Finite Group Databasebeta

← #11870391

Subgroups — #11870391

Order 1152.

943 conjugacy classes of subgroups.

The subgroup lattice has 815 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595994C211yesmaximal, characteristic, complemented
2#10594923C211yesmaximal, characteristic
3C3×#5003C211yesmaximal, characteristic, complemented
4C3×#4996C211yesmaximal, characteristic, complemented
5#10591153C211yesmaximal, characteristic, complemented
6#10591126C211yesmaximal, characteristic, complemented
7#10591092C211yesmaximal, characteristic, complemented
8#10590612C211yesmaximal, characteristic, complemented
9#10590611C211yesmaximal, characteristic, complemented
10#10590582C211yesmaximal, characteristic, complemented
11#10590575C211yesmaximal, characteristic, complemented
12#10590529C211yesmaximal, characteristic, complemented
13#10590526C211yesmaximal, characteristic, complemented
14#10590512C211yesmaximal, characteristic, complemented
15#10590511C211yesmaximal, characteristic, complemented
16#81521—31nomaximal
17#81377—31nomaximal
18C2×#3828C2211yescharacteristic
19C2×#3796C2211yescharacteristic
20C32×#117C2211yescharacteristic
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22#64101C2211yescharacteristic
23#64101C2211yescharacteristic
24C4⋊C4×C3⋊D3C2211yescharacteristic
25C4⋊C4×C3⋊D3C2211yescharacteristic
26#64090—21no—
27#64090—21no—
28C4×C4⋊(C3⋊D3)—21no—
29C4×#634—21no—
30C3×#930C2211yescharacteristic
31C3×#924C2211yescharacteristic
32#63971—21no—
33#63958—21no—
34#63916C2211yescharacteristic
35#63910—21no—
36#63900C2211yescharacteristic
37#63896—21no—
38#63871C2211yescharacteristic
39C2×#3712C2211yescharacteristic
40C2×#3710C2211yescharacteristic
41C3×#830C2211yescharacteristic
42C3×#830C2211yescharacteristic
43C3×#810C2211yescharacteristic
44C3×#810C2211yescharacteristic
45C3×#809C2211yescharacteristic
46C3×#809C2211yescharacteristic
47C3×#808C2211yescharacteristic
48C3×#808C2211yescharacteristic
49C3×#807C2211yescharacteristic
50C3×#807C2211yescharacteristic
51#63573C2211yescharacteristic
52#63573C2211yescharacteristic
53#63573C2211yescharacteristic
54#63573C2211yescharacteristic
55#63566C2211yescharacteristic
56#63566C2211yescharacteristic
57#63563C2211yescharacteristic
58#63563C2211yescharacteristic
59#63557C2211yescharacteristic
60#63557C2211yescharacteristic
61#5629—31no—
62#5608—31no—
63#5523—31no—
64#5523—31no—
65#5523—61no—
66C3×#485—31no—
67C3×#482—31no—
68#5043—31no—
69#5034—31no—
70#5003D311yescharacteristic, complemented
71#4996D311yescharacteristic, complemented
72#4888—31no—
73#4885—31no—
74#4881—31no—
75#4881—31no—
76#4863—31no—
77#4862—31no—
78D3×#106—31no—
79D3×#106—31no—
80#4815—31no—
81#4805—31no—
82#4804—31no—
83#4803—31no—
84#4779—31no—
85#4777—31no—
86#4772—31no—
87#4771—31no—
88#4735—31no—
89#4727—31no—
90#4727—31no—
91#4721—31no—
92C22×C32×C4C2311yescharacteristic
93C2×#638D411yescharacteristic
94C2×#638D411yescharacteristic
95C22×C3⋊Dic3—21no—
96#3828—22no—
97#3828—22no—
98C2×C4⋊(C3⋊D3)D411yescharacteristic
99C2×C4×C3⋊D3—21no—
100C2×C4×C3⋊D3—21no—
101C2×C4×C3⋊D3C2311yescharacteristic
102C2×C4×C3⋊D3C2311yescharacteristic
103C2×#634D411yescharacteristic
104C2×C3×#67—21no—
105C2×C3×D12C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C2×#626—21no—
108C2×#626—21no—
109C2×#624—21no—
110C2×D3×Dic3—21no—
111#3796—22no—
112#3796—22no—
113C32×C4⋊C4C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115C32×C22⋊C4—21no—
116C32×C42—21no—
117#3752—21no—
118#3752—21no—
119C4⋊(C3⋊Dic3)—21no—
120C4⋊(C3⋊Dic3)C2311yescharacteristic
121C4⋊(C3⋊Dic3)C2311yescharacteristic
122#3750—21no—
123#3750—21no—
124C4×C3⋊Dic3—21no—
125C4×C3⋊Dic3—21no—
126C3×#217—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—21no—
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135#3724—21no—
136Dic3⋊Dic3—21no—
137#3722—21no—
138(C2×D3)⋊Dic3—21no—
139#3712—22no—
140#3710—22no—
141#3099—91noSylow
142C2×#239—31no—
143C2×#237—31no—
144C2×#235—31no—
145C2×#235—31no—
146C2×#235—61no—
147C3×C22⋊Q8—31no—
148C3×#121—31no—
149C3×#117—21no—
150C3×#117C2×D311yescharacteristic
151C3×#117C2×D311yescharacteristic
152#946—31no—
153#939—61no—
154#938—31no—
155#938—61no—
156#930C2×D311yescharacteristic
157C2×C4⋊Dic3—31no—
158C2×C4⋊Dic3—31no—
159C2×C4⋊Dic3—61no—
160#924C2×D311yescharacteristic
161C2×ΓL(1,𝔽25)—31no—
162C2×ΓL(1,𝔽25)—31no—
163C2×D3×C8—31no—
164C2×D3×C8—31no—
165#897—31no—
166#896—61no—
167#895—31no—
168#895—61no—
169#892—31no—
170#892—31no—
171#892—31no—
172#892—31no—
173#892—61no—
174#892—61no—
175D3×C4⋊C4—31no—
176D3×C4⋊C4—31no—
177D3×C4⋊C4—31no—
178D3×C4⋊C4—31no—
179D3×C4⋊C4—31no—
180D3×C4⋊C4—31no—
181D3×C4⋊C4—61no—
182D3×C4⋊C4—61no—
183#884—61no—
184#884—61no—
185#884—61no—
186#67⋊C4—61no—
187#67⋊C4—61no—
188#67⋊C4—61no—
189#67⋊C4—61no—
190#67⋊C4—62no—
191#67⋊C4—62no—
192#878—61no—
193C4×D12—61no—
194C4×D12—61no—
195C4×D12—62no—
196C4×Dic6—61no—
197C4×Dic6—61no—
198C4×Dic6—62no—
199C3×#107—31no—
200C3×#107—31no—
201C3×#106—31no—
202C3×#106—31no—
203C3×#103—31no—
204C3×#103—31no—
205C3×#102—31no—
206C3×#102—31no—
207C3×C22⋊C8—31no—
208C3×C22⋊C8—31no—
209#835—31no—
210#835—31no—
211#832—31no—
212#832—31no—
213#830C2×D311yescharacteristic
214#830C2×D311yescharacteristic
215#821—31no—
216#821—31no—
217(C2×D3)⋊C8—31no—
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8—31no—
220(C2×D3)⋊C8—31no—
221#817—31no—
222#817—31no—
223#817—31no—
224#817—31no—
225#816—31no—
226#816—31no—
227#810C2×D311yescharacteristic
228#810C2×D311yescharacteristic
229#809C2×D311yescharacteristic
230#809C2×D311yescharacteristic
231#808—31no—
232#808—31no—
233#808—31no—
234#808—31no—
235#808C2×D311yescharacteristic
236#808C2×D311yescharacteristic
237#807C2×D311yescharacteristic
238#807C2×D311yescharacteristic
239C23×C32C2×D411yescharacteristic
240C22×C3⋊D3C2×D411yescharacteristic
241C22×C3⋊D3C2×D411yescharacteristic
242C22×C3×D3—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2411yescharacteristic
249#638—22no—
250#638—22no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3—81no—
254C2×C3⋊Dic3C2×D411yescharacteristic
255C2×C3⋊Dic3C2×D411yescharacteristic
256C4⋊(C3⋊D3)—22no—
257C4×C3⋊D3—21no—
258C4×C3⋊D3—21no—
259C4×C3⋊D3—81no—
260C4×C3⋊D3—81no—
261C4×C3⋊D3#4112yes—
262C4×C3⋊D3#4112yes—
263#634—22no—
264C3×#67—81no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C3×D12—21no—
269C3×D12—21no—
270C3×Dic6—21no—
271C3×Dic6—21no—
272#626—42no—
273#626—81no—
274#624—81no—
275D3×Dic3—42no—
276C3×C3⋊C8—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279C3×C3⋊C8—21no—
280#537—91no—
281#520—91no—
282#485—31no—
283#485—91no—
284#483—91no—
285#483—91no—
286#482—31no—
287#482—91no—
288#481—91no—
289#481—91no—
290#428—91no—
291C2×#106—91no—
292#417—91no—
293#416—91no—
294#408—91no—
295C2×C3×Q8—31no—
296C2×C3×D4—31no—
297C2×C3×D4—61no—
298C22×C3×C4—21no—
299C22×C3×C4C22×D311yescharacteristic
300C22×C3×C4C22×D311yescharacteristic
301C2×#67—21no—
302C2×#67—31no—
303C2×#67—31no—
304C2×#67—31no—
305C2×#67—31no—
306C2×#67—61no—
307C2×#67—61no—
308C2×#67—61no—
309C2×#67—61no—
310C22×Dic3—61no—
311C22×Dic3—62no—
312C22×Dic3—61no—
313C22×Dic3—61no—
314#239—62no—
315#239—62no—
316#237—62no—
317#237—62no—
318#235—62no—
319#235—62no—
320#235—62no—
321#235—62no—
322#235—64no—
323#235—64no—
324C2×D12—31no—
325C2×D12—31no—
326C2×D12—61no—
327C2×D12—61no—
328C2×D12—61no—
329C2×D12C22×D311yescharacteristic
330C2×C4×D3—31no—
331C2×C4×D3—31no—
332C2×C4×D3—31no—
333C2×C4×D3—31no—
334C2×C4×D3—61no—
335C2×C4×D3—61no—
336C2×C4×D3—61no—
337C2×C4×D3—61no—
338C2×C4×D3—61no—
339C2×C4×D3—61no—
340C2×C4×D3—61no—
341C2×C4×D3—61no—
342C2×C4×D3—61no—
343C2×C4×D3—62no—
344C2×C4×D3—62no—
345C2×Dic6—31no—
346C2×Dic6—31no—
347C2×Dic6—61no—
348C2×Dic6C22×D311yescharacteristic
349C2×C3×C8—31no—
350C2×C3×C8—31no—
351C2×C3×C8—31no—
352C2×C3×C8—31no—
353C3×C4⋊C4—21no—
354C3×C4⋊C4—21no—
355C3×C4⋊C4—31no—
356C3×C4⋊C4—31no—
357C3×C4⋊C4—61no—
358C3×C4⋊C4C22×D311yescharacteristic
359C3×C4⋊C4C22×D311yescharacteristic
360C3×C4⋊C4C22×D311yescharacteristic
361C3×C4⋊C4C22×D311yescharacteristic
362C3×C22⋊C4—22no—
363C3×C22⋊C4—21no—
364C3×C22⋊C4—21no—
365C3×C22⋊C4—61no—
366C3×C22⋊C4—61no—
367C3×C42—22no—
368C3×C42—21no—
369C3×C42—21no—
370#217—21no—
371#217—61no—
372(C2×D3)⋊C4—21no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—62no—
381(C2×D3)⋊C4—62no—
382C4⋊Dic3—31no—
383C4⋊Dic3—31no—
384C4⋊Dic3—31no—
385C4⋊Dic3—31no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3—61no—
389C4⋊Dic3—62no—
390C4⋊Dic3—61no—
391C4⋊Dic3—61no—
392C4⋊Dic3C22×D311yescharacteristic
393C4⋊Dic3C22×D311yescharacteristic
394Dic3⋊C4—21no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402Dic3⋊C4—62no—
403Dic3⋊C4—62no—
404C4×Dic3—61no—
405C4×Dic3—61no—
406C4×Dic3—61no—
407C4×Dic3—61no—
408C4×Dic3—62no—
409C4×Dic3—62no—
410C2×C3⋊C8C22×D311yescharacteristic
411C2×C3⋊C8C22×D311yescharacteristic
412C2×C3⋊C8C22×D311yescharacteristic
413C2×C3⋊C8C22×D311yescharacteristic
414ΓL(1,𝔽25)—62no—
415ΓL(1,𝔽25)—62no—
416D3×C8—62no—
417D3×C8—62no—
418C22×C32—21no—
419C22×C32—21no—
420C22×C32—21no—
421C22×C32C22×D411yescharacteristic
422C2×C3⋊D3—21no—
423C2×C3⋊D3—21no—
424C2×C3⋊D3—21no—
425C2×C3⋊D3—21no—
426C2×C3⋊D3—21no—
427C2×C3⋊D3#12312yes—
428C2×C3×D3—41no—
429C2×C3×D3—41no—
430C2×C3×D3—41no—
431C32×C4—21no—
432C32×C4—41no—
433C32×C4—41no—
434C32×C4C2×#4111yescharacteristic
435C32×C4C2×#4111yescharacteristic
436C3⋊Dic3—21no—
437C3⋊Dic3—41no—
438C3⋊Dic3—41no—
439C3⋊Dic3#12312yes—
440C3×Dic3—41no—
441C3×Dic3—41no—
442C3×Dic3—41no—
443C2×#41—91no—
444C2×#41—91no—
445C2×M16—91no—
446C22×C8—91no—
447C22⋊Q8—31no—
448C22⋊Q8—91no—
449C22⋊Q8—181no—
450#121—31no—
451#121—91no—
452#121—181no—
453#121—181no—
454#121—181no—
455C4×Q8—181no—
456C4×D4—181no—
457C4×D4—181no—
458C4×D4—181no—
459#117—91no—
460#117—91no—
461#117D3211yescharacteristic
462C2×C4⋊C4—91no—
463C2×C4⋊C4—91no—
464C2×C4⋊C4—91no—
465C2×C4⋊C4—91no—
466#107—31no—
467#107—31no—
468#106—31no—
469#106—31no—
470#106—91no—
471#106—91no—
472#106—91no—
473#106—91no—
474#103—31no—
475#103—31no—
476#103—91no—
477#103—91no—
478#102—31no—
479#102—31no—
480#102—91no—
481#102—91no—
482C22⋊C8—31no—
483C22⋊C8—31no—
484C22⋊C8—91no—
485C22⋊C8—91no—
486C23×C3—21no—
487C23×C3—61no—
488C23×C3D3×D411yescharacteristic
489C23×C3D3×D411yescharacteristic
490C22×D3—21no—
491C22×D3—31no—
492C22×D3—31no—
493C22×D3—31no—
494C22×D3—31no—
495C22×D3—61no—
496C22×D3—61no—
497C3×Q8—61no—
498C3×Q8—61no—
499C3×D4—61no—
500C3×D4—61no—
501C3×D4—241no—
502C2×C3×C4—22no—
503C2×C3×C4—22no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—22no—
509C2×C3×C4—22no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4D3×D411yescharacteristic
520C2×C3×C4D3×D411yescharacteristic
521C2×C3×C4C23×D311yescharacteristic
522C2×C3×C4C23×D311yescharacteristic
523#67—62no—
524#67—62no—
525#67—62no—
526#67—62no—
527#67—64no—
528#67—64no—
529#67—81no—
530#67—122no—
531#67—241no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—31no—
536C2×Dic3—31no—
537C2×Dic3—31no—
538C2×Dic3—31no—
539C2×Dic3—61no—
540C2×Dic3—61no—
541C2×Dic3—62no—
542C2×Dic3—62no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—122no—
548C2×Dic3—241no—
549C2×Dic3—241no—
550C2×Dic3—242no—
551D12—21no—
552D12—21no—
553D12—62no—
554D12—62no—
555D12—64no—
556D12—122no—
557D12—241no—
558C4×D3—32no—
559C4×D3—32no—
560C4×D3—32no—
561C4×D3—32no—
562C4×D3—62no—
563C4×D3—62no—
564C4×D3—62no—
565C4×D3—62no—
566C4×D3—61no—
567C4×D3—61no—
568C4×D3—61no—
569C4×D3—61no—
570C4×D3—122no—
571C4×D3—241no—
572C4×D3—241no—
573C4×D3—241no—
574C4×D3—241no—
575C4×D3—241no—
576C4×D3—241no—
577C4×D3—242no—
578C4×D3—242no—
579Dic6—21no—
580Dic6—21no—
581Dic6—62no—
582Dic6—62no—
583Dic6—64no—
584C3×C8—61no—
585C3×C8—61no—
586C3×C8—61no—
587C3×C8—61no—
588C3⋊C8—21no—
589C3⋊C8—21no—
590C3⋊C8—21no—
591C3⋊C8—21no—
592C2×C32—41no—
593C2×C32C2×#12311yescharacteristic
594C2×C32#57711yescharacteristic
595C2×C32#57711yescharacteristic
596C3⋊D3—22no—
597C3⋊D3—41no—
598C3×D3—81no—
599#41—182no—
600#41—182no—
601#41—182no—
602#41—182no—
603C2×Q8—31no—
604C2×Q8—91no—
605C2×D4—31no—
606C2×D4—61no—
607C2×D4—91no—
608C2×D4—91no—
609C2×D4—91no—
610C2×D4—181no—
611C2×D4—181no—
612C22×C4—91no—
613C22×C4—91no—
614C22×C4—181no—
615C22×C4—181no—
616C22×C4—181no—
617C22×C4—181no—
618C22×C4—181no—
619C22×C4C2×D3211yescharacteristic
620M16—182no—
621C2×C8—31no—
622C2×C8—31no—
623C2×C8—31no—
624C2×C8—31no—
625C2×C8—182no—
626C4⋊C4—31no—
627C4⋊C4—31no—
628C4⋊C4—61no—
629C4⋊C4—91no—
630C4⋊C4—91no—
631C4⋊C4—181no—
632C4⋊C4—181no—
633C4⋊C4—181no—
634C4⋊C4—181no—
635C4⋊C4—181no—
636C4⋊C4C2×D3211yescharacteristic
637C4⋊C4C2×D3211yescharacteristic
638C22⋊C4—21no—
639C22⋊C4—61no—
640C22⋊C4—61no—
641C22⋊C4—181no—
642C22⋊C4—181no—
643C22⋊C4—181no—
644C22⋊C4—181no—
645C42—21no—
646C42—181no—
647C42—181no—
648C22×C3—22no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—21no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—21no—
655C22×C3—21no—
656C22×C3—41no—
657C22×C3—41no—
658C22×C3—121no—
659C22×C3—121no—
660C22×C3—121no—
661C22×C3C2×D3×D411yescharacteristic
662C22×C3C2×D3×D411yescharacteristic
663C2×D3—32no—
664C2×D3—32no—
665C2×D3—41no—
666C2×D3—41no—
667C2×D3—41no—
668C2×D3—62no—
669C2×D3—61no—
670C2×D3—61no—
671C2×D3—61no—
672C2×D3—61no—
673C2×D3—62no—
674C2×D3—61no—
675C2×D3—61no—
676C2×D3—61no—
677C2×D3—61no—
678C2×D3—61no—
679C2×D3—61no—
680C2×D3—121no—
681C2×D3—121no—
682C2×D3—121no—
683C2×D3—121no—
684C3×C4—22no—
685C3×C4—21no—
686C3×C4—21no—
687C3×C4—21no—
688C3×C4—21no—
689C3×C4—42no—
690C3×C4—42no—
691C3×C4—41no—
692C3×C4—41no—
693C3×C4—41no—
694C3×C4—41no—
695C3×C4—121no—
696C3×C4—121no—
697C3×C4—121no—
698C3×C4D3×#4111yescharacteristic
699C3×C4D3×#4111yescharacteristic
700C3×C4D3×#4111yescharacteristic
701C3×C4D3×#4111yescharacteristic
702Dic3—32no—
703Dic3—32no—
704Dic3—41no—
705Dic3—41no—
706Dic3—41no—
707Dic3—62no—
708Dic3—62no—
709Dic3—61no—
710Dic3—61no—
711Dic3—122no—
712Dic3—122no—
713Dic3—121no—
714Dic3—121no—
715Dic3—121no—
716Dic3—121no—
717C32#309911yescharacteristic, complemented, Sylow
718C23—61no—
719C23—91no—
720C23—91no—
721C23#381111yescharacteristic
722Q8—61no—
723Q8—61no—
724Q8—182no—
725D4—61no—
726D4—61no—
727D4—182no—
728D4—182no—
729D4—182no—
730D4—241no—
731D4—362no—
732D4—721no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—61no—
740C2×C4—91no—
741C2×C4—92no—
742C2×C4—92no—
743C2×C4—91no—
744C2×C4—181no—
745C2×C4—181no—
746C2×C4—181no—
747C2×C4—181no—
748C2×C4—362no—
749C2×C4—721no—
750C2×C4—721no—
751C2×C4—721no—
752C2×C4—721no—
753C2×C4#381111yescharacteristic
754C2×C4C22×D3211yescharacteristic
755C8—61no—
756C8—61no—
757C8—61no—
758C8—61no—
759C2×C3—21no—
760C2×C3—21no—
761C2×C3—21no—
762C2×C3—42no—
763C2×C3—41no—
764C2×C3—41no—
765C2×C3—241no—
766C2×C3D3×#12311yescharacteristic
767C2×C3D3×#12311yescharacteristic
768C2×C3#577011yescharacteristic
769C2×C3#577011yescharacteristic
770C2×C3#577511yescharacteristic
771C2×C3#577811yescharacteristic
772D3—62no—
773D3—62no—
774D3—81no—
775D3—122no—
776D3—122no—
777D3—121no—
778D3—121no—
779C22—21no—
780C22—21no—
781C22—21no—
782C22—92no—
783C22—121no—
784C22—121no—
785C22—121no—
786C22—181no—
787C22—181no—
788C22—181no—
789C22—181no—
790C22—181no—
791C22C2×#381111yescharacteristic
792C4—21no—
793C4—41no—
794C4—41no—
795C4—92no—
796C4—121no—
797C4—121no—
798C4—121no—
799C4—181no—
800C4—361no—
801C4—361no—
802C4#6430611yescharacteristic
803C4#6430611yescharacteristic
804C3—21no—
805C3#8137711yescharacteristic, complemented
806C3#8152111yescharacteristic, complemented
807C2—41no—
808C2—182no—
809C2—241no—
810C2—361no—
811C2#1059507911yescharacteristic
812C2#1059546211yescharacteristic
813C2#1059547311yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radical#10594923C2
hypercenter#117D32
hypocenterC32#3099
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #10595994C2semidirect
3. C3×#5003C2semidirect
4. C3×#4996C2semidirect
5. #10591153C2semidirect
6. #10591126C2semidirect
7. #10591092C2semidirect
8. #10590612C2semidirect
9. #10590611C2semidirect
10. #10590582C2semidirect
11. #10590575C2semidirect
12. #10590529C2semidirect
13. #10590526C2semidirect
14. #10590512C2semidirect
15. #10590511C2semidirect
70. #5003D3semidirect
71. #4996D3semidirect
717. C32#3099semidirect
805. C3#81377semidirect
806. C3#81521semidirect

Maximal subgroups

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

subgroupindex
#105959942
#105949232
C3×#50032
C3×#49962
#105911532
#105911262
#105910922
#105906122
#105906112
#105905822
#105905752
#105905292
#105905262
#105905122
#105905112
#815213
#813773