Finite Group Databasebeta

← #33994215

Subgroups — #33994215

Order 18688.

7094 conjugacy classes of subgroups.

The subgroup lattice has 944 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22624021C214yesmaximal, complemented
2#22624010C214yesmaximal, complemented
3#22623926C214yesmaximal, complemented
4#22623916C214yesmaximal, complemented
5#22623789C216yesmaximal, complemented
6#22623737C211yesmaximal, characteristic, complemented
7#22623698C211yesmaximal, characteristic, complemented
8#22623634C216yesmaximal, complemented
9#22623583C211yesmaximal, characteristic, complemented
10#22623579C211yesmaximal, characteristic, complemented
11#22623553C214yesmaximal, complemented
12#22623548C214yesmaximal, complemented
13#22623529C214yesmaximal, complemented
14Q8×#11924028C214yesmaximal, complemented
15#22623358C216yesmaximal, complemented
16#22623224C216yesmaximal, complemented
17C4×#14556639C211yesmaximal, characteristic, complemented
18C2×C4×Q8×D73C211yesmaximal, characteristic, complemented
19C4×2−1+4×C73C211yesmaximal, characteristic, complemented
20C2×#14556639C2211yescharacteristic
21C22×Q8×D73C2211yescharacteristic
22#17989320C22112yescomplemented
23Q8×Dic146C2214yescomplemented
24#17989316C2214yescomplemented
25#17989315C22112yescomplemented
26#17989313C2214yescomplemented
27#17989313C2214yescomplemented
28#17989309C22112yescomplemented
29#17989307C22112yescomplemented
30#17989305C22112yescomplemented
31#17989297C22112yes—
32#17989292C22112yes—
33#17989292C22112yescomplemented
34#17989287C22112yes—
35#17989281C22112yes—
36#17989278C22112yes—
37#17989276C22112yes—
38#17989276C22112yescomplemented
39#17989272C22112yescomplemented
40#17989256C2214yescomplemented
41Q8×D292C2214yes—
42Q8×D292C2214yes—
43Q8×C22⋊D73C2214yes—
44Q8×C22⋊D73C2214yes—
45Q8×C22⋊D73C2214yescomplemented
46#17989249C2214yes—
47#17989249C2214yes—
48#17989248C2214yescomplemented
49#17989244C2214yes—
50#17989244C2214yes—
51#17989244C2214yescomplemented
52#17989242C22112yes—
53#17989238C22112yes—
54#17989215C2216yes—
55#17989208C22112yescomplemented
56#17989202C22112yescomplemented
57#17989199C22112yescomplemented
58#17989195C22112yescomplemented
59#17989179C22124yes—
60#17989165C2216yes—
61#17989163C2216yes—
62#17989158C2216yes—
63#17989144C22112yescomplemented
64#17989141C2216yes—
65#17989141C2216yes—
66#17989141C22112yescomplemented
67#17989140C2216yes—
68#17989134C2216yes—
69#17989134C2216yes—
70#17989133C2216yes—
71#17989124C2216yes—
72#17989124C2216yes—
73#17989121C22112yescomplemented
74#17989119C2216yes—
75#17989119C2216yes—
76#17989119C22112yescomplemented
77#17989117C22112yes—
78#17989117C22112yes—
79#17989115C22112yes—
80#17989115C22112yes—
81#17989099C2216yes—
82#17989096C22112yes—
83#17989096C2214yes—
84#17989094C2216yes—
85#17989069C2214yescomplemented
86#17989068C2216yes—
87#17989065C2211yescharacteristic
88#17989063C2214yescomplemented
89C4×#11924029C2214yescomplemented
90C4×#11924028C22112yes—
91C4×#11924028C22112yes—
92C4×#11924028C2216yes—
93C2×Q8×Dic73C2211yescharacteristic
94C2×C4×Dic146C2213yes—
95C2×#14556556C2213yes—
96C4×Q8×D73C2214yes—
97C4×Q8×D73C2214yes—
98C4×Q8×D73C2214yes—
99C4×Q8×D73C2214yes—
100C4×Q8×D73C2214yescomplemented
101C2×C4⋊C4×D73C2213yes—
102C2×C42×D73C2213yes—
103C2×2−1+4×C73C2211yescharacteristic
104#520×C73C2216yes—
105#520×C73C2214yescomplemented
106#519×C73C2211yescharacteristic
107#519×C73C2214yescomplemented
108C4×#41×C73C2216yes—
109C4×#41×C73C2214yescomplemented
110C2×C4×Q8×C73C2211yescharacteristic
111C2×C4×Q8×C73C2214yescomplemented
112#14556639—28no—
113C2×#11924029C2314yes—
114C2×#11924028C2316yes—
115C2×#11924028C2314yes—
116C2×#11924028C23112yes—
117C22×Dic146C2313yes—
118C2×Q8×D73—28no—
119C2×Q8×D73C2314yes—
120C2×Q8×D73C2314yes—
121C2×Q8×D73C2314yes—
122C22×C4×D73C2313yes—
123C22×C4×D73C2311yescharacteristic
124C22×C4×D73C2313yes—
125#14556591C23112yes—
126#14556591C23112yes—
127#14556590C2316yes—
128#14556590C2316yes—
129#14556590C23112yes—
130#14556589C2316yes—
131#14556589C23112yes—
132#14556587C2316yes—
133#14556586C23112yes—
134#14556586C23112yes—
135#14556585C23124yes—
136#14556584C23124yes—
137#14556584C23112yes—
138#14556584C23112yes—
139#14556583C23112yes—
140#14556583C23124yes—
141#14556582C2316yes—
142#14556582C2316yes—
143#14556582C23112yes—
144#14556581C23112yes—
145#14556581C23112yes—
146#14556581C23124yes—
147#14556580C2316yes—
148#14556579C23112yes—
149#14556578C2316yes—
150#14556578C23112yes—
151#14556577C23112yes—
152#14556577C23112yes—
153#14556576C2314yes—
154#14556576C23112yes—
155#14556575C23112yes—
156#14556574C23124yes—
157#14556573C23124yes—
158#14556573C23112yes—
159#14556573C2314yes—
160#14556572C23112yes—
161#14556571C2316yes—
162#14556571C2316yes—
163#14556571C23112yes—
164#14556571C23112yes—
165#14556570C23112yes—
166#14556570C23112yes—
167#14556570C23112yes—
168#14556570C23124yes—
169#14556569C2314yes—
170#14556569C23112yes—
171#14556569C23124yes—
172#14556568C2314yes—
173#14556568C23112yes—
174#14556567C2316yes—
175#14556567C2316yes—
176#14556567C23112yes—
177#14556566C2316yes—
178#14556566C2316yes—
179#14556565C23112yes—
180#14556564C2314yes—
181#14556564C23112yes—
182#14556563C2314yes—
183#14556563C23112yes—
184#14556562C2316yes—
185#14556562C2316yes—
186#14556562C23112yes—
187#14556561C2314yes—
188#14556559C2314yes—
189Q8×Dic73C2314yes—
190Q8×Dic73C2314yes—
191Q8×Dic73C2314yes—
192Q8×Dic73C2314yes—
193C4×Dic146C23112yes—
194C4×Dic146C23112yes—
195C4×Dic146C23112yes—
196C4×Dic146C23112yes—
197C4×Dic146C2316yes—
198C4×Dic146C2316yes—
199C4×Dic146C23112yes—
200C4×Dic146C23112yes—
201#14556556C23112yes—
202#14556556C23112yes—
203#14556556C23112yes—
204C4×D292C2316yes—
205C4×D292C2314yes—
206C4×D292C2316yes—
207C4×D292C23112yes—
208C4×D292C23112yes—
209C4×D292C23112yes—
210#14556553C23112yes—
211C4×C22⋊D73C23112yes—
212C4×C22⋊D73C23112yes—
213C4×C22⋊D73C23112yes—
214C4×C22⋊D73C23112yes—
215C4×C22⋊D73C23112yes—
216C4×C22⋊D73C23112yes—
217C4×C22⋊D73C23112yes—
218C4×C22⋊D73C23112yes—
219C4×C22⋊D73C2314yes—
220C4×C22⋊D73C2314yes—
221#14556550C2316yes—
222#14556550C23112yes—
223#14556550C23112yes—
224#14556549C23112yes—
225#14556548C23112yes—
226#14556548C23112yes—
227#14556548C2314yes—
228#14556548C23112yes—
229#14556548C23112yes—
230C2×C4⋊Dic73C2313yes—
231C2×#11924007C2316yes—
232C4⋊C4×D73C23112yes—
233C4⋊C4×D73C23112yes—
234C4⋊C4×D73C23112yes—
235C2×C4×Dic73C2313yes—
236C2×C4×Dic73C2313yes—
237C2×C4×Dic73C2313yes—
238C42×D73C2316yes—
239C42×D73C2316yes—
240C42×D73C2316yes—
241C42×D73C2316yes—
242C42×D73C23112yes—
2432−1+4×C73—28no—
244C2×#41×C73C2316yes—
245C2×#41×C73C2314yes—
246C22×Q8×C73C2314yes—
247C22×Q8×C73C2311yescharacteristic
248C4×Q8×C73C2316yes—
249C4×Q8×C73C2316yes—
250C4×Q8×C73C2314yes—
251C4×Q8×C73C2314yes—
252C4×Q8×C73C2314yes—
253C4×Q8×C73C2314yes—
254C4×Q8×C73C23112yes—
255C4×D4×C73C2316yes—
256C4×D4×C73C2316yes—
257C4×D4×C73C23112yes—
258C4×D4×C73C23112yes—
259C4×D4×C73C2314yes—
260#117×C73C2316yes—
261#117×C73C23112yes—
262#117×C73C23112yes—
263C2×C4⋊C4×C73C23112yes—
264C2×C4⋊C4×C73C2313yes—
265C2×C42×C73C23112yes—
266C2×C42×C73C2313yes—
267C23×D73C2411yescharacteristic
268#11924029—216no—
269#11924028—224no—
270#11924028—216no—
271#11924028—424no—
272C2×Dic146—212no—
273C2×Dic146C24112yes—
274C2×Dic146C2416yes—
275C2×Dic146C2414yes—
276C2×Dic146C24112yes—
277Q8×D73—216no—
278Q8×D73—216no—
279Q8×D73—216no—
280C2×D292C2416yes—
281C2×D292C2414yes—
282C2×D292C2414yes—
283C2×C22⋊D73C2414yes—
284C2×C22⋊D73C2414yes—
285C2×C22⋊D73C2414yes—
286C2×C22⋊D73C2414yes—
287C2×C22⋊D73C24112yes—
288C22×Dic73C2411yescharacteristic
289C22×Dic73C2413yes—
290C22×Dic73C2413yes—
291C2×C4×D73—212no—
292C2×C4×D73—24no—
293C2×C4×D73—46no—
294C2×C4×D73C2411yescharacteristic
295C2×C4×D73C2411yescharacteristic
296C2×C4×D73C2411yescharacteristic
297C2×C4×D73C2414yes—
298C2×C4×D73C2416yes—
299C2×C4×D73C2416yes—
300C2×C4×D73C2416yes—
301C2×C4×D73C24112yes—
302C2×C4×D73C2416yes—
303C2×C4×D73C24112yes—
304C2×C4×D73C2411yescharacteristic
305C4⋊Dic73C24112yes—
306C4⋊Dic73C2416yes—
307C4⋊Dic73C2416yes—
308C4⋊Dic73C2414yes—
309C4⋊Dic73C24112yes—
310C4⋊Dic73C24112yes—
311C4⋊Dic73C24112yes—
312#11924007C24124yes—
313#11924007C24112yes—
314#11924007C2414yes—
315#11924007C2414yes—
316#11924007C2414yes—
317#11924007C2414yes—
318#11924007C24112yes—
319#11924007C24112yes—
320#11924007C24112yes—
321#11924007C24112yes—
322#11924007C24112yes—
323C22⋊Dic73C2414yes—
324C22⋊Dic73C2414yes—
325C22⋊Dic73C24112yes—
326C22⋊Dic73C24112yes—
327C22⋊Dic73C24112yes—
328#11924005C2414yes—
329#11924005C2414yes—
330#11924005C2414yes—
331#11924005C2414yes—
332#11924005C24112yes—
333#11924005C2414yes—
334#11924005C2414yes—
335#11924005C24112yes—
336#11924005C24112yes—
337#11924005C24112yes—
338C4×Dic73C2414yes—
339C4×Dic73C2416yes—
340C4×Dic73C2416yes—
341C4×Dic73C2416yes—
342C4×Dic73C2416yes—
343C4×Dic73C2416yes—
344C4×Dic73C2416yes—
345C4×Dic73C24112yes—
346C4×Dic73C24112yes—
347#41×C73—216no—
348#41×C73—224no—
349C2×Q8×C73—216no—
350C2×Q8×C73#4118yescomplemented
351C2×Q8×C73C2416yes—
352C2×Q8×C73C2414yes—
353C2×D4×C73C2414yes—
354C2×D4×C73C2416yes—
355C22×C4×C73C2411yescharacteristic
356C22×C4×C73C2414yes—
357C22×C4×C73C24112yes—
358C22×C4×C73C2413yes—
359C22×C4×C73C24112yes—
360C22×C4×C73C2413yes—
361C4⋊C4×C73C24112yes—
362C4⋊C4×C73C2416yes—
363C4⋊C4×C73C24112yes—
364C4⋊C4×C73C2416yes—
365C4⋊C4×C73C2414yes—
366C22⋊C4×C73C2414yes—
367C22⋊C4×C73C24112yes—
368C22⋊C4×C73C2414yes—
369C42×C73C2416yes—
370C42×C73C2414yes—
371C42×C73C2416yes—
372C42×C73C24112yes—
373C42×C73C24112yes—
374C23×C73C2514yes—
375C23×C73C2511yescharacteristic
376C22×D73—22no—
377C22×D73—22no—
378C22×D73—22no—
379C22×D73C2514yes—
380C22×D73C2511yescharacteristic
381C22×D73C2511yescharacteristic
382Q8×C73—212no—
383Q8×C73C2×#41116yes—
384D4×C73—28no—
385D4×C73—212no—
386C2×C4×C73—224no—
387C2×C4×C73—22no—
388C2×C4×C73—28no—
389C2×C4×C73—43no—
390C2×C4×C73—412no—
391C2×C4×C73C2×#41112yes—
392C2×C4×C73C2511yescharacteristic
393C2×C4×C73C2514yes—
394C2×C4×C73C2516yes—
395C2×C4×C73C2514yes—
396C2×C4×C73C2514yes—
397C2×C4×C73C2516yes—
398C2×C4×C73C2511yescharacteristic
399C22⋊D73—28no—
400C22⋊D73—28no—
401C22⋊D73—28no—
402C22⋊D73—28no—
403C22⋊D73—412no—
404C2×Dic73—26no—
405C2×Dic73—22no—
406C2×Dic73—43no—
407C2×Dic73C2511yescharacteristic
408C2×Dic73C2514yes—
409C2×Dic73C2516yes—
410C2×Dic73C2514yes—
411C2×Dic73C2514yes—
412C2×Dic73C2516yes—
413C2×Dic73C2511yescharacteristic
414D292—28no—
415D292—28no—
416D292—212no—
417C4×D73—22no—
418C4×D73—212no—
419C4×D73—212no—
420C4×D73—212no—
421C4×D73—224no—
422C4×D73—22no—
423C4×D73—28no—
424C4×D73—22no—
425C4×D73—46no—
426C4×D73—412no—
427C4×D732−1+414yescomplemented
428Dic146—224no—
429Dic146—212no—
430Dic146—28no—
431Dic146—412no—
432C22×C73—21no—
433C22×C73—21no—
434C22×C73—24no—
435C22×C73—24no—
436C22×C73—24no—
437C22×C73C22×#4112yes—
438C22×C73C2611yescharacteristic
439C2×D73—28no—
440C2×D73—21no—
441C2×D73—21no—
442C2×D73—21no—
443C2×D73—21no—
444C2×D73—24no—
445C2×D73—24no—
446C2×D73—24no—
447C2×D73C2×2−1+412yes—
448C2×D73#58512yes—
449C4×C73—24no—
450C4×C73—24no—
451C4×C73—21no—
452C4×C73—24no—
453C4×C73—26no—
454C4×C73C22×#41112yes—
455C4×C73C2×2−1+412yes—
456Dic73—26no—
457Dic73—24no—
458Dic73—24no—
459Dic73—21no—
460Dic73—24no—
461Dic73—26no—
462Dic73C2×2−1+412yes—
463#62788—731nomaximal, Sylow
464C2×C73—22no—
465C2×C73—44no—
466C2×C73C23×#4111yescharacteristic
467C2×C73C22×2−1+411yescharacteristic
468C2×C73C2×#58511yescharacteristic
469D73—22no—
470D73—22no—
471D73—44no—
472#3523—734no—
473#3522—734no—
474#3516—734no—
475#3516—734no—
476#3507—736no—
477#3502—731no—
478#3497—731no—
479#3492—736no—
480#3486—731no—
481#3486—731no—
482#3482—734no—
483#3482—734no—
484#3480—734no—
485Q8×#41—734no—
486#3461—736no—
487#3444—736no—
488C4×2−1+4—731no—
489C4×2−1+4D7311yescharacteristic, complemented
490C22×C4×Q8—731no—
491C73#6278811yescharacteristic, complemented, Sylow
492C2×2−1+4—731no—
493C2×2−1+4C2×D7311yescharacteristic
494C23×Q8—731no—
495#559—7312no—
496Q82—734no—
497#557—7312no—
498#557—734no—
499#557—734no—
500#557—734no—
501#556—7312no—
502#556—7312no—
503#556—7312no—
504#554—7312no—
505#554—7312no—
506#554—7312no—
507#553—7312no—
508#553—7312no—
509#552—7312no—
510#552—7312no—
511#552—7312no—
512#552—7312no—
513#550—734no—
514D4×Q8—734no—
515D4×Q8—734no—
516D4×Q8—734no—
517D4×Q8—734no—
518D4×Q8—734no—
519#548—734no—
520#548—734no—
521#548—734no—
522#548—734no—
523#548—734no—
524#548—734no—
525#547—7312no—
526#547—7312no—
527#544—736no—
528#542—7312no—
529#542—7312no—
530#541—7312no—
531#541—7312no—
532#539—7324no—
533#537—736no—
534#536—736no—
535#536—736no—
536#533—736no—
537#533—736no—
538#533—7312no—
539#533—736no—
540#533—7312no—
541#532—736no—
542#532—736no—
543#532—736no—
544#529—736no—
545#529—736no—
546#529—7312no—
547#529—736no—
548#529—7312no—
549#529—736no—
550#529—7312no—
551#529—7312no—
552#529—7312no—
553#529—7312no—
554#525—736no—
555#525—734no—
556#525—7312no—
557#525—736no—
558#520—734no—
559#520—736no—
560#520C2×D7316yes—
561#520C2×D7314yescomplemented
562#519—731no—
563#519—734no—
564#519C2×D7311yescharacteristic
565#519C2×D7314yescomplemented
566C4×#41—734no—
567C4×#41—736no—
568C4×#41—7312no—
569C4×#41—7312no—
570C4×#41C2×D7316yes—
571C4×#41C2×D7314yescomplemented
572C2×C4×Q8—731no—
573C2×C4×Q8—734no—
574C2×C4×Q8—734no—
575C2×C4×Q8—734no—
576C2×C4×Q8—734no—
577C2×C4×Q8—734no—
578C2×C4×Q8—733no—
579C2×C4×Q8—733no—
580C2×C4×Q8C2×D7311yescharacteristic
581C2×C4×Q8C2×D7314yescomplemented
582C22×C4⋊C4—733no—
583C22×C42—733no—
5842−1+4—28no—
5852−1+4—1468no—
586C2×#41—734no—
587C2×#41—7312no—
588C2×#41—734no—
589C2×#41—736no—
590C2×#41C22×D7316yes—
591C2×#41C22×D7314yes—
592C22×Q8—734no—
593C22×Q8—734no—
594C22×Q8—734no—
595C22×Q8—733no—
596C22×Q8—1468no—
597C22×Q8C22×D7314yes—
598C22×Q8C22×D7311yescharacteristic
599C23×C4—733no—
600C23×C4—733no—
601C23×C4—731no—
602C4⋊Q8—736no—
603C4⋊Q8—7312no—
604C4⋊Q8—736no—
605C4⋊Q8—736no—
606C4⋊Q8—7312no—
607C4⋊Q8—7312no—
608C4⋊Q8—7312no—
609#127—736no—
610#126—7312no—
611#126—7312no—
612#126—7312no—
613#126—7312no—
614#126—7324no—
615#126—7324no—
616#125—7312no—
617#125—736no—
618#125—736no—
619#125—7312no—
620#125—7312no—
621#125—7324no—
622#125—7312no—
623#125—7324no—
624#124—736no—
625#124—736no—
626#124—7312no—
627#124—7312no—
628#124—7312no—
629#124—7312no—
630#123—7312no—
631#123—7324no—
632#123—734no—
633#123—7312no—
634#123—734no—
635#123—7312no—
636#123—7312no—
637#123—7324no—
638C22⋊Q8—736no—
639C22⋊Q8—736no—
640C22⋊Q8—7312no—
641C22⋊Q8—7312no—
642C22⋊Q8—7312no—
643C22⋊Q8—7312no—
644C22⋊Q8—7324no—
645C22⋊Q8—734no—
646C22⋊Q8—736no—
647C22⋊Q8—736no—
648C22⋊Q8—7312no—
649C22⋊Q8—7312no—
650C22⋊Q8—7312no—
651C22⋊Q8—7324no—
652C22⋊Q8—734no—
653C22⋊Q8—7312no—
654#121—734no—
655#121—7312no—
656#121—736no—
657#121—736no—
658#121—7312no—
659#121—7312no—
660#121—736no—
661#121—736no—
662#121—734no—
663#121—7312no—
664#120—734no—
665#120—734no—
666C4×Q8—734no—
667C4×Q8—734no—
668C4×Q8—734no—
669C4×Q8—734no—
670C4×Q8—7312no—
671C4×Q8—7312no—
672C4×Q8—7312no—
673C4×Q8—7312no—
674C4×Q8—7312no—
675C4×Q8—736no—
676C4×Q8—736no—
677C4×Q8—7312no—
678C4×Q8—7312no—
679C4×Q8—7312no—
680C4×Q8—7312no—
681C4×Q8C22×D7314yes—
682C4×Q8C22×D7314yes—
683C4×Q8C22×D7316yes—
684C4×Q8C22×D7314yes—
685C4×Q8C22×D73112yes—
686C4×Q8C22×D7316yes—
687C4×Q8C22×D7314yes—
688C4×D4—734no—
689C4×D4—734no—
690C4×D4—7312no—
691C4×D4—7312no—
692C4×D4—7312no—
693C4×D4—7312no—
694C4×D4—7312no—
695C4×D4—7312no—
696C4×D4—7312no—
697C4×D4—7312no—
698C4×D4—7312no—
699C4×D4—734no—
700C4×D4—736no—
701C4×D4—736no—
702C4×D4—7312no—
703C4×D4—7312no—
704C4×D4—7312no—
705C4×D4C22×D7314yes—
706C4×D4C22×D7316yes—
707C4×D4C22×D73112yes—
708C4×D4C22×D7316yes—
709C4×D4C22×D73112yes—
710#117—736no—
711#117—7312no—
712#117—7312no—
713#117—7312no—
714#117—734no—
715#117—7312no—
716#117—7312no—
717#117—7312no—
718#117—7312no—
719#117C22×D7316yes—
720#117C22×D73112yes—
721#117C22×D73112yes—
722C2×C4⋊C4—733no—
723C2×C4⋊C4—736no—
724C2×C4⋊C4—7312no—
725C2×C4⋊C4—7312no—
726C2×C4⋊C4—7312no—
727C2×C4⋊C4C22×D7313yes—
728C2×C4⋊C4C22×D73112yes—
729C2×C42—733no—
730C2×C42—733no—
731C2×C42—733no—
732C2×C42—736no—
733C2×C42—736no—
734C2×C42—736no—
735C2×C42—736no—
736C2×C42—7312no—
737C2×C42C22×D7313yes—
738C2×C42C22×D73112yes—
739C24—731no—
740#41—216no—
741#41—224no—
742#41—29224no—
743#41—14616no—
744#41—14616no—
745#41—14624no—
746C2×Q8—216no—
747C2×Q8—7312no—
748C2×Q8—734no—
749C2×Q8—7312no—
750C2×Q8—736no—
751C2×Q8—14616no—
752C2×Q8—14616no—
753C2×Q8—14616no—
754C2×Q8—14612no—
755C2×Q8#1192402818yescomplemented
756C2×Q8C23×D7316yes—
757C2×Q8C23×D7314yes—
758C2×D4—7312no—
759C2×D4—734no—
760C2×D4—734no—
761C2×D4—734no—
762C2×D4—734no—
763C2×D4—734no—
764C2×D4—734no—
765C2×D4—736no—
766C2×D4C23×D7314yes—
767C2×D4C23×D7316yes—
768C22×C4—2926no—
769C22×C4—733no—
770C22×C4—736no—
771C22×C4—7312no—
772C22×C4—731no—
773C22×C4—731no—
774C22×C4—733no—
775C22×C4—731no—
776C22×C4—731no—
777C22×C4—736no—
778C22×C4—736no—
779C22×C4—736no—
780C22×C4—7312no—
781C22×C4—731no—
782C22×C4—734no—
783C22×C4—1464no—
784C22×C4—14612no—
785C22×C4C23×D73112yes—
786C22×C4C23×D7311yescharacteristic
787C22×C4C23×D7314yes—
788C22×C4C23×D7313yes—
789C22×C4C23×D73112yes—
790C22×C4C23×D7313yes—
791C4⋊C4—7324no—
792C4⋊C4—7312no—
793C4⋊C4—734no—
794C4⋊C4—734no—
795C4⋊C4—734no—
796C4⋊C4—734no—
797C4⋊C4—7312no—
798C4⋊C4—7312no—
799C4⋊C4—7312no—
800C4⋊C4—7312no—
801C4⋊C4—7312no—
802C4⋊C4—7312no—
803C4⋊C4—736no—
804C4⋊C4—736no—
805C4⋊C4—734no—
806C4⋊C4—7312no—
807C4⋊C4—7312no—
808C4⋊C4—7312no—
809C4⋊C4C23×D73112yes—
810C4⋊C4C23×D7316yes—
811C4⋊C4C23×D73112yes—
812C4⋊C4C23×D7316yes—
813C4⋊C4C23×D7314yes—
814C22⋊C4—734no—
815C22⋊C4—734no—
816C22⋊C4—7312no—
817C22⋊C4—7312no—
818C22⋊C4—7312no—
819C22⋊C4—734no—
820C22⋊C4—734no—
821C22⋊C4—7312no—
822C22⋊C4—734no—
823C22⋊C4—734no—
824C22⋊C4—734no—
825C22⋊C4—734no—
826C22⋊C4—7312no—
827C22⋊C4—7312no—
828C22⋊C4—7312no—
829C22⋊C4C23×D7314yes—
830C22⋊C4C23×D73112yes—
831C22⋊C4C23×D7314yes—
832C42—736no—
833C42—736no—
834C42—736no—
835C42—736no—
836C42—736no—
837C42—7312no—
838C42—7312no—
839C42—736no—
840C42—734no—
841C42C23×D7316yes—
842C42C23×D73112yes—
843C42C23×D73112yes—
844C42C23×D7316yes—
845C42C23×D7314yes—
846C23—731no—
847C23—731no—
848C23—734no—
849C23—1462no—
850C23—1462no—
851C23—1462no—
852C23C24×D7314yes—
853C23C24×D7311yescharacteristic
854Q8—212no—
855Q8—29212no—
856Q8—1468no—
857Q8—14624no—
858Q8—14612no—
859Q8C2×#11924028116yes—
860D4—28no—
861D4—212no—
862D4—29212no—
863D4—1468no—
864D4—1468no—
865D4—1468no—
866D4—1468no—
867D4—1468no—
868D4—1468no—
869D4—14612no—
870C2×C4—224no—
871C2×C4—22no—
872C2×C4—28no—
873C2×C4—43no—
874C2×C4—412no—
875C2×C4—2926no—
876C2×C4—29212no—
877C2×C4—2923no—
878C2×C4—731no—
879C2×C4—734no—
880C2×C4—731no—
881C2×C4—734no—
882C2×C4—736no—
883C2×C4—734no—
884C2×C4—734no—
885C2×C4—736no—
886C2×C4—1462no—
887C2×C4—14612no—
888C2×C4—1462no—
889C2×C4—1462no—
890C2×C4—1466no—
891C2×C4—14612no—
892C2×C4—14612no—
893C2×C4—14624no—
894C2×C4—1462no—
895C2×C4—1468no—
896C2×C4C2×#11924028112yes—
897C2×C4C24×D7311yescharacteristic
898C2×C4C24×D7316yes—
899C2×C4C24×D7314yes—
900C2×C4C24×D7314yes—
901C2×C4C24×D7314yes—
902C2×C4C24×D7316yes—
903C2×C4C24×D7311yescharacteristic
904C22—21no—
905C22—21no—
906C22—24no—
907C22—24no—
908C22—24no—
909C22—732no—
910C22—732no—
911C22—1468no—
912C22—1464no—
913C22—1464no—
914C22—1464no—
915C22—1461no—
916C22—1461no—
917C22—1461no—
918C22—1461no—
919C22C22×#1192402812yes—
920C22C25×D7311yescharacteristic
921C4—24no—
922C4—21no—
923C4—24no—
924C4—26no—
925C4—24no—
926C4—732no—
927C4—1464no—
928C4—1466no—
929C4—1461no—
930C4—1464no—
931C4—1464no—
932C4—1466no—
933C4C22×#11924028112yes—
934C42−1+4×D7312yes—
935C2—22no—
936C2—44no—
937C2—2924no—
938C2—1462no—
939C2—1462no—
940C2C23×#1192402811yescharacteristic
941C2C2×2−1+4×D7311yescharacteristic
942C2#585×D7311yescharacteristic
subgroupG/H
centerC2×C4C24×D73
commutator, socle, cosocleC22×C73C26
FrattiniC22C25×D73
FittingC4×2−1+4×C73C2
hypercenterC4×2−1+4D73
hypocenterC73#62788
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C4×2−1+4

Complements

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

NH ≅ G/Ntype
1. #22624021C2semidirect
2. #22624010C2semidirect
3. #22623926C2semidirect
4. #22623916C2semidirect
5. #22623789C2semidirect
6. #22623737C2semidirect
7. #22623698C2semidirect
8. #22623634C2semidirect
9. #22623583C2semidirect
10. #22623579C2semidirect
11. #22623553C2semidirect
12. #22623548C2semidirect
13. #22623529C2semidirect
14. Q8×#11924028C2semidirect
15. #22623358C2semidirect
16. #22623224C2semidirect
17. C4×#14556639C2semidirect
18. C2×C4×Q8×D73C2semidirect
19. C4×2−1+4×C73C2semidirect
22. #17989320C22semidirect
23. Q8×Dic146C22semidirect
24. #17989316C22semidirect
25. #17989315C22semidirect
26. #17989313C22semidirect
27. #17989313C22semidirect
28. #17989309C22semidirect
29. #17989307C22semidirect
30. #17989305C22semidirect
33. #17989292C22semidirect
38. #17989276C22semidirect
39. #17989272C22semidirect
40. #17989256C22semidirect
45. Q8×C22⋊D73C22semidirect
48. #17989248C22semidirect
51. #17989244C22semidirect
55. #17989208C22semidirect
56. #17989202C22semidirect
57. #17989199C22semidirect
58. #17989195C22semidirect
63. #17989144C22semidirect
66. #17989141C22semidirect
73. #17989121C22semidirect
76. #17989119C22semidirect
85. #17989069C22semidirect
88. #17989063C22semidirect
89. C4×#11924029C22semidirect
100. C4×Q8×D73C22semidirect
105. #520×C73C22semidirect
107. #519×C73C22semidirect
109. C4×#41×C73C22semidirect
111. C2×C4×Q8×C73C22semidirect
350. C2×Q8×C73#41semidirect
427. C4×D732−1+4semidirect
489. C4×2−1+4D73semidirect
491. C73#62788semidirect
561. #520C2×D73semidirect
565. #519C2×D73semidirect
571. C4×#41C2×D73semidirect
581. C2×C4×Q8C2×D73semidirect
755. C2×Q8#11924028semidirect

Maximal subgroups

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

subgroupindex
#226240212
#226240102
#226239262
#226239162
#226237892
#226237372
#226236982
#226236342
#226235832
#226235792
#226235532
#226235482
#226235292
Q8×#119240282
#226233582
#226232242
C4×#145566392
C2×C4×Q8×D732
C4×2−1+4×C732
#6278873