Finite Group Databasebeta

← #11664228

Subgroups — #11664228

Order 768.

1990 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×2−1+4C211yesmaximal, characteristic
2#85830C211yesmaximal, characteristic, complemented
3#84117C212yesmaximal
4#82575C214yesmaximal, complemented
5#82573C212yesmaximal, complemented
6#82571C212yesmaximal, complemented
7#82555C214yesmaximal, complemented
8#82549C212yesmaximal, complemented
9#82535C212yesmaximal, complemented
10#82534C212yesmaximal, complemented
11#82533C211yesmaximal, characteristic, complemented
12#82515C211yesmaximal, characteristic, complemented
13#82507C211yesmaximal, characteristic, complemented
14#82448C212yesmaximal, complemented
15#82447C212yesmaximal, complemented
16C2×#5031C211yesmaximal, characteristic, complemented
17#82431C211yesmaximal, characteristic, complemented
18#60594—31nomaximal, Sylow
19C2×C3×2−1+4C2211yescharacteristic
20C3×#520—22no—
21C3×#520—21no—
22C3×#520C2211yescharacteristic
23C3×#520C2212yes—
24C3×#520C2211yescharacteristic
25C3×#519—21no—
26C3×#519C2211yescharacteristic
27C3×#519C2212yes—
28C3×C4×#41—22no—
29C3×C4×#41—21no—
30C3×C4×#41C2211yescharacteristic
31C3×C4×#41C2212yes—
32C3×C4×#41C2211yescharacteristic
33C2×C3×C4×Q8—21no—
34C2×C3×C4×Q8C2211yescharacteristic
35C2×C3×C4×Q8C2212yes—
36#5825C2212yes—
37C2×#951C2212yes—
38C22×#216C2212yes—
39#5567—21no—
40#5567—21no—
41#5542—21no—
42#5542—21no—
43#5541—22no—
44#5541—22no—
45#5518C2214yes—
46#5516C2212yes—
47#5470C2211yescharacteristic
48#5470C2212yes—
49#5470C2212yes—
50C2×#869C2211yescharacteristic
51#5239C2214yes—
52#5239C2214yes—
53#5234C2212yes—
54#5233C2212yes—
55#5228C2214yes—
56#5228C2214yes—
57#5225C2212yes—
58#5031C2212yes—
59#5031C2212yes—
60#5031C2214yes—
61#5031C2212yes—
62#5031C2212yes—
63#5030C2214yes—
64#5030C2214yes—
65#5030C2214yes—
66C4×#216C2214yes—
67C4×#216C2214yes—
68C4×#216C2214yes—
69#5022C2212yes—
70#5022C2214yes—
71#5021C2211yescharacteristic
72#5021C2212yes—
73#5020C2211yescharacteristic
74#5020C2212yes—
75#5019C2212yes—
76#5019C2212yes—
77#5018C2214yes—
78C4×#214C2214yes—
79#5009C2212yes—
80#5008C2211yescharacteristic
81#5007C2211yescharacteristic
82#5004C2212yes—
83#5000C2214yes—
84#4998C2212yes—
85#4997C2212yes—
86#4996C2214yes—
87#4996C2214yes—
88#4971C2214yes—
89#4970C2214yes—
90C2×#810C2212yes—
91#4964C2212yes—
92#4926C2212yes—
93#4925C2212yes—
94#4924C2211yescharacteristic
95C2×C4⋊(C3⋊C8)C2211yescharacteristic
96#3509—31no—
97C4×2−1+4D311yescharacteristic
98#3127—34no—
99#3120—34no—
100#3116—32no—
101#3113—32no—
102#3107—32no—
103#3104—32no—
104#3097—32no—
105#3078—31no—
106#3076—31no—
107#3039—31no—
108C2×#462—31no—
109#3011—32no—
110#2950—32no—
111#2947—32no—
112#2925—31no—
113C3×2−1+4—24no—
114C3×2−1+4—24no—
115C2×C3×#41—22no—
116C2×C3×#41—21no—
117C2×C3×#41C2312yes—
118C2×C3×#41C2311yescharacteristic
119C2×C3×#41C2311yescharacteristic
120C22×C3×Q8—21no—
121C22×C3×Q8C2312yes—
122C22×C3×Q8C2311yescharacteristic
123C22×Dic6C2312yes—
124C3×C4×Q8—21no—
125C3×C4×Q8—21no—
126C3×C4×Q8—22no—
127C3×C4×Q8—21no—
128C3×C4×Q8—22no—
129C3×C4×Q8—21no—
130C3×C4×Q8—22no—
131C3×C4×Q8—21no—
132C3×C4×Q8—22no—
133C3×C4×Q8D411yescharacteristic
134C3×C4×Q8D411yescharacteristic
135C3×C4×Q8C2311yescharacteristic
136C3×C4×Q8C2312yes—
137C3×C4×Q8C2312yes—
138C3×C4×Q8C2311yescharacteristic
139C3×C4×Q8C2312yes—
140C3×C4×Q8C2312yes—
141C3×C4×Q8C2312yes—
142C3×C4×D4—22no—
143C3×C4×D4—21no—
144C3×C4×D4—21no—
145C3×C4×D4—22no—
146C3×C4×D4—21no—
147C3×C4×D4—22no—
148C3×C4×D4—22no—
149C3×C4×D4—22no—
150C3×C4×D4—22no—
151C3×C4×D4D412yes—
152C3×C4×D4D412yes—
153C3×C4×D4D411yescharacteristic
154C3×C4×D4D411yescharacteristic
155C3×C4×D4C2311yescharacteristic
156C3×C4×D4C2311yescharacteristic
157C3×C4×D4C2312yes—
158C3×#117—21no—
159C3×#117—22no—
160C3×#117—22no—
161C3×#117—22no—
162C3×#117—22no—
163C3×#117—21no—
164C3×#117—22no—
165C3×#117C2312yes—
166C3×#117C2311yescharacteristic
167C3×#117C2311yescharacteristic
168C3×#117C2312yes—
169C2×C3×C4⋊C4—21no—
170C2×C3×C4⋊C4—22no—
171C2×C3×C4⋊C4—21no—
172C2×C3×C4⋊C4—22no—
173C2×C3×C4⋊C4C2311yescharacteristic
174C2×C3×C4⋊C4C2312yes—
175C2×C3×C42—21no—
176C2×C3×C42—22no—
177C2×C3×C42—21no—
178C2×C3×C42—22no—
179C2×C3×C42C2311yescharacteristic
180C2×C3×C42C2312yes—
181#951—28no—
182#944—22no—
183C2×#216—28no—
184C2×#216C2314yes—
185C2×#216C2314yes—
186C2×#216C2314yes—
187#936—22no—
188#935—24no—
189C2×#214C2314yes—
190#926—22no—
191#926—22no—
192#926C2312yes—
193C2×C4⋊Dic3—21no—
194C2×C4⋊Dic3—21no—
195#924—21no—
196#924—21no—
197#924—22no—
198#924—22no—
199#924C2314yes—
200#924C2314yes—
201C2×#208C2312yes—
202C22×C3⋊C8C2312yes—
203#889—24no—
204#889—24no—
205#887—22no—
206#887—22no—
207#879—24no—
208#879—24no—
209#877—24no—
210#870—22no—
211#870—22no—
212#870C2312yes—
213#869—21no—
214#869—21no—
215#869C2312yes—
216#869C2312yes—
217#869C2311yescharacteristic
218#869C2311yescharacteristic
219C4×Dic6—22no—
220C4×Dic6—22no—
221C4×Dic6—21no—
222C4×Dic6—21no—
223C4×Dic6C2314yes—
224C4×Dic6C2314yes—
225#835C2314yes—
226#835C2314yes—
227#835C2312yes—
228#835C2312yes—
229#832C2312yes—
230#832C2312yes—
231#830C2314yes—
232#830C2314yes—
233#810C2314yes—
234#810C2314yes—
235#810C2314yes—
236#810C2314yes—
237#808C2314yes—
238#808C2312yes—
239#808C2312yes—
240#807C2314yes—
241#807C2312yes—
242#807C2312yes—
243C4⋊(C3⋊C8)C2311yescharacteristic
244C4⋊(C3⋊C8)C2311yescharacteristic
245C4⋊(C3⋊C8)C2312yes—
246C4⋊(C3⋊C8)C2312yes—
247C4⋊(C3⋊C8)C2312yes—
248#803C2314yes—
249C4×C3⋊C8C2314yes—
250C2×2−1+4C2×D311yescharacteristic
251C2×#137—32no—
252C22×Q16—32no—
253#557—61no—
254#557—61no—
255#556—61no—
256#556—61no—
257#552—62no—
258#552—62no—
259#541—34no—
260#536—32no—
261#533—31no—
262#533—32no—
263#533—32no—
264C2×C4⋊Q8—31no—
265#520—22no—
266#520—21no—
267#520C2×D312yes—
268#520C2×D311yescharacteristic
269#520C2×D311yescharacteristic
270#519—21no—
271#519—32no—
272#519C2×D312yes—
273#519C2×D311yescharacteristic
274C4×#41—22no—
275C4×#41—21no—
276C4×#41C2×D311yescharacteristic
277C4×#41C2×D312yes—
278C4×#41C2×D311yescharacteristic
279C2×C4×Q8—21no—
280C2×C4×Q8C2×D311yescharacteristic
281C2×C4×Q8C2×D312yes—
282#485—34no—
283#485—34no—
284#484—34no—
285#483—34no—
286#479—32no—
287#479—34no—
288#478—32no—
289#477—31no—
290#477—32no—
291#476—31no—
292#475—31no—
293#475—32no—
294#474—31no—
295#462—32no—
296#462—32no—
297#462—32no—
298#462—34no—
299#462—32no—
300#461—32no—
301#461—32no—
302#452—34no—
303#452—34no—
304#451—34no—
305#451—34no—
306#441—34no—
307#441—34no—
308#441—34no—
309#440—34no—
310C4×Q16—34no—
311C4×Q16—34no—
312C4×Q16—34no—
313C4×SD16—34no—
314#433—34no—
315#432—32no—
316#431—32no—
317#428—32no—
318#427—32no—
319#423—31no—
320C2×C4⋊C8—31no—
321#419—32no—
322#419—32no—
323#416—32no—
324C2×#103—32no—
325#408—32no—
326#405—32no—
327C3×#41—216no—
328C3×#41—28no—
329C3×#41—24no—
330C3×#41—24no—
331C3×#41—22no—
332C3×#41—22no—
333C3×#41—22no—
334C3×#41#4114yes—
335C2×C3×Q8—28no—
336C2×C3×Q8—24no—
337C2×C3×Q8—24no—
338C2×C3×Q8—22no—
339C2×C3×Q8—21no—
340C2×C3×Q8—22no—
341C2×C3×Q8C2×D411yescharacteristic
342C2×C3×Q8#4114yes—
343C2×C3×Q8C2411yescharacteristic
344C2×C3×Q8C2412yes—
345C2×C3×D4—22no—
346C2×C3×D4—21no—
347C2×C3×D4C2×D412yes—
348C2×C3×D4C2×D411yescharacteristic
349C2×C3×D4C2411yescharacteristic
350C22×C3×C4—22no—
351C22×C3×C4—21no—
352C22×C3×C4—22no—
353C22×C3×C4—21no—
354C22×C3×C4—22no—
355C22×C3×C4—21no—
356C22×C3×C4—21no—
357C22×C3×C4—22no—
358C22×C3×C4—21no—
359C22×C3×C4C2×D411yescharacteristic
360C22×C3×C4C2×D412yes—
361C22×C3×C4C2×D411yescharacteristic
362C22×C3×C4C2×D412yes—
363C22×C3×C4C2412yes—
364C22×C3×C4C2411yescharacteristic
365C22×Dic3—22no—
366C2×Dic6—24no—
367C2×Dic6—24no—
368C2×Dic6—21no—
369C2×Dic6—21no—
370C2×Dic6—22no—
371C2×Dic6C2414yes—
372C3×C4⋊C4—22no—
373C3×C4⋊C4—22no—
374C3×C4⋊C4—22no—
375C3×C4⋊C4—22no—
376C3×C4⋊C4—21no—
377C3×C4⋊C4—22no—
378C3×C4⋊C4—21no—
379C3×C4⋊C4—22no—
380C3×C4⋊C4—21no—
381C3×C4⋊C4C2×D411yescharacteristic
382C3×C4⋊C4C2×D411yescharacteristic
383C3×C4⋊C4C2×D412yes—
384C3×C4⋊C4C2×D412yes—
385C3×C4⋊C4C2412yes—
386C3×C4⋊C4C2411yescharacteristic
387C3×C4⋊C4C2411yescharacteristic
388C3×C22⋊C4—22no—
389C3×C22⋊C4—21no—
390C3×C22⋊C4—21no—
391C3×C22⋊C4—22no—
392C3×C22⋊C4—21no—
393C3×C22⋊C4C2×D412yes—
394C3×C22⋊C4C2×D412yes—
395C3×C22⋊C4C2×D412yes—
396C3×C42—22no—
397C3×C42—21no—
398C3×C42—22no—
399C3×C42—21no—
400C3×C42—22no—
401C3×C42—22no—
402C3×C42—22no—
403C3×C42—22no—
404C3×C42—21no—
405C3×C42C2×D411yescharacteristic
406C3×C42C2×D411yescharacteristic
407C3×C42C2×D412yes—
408C3×C42C2×D412yes—
409C3×C42C2412yes—
410C3×C42C2411yescharacteristic
411C3×C42C2411yescharacteristic
412#217—22no—
413#217—24no—
414#217—24no—
415#216—28no—
416#216—28no—
417#216—28no—
418#214—28no—
419C4⋊Dic3—22no—
420C4⋊Dic3—22no—
421C4⋊Dic3—21no—
422C4⋊Dic3—21no—
423C4⋊Dic3—22no—
424C4⋊Dic3—22no—
425C4⋊Dic3C2412yes—
426C4⋊Dic3C2412yes—
427Dic3⋊C4—24no—
428Dic3⋊C4—24no—
429Dic3⋊C4—22no—
430Dic3⋊C4—22no—
431Dic3⋊C4—24no—
432Dic3⋊C4—24no—
433C4×Dic3—22no—
434C4×Dic3—24no—
435C4×Dic3—24no—
436#208—24no—
437C2×C3⋊C8—24no—
438C2×C3⋊C8C2412yes—
439C2×C3⋊C8C2414yes—
440C2×C3⋊C8C2412yes—
4412−1+4—24no—
4422−1+4—24no—
443C2×#41—22no—
444C2×#41—21no—
445C2×#41C22×D312yes—
446C2×#41C22×D311yescharacteristic
447C2×#41C22×D311yescharacteristic
448C22×Q8—21no—
449C22×Q8—32no—
450C22×Q8C22×D312yes—
451C22×Q8C22×D311yescharacteristic
452#137—68no—
453C2×Q16—34no—
454C2×Q16—34no—
455C2×Q16—34no—
456C2×Q16—68no—
457C2×SD16—34no—
458C2×M16—32no—
459C22×C8—32no—
460C4⋊Q8—31no—
461C4⋊Q8—31no—
462C4⋊Q8—32no—
463C4⋊Q8—32no—
464C4⋊Q8—62no—
465C4⋊Q8—61no—
466C4⋊Q8—61no—
467#126—64no—
468#126—64no—
469#125—32no—
470#125—64no—
471#125—64no—
472#125—62no—
473#125—62no—
474#124—62no—
475#123—64no—
476C22⋊Q8—34no—
477C22⋊Q8—34no—
478C22⋊Q8—61no—
479C22⋊Q8—61no—
480C22⋊Q8—62no—
481C22⋊Q8—62no—
482C4×Q8—21no—
483C4×Q8—21no—
484C4×Q8—22no—
485C4×Q8—21no—
486C4×Q8—22no—
487C4×Q8—22no—
488C4×Q8—21no—
489C4×Q8—22no—
490C4×Q8—21no—
491C4×Q8—34no—
492C4×Q8—34no—
493C4×Q8—62no—
494C4×Q8—62no—
495C4×Q8—62no—
496C4×Q8—62no—
497C4×Q8—61no—
498C4×Q8—61no—
499C4×Q8#6711yescharacteristic
500C4×Q8#6711yescharacteristic
501C4×Q8C22×D312yes—
502C4×Q8C22×D311yescharacteristic
503C4×Q8C22×D312yes—
504C4×Q8C22×D312yes—
505C4×Q8C22×D312yes—
506C4×Q8C22×D312yes—
507C4×Q8C22×D311yescharacteristic
508C4×D4—22no—
509C4×D4—21no—
510C4×D4—21no—
511C4×D4—22no—
512C4×D4—21no—
513C4×D4—22no—
514C4×D4—22no—
515C4×D4—22no—
516C4×D4—22no—
517C4×D4#6712yes—
518C4×D4#6711yescharacteristic
519C4×D4#6712yes—
520C4×D4#6711yescharacteristic
521C4×D4C22×D311yescharacteristic
522C4×D4C22×D312yes—
523C4×D4C22×D311yescharacteristic
524#117—21no—
525#117—22no—
526#117—22no—
527#117—22no—
528#117—22no—
529#117—22no—
530#117—21no—
531#117—32no—
532#117—62no—
533#117—62no—
534#117—64no—
535#117C22×D311yescharacteristic
536#117C22×D312yes—
537#117C22×D311yescharacteristic
538#117C22×D312yes—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—22no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—22no—
543C2×C4⋊C4—61no—
544C2×C4⋊C4—61no—
545C2×C4⋊C4C22×D311yescharacteristic
546C2×C4⋊C4C22×D312yes—
547C2×C42—21no—
548C2×C42—22no—
549C2×C42—22no—
550C2×C42—21no—
551C2×C42C22×D311yescharacteristic
552C2×C42C22×D312yes—
553#107—32no—
554#107—32no—
555#107—34no—
556#106—32no—
557#106—32no—
558#106—34no—
559C4⋊C8—31no—
560C4⋊C8—31no—
561C4⋊C8—32no—
562C4⋊C8—32no—
563C4⋊C8—32no—
564#103—32no—
565#103—32no—
566#103—34no—
567#103—34no—
568#103—34no—
569#103—34no—
570#103—34no—
571#103—34no—
572#102—32no—
573#102—32no—
574C22⋊C8—34no—
575C22⋊C8—34no—
576#97—34no—
577C4×C8—34no—
578C23×C3—21no—
579C23×C3C22×D412yes—
580C23×C3C22×D411yescharacteristic
581C3×Q8—28no—
582C3×Q8—22no—
583C3×Q8—24no—
584C3×Q8—21no—
585C3×Q8—22no—
586C3×Q8C2×#4112yes—
587C3×Q8C2×#4114yes—
588C3×D4—28no—
589C3×D4—24no—
590C3×D4—24no—
591C3×D4—22no—
592C3×D4—21no—
593C3×D4C2×#4112yes—
594C2×C3×C4—28no—
595C2×C3×C4—28no—
596C2×C3×C4—24no—
597C2×C3×C4—22no—
598C2×C3×C4—21no—
599C2×C3×C4—24no—
600C2×C3×C4—22no—
601C2×C3×C4—24no—
602C2×C3×C4—22no—
603C2×C3×C4—22no—
604C2×C3×C4—21no—
605C2×C3×C4—21no—
606C2×C3×C4—22no—
607C2×C3×C4—41no—
608C2×C3×C4—42no—
609C2×C3×C4—42no—
610C2×C3×C4—82no—
611C2×C3×C4—81no—
612C2×C3×C4—81no—
613C2×C3×C4—82no—
614C2×C3×C4C22×D412yes—
615C2×C3×C4C22×D412yes—
616C2×C3×C4C22×D412yes—
617C2×C3×C4C22×D411yescharacteristic
618C2×C3×C4C22×D411yescharacteristic
619C2×C3×C4C22×D411yescharacteristic
620C2×C3×C4C22×D411yescharacteristic
621C2×C3×C4C22×D411yescharacteristic
622C2×C3×C4C2×#4112yes—
623C2×C3×C4C2×#4112yes—
624C2×C3×C4C2511yescharacteristic
625C2×Dic3—22no—
626C2×Dic3—22no—
627C2×Dic3—24no—
628C2×Dic3—44no—
629Dic6—24no—
630Dic6—24no—
631Dic6—42no—
632Dic6—44no—
633Dic6—42no—
634C3⋊C8—22no—
635C3⋊C8—22no—
636C3⋊C8—24no—
637#41—216no—
638#41—28no—
639#41—24no—
640#41—24no—
641#41—22no—
642#41—22no—
643#41—22no—
644#41#23514yes—
645C2×Q8—28no—
646C2×Q8—24no—
647C2×Q8—24no—
648C2×Q8—22no—
649C2×Q8—22no—
650C2×Q8—21no—
651C2×Q8—34no—
652C2×Q8—61no—
653C2×Q8—61no—
654C2×Q8—62no—
655C2×Q8—64no—
656C2×Q8—64no—
657C2×Q8#23514yes—
658C2×Q8C2×#6711yescharacteristic
659C2×Q8C23×D311yescharacteristic
660C2×Q8C23×D312yes—
661C2×D4—22no—
662C2×D4—21no—
663C2×D4C2×#6712yes—
664C2×D4C2×#6711yescharacteristic
665C2×D4C23×D311yescharacteristic
666C22×C4—22no—
667C22×C4—21no—
668C22×C4—22no—
669C22×C4—21no—
670C22×C4—22no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—22no—
674C22×C4—21no—
675C22×C4—62no—
676C22×C4C2×#6711yescharacteristic
677C22×C4C2×#6712yes—
678C22×C4C2×#6711yescharacteristic
679C22×C4C2×#6712yes—
680C22×C4C23×D312yes—
681C22×C4C23×D311yescharacteristic
682Q16—68no—
683Q16—68no—
684Q16—68no—
685SD16—68no—
686M16—64no—
687C2×C8—32no—
688C2×C8—34no—
689C2×C8—32no—
690C2×C8—64no—
691C4⋊C4—22no—
692C4⋊C4—22no—
693C4⋊C4—22no—
694C4⋊C4—22no—
695C4⋊C4—21no—
696C4⋊C4—22no—
697C4⋊C4—21no—
698C4⋊C4—22no—
699C4⋊C4—21no—
700C4⋊C4—32no—
701C4⋊C4—32no—
702C4⋊C4—62no—
703C4⋊C4—62no—
704C4⋊C4—62no—
705C4⋊C4—62no—
706C4⋊C4—61no—
707C4⋊C4—61no—
708C4⋊C4—64no—
709C4⋊C4—64no—
710C4⋊C4—64no—
711C4⋊C4—64no—
712C4⋊C4—62no—
713C4⋊C4—62no—
714C4⋊C4C2×#6711yescharacteristic
715C4⋊C4C2×#6712yes—
716C4⋊C4C2×#6711yescharacteristic
717C4⋊C4C2×#6712yes—
718C4⋊C4C23×D312yes—
719C4⋊C4C23×D311yescharacteristic
720C4⋊C4C23×D311yescharacteristic
721C22⋊C4—22no—
722C22⋊C4—21no—
723C22⋊C4—21no—
724C22⋊C4—22no—
725C22⋊C4—21no—
726C22⋊C4—62no—
727C22⋊C4—64no—
728C22⋊C4—64no—
729C22⋊C4C2×#6712yes—
730C22⋊C4C2×#6712yes—
731C22⋊C4C2×#6712yes—
732C42—22no—
733C42—21no—
734C42—22no—
735C42—21no—
736C42—22no—
737C42—22no—
738C42—22no—
739C42—22no—
740C42—21no—
741C42—62no—
742C42—64no—
743C42—64no—
744C42C2×#6712yes—
745C42C2×#6711yescharacteristic
746C42C2×#6712yes—
747C42C2×#6711yescharacteristic
748C42C23×D312yes—
749C42C23×D311yescharacteristic
750C42C23×D311yescharacteristic
751C22×C3—21no—
752C22×C3—21no—
753C22×C3—22no—
754C22×C3—22no—
755C22×C3—22no—
756C22×C3—22no—
757C22×C3—41no—
758C22×C3—41no—
759C22×C3#52512yes—
760C22×C3C23×D411yescharacteristic
761C3×C4—21no—
762C3×C4—22no—
763C3×C4—21no—
764C3×C4—24no—
765C3×C4—22no—
766C3×C4—22no—
767C3×C4—22no—
768C3×C4—21no—
769C3×C4—42no—
770C3×C4—41no—
771C3×C4—41no—
772C3×C4#52512yes—
773C3×C4#57812yes—
774C3×C4C22×#4111yescharacteristic
775C3×C4C22×#4111yescharacteristic
776Dic3—42no—
777Dic3—44no—
778Dic3—42no—
779C23—21no—
780C23C22×#6712yes—
781C23C22×#6711yescharacteristic
782Q8—28no—
783Q8—21no—
784Q8—22no—
785Q8—24no—
786Q8—22no—
787Q8—64no—
788Q8—64no—
789Q8—122no—
790Q8—124no—
791Q8—122no—
792Q8C2×#23512yes—
793Q8C2×#23514yes—
794D4—28no—
795D4—24no—
796D4—24no—
797D4—21no—
798D4—22no—
799D4C2×#23512yes—
800C2×C4—28no—
801C2×C4—28no—
802C2×C4—22no—
803C2×C4—21no—
804C2×C4—24no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—24no—
808C2×C4—22no—
809C2×C4—24no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—22no—
813C2×C4—41no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—62no—
817C2×C4—62no—
818C2×C4—64no—
819C2×C4—82no—
820C2×C4—81no—
821C2×C4—81no—
822C2×C4—82no—
823C2×C4—124no—
824C2×C4C2×#23512yes—
825C2×C4C2×#23512yes—
826C2×C4C22×#6712yes—
827C2×C4C22×#6711yescharacteristic
828C2×C4C22×#6712yes—
829C2×C4C22×#6712yes—
830C2×C4C22×#6711yescharacteristic
831C2×C4C22×#6711yescharacteristic
832C2×C4C22×#6711yescharacteristic
833C2×C4C22×#6711yescharacteristic
834C2×C4C24×D311yescharacteristic
835C8—62no—
836C8—62no—
837C8—64no—
838C2×C3—22no—
839C2×C3—42no—
840C2×C3—42no—
841C2×C3C2×#52511yescharacteristic
842C2×C3C2×#57811yescharacteristic
843C2×C3#358611yescharacteristic
844C22—21no—
845C22—21no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—41no—
851C22—41no—
852C22#579112yes—
853C22C23×#6711yescharacteristic
854C4—21no—
855C4—22no—
856C4—21no—
857C4—24no—
858C4—22no—
859C4—22no—
860C4—22no—
861C4—21no—
862C4—42no—
863C4—41no—
864C4—41no—
865C4—122no—
866C4—124no—
867C4—122no—
868C4#579112yes—
869C4#583812yes—
870C4C22×#23511yescharacteristic
871C4C22×#23511yescharacteristic
872C3#6059411yescharacteristic, complemented, Sylow
873C2—22no—
874C2—42no—
875C2—42no—
876C2C2×#579111yescharacteristic
877C2C2×#583811yescharacteristic
878C2#8729911yescharacteristic
subgroupG/H
centerC22C23×#67
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×C4×2−1+4C2
socleC22×C3C23×D4
prime radicalC2×C3×2−1+4C22
hypercenterC4×2−1+4D3
hypocenterC3#60594
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C4×#41 ◁ C4×2−1+4

Complements

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

NH ≅ G/Ntype
2. #85830C2semidirect
4. #82575C2semidirect
5. #82573C2semidirect
6. #82571C2semidirect
7. #82555C2semidirect
8. #82549C2semidirect
9. #82535C2semidirect
10. #82534C2semidirect
11. #82533C2semidirect
12. #82515C2semidirect
13. #82507C2semidirect
14. #82448C2semidirect
15. #82447C2semidirect
16. C2×#5031C2semidirect
17. #82431C2semidirect
872. C3#60594semidirect

Maximal subgroups

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

subgroupindex
C3×C4×2−1+42
#858302
#841172
#825752
#825732
#825712
#825552
#825492
#825352
#825342
#825332
#825152
#825072
#824482
#824472
C2×#50312
#824312
#605943