Finite Group Databasebeta

← #11887018

Subgroups — #11887018

Order 1152.

1087 conjugacy classes of subgroups.

The subgroup lattice has 891 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#626C211yesmaximal, characteristic, complemented
2#10594517C211yesmaximal, characteristic, complemented
3#10592472C211yesmaximal, characteristic, complemented
4C3×D3×#102C211yesmaximal, characteristic, complemented
5C3×#4759C211yesmaximal, characteristic, complemented
6#10591448C211yesmaximal, characteristic, complemented
7#10591416C211yesmaximal, characteristic, complemented
8#10591400C211yesmaximal, characteristic, complemented
9#10590832C211yesmaximal, characteristic, complemented
10#10590765C211yesmaximal, characteristic, complemented
11#10590720C211yesmaximal, characteristic, complemented
12#10590650C211yesmaximal, characteristic, complemented
13#10590548C211yesmaximal, characteristic, complemented
14#10590509C211yesmaximal, characteristic, complemented
15#10590422C211yesmaximal, characteristic, complemented
16#80980—31nomaximal
17#78757—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C22×#626—21no—
21C2×#3799—21no—
22C2×#3753C2211yescharacteristic
23C2×#3745C2211yescharacteristic, complemented
24#64104C2211yescharacteristic, complemented
25C3×D4×Dic3C2211yescharacteristic
26C2×C3×D3×C8C2211yescharacteristic, complemented
27C3×D3×C4⋊C4C2211yescharacteristic, complemented
28C3×#888C2211yescharacteristic, complemented
29#63981—21no—
30#63978—21no—
31#63977—21no—
32#63916C2211yescharacteristic
33#63911C2211yescharacteristic
34#63909C2211yescharacteristic
35#63909C2211yescharacteristic, complemented
36C4×#626C2211yescharacteristic
37#63900C2211yescharacteristic, complemented
38#63897—21no—
39#63894C2211yescharacteristic, complemented
40#63888—21no—
41#63850—21no—
42C2×#3714C2211yescharacteristic, complemented
43C2×#3710C2211yescharacteristic, complemented
44C32×#102C2211yescharacteristic
45#63647C2211yescharacteristic, complemented
46#63636C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#821C2211yescharacteristic, complemented
50C3×#818C2211yescharacteristic, complemented
51C3×Dic3⋊C8C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic, complemented
53C3×#807C2211yescharacteristic, complemented
54#63576C2211yescharacteristic, complemented
55#63564C2211yescharacteristic, complemented
56#63564C2211yescharacteristic, complemented
57#63564C2211yescharacteristic, complemented
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61D4×#67—31no—
62#5726—31no—
63D4×D12—31no—
64#5507—31no—
65C3×#474—31no—
66C2×C3×#102—31no—
67#5217—31no—
68#5115—31no—
69C8×#67—31no—
70#5088—31no—
71C4×#213—31no—
72#4967—31no—
73#4883—31no—
74#4883—31no—
75#4882—31no—
76#4882—31no—
77#4843—31no—
78#4834—31no—
79#4786—31no—
80#4775—31no—
81#4774—31no—
82#4773—31no—
83#4773—31no—
84#4773—31no—
85#4773—61no—
86D3×#102—31no—
87D3×#102—31no—
88D3×#102D311yescharacteristic, complemented
89#4760—31no—
90#4759D311yescharacteristic, complemented
91#4756—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)—21no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C4×C3⋊D3C2311yescharacteristic
102C2×C3×#67—21no—
103C22×C3×Dic3—21no—
104C3×D3×D4—22no—
105C3×D3×D4—41no—
106C2×C3×D12C2311yescharacteristic
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×Dic6—21no—
110C2×#626—21no—
111C2×#626—21no—
112C2×#626—21no—
113C2×#626—21no—
114C2×#626—21no—
115C2×#626—44no—
116C2×#626D411yescharacteristic
117C2×#624—21no—
118C2×#624—21no—
119#3799—44no—
120C2×C32×C8C2311yescharacteristic
121C32×C4⋊C4C2311yescharacteristic
122#3753—22no—
123#3752—21no—
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125#3745—41no—
126C3×#217—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×C4×Dic3C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C3×D3×C8—41no—
136#3724—21no—
137Dic3⋊Dic3D411yescharacteristic
138#3722—21no—
139#3722—21no—
140#3722—21no—
141#3722D411yescharacteristic
142(C2×D3)⋊Dic3—21no—
143(C2×D3)⋊Dic3D411yescharacteristic
144#3714—41no—
145#3710—41no—
146#3294—91noSylow
147C22×C3×D4—31no—
148C22×#67—61no—
149C2×#239—61no—
150C2×D3×D4—31no—
151C2×D3×D4—31no—
152C2×D3×D4—61no—
153C2×D3×D4C2×D311yescharacteristic
154C2×#235—61no—
155C22×D12—61no—
156C22×C3×C8—31no—
157C3×C4⋊Q8—31no—
158C3×C4×D4—31no—
159C2×C3×C4⋊C4—31no—
160#953—61no—
161#946—61no—
162#940—31no—
163#939—61no—
164#938—31no—
165#937—61no—
166D4×Dic3C2×D311yescharacteristic
167C2×#213—31no—
168C2×#213—31no—
169C2×#213—31no—
170C2×#213—61no—
171#930—31no—
172#930—31no—
173#930—61no—
174#929—61no—
175C4×#67—31no—
176C2×D24—31no—
177C2×D24—31no—
178C2×D24—31no—
179C2×D24—61no—
180C2×D3×C8—31no—
181C2×D3×C8—31no—
182C2×D3×C8C2×D311yescharacteristic, complemented
183#896—61no—
184#895—31no—
185#895—31no—
186#895—31no—
187#895—31no—
188#895—31no—
189#895—61no—
190#894—61no—
191#894—61no—
192#894—61no—
193#893—31no—
194D3×C4⋊C4—31no—
195D3×C4⋊C4—31no—
196D3×C4⋊C4C2×D311yescharacteristic, complemented
197#888C2×D311yescharacteristic, complemented
198#882—61no—
199#882—61no—
200#874—31no—
201C4×D12—31no—
202C4×D12—31no—
203C3×#107—31no—
204C3×#107—31no—
205C3×C4⋊C8—31no—
206C3×#102—21no—
207C3×#102—31no—
208C3×#102—31no—
209C3×#102—31no—
210C3×#102—31no—
211C3×#102C2×D311yescharacteristic
212C3×#102C2×D311yescharacteristic
213#832—31no—
214#832C2×D311yescharacteristic
215#832C2×D311yescharacteristic
216#830—31no—
217#821—31no—
218#821—31no—
219#821—31no—
220#821C2×D311yescharacteristic, complemented
221(C2×D3)⋊C8—31no—
222(C2×D3)⋊C8—31no—
223(C2×D3)⋊C8—31no—
224(C2×D3)⋊C8—61no—
225#818C2×D311yescharacteristic, complemented
226Dic3⋊C8C2×D311yescharacteristic, complemented
227C8×Dic3—31no—
228#809—31no—
229#809—31no—
230#809—31no—
231#809—31no—
232#809—31no—
233#809—31no—
234#809—61no—
235#809C2×D311yescharacteristic, complemented
236#807—31no—
237#807—31no—
238#807C2×D311yescharacteristic, complemented
239C4×C3⋊C8—31no—
240C23×C32—21no—
241C22×C3⋊D3—21no—
242C22×C3⋊D3—21no—
243C22×C3⋊D3—42no—
244C22×C3⋊D3—42no—
245C22×C3⋊D3—81no—
246C22×C3⋊D3C2×D411yescharacteristic
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⋊Dic3C2×D411yescharacteristic
258C4⋊(C3⋊D3)—21no—
259C4⋊(C3⋊D3)—21no—
260C4⋊(C3⋊D3)—21no—
261C4⋊(C3⋊D3)—21no—
262C4⋊(C3⋊D3)—42no—
263C4×C3⋊D3—21no—
264C4×C3⋊D3—21no—
265C3×#67—42no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—42no—
270C2×C3×Dic3C2×D411yescharacteristic
271C2×C3×Dic3C2×D411yescharacteristic
272C2×C3×Dic3C2×D411yescharacteristic
273C3×D12—21no—
274C3×D12—21no—
275C3×C4×D3—21no—
276C3×C4×D3—21no—
277C3×C4×D3—42no—
278C3×Dic6—42no—
279#626—42no—
280#626—42no—
281#626—42no—
282#626—42no—
283#626—81no—
284#626D814yescomplemented
285#624—42no—
286#624—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—31no—
297#466—91no—
298#466—91no—
299#459—91no—
300#447—91no—
301#447—91no—
302C4×D8—91no—
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×Q8—61no—
312C2×C3×D4—21no—
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—
322C2×#67—21no—
323C2×#67—31no—
324C2×#67—61no—
325C2×#67—61no—
326C2×#67—61no—
327C2×#67—61no—
328C2×#67—61no—
329C2×#67—61no—
330C2×#67—61no—
331C2×#67—121no—
332C2×#67—124no—
333C22×Dic3—21no—
334#239—124no—
335D3×D4—22no—
336D3×D4—41no—
337D3×D4—62no—
338D3×D4—62no—
339D3×D4—122no—
340D3×D4—121no—
341D3×D4—121no—
342D3×D4—122no—
343#235—124no—
344C2×D12—31no—
345C2×D12—31no—
346C2×D12—31no—
347C2×D12—31no—
348C2×D12—31no—
349C2×D12—61no—
350C2×D12—61no—
351C2×D12—61no—
352C2×D12—61no—
353C2×D12—61no—
354C2×D12—61no—
355C2×D12—61no—
356C2×D12—61no—
357C2×D12—61no—
358C2×D12—121no—
359C2×D12—124no—
360C2×D12C22×D311yescharacteristic
361C2×C4×D3—21no—
362C2×C4×D3—31no—
363C2×C4×D3—31no—
364C2×C4×D3—61no—
365C2×C4×D3—61no—
366C2×C4×D3—61no—
367C2×C4×D3—61no—
368C2×C4×D3—61no—
369C2×C4×D3C22×D311yescharacteristic
370C2×Dic6—21no—
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—31no—
381C3×C4⋊C4—61no—
382C3×C4⋊C4—61no—
383C3×C4⋊C4C22×D311yescharacteristic
384C3×C4⋊C4C22×D311yescharacteristic
385C3×C22⋊C4—61no—
386C3×C42—31no—
387#217—21no—
388#217—31no—
389#217—61no—
390#213—62no—
391#213—62no—
392#213—122no—
393#213—121no—
394(C2×D3)⋊C4—31no—
395(C2×D3)⋊C4—31no—
396(C2×D3)⋊C4—31no—
397(C2×D3)⋊C4—61no—
398(C2×D3)⋊C4—61no—
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—
404(C2×D3)⋊C4—61no—
405(C2×D3)⋊C4—61no—
406(C2×D3)⋊C4—121no—
407C4⋊Dic3—31no—
408C4⋊Dic3C22×D311yescharacteristic
409C4⋊Dic3C22×D311yescharacteristic
410C4⋊Dic3C22×D311yescharacteristic
411Dic3⋊C4—21no—
412Dic3⋊C4—21no—
413Dic3⋊C4—31no—
414Dic3⋊C4—61no—
415Dic3⋊C4—61no—
416C4×Dic3C22×D311yescharacteristic
417C2×C3⋊C8—31no—
418C2×C3⋊C8—31no—
419C2×C3⋊C8—61no—
420C2×C3⋊C8C22×D311yescharacteristic
421C2×C3⋊C8C22×D311yescharacteristic
422D24—121no—
423D24—121no—
424D24—122no—
425D24—121no—
426D3×C8—41no—
427D3×C8—121no—
428D3×C8—121no—
429C22×C32—22no—
430C22×C32—41no—
431C22×C32—41no—
432C22×C32C22×D411yescharacteristic
433C2×C3⋊D3—21no—
434C2×C3⋊D3—21no—
435C2×C3⋊D3—41no—
436C2×C3⋊D3—41no—
437C2×C3⋊D3—41no—
438C2×C3⋊D3—41no—
439C2×C3⋊D3—41no—
440C2×C3⋊D3—41no—
441C2×C3⋊D3—84no—
442C2×C3⋊D3C2×D812yes—
443C2×C3×D3—21no—
444C2×C3×D3—21no—
445C2×C3×D3—41no—
446C2×C3×D3—41no—
447C2×C3×D3—41no—
448C2×C3×D3—84no—
449C2×C3×D3C2×D812yes—
450C32×C4—41no—
451C32×C4C2×#4111yescharacteristic
452C32×C4H(5,𝔽2)11yescharacteristic
453C3⋊Dic3—21no—
454C3×Dic3—21no—
455C3×Dic3—21no—
456C3×Dic3—41no—
457C3×Dic3—41no—
458C3×Dic3—41no—
459C3×Dic3C2×D812yes—
460C2×#41—181no—
461C22×D4—31no—
462C22×D4—91no—
463C22×D4—181no—
464C2×D8—91no—
465C2×D8—91no—
466C2×D8—91no—
467C22×C8—31no—
468C22×C8—91no—
469C4⋊Q8—31no—
470#127—91no—
471#123—181no—
472#123—181no—
473C22⋊Q8—181no—
474#121—91no—
475#121—91no—
476#121—91no—
477#121—91no—
478#121—181no—
479#120—181no—
480#120—181no—
481C4×D4—31no—
482C4×D4—91no—
483C4×D4—91no—
484C2×C4⋊C4—31no—
485C2×C4⋊C4—91no—
486#107—31no—
487#107—31no—
488#107—91no—
489C4⋊C8—31no—
490#102—31no—
491#102—31no—
492#102—31no—
493#102—31no—
494#102—91no—
495#102—91no—
496#102—91no—
497#102—91no—
498#102—91no—
499#102D3211yescharacteristic
500C22⋊C8—91no—
501C22⋊C8—91no—
502C4×C8—91no—
503C23×C3—21no—
504C23×C3—21no—
505C23×C3—31no—
506C23×C3—41no—
507C23×C3—61no—
508C23×C3—122no—
509C23×C3—122no—
510C23×C3—241no—
511C22×D3—21no—
512C22×D3—31no—
513C22×D3—31no—
514C22×D3—42no—
515C22×D3—42no—
516C22×D3—61no—
517C22×D3—61no—
518C22×D3—61no—
519C22×D3—61no—
520C22×D3—61no—
521C22×D3—81no—
522C22×D3—121no—
523C22×D3—121no—
524C22×D3—122no—
525C22×D3—122no—
526C22×D3—122no—
527C22×D3—122no—
528C22×D3—124no—
529C22×D3—242no—
530C22×D3—241no—
531C22×D3—241no—
532C22×D3—242no—
533C22×D3D3×D411yescharacteristic
534C3×Q8—122no—
535C3×D4—21no—
536C3×D4—21no—
537C3×D4—22no—
538C3×D4—41no—
539C3×D4—61no—
540C3×D4—61no—
541C3×D4—122no—
542C3×D4#23512yescomplemented
543C3×D4#23912yescomplemented
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—31no—
548C2×C3×C4—31no—
549C2×C3×C4—31no—
550C2×C3×C4—41no—
551C2×C3×C4—61no—
552C2×C3×C4—61no—
553C2×C3×C4—61no—
554C2×C3×C4—61no—
555C2×C3×C4—61no—
556C2×C3×C4—122no—
557C2×C3×C4—122no—
558C2×C3×C4C23×D311yescharacteristic
559C2×C3×C4C23×D311yescharacteristic
560#67—34no—
561#67—42no—
562#67—122no—
563#67—122no—
564#67—122no—
565#67—122no—
566#67—122no—
567#67—124no—
568#67—122no—
569#67—241no—
570C2×Dic3—21no—
571C2×Dic3—21no—
572C2×Dic3—21no—
573C2×Dic3—31no—
574C2×Dic3—31no—
575C2×Dic3—42no—
576C2×Dic3—61no—
577C2×Dic3D3×D411yescharacteristic
578C2×Dic3D3×D411yescharacteristic
579C2×Dic3D3×D411yescharacteristic
580D12—21no—
581D12—21no—
582D12—34no—
583D12—62no—
584D12—61no—
585D12—61no—
586D12—61no—
587D12—61no—
588D12—61no—
589D12—61no—
590D12—61no—
591D12—61no—
592D12—121no—
593D12—121no—
594D12—121no—
595D12—122no—
596D12—122no—
597D12—122no—
598D12—122no—
599D12—122no—
600D12—122no—
601D12—242no—
602D12—241no—
603C4×D3—21no—
604C4×D3—21no—
605C4×D3—42no—
606C4×D3—61no—
607C4×D3—61no—
608C4×D3—61no—
609C4×D3—61no—
610C4×D3—121no—
611C4×D3—121no—
612C4×D3—122no—
613C4×D3—122no—
614C4×D3—122no—
615C4×D3—122no—
616Dic6—42no—
617C3×C8—21no—
618C3×C8—21no—
619C3×C8—41no—
620C3×C8—61no—
621C3×C8—61no—
622C3⋊C8—21no—
623C3⋊C8—21no—
624C3⋊C8—61no—
625C3⋊C8—61no—
626C3⋊C8—121no—
627C2×C32—42no—
628C2×C32#54611yescharacteristic
629C2×C32C22×D811yescharacteristic
630C2×C32#57711yescharacteristic
631C3⋊D3—22no—
632C3⋊D3—81no—
633C3⋊D3—81no—
634C3×D3—22no—
635C3×D3—81no—
636C24—61no—
637C24—181no—
638#41—364no—
639C2×Q8—61no—
640C2×D4—31no—
641C2×D4—61no—
642C2×D4—62no—
643C2×D4—91no—
644C2×D4—91no—
645C2×D4—91no—
646C2×D4—121no—
647C2×D4—181no—
648C2×D4—181no—
649C2×D4—181no—
650C2×D4—181no—
651C2×D4—181no—
652C2×D4—181no—
653C2×D4—181no—
654C2×D4—182no—
655C2×D4—364no—
656C2×D4—361no—
657C2×D4C2×D3211yescharacteristic
658C22×C4—31no—
659C22×C4—61no—
660C22×C4—61no—
661C22×C4—91no—
662C22×C4—181no—
663C22×C4—181no—
664D8—182no—
665D8—361no—
666D8—361no—
667C2×C8—31no—
668C2×C8—31no—
669C2×C8—91no—
670C2×C8—121no—
671C2×C8—361no—
672C2×C8C2×D3211yescharacteristic
673C4⋊C4—31no—
674C4⋊C4—31no—
675C4⋊C4—31no—
676C4⋊C4—61no—
677C4⋊C4—61no—
678C4⋊C4—91no—
679C4⋊C4—181no—
680C4⋊C4C2×D3211yescharacteristic
681C22⋊C4—61no—
682C22⋊C4—91no—
683C22⋊C4—91no—
684C22⋊C4—181no—
685C22⋊C4—181no—
686C22⋊C4—181no—
687C22⋊C4—181no—
688C22⋊C4—181no—
689C42—31no—
690C22×C3—22no—
691C22×C3—22no—
692C22×C3—21no—
693C22×C3—32no—
694C22×C3—42no—
695C22×C3—41no—
696C22×C3—41no—
697C22×C3—41no—
698C22×C3—41no—
699C22×C3—61no—
700C22×C3—61no—
701C22×C3—81no—
702C22×C3—81no—
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—62no—
717C2×D3—61no—
718C2×D3—61no—
719C2×D3—61no—
720C2×D3—61no—
721C2×D3—84no—
722C2×D3—121no—
723C2×D3—121no—
724C2×D3—122no—
725C2×D3—121no—
726C2×D3—121no—
727C2×D3—121no—
728C2×D3—121no—
729C2×D3—121no—
730C2×D3—121no—
731C2×D3—121no—
732C2×D3—121no—
733C2×D3—121no—
734C2×D3—121no—
735C2×D3—121no—
736C2×D3—121no—
737C2×D3—241no—
738C2×D3—241no—
739C2×D3—241no—
740C2×D3—241no—
741C2×D3—241no—
742C2×D3—244no—
743C2×D3—244no—
744C2×D3—248no—
745C2×D3D3×D812yes—
746C3×C4—21no—
747C3×C4—21no—
748C3×C4—32no—
749C3×C4—41no—
750C3×C4—41no—
751C3×C4—61no—
752C3×C4—61no—
753C3×C4—81no—
754C3×C4—121no—
755C3×C4—121no—
756C3×C4—121no—
757C3×C4C2×#23511yescharacteristic
758C3×C4#100411yescharacteristic
759C3×C4C2×#23911yescharacteristic
760C3×C4#100911yescharacteristic
761Dic3—21no—
762Dic3—21no—
763Dic3—41no—
764Dic3—41no—
765Dic3—41no—
766Dic3—61no—
767Dic3—61no—
768Dic3—121no—
769Dic3D3×D812yes—
770C32#329411yescharacteristic, complemented, Sylow
771C23—21no—
772C23—31no—
773C23—61no—
774C23—91no—
775C23—122no—
776C23—122no—
777C23—181no—
778C23—181no—
779C23—241no—
780C23—362no—
781C23—362no—
782C23—721no—
783Q8—122no—
784D4—21no—
785D4—61no—
786D4—61no—
787D4—94no—
788D4—122no—
789D4—181no—
790D4—181no—
791D4—181no—
792D4—181no—
793D4—362no—
794D4—362no—
795D4—362no—
796D4—362no—
797D4—362no—
798D4—362no—
799D4—721no—
800D4#379912yescomplemented
801C2×C4—21no—
802C2×C4—31no—
803C2×C4—31no—
804C2×C4—31no—
805C2×C4—61no—
806C2×C4—61no—
807C2×C4—61no—
808C2×C4—61no—
809C2×C4—61no—
810C2×C4—91no—
811C2×C4—122no—
812C2×C4—122no—
813C2×C4—181no—
814C2×C4—181no—
815C2×C4—362no—
816C2×C4—362no—
817C2×C4C22×D3211yescharacteristic
818C8—21no—
819C8—61no—
820C8—61no—
821C8—181no—
822C2×C3—21no—
823C2×C3—21no—
824C2×C3—21no—
825C2×C3—42no—
826C2×C3—42no—
827C2×C3—62no—
828C2×C3—82no—
829C2×C3—241no—
830C2×C3#549011yescharacteristic
831C2×C3#563011yescharacteristic
832C2×C3C2×D3×D811yescharacteristic
833C2×C3C2×D3×D811yescharacteristic
834C2×C3#576211yescharacteristic
835C2×C3#577811yescharacteristic
836D3—22no—
837D3—62no—
838D3—62no—
839D3—81no—
840D3—122no—
841D3—242no—
842D3—241no—
843D3—241no—
844D3—241no—
845D3—241no—
846D3—481no—
847C22—22no—
848C22—32no—
849C22—41no—
850C22—41no—
851C22—61no—
852C22—61no—
853C22—92no—
854C22—121no—
855C22—121no—
856C22—121no—
857C22—181no—
858C22—181no—
859C22—244no—
860C22—361no—
861C22—361no—
862C22—361no—
863C22—361no—
864C22—361no—
865C22—361no—
866C22—724no—
867C22D32×D411yescharacteristic
868C4—32no—
869C4—41no—
870C4—61no—
871C4—61no—
872C4—121no—
873C4—121no—
874C4—121no—
875C4—181no—
876C4C2×#379911yescharacteristic
877C4#6431411yescharacteristic
878C3—21no—
879C3#7875711yescharacteristic, complemented
880C3#8098011yescharacteristic, complemented
881C2—42no—
882C2—62no—
883C2—182no—
884C2—241no—
885C2—721no—
886C2—721no—
887C2#1059418711yescharacteristic
888C2D32×D811yescharacteristic
889C2#1059475111yescharacteristic
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. #10594517C2semidirect
3. #10592472C2semidirect
4. C3×D3×#102C2semidirect
5. C3×#4759C2semidirect
6. #10591448C2semidirect
7. #10591416C2semidirect
8. #10591400C2semidirect
9. #10590832C2semidirect
10. #10590765C2semidirect
11. #10590720C2semidirect
12. #10590650C2semidirect
13. #10590548C2semidirect
14. #10590509C2semidirect
15. #10590422C2semidirect
23. C2×#3745C22semidirect
24. #64104C22semidirect
26. C2×C3×D3×C8C22semidirect
27. C3×D3×C4⋊C4C22semidirect
28. C3×#888C22semidirect
35. #63909C22semidirect
37. #63900C22semidirect
39. #63894C22semidirect
42. C2×#3714C22semidirect
43. C2×#3710C22semidirect
45. #63647C22semidirect
46. #63636C22semidirect
49. C3×#821C22semidirect
50. C3×#818C22semidirect
51. C3×Dic3⋊C8C22semidirect
52. C3×#809C22semidirect
53. C3×#807C22semidirect
54. #63576C22semidirect
55. #63564C22semidirect
56. #63564C22semidirect
57. #63564C22semidirect
58. #63562C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. Dic3×C3⋊C8C22semidirect
88. D3×#102D3semidirect
90. #4759D3semidirect
182. C2×D3×C8C2×D3semidirect
196. D3×C4⋊C4C2×D3semidirect
197. #888C2×D3semidirect
220. #821C2×D3semidirect
225. #818C2×D3semidirect
226. Dic3⋊C8C2×D3semidirect
235. #809C2×D3semidirect
238. #807C2×D3semidirect
253. C32×D4#41semidirect
284. #626D8semidirect
542. C3×D4#235semidirect
543. C3×D4#239semidirect
770. C32#3294semidirect
800. D4#3799semidirect
879. C3#78757semidirect
880. C3#80980semidirect

Maximal subgroups

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

subgroupindex
D4×#6262
#105945172
#105924722
C3×D3×#1022
C3×#47592
#105914482
#105914162
#105914002
#105908322
#105907652
#105907202
#105906502
#105905482
#105905092
#105904222
#809803
#787573