Finite Group Databasebeta

← #11887026

Subgroups — #11887026

Order 1152.

1089 conjugacy classes of subgroups.

The subgroup lattice has 885 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#626C211yesmaximal, characteristic, complemented
2#10594515C211yesmaximal, characteristic, complemented
3C3⋊D3×#102C211yesmaximal, characteristic, complemented
4C3×D3×#102C211yesmaximal, characteristic, complemented
5C3×#4756C211yesmaximal, characteristic, complemented
6#10591456C211yesmaximal, characteristic, complemented
7#10591447C211yesmaximal, characteristic, complemented
8#10591410C211yesmaximal, characteristic, complemented
9#10590878C211yesmaximal, characteristic, complemented
10#10590839C211yesmaximal, characteristic, complemented
11#10590826C211yesmaximal, characteristic, complemented
12C8×#626C211yesmaximal, characteristic, complemented
13#10590547C211yesmaximal, characteristic, complemented
14#10590510C211yesmaximal, characteristic, complemented
15#10590422C211yesmaximal, characteristic, complemented
16#79608—31nomaximal
17#78757—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C22×#626—21no—
21C2×#3798—21no—
22C2×C8×C3⋊D3C2211yescharacteristic, complemented
23C4⋊C4×C3⋊D3C2211yescharacteristic, complemented
24C3×D4×Dic3C2211yescharacteristic
25C2×C3×#213C2211yescharacteristic
26C2×C3×D3×C8C2211yescharacteristic, complemented
27C3×#893C2211yescharacteristic, complemented
28C3×D3×C4⋊C4C2211yescharacteristic, complemented
29#63981—21no—
30#63978—21no—
31#63977—21no—
32#63918C2211yescharacteristic, complemented
33#63916C2211yescharacteristic
34#63916C2211yescharacteristic, complemented
35#63911C2211yescharacteristic
36#63909C2211yescharacteristic
37#63908C2211yescharacteristic, complemented
38#63905—21no—
39C4×#626C2211yescharacteristic
40#63853—21no—
41#63851—21no—
42C2×#3714C2211yescharacteristic, complemented
43C2×#3713C2211yescharacteristic, complemented
44C32×#102C2211yescharacteristic
45#63659C2211yescharacteristic
46#63648C2211yescharacteristic, complemented
47#63636C2211yescharacteristic, complemented
48C3×#832C2211yescharacteristic
49C3×#821C2211yescharacteristic, complemented
50C3×#821C2211yescharacteristic, complemented
51C3×C8×Dic3C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic, complemented
53C3×#807C2211yescharacteristic, complemented
54#63576C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63564C2211yescharacteristic, complemented
58#63563C2211yescharacteristic, complemented
59#63557C2211yescharacteristic, complemented
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
61D4×#67—31no—
62#5551—31no—
63D4×D12—31no—
64#5507—31no—
65C3×C4×D8—31no—
66C2×C3×#102—31no—
67#5217—31no—
68#5156—31no—
69#5156—31no—
70#5115—31no—
71C8×#67—31no—
72#5015—31no—
73#5007—31no—
74#4967—31no—
75#4882—31no—
76#4882—31no—
77#4786—31no—
78#4775—31no—
79#4775—31no—
80#4775—31no—
81#4774—31no—
82#4773—31no—
83D3×#102—31no—
84D3×#102—31no—
85D3×#102—61no—
86D3×#102D311yescharacteristic, complemented
87#4760—31no—
88#4759—31no—
89#4756D311yescharacteristic, complemented
90#4694—31no—
91C8×D12—31no—
92C23×C3⋊D3—21no—
93C23×C3×D3—21no—
94C2×C32×D4C2311yescharacteristic
95C2×#638—21no—
96D4×C3⋊D3—22no—
97D4×C3⋊D3—41no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4×C3⋊D3—21no—
100C2×C4×C3⋊D3C2311yescharacteristic
101C2×C3×#67—21no—
102C22×C3×Dic3—21no—
103C3×D3×D4—22no—
104C3×D3×D4—41no—
105C2×C3×D12C2311yescharacteristic
106C2×C3×D12C2311yescharacteristic
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3C2311yescharacteristic
110C2×#627—21no—
111C2×#626—21no—
112C2×#626—21no—
113C2×#626—21no—
114C2×#626—21no—
115C2×#626—21no—
116C2×#626—44no—
117C2×#626D411yescharacteristic
118C2×#625—21no—
119#3798—44no—
120C2×C32×C8C2311yescharacteristic
121C32×C4⋊C4C2311yescharacteristic
122C4⋊(C3⋊Dic3)C2311yescharacteristic
123#3750—21no—
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C8×C3⋊D3—41no—
126C3×#217—21no—
127C3×#213—22no—
128C3×(C2×D3)⋊C4—21no—
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×Dic3⋊C4—21no—
132C3×C4×Dic3C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C3×D3×C8—41no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3D411yescharacteristic
138#3722—21no—
139#3722D411yescharacteristic
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143(C2×D3)⋊Dic3D411yescharacteristic
144#3714—41no—
145#3713—41no—
146#3294—91noSylow
147C22×C3×D4—31no—
148C22×#67—61no—
149C2×D3×D4—31no—
150C2×D3×D4—31no—
151C2×D3×D4—61no—
152C2×D3×D4C2×D311yescharacteristic
153C2×#235—61no—
154C2×#235—61no—
155C22×D12—61no—
156C2×C3×D8—31no—
157C22×C3×C8—31no—
158C3×C4×D4—31no—
159C3×C4×D4—31no—
160C2×C3×C4⋊C4—31no—
161#953—61no—
162#940—31no—
163#939—61no—
164#938—31no—
165#938—31no—
166#938—31no—
167#937—61no—
168D4×Dic3C2×D311yescharacteristic
169C2×#213—31no—
170C2×#213—31no—
171C2×#213—31no—
172C2×#213C2×D311yescharacteristic
173#930—31no—
174#930—31no—
175#930—61no—
176#929—61no—
177C4×#67—31no—
178#924—61no—
179C2×D24—31no—
180C2×D3×C8—31no—
181C2×D3×C8—31no—
182C2×D3×C8—61no—
183C2×D3×C8C2×D311yescharacteristic, complemented
184#896—61no—
185#895—31no—
186#895—31no—
187#895—31no—
188#894—61no—
189#893C2×D311yescharacteristic, complemented
190D3×C4⋊C4—31no—
191D3×C4⋊C4—31no—
192D3×C4⋊C4—61no—
193D3×C4⋊C4C2×D311yescharacteristic, complemented
194#888—31no—
195#883—61no—
196#883—61no—
197#882—61no—
198#882—61no—
199#874—31no—
200C4×D12—31no—
201#869—31no—
202C3×#107—31no—
203C3×#102—21no—
204C3×#102—31no—
205C3×#102—31no—
206C3×#102—31no—
207C3×#102—31no—
208C3×#102C2×D311yescharacteristic
209C3×#102C2×D311yescharacteristic
210C3×C4×C8—31no—
211#832—31no—
212#832—31no—
213#832—31no—
214#832—61no—
215#832C2×D311yescharacteristic
216#830—31no—
217#821—31no—
218#821—31no—
219#821—31no—
220#821—31no—
221#821—61no—
222#821C2×D311yescharacteristic, complemented
223#821C2×D311yescharacteristic, complemented
224(C2×D3)⋊C8—31no—
225(C2×D3)⋊C8—31no—
226(C2×D3)⋊C8—31no—
227#818—31no—
228Dic3⋊C8—31no—
229C8×Dic3C2×D311yescharacteristic, complemented
230#809—31no—
231#809—31no—
232#809—31no—
233#809—61no—
234#809C2×D311yescharacteristic, complemented
235#807—31no—
236#807—31no—
237#807—31no—
238#807C2×D311yescharacteristic, complemented
239C4⋊(C3⋊C8)—31no—
240C23×C32—21no—
241C22×C3⋊D3—21no—
242C22×C3⋊D3—42no—
243C22×C3⋊D3—42no—
244C22×C3⋊D3—81no—
245C22×C3⋊D3C2×D411yescharacteristic
246C22×C3×D3—21no—
247C22×C3×D3—21no—
248C22×C3×D3—42no—
249C22×C3×D3—42no—
250C22×C3×D3—81no—
251C22×C3×D3C2×D411yescharacteristic
252C32×D4—21no—
253C32×D4#4112yescomplemented
254C2×C32×C4—21no—
255C2×C32×C4C2411yescharacteristic
256#638—42no—
257C2×C3⋊Dic3—21no—
258C2×C3⋊Dic3C2×D411yescharacteristic
259C4⋊(C3⋊D3)—21no—
260C4⋊(C3⋊D3)—21no—
261C4×C3⋊D3—21no—
262C4×C3⋊D3—21no—
263C4×C3⋊D3—42no—
264C3×#67—42no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—42no—
268C2×C3×Dic3C2×D411yescharacteristic
269C2×C3×Dic3C2×D411yescharacteristic
270C2×C3×Dic3C2×D411yescharacteristic
271C3×D12—21no—
272C3×D12—21no—
273C3×D12—21no—
274C3×D12—21no—
275C3×C4×D3—21no—
276C3×C4×D3—21no—
277C3×C4×D3—42no—
278C3×C4×D3—42no—
279#627—42no—
280#626—42no—
281#626—42no—
282#626—42no—
283#626—42no—
284#626—81no—
285#626D814yescomplemented
286#625—42no—
287C32×C8—21no—
288C3⋊(C3⋊C8)—21no—
289C3×C3⋊C8—21no—
290C3×C3⋊C8—21no—
291#547—91no—
292D42—91no—
293#486—91no—
294#480—91no—
295#480—91no—
296#474—91no—
297#466—91no—
298#466—91no—
299#459—91no—
300#447—91no—
301#447—91no—
302C4×D8—31no—
303C8×D4—91no—
304C2×#102—31no—
305C2×#102—91no—
306C24×C3—61no—
307C23×D3—21no—
308C23×D3—61no—
309C23×D3—61no—
310C23×D3—121no—
311C2×C3×D4—21no—
312C2×C3×D4—31no—
313C2×C3×D4—31no—
314C2×C3×D4—61no—
315C2×C3×D4—62no—
316C2×C3×D4—121no—
317C2×C3×D4C22×D311yescharacteristic
318C2×C3×D4C22×D311yescharacteristic
319C22×C3×C4—31no—
320C22×C3×C4—61no—
321C22×C3×C4—61no—
322C22×C3×C4—61no—
323C2×#67—21no—
324C2×#67—31no—
325C2×#67—61no—
326C2×#67—61no—
327C2×#67—61no—
328C2×#67—61no—
329C2×#67—61no—
330C2×#67—61no—
331C2×#67—61no—
332C2×#67—61no—
333C2×#67—61no—
334C2×#67—121no—
335C2×#67—124no—
336C22×Dic3—21no—
337D3×D4—22no—
338D3×D4—41no—
339D3×D4—64no—
340D3×D4—62no—
341D3×D4—62no—
342D3×D4—121no—
343D3×D4—121no—
344D3×D4—122no—
345#235—124no—
346#235—124no—
347C2×D12—31no—
348C2×D12—31no—
349C2×D12—31no—
350C2×D12—61no—
351C2×D12—61no—
352C2×D12—61no—
353C2×D12—61no—
354C2×D12—61no—
355C2×D12—61no—
356C2×D12—124no—
357C2×D12C22×D311yescharacteristic
358C2×D12C22×D311yescharacteristic
359C2×C4×D3—21no—
360C2×C4×D3—21no—
361C2×C4×D3—31no—
362C2×C4×D3—31no—
363C2×C4×D3—61no—
364C2×C4×D3—61no—
365C2×C4×D3—61no—
366C2×C4×D3—121no—
367C2×C4×D3C22×D311yescharacteristic
368C2×Dic6—61no—
369C2×Dic6—61no—
370C3×D8—62no—
371C2×C3×C8—21no—
372C2×C3×C8—31no—
373C2×C3×C8—31no—
374C2×C3×C8—121no—
375C2×C3×C8C22×D311yescharacteristic
376C2×C3×C8C22×D311yescharacteristic
377C3×C4⋊C4—21no—
378C3×C4⋊C4—31no—
379C3×C4⋊C4—31no—
380C3×C4⋊C4—61no—
381C3×C4⋊C4C22×D311yescharacteristic
382C3×C4⋊C4C22×D311yescharacteristic
383C3×C22⋊C4—61no—
384C3×C22⋊C4—61no—
385C3×C42—31no—
386#217—21no—
387#217—31no—
388#217—61no—
389#217—61no—
390#217—61no—
391#213—22no—
392#213—121no—
393#213—121no—
394#213—121no—
395(C2×D3)⋊C4—21no—
396(C2×D3)⋊C4—31no—
397(C2×D3)⋊C4—31no—
398(C2×D3)⋊C4—31no—
399(C2×D3)⋊C4—61no—
400(C2×D3)⋊C4—61no—
401(C2×D3)⋊C4—61no—
402(C2×D3)⋊C4—61no—
403(C2×D3)⋊C4—61no—
404C4⋊Dic3—31no—
405C4⋊Dic3—31no—
406C4⋊Dic3—31no—
407C4⋊Dic3—61no—
408C4⋊Dic3—61no—
409C4⋊Dic3C22×D311yescharacteristic
410C4⋊Dic3C22×D311yescharacteristic
411Dic3⋊C4—21no—
412Dic3⋊C4—31no—
413Dic3⋊C4—61no—
414Dic3⋊C4—61no—
415Dic3⋊C4—61no—
416Dic3⋊C4—121no—
417C4×Dic3C22×D311yescharacteristic
418C2×C3⋊C8—31no—
419C2×C3⋊C8—31no—
420C2×C3⋊C8—61no—
421C2×C3⋊C8C22×D311yescharacteristic
422C2×C3⋊C8C22×D311yescharacteristic
423D24—121no—
424D3×C8—41no—
425D3×C8—121no—
426D3×C8—121no—
427D3×C8—122no—
428C22×C32—22no—
429C22×C32—41no—
430C22×C32—41no—
431C22×C32C22×D411yescharacteristic
432C2×C3⋊D3—21no—
433C2×C3⋊D3—21no—
434C2×C3⋊D3—41no—
435C2×C3⋊D3—41no—
436C2×C3⋊D3—41no—
437C2×C3⋊D3—84no—
438C2×C3⋊D3C2×D812yes—
439C2×C3×D3—21no—
440C2×C3×D3—21no—
441C2×C3×D3—41no—
442C2×C3×D3—41no—
443C2×C3×D3—41no—
444C2×C3×D3—41no—
445C2×C3×D3—41no—
446C2×C3×D3—41no—
447C2×C3×D3—84no—
448C2×C3×D3C2×D812yes—
449C32×C4—41no—
450C32×C4C2×#4111yescharacteristic
451C32×C4H(5,𝔽2)11yescharacteristic
452C3⋊Dic3—21no—
453C3⋊Dic3—41no—
454C3×Dic3—21no—
455C3×Dic3—21no—
456C3×Dic3—41no—
457C3×Dic3—41no—
458C3×Dic3C2×D812yes—
459C2×#41—181no—
460C22×D4—31no—
461C22×D4—91no—
462C22×D4—181no—
463C2×D8—31no—
464C2×D8—91no—
465C2×D8—91no—
466C22×C8—31no—
467C22×C8—91no—
468C4⋊Q8—91no—
469#127—91no—
470#123—181no—
471#123—181no—
472C22⋊Q8—181no—
473#121—91no—
474#121—91no—
475#121—91no—
476#121—91no—
477#121—181no—
478#120—181no—
479#120—181no—
480C4×D4—31no—
481C4×D4—31no—
482C4×D4—91no—
483C2×C4⋊C4—31no—
484C2×C4⋊C4—91no—
485#107—31no—
486#107—91no—
487#107—91no—
488C4⋊C8—91no—
489#102—31no—
490#102—31no—
491#102—31no—
492#102—31no—
493#102—91no—
494#102—91no—
495#102—91no—
496#102—91no—
497#102—91no—
498#102D3211yescharacteristic
499C22⋊C8—91no—
500C22⋊C8—91no—
501C4×C8—31no—
502C23×C3—21no—
503C23×C3—21no—
504C23×C3—31no—
505C23×C3—41no—
506C23×C3—61no—
507C23×C3—61no—
508C23×C3—122no—
509C23×C3—122no—
510C23×C3—241no—
511C22×D3—21no—
512C22×D3—21no—
513C22×D3—31no—
514C22×D3—31no—
515C22×D3—42no—
516C22×D3—42no—
517C22×D3—61no—
518C22×D3—61no—
519C22×D3—61no—
520C22×D3—81no—
521C22×D3—121no—
522C22×D3—122no—
523C22×D3—122no—
524C22×D3—122no—
525C22×D3—122no—
526C22×D3—124no—
527C22×D3—242no—
528C22×D3—241no—
529C22×D3—241no—
530C22×D3—242no—
531C22×D3D3×D411yescharacteristic
532C3×D4—21no—
533C3×D4—21no—
534C3×D4—22no—
535C3×D4—41no—
536C3×D4—61no—
537C3×D4—61no—
538C3×D4—61no—
539C3×D4—61no—
540C3×D4—122no—
541C3×D4#23512yescomplemented
542C3×D4#23512yescomplemented
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—31no—
547C2×C3×C4—31no—
548C2×C3×C4—31no—
549C2×C3×C4—41no—
550C2×C3×C4—61no—
551C2×C3×C4—61no—
552C2×C3×C4—61no—
553C2×C3×C4—61no—
554C2×C3×C4—122no—
555C2×C3×C4—122no—
556C2×C3×C4—122no—
557C2×C3×C4C23×D311yescharacteristic
558C2×C3×C4C23×D311yescharacteristic
559#67—34no—
560#67—42no—
561#67—122no—
562#67—122no—
563#67—122no—
564#67—122no—
565#67—122no—
566#67—124no—
567#67—122no—
568#67—122no—
569#67—122no—
570#67—241no—
571C2×Dic3—21no—
572C2×Dic3—21no—
573C2×Dic3—31no—
574C2×Dic3—31no—
575C2×Dic3—42no—
576C2×Dic3—61no—
577C2×Dic3—61no—
578C2×Dic3—61no—
579C2×Dic3—121no—
580C2×Dic3D3×D411yescharacteristic
581C2×Dic3D3×D411yescharacteristic
582C2×Dic3D3×D411yescharacteristic
583D12—21no—
584D12—21no—
585D12—21no—
586D12—21no—
587D12—34no—
588D12—62no—
589D12—61no—
590D12—61no—
591D12—61no—
592D12—61no—
593D12—121no—
594D12—122no—
595D12—122no—
596D12—122no—
597D12—122no—
598D12—241no—
599C4×D3—21no—
600C4×D3—21no—
601C4×D3—42no—
602C4×D3—42no—
603C4×D3—62no—
604C4×D3—62no—
605C4×D3—61no—
606C4×D3—61no—
607C4×D3—61no—
608C4×D3—61no—
609C4×D3—122no—
610C4×D3—122no—
611C4×D3—242no—
612Dic6—122no—
613Dic6—122no—
614C3×C8—21no—
615C3×C8—21no—
616C3×C8—41no—
617C3×C8—61no—
618C3×C8—61no—
619C3⋊C8—21no—
620C3⋊C8—21no—
621C3⋊C8—61no—
622C3⋊C8—61no—
623C3⋊C8—121no—
624C2×C32—42no—
625C2×C32#54611yescharacteristic
626C2×C32C22×D811yescharacteristic
627C2×C32#57711yescharacteristic
628C3⋊D3—22no—
629C3⋊D3—81no—
630C3×D3—22no—
631C3×D3—81no—
632C3×D3—81no—
633C24—61no—
634C24—181no—
635#41—364no—
636C2×Q8—181no—
637C2×D4—31no—
638C2×D4—31no—
639C2×D4—61no—
640C2×D4—62no—
641C2×D4—91no—
642C2×D4—91no—
643C2×D4—121no—
644C2×D4—181no—
645C2×D4—181no—
646C2×D4—181no—
647C2×D4—181no—
648C2×D4—181no—
649C2×D4—181no—
650C2×D4—182no—
651C2×D4—181no—
652C2×D4—364no—
653C2×D4—361no—
654C2×D4C2×D3211yescharacteristic
655C22×C4—31no—
656C22×C4—61no—
657C22×C4—61no—
658C22×C4—61no—
659C22×C4—91no—
660C22×C4—181no—
661D8—62no—
662D8—361no—
663D8—361no—
664C2×C8—31no—
665C2×C8—31no—
666C2×C8—91no—
667C2×C8—121no—
668C2×C8—361no—
669C2×C8C2×D3211yescharacteristic
670C4⋊C4—31no—
671C4⋊C4—31no—
672C4⋊C4—61no—
673C4⋊C4—91no—
674C4⋊C4—91no—
675C4⋊C4—181no—
676C4⋊C4—181no—
677C4⋊C4C2×D3211yescharacteristic
678C22⋊C4—61no—
679C22⋊C4—61no—
680C22⋊C4—91no—
681C22⋊C4—91no—
682C22⋊C4—181no—
683C22⋊C4—181no—
684C22⋊C4—181no—
685C22⋊C4—181no—
686C42—31no—
687C22×C3—22no—
688C22×C3—22no—
689C22×C3—21no—
690C22×C3—32no—
691C22×C3—42no—
692C22×C3—41no—
693C22×C3—41no—
694C22×C3—41no—
695C22×C3—41no—
696C22×C3—61no—
697C22×C3—61no—
698C22×C3—81no—
699C22×C3—81no—
700C22×C3—121no—
701C22×C3—121no—
702C22×C3—121no—
703C22×C3—121no—
704C22×C3—121no—
705C22×C3—121no—
706C22×C3—244no—
707C22×C3C2×D3×D411yescharacteristic
708C22×C3C2×D3×D411yescharacteristic
709C2×D3—21no—
710C2×D3—21no—
711C2×D3—32no—
712C2×D3—32no—
713C2×D3—41no—
714C2×D3—41no—
715C2×D3—41no—
716C2×D3—41no—
717C2×D3—41no—
718C2×D3—41no—
719C2×D3—62no—
720C2×D3—62no—
721C2×D3—62no—
722C2×D3—61no—
723C2×D3—61no—
724C2×D3—61no—
725C2×D3—61no—
726C2×D3—84no—
727C2×D3—122no—
728C2×D3—121no—
729C2×D3—121no—
730C2×D3—121no—
731C2×D3—121no—
732C2×D3—121no—
733C2×D3—121no—
734C2×D3—241no—
735C2×D3—241no—
736C2×D3—244no—
737C2×D3—244no—
738C2×D3—248no—
739C2×D3D3×D812yes—
740C3×C4—21no—
741C3×C4—21no—
742C3×C4—32no—
743C3×C4—41no—
744C3×C4—41no—
745C3×C4—61no—
746C3×C4—61no—
747C3×C4—81no—
748C3×C4—121no—
749C3×C4—121no—
750C3×C4C2×#23511yescharacteristic
751C3×C4C2×#23511yescharacteristic
752C3×C4#100411yescharacteristic
753C3×C4#100911yescharacteristic
754Dic3—21no—
755Dic3—21no—
756Dic3—41no—
757Dic3—41no—
758Dic3—62no—
759Dic3—61no—
760Dic3—61no—
761Dic3—121no—
762Dic3—121no—
763Dic3—241no—
764Dic3D3×D812yes—
765C32#329411yescharacteristic, complemented, Sylow
766C23—21no—
767C23—31no—
768C23—61no—
769C23—61no—
770C23—91no—
771C23—122no—
772C23—122no—
773C23—181no—
774C23—241no—
775C23—362no—
776C23—362no—
777C23—721no—
778Q8—362no—
779D4—21no—
780D4—61no—
781D4—61no—
782D4—61no—
783D4—61no—
784D4—94no—
785D4—122no—
786D4—181no—
787D4—181no—
788D4—362no—
789D4—362no—
790D4—362no—
791D4—362no—
792D4—362no—
793D4—362no—
794D4—721no—
795D4#379812yescomplemented
796C2×C4—21no—
797C2×C4—31no—
798C2×C4—31no—
799C2×C4—31no—
800C2×C4—61no—
801C2×C4—61no—
802C2×C4—61no—
803C2×C4—61no—
804C2×C4—91no—
805C2×C4—122no—
806C2×C4—122no—
807C2×C4—122no—
808C2×C4—181no—
809C2×C4—181no—
810C2×C4—181no—
811C2×C4—362no—
812C2×C4C22×D3211yescharacteristic
813C8—21no—
814C8—61no—
815C8—61no—
816C8—181no—
817C2×C3—21no—
818C2×C3—21no—
819C2×C3—21no—
820C2×C3—42no—
821C2×C3—42no—
822C2×C3—62no—
823C2×C3—82no—
824C2×C3—241no—
825C2×C3—241no—
826C2×C3#549011yescharacteristic
827C2×C3#555011yescharacteristic
828C2×C3C2×D3×D811yescharacteristic
829C2×C3C2×D3×D811yescharacteristic
830C2×C3#576211yescharacteristic
831C2×C3#577011yescharacteristic
832D3—22no—
833D3—64no—
834D3—62no—
835D3—62no—
836D3—81no—
837D3—81no—
838D3—242no—
839D3—241no—
840D3—241no—
841C22—22no—
842C22—32no—
843C22—41no—
844C22—41no—
845C22—61no—
846C22—61no—
847C22—92no—
848C22—121no—
849C22—121no—
850C22—121no—
851C22—121no—
852C22—121no—
853C22—121no—
854C22—181no—
855C22—181no—
856C22—244no—
857C22—361no—
858C22—361no—
859C22—361no—
860C22—724no—
861C22D32×D411yescharacteristic
862C4—32no—
863C4—41no—
864C4—61no—
865C4—61no—
866C4—121no—
867C4—121no—
868C4—181no—
869C4—361no—
870C4C2×#379811yescharacteristic
871C4#6431411yescharacteristic
872C3—21no—
873C3#7875711yescharacteristic, complemented
874C3#7960811yescharacteristic, complemented
875C2—42no—
876C2—62no—
877C2—182no—
878C2—241no—
879C2—241no—
880C2—721no—
881C2#1059418611yescharacteristic
882C2D32×D811yescharacteristic
883C2#1059475311yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
hypercenter#102D32
hypocenterC32#3294
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. D4×#626C2semidirect
2. #10594515C2semidirect
3. C3⋊D3×#102C2semidirect
4. C3×D3×#102C2semidirect
5. C3×#4756C2semidirect
6. #10591456C2semidirect
7. #10591447C2semidirect
8. #10591410C2semidirect
9. #10590878C2semidirect
10. #10590839C2semidirect
11. #10590826C2semidirect
12. C8×#626C2semidirect
13. #10590547C2semidirect
14. #10590510C2semidirect
15. #10590422C2semidirect
22. C2×C8×C3⋊D3C22semidirect
23. C4⋊C4×C3⋊D3C22semidirect
26. C2×C3×D3×C8C22semidirect
27. C3×#893C22semidirect
28. C3×D3×C4⋊C4C22semidirect
32. #63918C22semidirect
34. #63916C22semidirect
37. #63908C22semidirect
42. C2×#3714C22semidirect
43. C2×#3713C22semidirect
46. #63648C22semidirect
47. #63636C22semidirect
49. C3×#821C22semidirect
50. C3×#821C22semidirect
51. C3×C8×Dic3C22semidirect
52. C3×#809C22semidirect
53. C3×#807C22semidirect
54. #63576C22semidirect
55. #63575C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63564C22semidirect
58. #63563C22semidirect
59. #63557C22semidirect
60. (C2×D3)⋊(C3⋊C8)C22semidirect
86. D3×#102D3semidirect
89. #4756D3semidirect
183. C2×D3×C8C2×D3semidirect
189. #893C2×D3semidirect
193. D3×C4⋊C4C2×D3semidirect
222. #821C2×D3semidirect
223. #821C2×D3semidirect
229. C8×Dic3C2×D3semidirect
234. #809C2×D3semidirect
238. #807C2×D3semidirect
253. C32×D4#41semidirect
285. #626D8semidirect
541. C3×D4#235semidirect
542. C3×D4#235semidirect
765. C32#3294semidirect
795. D4#3798semidirect
873. C3#78757semidirect
874. C3#79608semidirect

Maximal subgroups

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

subgroupindex
D4×#6262
#105945152
C3⋊D3×#1022
C3×D3×#1022
C3×#47562
#105914562
#105914472
#105914102
#105908782
#105908392
#105908262
C8×#6262
#105905472
#105905102
#105904222
#796083
#787573