Finite Group Databasebeta

← #11887464

Subgroups — #11887464

Order 1152.

902 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5676C211yesmaximal, characteristic, complemented
2#10593925C211yesmaximal, characteristic, complemented
3#10592756C211yesmaximal, characteristic, complemented
4C3×#5056C211yesmaximal, characteristic, complemented
5#10591588C211yesmaximal, characteristic, complemented
6#10591585C211yesmaximal, characteristic, complemented
7#10591556C211yesmaximal, characteristic, complemented
8#10591551C211yesmaximal, characteristic, complemented
9#10591449C211yesmaximal, characteristic, complemented
10#10591448C211yesmaximal, characteristic, complemented
11#10591423C211yesmaximal, characteristic, complemented
12D3×#832C211yesmaximal, characteristic, complemented
13C4×#3714C211yesmaximal, characteristic, complemented
14C3⋊C8×D12C211yesmaximal, characteristic, complemented
15#10590270C211yesmaximal, characteristic, complemented
16#83495—31nomaximal
17#81653—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C32×#124C2211yescharacteristic
21C2×#3755C2211yescharacteristic, complemented
22C2×#3753C2211yescharacteristic
23C4×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
24C3×#946C2211yescharacteristic
25C3×#938C2211yescharacteristic
26C3×#884—21no—
27C3×#883—21no—
28C3×#882—21no—
29C3×D3×C22⋊C4—21no—
30C3×C4×D12C2211yescharacteristic
31C3×C4×D12C2211yescharacteristic
32C3×#870C2211yescharacteristic, complemented
33#63909C2211yescharacteristic
34#63909C2211yescharacteristic, complemented
35D3×C4⋊Dic3C2211yescharacteristic
36#63886—21no—
37#63881—21no—
38#63853—21no—
39#63848—21no—
40#63841C2211yescharacteristic, complemented
41C2×#3714C2211yescharacteristic
42C2×D3×C3⋊C8C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44#63662C2211yescharacteristic, complemented
45#63659C2211yescharacteristic
46C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
47C3×#835C2211yescharacteristic, complemented
48C3×#835C2211yescharacteristic, complemented
49C3×#832C2211yescharacteristic
50C3×#832C2211yescharacteristic
51C3×C4×C3⋊C8C2211yescharacteristic, complemented
52#63576C2211yescharacteristic, complemented
53#63575C2211yescharacteristic, complemented
54#63574C2211yescharacteristic, complemented
55#63564C2211yescharacteristic, complemented
56#63563C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
61C3×#546—31no—
62#5695—31no—
63#5676D311yescharacteristic, complemented
64#5565—31no—
65C3×#488—31no—
66#5238—31no—
67#5233—31no—
68#5217—31no—
69C2×#832—31no—
70#5066—31no—
71#5057—31no—
72#5057—31no—
73#5057—61no—
74#5056D311yescharacteristic, complemented
75#5048—31no—
76#5044—31no—
77#5038—31no—
78#5035—31no—
79C4×#213—31no—
80D4×C3⋊C8—31no—
81#5009—31no—
82#4811—31no—
83#4810—31no—
84#4807—31no—
85#4804—31no—
86#4784—31no—
87#4775—31no—
88#4773—31no—
89D3×#102—31no—
90C4×D24—31no—
91C8×D12—31no—
92C23×C3×D3—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C32×D4C2311yescharacteristic
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C4×C3⋊D3—21no—
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C3×#239—22no—
100C3×#239—41no—
101C3×D3×D4—22no—
102C3×D3×D4—41no—
103C2×C3×D12—21no—
104C2×C3×D12D411yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×C4×D3C2311yescharacteristic
110C2×#626—21no—
111C2×#626—21no—
112C2×D3×Dic3—21no—
113C32×C22⋊C4—21no—
114C32×C22⋊C4—21no—
115C32×C42C2311yescharacteristic
116#3755—41no—
117#3753—41no—
118#3752—21no—
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C3×#217—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4D411yescharacteristic
126C3×(C2×D3)⋊C4D411yescharacteristic
127C3×C4⋊Dic3D411yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4—21no—
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136Dic3⋊Dic3—21no—
137#3722—21no—
138#3722—21no—
139(C2×D3)⋊Dic3—21no—
140Dic32—21no—
141#3714—22no—
142D3×C3⋊C8—41no—
143D3×C3⋊C8—41no—
144#3297—91noSylow
145C2×C3×#41—31no—
146C22×C3×D4—31no—
147C2×#239C2×D311yescharacteristic
148C2×D3×D4C2×D311yescharacteristic
149C3×#125—31no—
150C3×#124—21no—
151C3×#124C2×D311yescharacteristic
152C3×#124C2×D311yescharacteristic
153C3×#123—61no—
154C3×C22⋊Q8—31no—
155C3×#121—31no—
156C3×#121—61no—
157C3×#120—61no—
158C3×C4×D4—31no—
159C3×C4×D4—31no—
160C2×C3×C22⋊C4—61no—
161#946C2×D311yescharacteristic
162C2×#215—31no—
163C2×#215—31no—
164C2×#215—61no—
165#939—61no—
166#938C2×D311yescharacteristic
167C2×#213—31no—
168C2×#213—31no—
169C2×#213—31no—
170C2×#213—61no—
171#930—31no—
172#930—31no—
173#926—31no—
174C2×C4⋊Dic3—31no—
175C22×C3⋊C8—31no—
176C22×C3⋊C8—31no—
177C2×D24—31no—
178C2×D3×C8—31no—
179C2×D3×C8—31no—
180#898—61no—
181#898—61no—
182#895—31no—
183#895—31no—
184#895—61no—
185#894—61no—
186#893—61no—
187#892—31no—
188D3×C4⋊C4—31no—
189#884—21no—
190#883—21no—
191#883—61no—
192#882—21no—
193#67⋊C4—61no—
194D3×C22⋊C4—21no—
195C4×D12—31no—
196C4×D12—31no—
197C4×D12—61no—
198C4×D12C2×D311yescharacteristic
199C4×D12C2×D311yescharacteristic
200#870C2×D311yescharacteristic, complemented
201C3×#103—31no—
202C3×#103—31no—
203C3×#102—31no—
204C3×#102—31no—
205C3×C4×C8—31no—
206#835—31no—
207#835—31no—
208#835—61no—
209#835C2×D311yescharacteristic, complemented
210#835C2×D311yescharacteristic, complemented
211#832—31no—
212#832—31no—
213#832—31no—
214#832—31no—
215#832—31no—
216#832—61no—
217#832C2×D311yescharacteristic
218#832C2×D311yescharacteristic
219#830—31no—
220#830—31no—
221#821—31no—
222#821—31no—
223(C2×D3)⋊C8—31no—
224(C2×D3)⋊C8—31no—
225#818—31no—
226#809—31no—
227#809—31no—
228#809—31no—
229#808—31no—
230#808—31no—
231#807—31no—
232#807—31no—
233#807—31no—
234C4⋊(C3⋊C8)—31no—
235C4⋊(C3⋊C8)—31no—
236C4⋊(C3⋊C8)—61no—
237C4×C3⋊C8C2×D311yescharacteristic, complemented
238C23×C32—21no—
239C22×C3⋊D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3—42no—
242C22×C3×D3—42no—
243C22×C3×D3—81no—
244C22×C3×D3C2×D411yescharacteristic
245C22×C3×D3C2×D411yescharacteristic
246C32×Q8—21no—
247C32×Q8—21no—
248C32×D4—21no—
249C32×D4—21no—
250C2×C32×C4—21no—
251C2×C32×C4C2×D411yescharacteristic
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2411yescharacteristic
254C2×C3⋊Dic3—21no—
255C4⋊(C3⋊D3)—21no—
256C4⋊(C3⋊D3)—21no—
257C4×C3⋊D3—81no—
258C3×#67—42no—
259C3×#67—81no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×D12—22no—
266C3×D12—21no—
267C3×D12—42no—
268C3×D12#4112yes—
269C3×C4×D3—21no—
270C3×C4×D3—21no—
271C3×C4×D3—21no—
272C3×C4×D3—21no—
273C3×C4×D3—42no—
274C3×C4×D3—81no—
275#626—42no—
276#626—81no—
277D3×Dic3—81no—
278C3⋊(C3⋊C8)—21no—
279C3⋊(C3⋊C8)—21no—
280C3×C3⋊C8—21no—
281C3×C3⋊C8—21no—
282#553—91no—
283#546—31no—
284#488—31no—
285#484—91no—
286#482—91no—
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—
297C24×C3—61no—
298C23×D3—21no—
299C3×#41—62no—
300C3×#41—121no—
301C2×C3×Q8—21no—
302C2×C3×Q8C22×D311yescharacteristic
303C2×C3×Q8C22×D311yescharacteristic
304C2×C3×D4—21no—
305C2×C3×D4—31no—
306C2×C3×D4—31no—
307C2×C3×D4—61no—
308C2×C3×D4—61no—
309C2×C3×D4—62no—
310C2×C3×D4—61no—
311C2×C3×D4—121no—
312C2×C3×D4C22×D311yescharacteristic
313C2×C3×D4C22×D311yescharacteristic
314C22×C3×C4—31no—
315C22×C3×C4—31no—
316C22×C3×C4—61no—
317C22×C3×C4—61no—
318C2×#67—21no—
319C2×#67—21no—
320C2×#67—61no—
321C2×#67—61no—
322C22×Dic3—61no—
323#239—22no—
324#239—41no—
325D3×D4—22no—
326D3×D4—41no—
327C2×D12—21no—
328C2×D12—31no—
329C2×D12—31no—
330C2×D12—61no—
331C2×D12—61no—
332C2×D12—61no—
333C2×D12#6711yescharacteristic
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—121no—
341C2×C4×D3C22×D311yescharacteristic
342C2×C4×D3C22×D311yescharacteristic
343C2×C3×C8—31no—
344C2×C3×C8—31no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—61no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4—61no—
352C3×C22⋊C4—21no—
353C3×C22⋊C4—21no—
354C3×C22⋊C4—21no—
355C3×C22⋊C4—21no—
356C3×C22⋊C4—31no—
357C3×C22⋊C4—31no—
358C3×C22⋊C4—41no—
359C3×C22⋊C4—41no—
360C3×C22⋊C4—61no—
361C3×C22⋊C4—61no—
362C3×C22⋊C4—61no—
363C3×C42—21no—
364C3×C42C22×D311yescharacteristic
365C3×C42C22×D311yescharacteristic
366#217—21no—
367#217—61no—
368#215—121no—
369#215—121no—
370#215—122no—
371#213—62no—
372#213—121no—
373#213—121no—
374#213—122no—
375(C2×D3)⋊C4—21no—
376(C2×D3)⋊C4—21no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—121no—
385(C2×D3)⋊C4#6711yescharacteristic
386(C2×D3)⋊C4#6711yescharacteristic
387C4⋊Dic3—31no—
388C4⋊Dic3—31no—
389C4⋊Dic3—61no—
390C4⋊Dic3—61no—
391C4⋊Dic3#6711yescharacteristic
392C4⋊Dic3C22×D311yescharacteristic
393C4⋊Dic3C22×D311yescharacteristic
394C4⋊Dic3C22×D311yescharacteristic
395Dic3⋊C4—21no—
396Dic3⋊C4—21no—
397Dic3⋊C4—21no—
398Dic3⋊C4—61no—
399C4×Dic3—61no—
400C4×Dic3—61no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—31no—
405C2×C3⋊C8—61no—
406C2×C3⋊C8—61no—
407C2×C3⋊C8—121no—
408C2×C3⋊C8—121no—
409C2×C3⋊C8C22×D311yescharacteristic
410C2×C3⋊C8C22×D311yescharacteristic
411D24—62no—
412D3×C8—121no—
413D3×C8—121no—
414C22×C32—41no—
415C22×C32—41no—
416C22×C32—41no—
417C22×C32C22×D411yescharacteristic
418C2×C3⋊D3—41no—
419C2×C3⋊D3—41no—
420C2×C3⋊D3—41no—
421C2×C3×D3—21no—
422C2×C3×D3—21no—
423C2×C3×D3—21no—
424C2×C3×D3—22no—
425C2×C3×D3—21no—
426C2×C3×D3—21no—
427C2×C3×D3—41no—
428C2×C3×D3—41no—
429C2×C3×D3—84no—
430C2×C3×D3#13512yes—
431C32×C4—21no—
432C32×C4—21no—
433C32×C4—41no—
434C32×C4C2×#4111yescharacteristic
435C32×C4H(5,𝔽2)11yescharacteristic
436C3⋊Dic3—41no—
437C3×Dic3—21no—
438C3×Dic3—21no—
439C3×Dic3—41no—
440C3×Dic3—41no—
441C3×Dic3—41no—
442C2×#41—31no—
443C22×D4—31no—
444C2×SD16—91no—
445C2×D8—91no—
446C2×D8—91no—
447C22×C8—91no—
448C22×C8—91no—
449#126—181no—
450#125—31no—
451#124D3211yescharacteristic
452#123—61no—
453#123—181no—
454C22⋊Q8—31no—
455#121—31no—
456#121—61no—
457#121—91no—
458#121—91no—
459#121—181no—
460#120—61no—
461C4×D4—31no—
462C4×D4—31no—
463C4×D4—91no—
464C4×D4—181no—
465#117—91no—
466C2×C4⋊C4—91no—
467C2×C22⋊C4—61no—
468#107—91no—
469#107—91no—
470#106—91no—
471C4⋊C8—91no—
472#103—31no—
473#103—31no—
474#103—91no—
475#102—31no—
476#102—31no—
477#102—91no—
478#102—91no—
479#102—91no—
480#102—91no—
481#102—91no—
482C22⋊C8—91no—
483C22⋊C8—91no—
484C4×C8—31no—
485C23×C3—21no—
486C23×C3—21no—
487C23×C3—31no—
488C23×C3—31no—
489C23×C3—41no—
490C23×C3—61no—
491C23×C3—122no—
492C23×C3—122no—
493C23×C3—241no—
494C22×D3—21no—
495C22×D3—42no—
496C22×D3—42no—
497C22×D3—61no—
498C22×D3—61no—
499C22×D3—81no—
500C22×D3—121no—
501C22×D3C2×#6711yescharacteristic
502C22×D3C2×#6711yescharacteristic
503C3×Q8—21no—
504C3×Q8—21no—
505C3×Q8—21no—
506C3×Q8—21no—
507C3×Q8—41no—
508C3×Q8—41no—
509C3×D4—21no—
510C3×D4—21no—
511C3×D4—21no—
512C3×D4—21no—
513C3×D4—32no—
514C3×D4—41no—
515C3×D4—41no—
516C3×D4—62no—
517C3×D4—61no—
518C3×D4—122no—
519C3×D4—122no—
520C3×D4—241no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—31no—
527C2×C3×C4—31no—
528C2×C3×C4—41no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—122no—
537C2×C3×C4—241no—
538C2×C3×C4D3×D411yescharacteristic
539C2×C3×C4D3×D411yescharacteristic
540C2×C3×C4C2×#6711yescharacteristic
541C2×C3×C4C2×#6711yescharacteristic
542C2×C3×C4C23×D311yescharacteristic
543C2×C3×C4C23×D311yescharacteristic
544#67—42no—
545#67—81no—
546#67—122no—
547#67—241no—
548C2×Dic3—21no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—61no—
552C2×Dic3—61no—
553C2×Dic3—121no—
554C2×Dic3—241no—
555C2×Dic3C2×#6711yescharacteristic
556C2×Dic3C2×#6711yescharacteristic
557D12—22no—
558D12—21no—
559D12—42no—
560D12—62no—
561D12—61no—
562D12—61no—
563D12—61no—
564D12—61no—
565D12—121no—
566D12—122no—
567D12—241no—
568D12#23712yes—
569C4×D3—21no—
570C4×D3—21no—
571C4×D3—21no—
572C4×D3—21no—
573C4×D3—42no—
574C4×D3—81no—
575C4×D3—241no—
576C4×D3—241no—
577C4×D3—241no—
578C4×D3—242no—
579C3×C8—61no—
580C3×C8—61no—
581C3⋊C8—21no—
582C3⋊C8—21no—
583C3⋊C8—61no—
584C3⋊C8—61no—
585C3⋊C8—61no—
586C3⋊C8—61no—
587C3⋊C8—121no—
588C3⋊C8—121no—
589C2×C32—81no—
590C2×C32#54611yescharacteristic
591C2×C32C2×#13511yescharacteristic
592C2×C32#57611yescharacteristic
593C3⋊D3—81no—
594C3×D3—22no—
595C3×D3—41no—
596C3×D3—42no—
597C24—61no—
598#41—62no—
599#41—121no—
600C2×Q8C2×D3211yescharacteristic
601C2×D4—31no—
602C2×D4—31no—
603C2×D4—61no—
604C2×D4—61no—
605C2×D4—62no—
606C2×D4—61no—
607C2×D4—91no—
608C2×D4—121no—
609C2×D4—181no—
610C2×D4—181no—
611C2×D4C2×D3211yescharacteristic
612C22×C4—31no—
613C22×C4—31no—
614C22×C4—61no—
615C22×C4—61no—
616C22×C4—181no—
617C22×C4—181no—
618SD16—361no—
619D8—182no—
620D8—361no—
621C2×C8—31no—
622C2×C8—31no—
623C2×C8—91no—
624C2×C8—91no—
625C2×C8—361no—
626C2×C8—361no—
627C4⋊C4—31no—
628C4⋊C4—31no—
629C4⋊C4—31no—
630C4⋊C4—31no—
631C4⋊C4—61no—
632C4⋊C4—61no—
633C4⋊C4—61no—
634C4⋊C4—91no—
635C4⋊C4—181no—
636C22⋊C4—21no—
637C22⋊C4—21no—
638C22⋊C4—31no—
639C22⋊C4—31no—
640C22⋊C4—61no—
641C22⋊C4—61no—
642C22⋊C4—61no—
643C22⋊C4—181no—
644C22⋊C4—181no—
645C22⋊C4—181no—
646C22⋊C4—181no—
647C42—181no—
648C42C2×D3211yescharacteristic
649C22×C3—21no—
650C22×C3—32no—
651C22×C3—41no—
652C22×C3—41no—
653C22×C3—41no—
654C22×C3—41no—
655C22×C3—41no—
656C22×C3—41no—
657C22×C3—61no—
658C22×C3—61no—
659C22×C3—61no—
660C22×C3—62no—
661C22×C3—61no—
662C22×C3—61no—
663C22×C3—81no—
664C22×C3—81no—
665C22×C3—81no—
666C22×C3—121no—
667C22×C3—121no—
668C22×C3—244no—
669C22×C3C2×D3×D411yescharacteristic
670C22×C3C22×#6711yescharacteristic
671C2×D3—21no—
672C2×D3—21no—
673C2×D3—21no—
674C2×D3—22no—
675C2×D3—21no—
676C2×D3—21no—
677C2×D3—41no—
678C2×D3—41no—
679C2×D3—84no—
680C2×D3—122no—
681C2×D3—121no—
682C2×D3—121no—
683C2×D3—121no—
684C2×D3—121no—
685C2×D3—121no—
686C2×D3—121no—
687C2×D3—241no—
688C2×D3—241no—
689C2×D3#95012yes—
690C3×C4—21no—
691C3×C4—21no—
692C3×C4—21no—
693C3×C4—21no—
694C3×C4—21no—
695C3×C4—21no—
696C3×C4—41no—
697C3×C4—41no—
698C3×C4—41no—
699C3×C4—41no—
700C3×C4—61no—
701C3×C4—61no—
702C3×C4—81no—
703C3×C4—121no—
704C3×C4—121no—
705C3×C4—121no—
706C3×C4C2×#23711yescharacteristic
707C3×C4#100411yescharacteristic
708C3×C4D3×#4111yescharacteristic
709C3×C4#100911yescharacteristic
710Dic3—21no—
711Dic3—21no—
712Dic3—41no—
713Dic3—41no—
714Dic3—41no—
715Dic3—121no—
716Dic3—121no—
717Dic3—241no—
718C32#329711yescharacteristic, complemented, Sylow
719C23—21no—
720C23—31no—
721C23—31no—
722C23—61no—
723C23—122no—
724C23—122no—
725C23—181no—
726C23—241no—
727Q8—21no—
728Q8—21no—
729D4—21no—
730D4—21no—
731D4—32no—
732D4—62no—
733D4—61no—
734D4—122no—
735D4—122no—
736D4—181no—
737D4—181no—
738D4—241no—
739D4—362no—
740D4—721no—
741C2×C4—21no—
742C2×C4—31no—
743C2×C4—31no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—61no—
748C2×C4—61no—
749C2×C4—61no—
750C2×C4—61no—
751C2×C4—122no—
752C2×C4—181no—
753C2×C4—241no—
754C2×C4—721no—
755C2×C4—721no—
756C2×C4D3×#6711yescharacteristic
757C2×C4D3×#6711yescharacteristic
758C2×C4C22×D3211yescharacteristic
759C8—61no—
760C8—61no—
761C8—181no—
762C8—181no—
763C2×C3—21no—
764C2×C3—21no—
765C2×C3—21no—
766C2×C3—62no—
767C2×C3—81no—
768C2×C3—81no—
769C2×C3—121no—
770C2×C3—122no—
771C2×C3—161no—
772C2×C3#567611yescharacteristic
773C2×C3D3×#13511yescharacteristic
774C2×C3#576911yescharacteristic
775C2×C3#580611yescharacteristic
776C2×C3C2×#95011yescharacteristic
777C2×C3#583511yescharacteristic
778D3—22no—
779D3—41no—
780D3—42no—
781D3—242no—
782D3—241no—
783D3—241no—
784C22—32no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—61no—
789C22—61no—
790C22—61no—
791C22—61no—
792C22—61no—
793C22—62no—
794C22—121no—
795C22—121no—
796C22—244no—
797C22—361no—
798C22—361no—
799C22—361no—
800C22C2×D3×#6711yescharacteristic
801C4—21no—
802C4—21no—
803C4—41no—
804C4—61no—
805C4—61no—
806C4—121no—
807C4—121no—
808C4—121no—
809C4—361no—
810C4D3×#23711yescharacteristic
811C4#6431411yescharacteristic
812C3—21no—
813C3#8165311yescharacteristic, complemented
814C3#8349511yescharacteristic, complemented
815C2—62no—
816C2—81no—
817C2—121no—
818C2—122no—
819C2—721no—
820C2#1059522911yescharacteristic
821C2D3×#95011yescharacteristic
822C2#1059545611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#124C22
socleC22×C32C22×D4
hypercenter#124D32
hypocenterC32#3297
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. C3×#5676C2semidirect
2. #10593925C2semidirect
3. #10592756C2semidirect
4. C3×#5056C2semidirect
5. #10591588C2semidirect
6. #10591585C2semidirect
7. #10591556C2semidirect
8. #10591551C2semidirect
9. #10591449C2semidirect
10. #10591448C2semidirect
11. #10591423C2semidirect
12. D3×#832C2semidirect
13. C4×#3714C2semidirect
14. C3⋊C8×D12C2semidirect
15. #10590270C2semidirect
21. C2×#3755C22semidirect
23. C4×C4⋊(C3⋊D3)C22semidirect
32. C3×#870C22semidirect
34. #63909C22semidirect
40. #63841C22semidirect
43. C2×D3×C3⋊C8C22semidirect
44. #63662C22semidirect
46. C4⋊(C3⋊(C3⋊C8))C22semidirect
47. C3×#835C22semidirect
48. C3×#835C22semidirect
51. C3×C4×C3⋊C8C22semidirect
52. #63576C22semidirect
53. #63575C22semidirect
54. #63574C22semidirect
55. #63564C22semidirect
60. (C2×D3)⋊(C3⋊C8)C22semidirect
63. #5676D3semidirect
74. #5056D3semidirect
200. #870C2×D3semidirect
209. #835C2×D3semidirect
210. #835C2×D3semidirect
237. C4×C3⋊C8C2×D3semidirect
718. C32#3297semidirect
813. C3#81653semidirect
814. C3#83495semidirect

Maximal subgroups

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

subgroupindex
C3×#56762
#105939252
#105927562
C3×#50562
#105915882
#105915852
#105915562
#105915512
#105914492
#105914482
#105914232
D3×#8322
C4×#37142
C3⋊C8×D122
#105902702
#834953
#816533