Finite Group Databasebeta

← #11887403

Subgroups — #11887403

Order 1152.

939 conjugacy classes of subgroups.

The subgroup lattice has 839 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595254C211yesmaximal, characteristic, complemented
2#10594578C211yesmaximal, characteristic, complemented
3#10592472C211yesmaximal, characteristic, complemented
4C3×#4772C211yesmaximal, characteristic, complemented
5C3×#4766C211yesmaximal, characteristic, complemented
6#10591452C211yesmaximal, characteristic, complemented
7#10591416C211yesmaximal, characteristic, complemented
8#10591400C211yesmaximal, characteristic, complemented
9#10590832C211yesmaximal, characteristic, complemented
10#10590770C211yesmaximal, characteristic, complemented
11#10590720C211yesmaximal, characteristic, complemented
12#10590689C211yesmaximal, characteristic, complemented
13#10590537C211yesmaximal, characteristic, complemented
14#10590523C211yesmaximal, characteristic, complemented
15#10590425C211yesmaximal, characteristic, complemented
16#81187—31nomaximal
17#78846—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×#3753C2211yescharacteristic
21C2×#3745C2211yescharacteristic
22#64104C2211yescharacteristic
23C3×D4×Dic3C2211yescharacteristic
24C2×C3×D3×C8C2211yescharacteristic, complemented
25C3×#892C2211yescharacteristic, complemented
26C3×#890C2211yescharacteristic, complemented
27#63981—21no—
28#63978—21no—
29#63966—21no—
30C2×#3722—21no—
31#63910—21no—
32#63909C2211yescharacteristic
33#63909C2211yescharacteristic, complemented
34C4×#626C2211yescharacteristic
35#63900C2211yescharacteristic
36#63894—21no—
37#63894C2211yescharacteristic, complemented
38#63871C2211yescharacteristic
39#63868—21no—
40#63864C2211yescharacteristic
41#63854—21no—
42C2×#3717C2211yescharacteristic, complemented
43C2×#3710C2211yescharacteristic
44C32×#102C2211yescharacteristic
45#63647C2211yescharacteristic
46#63636C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#818C2211yescharacteristic, complemented
50C3×#816C2211yescharacteristic, complemented
51C3×Dic3⋊C8C2211yescharacteristic, complemented
52C3×#810C2211yescharacteristic, complemented
53C3×#808C2211yescharacteristic, complemented
54#63576C2211yescharacteristic, complemented
55#63565C2211yescharacteristic, complemented
56#63564C2211yescharacteristic
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61#5829—31no—
62#5695—31no—
63#5554—31no—
64#5530—31no—
65C3×#478—31no—
66C3×#416—31no—
67#5238—31no—
68#5115—31no—
69C8×#67—31no—
70#5068—31no—
71C4×#213—31no—
72#5003—31no—
73#4884—31no—
74#4883—31no—
75#4866—31no—
76#4864—31no—
77#4844—31no—
78#4834—31no—
79#4819—31no—
80#4811—31no—
81#4807—31no—
82#4800—31no—
83#4781—31no—
84#4773—31no—
85#4773—31no—
86#4773—61no—
87#4772D311yescharacteristic, complemented
88D3×#102—31no—
89D3×#102—31no—
90#4766D311yescharacteristic, complemented
91#4756—31no—
92C23×C3⋊D3—21no—
93C2×C32×D4C2311yescharacteristic
94C2×#638—21no—
95D4×C3⋊D3—22no—
96D4×C3⋊D3—41no—
97C2×C4⋊(C3⋊D3)—21no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4×C3⋊D3C2311yescharacteristic
101C2×C3×#67—21no—
102C22×C3×Dic3—21no—
103C22×C3×Dic3—21no—
104C3×#237—22no—
105C3×#237—41no—
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108C2×#626—21no—
109C2×#626—21no—
110C2×#626D411yescharacteristic
111C2×#624—21no—
112C2×#624—21no—
113C2×C32×C8C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115#3753—22no—
116#3752—21no—
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118#3745—41no—
119C3×#217—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×C4⋊Dic3—21no—
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×C4×Dic3—21no—
127C3×C4×Dic3C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C3×D3×C8—41no—
131#3724—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3D411yescharacteristic
134#3722—21no—
135#3722—21no—
136#3722—21no—
137#3722—21no—
138#3722—21no—
139#3722—21no—
140#3722D411yescharacteristic
141(C2×D3)⋊Dic3D411yescharacteristic
142#3717—41no—
143#3710—41no—
144#3297—91noSylow
145C2×C3×#41—31no—
146C2×#237C2×D311yescharacteristic
147C2×D3×D4—31no—
148C2×D3×D4—31no—
149C2×D3×D4—61no—
150C22×C3×C8—31no—
151C3×#125—31no—
152C3×C4×D4—31no—
153C3×#117—31no—
154#947—31no—
155#946—31no—
156C2×#215—31no—
157#939—61no—
158#937—61no—
159D4×Dic3C2×D311yescharacteristic
160C2×#213—31no—
161C2×#213—31no—
162C2×#213—61no—
163#930—31no—
164#930—31no—
165#930—61no—
166#929—61no—
167C4×#67—31no—
168C2×(C2×D3)⋊C4—61no—
169C2×(C2×D3)⋊C4—61no—
170C2×D24—31no—
171C2×D24—31no—
172C2×D24—61no—
173C2×#204—31no—
174C2×D3×C8—31no—
175C2×D3×C8—31no—
176C2×D3×C8C2×D311yescharacteristic, complemented
177#898—61no—
178#897—31no—
179#895—31no—
180#895—31no—
181#895—31no—
182#895—31no—
183#895—61no—
184#895—61no—
185#894—61no—
186#893—31no—
187#893—61no—
188#892C2×D311yescharacteristic, complemented
189D3×C4⋊C4—31no—
190D3×C4⋊C4—31no—
191#890C2×D311yescharacteristic, complemented
192#886—61no—
193#884—61no—
194#883—61no—
195#882—61no—
196#876—61no—
197#875—31no—
198C4×D12—31no—
199C4×D12—31no—
200C4×D12—61no—
201C3×#107—31no—
202C3×#106—31no—
203C3×C4⋊C8—31no—
204C3×#103—31no—
205C3×#103—31no—
206C3×#102—21no—
207C3×#102—31no—
208C3×#102—31no—
209C3×#102C2×D311yescharacteristic
210C3×#102C2×D311yescharacteristic
211#835—31no—
212#832C2×D311yescharacteristic
213#832C2×D311yescharacteristic
214#830—31no—
215#821—31no—
216#821—31no—
217#821—31no—
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8—31no—
220(C2×D3)⋊C8—31no—
221(C2×D3)⋊C8—61no—
222#818C2×D311yescharacteristic, complemented
223#816C2×D311yescharacteristic, complemented
224Dic3⋊C8C2×D311yescharacteristic, complemented
225C8×Dic3—31no—
226#810—31no—
227#810C2×D311yescharacteristic, complemented
228#809—31no—
229#809—31no—
230#809—31no—
231#809—31no—
232#809—31no—
233#809—61no—
234#808C2×D311yescharacteristic, complemented
235#807—31no—
236#807—31no—
237C4×C3⋊C8—31no—
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×D4—21no—
247C32×D4#4112yes—
248C2×C32×C4—21no—
249C2×C32×C4C2411yescharacteristic
250#638—42no—
251C2×C3⋊Dic3C2×D411yescharacteristic
252C4⋊(C3⋊D3)—21no—
253C4⋊(C3⋊D3)—21no—
254C4⋊(C3⋊D3)—21no—
255C4⋊(C3⋊D3)—21no—
256C4⋊(C3⋊D3)—42no—
257C4×C3⋊D3—21no—
258C4×C3⋊D3—21no—
259C3×#67—42no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—42no—
265C2×C3×Dic3—81no—
266C2×C3×Dic3C2×D411yescharacteristic
267C2×C3×Dic3C2×D411yescharacteristic
268C2×C3×Dic3C2×D411yescharacteristic
269C3×C4×D3—21no—
270C3×C4×D3—21no—
271C3×Dic6—21no—
272C3×Dic6—21no—
273#626—22no—
274#626—81no—
275#626—81no—
276#624—81no—
277#624—81no—
278C32×C8—21no—
279C3⋊(C3⋊C8)—21no—
280C3×C3⋊C8—21no—
281C3×C3⋊C8—21no—
282#553—91no—
283#546—91no—
284#488—91no—
285#484—91no—
286#482—91no—
287#478—31no—
288#466—91no—
289#465—91no—
290#463—91no—
291#449—91no—
292#447—91no—
293C4×D8—91no—
294C8×D4—91no—
295#416—31no—
296C2×#102—91no—
297C23×D3—61no—
298C23×D3—61no—
299C23×D3—121no—
300C3×#41—62no—
301C3×#41—121no—
302C2×C3×Q8—31no—
303C2×C3×D4—21no—
304C2×C3×D4—61no—
305C2×C3×D4C22×D311yescharacteristic
306C2×C3×D4C22×D311yescharacteristic
307C22×C3×C4—31no—
308C22×C3×C4—61no—
309C22×C3×C4—61no—
310C2×#67—21no—
311C2×#67—31no—
312C2×#67—61no—
313C2×#67—61no—
314C2×#67—61no—
315C2×#67—61no—
316C2×#67—121no—
317C22×Dic3—21no—
318C22×Dic3—21no—
319#237—22no—
320#237—41no—
321D3×D4—62no—
322D3×D4—62no—
323D3×D4—122no—
324D3×D4—121no—
325D3×D4—121no—
326D3×D4—122no—
327C2×D12—31no—
328C2×D12—31no—
329C2×D12—31no—
330C2×D12—31no—
331C2×D12—31no—
332C2×D12—61no—
333C2×D12—61no—
334C2×D12—61no—
335C2×D12—61no—
336C2×D12—61no—
337C2×D12—61no—
338C2×D12—121no—
339C2×C4×D3—31no—
340C2×C4×D3—31no—
341C2×C4×D3—61no—
342C2×C4×D3—61no—
343C2×C4×D3—61no—
344C2×C4×D3—61no—
345C2×C4×D3—61no—
346C2×C4×D3C22×D311yescharacteristic
347C2×Dic6C22×D311yescharacteristic
348C2×C3×C8—21no—
349C2×C3×C8—31no—
350C2×C3×C8—31no—
351C2×C3×C8—121no—
352C2×C3×C8C22×D311yescharacteristic
353C2×C3×C8C22×D311yescharacteristic
354C3×C4⋊C4—21no—
355C3×C4⋊C4—31no—
356C3×C4⋊C4—31no—
357C3×C4⋊C4—31no—
358C3×C4⋊C4—61no—
359C3×C4⋊C4—61no—
360C3×C4⋊C4C22×D311yescharacteristic
361C3×C4⋊C4C22×D311yescharacteristic
362C3×C22⋊C4—61no—
363C3×C22⋊C4—61no—
364C3×C42—31no—
365C3×C42—61no—
366#217—21no—
367#217—31no—
368#215—121no—
369#213—62no—
370#213—62no—
371#213—122no—
372(C2×D3)⋊C4—21no—
373(C2×D3)⋊C4—31no—
374(C2×D3)⋊C4—31no—
375(C2×D3)⋊C4—31no—
376(C2×D3)⋊C4—61no—
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—61no—
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—121no—
391C4⋊Dic3—21no—
392C4⋊Dic3—31no—
393C4⋊Dic3—61no—
394C4⋊Dic3C22×D311yescharacteristic
395C4⋊Dic3C22×D311yescharacteristic
396C4⋊Dic3C22×D311yescharacteristic
397Dic3⋊C4—21no—
398Dic3⋊C4—31no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402C4×Dic3—21no—
403C4×Dic3C22×D311yescharacteristic
404C2×C3⋊C8—31no—
405C2×C3⋊C8—31no—
406C2×C3⋊C8—61no—
407C2×C3⋊C8C22×D311yescharacteristic
408C2×C3⋊C8C22×D311yescharacteristic
409D24—121no—
410D24—121no—
411D24—122no—
412#204—121no—
413D3×C8—41no—
414D3×C8—121no—
415D3×C8—121no—
416C22×C32—22no—
417C22×C32—41no—
418C22×C32—41no—
419C22×C32C22×D411yescharacteristic
420C2×C3⋊D3—21no—
421C2×C3⋊D3—21no—
422C2×C3⋊D3—41no—
423C2×C3⋊D3—41no—
424C2×C3⋊D3—41no—
425C2×C3⋊D3—41no—
426C2×C3⋊D3—41no—
427C2×C3⋊D3—41no—
428C2×C3⋊D3—84no—
429C2×C3⋊D3#13512yes—
430C2×C3×D3—21no—
431C2×C3×D3—21no—
432C2×C3×D3—21no—
433C32×C4—41no—
434C32×C4C2×#4111yescharacteristic
435C32×C4H(5,𝔽2)11yescharacteristic
436C3⋊Dic3—21no—
437C3×Dic3—21no—
438C3×Dic3—21no—
439C3×Dic3—21no—
440C3×Dic3—41no—
441C3×Dic3—41no—
442C3×Dic3—41no—
443C3×Dic3—41no—
444C2×#41—31no—
445C22×D4—91no—
446C2×SD16—91no—
447C2×D8—91no—
448C2×D8—91no—
449C22×C8—31no—
450C22×C8—91no—
451#126—181no—
452#125—31no—
453#124—91no—
454#123—181no—
455#123—181no—
456C22⋊Q8—91no—
457#121—91no—
458#121—91no—
459#121—91no—
460#121—181no—
461#121—181no—
462#120—181no—
463C4×D4—31no—
464C4×D4—91no—
465C4×D4—91no—
466C4×D4—181no—
467#117—31no—
468C2×C4⋊C4—91no—
469C2×C22⋊C4—181no—
470#107—31no—
471#107—91no—
472#106—31no—
473C4⋊C8—31no—
474#103—31no—
475#103—31no—
476#103—91no—
477#102—31no—
478#102—31no—
479#102—91no—
480#102—91no—
481#102—91no—
482#102—91no—
483#102D3211yescharacteristic
484C22⋊C8—91no—
485C22⋊C8—91no—
486C4×C8—91no—
487C23×C3—21no—
488C23×C3—21no—
489C23×C3—31no—
490C23×C3—41no—
491C22×D3—31no—
492C22×D3—31no—
493C22×D3—61no—
494C22×D3—61no—
495C22×D3—61no—
496C22×D3—61no—
497C22×D3—61no—
498C22×D3—121no—
499C22×D3—121no—
500C22×D3—122no—
501C22×D3—122no—
502C22×D3—122no—
503C22×D3—122no—
504C22×D3—124no—
505C22×D3—242no—
506C22×D3—241no—
507C22×D3—241no—
508C22×D3—242no—
509C22×D3D3×D411yescharacteristic
510C3×Q8—61no—
511C3×Q8—61no—
512C3×D4—21no—
513C3×D4—21no—
514C3×D4—22no—
515C3×D4—41no—
516C3×D4—122no—
517C3×D4#23512yes—
518C3×D4#23912yes—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—31no—
523C2×C3×C4—31no—
524C2×C3×C4—31no—
525C2×C3×C4—41no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—122no—
533C2×C3×C4—241no—
534C2×C3×C4C23×D311yescharacteristic
535C2×C3×C4C23×D311yescharacteristic
536#67—42no—
537#67—62no—
538#67—122no—
539#67—122no—
540#67—124no—
541#67—241no—
542#67—241no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—21no—
546C2×Dic3—21no—
547C2×Dic3—31no—
548C2×Dic3—31no—
549C2×Dic3—42no—
550C2×Dic3—61no—
551C2×Dic3—81no—
552C2×Dic3D3×D411yescharacteristic
553C2×Dic3D3×D411yescharacteristic
554C2×Dic3D3×D411yescharacteristic
555D12—62no—
556D12—62no—
557D12—61no—
558D12—61no—
559D12—61no—
560D12—61no—
561D12—61no—
562D12—61no—
563D12—61no—
564D12—61no—
565D12—121no—
566D12—121no—
567D12—121no—
568D12—122no—
569D12—122no—
570D12—242no—
571D12—241no—
572D12—241no—
573C4×D3—21no—
574C4×D3—21no—
575C4×D3—61no—
576C4×D3—61no—
577C4×D3—61no—
578C4×D3—61no—
579C4×D3—121no—
580C4×D3—121no—
581C4×D3—241no—
582C4×D3—241no—
583C4×D3—241no—
584C4×D3—241no—
585Dic6—21no—
586Dic6—21no—
587C3×C8—21no—
588C3×C8—21no—
589C3×C8—41no—
590C3×C8—61no—
591C3×C8—61no—
592C3⋊C8—21no—
593C3⋊C8—21no—
594C3⋊C8—61no—
595C3⋊C8—61no—
596C3⋊C8—121no—
597C2×C32—42no—
598C2×C32#54611yescharacteristic
599C2×C32C2×#13511yescharacteristic
600C2×C32#57611yescharacteristic
601C3⋊D3—22no—
602C3⋊D3—81no—
603C3⋊D3—81no—
604C3×D3—41no—
605C24—181no—
606#41—62no—
607#41—121no—
608C2×Q8—31no—
609C2×D4—61no—
610C2×D4—91no—
611C2×D4—91no—
612C2×D4—91no—
613C2×D4—181no—
614C2×D4—181no—
615C2×D4—181no—
616C2×D4—181no—
617C2×D4—182no—
618C2×D4—361no—
619C2×D4C2×D3211yescharacteristic
620C22×C4—31no—
621C22×C4—61no—
622C22×C4—61no—
623C22×C4—91no—
624C22×C4—181no—
625C22×C4—181no—
626SD16—361no—
627D8—182no—
628D8—361no—
629C2×C8—31no—
630C2×C8—31no—
631C2×C8—91no—
632C2×C8—121no—
633C2×C8—361no—
634C2×C8C2×D3211yescharacteristic
635C4⋊C4—31no—
636C4⋊C4—31no—
637C4⋊C4—31no—
638C4⋊C4—61no—
639C4⋊C4—61no—
640C4⋊C4—91no—
641C4⋊C4—181no—
642C4⋊C4—181no—
643C4⋊C4C2×D3211yescharacteristic
644C22⋊C4—61no—
645C22⋊C4—61no—
646C22⋊C4—91no—
647C22⋊C4—91no—
648C22⋊C4—181no—
649C22⋊C4—181no—
650C22⋊C4—181no—
651C22⋊C4—181no—
652C22⋊C4—181no—
653C22⋊C4—181no—
654C22⋊C4—181no—
655C42—31no—
656C42—61no—
657C22×C3—22no—
658C22×C3—22no—
659C22×C3—21no—
660C22×C3—42no—
661C22×C3—41no—
662C22×C3—41no—
663C22×C3—41no—
664C22×C3—41no—
665C22×C3—61no—
666C22×C3—61no—
667C22×C3—61no—
668C22×C3—81no—
669C22×C3—81no—
670C22×C3C2×D3×D411yescharacteristic
671C22×C3C2×D3×D411yescharacteristic
672C2×D3—21no—
673C2×D3—21no—
674C2×D3—21no—
675C2×D3—32no—
676C2×D3—32no—
677C2×D3—62no—
678C2×D3—61no—
679C2×D3—61no—
680C2×D3—61no—
681C2×D3—61no—
682C2×D3—121no—
683C2×D3—121no—
684C2×D3—122no—
685C2×D3—121no—
686C2×D3—121no—
687C2×D3—121no—
688C2×D3—121no—
689C2×D3—121no—
690C2×D3—121no—
691C2×D3—121no—
692C2×D3—121no—
693C2×D3—121no—
694C2×D3—121no—
695C2×D3—121no—
696C2×D3—121no—
697C2×D3—241no—
698C2×D3—241no—
699C2×D3—241no—
700C2×D3—241no—
701C2×D3—241no—
702C2×D3—244no—
703C2×D3—244no—
704C2×D3—248no—
705C3×C4—21no—
706C3×C4—21no—
707C3×C4—41no—
708C3×C4—41no—
709C3×C4—61no—
710C3×C4—61no—
711C3×C4—61no—
712C3×C4—81no—
713C3×C4—121no—
714C3×C4—121no—
715C3×C4—121no—
716C3×C4—121no—
717C3×C4C2×#23511yescharacteristic
718C3×C4#100411yescharacteristic
719C3×C4C2×#23911yescharacteristic
720C3×C4#100911yescharacteristic
721Dic3—21no—
722Dic3—21no—
723Dic3—21no—
724Dic3—41no—
725Dic3—41no—
726Dic3—41no—
727Dic3—41no—
728Dic3—61no—
729Dic3—61no—
730Dic3—121no—
731C32#329711yescharacteristic, complemented, Sylow
732C23—21no—
733C23—31no—
734C23—91no—
735C23—181no—
736C23—181no—
737C23—362no—
738C23—362no—
739C23—721no—
740Q8—61no—
741Q8—61no—
742D4—21no—
743D4—122no—
744D4—182no—
745D4—181no—
746D4—181no—
747D4—181no—
748D4—181no—
749D4—362no—
750D4—362no—
751D4—721no—
752D4—721no—
753D4#379912yes—
754C2×C4—21no—
755C2×C4—31no—
756C2×C4—31no—
757C2×C4—31no—
758C2×C4—61no—
759C2×C4—61no—
760C2×C4—61no—
761C2×C4—61no—
762C2×C4—61no—
763C2×C4—61no—
764C2×C4—91no—
765C2×C4—122no—
766C2×C4—181no—
767C2×C4—181no—
768C2×C4—241no—
769C2×C4—721no—
770C2×C4—721no—
771C2×C4C22×D3211yescharacteristic
772C8—21no—
773C8—61no—
774C8—61no—
775C8—181no—
776C2×C3—21no—
777C2×C3—21no—
778C2×C3—21no—
779C2×C3—42no—
780C2×C3—42no—
781C2×C3—82no—
782C2×C3—121no—
783C2×C3#549011yescharacteristic
784C2×C3#563011yescharacteristic
785C2×C3D3×#13511yescharacteristic
786C2×C3D3×#13511yescharacteristic
787C2×C3#576911yescharacteristic
788C2×C3#577411yescharacteristic
789D3—41no—
790D3—62no—
791D3—62no—
792D3—122no—
793D3—242no—
794D3—241no—
795D3—241no—
796D3—241no—
797D3—241no—
798D3—481no—
799C22—22no—
800C22—41no—
801C22—41no—
802C22—61no—
803C22—61no—
804C22—61no—
805C22—92no—
806C22—181no—
807C22—181no—
808C22—361no—
809C22—361no—
810C22—361no—
811C22—361no—
812C22—361no—
813C22—361no—
814C22—724no—
815C22D32×D411yescharacteristic
816C4—41no—
817C4—61no—
818C4—61no—
819C4—61no—
820C4—121no—
821C4—121no—
822C4—121no—
823C4—121no—
824C4—181no—
825C4C2×#379911yescharacteristic
826C4#6431411yescharacteristic
827C3—21no—
828C3#7884611yescharacteristic, complemented
829C3#8118711yescharacteristic, complemented
830C2—42no—
831C2—121no—
832C2—182no—
833C2—721no—
834C2—721no—
835C2#1059418711yescharacteristic
836C2#1059473011yescharacteristic
837C2#1059475511yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
hypercenter#102D32
hypocenterC32#3297
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. #10595254C2semidirect
2. #10594578C2semidirect
3. #10592472C2semidirect
4. C3×#4772C2semidirect
5. C3×#4766C2semidirect
6. #10591452C2semidirect
7. #10591416C2semidirect
8. #10591400C2semidirect
9. #10590832C2semidirect
10. #10590770C2semidirect
11. #10590720C2semidirect
12. #10590689C2semidirect
13. #10590537C2semidirect
14. #10590523C2semidirect
15. #10590425C2semidirect
24. C2×C3×D3×C8C22semidirect
25. C3×#892C22semidirect
26. C3×#890C22semidirect
33. #63909C22semidirect
37. #63894C22semidirect
42. C2×#3717C22semidirect
49. C3×#818C22semidirect
50. C3×#816C22semidirect
51. C3×Dic3⋊C8C22semidirect
52. C3×#810C22semidirect
53. C3×#808C22semidirect
54. #63576C22semidirect
55. #63565C22semidirect
58. #63564C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. Dic3×C3⋊C8C22semidirect
87. #4772D3semidirect
90. #4766D3semidirect
176. C2×D3×C8C2×D3semidirect
188. #892C2×D3semidirect
191. #890C2×D3semidirect
222. #818C2×D3semidirect
223. #816C2×D3semidirect
224. Dic3⋊C8C2×D3semidirect
227. #810C2×D3semidirect
234. #808C2×D3semidirect
731. C32#3297semidirect
828. C3#78846semidirect
829. C3#81187semidirect

Maximal subgroups

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

subgroupindex
#105952542
#105945782
#105924722
C3×#47722
C3×#47662
#105914522
#105914162
#105914002
#105908322
#105907702
#105907202
#105906892
#105905372
#105905232
#105904252
#811873
#788463