C73C2×D411yescharacteristic
238C22×C4×C73C2×D411yescharacteristic
239C22×C4×C73C2×D411yescharacteristic
240C22×C4×C73C2×D411yescharacteristic
241C22×C4×C73#4111yescharacteristic
242C22×C4×C73#4111yescharacteristic
243C22×C4×C73#4111yescharacteristic
244C22×C4×C73C2411yescharacteristic
245M16×C73—216no—
246M16×C73—22no—
247M16×C73—22no—
248M16×C73—22no—
249M16×C73—22no—
250M16×C73—22no—
251M16×C73—22no—
252M16×C73—22no—
253M16×C73C2×D414yes—
254C2×C8×C73—216no—
255C2×C8×C73—22no—
256C2×C8×C73—22no—
257C2×C8×C73—22no—
258C2×C8×C73—22no—
259C2×C8×C73—22no—
260C2×C8×C73C2×D414yes—
261C23×C73—22no—
262C23×C73—22no—
263C23×C73—22no—
264C23×C73—42no—
265C23×C73—82no—
266C23×C73C4×D411yescharacteristic
267C23×C73C4×D411yescharacteristic
268C23×C73#12111yescharacteristic
269C23×C73#12111yescharacteristic
270C23×C73#12311yescharacteristic
271C23×C73#12311yescharacteristic
272C23×C73C2×#4111yescharacteristic
273Q8×C73—22no—
274Q8×C73—22no—
275Q8×C73—22no—
276Q8×C73C2×C22⋊C414yes—
277D4×C73—24no—
278D4×C73—24no—
279D4×C73—24no—
280D4×C73—24no—
281D4×C73—22no—
282D4×C73—22no—
283D4×C73—22no—
284D4×C73C2×C22⋊C414yes—
285C2×C4×C73—22no—
286C2×C4×C73—22no—
287C2×C4×C73—22no—
288C2×C4×C73—24no—
289C2×C4×C73—24no—
290C2×C4×C73—24no—
291C2×C4×C73—24no—
292C2×C4×C73C2×C22⋊C411yescharacteristic
293C2×C4×C73C2×C22⋊C411yescharacteristic
294C2×C4×C73C2×C22⋊C411yescharacteristic
295C2×C4×C73C2×C22⋊C411yescharacteristic
296C2×C4×C73C4×D411yescharacteristic
297C2×C4×C73C4×D411yescharacteristic
298C2×C4×C73C4×D411yescharacteristic
299C2×C4×C73C4×D411yescharacteristic
300C2×C4×C73C4×D411yescharacteristic
301C2×C4×C73C4×D411yescharacteristic
302C2×C4×C73#12011yescharacteristic
303C2×C4×C73#12011yescharacteristic
304C2×C4×C73#12011yescharacteristic
305C2×C4×C73#12011yescharacteristic
306C2×C4×C73#12111yescharacteristic
307C2×C4×C73#12111yescharacteristic
308C2×C4×C73#12111yescharacteristic
309C2×C4×C73#12111yescharacteristic
310C2×C4×C73#12111yescharacteristic
311C2×C4×C73#12111yescharacteristic
312C2×C4×C73#12311yescharacteristic
313C2×C4×C73#12311yescharacteristic
314C2×C4×C73C23×C411yescharacteristic
315C2×C4×C73C22×D411yescharacteristic
316C2×C4×C73C22×D411yescharacteristic
317C2×C4×C73C22×D411yescharacteristic
318C2×C4×C73C22×D411yescharacteristic
319C2×C4×C73C2×#4111yescharacteristic
320C2×Dic73—24no—
321C2×Dic73—42no—
322C2×Dic73—42no—
323C2×Dic73—42no—
324C2×Dic73—42no—
325C2×Dic73—42no—
326C2×Dic73—42no—
327C2×Dic73—42no—
328C2×Dic73—82no—
329Dic146—24no—
330Dic146—24no—
331Dic146—42no—
332Dic146—42no—
333Dic146—42no—
334Dic146—42no—
335Dic146—42no—
336Dic146—42no—
337C8×C73—24no—
338C8×C73—24no—
339#10596831—24no—
340#10596831—42no—
341C22×C73—22no—
342C22×C73—22no—
343C22×C73—22no—
344C22×C73—24no—
345C22×C73—41no—
346C22×C73—41no—
347C22×C73—41no—
348C22×C73—41no—
349C22×C73—44no—
350C22×C73—82no—
351C22×C73—82no—
352C22×C73#38611yescharacteristic
353C22×C73#38611yescharacteristic
354C22×C73#38611yescharacteristic
355C22×C73#38611yescharacteristic
356C22×C73C2×C4×D411yescharacteristic
357C22×C73C2×#12111yescharacteristic
358C22×C73C2×#12311yescharacteristic
359C4×C73—24no—
360C4×C73#38611yescharacteristic
361C4×C73#38611yescharacteristic
362C4×C73#38611yescharacteristic
363C4×C73#38611yescharacteristic
364C4×C73C22×C22⋊C411yescharacteristic
365C4×C73C2×C4×D411yescharacteristic
366C4×C73C2×#12011yescharacteristic
367C4×C73C2×#12111yescharacteristic
368Dic73—44no—
369Dic73—82no—
370C2×#1902—731nomaximal, Sylow
371C2×C73—21no—
372C2×C73—21no—
373C2×C73—21no—
374C2×C73—21no—
375C2×C73—21no—
376C2×C73—21no—
377C2×C73—44no—
378C2×C73#190212yescomplemented
379C2×C73C2×#38611yescharacteristic
380C22×#137—731no—
381C2×#568D7311yescharacteristic
382C2×#421—731no—
383C2×#419—731no—
384C22×#101—731no—
385#1902—738no—
386C2×#344—731no—
387C2×#338—731no—
388C73C2×#190211yescharacteristic, complemented, Sylow
389C22×#41C2×D7311yescharacteristic
390C23×Q8—731no—
391C2×#137—734no—
392C2×#137—734no—
393C2×#137—1462no—
394C2×#137—1462no—
395C2×#137—1462no—
396C2×#137—1462no—
397C22×Q16—732no—
398C22×SD16—732no—
399#568—22no—
400#568—22no—
401#568—22no—
402#568C2×D7314yes—
403C2×#131—22no—
404C2×#131—22no—
405C22×M16—22no—
406C22×M16—731no—
407C22×M16—731no—
408C22×M16C2×D7311yescharacteristic
409C22×M16C2×D7311yescharacteristic
410C2×#117—731no—
411#421—734no—
412#421—1462no—
413C2×#104—1462no—
414#419—734no—
415#419—1462no—
416C2×#103—1462no—
417C2×#101—734no—
418C2×#101—1462no—
419C2×#101—1462no—
420#344—734no—
421#338—734no—
422C2×#41—21no—
423C2×#41—21no—
424C2×#41—21no—
425C2×#41—21no—
426C2×#41—21no—
427C2×#41—21no—
428C2×#41C4×D7312yes—
429C2×#41D29212yes—
430C2×#41D29212yes—
431C2×#41C22⋊D7312yes—
432C2×#41C22⋊D7312yes—
433C2×#41C22×D7312yes—
434C22×Q8—732no—
435C22×Q8—732no—
436C22×Q8—732no—
437C22×Q8—1461no—
438C22×Q8—1461no—
439C22×Q8—1461no—
440C22×Q8—1461no—
441C22×Q8—1461no—
442C22×Q8—1461no—
443C22×Q8—1461no—
444C22×Q8—1461no—
445C22×Q8—1461no—
446C22×Q8—1461no—
447C22×Q8—1461no—
448C22×Q8C4×D7311yescharacteristic
449C22×D4—21no—
450C22×D4C4×D7311yescharacteristic
451C23×C4—21no—
452C23×C4—1461no—
453C23×C4C22×D7311yescharacteristic
454#137—1468no—
455#137—1468no—
456#137—1468no—
457#137—1468no—
458C2×Q16—738no—
459C2×Q16—1464no—
460C2×Q16—1464no—
461C2×SD16—738no—
462C2×SD16—1464no—
463C2×SD16—1464no—
464#131—28no—
465#131—28no—
466#131—28no—
467#131—28no—
468C2×M16—24no—
469C2×M16—28no—
470C2×M16—21no—
471C2×M16—21no—
472C2×M16—21no—
473C2×M16—21no—
474C2×M16—21no—
475C2×M16—21no—
476C2×M16—21no—
477C2×M16—28no—
478C2×M16—732no—
479C2×M16—732no—
480C2×M16—732no—
481C2×M16—1461no—
482C2×M16—1461no—
483C2×M16—1461no—
484C2×M16—1461no—
485C2×M16—1461no—
486C2×M16—1461no—
487C2×M16—1461no—
488C2×M16—1461no—
489C2×M16—1461no—
490C2×M16C22⋊D7312yes—
491C2×M16C22⋊D7312yes—
492C2×M16C22⋊D7312yes—
493C2×M16C22×D7312yes—
494C2×M16C22×D7312yes—
495C22×C8—24no—
496C22×C8—21no—
497C22×C8—732no—
498C22×C8—1461no—
499C22×C8C22⋊D7312yes—
500#117—732no—
501#117—1461no—
502#117—1461no—
503#117—1461no—
504C2×C4⋊C4—1461no—
505C2×C22⋊C4—1461no—
506C2×C42—1461no—
507#104—1468no—
508#103—1468no—
509#101—1468no—
510C24—21no—
511C24#1192402811yescharacteristic
512#41—22no—
513#41—22no—
514#41—22no—
515#41—22no—
516#41—22no—
517#41—22no—
518#41—22no—
519#41—22no—
520#41—22no—
521#41—22no—
522#41—22no—
523#41—22no—
524#41#1192400514yes—
525#41#1192400514yes—
526#41C2×C22⋊D7314yes—
527#41C2×D29214yes—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—2921no—
532C2×Q8—2921no—
533C2×Q8—2921no—
534C2×Q8—2921no—
535C2×Q8—2921no—
536C2×Q8—2921no—
537C2×Q8—2921no—
538C2×Q8—2921no—
539C2×Q8—2921no—
540C2×Q8—2921no—
541C2×Q8—2921no—
542C2×Q8—2921no—
543C2×Q8—734no—
544C2×Q8—1462no—
545C2×Q8—1462no—
546C2×Q8—1462no—
547C2×Q8—1462no—
548C2×Q8—1462no—
549C2×Q8—1462no—
550C2×Q8—1462no—
551C2×Q8—1462no—
552C2×Q8—1462no—
553C2×Q8—1462no—
554C2×Q8—1462no—
555C2×Q8—1462no—
556C2×Q8—1462no—
557C2×Q8—1462no—
558C2×Q8—1462no—
559C2×Q8#1192400512yes—
560C2×Q8#1192400512yes—
561C2×Q8C2×C4×D7312yes—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4#1192400512yes—
572C2×D4#1192400512yes—
573C2×D4C2×C4×D7312yes—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—2921no—
582C22×C4—2921no—
583C22×C4—2921no—
584C22×C4—2921no—
585C22×C4—2921no—
586C22×C4—1462no—
587C22×C4—1462no—
588C22×C4—1462no—
589C22×C4C2×C4×D7311yescharacteristic
590C22×C4C2×C4×D7311yescharacteristic
591C22×C4C2×C22⋊D7311yescharacteristic
592C22×C4C2×C22⋊D7311yescharacteristic
593C22×C4C2×C22⋊D7311yescharacteristic
594C22×C4C2×C22⋊D7311yescharacteristic
595C22×C4C2×C22⋊D7311yescharacteristic
596C22×C4C2×C22⋊D7311yescharacteristic
597C22×C4C2×D29211yescharacteristic
598C22×C4C2×D29211yescharacteristic
599C22×C4#1192402811yescharacteristic
600C22×C4#1192402811yescharacteristic
601C22×C4#1192402811yescharacteristic
602C22×C4C23×D7311yescharacteristic
603Q16—14616no—
604SD16—14616no—
605M16—216no—
606M16—22no—
607M16—22no—
608M16—22no—
609M16—22no—
610M16—22no—
611M16—22no—
612M16—22no—
613M16—2921no—
614M16—2921no—
615M16—1462no—
616M16—1462no—
617M16—1462no—
618M16—1462no—
619M16—1462no—
620M16—1462no—
621M16C2×C22⋊D7314yes—
622C2×C8—216no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8—2921no—
629C2×C8—2921no—
630C2×C8—734no—
631C2×C8—1462no—
632C2×C8—1462no—
633C2×C8—1462no—
634C2×C8C2×C22⋊D7314yes—
635C4⋊C4—2921no—
636C4⋊C4—1462no—
637C22⋊C4—2921no—
638C22⋊C4—1462no—
639C42—2921no—
640C42—1462no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—42no—
645C23—82no—
646C23C4×C22⋊D7311yescharacteristic
647C23C4×C22⋊D7311yescharacteristic
648C23#1455656511yescharacteristic
649C23#1455656511yescharacteristic
650C23#1455657411yescharacteristic
651C23#1455657411yescharacteristic
652C23C2×#1192402811yescharacteristic
653Q8—22no—
654Q8—22no—
655Q8—22no—
656Q8—2922no—
657Q8—2922no—
658Q8—2922no—
659Q8—2922no—
660Q8—2922no—
661Q8—2922no—
662Q8—1464no—
663Q8—1464no—
664Q8C2×#1192400514yes—
665D4—24no—
666D4—24no—
667D4—24no—
668D4—24no—
669D4—22no—
670D4—22no—
671D4—22no—
672D4C2×#1192400514yes—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—2922no—
681C2×C4—2922no—
682C2×C4—2922no—
683C2×C4—2922no—
684C2×C4—2922no—
685C2×C4—2922no—
686C2×C4—2922no—
687C2×C4—5842no—
688C2×C4—1464no—
689C2×C4C2×#1192400511yescharacteristic
690C2×C4C2×#1192400511yescharacteristic
691C2×C4C2×#1192400511yescharacteristic
692C2×C4C2×#1192400511yescharacteristic
693C2×C4C4×C22⋊D7311yescharacteristic
694C2×C4C4×C22⋊D7311yescharacteristic
695C2×C4C4×C22⋊D7311yescharacteristic
696C2×C4C4×C22⋊D7311yescharacteristic
697C2×C4C4×C22⋊D7311yescharacteristic
698C2×C4C4×C22⋊D7311yescharacteristic
699C2×C4#1455656011yescharacteristic
700C2×C4#1455656011yescharacteristic
701C2×C4#1455656011yescharacteristic
702C2×C4#1455656011yescharacteristic
703C2×C4#1455656511yescharacteristic
704C2×C4#1455656511yescharacteristic
705C2×C4#1455656511yescharacteristic
706C2×C4#1455656511yescharacteristic
707C2×C4#1455656511yescharacteristic
708C2×C4#1455656511yescharacteristic
709C2×C4#1455657411yescharacteristic
710C2×C4#1455657411yescharacteristic
711C2×C4C22×C4×D7311yescharacteristic
712C2×C4C22×C22⋊D7311yescharacteristic
713C2×C4C22×C22⋊D7311yescharacteristic
714C2×C4C22×C22⋊D7311yescharacteristic
715C2×C4C22×D29211yescharacteristic
716C2×C4C2×#1192402811yescharacteristic
717C8—24no—
718C8—24no—
719C8—2922no—
720C8—1464no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—24no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—44no—
730C22—82no—
731C22—82no—
732C22#1798846611yescharacteristic
733C22#1798846611yescharacteristic
734C22#1798846611yescharacteristic
735C22#1798846611yescharacteristic
736C22C2×C4×C22⋊D7311yescharacteristic
737C22C2×#1455656511yescharacteristic
738C22C2×#1455657411yescharacteristic
739C4—24no—
740C4—2924no—
741C4—5842no—
742C4#1798846611yescharacteristic
743C4#1798846611yescharacteristic
744C4#1798846611yescharacteristic
745C4#1798846611yescharacteristic
746C4C22×#1192400511yescharacteristic
747C4C2×C4×C22⋊D7311yescharacteristic
748C4C2×#1455656011yescharacteristic
749C4C2×#1455656511yescharacteristic
750C2—21no—
751C2—21no—
752C2—21no—
753C2—21no—
754C2—21no—
755C2—21no—
756C2—44no—
757C2#2261040412yesdirect product factor
758C2C2×#1798846611yescharacteristic
subgroupG/H
centerC22#17988466
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC2×#568×C73C2
socleC22×C73#386
prime radicalC22×#41×C73C22
cosocleC22×C4×C73C24
hypercenterC2×#568D73
hypocenterC73C2×#1902
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#568

Complements

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

NH ≅ G/Ntype
3. C2×#17988597C2semidirect
4. C22×#14556509C2semidirect
5. #22610404C2direct (N × H)
6. C2×#17988359C2semidirect
7. C2×#17988345C2semidirect
14. C2×#14556621C4semidirect
16. C22×#11924018C4semidirect
17. C22×#11924016C4semidirect
25. #17988597C22semidirect
29. C2×#14556509C22semidirect
30. #17988359C22semidirect
31. #17988345C22semidirect
63. C2×#11924018C2×C4semidirect
66. C2×#11924016C2×C4semidirect
378. C2×C73#1902semidirect
388. C73C2×#1902semidirect
757. C2#22610404direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145566212
C2×#179886042
C2×#179885972
C22×#145565092
#226104042
C2×#179883592
C2×#179883452
C2×#568×C732
C2×#190273