Finite Group Databasebeta

← #11887394

Subgroups — #11887394

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#10595122C211yesmaximal, characteristic, complemented
3#10592855C211yesmaximal, characteristic, complemented
4C3×#5158C211yesmaximal, characteristic, complemented
5C3×Dic3×D8C211yesmaximal, characteristic, complemented
6#10591471C211yesmaximal, characteristic, complemented
7#10591465C211yesmaximal, characteristic, complemented
8#10591449C211yesmaximal, characteristic, complemented
9#10591420C211yesmaximal, characteristic, complemented
10#10591416C211yesmaximal, characteristic, complemented
11#10591409C211yesmaximal, characteristic, complemented
12#10590872C211yesmaximal, characteristic, complemented
13#10590721C211yesmaximal, characteristic, complemented
14#10590705C211yesmaximal, characteristic, complemented
15#10590689C211yesmaximal, characteristic, complemented
16#80102—31nomaximal
17#79609—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×C32×D8C2211yescharacteristic
21#64147C2211yescharacteristic
22C2×#3753C2211yescharacteristic
23C3×#938C2211yescharacteristic, complemented
24C3×D4×Dic3C2211yescharacteristic
25C3×D4×Dic3C2211yescharacteristic, complemented
26C2×C3×#214C2211yescharacteristic, complemented
27#63981—21no—
28#63978—21no—
29#63966—21no—
30C2×#3722—21no—
31#63961—21no—
32#63958—21no—
33#63956—21no—
34#63952—21no—
35#63909C2211yescharacteristic
36C4×#626C2211yescharacteristic
37#63900C2211yescharacteristic
38#63871C2211yescharacteristic
39#63869C2211yescharacteristic, complemented
40#63864C2211yescharacteristic
41#63841C2211yescharacteristic, complemented
42C2×#3710C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44#63659C2211yescharacteristic
45#63648C2211yescharacteristic
46#63647C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#832C2211yescharacteristic, complemented
50C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
51C3×#818C2211yescharacteristic, complemented
52C3×#816C2211yescharacteristic, complemented
53C3×C8×Dic3C2211yescharacteristic, complemented
54#63576C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63566C2211yescharacteristic, complemented
58#63565C2211yescharacteristic, complemented
59#63564C2211yescharacteristic
60#63564C2211yescharacteristic
61#5829—31no—
62#5614—31no—
63#5558—31no—
64#5554—31no—
65C3×#449—31no—
66C3×C4×D8—31no—
67#5233—31no—
68#5171—31no—
69#5165—31no—
70#5158D311yescharacteristic, complemented
71#5156—31no—
72#5156—31no—
73#5156—61no—
74Dic3×D8D311yescharacteristic, complemented
75#5038—31no—
76#5016—31no—
77#5009—31no—
78#4885—31no—
79#4884—31no—
80#4811—31no—
81#4800—31no—
82#4778—31no—
83#4775—31no—
84#4772—31no—
85D3×#102—31no—
86D3×#102—31no—
87#4763—31no—
88#4737—31no—
89#67⋊C8—31no—
90#4697—31no—
91C8×D12—31no—
92C23×C3⋊D3—21no—
93C2×C32×D4C2311yescharacteristic
94C2×C32×D4C2311yescharacteristic
95C2×#638—21no—
96C2×#638—21no—
97D4×C3⋊D3—22no—
98D4×C3⋊D3—41no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4×C3⋊D3C2311yescharacteristic
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C22×C3×Dic3—21no—
104C22×C3×Dic3—21no—
105C22×C3×Dic3—21no—
106C3×#237—22no—
107C3×#237—41no—
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×Dic6C2311yescharacteristic
110C2×#626—21no—
111C2×#626D411yescharacteristic
112C2×#624—21no—
113C32×D8—22no—
114C2×C32×C8C2311yescharacteristic
115#3757—21no—
116#3753—41no—
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C3×#217—21no—
120C3×#217—21no—
121C3×#217—21no—
122C3×#214—41no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4×Dic3C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129#3724—21no—
130#3724—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3D411yescharacteristic
134#3722—21no—
135#3722—21no—
136#3722—21no—
137#3722—21no—
138#3722D411yescharacteristic
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3D411yescharacteristic
141Dic32—21no—
142#3710—41no—
143D3×C3⋊C8—41no—
144#3297—91noSylow
145C2×C3×#41—31no—
146C2×#237C2×D311yescharacteristic
147C2×D3×D4—31no—
148C2×D3×D4—31no—
149C2×D3×D4—61no—
150C2×C3×SD16—31no—
151C2×C3×D8—21no—
152C2×C3×D8C2×D311yescharacteristic
153C2×C3×D8C2×D311yescharacteristic
154C3×#121—31no—
155C3×C4×D4—31no—
156C3×C4×D4—31no—
157#947—31no—
158#946—31no—
159#939—61no—
160#938—31no—
161#938—31no—
162#938—61no—
163#938—61no—
164#938C2×D311yescharacteristic, complemented
165#937—61no—
166#935—61no—
167D4×Dic3C2×D311yescharacteristic
168D4×Dic3C2×D311yescharacteristic, complemented
169C2×#214C2×D311yescharacteristic, complemented
170C2×#213—31no—
171C2×#213—31no—
172C2×#213—61no—
173#930—31no—
174#930—61no—
175#929—61no—
176#929—61no—
177C4×#67—31no—
178C4×#67—61no—
179C2×(C2×D3)⋊C4—61no—
180C2×(C2×D3)⋊C4—61no—
181#926—31no—
182C22×C3⋊C8—31no—
183C2×D3×C8—31no—
184C2×D3×C8—31no—
185C2×D3×C8—31no—
186#897—31no—
187#895—31no—
188#892—31no—
189D3×C4⋊C4—31no—
190D3×C4⋊C4—31no—
191#890—31no—
192#886—61no—
193#884—61no—
194#882—61no—
195#67⋊C4—61no—
196#879—61no—
197#879—61no—
198#875—31no—
199C4×D12—31no—
200#870—31no—
201C3×#107—31no—
202C3×#103—31no—
203C3×#102—31no—
204C3×#102—31no—
205C3×#102—31no—
206C3×C22⋊C8—31no—
207C3×C4×C8—31no—
208#835—31no—
209#835—31no—
210#832—31no—
211#832—31no—
212#832—61no—
213#832C2×D311yescharacteristic
214#832C2×D311yescharacteristic
215#832C2×D311yescharacteristic, complemented
216#821—31no—
217#821—31no—
218#821—31no—
219#821—31no—
220#821—61no—
221(C2×D3)⋊C8—31no—
222(C2×D3)⋊C8—31no—
223(C2×D3)⋊C8—61no—
224(C2×D3)⋊C8C2×D311yescharacteristic, complemented
225#818C2×D311yescharacteristic, complemented
226#817—31no—
227#816—31no—
228#816C2×D311yescharacteristic, complemented
229Dic3⋊C8—31no—
230C8×Dic3C2×D311yescharacteristic, complemented
231#810—31no—
232#809—31no—
233#809—31no—
234#808—31no—
235#807—31no—
236#807—31no—
237C4⋊(C3⋊C8)—31no—
238C23×C32—21no—
239C23×C32—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—21no—
248C32×D4—21no—
249C32×D4#4112yes—
250C2×C32×C4C2411yescharacteristic
251#638—42no—
252#638—42no—
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3C2×D411yescharacteristic
255C4⋊(C3⋊D3)—21no—
256C4⋊(C3⋊D3)—21no—
257C4×C3⋊D3—21no—
258C4×C3⋊D3—21no—
259C3×#67—42no—
260C3×#67—81no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—42no—
266C2×C3×Dic3—81no—
267C2×C3×Dic3—81no—
268C2×C3×Dic3C2×D411yescharacteristic
269C2×C3×Dic3C2×D411yescharacteristic
270C2×C3×Dic3C2×D411yescharacteristic
271C3×C4×D3—21no—
272C3×C4×D3—21no—
273C3×Dic6—21no—
274C3×Dic6—21no—
275#626—22no—
276#626—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—91no—
288#466—91no—
289#465—91no—
290#463—91no—
291#449—31no—
292#447—91no—
293C4×D8—31no—
294C8×D4—91no—
295#416—91no—
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—21no—
305C2×C3×D4—61no—
306C2×C3×D4—61no—
307C2×C3×D4C22×D311yescharacteristic
308C2×C3×D4C22×D311yescharacteristic
309C2×C3×D4C22×D311yescharacteristic
310C2×C3×D4C22×D311yescharacteristic
311C22×C3×C4—31no—
312C22×C3×C4—61no—
313C22×C3×C4—61no—
314C22×C3×C4—61no—
315C2×#67—21no—
316C2×#67—21no—
317C2×#67—31no—
318C2×#67—61no—
319C2×#67—61no—
320C2×#67—61no—
321C2×#67—61no—
322C2×#67—61no—
323C2×#67—121no—
324C2×#67—121no—
325C22×Dic3—21no—
326C22×Dic3—21no—
327C22×Dic3—21no—
328#237—22no—
329#237—41no—
330D3×D4—62no—
331D3×D4—62no—
332D3×D4—122no—
333D3×D4—121no—
334D3×D4—121no—
335D3×D4—122no—
336C2×D12—31no—
337C2×D12—31no—
338C2×D12—31no—
339C2×D12—61no—
340C2×D12—61no—
341C2×C4×D3—31no—
342C2×C4×D3—31no—
343C2×C4×D3—61no—
344C2×C4×D3—61no—
345C2×C4×D3—61no—
346C2×C4×D3C22×D311yescharacteristic
347C2×Dic6C22×D311yescharacteristic
348C3×SD16—121no—
349C3×D8—22no—
350C3×D8—22no—
351C3×D8—42no—
352C2×C3×C8—21no—
353C2×C3×C8—31no—
354C2×C3×C8—31no—
355C2×C3×C8C22×D311yescharacteristic
356C2×C3×C8C22×D311yescharacteristic
357C3×C4⋊C4—31no—
358C3×C4⋊C4—31no—
359C3×C4⋊C4—31no—
360C3×C22⋊C4—61no—
361C3×C22⋊C4—61no—
362C3×C22⋊C4—61no—
363C3×C42—31no—
364#217—21no—
365#217—21no—
366#217—21no—
367#217—31no—
368#217—61no—
369#217—61no—
370#217—61no—
371#217—121no—
372#214—41no—
373#213—121no—
374#213—121no—
375#213—122no—
376(C2×D3)⋊C4—31no—
377(C2×D3)⋊C4—31no—
378(C2×D3)⋊C4—31no—
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—
388C4⋊Dic3—31no—
389C4⋊Dic3—31no—
390C4⋊Dic3—31no—
391C4⋊Dic3—61no—
392C4⋊Dic3—61no—
393C4⋊Dic3—61no—
394C4⋊Dic3C22×D311yescharacteristic
395C4⋊Dic3C22×D311yescharacteristic
396C4⋊Dic3C22×D311yescharacteristic
397Dic3⋊C4—31no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402Dic3⋊C4—61no—
403Dic3⋊C4—61no—
404C4×Dic3—61no—
405C4×Dic3—61no—
406C4×Dic3C22×D311yescharacteristic
407C2×C3⋊C8—31no—
408C2×C3⋊C8—31no—
409C2×C3⋊C8—61no—
410C2×C3⋊C8—121no—
411C2×C3⋊C8C22×D311yescharacteristic
412C2×C3⋊C8C22×D311yescharacteristic
413D3×C8—121no—
414D3×C8—121no—
415D3×C8—121no—
416C22×C32—22no—
417C22×C32—41no—
418C22×C32—41no—
419C22×C32—41no—
420C22×C32—41no—
421C22×C32—41no—
422C22×C32C22×D411yescharacteristic
423C2×C3⋊D3—21no—
424C2×C3⋊D3—21no—
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×C4C2×#4111yescharacteristic
434C32×C4H(5,𝔽2)11yescharacteristic
435C3⋊Dic3—21no—
436C3⋊Dic3—41no—
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—31no—
447C2×D8—91no—
448C2×D8D3211yescharacteristic
449C22×C8—91no—
450C22×C8—91no—
451#126—181no—
452#125—91no—
453#124—91no—
454#123—181no—
455#123—181no—
456C22⋊Q8—91no—
457#121—31no—
458#121—91no—
459#121—91no—
460#121—181no—
461#121—181no—
462#120—181no—
463C4×D4—31no—
464C4×D4—31no—
465C4×D4—91no—
466C4×D4—181no—
467#117—91no—
468C2×C4⋊C4—91no—
469C2×C22⋊C4—181no—
470#107—31no—
471#107—91no—
472#106—91no—
473C4⋊C8—91no—
474#103—31no—
475#103—91no—
476#103—91no—
477#102—31no—
478#102—31no—
479#102—31no—
480#102—91no—
481#102—91no—
482#102—91no—
483#102—91no—
484C22⋊C8—31no—
485C22⋊C8—91no—
486C4×C8—31no—
487C23×C3—21no—
488C23×C3—21no—
489C23×C3—21no—
490C23×C3—21no—
491C23×C3—31no—
492C23×C3—41no—
493C23×C3—41no—
494C22×D3—31no—
495C22×D3—31no—
496C22×D3—61no—
497C22×D3—61no—
498C22×D3—61no—
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—21no—
515C3×D4—21no—
516C3×D4—21no—
517C3×D4—21no—
518C3×D4—22no—
519C3×D4—41no—
520C3×D4—41no—
521C3×D4—41no—
522C3×D4—122no—
523C3×D4—241no—
524C3×D4#23512yes—
525C3×D4#23712yes—
526C2×C3×C4—21no—
527C2×C3×C4—31no—
528C2×C3×C4—31no—
529C2×C3×C4—31no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—122no—
537C2×C3×C4—241no—
538C2×C3×C4—241no—
539C2×C3×C4C23×D311yescharacteristic
540C2×C3×C4C23×D311yescharacteristic
541#67—42no—
542#67—62no—
543#67—81no—
544#67—122no—
545#67—122no—
546#67—122no—
547#67—122no—
548#67—124no—
549#67—242no—
550#67—241no—
551C2×Dic3—21no—
552C2×Dic3—21no—
553C2×Dic3—21no—
554C2×Dic3—21no—
555C2×Dic3—31no—
556C2×Dic3—31no—
557C2×Dic3—42no—
558C2×Dic3—61no—
559C2×Dic3—61no—
560C2×Dic3—61no—
561C2×Dic3—81no—
562C2×Dic3—81no—
563C2×Dic3—121no—
564C2×Dic3D3×D411yescharacteristic
565C2×Dic3D3×D411yescharacteristic
566C2×Dic3D3×D411yescharacteristic
567D12—62no—
568D12—62no—
569D12—61no—
570D12—61no—
571D12—61no—
572D12—61no—
573D12—121no—
574D12—241no—
575C4×D3—21no—
576C4×D3—21no—
577C4×D3—61no—
578C4×D3—61no—
579C4×D3—61no—
580C4×D3—61no—
581C4×D3—121no—
582C4×D3—121no—
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—81no—
599C2×C32#54611yescharacteristic
600C2×C32C2×#13511yescharacteristic
601C2×C32#57611yescharacteristic
602C3⋊D3—22no—
603C3⋊D3—81no—
604C3×D3—41no—
605C24—181no—
606#41—62no—
607#41—121no—
608C2×Q8—31no—
609C2×D4—61no—
610C2×D4—61no—
611C2×D4—91no—
612C2×D4—91no—
613C2×D4—181no—
614C2×D4—181no—
615C2×D4—182no—
616C2×D4—181no—
617C2×D4—361no—
618C2×D4C2×D3211yescharacteristic
619C2×D4C2×D3211yescharacteristic
620C22×C4—31no—
621C22×C4—61no—
622C22×C4—61no—
623C22×C4—61no—
624C22×C4—91no—
625C22×C4—181no—
626SD16—121no—
627D8—22no—
628D8—361no—
629C2×C8—31no—
630C2×C8—31no—
631C2×C8—91no—
632C2×C8—361no—
633C2×C8—361no—
634C2×C8C2×D3211yescharacteristic
635C4⋊C4—31no—
636C4⋊C4—31no—
637C4⋊C4—31no—
638C4⋊C4—91no—
639C4⋊C4—91no—
640C4⋊C4—181no—
641C4⋊C4—181no—
642C4⋊C4—181no—
643C4⋊C4—181no—
644C22⋊C4—61no—
645C22⋊C4—61no—
646C22⋊C4—61no—
647C22⋊C4—91no—
648C22⋊C4—91no—
649C22⋊C4—181no—
650C22⋊C4—181no—
651C22⋊C4—181no—
652C22⋊C4—181no—
653C22⋊C4—181no—
654C22⋊C4—181no—
655C42—31no—
656C42—181no—
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—41no—
666C22×C3—41no—
667C22×C3—41no—
668C22×C3—41no—
669C22×C3—41no—
670C22×C3—41no—
671C22×C3—61no—
672C22×C3—61no—
673C22×C3—61no—
674C22×C3—81no—
675C22×C3—81no—
676C22×C3—81no—
677C22×C3—81no—
678C22×C3—81no—
679C22×C3C2×D3×D411yescharacteristic
680C22×C3C2×D3×D411yescharacteristic
681C2×D3—21no—
682C2×D3—21no—
683C2×D3—21no—
684C2×D3—32no—
685C2×D3—32no—
686C2×D3—62no—
687C2×D3—61no—
688C2×D3—61no—
689C2×D3—61no—
690C2×D3—61no—
691C2×D3—121no—
692C2×D3—121no—
693C2×D3—122no—
694C2×D3—121no—
695C2×D3—121no—
696C2×D3—121no—
697C2×D3—121no—
698C2×D3—121no—
699C2×D3—121no—
700C2×D3—241no—
701C2×D3—241no—
702C2×D3—244no—
703C2×D3—244no—
704C2×D3—248no—
705C3×C4—21no—
706C3×C4—21no—
707C3×C4—61no—
708C3×C4—61no—
709C3×C4—61no—
710C3×C4—121no—
711C3×C4—121no—
712C3×C4—121no—
713C3×C4—121no—
714C3×C4C2×#23511yescharacteristic
715C3×C4C2×#23711yescharacteristic
716C3×C4#100411yescharacteristic
717C3×C4#100911yescharacteristic
718Dic3—21no—
719Dic3—21no—
720Dic3—21no—
721Dic3—41no—
722Dic3—41no—
723Dic3—41no—
724Dic3—41no—
725Dic3—61no—
726Dic3—61no—
727Dic3—121no—
728Dic3—121no—
729Dic3—121no—
730Dic3—241no—
731C32#329711yescharacteristic, complemented, Sylow
732C23—21no—
733C23—21no—
734C23—31no—
735C23—91no—
736C23—181no—
737C23—362no—
738C23—362no—
739C23—721no—
740Q8—61no—
741Q8—61no—
742D4—21no—
743D4—21no—
744D4—21no—
745D4—122no—
746D4—182no—
747D4—181no—
748D4—181no—
749D4—241no—
750D4—362no—
751D4—362no—
752D4—721no—
753D4#380412yes—
754C2×C4—31no—
755C2×C4—31no—
756C2×C4—31no—
757C2×C4—61no—
758C2×C4—61no—
759C2×C4—61no—
760C2×C4—61no—
761C2×C4—61no—
762C2×C4—61no—
763C2×C4—91no—
764C2×C4—122no—
765C2×C4—181no—
766C2×C4—181no—
767C2×C4—181no—
768C2×C4—241no—
769C2×C4—241no—
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—81no—
783C2×C3—81no—
784C2×C3—121no—
785C2×C3—161no—
786C2×C3#555011yescharacteristic
787C2×C3#559111yescharacteristic
788C2×C3#575711yescharacteristic
789C2×C3D3×#13511yescharacteristic
790C2×C3D3×#13511yescharacteristic
791C2×C3#577411yescharacteristic
792D3—41no—
793D3—62no—
794D3—62no—
795D3—122no—
796D3—242no—
797D3—241no—
798D3—241no—
799C22—22no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—61no—
806C22—61no—
807C22—61no—
808C22—92no—
809C22—181no—
810C22—181no—
811C22—361no—
812C22—361no—
813C22—361no—
814C22—724no—
815C22D32×D411yescharacteristic
816C4—61no—
817C4—61no—
818C4—61no—
819C4—121no—
820C4—121no—
821C4—121no—
822C4—121no—
823C4—181no—
824C4—361no—
825C4#6431411yescharacteristic
826C4C2×#380411yescharacteristic
827C3—21no—
828C3#7960911yescharacteristic, complemented
829C3#8010211yescharacteristic, complemented
830C2—42no—
831C2—81no—
832C2—121no—
833C2—182no—
834C2—721no—
835C2#1059473011yescharacteristic
836C2#1059473211yescharacteristic
837C2#1059513511yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
hypercenterC2×D8D32
hypocenterC32#3297
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. #10595254C2semidirect
2. #10595122C2semidirect
3. #10592855C2semidirect
4. C3×#5158C2semidirect
5. C3×Dic3×D8C2semidirect
6. #10591471C2semidirect
7. #10591465C2semidirect
8. #10591449C2semidirect
9. #10591420C2semidirect
10. #10591416C2semidirect
11. #10591409C2semidirect
12. #10590872C2semidirect
13. #10590721C2semidirect
14. #10590705C2semidirect
15. #10590689C2semidirect
23. C3×#938C22semidirect
25. C3×D4×Dic3C22semidirect
26. C2×C3×#214C22semidirect
39. #63869C22semidirect
41. #63841C22semidirect
43. C2×D3×C3⋊C8C22semidirect
49. C3×#832C22semidirect
50. C3×(C2×D3)⋊C8C22semidirect
51. C3×#818C22semidirect
52. C3×#816C22semidirect
53. C3×C8×Dic3C22semidirect
54. #63576C22semidirect
55. #63573C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63566C22semidirect
58. #63565C22semidirect
70. #5158D3semidirect
74. Dic3×D8D3semidirect
164. #938C2×D3semidirect
168. D4×Dic3C2×D3semidirect
169. C2×#214C2×D3semidirect
215. #832C2×D3semidirect
224. (C2×D3)⋊C8C2×D3semidirect
225. #818C2×D3semidirect
228. #816C2×D3semidirect
230. C8×Dic3C2×D3semidirect
731. C32#3297semidirect
828. C3#79609semidirect
829. C3#80102semidirect

Maximal subgroups

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

subgroupindex
#105952542
#105951222
#105928552
C3×#51582
C3×Dic3×D82
#105914712
#105914652
#105914492
#105914202
#105914162
#105914092
#105908722
#105907212
#105907052
#105906892
#801023
#796093