Finite Group Databasebeta

← #11861158

Subgroups — #11861158

Order 1152.

968 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595453C211yesmaximal, characteristic
2#10595441C211yesmaximal, characteristic, complemented
3#10594706C211yesmaximal, characteristic, complemented
4#10592522C211yesmaximal, characteristic, complemented
5C3×#4823C211yesmaximal, characteristic, complemented
6C3×D3×#104C211yesmaximal, characteristic, complemented
7#10591675C211yesmaximal, characteristic, complemented
8#10591662C211yesmaximal, characteristic, complemented
9#10590977C211yesmaximal, characteristic, complemented
10#10590975C211yesmaximal, characteristic, complemented
11#10590973C211yesmaximal, characteristic, complemented
12D3×#805C211yesmaximal, characteristic, complemented
13#10590390C211yesmaximal, characteristic, complemented
14#10590342C211yesmaximal, characteristic, complemented
15#10590334C211yesmaximal, characteristic, complemented
16#79898—31nomaximal
17#78980—31nomaximal
18C3×D3×#41C2211yescharacteristic
19D3×#235C2211yescharacteristic
20#64159C2211yescharacteristic
21#64157C2211yescharacteristic, complemented
22#64116C2211yescharacteristic, complemented
23C3×#950C2211yescharacteristic
24C3×#948C2211yescharacteristic, complemented
25C3×#907C2211yescharacteristic, complemented
26C3×D3×M16C2211yescharacteristic
27C3×C42×D3C2211yescharacteristic
28#63948C411yescharacteristic, complemented
29#63946C411yescharacteristic, complemented
30#63943C411yescharacteristic, complemented
31#63939C411yescharacteristic, complemented
32#63934C411yescharacteristic, complemented
33#63932C411yescharacteristic, complemented
34#63929C411yescharacteristic, complemented
35#63925C411yescharacteristic, complemented
36#63829C2211yescharacteristic
37#63822C2211yescharacteristic
38C2×#3711—21no—
39C2×#3711C2211yescharacteristic
40C2×#3711C2211yescharacteristic
41#63817C2211yescharacteristic, complemented
42#63815—21no—
43#63815C2211yescharacteristic, complemented
44#63815C2211yescharacteristic, complemented
45#63814—21no—
46#63814C2211yescharacteristic, complemented
47D3×#208—21no—
48D3×#208C2211yescharacteristic
49#63804—21no—
50#63803—21no—
51#63791—21no—
52D3×ΓL(1,𝔽25)—21no—
53C32×#104C2211yescharacteristic, complemented
54#63649C2211yescharacteristic, complemented
55#63632C2211yescharacteristic, complemented
56#63630C2211yescharacteristic, complemented
57C3×#837C2211yescharacteristic, complemented
58C3×#825C2211yescharacteristic, complemented
59C3×#822C2211yescharacteristic, complemented
60C3×#805C2211yescharacteristic, complemented
61C3×#805C2211yescharacteristic, complemented
62C3×#803C2211yescharacteristic, complemented
63#63578C2211yescharacteristic, complemented
64#63577C2211yescharacteristic, complemented
65#63570C2211yescharacteristic, complemented
66#63569C2211yescharacteristic, complemented
67Dic3×C3⋊C8C2211yescharacteristic, complemented
68Dic3×C3⋊C8C2211yescharacteristic, complemented
69#5822—31no—
70#5819—31no—
71#5768—31no—
72#5750—31no—
73#5750—31no—
74#5745—31no—
75C3×#444—31no—
76C2×C3×#104—31no—
77#5196—31no—
78#5144—31no—
79#5144—31no—
80#5124—31no—
81C2×#805—31no—
82C4×#208—31no—
83#4895—31no—
84#4893—31no—
85#4824—31no—
86#4824—31no—
87#4824—31no—
88#4824—31no—
89#4823—31no—
90#4823—31no—
91#4823—31no—
92#4823—31no—
93#4823—31no—
94#4823—61no—
95#4823D311yescharacteristic, complemented
96D3×#104—31no—
97D3×#104D311yescharacteristic, complemented
98#4717—31no—
99#4707—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×D3—21no—
113C2×C3×C4×D3C2311yescharacteristic
114D3×#67—21no—
115#3804—21no—
116D3×D12C2×C411yescharacteristic
117C4×D32—21no—
118#3799C2×C411yescharacteristic
119#3798—21no—
120#3795C2×C411yescharacteristic
121D3×Dic6C2×C411yescharacteristic
122C32×M16C2311yescharacteristic
123C32×C42C2311yescharacteristic
124#3756C2×C411yescharacteristic, complemented
125#3755C2×C411yescharacteristic, complemented
126#3754C2×C411yescharacteristic, complemented
127#3753C2×C411yescharacteristic, complemented
128#3748—21no—
129#3748C2311yescharacteristic
130C2×C3⋊(C3⋊C8)—21no—
131C2×C3⋊(C3⋊C8)C2311yescharacteristic
132C2×C3⋊(C3⋊C8)C2311yescharacteristic
133#3743—21no—
134C8×C3⋊D3—21no—
135C3×#216C2×C411yescharacteristic, complemented
136C3×#215C2×C411yescharacteristic, complemented
137C3×#214C2×C411yescharacteristic, complemented
138C3×#213C2×C411yescharacteristic, complemented
139C3×C4×Dic3—21no—
140C3×C4×Dic3C2311yescharacteristic
141C3×#208—21no—
142C3×#208C2311yescharacteristic
143C3×#208C2311yescharacteristic
144C2×C3×C3⋊C8—21no—
145C2×C3×C3⋊C8C2311yescharacteristic
146C2×C3×C3⋊C8C2311yescharacteristic
147C3×ΓL(1,𝔽25)—21no—
148C3×ΓL(1,𝔽25)—21no—
149C3×D3×C8—21no—
150C3×D3×C8—21no—
151#3719C2×C411yescharacteristic, complemented
152#3718C2×C411yescharacteristic, complemented
153#3717C2×C411yescharacteristic, complemented
154#3716C2×C411yescharacteristic, complemented
155#3715C2×C411yescharacteristic, complemented
156#3715C2×C411yescharacteristic, complemented
157#3714C2×C411yescharacteristic, complemented
158#3713C2×C411yescharacteristic, complemented
159#3712—21no—
160#3711—21no—
161#3711—21no—
162#3711—21no—
163#3711—21no—
164#3711C2×C411yescharacteristic
165#3711C2×C411yescharacteristic
166#3711C2×C411yescharacteristic
167#3711C2×C411yescharacteristic
168#3711D411yescharacteristic
169#3711D411yescharacteristic
170#3711D411yescharacteristic
171#3711D411yescharacteristic
172#3710—21no—
173D3×C3⋊C8—21no—
174D3×C3⋊C8—21no—
175D3×C3⋊C8—21no—
176D3×C3⋊C8—21no—
177#2956—91noSylow
178C2×C3×#41—31no—
179D3×#41—31no—
180D3×#41C2×D311yescharacteristic
181C2×#235—31no—
182C3×#135—31no—
183C3×#131—31no—
184C3×#131—31no—
185C2×C3×M16—31no—
186C2×C3×C42—31no—
187#951—31no—
188#951—31no—
189#950—31no—
190#950—31no—
191#950—31no—
192#950—31no—
193#950—31no—
194#950—61no—
195#950C2×D311yescharacteristic
196#949—31no—
197#949—31no—
198#948—31no—
199#948—31no—
200#948—31no—
201#948—31no—
202#948—31no—
203#948—61no—
204#948—61no—
205#948—61no—
206#948C2×D311yescharacteristic, complemented
207#942—31no—
208#942—31no—
209#932—31no—
210#932—31no—
211C2×#208—31no—
212C2×#208—31no—
213C2×#208—31no—
214C2×#208—61no—
215C2×#208—61no—
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—31no—
225#907—31no—
226#907—31no—
227#907—31no—
228#907—31no—
229#907—61no—
230#907—61no—
231#907—61no—
232#907C2×D311yescharacteristic, complemented
233D3×M16—31no—
234D3×M16—61no—
235D3×M16—61no—
236D3×M16—61no—
237D3×M16—61no—
238D3×M16C2×D311yescharacteristic
239#904—31no—
240#901—31no—
241#901—31no—
242#901—61no—
243#901—61no—
244#901—61no—
245#901—61no—
246C2×ΓL(1,𝔽25)—31no—
247C2×ΓL(1,𝔽25)—31no—
248C2×ΓL(1,𝔽25)—61no—
249C2×ΓL(1,𝔽25)—61no—
250C42×D3C2×D311yescharacteristic
251C3×#108—31no—
252C3×#104—21no—
253C3×#104—31no—
254C3×#104—31no—
255C3×#104—31no—
256C3×#104—31no—
257C3×#104C2×D311yescharacteristic, complemented
258C3×#104C2×D311yescharacteristic, complemented
259C3×#97—31no—
260#837—31no—
261#837C2×D311yescharacteristic, complemented
262#825—31no—
263#825C2×D311yescharacteristic, complemented
264#822—31no—
265#822—31no—
266#822—31no—
267#822—31no—
268#822—31no—
269#822—61no—
270#822C2×D311yescharacteristic, complemented
271#819—31no—
272C8×Dic3—31no—
273C8×Dic3—31no—
274#805—31no—
275#805—31no—
276#805—31no—
277#805—31no—
278#805—61no—
279#805C2×D311yescharacteristic, complemented
280#805C2×D311yescharacteristic, complemented
281#803—31no—
282#803—31no—
283#803—61no—
284#803C2×D311yescharacteristic, complemented
285C4×C3⋊C8—31no—
286C4×C3⋊C8—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×C4—21no—
295C2×C32×C4C2411yescharacteristic
296#638—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×D3—42no—
315C3×C4×D3C22×C411yescharacteristic
316C3×C4×D3C22×C411yescharacteristic
317C3×C4×D3C2×D411yescharacteristic
318C3×C4×D3C2×D411yescharacteristic
319C3×Dic6—21no—
320C3×Dic6C22×C411yescharacteristic
321C3×Dic6C22×C411yescharacteristic
322#627—21no—
323#626—21no—
324#626—21no—
325#625—21no—
326#624—21no—
327D3×Dic3—21no—
328D3×Dic3—21no—
329C32×C8—21no—
330C3⋊(C3⋊C8)—21no—
331C3⋊(C3⋊C8)C22×C411yescharacteristic
332C3⋊(C3⋊C8)C22×C411yescharacteristic
333C3⋊(C3⋊C8)C2×D411yescharacteristic
334C3⋊(C3⋊C8)C2×D411yescharacteristic
335C3×C3⋊C8—21no—
336C3×C3⋊C8—21no—
337C3×C3⋊C8C22×C411yescharacteristic
338C3×C3⋊C8C22×C411yescharacteristic
339C3×C3⋊C8C2×D411yescharacteristic
340C3×C3⋊C8C2×D411yescharacteristic
341#575—91no—
342#568—91no—
343#568—91no—
344#444—31no—
345#444—91no—
346#444—91no—
347#444—91no—
348#443—91no—
349#443—91no—
350#443—91no—
351#443—91no—
352#430—91no—
353C2×#104—31no—
354C2×#104—91no—
355C4×M16—91no—
356C3×#41—21no—
357C3×#41—31no—
358C3×#41—31no—
359C3×#41—31no—
360C3×#41—31no—
361C3×#41—61no—
362C3×#41—61no—
363C3×#41C22×D311yescharacteristic
364C3×#41C22×D311yescharacteristic
365C2×C3×Q8—31no—
366C2×C3×D4—31no—
367C2×C3×D4—61no—
368C22×C3×C4—31no—
369C22×C3×C4—61no—
370C22×C3×C4—61no—
371C2×#67—61no—
372#239—31no—
373#239C4×D311yescharacteristic
374D3×Q8—31no—
375D3×Q8C4×D311yescharacteristic
376#237—21no—
377#237—31no—
378#237—61no—
379#237C4×D311yescharacteristic
380D3×D4—21no—
381D3×D4—31no—
382D3×D4—61no—
383D3×D4C4×D311yescharacteristic
384#235—21no—
385#235—31no—
386#235—31no—
387#235—31no—
388#235—31no—
389#235—61no—
390#235—61no—
391#235—61no—
392#235—61no—
393#235C22×D311yescharacteristic
394#235C22×D311yescharacteristic
395C2×D12—31no—
396C2×C4×D3—21no—
397C2×C4×D3—21no—
398C2×C4×D3—61no—
399C2×C4×D3—61no—
400C2×C4×D3C22×D311yescharacteristic
401C2×Dic6—31no—
402C3×Q16—31no—
403C3×SD16—31no—
404C3×SD16—31no—
405C3×D8—31no—
406C3×M16—21no—
407C3×M16—31no—
408C3×M16—31no—
409C3×M16—61no—
410C3×M16—61no—
411C3×M16—61no—
412C3×M16C22×D311yescharacteristic
413C3×M16C22×D311yescharacteristic
414C2×C3×C8—31no—
415C2×C3×C8—31no—
416C2×C3×C8—61no—
417C2×C3×C8—61no—
418C2×C3×C8—61no—
419C3×C42—21no—
420C3×C42—31no—
421C3×C42—61no—
422C3×C42C22×D311yescharacteristic
423C3×C42C22×D311yescharacteristic
424#216—31no—
425#216—31no—
426#216—31no—
427#216—31no—
428#216—31no—
429#216—61no—
430#216C4×D311yescharacteristic, complemented
431#215—31no—
432#215—31no—
433#215—31no—
434#215—31no—
435#215—31no—
436#215—61no—
437#215C4×D311yescharacteristic, complemented
438#214—31no—
439#214—31no—
440#214—31no—
441#214—31no—
442#214—31no—
443#214—61no—
444#214C4×D311yescharacteristic, complemented
445#213—31no—
446#213—31no—
447#213—31no—
448#213—31no—
449#213—31no—
450#213—61no—
451#213C4×D311yescharacteristic, complemented
452C4×Dic3—21no—
453C4×Dic3C22×D311yescharacteristic
454#208—21no—
455#208—31no—
456#208—31no—
457#208—31no—
458#208—31no—
459#208—31no—
460#208—31no—
461#208—31no—
462#208—31no—
463#208—31no—
464#208—31no—
465#208—61no—
466#208—61no—
467#208—61no—
468#208—61no—
469#208—61no—
470#208—61no—
471#208—61no—
472#208—121no—
473#208C22×D311yescharacteristic
474#208C22×D311yescharacteristic
475C2×C3⋊C8—21no—
476C2×C3⋊C8—31no—
477C2×C3⋊C8—31no—
478C2×C3⋊C8—31no—
479C2×C3⋊C8—31no—
480C2×C3⋊C8—61no—
481C2×C3⋊C8—61no—
482C2×C3⋊C8—61no—
483C2×C3⋊C8—61no—
484C2×C3⋊C8—61no—
485C2×C3⋊C8—61no—
486C2×C3⋊C8—61no—
487C2×C3⋊C8—61no—
488C2×C3⋊C8—121no—
489C2×C3⋊C8C22×D311yescharacteristic
490C2×C3⋊C8C22×D311yescharacteristic
491Dic12—31no—
492D24—31no—
493#204—31no—
494#204—31no—
495ΓL(1,𝔽25)—21no—
496ΓL(1,𝔽25)—21no—
497ΓL(1,𝔽25)—31no—
498ΓL(1,𝔽25)—31no—
499ΓL(1,𝔽25)—31no—
500ΓL(1,𝔽25)—31no—
501ΓL(1,𝔽25)—31no—
502ΓL(1,𝔽25)—31no—
503ΓL(1,𝔽25)—31no—
504ΓL(1,𝔽25)—31no—
505ΓL(1,𝔽25)—61no—
506ΓL(1,𝔽25)—61no—
507ΓL(1,𝔽25)—61no—
508ΓL(1,𝔽25)—61no—
509ΓL(1,𝔽25)—61no—
510ΓL(1,𝔽25)—61no—
511ΓL(1,𝔽25)—61no—
512ΓL(1,𝔽25)—61no—
513ΓL(1,𝔽25)—121no—
514D3×C8—21no—
515D3×C8—21no—
516D3×C8—61no—
517D3×C8—61no—
518D3×C8—61no—
519D3×C8—61no—
520D3×C8—61no—
521D3×C8—61no—
522D3×C8—61no—
523D3×C8—61no—
524D3×C8—121no—
525C22×C32—21no—
526C22×C32C2×#4111yescharacteristic
527C2×C3⋊D3—21no—
528C2×C3×D3—21no—
529C2×C3×D3—21no—
530C2×C3×D3—41no—
531C2×C3×D3—81no—
532C2×C3×D3C4×D411yescharacteristic
533C2×C3×D3C4×D411yescharacteristic
534D32—81no—
535C32×C4—21no—
536C32×C4—41no—
537C32×C4C23×C411yescharacteristic
538C32×C4C22×D411yescharacteristic
539C3⋊Dic3—21no—
540C3×Dic3—22no—
541C3×Dic3—21no—
542C3×Dic3—21no—
543C3×Dic3C4×D411yescharacteristic
544C3×Dic3C4×D411yescharacteristic
545C2×#41—31no—
546C2×#41—91no—
547#137—91no—
548#137—91no—
549#137—91no—
550#137—91no—
551AGL(1,ℤ/8)—91no—
552AGL(1,ℤ/8)—91no—
553AGL(1,ℤ/8)—91no—
554AGL(1,ℤ/8)—91no—
555#135—31no—
556#135—91no—
557#135—91no—
558#135—91no—
559#131—31no—
560#131—31no—
561#131—91no—
562#131—91no—
563#131—91no—
564#131—91no—
565#131—91no—
566#131—91no—
567#131—181no—
568#131—181no—
569#131—181no—
570#131—181no—
571C2×M16—31no—
572C2×M16—91no—
573C2×M16—91no—
574C2×M16—91no—
575C2×M16—181no—
576C2×M16—181no—
577C2×M16—181no—
578C2×M16—181no—
579C2×C42—31no—
580#108—31no—
581#108—91no—
582#108—91no—
583#108—91no—
584#104—31no—
585#104—31no—
586#104—31no—
587#104—31no—
588#104—91no—
589#104—91no—
590#104—91no—
591#104D3211yescharacteristic, complemented
592#97—31no—
593#97—91no—
594C4×C8—91no—
595C4×C8—91no—
596C23×C3—31no—
597C23×C3—61no—
598C22×D3—21no—
599C22×D3—61no—
600C22×D3—61no—
601C22×D3#23711yescharacteristic
602C3×Q8—21no—
603C3×Q8—31no—
604C3×Q8—31no—
605C3×Q8—61no—
606C3×Q8C2×C4×D311yescharacteristic
607C3×Q8C2×C4×D311yescharacteristic
608C3×D4—21no—
609C3×D4—21no—
610C3×D4—21no—
611C3×D4—31no—
612C3×D4—31no—
613C3×D4—41no—
614C3×D4—61no—
615C3×D4—61no—
616C3×D4—61no—
617C3×D4—61no—
618C3×D4—61no—
619C3×D4C2×C4×D311yescharacteristic
620C3×D4C2×C4×D311yescharacteristic
621C2×C3×C4—21no—
622C2×C3×C4—21no—
623C2×C3×C4—21no—
624C2×C3×C4—21no—
625C2×C3×C4—21no—
626C2×C3×C4—31no—
627C2×C3×C4—31no—
628C2×C3×C4—31no—
629C2×C3×C4—31no—
630C2×C3×C4—31no—
631C2×C3×C4—41no—
632C2×C3×C4—41no—
633C2×C3×C4—61no—
634C2×C3×C4—61no—
635C2×C3×C4—61no—
636C2×C3×C4—61no—
637C2×C3×C4—61no—
638C2×C3×C4—61no—
639C2×C3×C4—122no—
640C2×C3×C4C23×D311yescharacteristic
641C2×C3×C4C23×D311yescharacteristic
642#67—21no—
643#67—21no—
644#67—21no—
645#67—21no—
646#67—61no—
647#67—61no—
648#67—61no—
649#67—61no—
650#67—61no—
651#67—61no—
652#67—121no—
653C2×Dic3—21no—
654C2×Dic3—21no—
655C2×Dic3—61no—
656C2×Dic3—61no—
657C2×Dic3#23711yescharacteristic
658D12—21no—
659D12—31no—
660D12—31no—
661D12—61no—
662D12—61no—
663D12—61no—
664D12C2×C4×D311yescharacteristic
665D12C2×C4×D311yescharacteristic
666C4×D3—21no—
667C4×D3—21no—
668C4×D3—21no—
669C4×D3—21no—
670C4×D3—42no—
671C4×D3—61no—
672C4×D3—61no—
673C4×D3—61no—
674C4×D3—61no—
675C4×D3—61no—
676C4×D3—61no—
677C4×D3—121no—
678C4×D3C2×C4×D311yescharacteristic
679C4×D3C2×C4×D311yescharacteristic
680C4×D3D3×D411yescharacteristic
681C4×D3D3×D411yescharacteristic
682Dic6—21no—
683Dic6—31no—
684Dic6—31no—
685Dic6—61no—
686Dic6—61no—
687Dic6—61no—
688Dic6C2×C4×D311yescharacteristic
689Dic6C2×C4×D311yescharacteristic
690C3×C8—21no—
691C3×C8—21no—
692C3×C8—31no—
693C3×C8—31no—
694C3×C8—31no—
695C3×C8—31no—
696C3×C8—41no—
697C3×C8—61no—
698C3×C8—61no—
699C3⋊C8—21no—
700C3⋊C8—21no—
701C3⋊C8—31no—
702C3⋊C8—31no—
703C3⋊C8—31no—
704C3⋊C8—31no—
705C3⋊C8—31no—
706C3⋊C8—31no—
707C3⋊C8—31no—
708C3⋊C8—31no—
709C3⋊C8—61no—
710C3⋊C8—61no—
711C3⋊C8—61no—
712C3⋊C8—61no—
713C3⋊C8—61no—
714C3⋊C8—61no—
715C3⋊C8—121no—
716C3⋊C8C2×C4×D311yescharacteristic
717C3⋊C8C2×C4×D311yescharacteristic
718C3⋊C8D3×D411yescharacteristic
719C3⋊C8D3×D411yescharacteristic
720C2×C32—21no—
721C2×C32—41no—
722C2×C32C2×C4×D411yescharacteristic
723C3⋊D3—41no—
724C3×D3—21no—
725C3×D3—21no—
726C3×D3—41no—
727C3×D3—41no—
728#41—31no—
729#41—31no—
730#41—31no—
731#41—31no—
732#41—61no—
733#41—61no—
734#41—91no—
735#41—91no—
736#41—91no—
737#41—181no—
738#41—181no—
739#41C2×D3211yescharacteristic
740C2×Q8—31no—
741C2×Q8—91no—
742C2×D4—31no—
743C2×D4—61no—
744C2×D4—91no—
745C2×D4—181no—
746C22×C4—31no—
747C22×C4—61no—
748C22×C4—61no—
749C22×C4—181no—
750Q16—31no—
751Q16—91no—
752Q16—91no—
753Q16—91no—
754SD16—31no—
755SD16—31no—
756SD16—91no—
757SD16—91no—
758SD16—91no—
759SD16—91no—
760SD16—91no—
761SD16—91no—
762D8—31no—
763D8—91no—
764D8—91no—
765D8—91no—
766M16—31no—
767M16—31no—
768M16—61no—
769M16—61no—
770M16—61no—
771M16—91no—
772M16—91no—
773M16—91no—
774M16—91no—
775M16—91no—
776M16—91no—
777M16—91no—
778M16—91no—
779M16—91no—
780M16—181no—
781M16—181no—
782M16—181no—
783M16—181no—
784M16—181no—
785M16—181no—
786M16—181no—
787M16C2×D3211yescharacteristic
788C2×C8—31no—
789C2×C8—31no—
790C2×C8—61no—
791C2×C8—61no—
792C2×C8—61no—
793C2×C8—91no—
794C2×C8—91no—
795C2×C8—181no—
796C2×C8—181no—
797C2×C8—181no—
798C2×C8—181no—
799C2×C8—181no—
800C2×C8—181no—
801C2×C8—181no—
802C42—31no—
803C42—61no—
804C42C2×D3211yescharacteristic
805C22×C3—21no—
806C22×C3—21no—
807C22×C3—21no—
808C22×C3—31no—
809C22×C3—31no—
810C22×C3—41no—
811C22×C3—61no—
812C22×C3—61no—
813C22×C3—121no—
814C22×C3—241no—
815C22×C3C2×#23711yescharacteristic
816C22×C3D3×#4111yescharacteristic
817C2×D3—21no—
818C2×D3—21no—
819C2×D3—41no—
820C2×D3—61no—
821C2×D3—61no—
822C2×D3—81no—
823C2×D3—121no—
824C2×D3—241no—
825C2×D3—241no—
826C2×D3#67⋊C411yescharacteristic
827C2×D3#67⋊C411yescharacteristic
828C3×C4—21no—
829C3×C4—21no—
830C3×C4—21no—
831C3×C4—21no—
832C3×C4—31no—
833C3×C4—31no—
834C3×C4—41no—
835C3×C4—41no—
836C3×C4—41no—
837C3×C4—62no—
838C3×C4—61no—
839C3×C4—61no—
840C3×C4—81no—
841C3×C4C22×C4×D311yescharacteristic
842C3×C4C22×C4×D311yescharacteristic
843C3×C4C2×D3×D411yescharacteristic
844C3×C4C2×D3×D411yescharacteristic
845Dic3—22no—
846Dic3—21no—
847Dic3—21no—
848Dic3—61no—
849Dic3—61no—
850Dic3—121no—
851Dic3#67⋊C411yescharacteristic
852Dic3#67⋊C411yescharacteristic
853C32#295611yescharacteristic, complemented, Sylow
854C23—31no—
855C23—61no—
856C23—181no—
857Q8—31no—
858Q8—31no—
859Q8—61no—
860Q8—91no—
861Q8—181no—
862Q8C4×D3211yescharacteristic
863D4—21no—
864D4—31no—
865D4—31no—
866D4—61no—
867D4—61no—
868D4—61no—
869D4—61no—
870D4—61no—
871D4—91no—
872D4—181no—
873D4—181no—
874D4—181no—
875D4—181no—
876D4C4×D3211yescharacteristic
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—31no—
880C2×C4—31no—
881C2×C4—31no—
882C2×C4—31no—
883C2×C4—31no—
884C2×C4—61no—
885C2×C4—61no—
886C2×C4—61no—
887C2×C4—61no—
888C2×C4—61no—
889C2×C4—61no—
890C2×C4—122no—
891C2×C4—181no—
892C2×C4—181no—
893C2×C4—181no—
894C2×C4—181no—
895C2×C4C22×D3211yescharacteristic
896C8—21no—
897C8—31no—
898C8—31no—
899C8—31no—
900C8—31no—
901C8—61no—
902C8—61no—
903C8—91no—
904C8—91no—
905C8—91no—
906C8—91no—
907C8—181no—
908C2×C3—21no—
909C2×C3—21no—
910C2×C3—21no—
911C2×C3—41no—
912C2×C3—41no—
913C2×C3—41no—
914C2×C3—61no—
915C2×C3—61no—
916C2×C3—81no—
917C2×C3—121no—
918C2×C3—121no—
919C2×C3C2×#67⋊C411yescharacteristic
920C2×C3C4×D3×D411yescharacteristic
921D3—21no—
922D3—21no—
923D3—41no—
924D3—41no—
925D3—121no—
926D3—121no—
927D3—241no—
928C22—21no—
929C22—31no—
930C22—31no—
931C22—61no—
932C22—61no—
933C22—121no—
934C22—181no—
935C22—241no—
936C22—721no—
937C22D3×#23711yescharacteristic
938C4—21no—
939C4—31no—
940C4—31no—
941C4—41no—
942C4—62no—
943C4—61no—
944C4—61no—
945C4—181no—
946C4C2×C4×D3211yescharacteristic
947C4D32×D411yescharacteristic
948C3—21no—
949C3#7898011yescharacteristic, complemented
950C3#7989811yescharacteristic, complemented
951C2—21no—
952C2—41no—
953C2—61no—
954C2—61no—
955C2—121no—
956C2—121no—
957C2—361no—
958C2D3×#67⋊C411yescharacteristic
subgroupG/H
centerC4D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#104C22
socleC2×C32C2×C4×D4
prime radical#10595453C2
cosocleC2×C32×C4C24
hypercenter#104D32
hypocenterC32#2956
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
2. #10595441C2semidirect
3. #10594706C2semidirect
4. #10592522C2semidirect
5. C3×#4823C2semidirect
6. C3×D3×#104C2semidirect
7. #10591675C2semidirect
8. #10591662C2semidirect
9. #10590977C2semidirect
10. #10590975C2semidirect
11. #10590973C2semidirect
12. D3×#805C2semidirect
13. #10590390C2semidirect
14. #10590342C2semidirect
15. #10590334C2semidirect
21. #64157C22semidirect
22. #64116C22semidirect
24. C3×#948C22semidirect
25. C3×#907C22semidirect
28. #63948C4semidirect
29. #63946C4semidirect
30. #63943C4semidirect
31. #63939C4semidirect
32. #63934C4semidirect
33. #63932C4semidirect
34. #63929C4semidirect
35. #63925C4semidirect
41. #63817C22semidirect
43. #63815C22semidirect
44. #63815C22semidirect
46. #63814C22semidirect
53. C32×#104C22semidirect
54. #63649C22semidirect
55. #63632C22semidirect
56. #63630C22semidirect
57. C3×#837C22semidirect
58. C3×#825C22semidirect
59. C3×#822C22semidirect
60. C3×#805C22semidirect
61. C3×#805C22semidirect
62. C3×#803C22semidirect
63. #63578C22semidirect
64. #63577C22semidirect
65. #63570C22semidirect
66. #63569C22semidirect
67. Dic3×C3⋊C8C22semidirect
68. Dic3×C3⋊C8C22semidirect
95. #4823D3semidirect
97. D3×#104D3semidirect
124. #3756C2×C4semidirect
125. #3755C2×C4semidirect
126. #3754C2×C4semidirect
127. #3753C2×C4semidirect
135. C3×#216C2×C4semidirect
136. C3×#215C2×C4semidirect
137. C3×#214C2×C4semidirect
138. C3×#213C2×C4semidirect
151. #3719C2×C4semidirect
152. #3718C2×C4semidirect
153. #3717C2×C4semidirect
154. #3716C2×C4semidirect
155. #3715C2×C4semidirect
156. #3715C2×C4semidirect
157. #3714C2×C4semidirect
158. #3713C2×C4semidirect
206. #948C2×D3semidirect
232. #907C2×D3semidirect
257. C3×#104C2×D3semidirect
258. C3×#104C2×D3semidirect
261. #837C2×D3semidirect
263. #825C2×D3semidirect
270. #822C2×D3semidirect
279. #805C2×D3semidirect
280. #805C2×D3semidirect
284. #803C2×D3semidirect
430. #216C4×D3semidirect
437. #215C4×D3semidirect
444. #214C4×D3semidirect
451. #213C4×D3semidirect
591. #104D32semidirect
853. C32#2956semidirect
949. C3#78980semidirect
950. C3#79898semidirect

Maximal subgroups

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

subgroupindex
#105954532
#105954412
#105947062
#105925222
C3×#48232
C3×D3×#1042
#105916752
#105916622
#105909772
#105909752
#105909732
D3×#8052
#105903902
#105903422
#105903342
#798983
#789803