Finite Group Databasebeta

← #33249039

Subgroups — #33249039

Order 18688.

2090 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989122C211yesmaximal, characteristic
2#22613095C212yesmaximal, complemented
3#22613086C212yesmaximal
4#22613057C212yesmaximal, complemented
5#22613045C212yesmaximal, complemented
6#22612885C212yesmaximal, complemented
7#22612876C212yesmaximal, complemented
8#22612855C212yesmaximal, complemented
9#22612855C212yesmaximal, complemented
10#22612744C211yesmaximal, characteristic, complemented
11#22612741C211yesmaximal, characteristic, complemented
12#22612737C211yesmaximal, characteristic, complemented
13#22612724C212yesmaximal, complemented
14#22612720C212yesmaximal, complemented
15#22612553C212yesmaximal, complemented
16#22612537C212yesmaximal, complemented
17#22612335C211yesmaximal, characteristic, complemented
18#22612328C211yesmaximal, characteristic, complemented
19C73×#2336C211yesmaximal, characteristic, complemented
20#17989122C4116yescomplemented
21C2×#14556586C2212yes—
22C2×#14556579C2211yescharacteristic
23C2×#14556576C2212yes—
24C2×#14556571C2211yescharacteristic
25C2×#14556566C2211yescharacteristic
26C2×#14556556C2211yescharacteristic
27C2×#14556553C2211yescharacteristic
28C2×#14556553C2212yes—
29C2×#14556549C2212yes—
30C2×#14556548C2212yes—
31C2×#14556548C2211yescharacteristic
32C2×#14556548C2211yescharacteristic
33C2×C4⋊C4×D73C2212yes—
34C2×C42×D73C2211yescharacteristic
35#17988491C2212yes—
36#17988491C2212yes—
37#17988489C2212yes—
38#17988488C2212yes—
39#17988486C2212yes—
40#17988485C2212yes—
41#17988483C2212yes—
42#17988479C2212yes—
43#17988479C2212yes—
44#17988479C2212yes—
45#17988478C2212yes—
46#17988478C2212yes—
47#17988478C2212yes—
48#17988477C2212yes—
49#17988477C2212yes—
50#17988477C2212yes—
51#17988476C2212yes—
52#17988476C2212yes—
53#17988476C2212yes—
54#17988474C2212yes—
55#17988473C2212yes—
56#17988473C2212yes—
57#17988473C2212yes—
58#17988473C2212yes—
59#17988472C2212yes—
60#17988470C2212yes—
61#17988468C2212yes—
62#17988465C2212yes—
63#17988465C2212yes—
64#17988465C2212yes—
65#17988465C2212yes—
66#17988461C2212yes—
67#17988461C2212yes—
68#17988458C2212yes—
69#17988458C2212yes—
70#17988456C2212yes—
71#17988456C2212yes—
72#17988455C2211yescharacteristic
73#17988451C2211yescharacteristic
74#17988451C2211yescharacteristic
75#17988451C2212yes—
76#17988451C2212yes—
77#17988449C2212yes—
78#17988446C2212yes—
79#17988446C2212yes—
80#17988446C2212yes—
81#17988446C2212yes—
82#17988444C2212yes—
83C4⋊C4×Dic73C2212yes—
84C4×#11924007C2211yescharacteristic
85C4×#11924007C2212yes—
86C4×#11924007C2212yes—
87C4×#11924007C2211yescharacteristic
88C4×C4⋊Dic73C2211yescharacteristic
89#17988438C2212yes—
90#17988438C2212yes—
91#17988438C2212yes—
92C4×#11924005C2212yes—
93C4×#11924005C2212yes—
94#17988434C2212yes—
95#17988434C2212yes—
96#17988434C2211yescharacteristic
97#17988434C2211yescharacteristic
98#17988432C2212yes—
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×D292C2311yescharacteristic
110C22×D292C2312yes—
111C22×C4×D73C2311yescharacteristic
112C22×C4×D73C2312yes—
113C22×C4×D73C2312yes—
114C22×C4×D73C2312yes—
115C22×C4×D73C2311yescharacteristic
116C22×C4×D73C2311yescharacteristic
117#14556586C2×C4116yescomplemented
118#14556579C2×C418yes—
119#14556576C2×C4116yescomplemented
120#14556571C2×C418yescomplemented
121#14556566C2×C418yes—
122#14556556C2×C418yescomplemented
123#14556553C2×C418yes—
124#14556553C2×C4116yescomplemented
125#14556549C2×C4116yescomplemented
126#14556548—42no—
127#14556548—44no—
128#14556548—42no—
129C2×C4⋊Dic73C2312yes—
130C2×C4⋊Dic73C2312yes—
131C2×C4⋊Dic73C2312yes—
132C2×C4⋊Dic73C2312yes—
133C2×#11924007C2312yes—
134C2×#11924007C2312yes—
135C2×#11924007C2312yes—
136C2×#11924007C2312yes—
137C2×#11924007C2312yes—
138C2×#11924007C2312yes—
139C2×#11924007C2312yes—
140C2×#11924007C2312yes—
141C2×#11924007C2312yes—
142C4⋊C4×D73—44no—
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×#11924005C2312yes—
157C2×#11924005C2312yes—
158C2×C4×Dic73C2312yes—
159C2×C4×Dic73C2312yes—
160C2×C4×Dic73C2311yescharacteristic
161C2×C4×Dic73C2312yes—
162C2×C4×Dic73C2312yes—
163C2×C4×Dic73C2312yes—
164C2×C4×Dic73C2312yes—
165C2×C4×Dic73C2311yescharacteristic
166C2×C4×Dic73C2311yescharacteristic
167C2×C4×Dic73C2311yescharacteristic
168C2×C4×Dic73C2312yes—
169C2×C4×Dic73C2311yescharacteristic
170C42×D73C2×C418yescomplemented
171#14556498C2312yes—
172#14556498C2312yes—
173#14556498C2312yes—
174#14556498C2312yes—
175#14556498C2311yescharacteristic
176#14556498C2311yescharacteristic
177#14556498C2312yes—
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×C73C2311yescharacteristic
205#95×C73C2312yes—
206#95×C73C2311yescharacteristic
207#95×C73C2312yes—
208#95×C73C2312yes—
209#95×C73C2312yes—
210C23×D73C2411yescharacteristic
211C23×D73C2412yes—
212C2×Dic146—42no—
213C2×Dic146C22×C414yes—
214C2×D292—42no—
215C2×D292—42no—
216C2×D292—42no—
217C2×D292C22×C414yes—
218C2×D292C22×C418yes—
219C22×Dic73C2412yes—
220C22×Dic73C2412yes—
221C22×Dic73C2412yes—
222C22×Dic73C2412yes—
223C22×Dic73C2411yescharacteristic
224C22×Dic73C2412yes—
225C22×Dic73C2411yescharacteristic
226C22×Dic73C2411yescharacteristic
227C2×C4×D73—24no—
228C2×C4×D73—22no—
229C2×C4×D73—22no—
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×D73C22×C414yes—
240C2×C4×D73C22×C418yes—
241C2×C4×D73C22×C414yes—
242C2×C4×D73C22×C414yes—
243C4⋊Dic73—42no—
244C4⋊Dic73—42no—
245C4⋊Dic73—42no—
246C4⋊Dic73C22×C418yes—
247#11924007—24no—
248#11924007—24no—
249#11924007—24no—
250#11924007—24no—
251#11924007—42no—
252#11924007—42no—
253#11924007—42no—
254#11924007—42no—
255#11924007C22×C418yes—
256#11924005—42no—
257#11924005—42no—
258#11924005—42no—
259#11924005—42no—
260#11924005—42no—
261#11924005—42no—
262#11924005—42no—
263#11924005—42no—
264#11924005—42no—
265#11924005—42no—
266#11924005C22×C418yes—
267#11924005C22×C418yes—
268#11924005C22×C418yes—
269#11924005C22×C418yes—
270#11924005C22×C418yes—
271C4×Dic73—42no—
272C4×Dic73—42no—
273C4×Dic73—42no—
274C4×Dic73—42no—
275C4×Dic73—42no—
276C4×Dic73—41no—
277C4×Dic73—42no—
278C4×Dic73—41no—
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—21no—
306C22×D73—22no—
307C22×D73—21no—
308C22×D73—22no—
309C22×D73—22no—
310C22×D73—22no—
311C22×D73—22no—
312C22×D73—22no—
313C22×D73—22no—
314C22×D73—22no—
315C22×D73C23×C414yes—
316C22×D73C23×C412yes—
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—22no—
343C2×Dic73—22no—
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×Dic73C23×C412yes—
359C2×Dic73C23×C412yes—
360C2×Dic73C23×C414yes—
361C2×Dic73C23×C412yes—
362C2×Dic73H(5,𝔽2)12yes—
363C2×Dic732−1+412yes—
364D292—44no—
365D292—48no—
366C4×D73—216no—
367C4×D73—28no—
368C4×D73—44no—
369C4×D73—44no—
370C4×D73—84no—
371C4×D73—84no—
372Dic146—44no—
373C22×C73C24×C411yescharacteristic
374C22×C73C2×H(5,𝔽2)11yescharacteristic
375C22×C73C2×2−1+411yescharacteristic
376C22×C73#58512yes—
377C22×C73#58512yes—
378C2×D73—22no—
379C2×D73—24no—
380C2×D73—22no—
381C2×D73—22no—
382C2×D73—24no—
383C2×D73—24no—
384C2×D73—42no—
385C2×D73—42no—
386C2×D73—42no—
387C2×D73—42no—
388C2×D73—42no—
389C2×D73—42no—
390C4×C73—22no—
391C4×C73—24no—
392C4×C73—22no—
393C4×C73—22no—
394C4×C73—24no—
395C4×C73—42no—
396C4×C73—42no—
397C4×C73—42no—
398C4×C73—42no—
399Dic73—24no—
400Dic73—22no—
401Dic73—22no—
402Dic73—42no—
403Dic73—42no—
404Dic73—42no—
405Dic73—42no—
406Dic73#52014yes—
407#34385—731nomaximal, Sylow
408C2×C73C2×#52011yescharacteristic
409C2×C73#342811yescharacteristic
410C2×C73#342811yescharacteristic
411C2×C73#356212yes—
412C2×C73#356512yes—
413D73—42no—
414D73—44no—
415C2×#529—731no—
416#2378—732no—
417#2377—732no—
418#2373—732no—
419#2373—732no—
420#2355—732no—
421#2354—732no—
422#2352—732no—
423#2352—732no—
424#2337—731no—
425#2337—731no—
426#2336—731no—
427#2336D7311yescharacteristic, complemented
428#2335—732no—
429#2335—732no—
430#2317—732no—
431#2314—732no—
432#2285—731no—
433#2283—731no—
434C73#3438511yescharacteristic, complemented, Sylow
435#529—7316no—
436C2×#126—732no—
437C2×#125C2×D7311yescharacteristic
438C2×#124—731no—
439C2×#123—732no—
440C2×C22⋊Q8—731no—
441C2×#121—731no—
442C2×C4×Q8—731no—
443C2×C4×D4—731no—
444C2×C4×D4—732no—
445C2×#117—732no—
446C2×#117—732no—
447C2×#117—731no—
448C2×#117—731no—
449C22×C4⋊C4—732no—
450C22×C42—731no—
451#391—732no—
452#391—732no—
453#390—732no—
454#390—732no—
455#389—732no—
456#389—732no—
457#389—732no—
458#389C2×D7312yes—
459#388—732no—
460#388—732no—
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#388—732no—
470#388—732no—
471#387—732no—
472#387—732no—
473#387—732no—
474#387—732no—
475#387—732no—
476#387—732no—
477#387—732no—
478#387—732no—
479#387C2×D7312yes—
480#387C2×D7312yes—
481#387C2×D7312yes—
482#387C2×D7312yes—
483#386—732no—
484#386—732no—
485#386—732no—
486#386—732no—
487#385—732no—
488#385—732no—
489#385—732no—
490#385—732no—
491#384—732no—
492#384—732no—
493#383—731no—
494#383C2×D7311yescharacteristic
495#382—731no—
496#382—731no—
497#382—732no—
498#382—732no—
499#381—732no—
500#380—732no—
501#380—732no—
502#380—732no—
503#380—732no—
504#380—732no—
505C4×C4⋊C4—732no—
506C4×C4⋊C4—732no—
507C4×C4⋊C4—732no—
508C4×C4⋊C4—731no—
509C4×C4⋊C4—731no—
510C4×C4⋊C4—731no—
511C4×C4⋊C4—732no—
512C4×C4⋊C4—732no—
513C4×C4⋊C4—732no—
514C4×C4⋊C4C2×D7311yescharacteristic
515C4×C4⋊C4C2×D7312yes—
516C4×C22⋊C4—732no—
517C4×C22⋊C4—732no—
518C4×C22⋊C4—731no—
519C4×C22⋊C4—731no—
520C4×C22⋊C4—732no—
521C4×C22⋊C4—732no—
522#376—732no—
523C22×Q8—731no—
524C22×D4—732no—
525C22×D4—731no—
526C23×C4—732no—
527C23×C4—732no—
528C23×C4—731no—
529C23×C4—731no—
530C23×C4—732no—
531C23×C4—731no—
532#126—7316no—
533#125C4×D7318yescomplemented
534#124—738no—
535#123—7316no—
536C22⋊Q8—738no—
537#121—738no—
538C4×Q8—738no—
539C4×D4—738no—
540C4×D4—7316no—
541#117—2922no—
542#117—2924no—
543#117—2922no—
544#117—7316no—
545C2×C4⋊C4—2924no—
546C2×C4⋊C4—732no—
547C2×C4⋊C4—732no—
548C2×C4⋊C4—732no—
549C2×C4⋊C4—732no—
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⋊C4C22×D7312yes—
560C2×C4⋊C4C22×D7312yes—
561C2×C4⋊C4C22×D7312yes—
562C2×C4⋊C4C22×D7312yes—
563C2×C4⋊C4C22×D7311yescharacteristic
564C2×C4⋊C4C22×D7312yes—
565C2×C4⋊C4C22×D7311yescharacteristic
566C2×C22⋊C4—732no—
567C2×C22⋊C4—732no—
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—732no—
583C2×C42—731no—
584C2×C42—732no—
585C2×C42—732no—
586C2×C42—732no—
587C2×C42—732no—
588C2×C42—732no—
589C2×C42—731no—
590C2×C42—732no—
591C2×C42—731no—
592C2×C42—731no—
593C2×C42—738no—
594C2×C42C22×D7311yescharacteristic
595C2×C42C22×D7312yes—
596C2×C42C22×D7311yescharacteristic
597C2×C42C22×D7312yes—
598C2×C42C22×D7311yescharacteristic
599#95—732no—
600#95—732no—
601#95—732no—
602#95—732no—
603#95—732no—
604#95—732no—
605#95—731no—
606#95—731no—
607#95—732no—
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#95C22×D7312yes—
617#95C22×D7312yes—
618#95C22×D7311yescharacteristic
619#95C22×D7311yescharacteristic
620#95C22×D7312yes—
621#95C22×D7312yes—
622#95C22×D7312yes—
623#95C22×D7312yes—
624#95C22×D7312yes—
625C24—732no—
626C24—731no—
627C2×Q8—2922no—
628C2×Q8—734no—
629C2×D4—2922no—
630C2×D4—2922no—
631C2×D4—2922no—
632C2×D4—738no—
633C2×D4—734no—
634C22×C4—2922no—
635C22×C4—2922no—
636C22×C4—2922no—
637C22×C4—2922no—
638C22×C4—2922no—
639C22×C4—2922no—
640C22×C4—2922no—
641C22×C4—2922no—
642C22×C4—734no—
643C22×C4—734no—
644C22×C4—731no—
645C22×C4—731no—
646C22×C4—732no—
647C22×C4—731no—
648C22×C4—734no—
649C22×C4—738no—
650C22×C4—732no—
651C22×C4—732no—
652C22×C4—732no—
653C22×C4—732no—
654C22×C4—1464no—
655C22×C4—1462no—
656C22×C4—1464no—
657C22×C4—1462no—
658C22×C4C23×D7312yes—
659C22×C4C23×D7312yes—
660C22×C4C23×D7312yes—
661C22×C4C23×D7312yes—
662C22×C4C23×D7311yescharacteristic
663C22×C4C23×D7311yescharacteristic
664C22×C4C23×D7312yes—
665C22×C4C23×D7312yes—
666C22×C4C23×D7311yescharacteristic
667C4⋊C4—42no—
668C4⋊C4—42no—
669C4⋊C4—42no—
670C4⋊C4—2922no—
671C4⋊C4—2922no—
672C4⋊C4—2922no—
673C4⋊C4—2922no—
674C4⋊C4—2922no—
675C4⋊C4—2922no—
676C4⋊C4—2922no—
677C4⋊C4—738no—
678C4⋊C4—738no—
679C4⋊C4—1464no—
680C4⋊C4—1464no—
681C4⋊C4—1464no—
682C4⋊C4—1464no—
683C4⋊C4C2×C4×D7318yes—
684C4⋊C4C2×C4×D7314yes—
685C4⋊C4C2×C4×D7318yes—
686C4⋊C4C2×C4×D7314yes—
687C22⋊C4—2922no—
688C22⋊C4—2922no—
689C22⋊C4—2922no—
690C22⋊C4—2922no—
691C22⋊C4—2922no—
692C22⋊C4—2922no—
693C22⋊C4—2922no—
694C22⋊C4—2922no—
695C22⋊C4—2922no—
696C22⋊C4—2922no—
697C22⋊C4—738no—
698C22⋊C4—738no—
699C22⋊C4—738no—
700C22⋊C4—738no—
701C22⋊C4—738no—
702C42—42no—
703C42—41no—
704C42—41no—
705C42—42no—
706C42—2922no—
707C42—2922no—
708C42—2922no—
709C42—2922no—
710C42—2922no—
711C42—2921no—
712C42—2921no—
713C42—2922no—
714C42—734no—
715C42—734no—
716C42—734no—
717C42—738no—
718C42C2×C4×D7314yes—
719C23—734no—
720C23—732no—
721C23—1461no—
722C23—1462no—
723C23—1462no—
724C23—1461no—
725C23—1462no—
726C23—1462no—
727C23—1462no—
728C23—1462no—
729C23—1462no—
730C23—1462no—
731C23C24×D7311yescharacteristic
732Q8—2924no—
733D4—2928no—
734D4—2924no—
735C2×C4—21no—
736C2×C4—22no—
737C2×C4—21no—
738C2×C4—22no—
739C2×C4—22no—
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—2924no—
756C2×C4—2924no—
757C2×C4—5844no—
758C2×C4—5844no—
759C2×C4—732no—
760C2×C4—732no—
761C2×C4—732no—
762C2×C4—732no—
763C2×C4—732no—
764C2×C4—734no—
765C2×C4—1468no—
766C2×C4—14616no—
767C2×C4—1462no—
768C2×C4—1462no—
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—1462no—
782C2×C4—1462no—
783C2×C4C22×C4×D7312yes—
784C2×C4C22×C4×D7312yes—
785C2×C4C22×C4×D7312yes—
786C2×C4C22×C4×D7314yes—
787C2×C4C22×C4×D7314yes—
788C22—2922no—
789C22—2922no—
790C22—2922no—
791C22—2922no—
792C22—2922no—
793C22—2922no—
794C22—1464no—
795C22—1462no—
796C22—1462no—
797C22—1464no—
798C22—1462no—
799C22—1464no—
800C22C23×C4×D7311yescharacteristic
801C22H(5,𝔽2)×D7311yescharacteristic
802C222−1+4×D7311yescharacteristic
803C22#1798942312yes—
804C22#1798942412yes—
805C4—22no—
806C4—24no—
807C4—22no—
808C4—24no—
809C4—22no—
810C4—42no—
811C4—42no—
812C4—42no—
813C4—42no—
814C4—2922no—
815C4—2922no—
816C4—2922no—
817C4—2922no—
818C4—734no—
819C4—1462no—
820C4—1462no—
821C4—1464no—
822C2—2924no—
823C2—2922no—
824C2#520×D7311yescharacteristic
825C2#2262313011yescharacteristic
826C2#2262313311yescharacteristic
827C2#2262451412yes—
828C2#2262457112yes—
subgroupG/H
center, FrattiniC23C24×D73
commutatorC22×C73C24×C4
FittingC73×#2336C2
socle, cosocleC23×C73C25
prime radicalC2×#14556566C22
hypercenter#2336D73
hypocenterC73#34385
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ #2336

Complements

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

NH ≅ G/Ntype
2. #22613095C2semidirect
4. #22613057C2semidirect
5. #22613045C2semidirect
6. #22612885C2semidirect
7. #22612876C2semidirect
8. #22612855C2semidirect
9. #22612855C2semidirect
10. #22612744C2semidirect
11. #22612741C2semidirect
12. #22612737C2semidirect
13. #22612724C2semidirect
14. #22612720C2semidirect
15. #22612553C2semidirect
16. #22612537C2semidirect
17. #22612335C2semidirect
18. #22612328C2semidirect
19. C73×#2336C2semidirect
20. #17989122C4semidirect
117. #14556586C2×C4semidirect
119. #14556576C2×C4semidirect
120. #14556571C2×C4semidirect
122. #14556556C2×C4semidirect
124. #14556553C2×C4semidirect
125. #14556549C2×C4semidirect
170. C42×D73C2×C4semidirect
188. #125×C73C2×C4semidirect
427. #2336D73semidirect
434. C73#34385semidirect
533. #125C4×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179891222
#226130952
#226130862
#226130572
#226130452
#226128852
#226128762
#226128552
#226127442
#226127412
#226127372
#226127242
#226127202
#226125532
#226125372
#226123352
#226123282
C73×#23362
#3438573