Finite Group Databasebeta

← #11887037

Subgroups — #11887037

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
1#10595297C211yesmaximal, characteristic, complemented
2#10594517C211yesmaximal, characteristic, complemented
3#10592472C211yesmaximal, characteristic, complemented
4C3×#4774C211yesmaximal, characteristic, complemented
5C3×#4760C211yesmaximal, characteristic, complemented
6#10591449C211yesmaximal, characteristic, complemented
7#10591429C211yesmaximal, characteristic, complemented
8#10591416C211yesmaximal, characteristic, complemented
9#10590947C211yesmaximal, characteristic, complemented
10#10590763C211yesmaximal, characteristic, complemented
11#10590721C211yesmaximal, characteristic, complemented
12#10590650C211yesmaximal, characteristic, complemented
13D3×#809C211yesmaximal, characteristic, complemented
14#10590509C211yesmaximal, characteristic, complemented
15#10590464C211yesmaximal, characteristic, complemented
16#81576—31nomaximal
17#81302—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×#3811—21no—
20C2×D3×D12C2211yescharacteristic
21C2×#3799—21no—
22C2×#3753C2211yescharacteristic, complemented
23C2×#3745C2211yescharacteristic
24#64104C2211yescharacteristic, complemented
25C3×#940C2211yescharacteristic
26C3×#938C2211yescharacteristic
27C3×D3×C4⋊C4C2211yescharacteristic, complemented
28C3×#888C2211yescharacteristic, complemented
29#63983—21no—
30#63981—21no—
31#63958—21no—
32#63916C2211yescharacteristic
33#63909C2211yescharacteristic, complemented
34C4×#626C2211yescharacteristic
35#63900C2211yescharacteristic, complemented
36#63897—21no—
37#63894C2211yescharacteristic
38#63894C2211yescharacteristic, complemented
39#63888—21no—
40#63850—21no—
41C2×#3714C2211yescharacteristic, complemented
42C2×#3710C2211yescharacteristic, complemented
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44C32×#102C2211yescharacteristic, complemented
45#63647C2211yescharacteristic, complemented
46#63636C2211yescharacteristic
47C3×#832C2211yescharacteristic, complemented
48C3×#832C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic, complemented
50C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
51C3×#818C2211yescharacteristic, complemented
52C3×C8×Dic3C2211yescharacteristic, complemented
53C3×#809C2211yescharacteristic, complemented
54C3×#807C2211yescharacteristic, complemented
55#63576C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59#63564C2211yescharacteristic, complemented
60#63562C2211yescharacteristic, complemented
61#5726—31no—
62#5717—31no—
63#5609—31no—
64#5507—31no—
65C3×#486—31no—
66C3×#480—31no—
67#5087—31no—
68#5072—31no—
69#5038—31no—
70C2×#809—31no—
71#4890—31no—
72#4883—31no—
73#4882—31no—
74#4872—31no—
75#4786—31no—
76#4775—31no—
77#4775—31no—
78#4774—31no—
79#4774D311yescharacteristic, complemented
80#4773—31no—
81#4773—31no—
82#4773—31no—
83#4773—61no—
84D3×#102—31no—
85D3×#102—31no—
86D3×#102—31no—
87#4760D311yescharacteristic, complemented
88#4732—31no—
89#67⋊C8—31no—
90C4×D24—31no—
91C8×D12—31no—
92C23×C3⋊D3—21no—
93C22×D32—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—
103C2×C3×#67—21no—
104C2×C3×#67—21no—
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×Dic6—21no—
109#3811—44no—
110C2×#626—21no—
111C2×#626—21no—
112C2×#626—21no—
113C2×#626D411yescharacteristic
114C2×#624—21no—
115C2×#624—21no—
116C2×#624—21no—
117D3×D12—22no—
118D3×D12—41no—
119#3799—44no—
120C2×C32×C8C2311yescharacteristic
121C32×C4⋊C4C2311yescharacteristic
122#3753—41no—
123#3752—21no—
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125#3745—22no—
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
135#3724—21no—
136Dic3⋊Dic3D411yescharacteristic
137#3722—21no—
138#3722—21no—
139#3722—21no—
140#3722D411yescharacteristic
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3D411yescharacteristic
143#3714—41no—
144#3710—41no—
145D3×C3⋊C8—41no—
146#3294—91noSylow
147C2×#239—61no—
148C2×D3×D4—31no—
149C2×D3×D4—31no—
150C2×D3×D4—31no—
151C2×D3×D4—61no—
152C2×D3×D4—61no—
153C2×D3×D4—61no—
154C2×#235—61no—
155C22×D12—31no—
156C3×C4⋊Q8—31no—
157C3×#127—31no—
158C3×#121—31no—
159C2×C3×C4⋊C4—31no—
160#946—61no—
161#940C2×D311yescharacteristic
162#938—31no—
163#938—61no—
164#938C2×D311yescharacteristic
165#937—61no—
166#937—61no—
167#937—61no—
168C2×#213—31no—
169C2×#213—31no—
170C2×#213—31no—
171C2×#213—61no—
172#930—31no—
173#929—61no—
174C4×#67—31no—
175C22×C3⋊C8—31no—
176C2×D24—31no—
177C2×D24—31no—
178C2×D24—31no—
179C2×D24—61no—
180C2×D3×C8—31no—
181C2×D3×C8—31no—
182C2×D3×C8—31no—
183#896—61no—
184#895—31no—
185#895—31no—
186#895—31no—
187#895—31no—
188#895—61no—
189#894—61no—
190#894—61no—
191#894—61no—
192#893—31no—
193#893—31no—
194D3×C4⋊C4—31no—
195D3×C4⋊C4—31no—
196D3×C4⋊C4C2×D311yescharacteristic, complemented
197#888C2×D311yescharacteristic, complemented
198#884—61no—
199#882—61no—
200C4×D12—31no—
201C4×D12—31no—
202C4×D12—31no—
203C3×#107—31no—
204C3×#107—31no—
205C3×#102—21no—
206C3×#102—31no—
207C3×#102—31no—
208C3×#102—31no—
209C3×#102—31no—
210C3×#102C2×D311yescharacteristic, complemented
211C3×#102C2×D311yescharacteristic, complemented
212C3×C22⋊C8—31no—
213C3×C4×C8—31no—
214#832—31no—
215#832C2×D311yescharacteristic, complemented
216#832C2×D311yescharacteristic, complemented
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—61no—
224(C2×D3)⋊C8C2×D311yescharacteristic, complemented
225#818C2×D311yescharacteristic, complemented
226Dic3⋊C8—31no—
227C8×Dic3C2×D311yescharacteristic, complemented
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×D3C2×D411yescharacteristic
249C2×D32—42no—
250C2×D32—42no—
251C2×D32—81no—
252C32×D4—21no—
253C32×D4—21no—
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)—42no—
262C4⋊(C3⋊D3)#4112yescomplemented
263C4×C3⋊D3—21no—
264C4×C3⋊D3—21no—
265C3×#67—42no—
266C3×#67—42no—
267C3×#67—81no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3C2×D411yescharacteristic
272C2×C3×Dic3C2×D411yescharacteristic
273C2×C3×Dic3C2×D411yescharacteristic
274C3×D12—21no—
275C3×D12—21no—
276C3×C4×D3—21no—
277C3×C4×D3—21no—
278C3×C4×D3—42no—
279C3×Dic6—42no—
280#626—42no—
281#626—42no—
282#626—42no—
283#626D814yescomplemented
284#624—42no—
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—31no—
294#480—31no—
295#480—91no—
296#474—91no—
297#466—91no—
298#466—91no—
299#459—91no—
300#447—91no—
301#447—91no—
302C4×D8—91no—
303C8×D4—91no—
304C2×#102—91no—
305C2×#102—91no—
306C23×D3—61no—
307C23×D3—61no—
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—61no—
316C2×C3×D4—61no—
317C2×C3×D4C22×D311yescharacteristic
318C2×C3×D4C22×D311yescharacteristic
319C22×C3×C4—31no—
320C22×C3×C4—61no—
321C2×#67—21no—
322C2×#67—21no—
323C2×#67—21no—
324C2×#67—31no—
325C2×#67—61no—
326C2×#67—61no—
327C2×#67—61no—
328C2×#67—61no—
329C2×#67—61no—
330C2×#67—121no—
331#239—124no—
332D3×D4—62no—
333D3×D4—62no—
334D3×D4—62no—
335D3×D4—122no—
336D3×D4—121no—
337D3×D4—121no—
338D3×D4—121no—
339D3×D4—124no—
340D3×D4—124no—
341D3×D4—122no—
342#235—124no—
343C2×D12—31no—
344C2×D12—31no—
345C2×D12—31no—
346C2×D12—31no—
347C2×D12—31no—
348C2×D12—61no—
349C2×D12—61no—
350C2×D12—62no—
351C2×D12—61no—
352C2×D12—61no—
353C2×D12—61no—
354C2×D12—61no—
355C2×D12—61no—
356C2×D12—121no—
357C2×D12—121no—
358C2×D12C22×D311yescharacteristic
359C2×C4×D3—21no—
360C2×C4×D3—31no—
361C2×C4×D3—31no—
362C2×C4×D3—61no—
363C2×C4×D3—61no—
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×C8C22×D311yescharacteristic
375C2×C3×C8C22×D311yescharacteristic
376C3×C4⋊C4—21no—
377C3×C4⋊C4—31no—
378C3×C4⋊C4—31no—
379C3×C4⋊C4—31no—
380C3×C4⋊C4—61no—
381C3×C4⋊C4—61no—
382C3×C4⋊C4C22×D311yescharacteristic
383C3×C4⋊C4C22×D311yescharacteristic
384C3×C22⋊C4—61no—
385C3×C42—31no—
386#217—21no—
387#217—31no—
388#217—61no—
389#213—121no—
390#213—121no—
391#213—121no—
392#213—122no—
393(C2×D3)⋊C4—31no—
394(C2×D3)⋊C4—31no—
395(C2×D3)⋊C4—31no—
396(C2×D3)⋊C4—61no—
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—121no—
406C4⋊Dic3—31no—
407C4⋊Dic3C22×D311yescharacteristic
408C4⋊Dic3C22×D311yescharacteristic
409C4⋊Dic3C22×D311yescharacteristic
410Dic3⋊C4—21no—
411Dic3⋊C4—21no—
412Dic3⋊C4—31no—
413Dic3⋊C4—61no—
414Dic3⋊C4—61no—
415C4×Dic3C22×D311yescharacteristic
416C2×C3⋊C8—31no—
417C2×C3⋊C8—31no—
418C2×C3⋊C8—61no—
419C2×C3⋊C8—121no—
420C2×C3⋊C8C22×D311yescharacteristic
421C2×C3⋊C8C22×D311yescharacteristic
422D24—62no—
423D24—62no—
424D24—122no—
425D24—121no—
426D3×C8—121no—
427D3×C8—121no—
428D3×C8—121no—
429C22×C32—41no—
430C22×C32—41no—
431C22×C32—41no—
432C22×C32C22×D411yescharacteristic
433C2×C3⋊D3—21no—
434C2×C3⋊D3—21no—
435C2×C3⋊D3—22no—
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×D3C2×D812yes—
449D32—84no—
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—91no—
462C22×D4—91no—
463C22×D4—181no—
464C2×D8—91no—
465C2×D8—91no—
466C2×D8—91no—
467C22×C8—91no—
468C22×C8—91no—
469C4⋊Q8—31no—
470#127—31no—
471#123—181no—
472#123—181no—
473C22⋊Q8—181no—
474#121—31no—
475#121—91no—
476#121—91no—
477#121—91no—
478#121—181no—
479#120—181no—
480#120—181no—
481C4×D4—91no—
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—91no—
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, complemented
500C22⋊C8—31no—
501C22⋊C8—91no—
502C4×C8—31no—
503C23×C3—21no—
504C23×C3—21no—
505C23×C3—31no—
506C23×C3—41no—
507C23×C3—61no—
508C22×D3—21no—
509C22×D3—31no—
510C22×D3—31no—
511C22×D3—61no—
512C22×D3—61no—
513C22×D3—61no—
514C22×D3—61no—
515C22×D3—61no—
516C22×D3—121no—
517C22×D3—121no—
518C22×D3—122no—
519C22×D3—122no—
520C22×D3—122no—
521C22×D3—122no—
522C22×D3—122no—
523C22×D3—122no—
524C22×D3—122no—
525C22×D3—124no—
526C22×D3—122no—
527C22×D3—242no—
528C22×D3—241no—
529C22×D3—241no—
530C22×D3—241no—
531C22×D3—241no—
532C22×D3—242no—
533C22×D3D3×D411yescharacteristic
534C3×Q8—122no—
535C3×D4—22no—
536C3×D4—21no—
537C3×D4—21no—
538C3×D4—21no—
539C3×D4—21no—
540C3×D4—41no—
541C3×D4—61no—
542C3×D4—61no—
543C3×D4—122no—
544C3×D4—122no—
545C3×D4—241no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—21no—
549C2×C3×C4—31no—
550C2×C3×C4—31no—
551C2×C3×C4—31no—
552C2×C3×C4—41no—
553C2×C3×C4—61no—
554C2×C3×C4—61no—
555C2×C3×C4—61no—
556C2×C3×C4—61no—
557C2×C3×C4—61no—
558C2×C3×C4—122no—
559C2×C3×C4C23×D311yescharacteristic
560C2×C3×C4C23×D311yescharacteristic
561#67—34no—
562#67—42no—
563#67—42no—
564#67—81no—
565#67—122no—
566#67—122no—
567#67—122no—
568#67—122no—
569#67—122no—
570#67—124no—
571C2×Dic3—21no—
572C2×Dic3—21no—
573C2×Dic3—21no—
574C2×Dic3—31no—
575C2×Dic3—31no—
576C2×Dic3—61no—
577C2×Dic3D3×D411yescharacteristic
578C2×Dic3D3×D411yescharacteristic
579C2×Dic3D3×D411yescharacteristic
580D12—21no—
581D12—21no—
582D12—34no—
583D12—32no—
584D12—32no—
585D12—62no—
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—242no—
601C4×D3—21no—
602C4×D3—21no—
603C4×D3—42no—
604C4×D3—61no—
605C4×D3—61no—
606C4×D3—61no—
607C4×D3—61no—
608C4×D3—121no—
609C4×D3—121no—
610C4×D3—122no—
611C4×D3—122no—
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—81no—
628C2×C32#54611yescharacteristic
629C2×C32C22×D811yescharacteristic
630C2×C32#57711yescharacteristic
631C3⋊D3—22no—
632C3⋊D3—42no—
633C3⋊D3—81no—
634C3×D3—22no—
635C3×D3—81no—
636C24—181no—
637C24—181no—
638#41—364no—
639C2×Q8—61no—
640C2×D4—31no—
641C2×D4—61no—
642C2×D4—61no—
643C2×D4—61no—
644C2×D4—91no—
645C2×D4—91no—
646C2×D4—91no—
647C2×D4—181no—
648C2×D4—181no—
649C2×D4—182no—
650C2×D4—181no—
651C2×D4—181no—
652C2×D4—181no—
653C2×D4—182no—
654C2×D4—361no—
655C2×D4—361no—
656C2×D4—364no—
657C2×D4C2×D3211yescharacteristic
658C22×C4—31no—
659C22×C4—61no—
660C22×C4—91no—
661C22×C4—181no—
662C22×C4—181no—
663C22×C4—181no—
664D8—182no—
665D8—361no—
666D8—361no—
667C2×C8—31no—
668C2×C8—31no—
669C2×C8—91no—
670C2×C8—361no—
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—21no—
691C22×C3—32no—
692C22×C3—42no—
693C22×C3—41no—
694C22×C3—41no—
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×C3C2×D3×D411yescharacteristic
707C22×C3C2×D3×D411yescharacteristic
708C2×D3—21no—
709C2×D3—21no—
710C2×D3—32no—
711C2×D3—32no—
712C2×D3—41no—
713C2×D3—41no—
714C2×D3—41no—
715C2×D3—62no—
716C2×D3—61no—
717C2×D3—61no—
718C2×D3—61no—
719C2×D3—61no—
720C2×D3—62no—
721C2×D3—62no—
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—241no—
736C2×D3—241no—
737C2×D3—241no—
738C2×D3—241no—
739C2×D3—241no—
740C2×D3—244no—
741C2×D3—244no—
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×C4D3×#4111yescharacteristic
758C3×C4D3×#4111yescharacteristic
759C3×C4#100911yescharacteristic
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—181no—
776C23—181no—
777C23—362no—
778C23—362no—
779C23—362no—
780C23—362no—
781C23—721no—
782C23—721no—
783Q8—122no—
784D4—21no—
785D4—21no—
786D4—61no—
787D4—61no—
788D4—94no—
789D4—92no—
790D4—122no—
791D4—122no—
792D4—181no—
793D4—181no—
794D4—181no—
795D4—241no—
796D4—362no—
797D4—362no—
798D4—362no—
799D4—362no—
800D4—362no—
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—181no—
813C2×C4—181no—
814C2×C4—362no—
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—62no—
826C2×C3—82no—
827C2×C3—81no—
828C2×C3—81no—
829C2×C3—241no—
830C2×C3#565411yescharacteristic
831C2×C3#567611yescharacteristic
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—122no—
842D3—122no—
843D3—242no—
844D3—241no—
845D3—241no—
846D3—481no—
847C22—32no—
848C22—41no—
849C22—41no—
850C22—41no—
851C22—61no—
852C22—61no—
853C22—92no—
854C22—121no—
855C22—121no—
856C22—121no—
857C22—181no—
858C22—181no—
859C22—182no—
860C22—361no—
861C22—361no—
862C22—361no—
863C22—361no—
864C22—361no—
865C22—724no—
866C22—724no—
867C22D32×D411yescharacteristic
868C4—32no—
869C4—41no—
870C4—61no—
871C4—61no—
872C4—121no—
873C4—121no—
874C4—121no—
875C4—181no—
876C4#6430811yescharacteristic
877C4#6431211yescharacteristic
878C3—21no—
879C3#8130211yescharacteristic, complemented
880C3#8157611yescharacteristic, complemented
881C2—62no—
882C2—81no—
883C2—182no—
884C2—241no—
885C2—362no—
886C2—721no—
887C2#1059428211yescharacteristic
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. #10595297C2semidirect
2. #10594517C2semidirect
3. #10592472C2semidirect
4. C3×#4774C2semidirect
5. C3×#4760C2semidirect
6. #10591449C2semidirect
7. #10591429C2semidirect
8. #10591416C2semidirect
9. #10590947C2semidirect
10. #10590763C2semidirect
11. #10590721C2semidirect
12. #10590650C2semidirect
13. D3×#809C2semidirect
14. #10590509C2semidirect
15. #10590464C2semidirect
22. C2×#3753C22semidirect
24. #64104C22semidirect
27. C3×D3×C4⋊C4C22semidirect
28. C3×#888C22semidirect
33. #63909C22semidirect
35. #63900C22semidirect
38. #63894C22semidirect
41. C2×#3714C22semidirect
42. C2×#3710C22semidirect
43. C2×D3×C3⋊C8C22semidirect
44. C32×#102C22semidirect
45. #63647C22semidirect
47. C3×#832C22semidirect
48. C3×#832C22semidirect
49. C3×#821C22semidirect
50. C3×(C2×D3)⋊C8C22semidirect
51. C3×#818C22semidirect
52. C3×C8×Dic3C22semidirect
53. C3×#809C22semidirect
54. C3×#807C22semidirect
55. #63576C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
59. #63564C22semidirect
60. #63562C22semidirect
79. #4774D3semidirect
87. #4760D3semidirect
196. D3×C4⋊C4C2×D3semidirect
197. #888C2×D3semidirect
210. C3×#102C2×D3semidirect
211. C3×#102C2×D3semidirect
215. #832C2×D3semidirect
216. #832C2×D3semidirect
220. #821C2×D3semidirect
224. (C2×D3)⋊C8C2×D3semidirect
225. #818C2×D3semidirect
227. C8×Dic3C2×D3semidirect
235. #809C2×D3semidirect
238. #807C2×D3semidirect
262. C4⋊(C3⋊D3)#41semidirect
283. #626D8semidirect
499. #102D32semidirect
770. C32#3294semidirect
879. C3#81302semidirect
880. C3#81576semidirect

Maximal subgroups

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

subgroupindex
#105952972
#105945172
#105924722
C3×#47742
C3×#47602
#105914492
#105914292
#105914162
#105909472
#105907632
#105907212
#105906502
D3×#8092
#105905092
#105904642
#815763
#813023