Finite Group Databasebeta

← #11887013

Subgroups — #11887013

Order 1152.

1134 conjugacy classes of subgroups.

The subgroup lattice has 906 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595978C211yesmaximal, characteristic, complemented
2#10595069C211yesmaximal, characteristic, complemented
3C3×#4967C211yesmaximal, characteristic, complemented
4C2×C3×#809C211yesmaximal, characteristic, complemented
5#10591164C211yesmaximal, characteristic, complemented
6#10591162C211yesmaximal, characteristic, complemented
7#10591148C211yesmaximal, characteristic, complemented
8#10590598C211yesmaximal, characteristic, complemented
9#10590593C211yesmaximal, characteristic, complemented
10#10590552C211yesmaximal, characteristic, complemented
11#10590551C211yesmaximal, characteristic, complemented
12#10590510C211yesmaximal, characteristic, complemented
13#10590509C211yesmaximal, characteristic, complemented
14#10590471C211yesmaximal, characteristic, complemented
15#10590459C211yesmaximal, characteristic, complemented
16#81302—31nomaximal
17#78757—31nomaximal
18C2×#3828—21no—
19C22×C3×D12C2211yescharacteristic
20C2×D3×#67—21no—
21C2×#3802C2211yescharacteristic
22C2×C32×C4⋊C4C2211yescharacteristic, complemented
23#64139C2211yescharacteristic, complemented
24#64138—21no—
25C4×#638C2211yescharacteristic
26#64105—21no—
27#64104C2211yescharacteristic, complemented
28#64103—21no—
29#64102C2211yescharacteristic, complemented
30C4⋊C4×C3⋊D3C2211yescharacteristic, complemented
31#64097C2211yescharacteristic, complemented
32C3×#930C2211yescharacteristic
33C22×C3×C3⋊C8C2211yescharacteristic, complemented
34#63976—21no—
35#63922—21no—
36#63916C2211yescharacteristic
37#63914C2211yescharacteristic
38#63898C2211yescharacteristic
39#63885—21no—
40C2×#3714C2211yescharacteristic
41C2×#3714C2211yescharacteristic, complemented
42C2×#3714C2211yescharacteristic, complemented
43C2×#3710C2211yescharacteristic, complemented
44C3×#830C2211yescharacteristic, complemented
45C3×#809C2211yescharacteristic
46C3×#809C2211yescharacteristic
47C3×#809C2211yescharacteristic, complemented
48C3×#809C2211yescharacteristic, complemented
49C3×#809C2211yescharacteristic, complemented
50C3×#809C2211yescharacteristic, complemented
51C3×#807C2211yescharacteristic, complemented
52C3×#807C2211yescharacteristic, complemented
53#63575C2211yescharacteristic, complemented
54#63572C2211yescharacteristic, complemented
55#63564C2211yescharacteristic, complemented
56#63563C2211yescharacteristic
57#63563C2211yescharacteristic, complemented
58#63563C2211yescharacteristic, complemented
59#63557C2211yescharacteristic, complemented
60#63553C2211yescharacteristic, complemented
61D4×#67—31no—
62#5609—31no—
63#5507—31no—
64#5507—31no—
65#5507—61no—
66C3×#480—31no—
67C2×C3×#102—31no—
68#5217—31no—
69#5115—31no—
70C8×#67—31no—
71#5038—31no—
72#4967D311yescharacteristic, complemented
73C2×#809D311yescharacteristic, complemented
74#4890—31no—
75#4883—31no—
76#4882—31no—
77#4872—31no—
78#4786—31no—
79#4786—31no—
80#4775—31no—
81#4774—31no—
82#4773—31no—
83#4773—31no—
84D3×#102—31no—
85D3×#102—31no—
86#4760—31no—
87#4760—31no—
88#4759—31no—
89#4756—31no—
90#4732—31no—
91#67⋊C8—31no—
92C23×C3×D3—21no—
93C22×D32—21no—
94C22×C32×C4—21no—
95C22×C32×C4C2311yescharacteristic
96C2×#638—21no—
97C2×#638D411yescharacteristic
98#3828—44no—
99C2×C4⋊(C3⋊D3)—21no—
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C4×C3⋊D3—21no—
102C2×C4×C3⋊D3—21no—
103C2×C4×C3⋊D3C2311yescharacteristic
104C2×#634—21no—
105C2×C3×#67—21no—
106C2×C3×D12—22no—
107C2×C3×D12—21no—
108C2×C3×D12—41no—
109C2×C3×D12C2311yescharacteristic
110C2×C3×D12C2311yescharacteristic
111C2×C3×D12C2311yescharacteristic
112D3×#67—44no—
113C2×#626—21no—
114C2×#625—21no—
115C2×#625—21no—
116C2×#625—21no—
117C2×D3×Dic3—21no—
118#3802—22no—
119#3802—41no—
120C32×C4⋊C4—21no—
121C32×C4⋊C4C2311yescharacteristic
122C32×C4⋊C4C2311yescharacteristic
123#3757D411yescharacteristic
124#3752—21no—
125#3752—21no—
126#3752—21no—
127#3752D411yescharacteristic
128C4⋊(C3⋊Dic3)C2311yescharacteristic
129#3750—21no—
130#3750—21no—
131#3750D411yescharacteristic
132C4×C3⋊Dic3C2311yescharacteristic
133C3×(C2×D3)⋊C4—21no—
134C3×C4⋊Dic3C2311yescharacteristic
135C2×C3×C3⋊C8—41no—
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142#3714—22no—
143#3714—41no—
144#3714—41no—
145#3710—41no—
146#3294—91noSylow
147C22×C3×D4—31no—
148C22×#67—61no—
149C2×D3×D4—31no—
150C2×D3×D4—31no—
151C2×D3×D4—61no—
152C2×#235—61no—
153C2×#235—61no—
154C2×#235—62no—
155C22×D12C2×D311yescharacteristic
156C22×C3×C8—31no—
157C3×#121—31no—
158C2×C3×C4⋊C4—21no—
159C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
160C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
161#953—61no—
162#940—31no—
163#940—31no—
164#939—61no—
165#938—31no—
166#937—61no—
167#937—61no—
168D4×Dic3—31no—
169C2×#213—31no—
170C2×#213—31no—
171C2×#213—31no—
172#930—31no—
173#930—31no—
174#930—61no—
175#930C2×D311yescharacteristic
176#929—61no—
177#929—61no—
178#929—62no—
179C4×#67—31no—
180C4×#67—31no—
181C4×#67—61no—
182C22×C3⋊C8C2×D311yescharacteristic, complemented
183C2×D24—31no—
184C2×D24—31no—
185C2×D24—31no—
186C2×D3×C8—31no—
187C2×D3×C8—31no—
188#896—61no—
189#896—61no—
190#896—62no—
191#895—31no—
192#895—31no—
193#895—31no—
194#895—61no—
195#894—61no—
196#894—61no—
197#894—62no—
198#893—31no—
199#893—31no—
200#893—31no—
201#893—61no—
202D3×C4⋊C4—31no—
203D3×C4⋊C4—31no—
204D3×C4⋊C4—61no—
205#888—31no—
206#888—31no—
207#888—61no—
208#884—61no—
209#882—61no—
210C3×#107—31no—
211C3×#107—31no—
212C3×#102—31no—
213C3×#102—31no—
214C3×#102—31no—
215C3×#102—31no—
216C3×#102—31no—
217C3×#102—31no—
218C3×C22⋊C8—31no—
219#832—31no—
220#832—31no—
221#832—31no—
222#830C2×D311yescharacteristic, complemented
223#821—31no—
224#821—31no—
225#821—31no—
226#821—31no—
227(C2×D3)⋊C8—31no—
228(C2×D3)⋊C8—31no—
229#818—31no—
230Dic3⋊C8—31no—
231Dic3⋊C8—31no—
232C8×Dic3—31no—
233C8×Dic3—31no—
234#809—31no—
235#809C2×D311yescharacteristic
236#809C2×D311yescharacteristic
237#809C2×D311yescharacteristic, complemented
238#809C2×D311yescharacteristic, complemented
239#809C2×D311yescharacteristic, complemented
240#809C2×D311yescharacteristic, complemented
241#807—31no—
242#807C2×D311yescharacteristic, complemented
243#807C2×D311yescharacteristic, complemented
244C23×C32C2×D411yescharacteristic
245C22×C3⋊D3—21no—
246C22×C3⋊D3C2×D411yescharacteristic
247C22×C3×D3—21no—
248C22×C3×D3—21no—
249C22×C3×D3—21no—
250C22×C3×D3—42no—
251C22×C3×D3—42no—
252C22×C3×D3—81no—
253C2×D32—42no—
254C2×D32—42no—
255C2×D32—81no—
256C2×C32×C4—21no—
257C2×C32×C4—21no—
258C2×C32×C4—21no—
259C2×C32×C4—21no—
260C2×C32×C4—42no—
261C2×C32×C4C2×D411yescharacteristic
262C2×C32×C4C2411yescharacteristic
263#638—42no—
264#638D814yescomplemented
265C2×C3⋊Dic3—21no—
266C2×C3⋊Dic3C2×D411yescharacteristic
267C2×C3⋊Dic3C2×D411yescharacteristic
268C2×C3⋊Dic3C2×D411yescharacteristic
269C4⋊(C3⋊D3)—21no—
270C4⋊(C3⋊D3)—21no—
271C4⋊(C3⋊D3)—42no—
272C4×C3⋊D3—21no—
273C4×C3⋊D3—21no—
274C4×C3⋊D3—42no—
275C4×C3⋊D3—42no—
276#634—42no—
277C3×#67—42no—
278C2×C3×Dic3—21no—
279C3×D12—21no—
280C3×D12—21no—
281C3×D12—21no—
282C3×D12—21no—
283C3×D12—21no—
284C3×D12—42no—
285C3×D12#4112yescomplemented
286#626—42no—
287#625—42no—
288#625—42no—
289#625—81no—
290D3×Dic3—42no—
291C3×C3⋊C8—21no—
292C3×C3⋊C8—21no—
293C3×C3⋊C8—21no—
294C3×C3⋊C8—21no—
295#547—91no—
296D42—91no—
297#486—91no—
298#480—31no—
299#480—91no—
300#474—91no—
301#466—91no—
302#466—91no—
303#459—91no—
304#447—91no—
305#447—91no—
306C4×D8—91no—
307C8×D4—91no—
308C2×#102—31no—
309C2×#102—91no—
310C24×C3—61no—
311C23×D3—21no—
312C23×D3—61no—
313C23×D3—61no—
314C2×C3×D4—31no—
315C2×C3×D4—31no—
316C2×C3×D4—31no—
317C2×C3×D4—62no—
318C2×C3×D4—61no—
319C2×C3×D4—61no—
320C2×C3×D4—121no—
321C22×C3×C4—22no—
322C22×C3×C4—21no—
323C22×C3×C4—21no—
324C22×C3×C4—21no—
325C22×C3×C4C22×D311yescharacteristic
326C22×C3×C4C22×D311yescharacteristic
327C2×#67—21no—
328C2×#67—31no—
329C2×#67—31no—
330C2×#67—61no—
331C2×#67—61no—
332C2×#67—61no—
333C2×#67—61no—
334C2×#67—61no—
335C2×#67—61no—
336C2×#67—61no—
337C2×#67—61no—
338C2×#67—62no—
339C2×#67—61no—
340C2×#67—61no—
341C2×#67—124no—
342C22×Dic3—61no—
343D3×D4—62no—
344D3×D4—62no—
345D3×D4—121no—
346D3×D4—121no—
347D3×D4—124no—
348#235—124no—
349#235—124no—
350#235—128no—
351C2×D12—22no—
352C2×D12—21no—
353C2×D12—31no—
354C2×D12—31no—
355C2×D12—41no—
356C2×D12—61no—
357C2×D12—61no—
358C2×D12—61no—
359C2×D12—62no—
360C2×D12—61no—
361C2×D12C22×D311yescharacteristic
362C2×D12C22×D311yescharacteristic
363C2×D12C22×D311yescharacteristic
364C2×C4×D3—31no—
365C2×C4×D3—31no—
366C2×C4×D3—61no—
367C2×C4×D3—61no—
368C2×C4×D3—61no—
369C2×C4×D3—61no—
370C2×C4×D3—61no—
371C2×C4×D3—61no—
372C2×C4×D3—62no—
373C2×C4×D3—62no—
374C2×Dic6—61no—
375C2×Dic6—61no—
376C2×Dic6—62no—
377C2×C3×C8—31no—
378C2×C3×C8—31no—
379C2×C3×C8—31no—
380C2×C3×C8—31no—
381C2×C3×C8—121no—
382C3×C4⋊C4—22no—
383C3×C4⋊C4—21no—
384C3×C4⋊C4—21no—
385C3×C4⋊C4—21no—
386C3×C4⋊C4—21no—
387C3×C4⋊C4—31no—
388C3×C4⋊C4C22×D311yescharacteristic
389C3×C4⋊C4C22×D311yescharacteristic
390C3×C4⋊C4C22×D311yescharacteristic
391C3×C4⋊C4C22×D311yescharacteristic
392C3×C22⋊C4—61no—
393#217—31no—
394#217—31no—
395#217—61no—
396#217—61no—
397#217—61no—
398#213—62no—
399#213—121no—
400#213—121no—
401(C2×D3)⋊C4—21no—
402(C2×D3)⋊C4—31no—
403(C2×D3)⋊C4—31no—
404(C2×D3)⋊C4—61no—
405(C2×D3)⋊C4—61no—
406(C2×D3)⋊C4—61no—
407(C2×D3)⋊C4—61no—
408(C2×D3)⋊C4—61no—
409(C2×D3)⋊C4—61no—
410(C2×D3)⋊C4—61no—
411(C2×D3)⋊C4—62no—
412(C2×D3)⋊C4—62no—
413(C2×D3)⋊C4—62no—
414(C2×D3)⋊C4—61no—
415(C2×D3)⋊C4—61no—
416C4⋊Dic3—31no—
417C4⋊Dic3—31no—
418C4⋊Dic3—61no—
419C4⋊Dic3C22×D311yescharacteristic
420Dic3⋊C4—31no—
421Dic3⋊C4—31no—
422Dic3⋊C4—61no—
423Dic3⋊C4—61no—
424Dic3⋊C4—61no—
425Dic3⋊C4—61no—
426Dic3⋊C4—61no—
427Dic3⋊C4—62no—
428Dic3⋊C4—62no—
429C4×Dic3—31no—
430C4×Dic3—31no—
431C4×Dic3—61no—
432C2×C3⋊C8—41no—
433C2×C3⋊C8C22×D311yescharacteristic
434C2×C3⋊C8C22×D311yescharacteristic
435C2×C3⋊C8C22×D311yescharacteristic
436C2×C3⋊C8C22×D311yescharacteristic
437D24—62no—
438D24—121no—
439D24—121no—
440D3×C8—121no—
441D3×C8—121no—
442C22×C32—21no—
443C22×C32—21no—
444C22×C32C2×D812yes—
445C22×C32C22×D411yescharacteristic
446C2×C3⋊D3—21no—
447C2×C3⋊D3—21no—
448C2×C3⋊D3—41no—
449C2×C3⋊D3—41no—
450C2×C3⋊D3—41no—
451C2×C3⋊D3C2×D812yes—
452C2×C3×D3—22no—
453C2×C3×D3—41no—
454C2×C3×D3—41no—
455C2×C3×D3—41no—
456C2×C3×D3—41no—
457C2×C3×D3—41no—
458C2×C3×D3—41no—
459C2×C3×D3—41no—
460C2×C3×D3—41no—
461C2×C3×D3—84no—
462D32—84no—
463C32×C4—21no—
464C32×C4—41no—
465C32×C4—41no—
466C32×C4C2×#4111yescharacteristic
467C32×C4H(5,𝔽2)11yescharacteristic
468C3⋊Dic3—21no—
469C3⋊Dic3—21no—
470C3⋊Dic3—41no—
471C3⋊Dic3C2×D812yes—
472C3×Dic3—41no—
473C2×#41—181no—
474C22×D4—31no—
475C22×D4—91no—
476C22×D4—181no—
477C2×D8—91no—
478C2×D8—91no—
479C2×D8—91no—
480C22×C8—31no—
481C22×C8—91no—
482C4⋊Q8—91no—
483#127—91no—
484#123—181no—
485#123—181no—
486C22⋊Q8—181no—
487#121—31no—
488#121—91no—
489#121—91no—
490#121—91no—
491#121—181no—
492#120—181no—
493#120—181no—
494C4×D4—91no—
495C4×D4—91no—
496C4×D4—91no—
497C2×C4⋊C4—91no—
498C2×C4⋊C4D3211yescharacteristic, complemented
499#107—31no—
500#107—31no—
501#107—91no—
502C4⋊C8—91no—
503#102—31no—
504#102—31no—
505#102—31no—
506#102—31no—
507#102—31no—
508#102—31no—
509#102—91no—
510#102—91no—
511#102—91no—
512#102—91no—
513C22⋊C8—31no—
514C22⋊C8—91no—
515C4×C8—91no—
516C23×C3—21no—
517C23×C3—61no—
518C23×C3—61no—
519C23×C3—61no—
520C23×C3—122no—
521C23×C3—122no—
522C23×C3—241no—
523C23×C3D3×D411yescharacteristic
524C23×C3D3×D411yescharacteristic
525C22×D3—21no—
526C22×D3—21no—
527C22×D3—21no—
528C22×D3—31no—
529C22×D3—31no—
530C22×D3—42no—
531C22×D3—42no—
532C22×D3—61no—
533C22×D3—62no—
534C22×D3—61no—
535C22×D3—61no—
536C22×D3—81no—
537C22×D3—122no—
538C22×D3—122no—
539C22×D3—122no—
540C22×D3—122no—
541C22×D3—241no—
542C22×D3—241no—
543C3×D4—32no—
544C3×D4—61no—
545C3×D4—61no—
546C3×D4—61no—
547C3×D4—61no—
548C3×D4—61no—
549C3×D4—122no—
550C3×D4—122no—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4—22no—
556C2×C3×C4—22no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—41no—
564C2×C3×C4—41no—
565C2×C3×C4—44no—
566C2×C3×C4—42no—
567C2×C3×C4—42no—
568C2×C3×C4—61no—
569C2×C3×C4D3×D411yescharacteristic
570C2×C3×C4D3×D411yescharacteristic
571C2×C3×C4C23×D311yescharacteristic
572C2×C3×C4C23×D311yescharacteristic
573#67—34no—
574#67—34no—
575#67—42no—
576#67—64no—
577#67—122no—
578#67—122no—
579#67—122no—
580#67—122no—
581#67—122no—
582#67—124no—
583#67—122no—
584#67—122no—
585#67—241no—
586#67—241no—
587C2×Dic3—21no—
588C2×Dic3—31no—
589C2×Dic3—31no—
590C2×Dic3—31no—
591C2×Dic3—31no—
592C2×Dic3—31no—
593C2×Dic3—31no—
594C2×Dic3—61no—
595C2×Dic3—61no—
596C2×Dic3—61no—
597C2×Dic3—62no—
598C2×Dic3—61no—
599C2×Dic3—61no—
600C2×Dic3—122no—
601D12—21no—
602D12—21no—
603D12—21no—
604D12—21no—
605D12—21no—
606D12—42no—
607D12—61no—
608D12—61no—
609D12—61no—
610D12—61no—
611D12—121no—
612D12—121no—
613D12—122no—
614D12—122no—
615D12—124no—
616D12—122no—
617D12#23512yescomplemented
618C4×D3—61no—
619C4×D3—61no—
620C4×D3—61no—
621C4×D3—61no—
622C4×D3—121no—
623C4×D3—121no—
624C4×D3—122no—
625C4×D3—122no—
626C4×D3—122no—
627C4×D3—124no—
628C4×D3—122no—
629C4×D3—122no—
630C4×D3—124no—
631Dic6—122no—
632Dic6—122no—
633Dic6—124no—
634C3×C8—61no—
635C3×C8—61no—
636C3×C8—61no—
637C3×C8—61no—
638C3⋊C8—21no—
639C3⋊C8—21no—
640C3⋊C8—21no—
641C3⋊C8—21no—
642C2×C32—22no—
643C2×C32#54611yescharacteristic
644C2×C32C22×D811yescharacteristic
645C2×C32#57711yescharacteristic
646C3⋊D3—22no—
647C3⋊D3—81no—
648C3×D3—42no—
649C3×D3—81no—
650C3×D3—81no—
651C24—61no—
652C24—181no—
653#41—364no—
654C2×Q8—181no—
655C2×D4—31no—
656C2×D4—31no—
657C2×D4—31no—
658C2×D4—62no—
659C2×D4—61no—
660C2×D4—61no—
661C2×D4—91no—
662C2×D4—91no—
663C2×D4—121no—
664C2×D4—181no—
665C2×D4—181no—
666C2×D4—181no—
667C2×D4—181no—
668C2×D4—181no—
669C2×D4—182no—
670C2×D4—181no—
671C2×D4—361no—
672C2×D4—364no—
673C22×C4—21no—
674C22×C4—91no—
675C22×C4—181no—
676C22×C4—181no—
677C22×C4—181no—
678C22×C4C2×D3211yescharacteristic
679D8—182no—
680D8—361no—
681D8—361no—
682C2×C8—31no—
683C2×C8—31no—
684C2×C8—31no—
685C2×C8—31no—
686C2×C8—121no—
687C2×C8—361no—
688C4⋊C4—21no—
689C4⋊C4—31no—
690C4⋊C4—91no—
691C4⋊C4—91no—
692C4⋊C4—181no—
693C4⋊C4—181no—
694C4⋊C4C2×D3211yescharacteristic
695C4⋊C4C2×D3211yescharacteristic
696C22⋊C4—61no—
697C22⋊C4—91no—
698C22⋊C4—91no—
699C22⋊C4—181no—
700C22⋊C4—181no—
701C22⋊C4—181no—
702C22⋊C4—181no—
703C22⋊C4—181no—
704C42—91no—
705C22×C3—21no—
706C22×C3—21no—
707C22×C3—21no—
708C22×C3—21no—
709C22×C3—21no—
710C22×C3—22no—
711C22×C3—41no—
712C22×C3—41no—
713C22×C3—62no—
714C22×C3—121no—
715C22×C3—121no—
716C22×C3—121no—
717C22×C3—121no—
718C22×C3—121no—
719C22×C3—121no—
720C22×C3—121no—
721C22×C3—121no—
722C22×C3—244no—
723C22×C3D3×D812yes—
724C22×C3D3×D812yes—
725C22×C3C2×D3×D411yescharacteristic
726C22×C3C2×D3×D411yescharacteristic
727C2×D3—22no—
728C2×D3—32no—
729C2×D3—32no—
730C2×D3—41no—
731C2×D3—41no—
732C2×D3—41no—
733C2×D3—41no—
734C2×D3—41no—
735C2×D3—41no—
736C2×D3—41no—
737C2×D3—41no—
738C2×D3—62no—
739C2×D3—61no—
740C2×D3—61no—
741C2×D3—61no—
742C2×D3—61no—
743C2×D3—84no—
744C2×D3—121no—
745C2×D3—121no—
746C2×D3—122no—
747C2×D3—122no—
748C2×D3—122no—
749C2×D3—121no—
750C2×D3—121no—
751C2×D3—121no—
752C2×D3—121no—
753C2×D3—121no—
754C2×D3—121no—
755C2×D3—244no—
756C2×D3—244no—
757C3×C4—21no—
758C3×C4—21no—
759C3×C4—21no—
760C3×C4—21no—
761C3×C4—41no—
762C3×C4—42no—
763C3×C4—42no—
764C3×C4—41no—
765C3×C4—41no—
766C3×C4—41no—
767C3×C4—41no—
768C3×C4—121no—
769C3×C4C2×#23511yescharacteristic
770C3×C4#100411yescharacteristic
771C3×C4D3×#4111yescharacteristic
772C3×C4#100911yescharacteristic
773Dic3—32no—
774Dic3—32no—
775Dic3—41no—
776Dic3—62no—
777Dic3—61no—
778Dic3—61no—
779Dic3—61no—
780Dic3—61no—
781Dic3—121no—
782Dic3—121no—
783Dic3—122no—
784Dic3—121no—
785Dic3—121no—
786C32#329411yescharacteristic, complemented, Sylow
787C23—61no—
788C23—61no—
789C23—61no—
790C23—91no—
791C23—122no—
792C23—122no—
793C23—181no—
794C23—241no—
795C23—362no—
796C23—362no—
797C23—721no—
798C23#381111yescharacteristic
799Q8—362no—
800D4—32no—
801D4—61no—
802D4—61no—
803D4—61no—
804D4—61no—
805D4—61no—
806D4—94no—
807D4—122no—
808D4—122no—
809D4—181no—
810D4—181no—
811D4—362no—
812D4—362no—
813D4—362no—
814D4—362no—
815D4—362no—
816D4—721no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—42no—
822C2×C4—61no—
823C2×C4—91no—
824C2×C4—91no—
825C2×C4—91no—
826C2×C4—181no—
827C2×C4—181no—
828C2×C4—181no—
829C2×C4—362no—
830C2×C4—362no—
831C2×C4—362no—
832C2×C4#381111yescharacteristic
833C2×C4C22×D3211yescharacteristic
834C8—61no—
835C8—61no—
836C8—61no—
837C8—61no—
838C2×C3—22no—
839C2×C3—22no—
840C2×C3—21no—
841C2×C3—21no—
842C2×C3—21no—
843C2×C3—42no—
844C2×C3—122no—
845C2×C3—241no—
846C2×C3—241no—
847C2×C3#549011yescharacteristic
848C2×C3#565411yescharacteristic
849C2×C3C2×D3×D811yescharacteristic
850C2×C3C2×D3×D811yescharacteristic
851C2×C3#576211yescharacteristic
852C2×C3#577811yescharacteristic
853D3—42no—
854D3—62no—
855D3—62no—
856D3—81no—
857D3—81no—
858D3—122no—
859D3—242no—
860D3—241no—
861D3—241no—
862C22—21no—
863C22—21no—
864C22—62no—
865C22—92no—
866C22—121no—
867C22—121no—
868C22—121no—
869C22—121no—
870C22—121no—
871C22—121no—
872C22—121no—
873C22—121no—
874C22—181no—
875C22—181no—
876C22—244no—
877C22—361no—
878C22—361no—
879C22—361no—
880C22—724no—
881C22#6392612yes—
882C22C2×#381111yescharacteristic
883C4—21no—
884C4—41no—
885C4—41no—
886C4—92no—
887C4—121no—
888C4—181no—
889C4—181no—
890C4—361no—
891C4D3×#23511yescharacteristic
892C4#6430711yescharacteristic
893C3—21no—
894C3#7875711yescharacteristic, complemented
895C3#8130211yescharacteristic, complemented
896C2—22no—
897C2—122no—
898C2—182no—
899C2—241no—
900C2—241no—
901C2—721no—
902C2#1059507711yescharacteristic
903C2C2×#6392611yescharacteristic
904C2#1059532411yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
hypercenterC2×C4⋊C4D32
hypocenterC32#3294
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #10595978C2semidirect
2. #10595069C2semidirect
3. C3×#4967C2semidirect
4. C2×C3×#809C2semidirect
5. #10591164C2semidirect
6. #10591162C2semidirect
7. #10591148C2semidirect
8. #10590598C2semidirect
9. #10590593C2semidirect
10. #10590552C2semidirect
11. #10590551C2semidirect
12. #10590510C2semidirect
13. #10590509C2semidirect
14. #10590471C2semidirect
15. #10590459C2semidirect
22. C2×C32×C4⋊C4C22semidirect
23. #64139C22semidirect
27. #64104C22semidirect
29. #64102C22semidirect
30. C4⋊C4×C3⋊D3C22semidirect
31. #64097C22semidirect
33. C22×C3×C3⋊C8C22semidirect
41. C2×#3714C22semidirect
42. C2×#3714C22semidirect
43. C2×#3710C22semidirect
44. C3×#830C22semidirect
47. C3×#809C22semidirect
48. C3×#809C22semidirect
49. C3×#809C22semidirect
50. C3×#809C22semidirect
51. C3×#807C22semidirect
52. C3×#807C22semidirect
53. #63575C22semidirect
54. #63572C22semidirect
55. #63564C22semidirect
57. #63563C22semidirect
58. #63563C22semidirect
59. #63557C22semidirect
60. #63553C22semidirect
72. #4967D3semidirect
73. C2×#809D3semidirect
159. C2×C3×C4⋊C4C2×D3semidirect
160. C2×C3×C4⋊C4C2×D3semidirect
182. C22×C3⋊C8C2×D3semidirect
222. #830C2×D3semidirect
237. #809C2×D3semidirect
238. #809C2×D3semidirect
239. #809C2×D3semidirect
240. #809C2×D3semidirect
242. #807C2×D3semidirect
243. #807C2×D3semidirect
264. #638D8semidirect
285. C3×D12#41semidirect
498. C2×C4⋊C4D32semidirect
617. D12#235semidirect
786. C32#3294semidirect
894. C3#78757semidirect
895. C3#81302semidirect

Maximal subgroups

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

subgroupindex
#105959782
#105950692
C3×#49672
C2×C3×#8092
#105911642
#105911622
#105911482
#105905982
#105905932
#105905522
#105905512
#105905102
#105905092
#105904712
#105904592
#813023
#787573