Finite Group Databasebeta

← #10815962

Subgroups — #10815962

Order 768.

1020 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5139C211yesmaximal, characteristic, complemented
2#83757C211yesmaximal, characteristic, complemented
3C2×#4895C211yesmaximal, characteristic, complemented
4#78631C211yesmaximal, characteristic, complemented
5#78610C211yesmaximal, characteristic
6C3×#1855C211yesmaximal, characteristic, complemented
7#70722C211yesmaximal, characteristic, complemented
8#70699C211yesmaximal, characteristic, complemented
9#70697C211yesmaximal, characteristic, complemented
10#69966C211yesmaximal, characteristic, complemented
11#69907C211yesmaximal, characteristic, complemented
12#68946C211yesmaximal, characteristic, complemented
13#68946C211yesmaximal, characteristic, complemented
14#68927C211yesmaximal, characteristic, complemented
15#68918C211yesmaximal, characteristic, complemented
16#22889—31nomaximal, Sylow
17C22×#235C2211yescharacteristic
18C22×C3×M16C2211yescharacteristic
19#5791C2211yescharacteristic
20C2×#926C2211yescharacteristic
21C2×#907C2211yescharacteristic
22C2×#907C2211yescharacteristic
23C2×#907C2211yescharacteristic, complemented
24C2×#904C2211yescharacteristic
25C2×#904C2211yescharacteristic
26C2×C3×#108C2211yescharacteristic, complemented
27C2×C3×#108C2211yescharacteristic, complemented
28C3×#407C2211yescharacteristic
29C2×C3×C22⋊C8C2211yescharacteristic
30C2×#830C2211yescharacteristic
31#5139—24no—
32C2×#825C2211yescharacteristic
33C2×#825C2211yescharacteristic
34C2×#825C2211yescharacteristic
35C2×#825C2211yescharacteristic
36C2×#825C2211yescharacteristic, complemented
37C2×#825C2211yescharacteristic, complemented
38#5129C2211yescharacteristic
39#5129C2211yescharacteristic
40#5129C2211yescharacteristic, complemented
41#5128—21no—
42#5127—21no—
43#5122C2211yescharacteristic, complemented
44#5119C2211yescharacteristic, complemented
45#5113C2211yescharacteristic
46#5113C2211yescharacteristic
47#5111—21no—
48C8×#67—21no—
49C2×#815C2211yescharacteristic, complemented
50C2×C8×Dic3C2211yescharacteristic, complemented
51#4895—24no—
52#4739C411yescharacteristic, complemented
53#4738C411yescharacteristic, complemented
54#4734C411yescharacteristic, complemented
55#4734C411yescharacteristic, complemented
56#4733C411yescharacteristic, complemented
57#4733C411yescharacteristic, complemented
58#4732C411yescharacteristic, complemented
59#4731C411yescharacteristic, complemented
60#4727—21no—
61#4727—21no—
62#4726—21no—
63D3×C22⋊C8—21no—
64C3×#341C2211yescharacteristic, complemented
65C3×#341C2211yescharacteristic, complemented
66#4555C2211yescharacteristic, complemented
67#4555C2211yescharacteristic, complemented
68#4550C2211yescharacteristic, complemented
69#4550C2211yescharacteristic, complemented
70#3002—31no—
71C2×#443—31no—
72#2933—31no—
73C2×#421—31no—
74#2880—31no—
75#1975—31no—
76#1937—31no—
77#1929—31no—
78#1897—31no—
79#1876—31no—
80#1876—31no—
81#1866—31no—
82#1855D311yescharacteristic, complemented
83#1765—31no—
84#1750—31no—
85C23×C3×C4C2311yescharacteristic
86C22×#67—21no—
87C2×#235—21no—
88C2×#235—21no—
89C2×#235—22no—
90C2×#235—22no—
91C2×#235—41no—
92C2×#235—41no—
93C2×#235C2×C411yescharacteristic
94C2×#235C2×C411yescharacteristic
95C2×#235C2311yescharacteristic
96C2×#235C2311yescharacteristic
97C2×#235C2311yescharacteristic
98C22×D12C2×C411yescharacteristic
99C22×C4×D3—21no—
100C22×Dic6C2×C411yescharacteristic
101C2×C3×M16—21no—
102C2×C3×M16—22no—
103C2×C3×M16—41no—
104C2×C3×M16C2311yescharacteristic
105C2×C3×M16C2311yescharacteristic
106C2×C3×M16C2311yescharacteristic
107C2×C3×M16C2311yescharacteristic
108C22×C3×C8—21no—
109C22×C3×C8C2311yescharacteristic
110C22×C3×C8C2311yescharacteristic
111#953—21no—
112C2×#217—21no—
113#930C2×C411yescharacteristic
114#930C2×C411yescharacteristic
115#929—21no—
116C4×#67—21no—
117C4×#67—21no—
118#926—22no—
119#926—41no—
120#926C2311yescharacteristic
121C2×C4⋊Dic3—21no—
122#924C2×C411yescharacteristic
123#924C2×C411yescharacteristic
124C2×C4×Dic3C2311yescharacteristic
125C2×C4×Dic3C2311yescharacteristic
126C22×C3⋊C8C2311yescharacteristic
127C22×C3⋊C8C2311yescharacteristic
128#907—22no—
129#907—22no—
130#907—22no—
131#907—41no—
132#907—41no—
133#907—41no—
134C2×Dic12C2×C411yescharacteristic
135C2×Dic12C2×C411yescharacteristic
136#904—22no—
137#904—22no—
138#904—41no—
139#904—41no—
140C2×D24C2×C411yescharacteristic
141C2×D24C2×C411yescharacteristic
142C2×#204C2×C411yescharacteristic
143C2×#204C2×C411yescharacteristic
144C2×#204C2×C411yescharacteristic
145C2×#204C2×C411yescharacteristic
146C2×ΓL(1,𝔽25)—21no—
147C2×ΓL(1,𝔽25)—21no—
148C2×ΓL(1,𝔽25)—21no—
149C2×D3×C8—21no—
150C2×D3×C8—21no—
151C2×D3×C8—21no—
152C3×#108—22no—
153C3×#108—41no—
154C3×C22⋊C8—21no—
155C3×C22⋊C8—21no—
156C3×C22⋊C8C2×C411yescharacteristic
157C3×C22⋊C8C2×C411yescharacteristic
158C3×C22⋊C8C2×C411yescharacteristic
159C3×C22⋊C8C2×C411yescharacteristic
160#830D411yescharacteristic
161#830D411yescharacteristic
162#830D411yescharacteristic
163#830D411yescharacteristic
164#825—22no—
165#825—22no—
166#825—22no—
167#825—22no—
168#825—41no—
169#825D414yescomplemented
170#821C2×C411yescharacteristic
171#821C2×C411yescharacteristic
172#821C2×C411yescharacteristic
173#821C2×C411yescharacteristic
174(C2×D3)⋊C8—21no—
175(C2×D3)⋊C8—21no—
176(C2×D3)⋊C8—21no—
177(C2×D3)⋊C8—21no—
178(C2×D3)⋊C8—21no—
179(C2×D3)⋊C8—21no—
180#816C2×C411yescharacteristic
181#816C2×C411yescharacteristic
182#816C2×C411yescharacteristic
183#816C2×C411yescharacteristic
184#815—21no—
185#815—41no—
186Dic3⋊C8—21no—
187Dic3⋊C8—21no—
188C8×Dic3—22no—
189C8×Dic3—21no—
190C22×#41—31no—
191C2×#135—31no—
192C2×#135—31no—
193C2×#131—31no—
194C2×#131—31no—
195C2×#131—31no—
196C22×M16C2×D311yescharacteristic
197#525—31no—
198C2×#117—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×#108C2×D311yescharacteristic, complemented
213C2×#108C2×D311yescharacteristic, complemented
214#424—31no—
215#421—64no—
216C2×#104—31no—
217C2×#104—31no—
218C2×#104—31no—
219C2×#104—31no—
220C2×#104—31no—
221C2×#104—31no—
222#416—31no—
223#416—31no—
224#408—31no—
225#408—31no—
226#408—31no—
227#408—61no—
228#408—61no—
229#407—61no—
230#407C2×D311yescharacteristic
231C2×C22⋊C8—31no—
232C2×C22⋊C8—61no—
233C2×C22⋊C8C2×D311yescharacteristic
234#405—31no—
235C2×#97—31no—
236C2×C4×C8—31no—
237#341C2×D311yescharacteristic, complemented
238#341C2×D311yescharacteristic, complemented
239#339—31no—
240#339—31no—
241#336—31no—
242#336—31no—
243C24×C3#4111yescharacteristic
244C23×D3—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4C22×C411yescharacteristic
250C22×C3×C4C22×C411yescharacteristic
251C22×C3×C4C2×D411yescharacteristic
252C22×C3×C4C2×D411yescharacteristic
253C22×C3×C4#4111yescharacteristic
254C22×C3×C4C2411yescharacteristic
255C2×#67—21no—
256C2×#67—21no—
257C2×#67—21no—
258C2×#67—21no—
259C2×#67—21no—
260C2×#67—21no—
261C2×#67—21no—
262C2×#67—42no—
263C2×#67—42no—
264C22×Dic3—21no—
265C22×Dic3—21no—
266C22×Dic3—21no—
267#235—21no—
268#235—21no—
269#235—21no—
270#235—21no—
271#235—21no—
272#235—21no—
273#235—21no—
274#235—21no—
275#235—21no—
276#235—21no—
277#235—22no—
278#235—22no—
279#235—41no—
280#235—41no—
281#235—42no—
282#235—42no—
283#235—42no—
284#235—42no—
285#235C2×D412yes—
286#235#4112yes—
287C2×D12—22no—
288C2×D12—21no—
289C2×D12—41no—
290C2×D12C22×C411yescharacteristic
291C2×D12C22×C411yescharacteristic
292C2×D12C22×C411yescharacteristic
293C2×C4×D3—21no—
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×Dic6—22no—
301C2×Dic6—21no—
302C2×Dic6—41no—
303C2×Dic6C22×C411yescharacteristic
304C2×Dic6C22×C411yescharacteristic
305C2×Dic6C22×C411yescharacteristic
306C3×M16—21no—
307C3×M16—21no—
308C3×M16—21no—
309C3×M16—21no—
310C3×M16—21no—
311C3×M16—21no—
312C3×M16—21no—
313C3×M16—42no—
314C3×M16C2×D412yes—
315C2×C3×C8—21no—
316C2×C3×C8—21no—
317C2×C3×C8—21no—
318C2×C3×C8—21no—
319C2×C3×C8—21no—
320C2×C3×C8—21no—
321C2×C3×C8—21no—
322C2×C3×C8—21no—
323C2×C3×C8—42no—
324C2×C3×C8C22×C411yescharacteristic
325C2×C3×C8C22×C411yescharacteristic
326C2×C3×C8C22×C411yescharacteristic
327C2×C3×C8C22×C411yescharacteristic
328#217—21no—
329#217—21no—
330#217—21no—
331#217—42no—
332(C2×D3)⋊C4—21no—
333(C2×D3)⋊C4—21no—
334C4⋊Dic3—42no—
335C4⋊Dic3C22×C411yescharacteristic
336C4⋊Dic3C22×C411yescharacteristic
337Dic3⋊C4—21no—
338Dic3⋊C4—21no—
339C4×Dic3—21no—
340C4×Dic3—21no—
341C4×Dic3—21no—
342C4×Dic3—21no—
343C4×Dic3C2×D412yes—
344C2×C3⋊C8—21no—
345C2×C3⋊C8—21no—
346C2×C3⋊C8—21no—
347C2×C3⋊C8—21no—
348C2×C3⋊C8C2×D411yescharacteristic
349C2×C3⋊C8C2×D411yescharacteristic
350C2×C3⋊C8C2×D411yescharacteristic
351C2×C3⋊C8C2×D411yescharacteristic
352Dic12—22no—
353Dic12—41no—
354D24—22no—
355D24—41no—
356#204—22no—
357#204—22no—
358#204—41no—
359#204—41no—
360ΓL(1,𝔽25)—42no—
361ΓL(1,𝔽25)—42no—
362ΓL(1,𝔽25)—42no—
363D3×C8—42no—
364D3×C8—42no—
365D3×C8—42no—
366C2×#41—31no—
367C2×#41—31no—
368C2×#41—31no—
369C2×#41—31no—
370C2×#41—31no—
371C2×#41—62no—
372C2×#41—62no—
373C2×#41—61no—
374C2×#41—61no—
375C2×#41—121no—
376C2×#41—121no—
377C22×Q8—31no—
378C22×D4—31no—
379C22×D4—61no—
380C23×C4—61no—
381C23×C4C22×D311yescharacteristic
382#135—62no—
383#135—62no—
384#135—121no—
385#135—121no—
386C2×Q16—31no—
387C2×Q16—31no—
388C2×SD16—31no—
389C2×SD16—31no—
390C2×SD16—31no—
391C2×SD16—31no—
392C2×D8—31no—
393C2×D8—31no—
394#131—62no—
395#131—62no—
396#131—62no—
397#131—121no—
398#131—121no—
399#131—121no—
400C2×M16—21no—
401C2×M16—22no—
402C2×M16—41no—
403C2×M16—61no—
404C2×M16—61no—
405C2×M16—61no—
406C2×M16C22×D311yescharacteristic
407C2×M16C22×D311yescharacteristic
408C2×M16C22×D311yescharacteristic
409C2×M16C22×D311yescharacteristic
410C22×C8—21no—
411C22×C8—31no—
412C22×C8—31no—
413C22×C8—61no—
414C22×C8—61no—
415C22×C8—61no—
416C22×C8C22×D311yescharacteristic
417C22×C8C22×D311yescharacteristic
418#123—61no—
419C22⋊Q8—31no—
420C22⋊Q8—31no—
421#121—31no—
422#121—31no—
423#120—61no—
424C4×D4—61no—
425C4×D4—61no—
426#117—31no—
427#117—62no—
428#117—121no—
429C2×C4⋊C4—61no—
430C2×C22⋊C4—61no—
431C2×C42—31no—
432C2×C42—31no—
433#108—22no—
434#108—41no—
435C4⋊C8—61no—
436C4⋊C8—61no—
437#104—34no—
438#104—62no—
439#104—62no—
440#104—62no—
441#104—62no—
442#104—121no—
443#103—31no—
444#103—31no—
445#103—31no—
446#103—31no—
447#102—31no—
448#102—31no—
449#102—31no—
450#102—31no—
451C22⋊C8—21no—
452C22⋊C8—21no—
453C22⋊C8—31no—
454C22⋊C8—31no—
455C22⋊C8—31no—
456C22⋊C8—31no—
457C22⋊C8—61no—
458C22⋊C8—61no—
459C22⋊C8—61no—
460C22⋊C8—61no—
461C22⋊C8—61no—
462C22⋊C8—61no—
463C22⋊C8C4×D311yescharacteristic
464C22⋊C8C4×D311yescharacteristic
465C22⋊C8C4×D311yescharacteristic
466C22⋊C8C4×D311yescharacteristic
467#97—61no—
468#97—121no—
469C4×C8—62no—
470C4×C8—61no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—41no—
474C23×C3—41no—
475C23×C3C4×D411yescharacteristic
476C23×C3C4×D411yescharacteristic
477C23×C3C2×#4111yescharacteristic
478C22×D3—21no—
479C22×D3—21no—
480C22×D3—21no—
481C22×D3—42no—
482C22×D3—42no—
483C22×D3—81no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4C4×D411yescharacteristic
495C2×C3×C4C4×D411yescharacteristic
496C2×C3×C4C23×C411yescharacteristic
497C2×C3×C4C22×D411yescharacteristic
498C2×C3×C4C22×D411yescharacteristic
499C2×C3×C4C2×#4111yescharacteristic
500C2×C3×C4H(5,𝔽2)11yescharacteristic
501C2×C3×C4H(5,𝔽2)11yescharacteristic
502#67—22no—
503#67—22no—
504#67—42no—
505#67—42no—
506#67—42no—
507#67—41no—
508#67—41no—
509#67—41no—
510#67—41no—
511#67—81no—
512C2×Dic3—21no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—22no—
518C2×Dic3—42no—
519C2×Dic3—41no—
520C2×Dic3—41no—
521C2×Dic3—41no—
522C2×Dic3—41no—
523C2×Dic3—41no—
524D12—21no—
525D12—21no—
526D12—21no—
527D12—21no—
528D12—21no—
529D12—42no—
530D12C4×D412yes—
531C4×D3—22no—
532C4×D3—22no—
533C4×D3—42no—
534C4×D3—42no—
535C4×D3—41no—
536C4×D3—41no—
537C4×D3—41no—
538C4×D3—41no—
539Dic6—21no—
540Dic6—21no—
541Dic6—21no—
542Dic6—21no—
543Dic6—21no—
544Dic6—42no—
545Dic6C4×D412yes—
546C3×C8—21no—
547C3×C8—21no—
548C3×C8—21no—
549C3×C8—21no—
550C3×C8—22no—
551C3×C8—41no—
552C3×C8—41no—
553C3×C8—41no—
554C3⋊C8—21no—
555C3⋊C8—21no—
556C3⋊C8—21no—
557C3⋊C8—21no—
558C24—61no—
559C24#23911yescharacteristic
560#41—32no—
561#41—32no—
562#41—62no—
563#41—62no—
564#41—61no—
565#41—61no—
566#41—61no—
567#41—61no—
568#41—61no—
569#41—61no—
570#41—61no—
571#41—61no—
572#41—61no—
573#41—61no—
574#41—122no—
575#41—122no—
576#41—121no—
577#41—121no—
578#41—122no—
579#41—122no—
580C2×Q8—31no—
581C2×Q8—31no—
582C2×Q8—31no—
583C2×Q8—62no—
584C2×Q8—61no—
585C2×Q8—121no—
586C2×D4—31no—
587C2×D4—31no—
588C2×D4—31no—
589C2×D4—62no—
590C2×D4—61no—
591C2×D4—61no—
592C2×D4—61no—
593C2×D4—61no—
594C2×D4—61no—
595C2×D4—61no—
596C2×D4—61no—
597C2×D4—61no—
598C2×D4—121no—
599C2×D4—122no—
600C2×D4—122no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—61no—
606C22×C4—61no—
607C22×C4—61no—
608C22×C4—61no—
609C22×C4—61no—
610C22×C4—61no—
611C22×C4—61no—
612C22×C4—61no—
613C22×C4—122no—
614C22×C4—122no—
615C22×C4C2×C4×D311yescharacteristic
616C22×C4C2×C4×D311yescharacteristic
617C22×C4D3×D411yescharacteristic
618C22×C4D3×D411yescharacteristic
619C22×C4#23911yescharacteristic
620C22×C4C23×D311yescharacteristic
621Q16—62no—
622Q16—121no—
623SD16—62no—
624SD16—62no—
625SD16—121no—
626SD16—121no—
627D8—62no—
628D8—121no—
629M16—21no—
630M16—21no—
631M16—21no—
632M16—21no—
633M16—21no—
634M16—21no—
635M16—21no—
636M16—42no—
637M16—122no—
638M16—122no—
639M16—122no—
640M16D3×D412yes—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—31no—
650C2×C8—31no—
651C2×C8—31no—
652C2×C8—31no—
653C2×C8—42no—
654C2×C8—61no—
655C2×C8—61no—
656C2×C8—61no—
657C2×C8—61no—
658C2×C8—122no—
659C2×C8—122no—
660C2×C8—122no—
661C2×C8C2×C4×D311yescharacteristic
662C2×C8C2×C4×D311yescharacteristic
663C2×C8C2×C4×D311yescharacteristic
664C2×C8C2×C4×D311yescharacteristic
665C4⋊C4—31no—
666C4⋊C4—31no—
667C4⋊C4—61no—
668C4⋊C4—61no—
669C4⋊C4—122no—
670C22⋊C4—61no—
671C22⋊C4—61no—
672C22⋊C4—61no—
673C22⋊C4—61no—
674C22⋊C4—61no—
675C22⋊C4—122no—
676C42—32no—
677C42—61no—
678C42—61no—
679C42—61no—
680C42—61no—
681C22×C3—21no—
682C22×C3—21no—
683C22×C3—21no—
684C22×C3—21no—
685C22×C3—21no—
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—21no—
689C22×C3—81no—
690C22×C3—81no—
691C22×C3C2×C4×D411yescharacteristic
692C22×C3#54611yescharacteristic
693C22×C3#55111yescharacteristic
694C2×D3—22no—
695C2×D3—41no—
696C2×D3—41no—
697C2×D3—41no—
698C2×D3—41no—
699C2×D3—41no—
700C2×D3—41no—
701C2×D3—41no—
702C2×D3—41no—
703C2×D3—84no—
704C3×C4—21no—
705C3×C4—21no—
706C3×C4C2×C4×D411yescharacteristic
707C3×C4#51811yescharacteristic
708C3×C4D4211yescharacteristic
709C3×C4#54611yescharacteristic
710Dic3—22no—
711Dic3—42no—
712Dic3—41no—
713Dic3—41no—
714Dic3—41no—
715Dic3—41no—
716Dic3—81no—
717C23—21no—
718C23—21no—
719C23—41no—
720C23—41no—
721C23—61no—
722C23—61no—
723C23—61no—
724C23—122no—
725C23—122no—
726C23—241no—
727C23#89311yescharacteristic
728C23#89311yescharacteristic
729C23C2×#23911yescharacteristic
730Q8—32no—
731Q8—61no—
732Q8—61no—
733Q8—61no—
734Q8—61no—
735Q8—61no—
736Q8—122no—
737D4—32no—
738D4—62no—
739D4—62no—
740D4—61no—
741D4—61no—
742D4—61no—
743D4—61no—
744D4—61no—
745D4—122no—
746D4—122no—
747D4—122no—
748D4—122no—
749D4—121no—
750D4—121no—
751D4—121no—
752D4—121no—
753D4—241no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—61no—
765C2×C4—62no—
766C2×C4—62no—
767C2×C4—61no—
768C2×C4—61no—
769C2×C4—61no—
770C2×C4—61no—
771C2×C4—62no—
772C2×C4—122no—
773C2×C4—122no—
774C2×C4—122no—
775C2×C4—121no—
776C2×C4—121no—
777C2×C4—121no—
778C2×C4—121no—
779C2×C4—121no—
780C2×C4—121no—
781C2×C4—121no—
782C2×C4—121no—
783C2×C4—121no—
784C2×C4#89311yescharacteristic
785C2×C4#89311yescharacteristic
786C2×C4C22×C4×D311yescharacteristic
787C2×C4C2×D3×D411yescharacteristic
788C2×C4C2×D3×D411yescharacteristic
789C2×C4#100411yescharacteristic
790C2×C4D3×#4111yescharacteristic
791C2×C4#100911yescharacteristic
792C8—21no—
793C8—21no—
794C8—21no—
795C8—21no—
796C8—22no—
797C8—41no—
798C8—41no—
799C8—41no—
800C8—61no—
801C8—61no—
802C8—61no—
803C8—61no—
804C2×C3—21no—
805C2×C3—21no—
806C2×C3—41no—
807C2×C3—41no—
808C2×C3#235811yescharacteristic
809C2×C3#295511yescharacteristic
810C2×C3#295711yescharacteristic
811D3—42no—
812D3—81no—
813D3—81no—
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—21no—
821C22—21no—
822C22—62no—
823C22—81no—
824C22—81no—
825C22—121no—
826C22—121no—
827C22—121no—
828C22—121no—
829C22—121no—
830C22—121no—
831C22—121no—
832C22—121no—
833C22—244no—
834C22C2×#89311yescharacteristic
835C22#563011yescharacteristic
836C22#563711yescharacteristic
837C4—21no—
838C4—21no—
839C4—62no—
840C4—122no—
841C4—121no—
842C4—121no—
843C4—121no—
844C4—121no—
845C4—241no—
846C4C4×D3×D411yescharacteristic
847C4#554511yescharacteristic
848C4#559011yescharacteristic
849C4#565411yescharacteristic
850C3#2288911yescharacteristic, complemented, Sylow
851C2—21no—
852C2—21no—
853C2—41no—
854C2—41no—
855C2—122no—
856C2—241no—
857C2—241no—
858C2#7459611yescharacteristic
859C2#7924911yescharacteristic
860C2#7925711yescharacteristic
subgroupG/H
centerC2×C4C2×D3×D4
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC3×#1855C2
socleC22×C3C2×C4×D4
prime radical#78610C2
cosocleC22×C3×C4C24
hypercenter#1855D3
hypocenterC3#22889
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1855

Complements

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

NH ≅ G/Ntype
1. C2×#5139C2semidirect
2. #83757C2semidirect
3. C2×#4895C2semidirect
4. #78631C2semidirect
6. C3×#1855C2semidirect
7. #70722C2semidirect
8. #70699C2semidirect
9. #70697C2semidirect
10. #69966C2semidirect
11. #69907C2semidirect
12. #68946C2semidirect
13. #68946C2semidirect
14. #68927C2semidirect
15. #68918C2semidirect
23. C2×#907C22semidirect
26. C2×C3×#108C22semidirect
27. C2×C3×#108C22semidirect
36. C2×#825C22semidirect
37. C2×#825C22semidirect
40. #5129C22semidirect
43. #5122C22semidirect
44. #5119C22semidirect
49. C2×#815C22semidirect
50. C2×C8×Dic3C22semidirect
52. #4739C4semidirect
53. #4738C4semidirect
54. #4734C4semidirect
55. #4734C4semidirect
56. #4733C4semidirect
57. #4733C4semidirect
58. #4732C4semidirect
59. #4731C4semidirect
64. C3×#341C22semidirect
65. C3×#341C22semidirect
66. #4555C22semidirect
67. #4555C22semidirect
68. #4550C22semidirect
69. #4550C22semidirect
82. #1855D3semidirect
169. #825D4semidirect
212. C2×#108C2×D3semidirect
213. C2×#108C2×D3semidirect
237. #341C2×D3semidirect
238. #341C2×D3semidirect
850. C3#22889semidirect

Maximal subgroups

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

subgroupindex
C2×#51392
#837572
C2×#48952
#786312
#786102
C3×#18552
#707222
#706992
#706972
#699662
#699072
#689462
#689272
#689182
#228893