Finite Group Databasebeta

← #10815956

Subgroups — #10815956

Order 768.

1070 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#83793C211yesmaximal, characteristic, complemented
2C2×D3×#104C211yesmaximal, characteristic, complemented
3C2×#4824C211yesmaximal, characteristic, complemented
4#78833C211yesmaximal, characteristic
5#78555C211yesmaximal, characteristic, complemented
6C3×#1764C211yesmaximal, characteristic, complemented
7#72010C211yesmaximal, characteristic, complemented
8#70292C211yesmaximal, characteristic, complemented
9#69900C211yesmaximal, characteristic, complemented
10#69795C211yesmaximal, characteristic, complemented
11C4×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
12#68946C211yesmaximal, characteristic, complemented
13#68941C211yesmaximal, characteristic, complemented
14#68756C211yesmaximal, characteristic, complemented
15#68745C211yesmaximal, characteristic, complemented
16#22888—31nomaximal, Sylow
17C2×D3×#41C2211yescharacteristic
18C2×C3×#131C2211yescharacteristic
19C2×#950C2211yescharacteristic
20C2×#948C2211yescharacteristic
21C2×#907C2211yescharacteristic, complemented
22C2×D3×M16C2211yescharacteristic
23C2×#904C2211yescharacteristic
24#5524C2211yescharacteristic
25C2×C42×D3C2211yescharacteristic
26C2×C3×#104C2211yescharacteristic
27C3×#416C2211yescharacteristic
28C3×#405C2211yescharacteristic, complemented
29C2×C3×C4×C8C2211yescharacteristic, complemented
30C2×#837C2211yescharacteristic
31C2×#825C2211yescharacteristic
32C2×#825C2211yescharacteristic, complemented
33#5129—21no—
34#5129C2211yescharacteristic
35#5126—21no—
36#5126C2211yescharacteristic
37C2×#822C2211yescharacteristic, complemented
38#5110—21no—
39#5110C2211yescharacteristic
40#5110C2211yescharacteristic, complemented
41C2×(C2×D3)⋊C8—21no—
42C2×(C2×D3)⋊C8C2211yescharacteristic
43C2×(C2×D3)⋊C8C2211yescharacteristic
44C2×#819C2211yescharacteristic, complemented
45#5002C2211yescharacteristic
46#4999C2211yescharacteristic, complemented
47C2×#805C2211yescharacteristic
48C2×#805C2211yescharacteristic, complemented
49C2×C4×C3⋊C8C2211yescharacteristic, complemented
50#4824—24no—
51D3×#104—24no—
52#4810C411yescharacteristic, complemented
53#4809C411yescharacteristic, complemented
54#4808C411yescharacteristic, complemented
55#4806C411yescharacteristic, complemented
56#4783C411yescharacteristic, complemented
57#4781C411yescharacteristic, complemented
58#4776C411yescharacteristic, complemented
59#4773C411yescharacteristic, complemented
60#4706—21no—
61#4706—21no—
62#4688—21no—
63C8×D12—21no—
64C3×#341C2211yescharacteristic, complemented
65C3×#339C2211yescharacteristic, complemented
66#4558C2211yescharacteristic, complemented
67#4550C2211yescharacteristic, complemented
68#4550C2211yescharacteristic, complemented
69#4532C2211yescharacteristic, complemented
70#3002—31no—
71C2×#443—31no—
72#2933—31no—
73C22×#104—31no—
74#2880—31no—
75#1974—31no—
76#1937—31no—
77#1929—31no—
78#1896—31no—
79#1876—31no—
80#1876—31no—
81#1866—31no—
82#1855—31no—
83#1764D311yescharacteristic, complemented
84C4×C22⋊C8—31no—
85C2×C3×#41C2311yescharacteristic
86D3×#41—22no—
87D3×#41—22no—
88D3×#41—41no—
89D3×#41—41no—
90C2×#239C2×C411yescharacteristic
91C2×D3×Q8C2×C411yescharacteristic
92C2×#237—21no—
93C2×#237C2×C411yescharacteristic
94C2×D3×D4—21no—
95C2×D3×D4C2×C411yescharacteristic
96C2×#235—21no—
97C2×#235C2311yescharacteristic
98C2×#235C2311yescharacteristic
99C22×C4×D3—21no—
100C22×C4×D3—21no—
101C22×C4×D3C2311yescharacteristic
102C3×#131—22no—
103C3×#131—41no—
104C2×C3×M16—21no—
105C2×C3×M16C2311yescharacteristic
106C2×C3×M16C2311yescharacteristic
107C22×C3×C8—21no—
108C22×C3×C8C2311yescharacteristic
109C22×C3×C8C2311yescharacteristic
110C3×#117C2311yescharacteristic
111C2×C3×C42C2311yescharacteristic
112#950—22no—
113#950—22no—
114#948—22no—
115#948—41no—
116C2×#216C2×C411yescharacteristic, complemented
117C2×#215C2×C411yescharacteristic, complemented
118C2×#214C2×C411yescharacteristic, complemented
119C2×#213C2×C411yescharacteristic, complemented
120C2×C4×Dic3—21no—
121C2×C4×Dic3C2311yescharacteristic
122C2×#208—21no—
123C2×#208C2311yescharacteristic
124C2×#208C2311yescharacteristic
125C22×C3⋊C8—21no—
126C22×C3⋊C8C2311yescharacteristic
127C22×C3⋊C8C2311yescharacteristic
128#907—22no—
129#907—41no—
130D3×M16—22no—
131D3×M16—41no—
132C2×Dic12C2×C411yescharacteristic, complemented
133#904—41no—
134#904—41no—
135C2×D24C2×C411yescharacteristic, complemented
136C2×#204C2×C411yescharacteristic, complemented
137C2×#204C2×C411yescharacteristic, complemented
138C2×ΓL(1,𝔽25)—21no—
139C2×ΓL(1,𝔽25)—21no—
140C2×D3×C8—21no—
141C2×D3×C8—21no—
142#897C2×C411yescharacteristic
143#897C2×C411yescharacteristic
144#895C2×C411yescharacteristic
145#895C2×C411yescharacteristic
146#886—21no—
147#882—21no—
148C4×D12—21no—
149C4×D12—21no—
150C42×D3—22no—
151C42×D3—41no—
152C3×#104D414yescomplemented
153C3×#103C2×C411yescharacteristic, complemented
154C3×#103C2×C411yescharacteristic, complemented
155C3×#102C2×C411yescharacteristic, complemented
156C3×#102C2×C411yescharacteristic, complemented
157C3×#97—21no—
158C3×C4×C8—21no—
159C3×C4×C8—41no—
160#837—22no—
161#825—22no—
162#825—41no—
163#822—22no—
164(C2×D3)⋊C8—21no—
165(C2×D3)⋊C8—21no—
166(C2×D3)⋊C8—21no—
167(C2×D3)⋊C8—21no—
168(C2×D3)⋊C8—21no—
169(C2×D3)⋊C8—21no—
170(C2×D3)⋊C8—21no—
171(C2×D3)⋊C8—21no—
172(C2×D3)⋊C8C2×C411yescharacteristic
173(C2×D3)⋊C8C2×C411yescharacteristic
174(C2×D3)⋊C8C2×C411yescharacteristic
175(C2×D3)⋊C8C2×C411yescharacteristic
176(C2×D3)⋊C8D411yescharacteristic
177(C2×D3)⋊C8D411yescharacteristic
178(C2×D3)⋊C8D411yescharacteristic
179(C2×D3)⋊C8D411yescharacteristic
180#819—41no—
181#810C2×C411yescharacteristic, complemented
182#810C2×C411yescharacteristic, complemented
183#809C2×C411yescharacteristic, complemented
184#809C2×C411yescharacteristic, complemented
185#805—22no—
186#805—22no—
187C4⋊(C3⋊C8)—21no—
188C4⋊(C3⋊C8)—21no—
189C4×C3⋊C8—22no—
190C22×#41—31no—
191C2×#135—31no—
192C2×#135—31no—
193C2×#131—31no—
194C2×#131—31no—
195C2×#131C2×D311yescharacteristic
196C22×M16—31no—
197#525—31no—
198C22×C42—31no—
199#452—31no—
200#452—31no—
201#451—31no—
202#450—31no—
203#449—31no—
204#449—31no—
205#448—31no—
206#447—31no—
207#443—64no—
208#436—61no—
209#435—61no—
210#435—61no—
211C8×D4—61no—
212C2×#108—31no—
213C2×#108—31no—
214#424—31no—
215C2×#104—31no—
216C2×#104—31no—
217C2×#104—31no—
218C2×#104—31no—
219C2×#104—31no—
220C2×#104—64no—
221C2×#104C2×D311yescharacteristic
222#416—31no—
223#416C2×D311yescharacteristic
224#408—31no—
225#408—31no—
226#408—31no—
227#408—61no—
228#408—61no—
229#407—31no—
230#407—61no—
231C2×C22⋊C8—31no—
232C2×C22⋊C8—31no—
233C2×C22⋊C8—61no—
234#405C2×D311yescharacteristic, complemented
235C2×C4×C8—31no—
236C2×C4×C8C2×D311yescharacteristic, complemented
237#341—31no—
238#341C2×D311yescharacteristic, complemented
239#339—31no—
240#339C2×D311yescharacteristic, complemented
241#336—31no—
242#336—31no—
243C23×D3—21no—
244C23×D3#4111yescharacteristic
245C3×#41—21no—
246C3×#41—21no—
247C3×#41C2×D412yes—
248C3×#41#4112yes—
249C2×C3×Q8C22×C411yescharacteristic
250C2×C3×D4—21no—
251C2×C3×D4C22×C411yescharacteristic
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4C2411yescharacteristic
255C2×#67—21no—
256C2×#67—21no—
257C2×#67—21no—
258C2×#67—21no—
259C22×Dic3—21no—
260C22×Dic3—21no—
261C22×Dic3#4111yescharacteristic
262#239—22no—
263#239—41no—
264D3×Q8—22no—
265D3×Q8—41no—
266#237—22no—
267#237—41no—
268#237—42no—
269#237—42no—
270D3×D4—22no—
271D3×D4—41no—
272D3×D4—42no—
273D3×D4—42no—
274#235—21no—
275#235—21no—
276#235—21no—
277#235—21no—
278#235—21no—
279#235—21no—
280#235—21no—
281#235—21no—
282#235—42no—
283#235—42no—
284C2×D12—21no—
285C2×D12—21no—
286C2×D12—21no—
287C2×D12C22×C411yescharacteristic
288C2×D12C22×C411yescharacteristic
289C2×C4×D3—21no—
290C2×C4×D3—21no—
291C2×C4×D3—21no—
292C2×C4×D3—21no—
293C2×C4×D3—24no—
294C2×C4×D3—21no—
295C2×C4×D3—21no—
296C2×C4×D3—21no—
297C2×C4×D3—21no—
298C2×C4×D3—42no—
299C2×C4×D3—42no—
300C2×C4×D3—42no—
301C2×C4×D3—42no—
302C2×C4×D3C22×C411yescharacteristic
303C2×C4×D3C22×C411yescharacteristic
304C2×C4×D3C2×D411yescharacteristic
305C2×C4×D3C2×D411yescharacteristic
306C2×Dic6—21no—
307C2×Dic6C22×C411yescharacteristic
308C2×Dic6C22×C411yescharacteristic
309C3×M16—21no—
310C3×M16—21no—
311C3×M16—21no—
312C3×M16—42no—
313C3×M16C2×D412yes—
314C2×C3×C8—21no—
315C2×C3×C8—21no—
316C2×C3×C8—21no—
317C2×C3×C8—21no—
318C2×C3×C8—21no—
319C2×C3×C8—21no—
320C2×C3×C8—42no—
321C2×C3×C8C22×C411yescharacteristic
322C2×C3×C8C22×C411yescharacteristic
323C2×C3×C8C2×D411yescharacteristic
324C2×C3×C8C2×D411yescharacteristic
325C3×C4⋊C4C22×C411yescharacteristic
326C3×C4⋊C4C22×C411yescharacteristic
327C3×C22⋊C4—21no—
328C3×C42—21no—
329C3×C42—21no—
330C3×C42C2×D412yes—
331#216—22no—
332#215—22no—
333#214—22no—
334#213—22no—
335(C2×D3)⋊C4—21no—
336(C2×D3)⋊C4—21no—
337(C2×D3)⋊C4—21no—
338(C2×D3)⋊C4—21no—
339C4⋊Dic3—21no—
340C4⋊Dic3—21no—
341C4×Dic3—21no—
342C4×Dic3—21no—
343C4×Dic3—42no—
344#208—21no—
345#208—21no—
346#208—21no—
347#208—21no—
348#208—42no—
349C2×C3⋊C8—21no—
350C2×C3⋊C8—21no—
351C2×C3⋊C8—21no—
352C2×C3⋊C8—21no—
353C2×C3⋊C8—21no—
354C2×C3⋊C8—21no—
355C2×C3⋊C8—42no—
356C2×C3⋊C8C22×C411yescharacteristic
357C2×C3⋊C8C22×C411yescharacteristic
358C2×C3⋊C8C2×D411yescharacteristic
359C2×C3⋊C8C2×D411yescharacteristic
360Dic12—41no—
361D24—41no—
362#204—41no—
363#204—41no—
364ΓL(1,𝔽25)—42no—
365ΓL(1,𝔽25)—42no—
366D3×C8—42no—
367D3×C8—42no—
368C2×#41—31no—
369C2×#41—31no—
370C2×#41—31no—
371C2×#41—31no—
372C2×#41—61no—
373C2×#41—61no—
374C2×#41—62no—
375C2×#41—62no—
376C2×#41—121no—
377C2×#41—121no—
378C2×#41C22×D311yescharacteristic
379C22×Q8—31no—
380C22×D4—31no—
381C22×D4—61no—
382C23×C4—31no—
383C23×C4—61no—
384C23×C4—61no—
385#135—62no—
386#135—62no—
387#135—121no—
388#135—121no—
389C2×Q16—31no—
390C2×Q16—31no—
391C2×SD16—31no—
392C2×SD16—31no—
393C2×SD16—31no—
394C2×SD16—31no—
395C2×D8—31no—
396C2×D8—31no—
397#131—22no—
398#131—41no—
399#131—62no—
400#131—62no—
401#131—121no—
402#131—121no—
403C2×M16—21no—
404C2×M16—31no—
405C2×M16—31no—
406C2×M16—61no—
407C2×M16—61no—
408C2×M16—61no—
409C2×M16—62no—
410C2×M16—121no—
411C2×M16C22×D311yescharacteristic
412C2×M16C22×D311yescharacteristic
413C22×C8—21no—
414C22×C8—31no—
415C22×C8—31no—
416C22×C8—61no—
417C22×C8—61no—
418C22×C8—61no—
419C22×C8C22×D311yescharacteristic
420C22×C8C22×D311yescharacteristic
421#123—61no—
422C22⋊Q8—31no—
423C22⋊Q8—31no—
424#121—31no—
425#121—31no—
426#120—61no—
427C4×D4—61no—
428C4×D4—61no—
429#117C22×D311yescharacteristic
430C2×C42—31no—
431C2×C42—62no—
432C2×C42—61no—
433C2×C42—121no—
434C2×C42C22×D311yescharacteristic
435#108—62no—
436#108—121no—
437C4⋊C8—61no—
438C4⋊C8—61no—
439#104—62no—
440#104—62no—
441#104—62no—
442#104—62no—
443#104—121no—
444#104D1214yescomplemented
445#103—31no—
446#103—31no—
447#103C4×D311yescharacteristic, complemented
448#103C4×D311yescharacteristic, complemented
449#102—31no—
450#102—31no—
451#102C4×D311yescharacteristic, complemented
452#102C4×D311yescharacteristic, complemented
453C22⋊C8—31no—
454C22⋊C8—31no—
455C22⋊C8—31no—
456C22⋊C8—31no—
457C22⋊C8—31no—
458C22⋊C8—31no—
459C22⋊C8—31no—
460C22⋊C8—31no—
461C22⋊C8—61no—
462C22⋊C8—61no—
463C22⋊C8—61no—
464C22⋊C8—61no—
465C22⋊C8—61no—
466C22⋊C8—61no—
467C22⋊C8—61no—
468C22⋊C8—61no—
469#97—21no—
470C4×C8—21no—
471C4×C8—41no—
472C4×C8—62no—
473C23×C3—21no—
474C23×C3C2×#4111yescharacteristic
475C22×D3—21no—
476C22×D3—21no—
477C22×D3—22no—
478C22×D3—21no—
479C22×D3—21no—
480C22×D3—41no—
481C22×D3—42no—
482C22×D3—42no—
483C22×D3—81no—
484C22×D3C4×D411yescharacteristic
485C22×D3C4×D411yescharacteristic
486C3×Q8—21no—
487C3×Q8C4×D412yes—
488C3×D4—22no—
489C3×D4—22no—
490C3×D4—21no—
491C3×D4C4×D412yes—
492C2×C3×C4—22no—
493C2×C3×C4—22no—
494C2×C3×C4—21no—
495C2×C3×C4—22no—
496C2×C3×C4—22no—
497C2×C3×C4—22no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4C23×C411yescharacteristic
501C2×C3×C4C22×D411yescharacteristic
502C2×C3×C4C22×D411yescharacteristic
503C2×C3×C4C2×#4111yescharacteristic
504C2×C3×C4H(5,𝔽2)11yescharacteristic
505C2×C3×C4H(5,𝔽2)11yescharacteristic
506#67—42no—
507#67—42no—
508#67—41no—
509#67—41no—
510#67—41no—
511#67—41no—
512C2×Dic3—21no—
513C2×Dic3—21no—
514C2×Dic3—22no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—42no—
518C2×Dic3—41no—
519C2×Dic3—41no—
520C2×Dic3C4×D411yescharacteristic
521C2×Dic3C4×D411yescharacteristic
522D12—21no—
523D12—21no—
524D12—21no—
525D12—21no—
526D12—42no—
527D12—42no—
528D12—81no—
529C4×D3—21no—
530C4×D3—21no—
531C4×D3—21no—
532C4×D3—21no—
533C4×D3—21no—
534C4×D3—21no—
535C4×D3—21no—
536C4×D3—21no—
537C4×D3—42no—
538C4×D3—42no—
539C4×D3—48no—
540C4×D3—41no—
541C4×D3—41no—
542C4×D3—41no—
543C4×D3—41no—
544Dic6—21no—
545Dic6—21no—
546Dic6—21no—
547Dic6—21no—
548Dic6—42no—
549C3×C8—21no—
550C3×C8—21no—
551C3×C8—22no—
552C3×C8—21no—
553C3×C8—21no—
554C3×C8—41no—
555C3⋊C8—21no—
556C3⋊C8—21no—
557C3⋊C8—21no—
558C3⋊C8—21no—
559C3⋊C8—41no—
560C3⋊C8—41no—
561C24—31no—
562C24—61no—
563#41—21no—
564#41—21no—
565#41—62no—
566#41—62no—
567#41—61no—
568#41—61no—
569#41—61no—
570#41—61no—
571#41—61no—
572#41—61no—
573#41—61no—
574#41—61no—
575#41—122no—
576#41—122no—
577#41—121no—
578#41—122no—
579#41—122no—
580#41—121no—
581#41C2×D1212yes—
582#41#23512yes—
583C2×Q8—31no—
584C2×Q8—31no—
585C2×Q8—61no—
586C2×Q8—62no—
587C2×Q8—121no—
588C2×Q8C2×C4×D311yescharacteristic
589C2×D4—21no—
590C2×D4—31no—
591C2×D4—31no—
592C2×D4—61no—
593C2×D4—61no—
594C2×D4—61no—
595C2×D4—61no—
596C2×D4—62no—
597C2×D4—61no—
598C2×D4—61no—
599C2×D4—61no—
600C2×D4—121no—
601C2×D4—122no—
602C2×D4—122no—
603C2×D4C2×C4×D311yescharacteristic
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—31no—
607C22×C4—31no—
608C22×C4—31no—
609C22×C4—31no—
610C22×C4—31no—
611C22×C4—61no—
612C22×C4—61no—
613C22×C4—64no—
614C22×C4—61no—
615C22×C4—61no—
616C22×C4—61no—
617C22×C4—61no—
618C22×C4—61no—
619C22×C4—61no—
620C22×C4—61no—
621C22×C4—61no—
622C22×C4—122no—
623C22×C4—122no—
624C22×C4—122no—
625C22×C4—122no—
626C22×C4C23×D311yescharacteristic
627Q16—62no—
628Q16—121no—
629SD16—62no—
630SD16—62no—
631SD16—121no—
632SD16—121no—
633D8—62no—
634D8—121no—
635M16—21no—
636M16—21no—
637M16—21no—
638M16—42no—
639M16—61no—
640M16—61no—
641M16—61no—
642M16—61no—
643M16—122no—
644M16—122no—
645M16—122no—
646M16C2×D1212yes—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—31no—
654C2×C8—31no—
655C2×C8—31no—
656C2×C8—31no—
657C2×C8—42no—
658C2×C8—61no—
659C2×C8—61no—
660C2×C8—61no—
661C2×C8—61no—
662C2×C8—61no—
663C2×C8—61no—
664C2×C8—122no—
665C2×C8—122no—
666C2×C8—122no—
667C2×C8C2×C4×D311yescharacteristic
668C2×C8C2×C4×D311yescharacteristic
669C2×C8D3×D411yescharacteristic
670C2×C8D3×D411yescharacteristic
671C4⋊C4—61no—
672C4⋊C4—61no—
673C4⋊C4C2×C4×D311yescharacteristic
674C4⋊C4C2×C4×D311yescharacteristic
675C22⋊C4—21no—
676C22⋊C4—61no—
677C22⋊C4—61no—
678C22⋊C4—61no—
679C22⋊C4—61no—
680C42—21no—
681C42—21no—
682C42—61no—
683C42—61no—
684C42—122no—
685C42C2×D1212yes—
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—22no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3C2×C4×D411yescharacteristic
692C22×C3#54611yescharacteristic
693C22×C3#55111yescharacteristic
694C2×D3—21no—
695C2×D3—21no—
696C2×D3—21no—
697C2×D3—21no—
698C2×D3—21no—
699C2×D3—42no—
700C2×D3—42no—
701C2×D3—41no—
702C2×D3—41no—
703C2×D3—41no—
704C2×D3—41no—
705C2×D3—41no—
706C2×D3—41no—
707C2×D3—84no—
708C2×D3#44312yescomplemented
709C3×C4—24no—
710C3×C4—22no—
711C3×C4—41no—
712C3×C4—41no—
713C3×C4C2×C4×D411yescharacteristic
714C3×C4#51811yescharacteristic
715C3×C4D4211yescharacteristic
716C3×C4#54611yescharacteristic
717Dic3—21no—
718Dic3—21no—
719Dic3—42no—
720Dic3—41no—
721Dic3—41no—
722C23—21no—
723C23—31no—
724C23—31no—
725C23—62no—
726C23—61no—
727C23—61no—
728C23—61no—
729C23—61no—
730C23—121no—
731C23—122no—
732C23—122no—
733C23—241no—
734C23D3×#4111yescharacteristic
735Q8—21no—
736Q8—61no—
737Q8—61no—
738Q8—61no—
739Q8—61no—
740Q8—122no—
741Q8C4×D1212yes—
742D4—22no—
743D4—22no—
744D4—21no—
745D4—61no—
746D4—61no—
747D4—61no—
748D4—61no—
749D4—122no—
750D4—122no—
751D4—122no—
752D4—122no—
753D4—121no—
754D4—121no—
755D4—121no—
756D4—121no—
757D4—241no—
758D4C4×D1212yes—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—21no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—31no—
768C2×C4—31no—
769C2×C4—61no—
770C2×C4—61no—
771C2×C4—61no—
772C2×C4—61no—
773C2×C4—61no—
774C2×C4—61no—
775C2×C4—61no—
776C2×C4—61no—
777C2×C4—61no—
778C2×C4—61no—
779C2×C4—62no—
780C2×C4—61no—
781C2×C4—61no—
782C2×C4—122no—
783C2×C4—122no—
784C2×C4—128no—
785C2×C4—122no—
786C2×C4—121no—
787C2×C4—121no—
788C2×C4—121no—
789C2×C4—121no—
790C2×C4—121no—
791C2×C4—121no—
792C2×C4C22×C4×D311yescharacteristic
793C2×C4C22×D1211yescharacteristic
794C2×C4C2×#23511yescharacteristic
795C2×C4C2×D3×D411yescharacteristic
796C2×C4#100411yescharacteristic
797C2×C4#100911yescharacteristic
798C8—21no—
799C8—21no—
800C8—21no—
801C8—21no—
802C8—22no—
803C8—41no—
804C8—61no—
805C8—61no—
806C8—61no—
807C8—61no—
808C8—121no—
809C8—121no—
810C2×C3—21no—
811C2×C3—21no—
812C2×C3—42no—
813C2×C3#235811yescharacteristic
814C2×C3C2×#44311yescharacteristic
815C2×C3#295611yescharacteristic
816D3—22no—
817D3—41no—
818D3—81no—
819D3—81no—
820C22—21no—
821C22—21no—
822C22—22no—
823C22—32no—
824C22—41no—
825C22—41no—
826C22—61no—
827C22—61no—
828C22—61no—
829C22—61no—
830C22—61no—
831C22—122no—
832C22—122no—
833C22—121no—
834C22—121no—
835C22—121no—
836C22—121no—
837C22—121no—
838C22—121no—
839C22—244no—
840C22#552711yescharacteristic
841C22C4×D3×D411yescharacteristic
842C22#555411yescharacteristic
843C4—24no—
844C4—22no—
845C4—41no—
846C4—41no—
847C4—61no—
848C4—61no—
849C4—122no—
850C4—121no—
851C4—121no—
852C4C2×C4×D1211yescharacteristic
853C4#549011yescharacteristic
854C4#554511yescharacteristic
855C4D4×D1211yescharacteristic
856C3#2288811yescharacteristic, complemented, Sylow
857C2—21no—
858C2—21no—
859C2—42no—
860C2—62no—
861C2—121no—
862C2—241no—
863C2—241no—
864C2#7357711yescharacteristic
865C2D3×#44311yescharacteristic
866C2#7988911yescharacteristic
subgroupG/H
centerC2×C4C2×D3×D4
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC3×#1764C2
socleC22×C3C2×C4×D4
prime radical#78833C2
cosocleC22×C3×C4C24
hypercenter#1764D3
hypocenterC3#22888
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1764

Complements

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

NH ≅ G/Ntype
1. #83793C2semidirect
2. C2×D3×#104C2semidirect
3. C2×#4824C2semidirect
5. #78555C2semidirect
6. C3×#1764C2semidirect
7. #72010C2semidirect
8. #70292C2semidirect
9. #69900C2semidirect
10. #69795C2semidirect
11. C4×(C2×D3)⋊C8C2semidirect
12. #68946C2semidirect
13. #68941C2semidirect
14. #68756C2semidirect
15. #68745C2semidirect
21. C2×#907C22semidirect
28. C3×#405C22semidirect
29. C2×C3×C4×C8C22semidirect
32. C2×#825C22semidirect
37. C2×#822C22semidirect
40. #5110C22semidirect
44. C2×#819C22semidirect
46. #4999C22semidirect
48. C2×#805C22semidirect
49. C2×C4×C3⋊C8C22semidirect
52. #4810C4semidirect
53. #4809C4semidirect
54. #4808C4semidirect
55. #4806C4semidirect
56. #4783C4semidirect
57. #4781C4semidirect
58. #4776C4semidirect
59. #4773C4semidirect
64. C3×#341C22semidirect
65. C3×#339C22semidirect
66. #4558C22semidirect
67. #4550C22semidirect
68. #4550C22semidirect
69. #4532C22semidirect
83. #1764D3semidirect
116. C2×#216C2×C4semidirect
117. C2×#215C2×C4semidirect
118. C2×#214C2×C4semidirect
119. C2×#213C2×C4semidirect
132. C2×Dic12C2×C4semidirect
135. C2×D24C2×C4semidirect
136. C2×#204C2×C4semidirect
137. C2×#204C2×C4semidirect
152. C3×#104D4semidirect
153. C3×#103C2×C4semidirect
154. C3×#103C2×C4semidirect
155. C3×#102C2×C4semidirect
156. C3×#102C2×C4semidirect
181. #810C2×C4semidirect
182. #810C2×C4semidirect
183. #809C2×C4semidirect
184. #809C2×C4semidirect
234. #405C2×D3semidirect
236. C2×C4×C8C2×D3semidirect
238. #341C2×D3semidirect
240. #339C2×D3semidirect
444. #104D12semidirect
447. #103C4×D3semidirect
448. #103C4×D3semidirect
451. #102C4×D3semidirect
452. #102C4×D3semidirect
708. C2×D3#443semidirect
856. C3#22888semidirect

Maximal subgroups

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

subgroupindex
#837932
C2×D3×#1042
C2×#48242
#788332
#785552
C3×#17642
#720102
#702922
#699002
#697952
C4×(C2×D3)⋊C82
#689462
#689412
#687562
#687452
#228883