Finite Group Databasebeta

← #11887043

Subgroups — #11887043

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
1#10595297C211yesmaximal, characteristic, complemented
2#10594515C211yesmaximal, characteristic, complemented
3C3⋊D3×#102C211yesmaximal, characteristic, complemented
4C3×#4786C211yesmaximal, characteristic, complemented
5C3×#4774C211yesmaximal, characteristic, complemented
6#10591498C211yesmaximal, characteristic, complemented
7#10591487C211yesmaximal, characteristic, complemented
8#10591456C211yesmaximal, characteristic, complemented
9#10590944C211yesmaximal, characteristic, complemented
10#10590906C211yesmaximal, characteristic, complemented
11#10590844C211yesmaximal, characteristic, complemented
12#10590764C211yesmaximal, characteristic, complemented
13D3×#809C211yesmaximal, characteristic, complemented
14#10590510C211yesmaximal, characteristic, complemented
15#10590456C211yesmaximal, characteristic, complemented
16#81302—31nomaximal
17#80352—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×#3811—21no—
20C2×D3×D12C2211yescharacteristic
21C2×#3798—21no—
22C2×C8×C3⋊D3C2211yescharacteristic, complemented
23C4⋊C4×C3⋊D3C2211yescharacteristic, complemented
24C3×#940C2211yescharacteristic
25C3×#938C2211yescharacteristic
26C2×C3×#213C2211yescharacteristic, complemented
27C2×C3×D24C2211yescharacteristic, complemented
28C3×#893C2211yescharacteristic, complemented
29C3×D3×C4⋊C4C2211yescharacteristic, complemented
30#63983—21no—
31#63981—21no—
32#63958—21no—
33#63918C2211yescharacteristic, complemented
34#63916C2211yescharacteristic
35#63916C2211yescharacteristic, complemented
36#63908C2211yescharacteristic, complemented
37#63905—21no—
38C4×#626C2211yescharacteristic
39#63894C2211yescharacteristic
40#63853—21no—
41#63851—21no—
42C2×#3714C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44C32×#102C2211yescharacteristic, complemented
45#63659C2211yescharacteristic, complemented
46#63648C2211yescharacteristic
47#63636C2211yescharacteristic
48C3×#832C2211yescharacteristic, complemented
49C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
50C3×#818C2211yescharacteristic, complemented
51C3×Dic3⋊C8C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic, complemented
53C3×#807C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63564C2211yescharacteristic
56#63563C2211yescharacteristic, complemented
57#63562C2211yescharacteristic, complemented
58#63562C2211yescharacteristic, complemented
59#63557C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61#5717—31no—
62#5609—31no—
63#5551—31no—
64#5507—31no—
65C3×#480—31no—
66C3×#459—31no—
67#5157—31no—
68#5157—31no—
69#5156—31no—
70#5156—31no—
71#5070—31no—
72#5038—31no—
73C4×#213—31no—
74C2×#809—31no—
75#4890—31no—
76#4883—31no—
77#4882—31no—
78#4872—31no—
79#4846—31no—
80#4834—31no—
81#4786D311yescharacteristic, complemented
82#4774—31no—
83#4774D311yescharacteristic, complemented
84#4773—31no—
85D3×#102—31no—
86D3×#102—31no—
87D3×#102—31no—
88D3×#102—61no—
89#4760—31no—
90#4732—31no—
91#67⋊C8—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)C2311yescharacteristic
99C2×C4×C3⋊D3—21no—
100C2×C4×C3⋊D3C2311yescharacteristic
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C2×C3×#67—21no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3C2311yescharacteristic
109#3811—44no—
110C2×#627—21no—
111C2×#626—21no—
112C2×#626—21no—
113C2×#626—21no—
114C2×#626D411yescharacteristic
115C2×#625—21no—
116C2×#624—21no—
117D3×D12—22no—
118D3×D12—41no—
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—41no—
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×D24—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—22no—
145D3×C3⋊C8—41no—
146#3294—91noSylow
147C2×D3×D4—31no—
148C2×D3×D4—31no—
149C2×D3×D4—31no—
150C2×D3×D4—61no—
151C2×D3×D4—61no—
152C2×D3×D4—61no—
153C2×#235—61no—
154C2×#235—61no—
155C22×D12—31no—
156C2×C3×D8—31no—
157C2×C3×D8—31no—
158C3×#127—31no—
159C3×#121—31no—
160C3×C4×D4—31no—
161C2×C3×C4⋊C4—31no—
162#940C2×D311yescharacteristic
163#938—31no—
164#938—31no—
165#938—31no—
166#938—61no—
167#938C2×D311yescharacteristic
168#937—61no—
169#937—61no—
170#937—61no—
171C2×#213—31no—
172C2×#213C2×D311yescharacteristic, complemented
173#930—31no—
174#929—61no—
175C4×#67—31no—
176#924—61no—
177C22×C3⋊C8—31no—
178C2×D24—31no—
179C2×D24C2×D311yescharacteristic, complemented
180C2×D3×C8—31no—
181C2×D3×C8—31no—
182C2×D3×C8—31no—
183C2×D3×C8—61no—
184#896—61no—
185#895—31no—
186#895—31no—
187#894—61no—
188#893—31no—
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#884—61no—
196#883—61no—
197#883—61no—
198#882—61no—
199C4×D12—31no—
200C4×D12—31no—
201#869—31no—
202C3×#107—31no—
203C3×#107—31no—
204C3×C4⋊C8—31no—
205C3×#102—21no—
206C3×#102—31no—
207C3×#102—31no—
208C3×#102C2×D311yescharacteristic, complemented
209C3×#102C2×D311yescharacteristic, complemented
210C3×C22⋊C8—31no—
211#832—31no—
212#832—31no—
213#832—31no—
214#832—31no—
215#832—31no—
216#832—61no—
217#832C2×D311yescharacteristic, complemented
218#821—31no—
219#821—31no—
220#821—31no—
221#821—31no—
222#821—61no—
223(C2×D3)⋊C8—31no—
224(C2×D3)⋊C8—31no—
225(C2×D3)⋊C8C2×D311yescharacteristic, complemented
226#818—31no—
227#818C2×D311yescharacteristic, complemented
228Dic3⋊C8C2×D311yescharacteristic, complemented
229C8×Dic3—31no—
230#809—31no—
231#809—31no—
232#809—31no—
233#809—31no—
234#809—31no—
235#809—61no—
236#809C2×D311yescharacteristic, complemented
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×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⋊Dic3—21no—
258C2×C3⋊Dic3C2×D411yescharacteristic
259C4⋊(C3⋊D3)—21no—
260C4⋊(C3⋊D3)#4112yescomplemented
261C4×C3⋊D3—21no—
262C4×C3⋊D3—21no—
263C4×C3⋊D3—42no—
264C3×#67—42no—
265C3×#67—42no—
266C3×#67—81no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3C2×D411yescharacteristic
270C2×C3×Dic3C2×D411yescharacteristic
271C2×C3×Dic3C2×D411yescharacteristic
272C3×D12—21no—
273C3×D12—21no—
274C3×D12—21no—
275C3×D12—21no—
276C3×C4×D3—21no—
277C3×C4×D3—21no—
278C3×C4×D3—42no—
279C3×C4×D3—42no—
280#627—42no—
281#626—42no—
282#626—42no—
283#626—42no—
284#626D814yescomplemented
285#625—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—31no—
295#480—91no—
296#474—91no—
297#466—91no—
298#466—91no—
299#459—31no—
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×D4—21no—
312C2×C3×D4—31no—
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—
321C22×C3×C4—61no—
322C2×#67—21no—
323C2×#67—21no—
324C2×#67—21no—
325C2×#67—31no—
326C2×#67—61no—
327C2×#67—61no—
328C2×#67—61no—
329C2×#67—61no—
330C2×#67—61no—
331C2×#67—61no—
332C2×#67—61no—
333C2×#67—121no—
334D3×D4—62no—
335D3×D4—62no—
336D3×D4—62no—
337D3×D4—64no—
338D3×D4—121no—
339D3×D4—121no—
340D3×D4—121no—
341D3×D4—122no—
342D3×D4—124no—
343D3×D4—124no—
344#235—124no—
345#235—124no—
346C2×D12—31no—
347C2×D12—31no—
348C2×D12—31no—
349C2×D12—61no—
350C2×D12—62no—
351C2×D12—61no—
352C2×D12—61no—
353C2×D12—61no—
354C2×D12—121no—
355C2×D12C22×D311yescharacteristic
356C2×D12C22×D311yescharacteristic
357C2×C4×D3—21no—
358C2×C4×D3—21no—
359C2×C4×D3—31no—
360C2×C4×D3—31no—
361C2×C4×D3—61no—
362C2×C4×D3—61no—
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—121no—
371C3×D8—121no—
372C2×C3×C8—21no—
373C2×C3×C8—31no—
374C2×C3×C8—31no—
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—41no—
392#213—62no—
393(C2×D3)⋊C4—21no—
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—
402C4⋊Dic3—31no—
403C4⋊Dic3—31no—
404C4⋊Dic3—31no—
405C4⋊Dic3—61no—
406C4⋊Dic3—61no—
407C4⋊Dic3C22×D311yescharacteristic
408C4⋊Dic3C22×D311yescharacteristic
409Dic3⋊C4—21no—
410Dic3⋊C4—31no—
411Dic3⋊C4—61no—
412Dic3⋊C4—61no—
413Dic3⋊C4—61no—
414Dic3⋊C4—121no—
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—41no—
423D24—62no—
424D3×C8—121no—
425D3×C8—121no—
426D3×C8—121no—
427D3×C8—122no—
428C22×C32—41no—
429C22×C32—41no—
430C22×C32—41no—
431C22×C32C22×D411yescharacteristic
432C2×C3⋊D3—21no—
433C2×C3⋊D3—21no—
434C2×C3⋊D3—22no—
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×D3C2×D812yes—
448D32—84no—
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—91no—
461C22×D4—91no—
462C22×D4—181no—
463C2×D8—31no—
464C2×D8—31no—
465C2×D8—91no—
466C22×C8—91no—
467C22×C8—91no—
468C4⋊Q8—91no—
469#127—31no—
470#123—181no—
471#123—181no—
472C22⋊Q8—181no—
473#121—31no—
474#121—91no—
475#121—91no—
476#121—91no—
477#121—181no—
478#120—181no—
479#120—181no—
480C4×D4—31no—
481C4×D4—91no—
482C4×D4—91no—
483C2×C4⋊C4—31no—
484C2×C4⋊C4—91no—
485#107—31no—
486#107—31no—
487#107—91no—
488C4⋊C8—31no—
489#102—31no—
490#102—31no—
491#102—91no—
492#102—91no—
493#102—91no—
494#102—91no—
495#102—91no—
496#102—91no—
497#102—91no—
498#102D3211yescharacteristic, complemented
499C22⋊C8—31no—
500C22⋊C8—91no—
501C4×C8—91no—
502C23×C3—21no—
503C23×C3—21no—
504C23×C3—31no—
505C23×C3—41no—
506C23×C3—61no—
507C23×C3—61no—
508C22×D3—21no—
509C22×D3—21no—
510C22×D3—31no—
511C22×D3—31no—
512C22×D3—61no—
513C22×D3—61no—
514C22×D3—61no—
515C22×D3—121no—
516C22×D3—122no—
517C22×D3—122no—
518C22×D3—122no—
519C22×D3—122no—
520C22×D3—122no—
521C22×D3—122no—
522C22×D3—122no—
523C22×D3—124no—
524C22×D3—122no—
525C22×D3—242no—
526C22×D3—241no—
527C22×D3—241no—
528C22×D3—241no—
529C22×D3—241no—
530C22×D3—242no—
531C22×D3D3×D411yescharacteristic
532C3×D4—22no—
533C3×D4—21no—
534C3×D4—21no—
535C3×D4—21no—
536C3×D4—21no—
537C3×D4—41no—
538C3×D4—61no—
539C3×D4—61no—
540C3×D4—61no—
541C3×D4—61no—
542C3×D4—122no—
543C3×D4—122no—
544C3×D4—241no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—31no—
549C2×C3×C4—31no—
550C2×C3×C4—31no—
551C2×C3×C4—41no—
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—42no—
563#67—81no—
564#67—122no—
565#67—122no—
566#67—122no—
567#67—122no—
568#67—122no—
569#67—124no—
570#67—122no—
571#67—122no—
572C2×Dic3—21no—
573C2×Dic3—21no—
574C2×Dic3—31no—
575C2×Dic3—31no—
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—32no—
589D12—32no—
590D12—62no—
591D12—61no—
592D12—61no—
593D12—121no—
594D12—122no—
595D12—122no—
596D12—122no—
597C4×D3—21no—
598C4×D3—21no—
599C4×D3—42no—
600C4×D3—42no—
601C4×D3—62no—
602C4×D3—62no—
603C4×D3—61no—
604C4×D3—61no—
605C4×D3—61no—
606C4×D3—61no—
607C4×D3—122no—
608C4×D3—122no—
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—81no—
625C2×C32#54611yescharacteristic
626C2×C32C22×D811yescharacteristic
627C2×C32#57711yescharacteristic
628C3⋊D3—22no—
629C3⋊D3—42no—
630C3×D3—22no—
631C3×D3—81no—
632C3×D3—81no—
633C24—181no—
634C24—181no—
635#41—364no—
636C2×Q8—181no—
637C2×D4—31no—
638C2×D4—31no—
639C2×D4—61no—
640C2×D4—61no—
641C2×D4—61no—
642C2×D4—91no—
643C2×D4—91no—
644C2×D4—181no—
645C2×D4—182no—
646C2×D4—181no—
647C2×D4—181no—
648C2×D4—181no—
649C2×D4—182no—
650C2×D4—181no—
651C2×D4—361no—
652C2×D4—361no—
653C2×D4—364no—
654C2×D4C2×D3211yescharacteristic
655C22×C4—31no—
656C22×C4—61no—
657C22×C4—61no—
658C22×C4—91no—
659C22×C4—181no—
660C22×C4—181no—
661D8—121no—
662D8—121no—
663D8—182no—
664C2×C8—31no—
665C2×C8—31no—
666C2×C8—91no—
667C2×C8—361no—
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—21no—
688C22×C3—32no—
689C22×C3—42no—
690C22×C3—41no—
691C22×C3—41no—
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×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—41no—
716C2×D3—41no—
717C2×D3—41no—
718C2×D3—62no—
719C2×D3—62no—
720C2×D3—62no—
721C2×D3—61no—
722C2×D3—61no—
723C2×D3—61no—
724C2×D3—61no—
725C2×D3—62no—
726C2×D3—62no—
727C2×D3—122no—
728C2×D3—121no—
729C2×D3—121no—
730C2×D3—121no—
731C2×D3—121no—
732C2×D3—241no—
733C2×D3—241no—
734C2×D3—244no—
735C2×D3—244no—
736C2×D3—244no—
737C2×D3—248no—
738C2×D3—244no—
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×C4#100411yescharacteristic
751C3×C4D3×#4111yescharacteristic
752C3×C4D3×#4111yescharacteristic
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—181no—
772C23—362no—
773C23—362no—
774C23—362no—
775C23—362no—
776C23—721no—
777C23—721no—
778Q8—362no—
779D4—21no—
780D4—21no—
781D4—61no—
782D4—61no—
783D4—61no—
784D4—61no—
785D4—94no—
786D4—92no—
787D4—122no—
788D4—122no—
789D4—181no—
790D4—241no—
791D4—362no—
792D4—362no—
793D4—362no—
794D4—362no—
795D4—362no—
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—181no—
808C2×C4—181no—
809C2×C4—181no—
810C2×C4—362no—
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—62no—
821C2×C3—82no—
822C2×C3—81no—
823C2×C3—81no—
824C2×C3—241no—
825C2×C3—241no—
826C2×C3#561211yescharacteristic
827C2×C3#565411yescharacteristic
828C2×C3C2×D3×D811yescharacteristic
829C2×C3C2×D3×D811yescharacteristic
830C2×C3#577511yescharacteristic
831C2×C3#577811yescharacteristic
832D3—22no—
833D3—64no—
834D3—62no—
835D3—62no—
836D3—81no—
837D3—81no—
838D3—122no—
839D3—122no—
840D3—242no—
841C22—32no—
842C22—41no—
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—182no—
857C22—361no—
858C22—361no—
859C22—724no—
860C22—724no—
861C22D32×D411yescharacteristic
862C4—32no—
863C4—41no—
864C4—61no—
865C4—61no—
866C4—121no—
867C4—121no—
868C4—181no—
869C4—361no—
870C4#6430611yescharacteristic
871C4#6431411yescharacteristic
872C3—21no—
873C3#8035211yescharacteristic, complemented
874C3#8130211yescharacteristic, complemented
875C2—62no—
876C2—81no—
877C2—182no—
878C2—241no—
879C2—241no—
880C2—362no—
881C2#1059427911yescharacteristic
882C2D32×D811yescharacteristic
883C2#1059475411yescharacteristic
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. #10594515C2semidirect
3. C3⋊D3×#102C2semidirect
4. C3×#4786C2semidirect
5. C3×#4774C2semidirect
6. #10591498C2semidirect
7. #10591487C2semidirect
8. #10591456C2semidirect
9. #10590944C2semidirect
10. #10590906C2semidirect
11. #10590844C2semidirect
12. #10590764C2semidirect
13. D3×#809C2semidirect
14. #10590510C2semidirect
15. #10590456C2semidirect
22. C2×C8×C3⋊D3C22semidirect
23. C4⋊C4×C3⋊D3C22semidirect
26. C2×C3×#213C22semidirect
27. C2×C3×D24C22semidirect
28. C3×#893C22semidirect
29. C3×D3×C4⋊C4C22semidirect
33. #63918C22semidirect
35. #63916C22semidirect
36. #63908C22semidirect
43. C2×D3×C3⋊C8C22semidirect
44. C32×#102C22semidirect
45. #63659C22semidirect
48. C3×#832C22semidirect
49. C3×(C2×D3)⋊C8C22semidirect
50. C3×#818C22semidirect
51. C3×Dic3⋊C8C22semidirect
52. C3×#809C22semidirect
53. C3×#807C22semidirect
54. #63575C22semidirect
56. #63563C22semidirect
57. #63562C22semidirect
58. #63562C22semidirect
59. #63557C22semidirect
60. Dic3×C3⋊C8C22semidirect
81. #4786D3semidirect
83. #4774D3semidirect
172. C2×#213C2×D3semidirect
179. C2×D24C2×D3semidirect
189. #893C2×D3semidirect
193. D3×C4⋊C4C2×D3semidirect
208. C3×#102C2×D3semidirect
209. C3×#102C2×D3semidirect
217. #832C2×D3semidirect
225. (C2×D3)⋊C8C2×D3semidirect
227. #818C2×D3semidirect
228. Dic3⋊C8C2×D3semidirect
236. #809C2×D3semidirect
238. #807C2×D3semidirect
260. C4⋊(C3⋊D3)#41semidirect
284. #626D8semidirect
498. #102D32semidirect
765. C32#3294semidirect
873. C3#80352semidirect
874. C3#81302semidirect

Maximal subgroups

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

subgroupindex
#105952972
#105945152
C3⋊D3×#1022
C3×#47862
C3×#47742
#105914982
#105914872
#105914562
#105909442
#105909062
#105908442
#105907642
D3×#8092
#105905102
#105904562
#813023
#803523