Finite Group Databasebeta

← #11887445

Subgroups — #11887445

Order 1152.

959 conjugacy classes of subgroups.

The subgroup lattice has 851 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596029C211yesmaximal, characteristic, complemented
2#10594005C211yesmaximal, characteristic, complemented
3C3×#5016C211yesmaximal, characteristic, complemented
4C3×C4×#213C211yesmaximal, characteristic, complemented
5#10591520C211yesmaximal, characteristic, complemented
6#10591516C211yesmaximal, characteristic, complemented
7#10591465C211yesmaximal, characteristic, complemented
8#10591455C211yesmaximal, characteristic, complemented
9#10590611C211yesmaximal, characteristic, complemented
10#10590593C211yesmaximal, characteristic, complemented
11#10590528C211yesmaximal, characteristic, complemented
12#10590512C211yesmaximal, characteristic, complemented
13#10590327C211yesmaximal, characteristic, complemented
14#10590274C211yesmaximal, characteristic, complemented
15#10590271C211yesmaximal, characteristic, complemented
16#80559—31nomaximal
17#79609—31nomaximal
18C2×#3802C2211yescharacteristic
19C2×#3796C2211yescharacteristic
20C32×C4×D4C2211yescharacteristic, complemented
21#64147C2211yescharacteristic
22#64147C2211yescharacteristic, complemented
23#64138—21no—
24C4×#638—21no—
25#64101C2211yescharacteristic, complemented
26C4⋊C4×C3⋊D3C2211yescharacteristic
27#64093—21no—
28#64088—21no—
29C4×C4⋊(C3⋊D3)C2211yescharacteristic
30#64079C2211yescharacteristic, complemented
31C2×C3×#214C2211yescharacteristic, complemented
32C2×C3×#213C2211yescharacteristic
33C2×C3×#213C2211yescharacteristic
34C3×#875C2211yescharacteristic
35C3×C4×D12C2211yescharacteristic
36#63923—21no—
37D3×(C2×D3)⋊C4—21no—
38#63916C2211yescharacteristic
39#63906—21no—
40#63891—21no—
41#63871C2211yescharacteristic
42C2×#3710C2211yescharacteristic
43C2×#3710C2211yescharacteristic, complemented
44C3×#832C2211yescharacteristic, complemented
45C3×#810C2211yescharacteristic, complemented
46C3×#809C2211yescharacteristic
47C3×#809C2211yescharacteristic
48C3×#807C2211yescharacteristic, complemented
49C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
50C3×C4×C3⋊C8C2211yescharacteristic, complemented
51#63575C2211yescharacteristic, complemented
52#63573C2211yescharacteristic, complemented
53#63566C2211yescharacteristic, complemented
54#63566C2211yescharacteristic, complemented
55#63563C2211yescharacteristic
56#63563C2211yescharacteristic
57#63563C2211yescharacteristic
58#63563C2211yescharacteristic
59#63557C2211yescharacteristic
60#63557C2211yescharacteristic, complemented
61#5676—31no—
62#5558—31no—
63#5558—31no—
64#5558—61no—
65#5554—31no—
66C3×#463—31no—
67C3×C4×D8—31no—
68#5172—31no—
69#5171—31no—
70#5158—31no—
71#5157—31no—
72#5156—31no—
73#5156—31no—
74#5056—31no—
75#5016D311yescharacteristic, complemented
76C4×#213D311yescharacteristic, complemented
77#5009—31no—
78#4885—31no—
79#4884—31no—
80#4847—31no—
81#4834—31no—
82#4811—31no—
83#4804—31no—
84#4779—31no—
85#4778—31no—
86#4775—31no—
87#4772—31no—
88D3×#102—31no—
89D3×#102—31no—
90#4697—31no—
91C8×D12—31no—
92C22×D32—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4—21no—
95C2×#638—21no—
96C2×#638—21no—
97C2×C4⋊(C3⋊D3)D411yescharacteristic
98C2×C4×C3⋊D3—21no—
99C2×C4×C3⋊D3C2311yescharacteristic
100C2×C4×C3⋊D3C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×C4×D3—21no—
104C2×C3×Dic6C2311yescharacteristic
105C2×#626—21no—
106C2×#626—21no—
107C2×#625—21no—
108C2×D3×Dic3—21no—
109#3802—22no—
110#3802—41no—
111#3796—22no—
112#3796—41no—
113C32×C4⋊C4C2311yescharacteristic
114C32×C22⋊C4—21no—
115C32×C42C2311yescharacteristic
116#3757—21no—
117#3757—21no—
118#3752—21no—
119#3752D411yescharacteristic
120#3752D411yescharacteristic
121C4⋊(C3⋊Dic3)D411yescharacteristic
122C4⋊(C3⋊Dic3)C2311yescharacteristic
123C4⋊(C3⋊Dic3)C2311yescharacteristic
124#3750—21no—
125#3750—21no—
126#3750—21no—
127C4×C3⋊Dic3—21no—
128C3×#214—41no—
129C3×#213—22no—
130C3×#213—41no—
131C3×(C2×D3)⋊C4—21no—
132C3×(C2×D3)⋊C4—21no—
133C3×(C2×D3)⋊C4—21no—
134C3×C4⋊Dic3C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139Dic3⋊Dic3—21no—
140#3722—21no—
141(C2×D3)⋊Dic3—21no—
142#3710—41no—
143#3710—41no—
144#3297—91noSylow
145C2×#239—31no—
146C2×#237—31no—
147C2×D3×D4—31no—
148C2×D3×D4—31no—
149C2×C3×SD16—31no—
150C2×C3×D8—31no—
151C2×C3×D8—31no—
152C3×#124—31no—
153C3×C4×D4—21no—
154C3×C4×D4—31no—
155C3×C4×D4C2×D311yescharacteristic, complemented
156C3×C4×D4C2×D311yescharacteristic, complemented
157#946—31no—
158#938—31no—
159#938—31no—
160#938—31no—
161#938—31no—
162#938—31no—
163#938—61no—
164#938—61no—
165C2×#214C2×D311yescharacteristic, complemented
166C2×#213C2×D311yescharacteristic
167C2×#213C2×D311yescharacteristic
168#930—61no—
169#929—61no—
170#929—61no—
171#929—62no—
172C4×#67—61no—
173C4×#67—61no—
174C4×#67—62no—
175C2×(C2×D3)⋊C4—61no—
176C2×D3×C8—31no—
177C2×D3×C8—31no—
178C2×D3×C8—31no—
179C2×D3×C8—31no—
180#897—31no—
181#895—31no—
182#892—31no—
183#892—31no—
184#892—61no—
185D3×C4⋊C4—31no—
186D3×C4⋊C4—31no—
187D3×C4⋊C4—61no—
188#886—61no—
189#884—61no—
190#884—61no—
191#884—61no—
192#884—62no—
193#883—61no—
194#882—61no—
195#882—61no—
196D3×C22⋊C4—61no—
197#879—61no—
198#879—61no—
199#879—62no—
200#875C2×D311yescharacteristic
201C4×D12—31no—
202C4×D12—31no—
203C4×D12—61no—
204C4×D12C2×D311yescharacteristic
205#870—31no—
206#870—31no—
207#870—61no—
208C3×#107—31no—
209C3×C4⋊C8—31no—
210C3×#103—31no—
211C3×#102—31no—
212C3×#102—31no—
213C3×#102—31no—
214C3×C4×C8—31no—
215#835—31no—
216#835—31no—
217#832—31no—
218#832—31no—
219#832—31no—
220#832—31no—
221#832C2×D311yescharacteristic, complemented
222#821—31no—
223#821—31no—
224#821—31no—
225#821—31no—
226(C2×D3)⋊C8—31no—
227(C2×D3)⋊C8—31no—
228(C2×D3)⋊C8—31no—
229(C2×D3)⋊C8—31no—
230#818—31no—
231#817—31no—
232#816—31no—
233#816—31no—
234#810C2×D311yescharacteristic, complemented
235#809C2×D311yescharacteristic
236#809C2×D311yescharacteristic
237#808—31no—
238#807—31no—
239#807C2×D311yescharacteristic, complemented
240C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
241C4×C3⋊C8C2×D311yescharacteristic, complemented
242C23×C32—21no—
243C22×C3⋊D3C2×D411yescharacteristic
244C22×C3⋊D3C2×D411yescharacteristic
245C22×C3×D3—21no—
246C22×C3×D3—21no—
247C2×D32—42no—
248C2×D32—42no—
249C2×D32—81no—
250C32×D4—21no—
251C32×D4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—81no—
254C2×C32×C4C2×D411yescharacteristic
255C2×C32×C4C2×D411yescharacteristic
256C2×C32×C4C2411yescharacteristic
257#638—42no—
258#638—81no—
259C2×C3⋊Dic3—21no—
260C2×C3⋊Dic3—21no—
261C2×C3⋊Dic3C2×D411yescharacteristic
262C2×C3⋊Dic3C2×D411yescharacteristic
263C4⋊(C3⋊D3)—22no—
264C4×C3⋊D3—21no—
265C4×C3⋊D3—21no—
266C4×C3⋊D3—21no—
267C4×C3⋊D3—21no—
268C4×C3⋊D3—81no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—21no—
271C3×D12—21no—
272C3×D12—21no—
273C3×D12—21no—
274C3×D12#4112yes—
275C3×C4×D3—81no—
276C3×Dic6—21no—
277C3×Dic6—21no—
278#626—42no—
279#626—81no—
280#625—42no—
281D3×Dic3—42no—
282C3×C3⋊C8—21no—
283C3×C3⋊C8—21no—
284C3×C3⋊C8—21no—
285C3×C3⋊C8—21no—
286#553—91no—
287#546—91no—
288#488—91no—
289#484—91no—
290#482—91no—
291#478—91no—
292#466—91no—
293#465—91no—
294#463—31no—
295#449—91no—
296#447—91no—
297C4×D8—31no—
298C8×D4—91no—
299#416—91no—
300C2×#102—91no—
301C23×D3—61no—
302C23×D3—61no—
303C2×C3×Q8—31no—
304C2×C3×D4—21no—
305C2×C3×D4—31no—
306C2×C3×D4—31no—
307C2×C3×D4C22×D311yescharacteristic
308C2×C3×D4C22×D311yescharacteristic
309C22×C3×C4—22no—
310C22×C3×C4—21no—
311C22×C3×C4—21no—
312C22×C3×C4—61no—
313C2×#67—61no—
314C2×#67—61no—
315C2×#67—61no—
316C2×#67—61no—
317C2×#67—61no—
318C2×#67—61no—
319C2×#67—62no—
320C2×#67—61no—
321C2×#67—61no—
322C2×#67—62no—
323C22×Dic3—61no—
324#239—62no—
325#239—121no—
326#237—62no—
327#237—121no—
328D3×D4—62no—
329D3×D4—62no—
330D3×D4—121no—
331D3×D4—121no—
332C2×D12—31no—
333C2×D12—31no—
334C2×D12—61no—
335C2×D12—61no—
336C2×D12—61no—
337C2×D12C22×D311yescharacteristic
338C2×D12C22×D311yescharacteristic
339C2×C4×D3—21no—
340C2×C4×D3—31no—
341C2×C4×D3—31no—
342C2×C4×D3—31no—
343C2×C4×D3—31no—
344C2×C4×D3—61no—
345C2×C4×D3—61no—
346C2×C4×D3—61no—
347C2×C4×D3—61no—
348C2×C4×D3—61no—
349C2×C4×D3—62no—
350C2×Dic6C22×D311yescharacteristic
351C3×SD16—121no—
352C3×D8—62no—
353C3×D8—121no—
354C2×C3×C8—31no—
355C2×C3×C8—31no—
356C2×C3×C8—31no—
357C2×C3×C8—31no—
358C3×C4⋊C4—21no—
359C3×C4⋊C4—31no—
360C3×C4⋊C4C22×D311yescharacteristic
361C3×C4⋊C4C22×D311yescharacteristic
362C3×C22⋊C4—22no—
363C3×C22⋊C4—21no—
364C3×C22⋊C4—21no—
365C3×C22⋊C4—61no—
366C3×C22⋊C4—61no—
367C3×C22⋊C4—61no—
368C3×C42—21no—
369C3×C42C22×D311yescharacteristic
370C3×C42C22×D311yescharacteristic
371#217—61no—
372#217—61no—
373#217—61no—
374#217—61no—
375#217—61no—
376#217—62no—
377#217—62no—
378#214—41no—
379#213—22no—
380#213—41no—
381(C2×D3)⋊C4—21no—
382(C2×D3)⋊C4—21no—
383(C2×D3)⋊C4—21no—
384(C2×D3)⋊C4—31no—
385(C2×D3)⋊C4—31no—
386(C2×D3)⋊C4—31no—
387(C2×D3)⋊C4—31no—
388(C2×D3)⋊C4—61no—
389(C2×D3)⋊C4—61no—
390(C2×D3)⋊C4—61no—
391(C2×D3)⋊C4—61no—
392(C2×D3)⋊C4—61no—
393(C2×D3)⋊C4—61no—
394(C2×D3)⋊C4—61no—
395(C2×D3)⋊C4—62no—
396C4⋊Dic3—31no—
397C4⋊Dic3—31no—
398C4⋊Dic3—31no—
399C4⋊Dic3—31no—
400C4⋊Dic3—31no—
401C4⋊Dic3—31no—
402C4⋊Dic3—61no—
403C4⋊Dic3—61no—
404C4⋊Dic3—61no—
405C4⋊Dic3—61no—
406C4⋊Dic3C22×D311yescharacteristic
407Dic3⋊C4—61no—
408Dic3⋊C4—61no—
409Dic3⋊C4—61no—
410Dic3⋊C4—62no—
411Dic3⋊C4—62no—
412Dic3⋊C4—62no—
413Dic3⋊C4—61no—
414Dic3⋊C4—61no—
415Dic3⋊C4—61no—
416Dic3⋊C4—61no—
417C4×Dic3—61no—
418C4×Dic3—61no—
419C4×Dic3—62no—
420C2×C3⋊C8C22×D311yescharacteristic
421C2×C3⋊C8C22×D311yescharacteristic
422C2×C3⋊C8C22×D311yescharacteristic
423C2×C3⋊C8C22×D311yescharacteristic
424D3×C8—121no—
425D3×C8—121no—
426D3×C8—121no—
427D3×C8—121no—
428C22×C32—41no—
429C22×C32—41no—
430C22×C32—41no—
431C22×C32C22×D411yescharacteristic
432C2×C3⋊D3—21no—
433C2×C3⋊D3—21no—
434C2×C3⋊D3—21no—
435C2×C3⋊D3—21no—
436C2×C3⋊D3—21no—
437C2×C3⋊D3#13512yes—
438C2×C3×D3—22no—
439C2×C3×D3—41no—
440C2×C3×D3—41no—
441C2×C3×D3—41no—
442C2×C3×D3—41no—
443C2×C3×D3—41no—
444D32—84no—
445C32×C4—21no—
446C32×C4—21no—
447C32×C4—41no—
448C32×C4C2×#4111yescharacteristic
449C32×C4H(5,𝔽2)11yescharacteristic
450C3⋊Dic3—21no—
451C3⋊Dic3—21no—
452C3⋊Dic3—41no—
453C3⋊Dic3—41no—
454C3×Dic3—41no—
455C3×Dic3—41no—
456C2×#41—91no—
457C22×D4—91no—
458C2×SD16—31no—
459C2×D8—31no—
460C2×D8—31no—
461C22×C8—91no—
462C22×C8—91no—
463#126—181no—
464#125—91no—
465#124—31no—
466#123—181no—
467#123—181no—
468C22⋊Q8—91no—
469#121—91no—
470#121—91no—
471#121—91no—
472#121—181no—
473#121—181no—
474#120—181no—
475C4×D4—31no—
476C4×D4—91no—
477C4×D4—181no—
478C4×D4D3211yescharacteristic, complemented
479#117—91no—
480C2×C4⋊C4—91no—
481C2×C22⋊C4—181no—
482#107—31no—
483#107—91no—
484#106—91no—
485C4⋊C8—31no—
486#103—31no—
487#103—91no—
488#103—91no—
489#102—31no—
490#102—31no—
491#102—31no—
492#102—91no—
493#102—91no—
494#102—91no—
495#102—91no—
496C22⋊C8—91no—
497C22⋊C8—91no—
498C4×C8—31no—
499C23×C3—22no—
500C23×C3—21no—
501C23×C3—21no—
502C23×C3—61no—
503C23×C3—61no—
504C22×D3—21no—
505C22×D3—21no—
506C22×D3—31no—
507C22×D3—31no—
508C22×D3—31no—
509C22×D3—31no—
510C22×D3—61no—
511C22×D3—61no—
512C22×D3—122no—
513C22×D3—122no—
514C22×D3—122no—
515C22×D3—122no—
516C22×D3—241no—
517C22×D3—241no—
518C3×Q8—61no—
519C3×Q8—61no—
520C3×D4—21no—
521C3×D4—21no—
522C3×D4—21no—
523C3×D4—21no—
524C3×D4—32no—
525C3×D4—41no—
526C3×D4—41no—
527C3×D4—61no—
528C3×D4—61no—
529C3×D4—61no—
530C2×C3×C4—22no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—81no—
539C2×C3×C4—81no—
540C2×C3×C4—82no—
541C2×C3×C4—241no—
542C2×C3×C4D3×D411yescharacteristic
543C2×C3×C4D3×D411yescharacteristic
544C2×C3×C4D3×D411yescharacteristic
545C2×C3×C4D3×D411yescharacteristic
546C2×C3×C4C23×D311yescharacteristic
547C2×C3×C4C23×D311yescharacteristic
548#67—122no—
549#67—122no—
550#67—122no—
551#67—122no—
552#67—122no—
553#67—124no—
554#67—241no—
555#67—241no—
556#67—241no—
557#67—242no—
558C2×Dic3—21no—
559C2×Dic3—21no—
560C2×Dic3—31no—
561C2×Dic3—31no—
562C2×Dic3—31no—
563C2×Dic3—31no—
564C2×Dic3—61no—
565C2×Dic3—61no—
566C2×Dic3—62no—
567C2×Dic3—62no—
568C2×Dic3—61no—
569C2×Dic3—61no—
570C2×Dic3—61no—
571C2×Dic3—61no—
572C2×Dic3—122no—
573D12—21no—
574D12—21no—
575D12—21no—
576D12—62no—
577D12—62no—
578D12—122no—
579D12—122no—
580D12—241no—
581D12#23512yes—
582C4×D3—61no—
583C4×D3—61no—
584C4×D3—61no—
585C4×D3—61no—
586C4×D3—61no—
587C4×D3—61no—
588C4×D3—61no—
589C4×D3—61no—
590C4×D3—81no—
591C4×D3—121no—
592C4×D3—121no—
593C4×D3—121no—
594C4×D3—121no—
595C4×D3—122no—
596C4×D3—241no—
597C4×D3—241no—
598C4×D3—242no—
599Dic6—21no—
600Dic6—21no—
601C3×C8—61no—
602C3×C8—61no—
603C3×C8—61no—
604C3×C8—61no—
605C3⋊C8—21no—
606C3⋊C8—21no—
607C3⋊C8—21no—
608C3⋊C8—21no—
609C2×C32—81no—
610C2×C32#54611yescharacteristic
611C2×C32C2×#13511yescharacteristic
612C2×C32#57611yescharacteristic
613C3⋊D3—22no—
614C3⋊D3—41no—
615C3×D3—42no—
616C3×D3—81no—
617C24—181no—
618#41—182no—
619#41—361no—
620C2×Q8—31no—
621C2×D4—31no—
622C2×D4—31no—
623C2×D4—91no—
624C2×D4—181no—
625C2×D4—181no—
626C2×D4—181no—
627C2×D4—182no—
628C2×D4—181no—
629C2×D4—181no—
630C2×D4—361no—
631C2×D4C2×D3211yescharacteristic
632C22×C4—21no—
633C22×C4—61no—
634C22×C4—91no—
635C22×C4—91no—
636C22×C4—181no—
637C22×C4—181no—
638SD16—121no—
639D8—62no—
640D8—121no—
641C2×C8—31no—
642C2×C8—31no—
643C2×C8—31no—
644C2×C8—31no—
645C2×C8—361no—
646C2×C8—361no—
647C4⋊C4—31no—
648C4⋊C4—91no—
649C4⋊C4—91no—
650C4⋊C4—91no—
651C4⋊C4—181no—
652C4⋊C4—181no—
653C4⋊C4—181no—
654C4⋊C4—181no—
655C4⋊C4C2×D3211yescharacteristic
656C22⋊C4—21no—
657C22⋊C4—61no—
658C22⋊C4—61no—
659C22⋊C4—61no—
660C22⋊C4—91no—
661C22⋊C4—91no—
662C22⋊C4—181no—
663C22⋊C4—181no—
664C22⋊C4—181no—
665C22⋊C4—181no—
666C22⋊C4—181no—
667C42—181no—
668C42C2×D3211yescharacteristic
669C22×C3—21no—
670C22×C3—42no—
671C22×C3—42no—
672C22×C3—42no—
673C22×C3—41no—
674C22×C3—41no—
675C22×C3—41no—
676C22×C3—41no—
677C22×C3—41no—
678C22×C3—41no—
679C22×C3—62no—
680C22×C3—121no—
681C22×C3—121no—
682C22×C3—121no—
683C22×C3—121no—
684C22×C3—121no—
685C22×C3C2×D3×D411yescharacteristic
686C22×C3C2×D3×D411yescharacteristic
687C2×D3—22no—
688C2×D3—32no—
689C2×D3—32no—
690C2×D3—41no—
691C2×D3—41no—
692C2×D3—41no—
693C2×D3—41no—
694C2×D3—41no—
695C2×D3—62no—
696C2×D3—61no—
697C2×D3—61no—
698C2×D3—61no—
699C2×D3—61no—
700C2×D3—61no—
701C2×D3—61no—
702C2×D3—61no—
703C2×D3—61no—
704C2×D3—61no—
705C2×D3—61no—
706C2×D3—121no—
707C2×D3—121no—
708C2×D3—121no—
709C2×D3—121no—
710C2×D3—121no—
711C2×D3—244no—
712C2×D3—244no—
713C3×C4—21no—
714C3×C4—21no—
715C3×C4—21no—
716C3×C4—21no—
717C3×C4—21no—
718C3×C4—21no—
719C3×C4—41no—
720C3×C4—41no—
721C3×C4—42no—
722C3×C4—41no—
723C3×C4—41no—
724C3×C4—121no—
725C3×C4—121no—
726C3×C4C2×#23511yescharacteristic
727C3×C4#100411yescharacteristic
728C3×C4D3×#4111yescharacteristic
729C3×C4#100911yescharacteristic
730Dic3—41no—
731Dic3—41no—
732Dic3—61no—
733Dic3—61no—
734Dic3—61no—
735Dic3—61no—
736Dic3—121no—
737Dic3—121no—
738Dic3—122no—
739Dic3—122no—
740Dic3—121no—
741Dic3—121no—
742Dic3—121no—
743Dic3—121no—
744C32#329711yescharacteristic, complemented, Sylow
745C23—21no—
746C23—61no—
747C23—61no—
748C23—91no—
749C23—91no—
750C23—362no—
751C23—362no—
752C23—721no—
753Q8—61no—
754Q8—61no—
755D4—21no—
756D4—21no—
757D4—32no—
758D4—61no—
759D4—61no—
760D4—61no—
761D4—182no—
762D4—362no—
763D4—362no—
764D4—362no—
765D4—721no—
766D4—721no—
767C2×C4—21no—
768C2×C4—61no—
769C2×C4—61no—
770C2×C4—81no—
771C2×C4—91no—
772C2×C4—91no—
773C2×C4—181no—
774C2×C4—181no—
775C2×C4—181no—
776C2×C4—181no—
777C2×C4—181no—
778C2×C4—181no—
779C2×C4—241no—
780C2×C4—362no—
781C2×C4—721no—
782C2×C4#381111yescharacteristic
783C2×C4#381111yescharacteristic
784C2×C4C22×D3211yescharacteristic
785C8—61no—
786C8—61no—
787C8—61no—
788C8—61no—
789C2×C3—21no—
790C2×C3—21no—
791C2×C3—21no—
792C2×C3—82no—
793C2×C3—81no—
794C2×C3—81no—
795C2×C3—122no—
796C2×C3—241no—
797C2×C3#555011yescharacteristic
798C2×C3#561211yescharacteristic
799C2×C3#575711yescharacteristic
800C2×C3D3×#13511yescharacteristic
801C2×C3D3×#13511yescharacteristic
802C2×C3#577411yescharacteristic
803D3—42no—
804D3—62no—
805D3—62no—
806D3—81no—
807D3—122no—
808D3—121no—
809D3—121no—
810D3—241no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—62no—
815C22—92no—
816C22—121no—
817C22—121no—
818C22—121no—
819C22—121no—
820C22—121no—
821C22—181no—
822C22—181no—
823C22—181no—
824C22—181no—
825C22—181no—
826C22—724no—
827C22C2×#381111yescharacteristic
828C4—21no—
829C4—21no—
830C4—41no—
831C4—121no—
832C4—121no—
833C4—181no—
834C4—181no—
835C4—361no—
836C4—361no—
837C4D3×#23511yescharacteristic
838C4#6430711yescharacteristic
839C3—21no—
840C3#7960911yescharacteristic, complemented
841C3#8055911yescharacteristic, complemented
842C2—81no—
843C2—122no—
844C2—182no—
845C2—241no—
846C2—361no—
847C2#1059507811yescharacteristic
848C2#1059510211yescharacteristic
849C2#1059545911yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
hypercenterC4×D4D32
hypocenterC32#3297
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #10596029C2semidirect
2. #10594005C2semidirect
3. C3×#5016C2semidirect
4. C3×C4×#213C2semidirect
5. #10591520C2semidirect
6. #10591516C2semidirect
7. #10591465C2semidirect
8. #10591455C2semidirect
9. #10590611C2semidirect
10. #10590593C2semidirect
11. #10590528C2semidirect
12. #10590512C2semidirect
13. #10590327C2semidirect
14. #10590274C2semidirect
15. #10590271C2semidirect
20. C32×C4×D4C22semidirect
22. #64147C22semidirect
25. #64101C22semidirect
30. #64079C22semidirect
31. C2×C3×#214C22semidirect
43. C2×#3710C22semidirect
44. C3×#832C22semidirect
45. C3×#810C22semidirect
48. C3×#807C22semidirect
49. C3×C4⋊(C3⋊C8)C22semidirect
50. C3×C4×C3⋊C8C22semidirect
51. #63575C22semidirect
52. #63573C22semidirect
53. #63566C22semidirect
54. #63566C22semidirect
60. #63557C22semidirect
75. #5016D3semidirect
76. C4×#213D3semidirect
155. C3×C4×D4C2×D3semidirect
156. C3×C4×D4C2×D3semidirect
165. C2×#214C2×D3semidirect
221. #832C2×D3semidirect
234. #810C2×D3semidirect
239. #807C2×D3semidirect
240. C4⋊(C3⋊C8)C2×D3semidirect
241. C4×C3⋊C8C2×D3semidirect
478. C4×D4D32semidirect
744. C32#3297semidirect
840. C3#79609semidirect
841. C3#80559semidirect

Maximal subgroups

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

subgroupindex
#105960292
#105940052
C3×#50162
C3×C4×#2132
#105915202
#105915162
#105914652
#105914552
#105906112
#105905932
#105905282
#105905122
#105903272
#105902742
#105902712
#805593
#796093