Finite Group Databasebeta

← #33249269

Subgroups — #33249269

Order 18688.

2118 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989122C211yesmaximal, characteristic
2#22613122C212yesmaximal, complemented
3#22613121C212yesmaximal, complemented
4#22612928C212yesmaximal, complemented
5#22612916C212yesmaximal, complemented
6#22612870C212yesmaximal, complemented
7#22612840C212yesmaximal, complemented
8#22612820C212yesmaximal, complemented
9#22612790C212yesmaximal, complemented
10#22612744C211yesmaximal, characteristic, complemented
11#22612741C211yesmaximal, characteristic, complemented
12#22612737C211yesmaximal, characteristic, complemented
13#22612660C212yesmaximal, complemented
14#22612630C212yesmaximal
15#22612580C212yesmaximal, complemented
16#22612563C212yesmaximal, complemented
17#22612335C211yesmaximal, characteristic, complemented
18#383×D73C211yesmaximal, characteristic, complemented
19C73×#2336C211yesmaximal, characteristic, complemented
20#17989122C4116yescomplemented
21C2×#14556586C2212yes—
22C2×#14556579C2211yescharacteristic
23C2×#14556576C2212yes—
24C2×#14556571C2211yescharacteristic
25C2×#14556566C2211yescharacteristic
26C2×#14556556C2211yescharacteristic
27C2×C4×D292C2212yes—
28C2×#14556553C2212yes—
29C2×#14556553C2211yescharacteristic
30C2×#14556553C2212yes—
31C2×#14556549C2212yes—
32C2×#14556548C2211yescharacteristic
33C2×#14556548C2211yescharacteristic
34C2×C42×D73C2211yescharacteristic
35#17988491C2212yes—
36#17988491C2212yes—
37#17988486C2212yes—
38#17988485C2212yes—
39#17988484C2212yes—
40#17988483C2212yes—
41#17988482C2212yes—
42#17988479C2212yes—
43#17988478C2212yes—
44#17988478C2212yes—
45#17988478C2212yes—
46#17988477C2212yes—
47#17988476C2212yes—
48#17988476C2212yes—
49#17988476C2212yes—
50#17988473C2212yes—
51#17988473C2212yes—
52#17988473C2212yes—
53#17988473C2212yes—
54#17988472C2212yes—
55#17988471C2212yes—
56#17988470C2212yes—
57#17988469C2212yes—
58#17988465C2212yes—
59#17988465C2212yes—
60#17988465C2212yes—
61#17988465C2212yes—
62#17988461C2212yes—
63#17988461C2212yes—
64#17988461C2212yes—
65#17988461C2212yes—
66#17988458C2212yes—
67#17988458C2212yes—
68#17988458C2212yes—
69#17988458C2212yes—
70#17988456C2212yes—
71#17988455C2211yescharacteristic
72#17988454C2212yes—
73#17988454C2212yes—
74#17988454C2212yes—
75#17988454C2211yescharacteristic
76#17988454C2211yescharacteristic
77#17988452C2212yes—
78#17988451C2212yes—
79#17988449C2212yes—
80#17988446C2212yes—
81#17988444C2212yes—
82#17988444C2212yes—
83C4⋊C4×Dic73C2212yes—
84C4×#11924007C2211yescharacteristic
85C4×#11924007C2211yescharacteristic
86C4×#11924007C2212yes—
87C4×C4⋊Dic73C2211yescharacteristic
88C4×#11924005C2212yes—
89C4×#11924005C2212yes—
90C4×#11924005C2212yes—
91#17988434C2212yes—
92#17988434C2212yes—
93#17988432C2212yes—
94#95×D73C2212yes—
95#95×D73C2211yescharacteristic
96#95×D73C2211yescharacteristic
97#95×D73C2212yes—
98#95×D73C2212yes—
99C2×#125×C73C2211yescharacteristic
100#389×C73C2212yes—
101#387×C73C2212yes—
102#387×C73C2212yes—
103#387×C73C2212yes—
104#387×C73C2212yes—
105#383×C73C2211yescharacteristic
106C4×C4⋊C4×C73C2211yescharacteristic
107C4×C4⋊C4×C73C2212yes—
108C22×Dic146C2311yescharacteristic
109C22×D292C2312yes—
110C22×D292C2311yescharacteristic
111C22×C4×D73C2311yescharacteristic
112C22×C4×D73C2312yes—
113C22×C4×D73C2312yes—
114C22×C4×D73C2312yes—
115C22×C4×D73C2312yes—
116C22×C4×D73C2311yescharacteristic
117C22×C4×D73C2311yescharacteristic
118C22×C4×D73C2312yes—
119#14556586C2×C4116yescomplemented
120#14556579C2×C418yescomplemented
121#14556576C2×C4116yescomplemented
122#14556571C2×C418yescomplemented
123#14556566C2×C418yes—
124#14556556C2×C418yescomplemented
125C4×D292—44no—
126#14556553—44no—
127#14556553C2×C418yescomplemented
128#14556553C2×C4116yescomplemented
129#14556549C2×C4116yescomplemented
130#14556548—42no—
131#14556548—42no—
132C2×C4⋊Dic73C2312yes—
133C2×C4⋊Dic73C2312yes—
134C2×C4⋊Dic73C2312yes—
135C2×C4⋊Dic73C2312yes—
136C2×#11924007C2312yes—
137C2×#11924007C2312yes—
138C2×#11924007C2312yes—
139C2×#11924007C2312yes—
140C2×#11924007C2312yes—
141C2×#11924007C2312yes—
142C2×#11924007C2312yes—
143C2×#11924005C2312yes—
144C2×#11924005C2312yes—
145C2×#11924005C2312yes—
146C2×#11924005C2312yes—
147C2×#11924005C2312yes—
148C2×#11924005C2312yes—
149C2×#11924005C2312yes—
150C2×#11924005C2312yes—
151C2×#11924005C2312yes—
152C2×#11924005C2312yes—
153C2×#11924005C2312yes—
154C2×#11924005C2312yes—
155C2×#11924005C2312yes—
156C2×C4×Dic73C2312yes—
157C2×C4×Dic73C2312yes—
158C2×C4×Dic73C2311yescharacteristic
159C2×C4×Dic73C2312yes—
160C2×C4×Dic73C2311yescharacteristic
161C2×C4×Dic73C2312yes—
162C2×C4×Dic73C2312yes—
163C2×C4×Dic73C2311yescharacteristic
164C2×C4×Dic73C2311yescharacteristic
165C2×C4×Dic73C2311yescharacteristic
166C42×D73C2×C418yescomplemented
167#14556498C2312yes—
168#14556498C2312yes—
169#14556498C2312yes—
170#14556498C2312yes—
171#14556498C2312yes—
172#14556498C2312yes—
173#14556498C2312yes—
174#14556498C2312yes—
175#14556498C2311yescharacteristic
176#14556498C2312yes—
177#14556498C2311yescharacteristic
178#14556498C2312yes—
179#14556498C2312yes—
180#14556498C2312yes—
181#14556498C2312yes—
182#14556498C2312yes—
183#14556498C2312yes—
184#14556498C2312yes—
185#14556498C2312yes—
186#14556498C2312yes—
187#14556498C2312yes—
188#125×C73C2×C418yescomplemented
189C2×C4⋊C4×C73C2312yes—
190C2×C4⋊C4×C73C2312yes—
191C2×C4⋊C4×C73C2312yes—
192C2×C4⋊C4×C73C2312yes—
193C2×C4⋊C4×C73C2311yescharacteristic
194C2×C4⋊C4×C73C2311yescharacteristic
195C2×C4⋊C4×C73C2312yes—
196C2×C42×C73C2311yescharacteristic
197C2×C42×C73C2311yescharacteristic
198C2×C42×C73C2312yes—
199C2×C42×C73C2312yes—
200C2×C42×C73C2311yescharacteristic
201#95×C73C2312yes—
202#95×C73C2312yes—
203#95×C73C2312yes—
204#95×C73C2312yes—
205#95×C73C2311yescharacteristic
206#95×C73C2311yescharacteristic
207#95×C73C2312yes—
208#95×C73C2312yes—
209#95×C73C2312yes—
210C23×D73C2412yes—
211C23×D73C2411yescharacteristic
212C2×Dic146—42no—
213C2×Dic146C22×C414yes—
214C2×D292—24no—
215C2×D292—24no—
216C2×D292—42no—
217C2×D292C22×C418yes—
218C2×D292C22×C414yes—
219C22×Dic73C2412yes—
220C22×Dic73C2412yes—
221C22×Dic73C2412yes—
222C22×Dic73C2412yes—
223C22×Dic73C2411yescharacteristic
224C22×Dic73C2412yes—
225C22×Dic73C2411yescharacteristic
226C22×Dic73C2411yescharacteristic
227C2×C4×D73—22no—
228C2×C4×D73—22no—
229C2×C4×D73—24no—
230C2×C4×D73—24no—
231C2×C4×D73—42no—
232C2×C4×D73—42no—
233C2×C4×D73—42no—
234C2×C4×D73—42no—
235C2×C4×D73—42no—
236C2×C4×D73—42no—
237C2×C4×D73—42no—
238C2×C4×D73—42no—
239C2×C4×D73—42no—
240C2×C4×D73—42no—
241C2×C4×D73—42no—
242C2×C4×D73—42no—
243C2×C4×D73—42no—
244C2×C4×D73—42no—
245C2×C4×D73C22×C414yes—
246C2×C4×D73C22×C414yes—
247C2×C4×D73C22×C414yes—
248C2×C4×D73C22×C418yes—
249C4⋊Dic73—42no—
250C4⋊Dic73—42no—
251C4⋊Dic73—42no—
252C4⋊Dic73C22×C418yes—
253#11924007—42no—
254#11924007—42no—
255#11924007—42no—
256#11924007—42no—
257#11924007—42no—
258#11924007—42no—
259#11924007C22×C418yes—
260#11924005—24no—
261#11924005—24no—
262#11924005—42no—
263#11924005—42no—
264#11924005—42no—
265#11924005—42no—
266#11924005—42no—
267#11924005—42no—
268#11924005C22×C418yes—
269#11924005C22×C418yes—
270#11924005C22×C418yes—
271#11924005C22×C418yes—
272#11924005C22×C418yes—
273C4×Dic73—42no—
274C4×Dic73—42no—
275C4×Dic73—42no—
276C4×Dic73—41no—
277C4×Dic73—41no—
278C4×Dic73—42no—
279C4×Dic73C22×C414yes—
280C4×Dic73C22×C414yes—
281C4×Dic73C22×C414yes—
282C4×Dic73C22×C418yes—
283C22×C4×C73C2412yes—
284C22×C4×C73C2412yes—
285C22×C4×C73C2412yes—
286C22×C4×C73C2412yes—
287C22×C4×C73C2411yescharacteristic
288C22×C4×C73C2411yescharacteristic
289C22×C4×C73C2412yes—
290C22×C4×C73C2412yes—
291C22×C4×C73C2411yescharacteristic
292C4⋊C4×C73—42no—
293C4⋊C4×C73—42no—
294C4⋊C4×C73—42no—
295C4⋊C4×C73C22×C418yes—
296C4⋊C4×C73C22×C414yes—
297C4⋊C4×C73C22×C418yes—
298C4⋊C4×C73C22×C414yes—
299C42×C73—42no—
300C42×C73—41no—
301C42×C73—41no—
302C42×C73—42no—
303C42×C73C22×C414yes—
304C23×C73C2511yescharacteristic
305C22×D73—22no—
306C22×D73—22no—
307C22×D73—22no—
308C22×D73—22no—
309C22×D73—22no—
310C22×D73—22no—
311C22×D73—22no—
312C22×D73—22no—
313C22×D73C23×C414yes—
314C22×D73C23×C412yes—
315C22×D73H(5,𝔽2)12yes—
316C22×D732−1+412yes—
317C2×C4×C73—21no—
318C2×C4×C73—22no—
319C2×C4×C73—21no—
320C2×C4×C73—22no—
321C2×C4×C73—22no—
322C2×C4×C73—22no—
323C2×C4×C73—22no—
324C2×C4×C73—22no—
325C2×C4×C73—22no—
326C2×C4×C73—22no—
327C2×C4×C73—22no—
328C2×C4×C73—22no—
329C2×C4×C73—22no—
330C2×C4×C73—22no—
331C2×C4×C73—22no—
332C2×C4×C73—22no—
333C2×C4×C73—22no—
334C2×C4×C73—22no—
335C2×C4×C73—22no—
336C2×C4×C73—22no—
337C2×C4×C73C23×C412yes—
338C2×C4×C73C23×C412yes—
339C2×C4×C73C23×C412yes—
340C2×C4×C73C23×C414yes—
341C2×C4×C73C23×C414yes—
342C2×Dic73—21no—
343C2×Dic73—21no—
344C2×Dic73—22no—
345C2×Dic73—22no—
346C2×Dic73—22no—
347C2×Dic73—22no—
348C2×Dic73—22no—
349C2×Dic73—22no—
350C2×Dic73—22no—
351C2×Dic73—22no—
352C2×Dic73—22no—
353C2×Dic73—22no—
354C2×Dic73—22no—
355C2×Dic73—22no—
356C2×Dic73—22no—
357C2×Dic73—22no—
358C2×Dic73—22no—
359C2×Dic73—22no—
360C2×Dic73C23×C412yes—
361C2×Dic73C23×C412yes—
362C2×Dic73C23×C412yes—
363C2×Dic73C23×C414yes—
364D292—216no—
365D292—44no—
366C4×D73—28no—
367C4×D73—44no—
368C4×D73—48no—
369C4×D73—44no—
370C4×D73—84no—
371C4×D73—84no—
372C4×D73—84no—
373C4×D73—84no—
374Dic146—44no—
375C22×C73C24×C411yescharacteristic
376C22×C73C2×H(5,𝔽2)11yescharacteristic
377C22×C73C2×2−1+411yescharacteristic
378C22×C73#58512yes—
379C22×C73#58512yes—
380C2×D73—22no—
381C2×D73—22no—
382C2×D73—24no—
383C2×D73—24no—
384C2×D73—24no—
385C2×D73—24no—
386C2×D73—24no—
387C2×D73—42no—
388C2×D73—42no—
389C2×D73—42no—
390C2×D73—42no—
391C2×D73#52014yes—
392C4×C73—22no—
393C4×C73—24no—
394C4×C73—22no—
395C4×C73—24no—
396C4×C73—22no—
397C4×C73—42no—
398C4×C73—42no—
399C4×C73—42no—
400C4×C73—42no—
401Dic73—22no—
402Dic73—24no—
403Dic73—22no—
404Dic73—22no—
405Dic73—42no—
406Dic73—42no—
407Dic73—42no—
408Dic73—42no—
409#34401—731nomaximal, Sylow
410C2×C73C2×#52011yescharacteristic
411C2×C73#342811yescharacteristic
412C2×C73#342811yescharacteristic
413C2×C73#356012yes—
414C2×C73#356412yes—
415D73—24no—
416D73—44no—
417C2×#529—731no—
418#2383—732no—
419#2383—732no—
420#2359—732no—
421#2359—732no—
422#2353—732no—
423#2349—732no—
424#2347—732no—
425#2343—732no—
426#2337—731no—
427#2337—731no—
428#2336—731no—
429#2336D7311yescharacteristic, complemented
430#2329—732no—
431#2325—732no—
432#2320—732no—
433#2318—732no—
434#2285—731no—
435C2×#383—731no—
436C73#3440111yescharacteristic, complemented, Sylow
437#529—7316no—
438C2×#126—732no—
439C2×#125C2×D7311yescharacteristic
440C2×#124—731no—
441C2×#123—732no—
442C2×C22⋊Q8—731no—
443C2×#121—731no—
444C2×C4×Q8—731no—
445C2×C4×D4—732no—
446C2×C4×D4—731no—
447C2×C4×D4—732no—
448C2×C4×D4—732no—
449C2×#117—732no—
450C2×#117—731no—
451C2×#117—731no—
452C22×C42—731no—
453#391—732no—
454#391—732no—
455#389—732no—
456#389—732no—
457#389—732no—
458#389—732no—
459#389—732no—
460#389C2×D7312yes—
461#388—732no—
462#388—732no—
463#388—732no—
464#388—732no—
465#388—732no—
466#388—732no—
467#388—732no—
468#388—732no—
469#387—732no—
470#387—732no—
471#387—732no—
472#387—732no—
473#387—732no—
474#387—732no—
475#387—732no—
476#387—732no—
477#387C2×D7312yes—
478#387C2×D7312yes—
479#387C2×D7312yes—
480#387C2×D7312yes—
481#386—732no—
482#386—732no—
483#386—732no—
484#386—732no—
485#385—732no—
486#385—732no—
487#385—732no—
488#385—732no—
489#385—732no—
490#385—732no—
491#385—732no—
492#385—732no—
493#384—732no—
494#383—731no—
495#383—732no—
496#383—732no—
497#383—732no—
498#383—731no—
499#383—731no—
500#383C2×D7311yescharacteristic
501#382—732no—
502#382—732no—
503#381—732no—
504#380—732no—
505#380—732no—
506#380—732no—
507C4×C4⋊C4—732no—
508C4×C4⋊C4—732no—
509C4×C4⋊C4—731no—
510C4×C4⋊C4—731no—
511C4×C4⋊C4—731no—
512C4×C4⋊C4C2×D7311yescharacteristic
513C4×C4⋊C4C2×D7312yes—
514C4×C22⋊C4—732no—
515C4×C22⋊C4—732no—
516C4×C22⋊C4—732no—
517C4×C22⋊C4—732no—
518C4×C22⋊C4—732no—
519#376—732no—
520C2×#95—732no—
521C2×#95—732no—
522C2×#95—731no—
523C2×#95—731no—
524C2×#95—732no—
525C22×Q8—731no—
526C22×D4—731no—
527C22×D4—732no—
528C23×C4—732no—
529C23×C4—732no—
530C23×C4—732no—
531C23×C4—731no—
532C23×C4—731no—
533C23×C4—732no—
534C23×C4—732no—
535C23×C4—731no—
536#126—7316no—
537#125C4×D7318yescomplemented
538#124—738no—
539#123—7316no—
540C22⋊Q8—738no—
541#121—738no—
542C4×Q8—738no—
543C4×D4—2924no—
544C4×D4—2924no—
545C4×D4—738no—
546C4×D4—7316no—
547#117—2922no—
548#117—2922no—
549#117—7316no—
550C2×C4⋊C4—732no—
551C2×C4⋊C4—732no—
552C2×C4⋊C4—732no—
553C2×C4⋊C4—732no—
554C2×C4⋊C4—732no—
555C2×C4⋊C4—732no—
556C2×C4⋊C4—732no—
557C2×C4⋊C4—732no—
558C2×C4⋊C4—732no—
559C2×C4⋊C4—732no—
560C2×C4⋊C4—732no—
561C2×C4⋊C4C22×D7312yes—
562C2×C4⋊C4C22×D7312yes—
563C2×C4⋊C4C22×D7312yes—
564C2×C4⋊C4C22×D7312yes—
565C2×C4⋊C4C22×D7311yescharacteristic
566C2×C4⋊C4C22×D7312yes—
567C2×C4⋊C4C22×D7311yescharacteristic
568C2×C22⋊C4—732no—
569C2×C22⋊C4—732no—
570C2×C22⋊C4—732no—
571C2×C22⋊C4—732no—
572C2×C22⋊C4—732no—
573C2×C22⋊C4—732no—
574C2×C22⋊C4—732no—
575C2×C22⋊C4—732no—
576C2×C22⋊C4—732no—
577C2×C22⋊C4—732no—
578C2×C22⋊C4—732no—
579C2×C22⋊C4—732no—
580C2×C22⋊C4—732no—
581C2×C42—731no—
582C2×C42—731no—
583C2×C42—732no—
584C2×C42—732no—
585C2×C42—732no—
586C2×C42—732no—
587C2×C42—731no—
588C2×C42—732no—
589C2×C42—731no—
590C2×C42—731no—
591C2×C42—738no—
592C2×C42C22×D7311yescharacteristic
593C2×C42C22×D7311yescharacteristic
594C2×C42C22×D7312yes—
595C2×C42C22×D7312yes—
596C2×C42C22×D7311yescharacteristic
597#95—732no—
598#95—732no—
599#95—732no—
600#95—732no—
601#95—731no—
602#95—732no—
603#95—732no—
604#95—732no—
605#95—732no—
606#95—732no—
607#95—731no—
608#95—732no—
609#95—732no—
610#95—732no—
611#95—732no—
612#95—732no—
613#95—732no—
614#95—732no—
615#95—732no—
616#95—732no—
617#95—732no—
618#95C22×D7312yes—
619#95C22×D7311yescharacteristic
620#95C22×D7312yes—
621#95C22×D7311yescharacteristic
622#95C22×D7312yes—
623#95C22×D7312yes—
624#95C22×D7312yes—
625#95C22×D7312yes—
626#95C22×D7312yes—
627C24—731no—
628C24—732no—
629C2×Q8—2922no—
630C2×Q8—734no—
631C2×D4—2922no—
632C2×D4—734no—
633C2×D4—738no—
634C2×D4—1464no—
635C2×D4—1464no—
636C22×C4—2922no—
637C22×C4—2922no—
638C22×C4—2922no—
639C22×C4—2922no—
640C22×C4—2922no—
641C22×C4—2922no—
642C22×C4—2922no—
643C22×C4—2922no—
644C22×C4—2922no—
645C22×C4—2922no—
646C22×C4—2922no—
647C22×C4—2922no—
648C22×C4—2922no—
649C22×C4—2922no—
650C22×C4—734no—
651C22×C4—734no—
652C22×C4—738no—
653C22×C4—731no—
654C22×C4—732no—
655C22×C4—731no—
656C22×C4—731no—
657C22×C4—734no—
658C22×C4—732no—
659C22×C4—732no—
660C22×C4—732no—
661C22×C4—732no—
662C22×C4—1464no—
663C22×C4—1464no—
664C22×C4—1462no—
665C22×C4—1462no—
666C22×C4C23×D7312yes—
667C22×C4C23×D7312yes—
668C22×C4C23×D7312yes—
669C22×C4C23×D7312yes—
670C22×C4C23×D7311yescharacteristic
671C22×C4C23×D7311yescharacteristic
672C22×C4C23×D7312yes—
673C22×C4C23×D7312yes—
674C22×C4C23×D7311yescharacteristic
675C4⋊C4—42no—
676C4⋊C4—42no—
677C4⋊C4—42no—
678C4⋊C4—2922no—
679C4⋊C4—2922no—
680C4⋊C4—2922no—
681C4⋊C4—2922no—
682C4⋊C4—2922no—
683C4⋊C4—2922no—
684C4⋊C4—2922no—
685C4⋊C4—2922no—
686C4⋊C4—2922no—
687C4⋊C4—738no—
688C4⋊C4—738no—
689C4⋊C4C2×C4×D7318yes—
690C4⋊C4C2×C4×D7314yes—
691C4⋊C4C2×C4×D7318yes—
692C4⋊C4C2×C4×D7314yes—
693C22⋊C4—2922no—
694C22⋊C4—2922no—
695C22⋊C4—2922no—
696C22⋊C4—2922no—
697C22⋊C4—2922no—
698C22⋊C4—2922no—
699C22⋊C4—738no—
700C22⋊C4—738no—
701C22⋊C4—738no—
702C22⋊C4—738no—
703C22⋊C4—738no—
704C22⋊C4—1464no—
705C22⋊C4—1464no—
706C42—42no—
707C42—41no—
708C42—41no—
709C42—42no—
710C42—2922no—
711C42—2922no—
712C42—2922no—
713C42—2921no—
714C42—2921no—
715C42—2922no—
716C42—734no—
717C42—734no—
718C42—734no—
719C42—738no—
720C42C2×C4×D7314yes—
721C23—732no—
722C23—732no—
723C23—732no—
724C23—734no—
725C23—1462no—
726C23—1462no—
727C23—1462no—
728C23—1462no—
729C23—1462no—
730C23—1462no—
731C23—1462no—
732C23—1462no—
733C23C24×D7311yescharacteristic
734Q8—2924no—
735D4—2924no—
736D4—14616no—
737C2×C4—21no—
738C2×C4—22no—
739C2×C4—21no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—2928no—
758C2×C4—2924no—
759C2×C4—2924no—
760C2×C4—5844no—
761C2×C4—5844no—
762C2×C4—5844no—
763C2×C4—5844no—
764C2×C4—732no—
765C2×C4—732no—
766C2×C4—732no—
767C2×C4—734no—
768C2×C4—1468no—
769C2×C4—1462no—
770C2×C4—1462no—
771C2×C4—1462no—
772C2×C4—1462no—
773C2×C4—1462no—
774C2×C4—1462no—
775C2×C4—1462no—
776C2×C4—1462no—
777C2×C4—1462no—
778C2×C4—1462no—
779C2×C4—1462no—
780C2×C4—1462no—
781C2×C4—1461no—
782C2×C4—1461no—
783C2×C4—1462no—
784C2×C4—1462no—
785C2×C4—1462no—
786C2×C4—1462no—
787C2×C4C22×C4×D7312yes—
788C2×C4C22×C4×D7312yes—
789C2×C4C22×C4×D7312yes—
790C2×C4C22×C4×D7314yes—
791C2×C4C22×C4×D7314yes—
792C22—2922no—
793C22—2922no—
794C22—2922no—
795C22—2922no—
796C22—734no—
797C22—1464no—
798C22—1464no—
799C22—1464no—
800C22—1464no—
801C22—1462no—
802C22—1462no—
803C22—1464no—
804C22C23×C4×D7311yescharacteristic
805C22H(5,𝔽2)×D7311yescharacteristic
806C222−1+4×D7311yescharacteristic
807C22#1798942312yes—
808C22#1798942412yes—
809C4—22no—
810C4—24no—
811C4—24no—
812C4—22no—
813C4—22no—
814C4—42no—
815C4—42no—
816C4—42no—
817C4—42no—
818C4—2922no—
819C4—2922no—
820C4—2922no—
821C4—2922no—
822C4—1462no—
823C4—1462no—
824C4—1462no—
825C4—1464no—
826C2—2924no—
827C2—1464no—
828C2#520×D7311yescharacteristic
829C2#2262313011yescharacteristic
830C2#2262313311yescharacteristic
831C2#2262448412yes—
832C2#2262454412yes—
subgroupG/H
center, FrattiniC23C24×D73
commutatorC22×C73C24×C4
FittingC73×#2336C2
socle, cosocleC23×C73C25
prime radicalC2×#14556566C22
hypercenter#2336D73
hypocenterC73#34401
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ #2336

Complements

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

NH ≅ G/Ntype
2. #22613122C2semidirect
3. #22613121C2semidirect
4. #22612928C2semidirect
5. #22612916C2semidirect
6. #22612870C2semidirect
7. #22612840C2semidirect
8. #22612820C2semidirect
9. #22612790C2semidirect
10. #22612744C2semidirect
11. #22612741C2semidirect
12. #22612737C2semidirect
13. #22612660C2semidirect
15. #22612580C2semidirect
16. #22612563C2semidirect
17. #22612335C2semidirect
18. #383×D73C2semidirect
19. C73×#2336C2semidirect
20. #17989122C4semidirect
119. #14556586C2×C4semidirect
120. #14556579C2×C4semidirect
121. #14556576C2×C4semidirect
122. #14556571C2×C4semidirect
124. #14556556C2×C4semidirect
127. #14556553C2×C4semidirect
128. #14556553C2×C4semidirect
129. #14556549C2×C4semidirect
166. C42×D73C2×C4semidirect
188. #125×C73C2×C4semidirect
429. #2336D73semidirect
436. C73#34401semidirect
537. #125C4×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179891222
#226131222
#226131212
#226129282
#226129162
#226128702
#226128402
#226128202
#226127902
#226127442
#226127412
#226127372
#226126602
#226126302
#226125802
#226125632
#226123352
#383×D732
C73×#23362
#3440173