Finite Group Databasebeta

← #11861104

Subgroups — #11861104

Order 1152.

965 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×#131C211yesmaximal, characteristic, complemented
2#10595453C211yesmaximal, characteristic
3D3×#901C211yesmaximal, characteristic, complemented
4#10592843C211yesmaximal, characteristic, complemented
5C3×#5144C211yesmaximal, characteristic, complemented
6#10591674C211yesmaximal, characteristic, complemented
7#10591670C211yesmaximal, characteristic, complemented
8#10591663C211yesmaximal, characteristic, complemented
9#10591005C211yesmaximal, characteristic, complemented
10#10590994C211yesmaximal, characteristic, complemented
11#10590976C211yesmaximal, characteristic, complemented
12#10590973C211yesmaximal, characteristic, complemented
13#10590923C211yesmaximal, characteristic, complemented
14#10590921C211yesmaximal, characteristic, complemented
15#10590692C211yesmaximal, characteristic, complemented
16#83792—31nomaximal
17#79888—31nomaximal
18C3×D3×#41C2211yescharacteristic
19D3×#235C2211yescharacteristic
20C32×#131C2211yescharacteristic, complemented
21#64159C2211yescharacteristic
22#64110C2211yescharacteristic, complemented
23C3×#950C2211yescharacteristic
24C3×#948C2211yescharacteristic, complemented
25C3×#907—21no—
26C3×#907C2211yescharacteristic, complemented
27C3×D3×M16—21no—
28C3×D3×M16C2211yescharacteristic
29C3×#901—21no—
30C3×#901C2211yescharacteristic, complemented
31C3×#901C2211yescharacteristic, complemented
32C2×C3×D3×C8—21no—
33C2×C3×D3×C8C2211yescharacteristic
34#63948C411yescharacteristic, complemented
35#63946C411yescharacteristic, complemented
36#63943C411yescharacteristic, complemented
37#63939C411yescharacteristic, complemented
38#63934C411yescharacteristic, complemented
39#63932C411yescharacteristic, complemented
40#63929C411yescharacteristic, complemented
41#63925C411yescharacteristic, complemented
42#63855C2211yescharacteristic
43#63829C2211yescharacteristic
44#63822C2211yescharacteristic
45C2×#3711C2211yescharacteristic
46#63817C2211yescharacteristic, complemented
47#63814C2211yescharacteristic, complemented
48D3×#208C2211yescharacteristic
49#63804—21no—
50#63803—21no—
51D3×ΓL(1,𝔽25)—21no—
52D32×C8—21no—
53#63664C2211yescharacteristic, complemented
54#63652C2211yescharacteristic, complemented
55#63649C2211yescharacteristic, complemented
56C8×C3⋊Dic3C2211yescharacteristic, complemented
57C3×#837C2211yescharacteristic, complemented
58C3×#825C2211yescharacteristic, complemented
59C3×#822C2211yescharacteristic, complemented
60C3×C8×Dic3C2211yescharacteristic, complemented
61#63578C2211yescharacteristic, complemented
62#63577C2211yescharacteristic, complemented
63#63570C2211yescharacteristic, complemented
64#63569C2211yescharacteristic, complemented
65#63568C2211yescharacteristic, complemented
66#63568C2211yescharacteristic, complemented
67#63555C2211yescharacteristic, complemented
68#63554C2211yescharacteristic, complemented
69C2×C3×#131—31no—
70#5822—31no—
71#5768—31no—
72D3×#131—31no—
73D3×#131D311yescharacteristic, complemented
74C2×#901—31no—
75C3×#443—31no—
76#5236—31no—
77#5197—31no—
78#5145—31no—
79#5145—31no—
80#5145—31no—
81#5145—31no—
82#5144—31no—
83#5144—31no—
84#5144—31no—
85#5144—31no—
86#5144—31no—
87#5144—61no—
88#5144D311yescharacteristic, complemented
89#5139—31no—
90#5124—31no—
91#5101—31no—
92#4894—31no—
93#4893—31no—
94#4823—31no—
95#4823—31no—
96#4821—31no—
97#4821—31no—
98#4700—31no—
99#4689—31no—
100C32×#41C2311yescharacteristic
101#3828C2311yescharacteristic
102C3×#239C2×C411yescharacteristic
103C3×D3×Q8C2×C411yescharacteristic
104C3×#237—21no—
105C3×#237C2×C411yescharacteristic
106C3×D3×D4—21no—
107C3×D3×D4C2×C411yescharacteristic
108C3×#235—21no—
109C3×#235C2311yescharacteristic
110C3×#235C2311yescharacteristic
111C2×C3×C4×D3—21no—
112C2×C3×C4×D3C2311yescharacteristic
113D3×#67—21no—
114#3804—21no—
115D3×D12C2×C411yescharacteristic
116C4×D32—21no—
117#3799C2×C411yescharacteristic
118#3798—21no—
119#3795C2×C411yescharacteristic
120D3×Dic6C2×C411yescharacteristic
121C32×M16—21no—
122C32×M16C2311yescharacteristic
123C2×C32×C8—21no—
124C2×C32×C8C2311yescharacteristic
125#3756C2×C411yescharacteristic
126#3755C2×C411yescharacteristic
127#3754C2×C411yescharacteristic
128#3753C2×C411yescharacteristic
129C4×C3⋊Dic3C2311yescharacteristic
130#3748C2311yescharacteristic
131C2×C3⋊(C3⋊C8)C2311yescharacteristic
132#3743—21no—
133C8×C3⋊D3—21no—
134C3×#216C2×C411yescharacteristic
135C3×#215C2×C411yescharacteristic
136C3×#214C2×C411yescharacteristic
137C3×#213C2×C411yescharacteristic
138C3×C4×Dic3C2311yescharacteristic
139C3×#208—21no—
140C3×#208C2311yescharacteristic
141C3×#208C2311yescharacteristic
142C2×C3×C3⋊C8—21no—
143C2×C3×C3⋊C8C2311yescharacteristic
144C2×C3×C3⋊C8C2311yescharacteristic
145C3×ΓL(1,𝔽25)—21no—
146C3×ΓL(1,𝔽25)—21no—
147C3×ΓL(1,𝔽25)—21no—
148C3×ΓL(1,𝔽25)—21no—
149C3×D3×C8—21no—
150C3×D3×C8—21no—
151C3×D3×C8—21no—
152C3×D3×C8—21no—
153C3×D3×C8D411yescharacteristic
154C3×D3×C8D411yescharacteristic
155C3×D3×C8D411yescharacteristic
156C3×D3×C8D411yescharacteristic
157Dic3⋊Dic3—21no—
158(C2×D3)⋊Dic3—21no—
159#3719C2×C411yescharacteristic
160#3718C2×C411yescharacteristic
161#3717C2×C411yescharacteristic
162#3716C2×C411yescharacteristic
163#3715C2×C411yescharacteristic
164#3715C2×C411yescharacteristic
165#3714C2×C411yescharacteristic
166#3713C2×C411yescharacteristic
167#3712—21no—
168#3711—21no—
169#3711—21no—
170#3711C2×C411yescharacteristic
171#3711C2×C411yescharacteristic
172#3711C2×C411yescharacteristic
173#3711C2×C411yescharacteristic
174#3710—21no—
175D3×C3⋊C8—21no—
176D3×C3⋊C8—21no—
177#2955—91noSylow
178C2×C3×#41—31no—
179D3×#41—31no—
180D3×#41C2×D311yescharacteristic
181C2×#235—31no—
182C3×#135—31no—
183C3×#131—21no—
184C3×#131—31no—
185C3×#131—31no—
186C3×#131—31no—
187C3×#131—31no—
188C3×#131—61no—
189C3×#131—61no—
190C3×#131C2×D311yescharacteristic, complemented
191C3×#131C2×D311yescharacteristic, complemented
192C2×C3×M16—31no—
193C2×C3×M16—61no—
194C22×C3×C8—31no—
195C22×C3×C8—61no—
196#951—31no—
197#951—31no—
198#950—31no—
199#950—31no—
200#950—31no—
201#950—31no—
202#950—31no—
203#950—61no—
204#950C2×D311yescharacteristic
205#949—31no—
206#949—31no—
207#948—31no—
208#948C2×D311yescharacteristic, complemented
209#942—31no—
210#942—31no—
211#932—31no—
212#932—31no—
213#926—31no—
214C2×#208—31no—
215C2×#208—31no—
216#918—31no—
217#918—31no—
218#915—31no—
219#915—31no—
220#914—31no—
221#914—31no—
222#911—31no—
223#911—31no—
224#907—21no—
225#907—31no—
226#907—61no—
227#907C2×D311yescharacteristic, complemented
228D3×M16—21no—
229D3×M16—31no—
230D3×M16—61no—
231D3×M16C2×D311yescharacteristic
232#904—31no—
233#901—21no—
234#901—31no—
235#901—31no—
236#901—31no—
237#901—31no—
238#901—61no—
239#901—61no—
240#901—61no—
241#901—61no—
242#901C2×D311yescharacteristic, complemented
243#901C2×D311yescharacteristic, complemented
244C2×ΓL(1,𝔽25)—31no—
245C2×ΓL(1,𝔽25)—61no—
246C2×D3×C8—21no—
247C2×D3×C8—61no—
248C2×D3×C8—61no—
249C2×D3×C8C2×D311yescharacteristic
250#872—31no—
251C3×#108—31no—
252C3×#104—31no—
253C3×#104—31no—
254C3×C4×C8—31no—
255#837—31no—
256#837—31no—
257#837—31no—
258#837—31no—
259#837—31no—
260#837—61no—
261#837C2×D311yescharacteristic, complemented
262#825—31no—
263#825—31no—
264#825—31no—
265#825—31no—
266#825—31no—
267#825—61no—
268#825C2×D311yescharacteristic, complemented
269#822—31no—
270#822—31no—
271#822—31no—
272#822—31no—
273#822—31no—
274#822—61no—
275#822C2×D311yescharacteristic, complemented
276#819—31no—
277#815—31no—
278#815—31no—
279#815—31no—
280C8×Dic3—31no—
281C8×Dic3—31no—
282C8×Dic3—61no—
283C8×Dic3C2×D311yescharacteristic, complemented
284#805—31no—
285#805—31no—
286#803—31no—
287C22×C3×D3—21no—
288C22×C3×D3#4111yescharacteristic
289C2×D32—21no—
290C32×Q8C22×C411yescharacteristic
291C32×D4—21no—
292C32×D4C22×C411yescharacteristic
293C2×C32×C4—21no—
294C2×C32×C4C2411yescharacteristic
295#638—21no—
296C2×C3⋊Dic3—21no—
297C4⋊(C3⋊D3)C22×C411yescharacteristic
298C4×C3⋊D3—21no—
299#634C22×C411yescharacteristic
300C3×#67—21no—
301C3×#67—21no—
302C3×#67—21no—
303C3×#67—21no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3#4111yescharacteristic
307C3×D12—21no—
308C3×D12C22×C411yescharacteristic
309C3×D12C22×C411yescharacteristic
310C3×C4×D3—21no—
311C3×C4×D3—21no—
312C3×C4×D3—21no—
313C3×C4×D3—21no—
314C3×C4×D3C22×C411yescharacteristic
315C3×C4×D3C22×C411yescharacteristic
316C3×C4×D3C2×D411yescharacteristic
317C3×C4×D3C2×D411yescharacteristic
318C3×Dic6—21no—
319C3×Dic6C22×C411yescharacteristic
320C3×Dic6C22×C411yescharacteristic
321#627—21no—
322#626—21no—
323#626—21no—
324#625—21no—
325#624—21no—
326D3×Dic3—21no—
327D3×Dic3—21no—
328C32×C8—21no—
329C32×C8C2×D411yescharacteristic
330C32×C8C2×D411yescharacteristic
331C3⋊(C3⋊C8)—21no—
332C3⋊(C3⋊C8)C22×C411yescharacteristic
333C3⋊(C3⋊C8)C22×C411yescharacteristic
334C3×C3⋊C8—21no—
335C3×C3⋊C8—21no—
336C3×C3⋊C8C22×C411yescharacteristic
337C3×C3⋊C8C22×C411yescharacteristic
338C3×C3⋊C8C2×D411yescharacteristic
339C3×C3⋊C8C2×D411yescharacteristic
340#575—91no—
341C2×#131—31no—
342C2×#131—91no—
343#444—91no—
344#444—91no—
345#444—91no—
346#444—91no—
347#443—31no—
348#443—91no—
349#443—91no—
350#443—91no—
351#430—91no—
352#421—91no—
353#421—91no—
354#405—91no—
355C3×#41—21no—
356C3×#41—31no—
357C3×#41—31no—
358C3×#41—31no—
359C3×#41—31no—
360C3×#41—61no—
361C3×#41—61no—
362C3×#41C22×D311yescharacteristic
363C3×#41C22×D311yescharacteristic
364C2×C3×Q8—31no—
365C2×C3×D4—31no—
366C2×C3×D4—61no—
367C22×C3×C4—31no—
368C22×C3×C4—61no—
369C2×#67—61no—
370#239—31no—
371#239C4×D311yescharacteristic
372D3×Q8—31no—
373D3×Q8C4×D311yescharacteristic
374#237—21no—
375#237—31no—
376#237—61no—
377#237C4×D311yescharacteristic
378D3×D4—21no—
379D3×D4—31no—
380D3×D4—61no—
381D3×D4C4×D311yescharacteristic
382#235—21no—
383#235—31no—
384#235—31no—
385#235—31no—
386#235—31no—
387#235—61no—
388#235—61no—
389#235—61no—
390#235—61no—
391#235C22×D311yescharacteristic
392#235C22×D311yescharacteristic
393C2×D12—31no—
394C2×C4×D3—21no—
395C2×C4×D3—61no—
396C2×C4×D3—61no—
397C2×C4×D3C22×D311yescharacteristic
398C2×Dic6—31no—
399C3×Q16—31no—
400C3×SD16—31no—
401C3×SD16—31no—
402C3×D8—31no—
403C3×M16—21no—
404C3×M16—21no—
405C3×M16—21no—
406C3×M16—31no—
407C3×M16—31no—
408C3×M16—41no—
409C3×M16—61no—
410C3×M16—61no—
411C3×M16—61no—
412C3×M16—61no—
413C3×M16—61no—
414C3×M16C22×D311yescharacteristic
415C3×M16C22×D311yescharacteristic
416C2×C3×C8—21no—
417C2×C3×C8—21no—
418C2×C3×C8—21no—
419C2×C3×C8—31no—
420C2×C3×C8—31no—
421C2×C3×C8—31no—
422C2×C3×C8—31no—
423C2×C3×C8—31no—
424C2×C3×C8—31no—
425C2×C3×C8—41no—
426C2×C3×C8—61no—
427C2×C3×C8—61no—
428C2×C3×C8—61no—
429C2×C3×C8—61no—
430C2×C3×C8—61no—
431C2×C3×C8C22×D311yescharacteristic
432C2×C3×C8C22×D311yescharacteristic
433C3×C42—31no—
434#217—61no—
435#216—31no—
436#216—31no—
437#216—31no—
438#216—31no—
439#216—31no—
440#216—61no—
441#216C4×D311yescharacteristic
442#215—31no—
443#215—31no—
444#215—31no—
445#215—31no—
446#215—31no—
447#215—61no—
448#215C4×D311yescharacteristic
449#214—31no—
450#214—31no—
451#214—31no—
452#214—31no—
453#214—31no—
454#214—61no—
455#214C4×D311yescharacteristic
456#213—31no—
457#213—31no—
458#213—31no—
459#213—31no—
460#213—31no—
461#213—61no—
462#213C4×D311yescharacteristic
463(C2×D3)⋊C4—61no—
464C4⋊Dic3—61no—
465Dic3⋊C4—61no—
466C4×Dic3—31no—
467C4×Dic3—31no—
468C4×Dic3—61no—
469C4×Dic3C22×D311yescharacteristic
470#208—21no—
471#208—31no—
472#208—31no—
473#208—31no—
474#208—31no—
475#208—31no—
476#208—31no—
477#208—61no—
478#208—61no—
479#208—61no—
480#208C22×D311yescharacteristic
481#208C22×D311yescharacteristic
482C2×C3⋊C8—21no—
483C2×C3⋊C8—31no—
484C2×C3⋊C8—31no—
485C2×C3⋊C8—61no—
486C2×C3⋊C8—61no—
487C2×C3⋊C8—61no—
488C2×C3⋊C8C22×D311yescharacteristic
489C2×C3⋊C8C22×D311yescharacteristic
490Dic12—31no—
491D24—31no—
492#204—31no—
493#204—31no—
494ΓL(1,𝔽25)—21no—
495ΓL(1,𝔽25)—21no—
496ΓL(1,𝔽25)—21no—
497ΓL(1,𝔽25)—21no—
498ΓL(1,𝔽25)—31no—
499ΓL(1,𝔽25)—31no—
500ΓL(1,𝔽25)—31no—
501ΓL(1,𝔽25)—31no—
502ΓL(1,𝔽25)—61no—
503ΓL(1,𝔽25)—61no—
504ΓL(1,𝔽25)—61no—
505ΓL(1,𝔽25)—61no—
506ΓL(1,𝔽25)—61no—
507ΓL(1,𝔽25)—61no—
508ΓL(1,𝔽25)—121no—
509D3×C8—21no—
510D3×C8—21no—
511D3×C8—21no—
512D3×C8—21no—
513D3×C8—61no—
514D3×C8—61no—
515D3×C8—61no—
516D3×C8—61no—
517D3×C8—61no—
518D3×C8—61no—
519D3×C8—121no—
520D3×C8#6711yescharacteristic
521D3×C8#6711yescharacteristic
522D3×C8#6711yescharacteristic
523D3×C8#6711yescharacteristic
524C22×C32—21no—
525C22×C32C2×#4111yescharacteristic
526C2×C3⋊D3—21no—
527C2×C3×D3—21no—
528C2×C3×D3—21no—
529C2×C3×D3—41no—
530C2×C3×D3—42no—
531C2×C3×D3C4×D411yescharacteristic
532C2×C3×D3C4×D411yescharacteristic
533D32—42no—
534C32×C4—21no—
535C32×C4C23×C411yescharacteristic
536C32×C4C22×D411yescharacteristic
537C3⋊Dic3—21no—
538C3⋊Dic3—41no—
539C3×Dic3—21no—
540C3×Dic3—21no—
541C3×Dic3—41no—
542C3×Dic3C4×D411yescharacteristic
543C3×Dic3C4×D411yescharacteristic
544C2×#41—31no—
545C2×#41—91no—
546#137—91no—
547#137—91no—
548#137—91no—
549#137—91no—
550AGL(1,ℤ/8)—91no—
551AGL(1,ℤ/8)—91no—
552AGL(1,ℤ/8)—91no—
553AGL(1,ℤ/8)—91no—
554#135—31no—
555#135—91no—
556#135—91no—
557#135—91no—
558#131—31no—
559#131—31no—
560#131—31no—
561#131—31no—
562#131—61no—
563#131—61no—
564#131—91no—
565#131—91no—
566#131—91no—
567#131—181no—
568#131—181no—
569#131D3211yescharacteristic, complemented
570C2×M16—31no—
571C2×M16—61no—
572C2×M16—91no—
573C2×M16—91no—
574C2×M16—181no—
575C22×C8—31no—
576C22×C8—61no—
577C22×C8—181no—
578#117—91no—
579#108—31no—
580#108—91no—
581#108—91no—
582#108—91no—
583#104—31no—
584#104—31no—
585#104—91no—
586#104—91no—
587#104—91no—
588#104—91no—
589#104—91no—
590#104—91no—
591#97—91no—
592#97—91no—
593C4×C8—31no—
594C4×C8—91no—
595C23×C3—31no—
596C23×C3—61no—
597C22×D3—21no—
598C22×D3—61no—
599C22×D3—61no—
600C22×D3#23511yescharacteristic
601C3×Q8—21no—
602C3×Q8—31no—
603C3×Q8—31no—
604C3×Q8—61no—
605C3×Q8C2×C4×D311yescharacteristic
606C3×Q8C2×C4×D311yescharacteristic
607C3×D4—21no—
608C3×D4—21no—
609C3×D4—21no—
610C3×D4—31no—
611C3×D4—31no—
612C3×D4—41no—
613C3×D4—61no—
614C3×D4—61no—
615C3×D4—61no—
616C3×D4—61no—
617C3×D4—61no—
618C3×D4C2×C4×D311yescharacteristic
619C3×D4C2×C4×D311yescharacteristic
620C2×C3×C4—21no—
621C2×C3×C4—21no—
622C2×C3×C4—21no—
623C2×C3×C4—31no—
624C2×C3×C4—31no—
625C2×C3×C4—31no—
626C2×C3×C4—31no—
627C2×C3×C4—31no—
628C2×C3×C4—41no—
629C2×C3×C4—61no—
630C2×C3×C4—61no—
631C2×C3×C4—61no—
632C2×C3×C4—61no—
633C2×C3×C4—61no—
634C2×C3×C4—61no—
635C2×C3×C4C23×D311yescharacteristic
636C2×C3×C4C23×D311yescharacteristic
637#67—21no—
638#67—21no—
639#67—21no—
640#67—21no—
641#67—61no—
642#67—61no—
643#67—61no—
644#67—61no—
645#67—61no—
646#67—61no—
647#67—121no—
648C2×Dic3—21no—
649C2×Dic3—21no—
650C2×Dic3—61no—
651C2×Dic3—61no—
652C2×Dic3—61no—
653C2×Dic3—61no—
654C2×Dic3—121no—
655C2×Dic3#23511yescharacteristic
656D12—21no—
657D12—31no—
658D12—31no—
659D12—61no—
660D12—61no—
661D12—61no—
662D12C2×C4×D311yescharacteristic
663D12C2×C4×D311yescharacteristic
664C4×D3—21no—
665C4×D3—21no—
666C4×D3—21no—
667C4×D3—21no—
668C4×D3—61no—
669C4×D3—61no—
670C4×D3—61no—
671C4×D3—61no—
672C4×D3—61no—
673C4×D3—61no—
674C4×D3—121no—
675C4×D3C2×C4×D311yescharacteristic
676C4×D3C2×C4×D311yescharacteristic
677C4×D3C2×#6711yescharacteristic
678C4×D3C2×#6711yescharacteristic
679Dic6—21no—
680Dic6—31no—
681Dic6—31no—
682Dic6—61no—
683Dic6—61no—
684Dic6—61no—
685Dic6C2×C4×D311yescharacteristic
686Dic6C2×C4×D311yescharacteristic
687C3×C8—21no—
688C3×C8—21no—
689C3×C8—21no—
690C3×C8—21no—
691C3×C8—31no—
692C3×C8—31no—
693C3×C8—31no—
694C3×C8—31no—
695C3×C8—41no—
696C3×C8—61no—
697C3×C8—61no—
698C3×C8D3×D411yescharacteristic
699C3×C8D3×D411yescharacteristic
700C3×C8C2×#6711yescharacteristic
701C3×C8C2×#6711yescharacteristic
702C3⋊C8—21no—
703C3⋊C8—21no—
704C3⋊C8—31no—
705C3⋊C8—31no—
706C3⋊C8—31no—
707C3⋊C8—31no—
708C3⋊C8—61no—
709C3⋊C8—61no—
710C3⋊C8—61no—
711C3⋊C8—61no—
712C3⋊C8—121no—
713C3⋊C8C2×C4×D311yescharacteristic
714C3⋊C8C2×C4×D311yescharacteristic
715C3⋊C8C2×#6711yescharacteristic
716C3⋊C8C2×#6711yescharacteristic
717C2×C32—21no—
718C2×C32—41no—
719C2×C32C2×C4×D411yescharacteristic
720C3⋊D3—41no—
721C3×D3—21no—
722C3×D3—21no—
723C3×D3—41no—
724C3×D3—41no—
725#41—31no—
726#41—31no—
727#41—31no—
728#41—31no—
729#41—61no—
730#41—61no—
731#41—91no—
732#41—91no—
733#41—91no—
734#41—181no—
735#41—181no—
736#41C2×D3211yescharacteristic
737C2×Q8—31no—
738C2×Q8—91no—
739C2×D4—31no—
740C2×D4—61no—
741C2×D4—91no—
742C2×D4—181no—
743C22×C4—31no—
744C22×C4—61no—
745C22×C4—181no—
746Q16—31no—
747Q16—91no—
748Q16—91no—
749Q16—91no—
750SD16—31no—
751SD16—31no—
752SD16—91no—
753SD16—91no—
754SD16—91no—
755SD16—91no—
756SD16—91no—
757SD16—91no—
758D8—31no—
759D8—91no—
760D8—91no—
761D8—91no—
762M16—21no—
763M16—31no—
764M16—31no—
765M16—61no—
766M16—61no—
767M16—61no—
768M16—61no—
769M16—61no—
770M16—91no—
771M16—91no—
772M16—91no—
773M16—91no—
774M16—91no—
775M16—181no—
776M16—181no—
777M16—181no—
778M16—181no—
779M16C2×D3211yescharacteristic
780C2×C8—21no—
781C2×C8—31no—
782C2×C8—31no—
783C2×C8—31no—
784C2×C8—31no—
785C2×C8—31no—
786C2×C8—31no—
787C2×C8—61no—
788C2×C8—61no—
789C2×C8—61no—
790C2×C8—61no—
791C2×C8—61no—
792C2×C8—91no—
793C2×C8—181no—
794C2×C8—181no—
795C2×C8—181no—
796C2×C8—181no—
797C2×C8C2×D3211yescharacteristic
798C4⋊C4—181no—
799C22⋊C4—181no—
800C42—31no—
801C42—91no—
802C22×C3—21no—
803C22×C3—21no—
804C22×C3—21no—
805C22×C3—31no—
806C22×C3—31no—
807C22×C3—41no—
808C22×C3—61no—
809C22×C3—61no—
810C22×C3—121no—
811C22×C3—122no—
812C22×C3C2×#23511yescharacteristic
813C22×C3D3×#4111yescharacteristic
814C2×D3—21no—
815C2×D3—21no—
816C2×D3—41no—
817C2×D3—42no—
818C2×D3—61no—
819C2×D3—61no—
820C2×D3—121no—
821C2×D3—122no—
822C2×D3—122no—
823C2×D3C4×#6711yescharacteristic
824C2×D3C4×#6711yescharacteristic
825C3×C4—21no—
826C3×C4—21no—
827C3×C4—21no—
828C3×C4—21no—
829C3×C4—31no—
830C3×C4—31no—
831C3×C4—41no—
832C3×C4—61no—
833C3×C4—61no—
834C3×C4—121no—
835C3×C4C22×C4×D311yescharacteristic
836C3×C4C22×C4×D311yescharacteristic
837C3×C4C2×D3×D411yescharacteristic
838C3×C4C22×#6711yescharacteristic
839Dic3—21no—
840Dic3—21no—
841Dic3—41no—
842Dic3—61no—
843Dic3—61no—
844Dic3—121no—
845Dic3—121no—
846Dic3—121no—
847Dic3—122no—
848Dic3C4×#6711yescharacteristic
849Dic3C4×#6711yescharacteristic
850C32#295511yescharacteristic, complemented, Sylow
851C23—31no—
852C23—61no—
853C23—181no—
854Q8—31no—
855Q8—31no—
856Q8—61no—
857Q8—91no—
858Q8—181no—
859Q8C4×D3211yescharacteristic
860D4—21no—
861D4—31no—
862D4—31no—
863D4—61no—
864D4—61no—
865D4—61no—
866D4—61no—
867D4—61no—
868D4—91no—
869D4—181no—
870D4—181no—
871D4—181no—
872D4—181no—
873D4C4×D3211yescharacteristic
874C2×C4—21no—
875C2×C4—31no—
876C2×C4—31no—
877C2×C4—31no—
878C2×C4—31no—
879C2×C4—31no—
880C2×C4—61no—
881C2×C4—61no—
882C2×C4—61no—
883C2×C4—61no—
884C2×C4—61no—
885C2×C4—61no—
886C2×C4—181no—
887C2×C4—181no—
888C2×C4—181no—
889C2×C4—181no—
890C2×C4—181no—
891C2×C4C22×D3211yescharacteristic
892C8—21no—
893C8—31no—
894C8—31no—
895C8—31no—
896C8—31no—
897C8—61no—
898C8—61no—
899C8—91no—
900C8—91no—
901C8—181no—
902C8D3×#6711yescharacteristic
903C8D3×#6711yescharacteristic
904C2×C3—21no—
905C2×C3—21no—
906C2×C3—21no—
907C2×C3—41no—
908C2×C3—41no—
909C2×C3—41no—
910C2×C3—61no—
911C2×C3—61no—
912C2×C3—81no—
913C2×C3—121no—
914C2×C3—121no—
915C2×C3C4×D3×D411yescharacteristic
916C2×C3C2×C4×#6711yescharacteristic
917D3—21no—
918D3—21no—
919D3—41no—
920D3—41no—
921D3—121no—
922D3—121no—
923D3—241no—
924C22—21no—
925C22—31no—
926C22—31no—
927C22—61no—
928C22—61no—
929C22—121no—
930C22—122no—
931C22—181no—
932C22—362no—
933C22D3×#23511yescharacteristic
934C4—21no—
935C4—31no—
936C4—31no—
937C4—61no—
938C4—61no—
939C4—121no—
940C4—181no—
941C4—361no—
942C4C2×C4×D3211yescharacteristic
943C4C2×D3×#6711yescharacteristic
944C3—21no—
945C3#7988811yescharacteristic, complemented
946C3#8379211yescharacteristic, complemented
947C2—21no—
948C2—41no—
949C2—61no—
950C2—61no—
951C2—121no—
952C2—121no—
953C2—361no—
954C2C4×D3×#6711yescharacteristic
subgroupG/H
centerC8D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#131C22
socleC2×C32C2×C4×D4
prime radical#10595453C2
cosocleC2×C32×C4C24
hypercenter#131D32
hypocenterC32#2955
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C8 ◁ C2×C8 ◁ #131

Complements

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

NH ≅ G/Ntype
1. C3×D3×#131C2semidirect
3. D3×#901C2semidirect
4. #10592843C2semidirect
5. C3×#5144C2semidirect
6. #10591674C2semidirect
7. #10591670C2semidirect
8. #10591663C2semidirect
9. #10591005C2semidirect
10. #10590994C2semidirect
11. #10590976C2semidirect
12. #10590973C2semidirect
13. #10590923C2semidirect
14. #10590921C2semidirect
15. #10590692C2semidirect
20. C32×#131C22semidirect
22. #64110C22semidirect
24. C3×#948C22semidirect
26. C3×#907C22semidirect
30. C3×#901C22semidirect
31. C3×#901C22semidirect
34. #63948C4semidirect
35. #63946C4semidirect
36. #63943C4semidirect
37. #63939C4semidirect
38. #63934C4semidirect
39. #63932C4semidirect
40. #63929C4semidirect
41. #63925C4semidirect
46. #63817C22semidirect
47. #63814C22semidirect
53. #63664C22semidirect
54. #63652C22semidirect
55. #63649C22semidirect
56. C8×C3⋊Dic3C22semidirect
57. C3×#837C22semidirect
58. C3×#825C22semidirect
59. C3×#822C22semidirect
60. C3×C8×Dic3C22semidirect
61. #63578C22semidirect
62. #63577C22semidirect
63. #63570C22semidirect
64. #63569C22semidirect
65. #63568C22semidirect
66. #63568C22semidirect
67. #63555C22semidirect
68. #63554C22semidirect
73. D3×#131D3semidirect
88. #5144D3semidirect
190. C3×#131C2×D3semidirect
191. C3×#131C2×D3semidirect
208. #948C2×D3semidirect
227. #907C2×D3semidirect
242. #901C2×D3semidirect
243. #901C2×D3semidirect
261. #837C2×D3semidirect
268. #825C2×D3semidirect
275. #822C2×D3semidirect
283. C8×Dic3C2×D3semidirect
569. #131D32semidirect
850. C32#2955semidirect
945. C3#79888semidirect
946. C3#83792semidirect

Maximal subgroups

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

subgroupindex
C3×D3×#1312
#105954532
D3×#9012
#105928432
C3×#51442
#105916742
#105916702
#105916632
#105910052
#105909942
#105909762
#105909732
#105909232
#105909212
#105906922
#837923
#798883