Finite Group Databasebeta

← #11887007

Subgroups — #11887007

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#10596082C211yesmaximal, characteristic, complemented
2#10595069C211yesmaximal, characteristic, complemented
3C3×#5038C211yesmaximal, characteristic, complemented
4C3×#5036C211yesmaximal, characteristic, complemented
5#10591516C211yesmaximal, characteristic, complemented
6#10591486C211yesmaximal, characteristic, complemented
7#10591455C211yesmaximal, characteristic, complemented
8#10591435C211yesmaximal, characteristic, complemented
9#10591148C211yesmaximal, characteristic, complemented
10#10591094C211yesmaximal, characteristic, complemented
11C2×#63563C211yesmaximal, characteristic, complemented
12#10590593C211yesmaximal, characteristic, complemented
13#10590552C211yesmaximal, characteristic, complemented
14#10590510C211yesmaximal, characteristic, complemented
15#10590471C211yesmaximal, characteristic, complemented
16#80731—31nomaximal
17#80014—31nomaximal
18C2×#3830—21no—
19C22×C3×D12C2211yescharacteristic
20C2×D3×#67—21no—
21C2×#3802C2211yescharacteristic
22C32×#121C2211yescharacteristic, complemented
23#64147C2211yescharacteristic, complemented
24#64144—21no—
25D4×C3⋊Dic3C2211yescharacteristic, complemented
26C4×#638C2211yescharacteristic
27C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
28C4⋊C4×C3⋊D3C2211yescharacteristic, complemented
29#64097C2211yescharacteristic, complemented
30#64092—21no—
31#64087—21no—
32C2×C3×#213C2211yescharacteristic
33C2×C3×#213C2211yescharacteristic, complemented
34C2×C3×#213C2211yescharacteristic, complemented
35C3×#930C2211yescharacteristic
36C22×C3×C3⋊C8C2211yescharacteristic, complemented
37#63976—21no—
38#63922—21no—
39#63916C2211yescharacteristic
40#63914C2211yescharacteristic
41#63898C2211yescharacteristic
42#63885—21no—
43C2×#3710C2211yescharacteristic, complemented
44C3×#832C2211yescharacteristic, complemented
45C3×#830C2211yescharacteristic, complemented
46C3×#809C2211yescharacteristic
47C3×#809C2211yescharacteristic, complemented
48C3×#809C2211yescharacteristic, complemented
49C3×#807C2211yescharacteristic, complemented
50#63575C2211yescharacteristic, complemented
51#63575C2211yescharacteristic, complemented
52#63572C2211yescharacteristic, complemented
53#63563C2211yescharacteristic
54#63563C2211yescharacteristic
55#63563C2211yescharacteristic, complemented
56#63563C2211yescharacteristic, complemented
57#63563C2211yescharacteristic, complemented
58#63563C2211yescharacteristic, complemented
59#63557C2211yescharacteristic, complemented
60#63553C2211yescharacteristic, complemented
61D4×#67—31no—
62#5611—31no—
63#5611—31no—
64#5611—61no—
65#5609—31no—
66C3×#466—31no—
67C3×#447—31no—
68C2×#832—31no—
69#5157—31no—
70#5156—31no—
71#5156—31no—
72#5150—31no—
73#5150—31no—
74Dic3×D8—31no—
75C2×#821—31no—
76C8×#67—31no—
77#5038D311yescharacteristic, complemented
78#5036D311yescharacteristic, complemented
79#5033—31no—
80#4890—31no—
81#4882—31no—
82#4775—31no—
83#4774—31no—
84D3×#102—31no—
85D3×#102—31no—
86#4760—31no—
87#4760—31no—
88#4759—31no—
89#4756—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×#638D411yescharacteristic
99C22×C3⋊Dic3—21no—
100C22×C3⋊Dic3—21no—
101#3830—44no—
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⋊C4C2311yescharacteristic
121C32×C22⋊C4—21no—
122#3757—21no—
123#3757—21no—
124#3757D411yescharacteristic
125#3752D411yescharacteristic
126C4⋊(C3⋊Dic3)—21no—
127C4⋊(C3⋊Dic3)C2311yescharacteristic
128C4⋊(C3⋊Dic3)C2311yescharacteristic
129#3750—21no—
130#3750—21no—
131#3750D411yescharacteristic
132C4×C3⋊Dic3C2311yescharacteristic
133C3×#213—22no—
134C3×#213—41no—
135C3×#213—41no—
136C3×(C2×D3)⋊C4—21no—
137C3×C4⋊Dic3C2311yescharacteristic
138C2×C3×C3⋊C8—41no—
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143(C2×D3)⋊Dic3—21no—
144(C2×D3)⋊Dic3—21no—
145#3710—41no—
146#3294—91noSylow
147C22×C3×D4—31no—
148C22×#67—61no—
149C2×#237—61no—
150C2×#237—61no—
151C2×#237—62no—
152C2×D3×D4—31no—
153C2×D3×D4—31no—
154C2×D3×D4—61no—
155C22×D12C2×D311yescharacteristic
156C2×C3×D8—31no—
157C2×C3×D8—31no—
158C2×C3×D8—31no—
159C22×C3×C8—31no—
160C3×#121—21no—
161C3×#121—31no—
162C3×#121C2×D311yescharacteristic, complemented
163C3×#121C2×D311yescharacteristic, complemented
164#953—61no—
165#940—31no—
166#940—31no—
167#939—61no—
168#938—31no—
169#938—31no—
170#938—31no—
171#938—61no—
172#937—61no—
173#937—61no—
174#935—61no—
175#935—61no—
176#935—62no—
177D4×Dic3—31no—
178D4×Dic3—31no—
179D4×Dic3—31no—
180D4×Dic3—61no—
181C2×#213C2×D311yescharacteristic
182C2×#213C2×D311yescharacteristic, complemented
183C2×#213C2×D311yescharacteristic, complemented
184#930C2×D311yescharacteristic
185C4×#67—31no—
186C4×#67—31no—
187C4×#67—61no—
188C2×C4⋊Dic3—31no—
189C2×C4⋊Dic3—31no—
190C2×C4⋊Dic3—61no—
191C22×C3⋊C8C2×D311yescharacteristic, complemented
192C2×D3×C8—31no—
193C2×D3×C8—31no—
194#895—31no—
195#893—31no—
196D3×C4⋊C4—31no—
197D3×C4⋊C4—31no—
198D3×C4⋊C4—61no—
199#888—31no—
200#888—31no—
201#888—61no—
202#884—61no—
203#883—61no—
204#883—61no—
205#883—62no—
206#882—61no—
207#878—61no—
208#878—61no—
209#878—62no—
210C3×#107—31no—
211C3×#102—31no—
212C3×#102—31no—
213C3×#102—31no—
214C3×#102—31no—
215C3×C22⋊C8—31no—
216#832—31no—
217#832—31no—
218#832—31no—
219#832—31no—
220#832—31no—
221#832—31no—
222#832C2×D311yescharacteristic, complemented
223#830C2×D311yescharacteristic, complemented
224#821—31no—
225#821—31no—
226#821—31no—
227#821—31no—
228#821—31no—
229#821—31no—
230(C2×D3)⋊C8—31no—
231(C2×D3)⋊C8—31no—
232#818—31no—
233#818—31no—
234Dic3⋊C8—31no—
235Dic3⋊C8—31no—
236C8×Dic3—31no—
237C8×Dic3—31no—
238#809C2×D311yescharacteristic
239#809C2×D311yescharacteristic, complemented
240#809C2×D311yescharacteristic, complemented
241#807—31no—
242#807—31no—
243#807C2×D311yescharacteristic, complemented
244C23×C32—21no—
245C23×C32C2×D411yescharacteristic
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—
256C32×D4—21no—
257C32×D4—21no—
258C32×D4—42no—
259C2×C32×C4—21no—
260C2×C32×C4—21no—
261C2×C32×C4—21no—
262C2×C32×C4C2×D411yescharacteristic
263C2×C32×C4C2411yescharacteristic
264#638—42no—
265#638D814yescomplemented
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
273C4×C3⋊D3—21no—
274C4×C3⋊D3—21no—
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—91no—
299#480—91no—
300#474—91no—
301#466—31no—
302#466—91no—
303#459—91no—
304#447—31no—
305#447—91no—
306C4×D8—91no—
307C8×D4—91no—
308C2×#102—91no—
309C2×#102—91no—
310C24×C3—61no—
311C23×D3—21no—
312C23×D3—61no—
313C23×D3—61no—
314C2×C3×D4—22no—
315C2×C3×D4—21no—
316C2×C3×D4—21no—
317C2×C3×D4—21no—
318C2×C3×D4—31no—
319C2×C3×D4—31no—
320C2×C3×D4—31no—
321C2×C3×D4—62no—
322C2×C3×D4—61no—
323C2×C3×D4—61no—
324C2×C3×D4—121no—
325C2×C3×D4C22×D311yescharacteristic
326C2×C3×D4C22×D311yescharacteristic
327C22×C3×C4—21no—
328C22×C3×C4C22×D311yescharacteristic
329C22×C3×C4C22×D311yescharacteristic
330C2×#67—21no—
331C2×#67—31no—
332C2×#67—31no—
333C2×#67—61no—
334C2×#67—61no—
335C2×#67—61no—
336C2×#67—61no—
337C2×#67—61no—
338C2×#67—61no—
339C2×#67—61no—
340C2×#67—61no—
341C2×#67—61no—
342C2×#67—61no—
343C2×#67—62no—
344C2×#67—124no—
345C22×Dic3—61no—
346C22×Dic3—61no—
347C22×Dic3—61no—
348C22×Dic3—62no—
349C22×Dic3—62no—
350C22×Dic3—61no—
351C22×Dic3—61no—
352#237—124no—
353#237—124no—
354#237—128no—
355D3×D4—62no—
356D3×D4—62no—
357D3×D4—121no—
358D3×D4—121no—
359D3×D4—124no—
360C2×D12—22no—
361C2×D12—21no—
362C2×D12—41no—
363C2×D12—61no—
364C2×D12C22×D311yescharacteristic
365C2×D12C22×D311yescharacteristic
366C2×D12C22×D311yescharacteristic
367C2×C4×D3—31no—
368C2×C4×D3—31no—
369C2×C4×D3—61no—
370C2×C4×D3—61no—
371C2×C4×D3—61no—
372C2×C4×D3—61no—
373C2×C4×D3—62no—
374C2×Dic6—61no—
375C2×Dic6—61no—
376C2×Dic6—62no—
377C3×D8—62no—
378C3×D8—121no—
379C3×D8—121no—
380C2×C3×C8—31no—
381C2×C3×C8—31no—
382C2×C3×C8—31no—
383C2×C3×C8—31no—
384C2×C3×C8—121no—
385C3×C4⋊C4—21no—
386C3×C4⋊C4—31no—
387C3×C4⋊C4C22×D311yescharacteristic
388C3×C4⋊C4C22×D311yescharacteristic
389C3×C22⋊C4—22no—
390C3×C22⋊C4—21no—
391C3×C22⋊C4—21no—
392C3×C22⋊C4—61no—
393#217—31no—
394#217—31no—
395#217—61no—
396#217—61no—
397#217—61no—
398#217—61no—
399#217—61no—
400#217—61no—
401#217—61no—
402#217—62no—
403#217—62no—
404#213—22no—
405#213—41no—
406#213—41no—
407(C2×D3)⋊C4—21no—
408(C2×D3)⋊C4—31no—
409(C2×D3)⋊C4—31no—
410(C2×D3)⋊C4—61no—
411(C2×D3)⋊C4—61no—
412(C2×D3)⋊C4—61no—
413C4⋊Dic3—31no—
414C4⋊Dic3—31no—
415C4⋊Dic3—31no—
416C4⋊Dic3—31no—
417C4⋊Dic3—61no—
418C4⋊Dic3—61no—
419C4⋊Dic3—62no—
420C4⋊Dic3—61no—
421C4⋊Dic3—61no—
422C4⋊Dic3C22×D311yescharacteristic
423Dic3⋊C4—31no—
424Dic3⋊C4—31no—
425Dic3⋊C4—61no—
426Dic3⋊C4—61no—
427Dic3⋊C4—61no—
428Dic3⋊C4—61no—
429Dic3⋊C4—61no—
430Dic3⋊C4—62no—
431Dic3⋊C4—62no—
432C4×Dic3—31no—
433C4×Dic3—31no—
434C4×Dic3—61no—
435C2×C3⋊C8—41no—
436C2×C3⋊C8C22×D311yescharacteristic
437C2×C3⋊C8C22×D311yescharacteristic
438C2×C3⋊C8C22×D311yescharacteristic
439C2×C3⋊C8C22×D311yescharacteristic
440D3×C8—121no—
441D3×C8—121no—
442C22×C32—21no—
443C22×C32—21no—
444C22×C32—41no—
445C22×C32—41no—
446C22×C32—41no—
447C22×C32C2×D812yes—
448C22×C32C22×D411yescharacteristic
449C2×C3⋊D3—21no—
450C2×C3⋊D3—21no—
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×C4C2×#4111yescharacteristic
466C32×C4H(5,𝔽2)11yescharacteristic
467C3⋊Dic3—21no—
468C3⋊Dic3—21no—
469C3⋊Dic3—41no—
470C3⋊Dic3—41no—
471C3⋊Dic3C2×D812yes—
472C3×Dic3—41no—
473C2×#41—181no—
474C22×D4—31no—
475C22×D4—91no—
476C22×D4—181no—
477C2×D8—31no—
478C2×D8—31no—
479C2×D8—31no—
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—181no—
491#121D3211yescharacteristic, complemented
492#120—181no—
493#120—181no—
494C4×D4—91no—
495C4×D4—91no—
496C4×D4—91no—
497C2×C4⋊C4—91no—
498C2×C4⋊C4—91no—
499#107—31no—
500#107—91no—
501#107—91no—
502C4⋊C8—91no—
503#102—31no—
504#102—31no—
505#102—31no—
506#102—31no—
507#102—91no—
508#102—91no—
509#102—91no—
510#102—91no—
511#102—91no—
512#102—91no—
513C22⋊C8—31no—
514C22⋊C8—91no—
515C4×C8—91no—
516C23×C3—22no—
517C23×C3—21no—
518C23×C3—21no—
519C23×C3—21no—
520C23×C3—61no—
521C23×C3—61no—
522C23×C3—61no—
523C23×C3—122no—
524C23×C3—122no—
525C23×C3—241no—
526C23×C3D3×D411yescharacteristic
527C23×C3D3×D411yescharacteristic
528C22×D3—21no—
529C22×D3—21no—
530C22×D3—21no—
531C22×D3—31no—
532C22×D3—31no—
533C22×D3—42no—
534C22×D3—42no—
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—21no—
544C3×D4—21no—
545C3×D4—21no—
546C3×D4—21no—
547C3×D4—32no—
548C3×D4—41no—
549C3×D4—41no—
550C3×D4—44no—
551C3×D4—42no—
552C3×D4—42no—
553C3×D4—61no—
554C3×D4—61no—
555C3×D4—61no—
556C3×D4—61no—
557C3×D4—61no—
558C3×D4—122no—
559C3×D4—122no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—22no—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—41no—
570C2×C3×C4—41no—
571C2×C3×C4—61no—
572C2×C3×C4D3×D411yescharacteristic
573C2×C3×C4D3×D411yescharacteristic
574C2×C3×C4C23×D311yescharacteristic
575C2×C3×C4C23×D311yescharacteristic
576#67—34no—
577#67—34no—
578#67—42no—
579#67—64no—
580#67—122no—
581#67—122no—
582#67—122no—
583#67—122no—
584#67—122no—
585#67—122no—
586#67—122no—
587#67—124no—
588#67—241no—
589#67—241no—
590C2×Dic3—21no—
591C2×Dic3—31no—
592C2×Dic3—31no—
593C2×Dic3—31no—
594C2×Dic3—31no—
595C2×Dic3—31no—
596C2×Dic3—31no—
597C2×Dic3—61no—
598C2×Dic3—61no—
599C2×Dic3—61no—
600C2×Dic3—62no—
601C2×Dic3—62no—
602C2×Dic3—61no—
603C2×Dic3—61no—
604C2×Dic3—61no—
605C2×Dic3—61no—
606C2×Dic3—122no—
607C2×Dic3—122no—
608C2×Dic3—122no—
609C2×Dic3—124no—
610C2×Dic3—124no—
611C2×Dic3—122no—
612C2×Dic3—122no—
613D12—21no—
614D12—21no—
615D12—21no—
616D12—21no—
617D12—21no—
618D12—42no—
619D12—122no—
620D12#23712yescomplemented
621C4×D3—61no—
622C4×D3—61no—
623C4×D3—61no—
624C4×D3—61no—
625C4×D3—121no—
626C4×D3—121no—
627C4×D3—122no—
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—81no—
644C2×C32#54611yescharacteristic
645C2×C32C22×D811yescharacteristic
646C2×C32#57711yescharacteristic
647C3⋊D3—22no—
648C3×D3—42no—
649C3×D3—81no—
650C3×D3—81no—
651C24—61no—
652C24—181no—
653#41—364no—
654C2×Q8—181no—
655C2×D4—21no—
656C2×D4—31no—
657C2×D4—31no—
658C2×D4—31no—
659C2×D4—62no—
660C2×D4—61no—
661C2×D4—61no—
662C2×D4—91no—
663C2×D4—121no—
664C2×D4—181no—
665C2×D4—181no—
666C2×D4—181no—
667C2×D4—181no—
668C2×D4—182no—
669C2×D4—181no—
670C2×D4—361no—
671C2×D4—364no—
672C2×D4C2×D3211yescharacteristic
673C22×C4—91no—
674C22×C4—181no—
675C22×C4—181no—
676C22×C4—181no—
677C22×C4—181no—
678C22×C4C2×D3211yescharacteristic
679D8—62no—
680D8—121no—
681D8—121no—
682C2×C8—31no—
683C2×C8—31no—
684C2×C8—31no—
685C2×C8—31no—
686C2×C8—121no—
687C2×C8—361no—
688C4⋊C4—31no—
689C4⋊C4—91no—
690C4⋊C4—91no—
691C4⋊C4—91no—
692C4⋊C4—181no—
693C4⋊C4—181no—
694C4⋊C4—181no—
695C4⋊C4C2×D3211yescharacteristic
696C22⋊C4—21no—
697C22⋊C4—61no—
698C22⋊C4—91no—
699C22⋊C4—91no—
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—42no—
714C22×C3—42no—
715C22×C3—42no—
716C22×C3—41no—
717C22×C3—41no—
718C22×C3—41no—
719C22×C3—41no—
720C22×C3—41no—
721C22×C3—41no—
722C22×C3—62no—
723C22×C3—121no—
724C22×C3—121no—
725C22×C3—121no—
726C22×C3—121no—
727C22×C3—121no—
728C22×C3—121no—
729C22×C3—121no—
730C22×C3—121no—
731C22×C3—244no—
732C22×C3D3×D812yes—
733C22×C3D3×D812yes—
734C22×C3C2×D3×D411yescharacteristic
735C22×C3C2×D3×D411yescharacteristic
736C2×D3—22no—
737C2×D3—32no—
738C2×D3—32no—
739C2×D3—41no—
740C2×D3—41no—
741C2×D3—41no—
742C2×D3—41no—
743C2×D3—41no—
744C2×D3—41no—
745C2×D3—41no—
746C2×D3—41no—
747C2×D3—62no—
748C2×D3—61no—
749C2×D3—61no—
750C2×D3—61no—
751C2×D3—61no—
752C2×D3—84no—
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—41no—
764C3×C4—41no—
765C3×C4—121no—
766C3×C4C2×#23711yescharacteristic
767C3×C4#100411yescharacteristic
768C3×C4#100411yescharacteristic
769C3×C4D3×#4111yescharacteristic
770Dic3—32no—
771Dic3—32no—
772Dic3—41no—
773Dic3—62no—
774Dic3—61no—
775Dic3—61no—
776Dic3—61no—
777Dic3—61no—
778Dic3—121no—
779Dic3—121no—
780Dic3—122no—
781Dic3—122no—
782Dic3—121no—
783Dic3—121no—
784Dic3—121no—
785Dic3—121no—
786C32#329411yescharacteristic, complemented, Sylow
787C23—21no—
788C23—61no—
789C23—61no—
790C23—61no—
791C23—91no—
792C23—122no—
793C23—122no—
794C23—241no—
795C23—362no—
796C23—362no—
797C23—721no—
798C23#381111yescharacteristic
799Q8—362no—
800D4—21no—
801D4—21no—
802D4—32no—
803D4—42no—
804D4—61no—
805D4—61no—
806D4—61no—
807D4—61no—
808D4—61no—
809D4—94no—
810D4—122no—
811D4—122no—
812D4—362no—
813D4—362no—
814D4—362no—
815D4—362no—
816D4—721no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—61no—
821C2×C4—91no—
822C2×C4—91no—
823C2×C4—91no—
824C2×C4—181no—
825C2×C4—181no—
826C2×C4—181no—
827C2×C4—181no—
828C2×C4—362no—
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—82no—
845C2×C3—81no—
846C2×C3—81no—
847C2×C3—122no—
848C2×C3—241no—
849C2×C3—241no—
850C2×C3#559111yescharacteristic
851C2×C3#561011yescharacteristic
852C2×C3C2×D3×D811yescharacteristic
853C2×C3C2×D3×D811yescharacteristic
854C2×C3#577011yescharacteristic
855C2×C3#577511yescharacteristic
856D3—42no—
857D3—62no—
858D3—62no—
859D3—81no—
860D3—81no—
861D3—122no—
862C22—21no—
863C22—21no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—62no—
868C22—92no—
869C22—121no—
870C22—121no—
871C22—121no—
872C22—121no—
873C22—121no—
874C22—121no—
875C22—121no—
876C22—121no—
877C22—181no—
878C22—181no—
879C22—244no—
880C22—724no—
881C22#6392612yes—
882C22C2×#381111yescharacteristic
883C4—21no—
884C4—41no—
885C4—92no—
886C4—121no—
887C4—181no—
888C4—181no—
889C4—361no—
890C4—361no—
891C4D3×#23711yescharacteristic
892C4#6431311yescharacteristic
893C3—21no—
894C3#8001411yescharacteristic, complemented
895C3#8073111yescharacteristic, complemented
896C2—22no—
897C2—81no—
898C2—122no—
899C2—182no—
900C2—241no—
901C2—241no—
902C2C2×#6392611yescharacteristic
903C2#1059530711yescharacteristic
904C2#1059546211yescharacteristic
subgroupG/H
centerC22C2×#3811
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. #10596082C2semidirect
2. #10595069C2semidirect
3. C3×#5038C2semidirect
4. C3×#5036C2semidirect
5. #10591516C2semidirect
6. #10591486C2semidirect
7. #10591455C2semidirect
8. #10591435C2semidirect
9. #10591148C2semidirect
10. #10591094C2semidirect
11. C2×#63563C2semidirect
12. #10590593C2semidirect
13. #10590552C2semidirect
14. #10590510C2semidirect
15. #10590471C2semidirect
22. C32×#121C22semidirect
23. #64147C22semidirect
25. D4×C3⋊Dic3C22semidirect
27. C2×C4⋊(C3⋊Dic3)C22semidirect
28. C4⋊C4×C3⋊D3C22semidirect
29. #64097C22semidirect
33. C2×C3×#213C22semidirect
34. C2×C3×#213C22semidirect
36. C22×C3×C3⋊C8C22semidirect
43. C2×#3710C22semidirect
44. C3×#832C22semidirect
45. C3×#830C22semidirect
47. C3×#809C22semidirect
48. C3×#809C22semidirect
49. C3×#807C22semidirect
50. #63575C22semidirect
51. #63575C22semidirect
52. #63572C22semidirect
55. #63563C22semidirect
56. #63563C22semidirect
57. #63563C22semidirect
58. #63563C22semidirect
59. #63557C22semidirect
60. #63553C22semidirect
77. #5038D3semidirect
78. #5036D3semidirect
162. C3×#121C2×D3semidirect
163. C3×#121C2×D3semidirect
182. C2×#213C2×D3semidirect
183. C2×#213C2×D3semidirect
191. C22×C3⋊C8C2×D3semidirect
222. #832C2×D3semidirect
223. #830C2×D3semidirect
239. #809C2×D3semidirect
240. #809C2×D3semidirect
243. #807C2×D3semidirect
265. #638D8semidirect
285. C3×D12#41semidirect
491. #121D32semidirect
620. D12#237semidirect
786. C32#3294semidirect
894. C3#80014semidirect
895. C3#80731semidirect

Maximal subgroups

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

subgroupindex
#105960822
#105950692
C3×#50382
C3×#50362
#105915162
#105914862
#105914552
#105914352
#105911482
#105910942
C2×#635632
#105905932
#105905522
#105905102
#105904712
#807313
#800143