Finite Group Databasebeta

← #11887381

Subgroups — #11887381

Order 1152.

919 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5530C211yesmaximal, characteristic, complemented
2#10595078C211yesmaximal, characteristic, complemented
3#10592701C211yesmaximal, characteristic, complemented
4C3×#5003C211yesmaximal, characteristic, complemented
5#10591182C211yesmaximal, characteristic, complemented
6#10591166C211yesmaximal, characteristic, complemented
7#67⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8#10590595C211yesmaximal, characteristic, complemented
9D3×#809C211yesmaximal, characteristic, complemented
10#10590578C211yesmaximal, characteristic, complemented
11#10590533C211yesmaximal, characteristic, complemented
12#10590530C211yesmaximal, characteristic, complemented
13#10590470C211yesmaximal, characteristic, complemented
14#10590456C211yesmaximal, characteristic, complemented
15#10590427C211yesmaximal, characteristic, complemented
16#83614—31nomaximal
17#81382—31nomaximal
18C2×#3828C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20C32×#117C2211yescharacteristic, complemented
21C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
22C3×#930C2211yescharacteristic
23C3×#930C2211yescharacteristic, complemented
24C3×C4×#67C2211yescharacteristic
25C3×#895C2211yescharacteristic
26C3×#893C2211yescharacteristic, complemented
27C3×D3×C4⋊C4C2211yescharacteristic
28C3×#890C2211yescharacteristic, complemented
29C3×#884—21no—
30C3×#883—21no—
31C3×#876—21no—
32C3×C4×D12—21no—
33#63983—21no—
34#63958—21no—
35#63921—21no—
36#63894C2211yescharacteristic
37#63860C2211yescharacteristic
38#63857C2211yescharacteristic
39#63853—21no—
40C2×#3716C2211yescharacteristic, complemented
41C2×#3714C2211yescharacteristic
42C2×#3713C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44#63637C2211yescharacteristic, complemented
45#63637C2211yescharacteristic, complemented
46#63636C2211yescharacteristic
47#63636C2211yescharacteristic
48C3×#830C2211yescharacteristic, complemented
49C3×#809C2211yescharacteristic
50C3×#809C2211yescharacteristic
51C3×#808C2211yescharacteristic, complemented
52C3×#807C2211yescharacteristic, complemented
53#63576C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63564C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C3×#553—31no—
62#5612—31no—
63#5550—31no—
64#5530D311yescharacteristic, complemented
65C3×#482—31no—
66#5068—31no—
67#5066—31no—
68#5041—31no—
69#5038—31no—
70#5038—31no—
71#5037—31no—
72#5036—31no—
73#5016—31no—
74C4×#213—31no—
75D4×C3⋊C8—31no—
76#5003D311yescharacteristic, complemented
77#5002—31no—
78#5002—31no—
79#5002—61no—
80#4970—31no—
81C2×#809—31no—
82#4884—31no—
83#4872—31no—
84#4871—31no—
85#4864—31no—
86#4787—31no—
87#4773—31no—
88D3×#102—31no—
89#4768—31no—
90#4734—31no—
91#67⋊C8—31no—
92C22×D32—21no—
93C22×C32×C4C2311yescharacteristic
94C2×#638—21no—
95#3828—22no—
96#3828—41no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3—21no—
99C2×#634C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C2×C3×#67D411yescharacteristic
103C2×C3×D12—21no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3C2311yescharacteristic
109C2×#626—21no—
110C2×#624—21no—
111D3×D12—22no—
112D3×D12—41no—
113C32×C4⋊C4C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115C32×C22⋊C4—21no—
116C32×C42—21no—
117C2×C3⋊(C3⋊C8)—41no—
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C3×#217D411yescharacteristic
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4D411yescharacteristic
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4D411yescharacteristic
132C3×C4×Dic3C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135Dic3⋊Dic3—21no—
136#3722—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140#3716—41no—
141#3714—22no—
142#3713—41no—
143D3×C3⋊C8—41no—
144#3297—91noSylow
145C2×D3×D4—31no—
146C2×#235—31no—
147C2×#235—31no—
148C2×#235—61no—
149C22×D12—31no—
150C3×#126—61no—
151C3×#125—31no—
152C3×#123—61no—
153C3×#121—31no—
154C3×#121—31no—
155C3×#121—31no—
156C3×#121—61no—
157C3×C4×D4—31no—
158C3×C4×D4—31no—
159C3×C4×D4—61no—
160C3×#117—21no—
161C3×#117C2×D311yescharacteristic, complemented
162C3×#117C2×D311yescharacteristic, complemented
163C2×C3×C4⋊C4—31no—
164#938—61no—
165#937—61no—
166#937—61no—
167#936—31no—
168C2×#214—31no—
169C2×#213—31no—
170C2×#213—31no—
171C2×#213—31no—
172#930C2×D311yescharacteristic
173#930C2×D311yescharacteristic, complemented
174C4×#67C2×D311yescharacteristic
175#924—31no—
176C22×C3⋊C8—31no—
177C22×C3⋊C8—31no—
178C22×C3⋊C8—31no—
179C22×C3⋊C8—61no—
180C2×D24—31no—
181C2×#204—31no—
182C2×D3×C8—31no—
183#897—31no—
184#895C2×D311yescharacteristic
185#894—61no—
186#893—31no—
187#893C2×D311yescharacteristic, complemented
188D3×C4⋊C4C2×D311yescharacteristic
189#890C2×D311yescharacteristic, complemented
190#884—21no—
191#884—61no—
192#883—21no—
193#883—61no—
194D3×C22⋊C4—61no—
195D3×C22⋊C4—61no—
196#876—21no—
197#875—31no—
198C4×D12—21no—
199C4×D12—31no—
200C3×#107—31no—
201C3×#106—31no—
202C3×#102—31no—
203C3×#102—31no—
204C3×C22⋊C8—31no—
205#832—31no—
206#832—31no—
207#830—31no—
208#830C2×D311yescharacteristic, complemented
209#821—31no—
210(C2×D3)⋊C8—31no—
211#816—31no—
212Dic3⋊C8—31no—
213C8×Dic3—31no—
214#810—31no—
215#810—31no—
216#810—31no—
217#810—31no—
218#810—31no—
219#810—61no—
220#810—61no—
221#809—31no—
222#809—31no—
223#809—31no—
224#809—31no—
225#809—31no—
226#809—31no—
227#809—31no—
228#809—61no—
229#809—61no—
230#809C2×D311yescharacteristic
231#809C2×D311yescharacteristic
232#808C2×D311yescharacteristic, complemented
233#807—31no—
234#807—31no—
235#807C2×D311yescharacteristic, complemented
236C4⋊(C3⋊C8)—31no—
237C4×C3⋊C8—31no—
238C23×C32C2×D411yescharacteristic
239C22×C3⋊D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3C2×D411yescharacteristic
243C2×D32—42no—
244C2×D32—42no—
245C2×D32—81no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2411yescharacteristic
252#638—42no—
253C2×C3⋊Dic3—21no—
254C4⋊(C3⋊D3)—21no—
255C4⋊(C3⋊D3)#4112yes—
256C4×C3⋊D3—42no—
257#634—21no—
258#634—21no—
259C3×#67—22no—
260C3×#67—81no—
261C3×#67—81no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C3×D12—21no—
268C3×D12—21no—
269C3×D12—21no—
270C3×D12—21no—
271C3×D12—42no—
272C3×C4×D3—21no—
273C3×C4×D3—21no—
274C3×C4×D3—81no—
275C3×C4×D3—81no—
276#626—42no—
277#624—81no—
278C3⋊(C3⋊C8)—21no—
279C3⋊(C3⋊C8)—21no—
280C3×C3⋊C8—21no—
281C3×C3⋊C8—21no—
282#553—31no—
283#546—91no—
284#488—91no—
285#484—91no—
286#482—31no—
287#478—91no—
288#466—91no—
289#465—91no—
290#463—91no—
291#449—91no—
292#447—91no—
293C4×D8—91no—
294C8×D4—91no—
295#416—91no—
296C2×#102—91no—
297C23×D3—61no—
298C23×D3—61no—
299C2×C3×D4—31no—
300C2×C3×D4—31no—
301C2×C3×D4—31no—
302C2×C3×D4—61no—
303C2×C3×D4—61no—
304C2×C3×D4—61no—
305C22×C3×C4—21no—
306C22×C3×C4—31no—
307C22×C3×C4—61no—
308C22×C3×C4—61no—
309C22×C3×C4C22×D311yescharacteristic
310C22×C3×C4C22×D311yescharacteristic
311C2×#67—21no—
312C2×#67—21no—
313C2×#67—61no—
314C2×#67—61no—
315C2×#67—61no—
316C2×#67—121no—
317C2×#67#6711yescharacteristic
318D3×D4—62no—
319D3×D4—121no—
320#235—62no—
321#235—62no—
322#235—64no—
323#235—121no—
324#235—121no—
325#235—122no—
326C2×D12—21no—
327C2×D12—31no—
328C2×D12—31no—
329C2×D12—61no—
330C2×D12—62no—
331C2×D12—61no—
332C2×D12—121no—
333C2×D12C22×D311yescharacteristic
334C2×D12C22×D311yescharacteristic
335C2×C4×D3—21no—
336C2×C4×D3—21no—
337C2×C4×D3—61no—
338C2×C4×D3—61no—
339C2×C4×D3—61no—
340C2×C4×D3—61no—
341C2×C4×D3—121no—
342C2×C4×D3C22×D311yescharacteristic
343C2×Dic6—31no—
344C2×Dic6—31no—
345C2×Dic6—61no—
346C2×C3×C8—31no—
347C2×C3×C8—31no—
348C3×C4⋊C4—21no—
349C3×C4⋊C4—21no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4—61no—
355C3×C4⋊C4—61no—
356C3×C4⋊C4C22×D311yescharacteristic
357C3×C4⋊C4C22×D311yescharacteristic
358C3×C4⋊C4C22×D311yescharacteristic
359C3×C4⋊C4C22×D311yescharacteristic
360C3×C22⋊C4—21no—
361C3×C22⋊C4—21no—
362C3×C22⋊C4—31no—
363C3×C22⋊C4—31no—
364C3×C22⋊C4—41no—
365C3×C22⋊C4—61no—
366C3×C22⋊C4—61no—
367C3×C22⋊C4—61no—
368C3×C22⋊C4—61no—
369C3×C42—21no—
370C3×C42—21no—
371C3×C42—31no—
372C3×C42—41no—
373#217—61no—
374#217—61no—
375#217—61no—
376#217#6711yescharacteristic
377#214—121no—
378#213—62no—
379#213—121no—
380#213—121no—
381(C2×D3)⋊C4—21no—
382(C2×D3)⋊C4—21no—
383(C2×D3)⋊C4—21no—
384(C2×D3)⋊C4—21no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—61no—
387(C2×D3)⋊C4—61no—
388(C2×D3)⋊C4—61no—
389(C2×D3)⋊C4—61no—
390(C2×D3)⋊C4#6711yescharacteristic
391C4⋊Dic3—21no—
392C4⋊Dic3—61no—
393C4⋊Dic3C22×D311yescharacteristic
394C4⋊Dic3C22×D311yescharacteristic
395Dic3⋊C4—21no—
396Dic3⋊C4—21no—
397Dic3⋊C4—61no—
398Dic3⋊C4#6711yescharacteristic
399C4×Dic3C22×D311yescharacteristic
400C2×C3⋊C8—31no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—61no—
405C2×C3⋊C8—61no—
406C2×C3⋊C8—121no—
407C2×C3⋊C8—121no—
408C2×C3⋊C8—121no—
409C2×C3⋊C8—122no—
410C2×C3⋊C8C22×D311yescharacteristic
411C2×C3⋊C8C22×D311yescharacteristic
412D24—62no—
413#204—121no—
414D3×C8—121no—
415C22×C32—21no—
416C22×C32—21no—
417C22×C32—21no—
418C22×C32C22×D411yescharacteristic
419C2×C3⋊D3—22no—
420C2×C3⋊D3—41no—
421C2×C3⋊D3—41no—
422C2×C3×D3—21no—
423C2×C3×D3—21no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426C2×C3×D3—41no—
427C2×C3×D3—41no—
428C2×C3×D3—41no—
429C2×C3×D3—41no—
430C2×C3×D3#13512yes—
431D32—84no—
432C32×C4—21no—
433C32×C4—41no—
434C32×C4—41no—
435C32×C4C2×#4111yescharacteristic
436C32×C4H(5,𝔽2)11yescharacteristic
437C3⋊Dic3—41no—
438C3×Dic3—21no—
439C3×Dic3—21no—
440C3×Dic3—21no—
441C3×Dic3—41no—
442C3×Dic3—41no—
443C2×#41—91no—
444C22×D4—91no—
445C2×SD16—91no—
446C2×D8—91no—
447C2×D8—91no—
448C22×C8—91no—
449C22×C8—91no—
450#126—61no—
451#125—31no—
452#124—91no—
453#123—61no—
454#123—181no—
455C22⋊Q8—91no—
456#121—31no—
457#121—31no—
458#121—31no—
459#121—61no—
460#121—181no—
461#120—181no—
462C4×D4—31no—
463C4×D4—31no—
464C4×D4—61no—
465C4×D4—91no—
466#117D3211yescharacteristic, complemented
467C2×C4⋊C4—31no—
468C2×C22⋊C4—181no—
469#107—31no—
470#107—91no—
471#106—31no—
472C4⋊C8—91no—
473#103—91no—
474#103—91no—
475#103—91no—
476#102—31no—
477#102—31no—
478#102—91no—
479#102—91no—
480#102—91no—
481#102—91no—
482#102—91no—
483C22⋊C8—31no—
484C22⋊C8—91no—
485C4×C8—91no—
486C23×C3—21no—
487C23×C3—31no—
488C23×C3—61no—
489C23×C3—61no—
490C23×C3D3×D411yescharacteristic
491C23×C3C2×#6711yescharacteristic
492C22×D3—21no—
493C22×D3—21no—
494C22×D3—61no—
495C22×D3—61no—
496C22×D3—121no—
497C22×D3—122no—
498C22×D3—122no—
499C22×D3—122no—
500C22×D3—122no—
501C22×D3—241no—
502C22×D3—241no—
503C22×D3C2×#6711yescharacteristic
504C3×D4—62no—
505C3×D4—61no—
506C3×D4—61no—
507C3×D4—61no—
508C3×D4—61no—
509C3×D4—122no—
510C3×D4—241no—
511C3×D4—241no—
512C2×C3×C4—22no—
513C2×C3×C4—22no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—31no—
525C2×C3×C4—31no—
526C2×C3×C4—31no—
527C2×C3×C4—41no—
528C2×C3×C4—41no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—241no—
534C2×C3×C4—241no—
535C2×C3×C4D3×D411yescharacteristic
536C2×C3×C4C2×#6711yescharacteristic
537C2×C3×C4C23×D311yescharacteristic
538C2×C3×C4C23×D311yescharacteristic
539#67—22no—
540#67—81no—
541#67—81no—
542#67—122no—
543#67—122no—
544#67—122no—
545#67—124no—
546C2×Dic3—21no—
547C2×Dic3—21no—
548C2×Dic3—61no—
549C2×Dic3—61no—
550C2×Dic3—121no—
551C2×Dic3C2×#6711yescharacteristic
552C2×Dic3C2×#6711yescharacteristic
553C2×Dic3C2×#6711yescharacteristic
554D12—21no—
555D12—21no—
556D12—21no—
557D12—21no—
558D12—32no—
559D12—32no—
560D12—42no—
561D12—62no—
562D12—61no—
563D12—61no—
564D12—121no—
565D12—122no—
566C4×D3—21no—
567C4×D3—21no—
568C4×D3—81no—
569C4×D3—81no—
570C4×D3—122no—
571C4×D3—122no—
572C4×D3—124no—
573C4×D3—241no—
574C4×D3—241no—
575Dic6—62no—
576Dic6—61no—
577Dic6—61no—
578Dic6—61no—
579Dic6—61no—
580Dic6—121no—
581C3×C8—61no—
582C3×C8—61no—
583C3⋊C8—21no—
584C3⋊C8—21no—
585C3⋊C8—61no—
586C3⋊C8—61no—
587C3⋊C8—61no—
588C3⋊C8—61no—
589C3⋊C8—121no—
590C3⋊C8—121no—
591C2×C32—41no—
592C2×C32#54611yescharacteristic
593C2×C32C2×#13511yescharacteristic
594C2×C32#57611yescharacteristic
595C3⋊D3—42no—
596C3×D3—22no—
597C3×D3—81no—
598C3×D3—81no—
599C24—181no—
600#41—182no—
601#41—361no—
602C2×Q8—91no—
603C2×D4—31no—
604C2×D4—31no—
605C2×D4—31no—
606C2×D4—61no—
607C2×D4—61no—
608C2×D4—61no—
609C2×D4—91no—
610C2×D4—181no—
611C2×D4—182no—
612C2×D4—181no—
613C2×D4—361no—
614C22×C4—31no—
615C22×C4—61no—
616C22×C4—61no—
617C22×C4—181no—
618C22×C4—181no—
619C22×C4C2×D3211yescharacteristic
620SD16—361no—
621D8—182no—
622D8—361no—
623C2×C8—31no—
624C2×C8—31no—
625C2×C8—91no—
626C2×C8—91no—
627C2×C8—361no—
628C2×C8—361no—
629C4⋊C4—31no—
630C4⋊C4—31no—
631C4⋊C4—31no—
632C4⋊C4—61no—
633C4⋊C4—61no—
634C4⋊C4—61no—
635C4⋊C4—181no—
636C4⋊C4C2×D3211yescharacteristic
637C4⋊C4C2×D3211yescharacteristic
638C22⋊C4—21no—
639C22⋊C4—31no—
640C22⋊C4—31no—
641C22⋊C4—61no—
642C22⋊C4—61no—
643C22⋊C4—61no—
644C22⋊C4—61no—
645C22⋊C4—181no—
646C22⋊C4—181no—
647C22⋊C4—181no—
648C22⋊C4—181no—
649C42—21no—
650C42—31no—
651C22×C3—22no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—21no—
655C22×C3—21no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—32no—
660C22×C3—41no—
661C22×C3—41no—
662C22×C3—61no—
663C22×C3—61no—
664C22×C3—121no—
665C22×C3—121no—
666C22×C3—121no—
667C22×C3—121no—
668C22×C3—121no—
669C22×C3—121no—
670C22×C3C2×D3×D411yescharacteristic
671C22×C3C22×#6711yescharacteristic
672C2×D3—21no—
673C2×D3—21no—
674C2×D3—41no—
675C2×D3—41no—
676C2×D3—41no—
677C2×D3—41no—
678C2×D3—41no—
679C2×D3—41no—
680C2×D3—62no—
681C2×D3—62no—
682C2×D3—122no—
683C2×D3—121no—
684C2×D3—121no—
685C2×D3—121no—
686C2×D3—121no—
687C2×D3—241no—
688C2×D3—241no—
689C2×D3—244no—
690C2×D3—244no—
691C2×D3#95012yes—
692C3×C4—22no—
693C3×C4—21no—
694C3×C4—21no—
695C3×C4—21no—
696C3×C4—21no—
697C3×C4—41no—
698C3×C4—41no—
699C3×C4—41no—
700C3×C4—41no—
701C3×C4—61no—
702C3×C4—61no—
703C3×C4—61no—
704C3×C4—81no—
705C3×C4—81no—
706C3×C4—121no—
707C3×C4—121no—
708C3×C4D3×#4111yescharacteristic
709C3×C4D3×#4111yescharacteristic
710C3×C4#100911yescharacteristic
711C3×C4#100911yescharacteristic
712Dic3—21no—
713Dic3—21no—
714Dic3—21no—
715Dic3—41no—
716Dic3—41no—
717Dic3—122no—
718Dic3—121no—
719Dic3—121no—
720C32#329711yescharacteristic, complemented, Sylow
721C23—31no—
722C23—61no—
723C23—61no—
724C23—181no—
725C23—362no—
726C23—362no—
727C23—721no—
728C23D3×#6711yescharacteristic
729Q8—181no—
730Q8—181no—
731D4—62no—
732D4—61no—
733D4—61no—
734D4—61no—
735D4—61no—
736D4—92no—
737D4—122no—
738D4—181no—
739D4—241no—
740D4—241no—
741D4—362no—
742D4—362no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—31no—
748C2×C4—31no—
749C2×C4—31no—
750C2×C4—61no—
751C2×C4—61no—
752C2×C4—61no—
753C2×C4—61no—
754C2×C4—181no—
755C2×C4—241no—
756C2×C4—241no—
757C2×C4—362no—
758C2×C4—721no—
759C2×C4D3×#6711yescharacteristic
760C2×C4C22×D3211yescharacteristic
761C8—61no—
762C8—61no—
763C8—181no—
764C8—181no—
765C2×C3—21no—
766C2×C3—21no—
767C2×C3—21no—
768C2×C3—42no—
769C2×C3—41no—
770C2×C3—41no—
771C2×C3—62no—
772C2×C3—241no—
773C2×C3—241no—
774C2×C3#565411yescharacteristic
775C2×C3D3×#13511yescharacteristic
776C2×C3#577411yescharacteristic
777C2×C3C2×#95011yescharacteristic
778C2×C3#582911yescharacteristic
779C2×C3#583511yescharacteristic
780D3—22no—
781D3—81no—
782D3—81no—
783D3—122no—
784D3—122no—
785D3—242no—
786C22—21no—
787C22—21no—
788C22—21no—
789C22—32no—
790C22—61no—
791C22—61no—
792C22—121no—
793C22—121no—
794C22—121no—
795C22—121no—
796C22—121no—
797C22—121no—
798C22—182no—
799C22—361no—
800C22—361no—
801C22—724no—
802C22C2×D3×#6711yescharacteristic
803C4—21no—
804C4—41no—
805C4—41no—
806C4—61no—
807C4—61no—
808C4—61no—
809C4—121no—
810C4—121no—
811C4—361no—
812C4#6430611yescharacteristic
813C4#6430811yescharacteristic
814C3—21no—
815C3#8138211yescharacteristic, complemented
816C3#8361411yescharacteristic, complemented
817C2—41no—
818C2—62no—
819C2—241no—
820C2—241no—
821C2—362no—
822C2#1059506811yescharacteristic
823C2D3×#95011yescharacteristic
824C2#1059545411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
hypercenter#117D32
hypocenterC32#3297
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. C3×#5530C2semidirect
2. #10595078C2semidirect
3. #10592701C2semidirect
4. C3×#5003C2semidirect
5. #10591182C2semidirect
6. #10591166C2semidirect
7. #67⋊(C3⋊C8)C2semidirect
8. #10590595C2semidirect
9. D3×#809C2semidirect
10. #10590578C2semidirect
11. #10590533C2semidirect
12. #10590530C2semidirect
13. #10590470C2semidirect
14. #10590456C2semidirect
15. #10590427C2semidirect
20. C32×#117C22semidirect
21. C22×C3⋊(C3⋊C8)C22semidirect
23. C3×#930C22semidirect
26. C3×#893C22semidirect
28. C3×#890C22semidirect
40. C2×#3716C22semidirect
44. #63637C22semidirect
45. #63637C22semidirect
48. C3×#830C22semidirect
51. C3×#808C22semidirect
52. C3×#807C22semidirect
53. #63576C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63567C22semidirect
58. #63562C22semidirect
60. Dic3×C3⋊C8C22semidirect
64. #5530D3semidirect
76. #5003D3semidirect
161. C3×#117C2×D3semidirect
162. C3×#117C2×D3semidirect
173. #930C2×D3semidirect
187. #893C2×D3semidirect
189. #890C2×D3semidirect
208. #830C2×D3semidirect
232. #808C2×D3semidirect
235. #807C2×D3semidirect
466. #117D32semidirect
720. C32#3297semidirect
815. C3#81382semidirect
816. C3#83614semidirect

Maximal subgroups

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

subgroupindex
C3×#55302
#105950782
#105927012
C3×#50032
#105911822
#105911662
#67⋊(C3⋊C8)2
#105905952
D3×#8092
#105905782
#105905332
#105905302
#105904702
#105904562
#105904272
#836143
#813823