Finite Group Databasebeta

← #11887008

Subgroups — #11887008

Order 1152.

1055 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5611C211yesmaximal, characteristic, complemented
2D12×#67C211yesmaximal, characteristic, complemented
3#10592737C211yesmaximal, characteristic, complemented
4C3×#5036C211yesmaximal, characteristic, complemented
5#10591515C211yesmaximal, characteristic, complemented
6#10591498C211yesmaximal, characteristic, complemented
7#10591481C211yesmaximal, characteristic, complemented
8Dic3×#213C211yesmaximal, characteristic, complemented
9#67⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
10#10591133C211yesmaximal, characteristic, complemented
11C2×#63562C211yesmaximal, characteristic, complemented
12D3×#809C211yesmaximal, characteristic, complemented
13#10590548C211yesmaximal, characteristic, complemented
14#10590498C211yesmaximal, characteristic, complemented
15#10590463C211yesmaximal, characteristic, complemented
16#83525—31nomaximal
17#80014—31nomaximal
18C2×C3×#237—21no—
19C22×C3×D12C2211yescharacteristic
20C2×D3×#67—21no—
21C2×D3×D12C2211yescharacteristic
22C32×#121C2211yescharacteristic, complemented
23C2×#3753C2211yescharacteristic, complemented
24#64139C2211yescharacteristic
25C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
26C3×#938C2211yescharacteristic, complemented
27C3×#935—21no—
28C3×D4×Dic3C2211yescharacteristic, complemented
29C2×C3×#213C2211yescharacteristic
30C2×C3×#213C2211yescharacteristic, complemented
31C3×C4×#67C2211yescharacteristic
32C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
33C3×D3×C4⋊C4C2211yescharacteristic, complemented
34C3×#888C2211yescharacteristic, complemented
35C3×#883—21no—
36C3×#878—21no—
37#63977—21no—
38#63922—21no—
39#63911C2211yescharacteristic
40#63908C2211yescharacteristic
41Dic3×D12C2211yescharacteristic
42#63886—21no—
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44#63659C2211yescharacteristic, complemented
45#63636C2211yescharacteristic, complemented
46#63634C2211yescharacteristic, complemented
47C3×#830C2211yescharacteristic, complemented
48C3×#809C2211yescharacteristic
49C3×#809C2211yescharacteristic, complemented
50#63575C2211yescharacteristic, complemented
51#63575C2211yescharacteristic, complemented
52Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
53#63564C2211yescharacteristic, complemented
54#63564C2211yescharacteristic, complemented
55#63562C2211yescharacteristic
56#63562C2211yescharacteristic
57#63562C2211yescharacteristic, complemented
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C3×#547—31no—
62D4×#67—31no—
63#5611D311yescharacteristic, complemented
64D4×D12—31no—
65C3×#447—31no—
66C2×#832—31no—
67#5157—31no—
68#5156—31no—
69#5150—31no—
70Dic3×D8—31no—
71#5088—31no—
72#5087—31no—
73#5038—31no—
74#5038—31no—
75#5038—31no—
76#5038—61no—
77#5036—31no—
78#5036D311yescharacteristic, complemented
79#5015—31no—
80C4×#213—31no—
81D4×C3⋊C8—31no—
82#4967—31no—
83#4967—31no—
84C2×#809—31no—
85C2×#809—31no—
86#4774—31no—
87D3×#102—31no—
88#4760—31no—
89#4759—31no—
90#4736—31no—
91#67⋊C8—31no—
92C23×C3×D3—21no—
93C22×D32—21no—
94C2×C32×D4—21no—
95C2×C32×D4C2311yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C2×#638—21no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C3×#67—21no—
100C2×C3×#67D411yescharacteristic
101C22×C3×Dic3—21no—
102C22×C3×Dic3—21no—
103C3×#237—44no—
104C2×C3×D12—22no—
105C2×C3×D12—21no—
106C2×C3×D12—41no—
107C2×C3×D12C2311yescharacteristic
108C2×C3×D12C2311yescharacteristic
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3C2311yescharacteristic
111C2×C3×Dic6—21no—
112D3×#67—44no—
113C2×#626—21no—
114C2×#626—21no—
115C2×#626—21no—
116C2×#625—21no—
117C2×D3×Dic3—21no—
118D3×D12—22no—
119D3×D12—41no—
120C32×C4⋊C4C2311yescharacteristic
121C32×C22⋊C4—21no—
122#3753—41no—
123#3752—21no—
124C4⋊(C3⋊Dic3)C2311yescharacteristic
125C2×C3⋊(C3⋊C8)—41no—
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127C2×C3⋊(C3⋊C8)C2311yescharacteristic
128C3×#217—21no—
129C3×#217—21no—
130C3×#217D411yescharacteristic
131C3×#213—22no—
132C3×#213—41no—
133C3×(C2×D3)⋊C4D411yescharacteristic
134C3×C4⋊Dic3—21no—
135C3×C4⋊Dic3C2311yescharacteristic
136C3×C4⋊Dic3C2311yescharacteristic
137C3×Dic3⋊C4—21no—
138C3×Dic3⋊C4—21no—
139C3×Dic3⋊C4D411yescharacteristic
140C3×C4×Dic3C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143(C2×D3)⋊Dic3—21no—
144(C2×D3)⋊Dic3—21no—
145D3×C3⋊C8—41no—
146#3294—91noSylow
147C2×C3×#41—61no—
148C22×C3×D4—31no—
149C22×#67—61no—
150C2×#237—21no—
151C2×D3×D4—31no—
152C2×D3×D4—61no—
153C22×D12—31no—
154C22×D12C2×D311yescharacteristic
155C2×C3×D8—31no—
156C2×C3×D8—31no—
157C3×C4⋊Q8—31no—
158C3×#123—61no—
159C3×#123—61no—
160C3×C22⋊Q8—61no—
161C3×#121—21no—
162C3×#121—31no—
163C3×#121C2×D311yescharacteristic, complemented
164C3×#121C2×D311yescharacteristic, complemented
165C3×C4×D4—31no—
166C3×C4×D4—31no—
167C2×C3×C4⋊C4—31no—
168C2×C3×C4⋊C4—31no—
169#953—61no—
170#940—31no—
171#939—61no—
172#938—31no—
173#938C2×D311yescharacteristic, complemented
174#937—61no—
175#935—21no—
176D4×Dic3—31no—
177D4×Dic3C2×D311yescharacteristic, complemented
178C2×#213—31no—
179C2×#213—31no—
180C2×#213—61no—
181C2×#213C2×D311yescharacteristic
182C2×#213C2×D311yescharacteristic, complemented
183#930—31no—
184#930—31no—
185#930—31no—
186#930—61no—
187C4×#67C2×D311yescharacteristic
188C2×C4⋊Dic3C2×D311yescharacteristic, complemented
189C22×C3⋊C8—31no—
190C22×C3⋊C8—31no—
191C22×C3⋊C8—31no—
192C22×C3⋊C8—61no—
193C2×D3×C8—31no—
194#895—61no—
195D3×C4⋊C4C2×D311yescharacteristic, complemented
196#888C2×D311yescharacteristic, complemented
197#883—21no—
198#882—61no—
199#882—61no—
200#878—21no—
201#874—31no—
202C4×D12—31no—
203C3×#102—31no—
204C3×#102—31no—
205C3×C22⋊C8—31no—
206#832—31no—
207#832—31no—
208#832—31no—
209#832—31no—
210#832—31no—
211#832—31no—
212#832—61no—
213#830—31no—
214#830C2×D311yescharacteristic, complemented
215#821—31no—
216#821—31no—
217(C2×D3)⋊C8—31no—
218#818—31no—
219#818—31no—
220Dic3⋊C8—31no—
221C8×Dic3—31no—
222#809—31no—
223#809—31no—
224#809—31no—
225#809—31no—
226#809—31no—
227#809—31no—
228#809—31no—
229#809—31no—
230#809—61no—
231#809C2×D311yescharacteristic
232#809C2×D311yescharacteristic, complemented
233#807—31no—
234#807—31no—
235#807—31no—
236#807—31no—
237#807—61no—
238C4⋊(C3⋊C8)—31no—
239C4×C3⋊C8—31no—
240C23×C32—21no—
241C23×C32C2×D411yescharacteristic
242C22×C3⋊D3—21no—
243C22×C3×D3—21no—
244C22×C3×D3—21no—
245C22×C3×D3—42no—
246C22×C3×D3—42no—
247C22×C3×D3—81no—
248C22×C3×D3C2×D411yescharacteristic
249C2×D32—42no—
250C2×D32—42no—
251C2×D32—81no—
252C32×D4—21no—
253C32×D4—21no—
254C32×D4—42no—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4—21no—
258C2×C32×C4C2×D411yescharacteristic
259C2×C32×C4C2411yescharacteristic
260#638—42no—
261C2×C3⋊Dic3—21no—
262C4⋊(C3⋊D3)—21no—
263C4⋊(C3⋊D3)—21no—
264C3×#67—42no—
265C3×#67D814yescomplemented
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—42no—
269C2×C3×Dic3—42no—
270C2×C3×Dic3C2×D411yescharacteristic
271C2×C3×Dic3C2×D411yescharacteristic
272C2×C3×Dic3C2×D411yescharacteristic
273C3×D12—21no—
274C3×D12—21no—
275C3×D12—21no—
276C3×D12—42no—
277C3×D12#4112yescomplemented
278C3×C4×D3—21no—
279C3×C4×D3—21no—
280C3×C4×D3—42no—
281C3×Dic6—42no—
282#626—42no—
283#626—42no—
284#626—81no—
285#625—42no—
286D3×Dic3—42no—
287C3⋊(C3⋊C8)—21no—
288C3⋊(C3⋊C8)—21no—
289C3×C3⋊C8—21no—
290C3×C3⋊C8—21no—
291#547—31no—
292D42—91no—
293#486—91no—
294#480—91no—
295#480—91no—
296#474—91no—
297#466—91no—
298#466—91no—
299#459—91no—
300#447—31no—
301#447—91no—
302C4×D8—91no—
303C8×D4—91no—
304C2×#102—91no—
305C2×#102—91no—
306C24×C3—61no—
307C23×D3—21no—
308C23×D3—61no—
309C23×D3—61no—
310C3×#41—124no—
311C2×C3×Q8—61no—
312C2×C3×D4—21no—
313C2×C3×D4—21no—
314C2×C3×D4—21no—
315C2×C3×D4—31no—
316C2×C3×D4—31no—
317C2×C3×D4—31no—
318C2×C3×D4—41no—
319C2×C3×D4—62no—
320C2×C3×D4—61no—
321C2×C3×D4—61no—
322C2×C3×D4—121no—
323C2×C3×D4C22×D311yescharacteristic
324C2×C3×D4C22×D311yescharacteristic
325C22×C3×C4—21no—
326C22×C3×C4—31no—
327C22×C3×C4—61no—
328C22×C3×C4—61no—
329C22×C3×C4—61no—
330C22×C3×C4C22×D311yescharacteristic
331C22×C3×C4C22×D311yescharacteristic
332C2×#67—21no—
333C2×#67—61no—
334C2×#67—61no—
335C2×#67—61no—
336C2×#67—61no—
337C2×#67—61no—
338C2×#67—61no—
339C2×#67—61no—
340C2×#67—121no—
341C2×#67—124no—
342C2×#67#6711yescharacteristic
343C22×Dic3—21no—
344C22×Dic3—21no—
345C22×Dic3—61no—
346#237—44no—
347D3×D4—62no—
348D3×D4—121no—
349D3×D4—124no—
350C2×D12—22no—
351C2×D12—21no—
352C2×D12—31no—
353C2×D12—31no—
354C2×D12—41no—
355C2×D12—61no—
356C2×D12—62no—
357C2×D12—61no—
358C2×D12—61no—
359C2×D12—61no—
360C2×D12—121no—
361C2×D12C22×D311yescharacteristic
362C2×D12C22×D311yescharacteristic
363C2×C4×D3—21no—
364C2×C4×D3—61no—
365C2×C4×D3C22×D311yescharacteristic
366C2×Dic6—21no—
367C3×D8—62no—
368C3×D8—121no—
369C2×C3×C8—31no—
370C2×C3×C8—31no—
371C3×C4⋊C4—21no—
372C3×C4⋊C4—31no—
373C3×C4⋊C4—31no—
374C3×C4⋊C4—31no—
375C3×C4⋊C4—61no—
376C3×C4⋊C4—61no—
377C3×C4⋊C4—61no—
378C3×C4⋊C4C22×D311yescharacteristic
379C3×C4⋊C4C22×D311yescharacteristic
380C3×C22⋊C4—21no—
381C3×C22⋊C4—21no—
382C3×C22⋊C4—31no—
383C3×C22⋊C4—31no—
384C3×C22⋊C4—41no—
385C3×C22⋊C4—61no—
386C3×C22⋊C4—61no—
387C3×C42—31no—
388#217—21no—
389#217—21no—
390#217—61no—
391#217—61no—
392#217#6711yescharacteristic
393#213—22no—
394#213—41no—
395#213—121no—
396#213—121no—
397#213—122no—
398(C2×D3)⋊C4—61no—
399(C2×D3)⋊C4—61no—
400(C2×D3)⋊C4—61no—
401(C2×D3)⋊C4—61no—
402(C2×D3)⋊C4—121no—
403(C2×D3)⋊C4#6711yescharacteristic
404C4⋊Dic3—21no—
405C4⋊Dic3—31no—
406C4⋊Dic3—31no—
407C4⋊Dic3—61no—
408C4⋊Dic3C22×D311yescharacteristic
409C4⋊Dic3C22×D311yescharacteristic
410Dic3⋊C4—21no—
411Dic3⋊C4—21no—
412Dic3⋊C4#6711yescharacteristic
413C4×Dic3C22×D311yescharacteristic
414C2×C3⋊C8—31no—
415C2×C3⋊C8—31no—
416C2×C3⋊C8—31no—
417C2×C3⋊C8—31no—
418C2×C3⋊C8—61no—
419C2×C3⋊C8—61no—
420C2×C3⋊C8—121no—
421C2×C3⋊C8—121no—
422C2×C3⋊C8—121no—
423C2×C3⋊C8—122no—
424C2×C3⋊C8C22×D311yescharacteristic
425C2×C3⋊C8C22×D311yescharacteristic
426D3×C8—121no—
427C22×C32—21no—
428C22×C32—21no—
429C22×C32—41no—
430C22×C32—41no—
431C22×C32—41no—
432C22×C32C2×D812yes—
433C22×C32C22×D411yescharacteristic
434C2×C3⋊D3—41no—
435C2×C3⋊D3—41no—
436C2×C3⋊D3—41no—
437C2×C3×D3—21no—
438C2×C3×D3—21no—
439C2×C3×D3—22no—
440C2×C3×D3—41no—
441C2×C3×D3—41no—
442C2×C3×D3—41no—
443C2×C3×D3—41no—
444C2×C3×D3—41no—
445C2×C3×D3—84no—
446C2×C3×D3C2×D812yes—
447D32—84no—
448C32×C4—21no—
449C32×C4—41no—
450C32×C4C2×#4111yescharacteristic
451C32×C4H(5,𝔽2)11yescharacteristic
452C3⋊Dic3—41no—
453C3×Dic3—21no—
454C3×Dic3—21no—
455C3×Dic3—41no—
456C3×Dic3—41no—
457C3×Dic3C2×D812yes—
458C2×#41—61no—
459C22×D4—31no—
460C22×D4—91no—
461C22×D4—181no—
462C2×D8—31no—
463C2×D8—31no—
464C2×D8—91no—
465C22×C8—91no—
466C22×C8—91no—
467C4⋊Q8—31no—
468#127—91no—
469#123—61no—
470#123—61no—
471C22⋊Q8—61no—
472#121—31no—
473#121—91no—
474#121—91no—
475#121—181no—
476#121D3211yescharacteristic, complemented
477#120—181no—
478#120—181no—
479C4×D4—31no—
480C4×D4—31no—
481C4×D4—91no—
482C2×C4⋊C4—31no—
483C2×C4⋊C4—31no—
484#107—91no—
485#107—91no—
486#107—91no—
487C4⋊C8—91no—
488#102—31no—
489#102—31no—
490#102—91no—
491#102—91no—
492#102—91no—
493#102—91no—
494#102—91no—
495#102—91no—
496#102—91no—
497#102—91no—
498C22⋊C8—31no—
499C22⋊C8—91no—
500C4×C8—91no—
501C23×C3—21no—
502C23×C3—21no—
503C23×C3—21no—
504C23×C3—31no—
505C23×C3—41no—
506C23×C3—61no—
507C23×C3—61no—
508C23×C3—122no—
509C23×C3—122no—
510C23×C3—241no—
511C23×C3D3×D411yescharacteristic
512C23×C3C2×#6711yescharacteristic
513C22×D3—21no—
514C22×D3—21no—
515C22×D3—42no—
516C22×D3—42no—
517C22×D3—61no—
518C22×D3—61no—
519C22×D3—81no—
520C22×D3—121no—
521C22×D3—122no—
522C22×D3—122no—
523C22×D3—122no—
524C22×D3—122no—
525C22×D3—241no—
526C22×D3—241no—
527C22×D3C2×#6711yescharacteristic
528C3×Q8—122no—
529C3×D4—21no—
530C3×D4—21no—
531C3×D4—21no—
532C3×D4—21no—
533C3×D4—34no—
534C3×D4—32no—
535C3×D4—41no—
536C3×D4—41no—
537C3×D4—42no—
538C3×D4—42no—
539C3×D4—61no—
540C3×D4—61no—
541C3×D4—61no—
542C3×D4—82no—
543C3×D4—122no—
544C3×D4—122no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—21no—
549C2×C3×C4—21no—
550C2×C3×C4—21no—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—31no—
554C2×C3×C4—31no—
555C2×C3×C4—31no—
556C2×C3×C4—41no—
557C2×C3×C4—41no—
558C2×C3×C4—41no—
559C2×C3×C4—61no—
560C2×C3×C4—61no—
561C2×C3×C4—61no—
562C2×C3×C4—61no—
563C2×C3×C4—122no—
564C2×C3×C4—122no—
565C2×C3×C4—122no—
566C2×C3×C4D3×D411yescharacteristic
567C2×C3×C4C2×#6711yescharacteristic
568C2×C3×C4C23×D311yescharacteristic
569C2×C3×C4C23×D311yescharacteristic
570#67—42no—
571#67—122no—
572#67—122no—
573#67—122no—
574#67—122no—
575#67—122no—
576#67—122no—
577#67—242no—
578#67—241no—
579#67#21314yescomplemented
580C2×Dic3—21no—
581C2×Dic3—21no—
582C2×Dic3—42no—
583C2×Dic3—42no—
584C2×Dic3—61no—
585C2×Dic3—61no—
586C2×Dic3—121no—
587C2×Dic3—122no—
588C2×Dic3C2×#6711yescharacteristic
589C2×Dic3C2×#6711yescharacteristic
590C2×Dic3C2×#6711yescharacteristic
591D12—21no—
592D12—21no—
593D12—21no—
594D12—42no—
595D12—61no—
596D12—61no—
597D12—61no—
598D12—61no—
599D12—121no—
600D12—121no—
601D12—122no—
602D12—122no—
603D12—241no—
604D12#23712yescomplemented
605C4×D3—21no—
606C4×D3—21no—
607C4×D3—42no—
608C4×D3—122no—
609Dic6—42no—
610C3×C8—61no—
611C3×C8—61no—
612C3⋊C8—21no—
613C3⋊C8—21no—
614C3⋊C8—62no—
615C3⋊C8—61no—
616C3⋊C8—61no—
617C3⋊C8—61no—
618C3⋊C8—61no—
619C3⋊C8—121no—
620C2×C32—22no—
621C2×C32—81no—
622C2×C32#54611yescharacteristic
623C2×C32C22×D811yescharacteristic
624C2×C32#57711yescharacteristic
625C3⋊D3—81no—
626C3×D3—22no—
627C3×D3—42no—
628C3×D3—81no—
629C24—61no—
630C24—181no—
631#41—124no—
632C2×Q8—61no—
633C2×D4—21no—
634C2×D4—31no—
635C2×D4—31no—
636C2×D4—31no—
637C2×D4—62no—
638C2×D4—61no—
639C2×D4—61no—
640C2×D4—91no—
641C2×D4—121no—
642C2×D4—181no—
643C2×D4—181no—
644C2×D4—181no—
645C2×D4—182no—
646C2×D4—181no—
647C2×D4—181no—
648C2×D4—361no—
649C2×D4—364no—
650C2×D4C2×D3211yescharacteristic
651C22×C4—31no—
652C22×C4—61no—
653C22×C4—61no—
654C22×C4—61no—
655C22×C4—181no—
656C22×C4C2×D3211yescharacteristic
657D8—62no—
658D8—121no—
659D8—361no—
660C2×C8—31no—
661C2×C8—31no—
662C2×C8—91no—
663C2×C8—91no—
664C2×C8—361no—
665C2×C8—361no—
666C4⋊C4—31no—
667C4⋊C4—31no—
668C4⋊C4—31no—
669C4⋊C4—61no—
670C4⋊C4—61no—
671C4⋊C4—61no—
672C4⋊C4—91no—
673C4⋊C4C2×D3211yescharacteristic
674C22⋊C4—21no—
675C22⋊C4—31no—
676C22⋊C4—31no—
677C22⋊C4—61no—
678C22⋊C4—61no—
679C22⋊C4—181no—
680C22⋊C4—181no—
681C22⋊C4—181no—
682C42—31no—
683C22×C3—21no—
684C22×C3—21no—
685C22×C3—21no—
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—22no—
689C22×C3—32no—
690C22×C3—41no—
691C22×C3—41no—
692C22×C3—41no—
693C22×C3—41no—
694C22×C3—41no—
695C22×C3—41no—
696C22×C3—41no—
697C22×C3—41no—
698C22×C3—61no—
699C22×C3—61no—
700C22×C3—62no—
701C22×C3—81no—
702C22×C3—81no—
703C22×C3—81no—
704C22×C3—121no—
705C22×C3—121no—
706C22×C3—121no—
707C22×C3—121no—
708C22×C3—121no—
709C22×C3—244no—
710C22×C3D3×D812yes—
711C22×C3C2×#21312yes—
712C22×C3C2×D3×D411yescharacteristic
713C22×C3C22×#6711yescharacteristic
714C2×D3—21no—
715C2×D3—21no—
716C2×D3—22no—
717C2×D3—41no—
718C2×D3—41no—
719C2×D3—41no—
720C2×D3—41no—
721C2×D3—41no—
722C2×D3—84no—
723C2×D3—121no—
724C2×D3—121no—
725C2×D3—121no—
726C2×D3—121no—
727C2×D3—121no—
728C2×D3—121no—
729C2×D3—241no—
730C2×D3—241no—
731C2×D3—241no—
732C2×D3—244no—
733C2×D3—244no—
734C2×D3C2×#21312yes—
735C3×C4—21no—
736C3×C4—21no—
737C3×C4—21no—
738C3×C4—21no—
739C3×C4—32no—
740C3×C4—41no—
741C3×C4—41no—
742C3×C4—41no—
743C3×C4—61no—
744C3×C4—61no—
745C3×C4—81no—
746C3×C4—121no—
747C3×C4—121no—
748C3×C4C2×#23711yescharacteristic
749C3×C4#100411yescharacteristic
750C3×C4D3×#4111yescharacteristic
751C3×C4#100911yescharacteristic
752Dic3—21no—
753Dic3—21no—
754Dic3—41no—
755Dic3—41no—
756Dic3—121no—
757Dic3—121no—
758Dic3—241no—
759Dic3C2×#21312yes—
760C32#329411yescharacteristic, complemented, Sylow
761C23—21no—
762C23—31no—
763C23—61no—
764C23—61no—
765C23—122no—
766C23—122no—
767C23—181no—
768C23—241no—
769C23—362no—
770C23—362no—
771C23—721no—
772C23D3×#6711yescharacteristic
773Q8—122no—
774D4—21no—
775D4—21no—
776D4—34no—
777D4—32no—
778D4—42no—
779D4—61no—
780D4—61no—
781D4—61no—
782D4—122no—
783D4—122no—
784D4—181no—
785D4—181no—
786D4—362no—
787D4—362no—
788D4—362no—
789D4—362no—
790D4—721no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—31no—
795C2×C4—31no—
796C2×C4—31no—
797C2×C4—61no—
798C2×C4—61no—
799C2×C4—61no—
800C2×C4—61no—
801C2×C4—122no—
802C2×C4—122no—
803C2×C4—122no—
804C2×C4—181no—
805C2×C4—362no—
806C2×C4D3×#6711yescharacteristic
807C2×C4C22×D3211yescharacteristic
808C8—61no—
809C8—61no—
810C8—181no—
811C8—181no—
812C2×C3—22no—
813C2×C3—22no—
814C2×C3—21no—
815C2×C3—21no—
816C2×C3—21no—
817C2×C3—42no—
818C2×C3—62no—
819C2×C3—81no—
820C2×C3—81no—
821C2×C3—122no—
822C2×C3—161no—
823C2×C3—241no—
824C2×C3#559111yescharacteristic
825C2×C3C2×D3×D811yescharacteristic
826C2×C3#577511yescharacteristic
827C2×C3C22×#21311yescharacteristic
828C2×C3#582911yescharacteristic
829C2×C3#583711yescharacteristic
830D3—22no—
831D3—42no—
832D3—81no—
833D3—241no—
834D3—241no—
835D3—481no—
836C22—21no—
837C22—21no—
838C22—32no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—61no—
843C22—61no—
844C22—62no—
845C22—121no—
846C22—121no—
847C22—121no—
848C22—121no—
849C22—121no—
850C22—244no—
851C22—361no—
852C22—361no—
853C22—361no—
854C22—724no—
855C22D3×#21312yes—
856C22C2×D3×#6711yescharacteristic
857C4—21no—
858C4—32no—
859C4—41no—
860C4—61no—
861C4—61no—
862C4—121no—
863C4—121no—
864C4—361no—
865C4D3×#23711yescharacteristic
866C4#6431411yescharacteristic
867C3—21no—
868C3#8001411yescharacteristic, complemented
869C3#8352511yescharacteristic, complemented
870C2—22no—
871C2—62no—
872C2—81no—
873C2—122no—
874C2—241no—
875C2—721no—
876C2C2×D3×#21311yescharacteristic
877C2#1059530411yescharacteristic
878C2#1059545511yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
hypercenter#121D32
hypocenterC32#3294
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C3×#5611C2semidirect
2. D12×#67C2semidirect
3. #10592737C2semidirect
4. C3×#5036C2semidirect
5. #10591515C2semidirect
6. #10591498C2semidirect
7. #10591481C2semidirect
8. Dic3×#213C2semidirect
9. #67⋊(C3⋊C8)C2semidirect
10. #10591133C2semidirect
11. C2×#63562C2semidirect
12. D3×#809C2semidirect
13. #10590548C2semidirect
14. #10590498C2semidirect
15. #10590463C2semidirect
22. C32×#121C22semidirect
23. C2×#3753C22semidirect
25. C22×C3⋊(C3⋊C8)C22semidirect
26. C3×#938C22semidirect
28. C3×D4×Dic3C22semidirect
30. C2×C3×#213C22semidirect
32. C2×C3×C4⋊Dic3C22semidirect
33. C3×D3×C4⋊C4C22semidirect
34. C3×#888C22semidirect
43. C2×D3×C3⋊C8C22semidirect
44. #63659C22semidirect
45. #63636C22semidirect
46. #63634C22semidirect
47. C3×#830C22semidirect
49. C3×#809C22semidirect
50. #63575C22semidirect
51. #63575C22semidirect
52. Dic3⋊(C3⋊C8)C22semidirect
53. #63564C22semidirect
54. #63564C22semidirect
57. #63562C22semidirect
58. #63562C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. Dic3×C3⋊C8C22semidirect
63. #5611D3semidirect
78. #5036D3semidirect
163. C3×#121C2×D3semidirect
164. C3×#121C2×D3semidirect
173. #938C2×D3semidirect
177. D4×Dic3C2×D3semidirect
182. C2×#213C2×D3semidirect
188. C2×C4⋊Dic3C2×D3semidirect
195. D3×C4⋊C4C2×D3semidirect
196. #888C2×D3semidirect
214. #830C2×D3semidirect
232. #809C2×D3semidirect
265. C3×#67D8semidirect
277. C3×D12#41semidirect
476. #121D32semidirect
579. #67#213semidirect
604. D12#237semidirect
760. C32#3294semidirect
868. C3#80014semidirect
869. C3#83525semidirect

Maximal subgroups

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

subgroupindex
C3×#56112
D12×#672
#105927372
C3×#50362
#105915152
#105914982
#105914812
Dic3×#2132
#67⋊(C3⋊C8)2
#105911332
C2×#635622
D3×#8092
#105905482
#105904982
#105904632
#835253
#800143