Finite Group Databasebeta

← #10815947

Subgroups — #10815947

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
1C22×#825C211yesmaximal, 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#70696C211yesmaximal, characteristic, complemented
10#69965C211yesmaximal, characteristic, complemented
11Dic3×C22⋊C8C211yesmaximal, characteristic, complemented
12#68946C211yesmaximal, characteristic, complemented
13#68946C211yesmaximal, characteristic, complemented
14#68926C211yesmaximal, characteristic, complemented
15#68918C211yesmaximal, characteristic, complemented
16#22888—31nomaximal, Sylow
17C22×#235C2211yescharacteristic
18C22×C3×M16C2211yescharacteristic
19#5791C2211yescharacteristic
20C22×C4×Dic3C2211yescharacteristic
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
31C2×#825—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×C8×Dic3C2211yescharacteristic, 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—
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#1855D311yescharacteristic, complemented
83#1764—31no—
84C4×C22⋊C8—31no—
85C23×C3×C4C2311yescharacteristic
86C22×#67—21no—
87C23×Dic3—21no—
88C2×#235—21no—
89C2×#235—21no—
90C2×#235—22no—
91C2×#235—22no—
92C2×#235—41no—
93C2×#235—41no—
94C2×#235C2×C411yescharacteristic
95C2×#235C2×C411yescharacteristic
96C2×#235C2311yescharacteristic
97C2×#235C2311yescharacteristic
98C2×#235C2311yescharacteristic
99C22×D12C2×C411yescharacteristic
100C22×C4×D3—21no—
101C22×Dic6C2×C411yescharacteristic
102C2×C3×M16—21no—
103C2×C3×M16—22no—
104C2×C3×M16—41no—
105C2×C3×M16C2311yescharacteristic
106C2×C3×M16C2311yescharacteristic
107C2×C3×M16C2311yescharacteristic
108C2×C3×M16C2311yescharacteristic
109C22×C3×C8—21no—
110C22×C3×C8C2311yescharacteristic
111C22×C3×C8C2311yescharacteristic
112#953—21no—
113#930C2×C411yescharacteristic
114#930C2×C411yescharacteristic
115#929—21no—
116C4×#67—21no—
117C4×#67—21no—
118#926C2311yescharacteristic
119#924C2×C411yescharacteristic
120#924C2×C411yescharacteristic
121C2×C4×Dic3—22no—
122C2×C4×Dic3—21no—
123C2×C4×Dic3—41no—
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, complemented
135C2×Dic12C2×C411yescharacteristic, complemented
136#904—22no—
137#904—22no—
138#904—41no—
139#904—41no—
140C2×D24C2×C411yescharacteristic, complemented
141C2×D24C2×C411yescharacteristic, complemented
142C2×#204C2×C411yescharacteristic, complemented
143C2×#204C2×C411yescharacteristic, complemented
144C2×#204C2×C411yescharacteristic, complemented
145C2×#204C2×C411yescharacteristic, complemented
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, complemented
171#821C2×C411yescharacteristic, complemented
172#821C2×C411yescharacteristic, complemented
173#821C2×C411yescharacteristic, complemented
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, complemented
181#816C2×C411yescharacteristic, complemented
182#816C2×C411yescharacteristic, complemented
183#816C2×C411yescharacteristic, complemented
184#815—21no—
185Dic3⋊C8—21no—
186Dic3⋊C8—21no—
187C8×Dic3—22no—
188C8×Dic3—21no—
189C8×Dic3—41no—
190C22×#41—31no—
191C2×#135—31no—
192C2×#135—31no—
193C2×#131—31no—
194C2×#131—31no—
195C2×#131—31no—
196C22×M16C2×D311yescharacteristic
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×#108C2×D311yescharacteristic, complemented
213C2×#108C2×D311yescharacteristic, complemented
214#424—31no—
215C2×#104—31no—
216C2×#104—31no—
217C2×#104—31no—
218C2×#104—31no—
219C2×#104—31no—
220C2×#104—31no—
221C2×#104—64no—
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×C4×C8—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—24no—
266C22×Dic3—21no—
267C22×Dic3—21no—
268C22×Dic3—42no—
269C22×Dic3—42no—
270#235—21no—
271#235—21no—
272#235—21no—
273#235—21no—
274#235—21no—
275#235—21no—
276#235—21no—
277#235—21no—
278#235—21no—
279#235—21no—
280#235—22no—
281#235—22no—
282#235—41no—
283#235—41no—
284#235—42no—
285#235—42no—
286#235—42no—
287#235—42no—
288#235C2×D412yes—
289#235#4112yes—
290C2×D12—22no—
291C2×D12—21no—
292C2×D12—41no—
293C2×D12C22×C411yescharacteristic
294C2×D12C22×C411yescharacteristic
295C2×D12C22×C411yescharacteristic
296C2×C4×D3—21no—
297C2×C4×D3—21no—
298C2×C4×D3—21no—
299C2×C4×D3—21no—
300C2×C4×D3—21no—
301C2×C4×D3—42no—
302C2×C4×D3—42no—
303C2×Dic6—22no—
304C2×Dic6—21no—
305C2×Dic6—41no—
306C2×Dic6C22×C411yescharacteristic
307C2×Dic6C22×C411yescharacteristic
308C2×Dic6C22×C411yescharacteristic
309C3×M16—21no—
310C3×M16—21no—
311C3×M16—21no—
312C3×M16—21no—
313C3×M16—21no—
314C3×M16—21no—
315C3×M16—21no—
316C3×M16—42no—
317C3×M16C2×D412yes—
318C2×C3×C8—21no—
319C2×C3×C8—21no—
320C2×C3×C8—21no—
321C2×C3×C8—21no—
322C2×C3×C8—21no—
323C2×C3×C8—21no—
324C2×C3×C8—21no—
325C2×C3×C8—21no—
326C2×C3×C8—42no—
327C2×C3×C8C22×C411yescharacteristic
328C2×C3×C8C22×C411yescharacteristic
329C2×C3×C8C22×C411yescharacteristic
330C2×C3×C8C22×C411yescharacteristic
331#217—21no—
332#217—21no—
333#217—21no—
334(C2×D3)⋊C4—21no—
335(C2×D3)⋊C4—21no—
336C4⋊Dic3C22×C411yescharacteristic
337C4⋊Dic3C22×C411yescharacteristic
338Dic3⋊C4—21no—
339Dic3⋊C4—21no—
340C4×Dic3—21no—
341C4×Dic3—21no—
342C4×Dic3—21no—
343C4×Dic3—21no—
344C4×Dic3—42no—
345C4×Dic3C2×D412yes—
346C2×C3⋊C8—21no—
347C2×C3⋊C8—21no—
348C2×C3⋊C8—21no—
349C2×C3⋊C8—21no—
350C2×C3⋊C8C2×D411yescharacteristic
351C2×C3⋊C8C2×D411yescharacteristic
352C2×C3⋊C8C2×D411yescharacteristic
353C2×C3⋊C8C2×D411yescharacteristic
354Dic12—22no—
355Dic12—41no—
356D24—22no—
357D24—41no—
358#204—22no—
359#204—22no—
360#204—41no—
361#204—41no—
362ΓL(1,𝔽25)—42no—
363ΓL(1,𝔽25)—42no—
364ΓL(1,𝔽25)—42no—
365D3×C8—42no—
366D3×C8—42no—
367D3×C8—42no—
368C2×#41—31no—
369C2×#41—31no—
370C2×#41—31no—
371C2×#41—31no—
372C2×#41—31no—
373C2×#41—62no—
374C2×#41—62no—
375C2×#41—61no—
376C2×#41—61no—
377C2×#41—121no—
378C2×#41—121no—
379C22×Q8—31no—
380C22×D4—31no—
381C22×D4—61no—
382C23×C4—61no—
383C23×C4—61no—
384C23×C4C22×D311yescharacteristic
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—62no—
398#131—62no—
399#131—62no—
400#131—121no—
401#131—121no—
402#131—121no—
403C2×M16—21no—
404C2×M16—22no—
405C2×M16—41no—
406C2×M16—61no—
407C2×M16—61no—
408C2×M16—61no—
409C2×M16C22×D311yescharacteristic
410C2×M16C22×D311yescharacteristic
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#117—31no—
430C2×C42—31no—
431C2×C42—31no—
432C2×C42—62no—
433C2×C42—61no—
434C2×C42—121no—
435#108—22no—
436#108—41no—
437C4⋊C8—61no—
438C4⋊C8—61no—
439#104—34no—
440#104—62no—
441#104—62no—
442#104—62no—
443#104—62no—
444#104—121no—
445#103—31no—
446#103—31no—
447#103—31no—
448#103—31no—
449#102—31no—
450#102—31no—
451#102—31no—
452#102—31no—
453C22⋊C8—21no—
454C22⋊C8—21no—
455C22⋊C8—31no—
456C22⋊C8—31no—
457C22⋊C8—31no—
458C22⋊C8—31no—
459C22⋊C8—61no—
460C22⋊C8—61no—
461C22⋊C8—61no—
462C22⋊C8—61no—
463C22⋊C8—61no—
464C22⋊C8—61no—
465C22⋊C8C4×D311yescharacteristic
466C22⋊C8C4×D311yescharacteristic
467C22⋊C8C4×D311yescharacteristic
468C22⋊C8C4×D311yescharacteristic
469#97—61no—
470C4×C8—62no—
471C4×C8—61no—
472C4×C8—121no—
473C23×C3—21no—
474C23×C3—21no—
475C23×C3—22no—
476C23×C3—41no—
477C23×C3C4×D411yescharacteristic
478C23×C3C4×D411yescharacteristic
479C23×C3C2×#4111yescharacteristic
480C22×D3—21no—
481C22×D3—21no—
482C22×D3—21no—
483C22×D3—42no—
484C22×D3—42no—
485C22×D3—81no—
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×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4C4×D411yescharacteristic
497C2×C3×C4C4×D411yescharacteristic
498C2×C3×C4C23×C411yescharacteristic
499C2×C3×C4C22×D411yescharacteristic
500C2×C3×C4C22×D411yescharacteristic
501C2×C3×C4C2×#4111yescharacteristic
502C2×C3×C4H(5,𝔽2)11yescharacteristic
503C2×C3×C4H(5,𝔽2)11yescharacteristic
504#67—22no—
505#67—22no—
506#67—42no—
507#67—42no—
508#67—41no—
509#67—41no—
510#67—41no—
511#67—41no—
512#67—42no—
513#67—81no—
514C2×Dic3—22no—
515C2×Dic3—22no—
516C2×Dic3—21no—
517C2×Dic3—22no—
518C2×Dic3—22no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—42no—
524C2×Dic3—48no—
525C2×Dic3—41no—
526C2×Dic3—41no—
527D12—21no—
528D12—21no—
529D12—21no—
530D12—21no—
531D12—21no—
532D12—42no—
533D12C4×D412yes—
534C4×D3—22no—
535C4×D3—22no—
536C4×D3—42no—
537C4×D3—42no—
538C4×D3—41no—
539C4×D3—41no—
540C4×D3—41no—
541C4×D3—41no—
542Dic6—21no—
543Dic6—21no—
544Dic6—21no—
545Dic6—21no—
546Dic6—21no—
547Dic6—42no—
548Dic6C4×D412yes—
549C3×C8—21no—
550C3×C8—21no—
551C3×C8—21no—
552C3×C8—21no—
553C3×C8—22no—
554C3×C8—41no—
555C3×C8—41no—
556C3×C8—41no—
557C3⋊C8—21no—
558C3⋊C8—21no—
559C3⋊C8—21no—
560C3⋊C8—21no—
561C24—61no—
562C24#23911yescharacteristic
563#41—32no—
564#41—32no—
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—61no—
576#41—61no—
577#41—122no—
578#41—122no—
579#41—121no—
580#41—121no—
581#41—122no—
582#41—122no—
583C2×Q8—31no—
584C2×Q8—31no—
585C2×Q8—31no—
586C2×Q8—62no—
587C2×Q8—61no—
588C2×Q8—121no—
589C2×D4—31no—
590C2×D4—31no—
591C2×D4—31no—
592C2×D4—62no—
593C2×D4—61no—
594C2×D4—61no—
595C2×D4—61no—
596C2×D4—61no—
597C2×D4—61no—
598C2×D4—61no—
599C2×D4—61no—
600C2×D4—61no—
601C2×D4—121no—
602C2×D4—122no—
603C2×D4—122no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—61no—
609C22×C4—61no—
610C22×C4—64no—
611C22×C4—61no—
612C22×C4—61no—
613C22×C4—61no—
614C22×C4—61no—
615C22×C4—61no—
616C22×C4—61no—
617C22×C4—122no—
618C22×C4—122no—
619C22×C4—122no—
620C22×C4—122no—
621C22×C4C2×C4×D311yescharacteristic
622C22×C4C2×C4×D311yescharacteristic
623C22×C4D3×D411yescharacteristic
624C22×C4D3×D411yescharacteristic
625C22×C4#23911yescharacteristic
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—21no—
639M16—21no—
640M16—21no—
641M16—21no—
642M16—42no—
643M16—122no—
644M16—122no—
645M16—122no—
646M16D3×D412yes—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—31no—
656C2×C8—31no—
657C2×C8—31no—
658C2×C8—31no—
659C2×C8—42no—
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×C8C2×C4×D311yescharacteristic
670C2×C8C2×C4×D311yescharacteristic
671C4⋊C4—31no—
672C4⋊C4—31no—
673C4⋊C4—61no—
674C4⋊C4—61no—
675C22⋊C4—61no—
676C22⋊C4—61no—
677C22⋊C4—61no—
678C22⋊C4—61no—
679C22⋊C4—61no—
680C42—32no—
681C42—61no—
682C42—61no—
683C42—61no—
684C42—61no—
685C42—122no—
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—21no—
689C22×C3—21no—
690C22×C3—21no—
691C22×C3—21no—
692C22×C3—21no—
693C22×C3—42no—
694C22×C3—42no—
695C22×C3#44312yescomplemented
696C22×C3C2×C4×D411yescharacteristic
697C22×C3#54611yescharacteristic
698C22×C3#55111yescharacteristic
699C2×D3—22no—
700C2×D3—41no—
701C2×D3—41no—
702C2×D3—41no—
703C2×D3—41no—
704C2×D3—41no—
705C2×D3—41no—
706C2×D3—41no—
707C2×D3—41no—
708C2×D3—84no—
709C3×C4—21no—
710C3×C4—21no—
711C3×C4C2×C4×D411yescharacteristic
712C3×C4#51811yescharacteristic
713C3×C4D4211yescharacteristic
714C3×C4#54611yescharacteristic
715Dic3—24no—
716Dic3—22no—
717Dic3—42no—
718Dic3—41no—
719Dic3—41no—
720Dic3—41no—
721Dic3—41no—
722C23—21no—
723C23—22no—
724C23—21no—
725C23—41no—
726C23—61no—
727C23—61no—
728C23—61no—
729C23—122no—
730C23—122no—
731C23—241no—
732C23#89311yescharacteristic
733C23#89311yescharacteristic
734C23C2×#23911yescharacteristic
735Q8—32no—
736Q8—61no—
737Q8—61no—
738Q8—61no—
739Q8—61no—
740Q8—61no—
741Q8—122no—
742D4—32no—
743D4—62no—
744D4—62no—
745D4—61no—
746D4—61no—
747D4—61no—
748D4—61no—
749D4—61no—
750D4—122no—
751D4—122no—
752D4—122no—
753D4—121no—
754D4—121no—
755D4—122no—
756D4—121no—
757D4—121no—
758D4—241no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—62no—
770C2×C4—62no—
771C2×C4—61no—
772C2×C4—62no—
773C2×C4—62no—
774C2×C4—62no—
775C2×C4—62no—
776C2×C4—61no—
777C2×C4—61no—
778C2×C4—61no—
779C2×C4—61no—
780C2×C4—122no—
781C2×C4—122no—
782C2×C4—122no—
783C2×C4—128no—
784C2×C4—121no—
785C2×C4—121no—
786C2×C4—121no—
787C2×C4—121no—
788C2×C4—121no—
789C2×C4—121no—
790C2×C4#89311yescharacteristic
791C2×C4#89311yescharacteristic
792C2×C4C22×C4×D311yescharacteristic
793C2×C4C2×D3×D411yescharacteristic
794C2×C4C2×D3×D411yescharacteristic
795C2×C4#100411yescharacteristic
796C2×C4D3×#4111yescharacteristic
797C2×C4#100911yescharacteristic
798C8—21no—
799C8—21no—
800C8—21no—
801C8—21no—
802C8—22no—
803C8—41no—
804C8—41no—
805C8—41no—
806C8—61no—
807C8—61no—
808C8—61no—
809C8—61no—
810C2×C3—21no—
811C2×C3—22no—
812C2×C3—21no—
813C2×C3—41no—
814C2×C3#235811yescharacteristic
815C2×C3C2×#44311yescharacteristic
816C2×C3#295611yescharacteristic
817D3—42no—
818D3—81no—
819D3—81no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—42no—
828C22—42no—
829C22—62no—
830C22—121no—
831C22—121no—
832C22—121no—
833C22—121no—
834C22—121no—
835C22—121no—
836C22—121no—
837C22—121no—
838C22—244no—
839C22#489512yescomplemented
840C22C2×#89311yescharacteristic
841C22#563011yescharacteristic
842C22#563711yescharacteristic
843C4—21no—
844C4—21no—
845C4—64no—
846C4—62no—
847C4—122no—
848C4—121no—
849C4—121no—
850C4—121no—
851C4—121no—
852C4C4×D3×D411yescharacteristic
853C4#554511yescharacteristic
854C4#559011yescharacteristic
855C4#565411yescharacteristic
856C3#2288811yescharacteristic, complemented, Sylow
857C2—21no—
858C2—22no—
859C2—21no—
860C2—41no—
861C2—122no—
862C2—241no—
863C2—241no—
864C2#7459611yescharacteristic
865C2C2×#489511yescharacteristic
866C2#7925811yescharacteristic
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#22888
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. C22×#825C2semidirect
2. #83757C2semidirect
3. C2×#4895C2semidirect
4. #78631C2semidirect
6. C3×#1855C2semidirect
7. #70722C2semidirect
8. #70699C2semidirect
9. #70696C2semidirect
10. #69965C2semidirect
11. Dic3×C22⋊C8C2semidirect
12. #68946C2semidirect
13. #68946C2semidirect
14. #68926C2semidirect
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×C8×Dic3C22semidirect
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
134. C2×Dic12C2×C4semidirect
135. C2×Dic12C2×C4semidirect
140. C2×D24C2×C4semidirect
141. C2×D24C2×C4semidirect
142. C2×#204C2×C4semidirect
143. C2×#204C2×C4semidirect
144. C2×#204C2×C4semidirect
145. C2×#204C2×C4semidirect
169. #825D4semidirect
170. #821C2×C4semidirect
171. #821C2×C4semidirect
172. #821C2×C4semidirect
173. #821C2×C4semidirect
180. #816C2×C4semidirect
181. #816C2×C4semidirect
182. #816C2×C4semidirect
183. #816C2×C4semidirect
212. C2×#108C2×D3semidirect
213. C2×#108C2×D3semidirect
237. #341C2×D3semidirect
238. #341C2×D3semidirect
695. C22×C3#443semidirect
839. C22#4895semidirect
856. C3#22888semidirect

Maximal subgroups

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

subgroupindex
C22×#8252
#837572
C2×#48952
#786312
#786102
C3×#18552
#707222
#706992
#706962
#699652
Dic3×C22⋊C82
#689462
#689262
#689182
#228883