Finite Group Databasebeta

← #11887463

Subgroups — #11887463

Order 1152.

1007 conjugacy classes of subgroups.

The subgroup lattice has 867 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596147C211yesmaximal, characteristic, complemented
2#10593982C211yesmaximal, characteristic, complemented
3C3×#5057C211yesmaximal, characteristic, complemented
4C3×#5056C211yesmaximal, characteristic, complemented
5#10591593C211yesmaximal, characteristic, complemented
6#10591591C211yesmaximal, characteristic, complemented
7#10591560C211yesmaximal, characteristic, complemented
8#10591555C211yesmaximal, characteristic, complemented
9#10591456C211yesmaximal, characteristic, complemented
10#10591455C211yesmaximal, characteristic, complemented
11#10591425C211yesmaximal, characteristic, complemented
12#10591416C211yesmaximal, characteristic, complemented
13C4×#3714C211yesmaximal, characteristic, complemented
14#10590327C211yesmaximal, characteristic, complemented
15#10590308C211yesmaximal, characteristic, complemented
16#81653—31nomaximal
17#80559—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×D4×C3⋊D3C2211yescharacteristic
20C32×#124C2211yescharacteristic
21#64155C2211yescharacteristic
22#64147C2211yescharacteristic
23#64093—21no—
24#64092—21no—
25#64091—21no—
26C22⋊C4×C3⋊D3—21no—
27C4×C4⋊(C3⋊D3)C2211yescharacteristic
28C4×C4⋊(C3⋊D3)C2211yescharacteristic
29C2×C3×#215C2211yescharacteristic, complemented
30C2×C3×#213C2211yescharacteristic
31C3×C4×D12C2211yescharacteristic, complemented
32C3×#870C2211yescharacteristic, complemented
33#63916C2211yescharacteristic
34#63916C2211yescharacteristic, complemented
35#63910—21no—
36#63904—21no—
37#63900C2211yescharacteristic
38#63861—21no—
39#63850—21no—
40#63849C2211yescharacteristic, complemented
41C2×#3714C2211yescharacteristic
42C2×#3710C2211yescharacteristic
43C2×#3710C2211yescharacteristic, complemented
44C3×#835C2211yescharacteristic, complemented
45C3×#835C2211yescharacteristic, complemented
46C3×#835C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
51C3×C4×C3⋊C8C2211yescharacteristic, complemented
52#63575C2211yescharacteristic, complemented
53#63575C2211yescharacteristic, complemented
54#63573C2211yescharacteristic, complemented
55#63564C2211yescharacteristic
56#63564C2211yescharacteristic
57#63564C2211yescharacteristic
58#63563C2211yescharacteristic, complemented
59#63557C2211yescharacteristic
60#63557C2211yescharacteristic, complemented
61#5695—31no—
62#5676—31no—
63#5676—31no—
64#5676—61no—
65#5558—31no—
66C3×#488—31no—
67C3×#463—31no—
68#5172—31no—
69#5171—31no—
70#5157—31no—
71#5156—31no—
72#5066—31no—
73#5057D311yescharacteristic, complemented
74#5056D311yescharacteristic, complemented
75C4×#213—31no—
76#4847—31no—
77#4834—31no—
78#4811—31no—
79#4811—31no—
80#4810—31no—
81#4807—31no—
82#4804—31no—
83#4804—31no—
84#4784—31no—
85#4779—31no—
86#4775—31no—
87#4773—31no—
88D3×#102—31no—
89D3×#102—31no—
90C4×D24—31no—
91C8×D12—31no—
92C23×C3⋊D3—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C32×D4C2311yescharacteristic
95C2×#638—21no—
96C2×#638—21no—
97#3832—22no—
98#3832—41no—
99D4×C3⋊D3—22no—
100D4×C3⋊D3—41no—
101C2×C4⋊(C3⋊D3)—21no—
102C2×C4⋊(C3⋊D3)D411yescharacteristic
103C2×C4⋊(C3⋊D3)C2311yescharacteristic
104C2×C4×C3⋊D3—21no—
105C2×C4×C3⋊D3—21no—
106C2×C4×C3⋊D3C2311yescharacteristic
107C2×C4×C3⋊D3C2311yescharacteristic
108C2×C3×D12C2311yescharacteristic
109C2×C3×C4×D3—21no—
110C2×#626—21no—
111C2×#626—21no—
112C2×#624—21no—
113C32×C22⋊C4—21no—
114C32×C22⋊C4—21no—
115C32×C42C2311yescharacteristic
116#3757—21no—
117#3752—21no—
118#3752—21no—
119#3752D411yescharacteristic
120#3752D411yescharacteristic
121C4⋊(C3⋊Dic3)D411yescharacteristic
122C4⋊(C3⋊Dic3)C2311yescharacteristic
123#3750—21no—
124C3×#215—41no—
125C3×#213—41no—
126C3×(C2×D3)⋊C4—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136#3724—21no—
137#3722—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140Dic32—21no—
141#3714—22no—
142#3710—41no—
143#3710—41no—
144#3297—91noSylow
145C2×#239—31no—
146C2×#239—31no—
147C2×#239—61no—
148C2×D3×D4—31no—
149C2×D3×D4—31no—
150C2×D3×D4—61no—
151C2×C3×SD16—31no—
152C2×C3×D8—31no—
153C3×#125—31no—
154C3×#124—21no—
155C3×#124C2×D311yescharacteristic
156C3×#124C2×D311yescharacteristic
157C3×C4×D4—31no—
158#946—31no—
159#946—31no—
160#946—61no—
161C2×#215C2×D311yescharacteristic, complemented
162#938—31no—
163#938—31no—
164#938—31no—
165#938—31no—
166#938—61no—
167C2×#213—31no—
168C2×#213C2×D311yescharacteristic
169#929—61no—
170C4×#67—61no—
171C2×D24—31no—
172C2×D3×C8—31no—
173C2×D3×C8—31no—
174C2×D3×C8—31no—
175C2×D3×C8—31no—
176#898—61no—
177#895—31no—
178#895—31no—
179#895—61no—
180#894—61no—
181#893—61no—
182#892—31no—
183#892—31no—
184D3×C4⋊C4—31no—
185D3×C4⋊C4—31no—
186#884—61no—
187#884—61no—
188#884—61no—
189#884—62no—
190#883—61no—
191#883—61no—
192#883—62no—
193#882—61no—
194#882—61no—
195#882—62no—
196D3×C22⋊C4—61no—
197D3×C22⋊C4—61no—
198D3×C22⋊C4—62no—
199#879—61no—
200C4×D12—31no—
201C4×D12—31no—
202C4×D12—31no—
203C4×D12—31no—
204C4×D12—61no—
205C4×D12—61no—
206C4×D12C2×D311yescharacteristic, complemented
207#870C2×D311yescharacteristic, complemented
208C3×C4⋊C8—31no—
209C3×#103—31no—
210C3×#103—31no—
211C3×#103—31no—
212C3×#102—31no—
213C3×#102—31no—
214C3×#102—31no—
215C3×C4×C8—31no—
216#835C2×D311yescharacteristic, complemented
217#835C2×D311yescharacteristic, complemented
218#835C2×D311yescharacteristic, complemented
219#832—31no—
220#832C2×D311yescharacteristic
221#832C2×D311yescharacteristic
222#832C2×D311yescharacteristic
223#821—31no—
224#821—31no—
225#821—31no—
226#821—31no—
227(C2×D3)⋊C8—31no—
228(C2×D3)⋊C8—31no—
229(C2×D3)⋊C8—31no—
230(C2×D3)⋊C8—31no—
231#818—31no—
232#818—31no—
233#817—31no—
234#809—31no—
235#809—31no—
236#809—31no—
237#808—31no—
238#807—31no—
239#807—31no—
240C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
241C4×C3⋊C8C2×D311yescharacteristic, complemented
242C23×C32—21no—
243C22×C3⋊D3—21no—
244C22×C3⋊D3—42no—
245C22×C3⋊D3—42no—
246C22×C3⋊D3—81no—
247C22×C3⋊D3C2×D411yescharacteristic
248C22×C3⋊D3C2×D411yescharacteristic
249C22×C3×D3—21no—
250C32×Q8—21no—
251C32×Q8—21no—
252C32×D4—21no—
253C32×D4—21no—
254C2×C32×C4—21no—
255C2×C32×C4C2×D411yescharacteristic
256C2×C32×C4C2×D411yescharacteristic
257C2×C32×C4C2411yescharacteristic
258#638—42no—
259#638—81no—
260C2×C3⋊Dic3—21no—
261C2×C3⋊Dic3C2×D411yescharacteristic
262C2×C3⋊Dic3C2×D411yescharacteristic
263C4⋊(C3⋊D3)—21no—
264C4⋊(C3⋊D3)—22no—
265C4⋊(C3⋊D3)—42no—
266C4⋊(C3⋊D3)#4112yes—
267C4×C3⋊D3—21no—
268C4×C3⋊D3—21no—
269C4×C3⋊D3—21no—
270C4×C3⋊D3—21no—
271C4×C3⋊D3—42no—
272C4×C3⋊D3—81no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C3×D12—21no—
277C3×D12—21no—
278C3×C4×D3—81no—
279#626—42no—
280#626—81no—
281#624—81no—
282C3×C3⋊C8—21no—
283C3×C3⋊C8—21no—
284C3×C3⋊C8—21no—
285C3×C3⋊C8—21no—
286#553—91no—
287#546—91no—
288#488—31no—
289#484—91no—
290#482—91no—
291#478—91no—
292#466—91no—
293#465—91no—
294#463—31no—
295#449—91no—
296#447—91no—
297C4×D8—91no—
298C8×D4—91no—
299#416—91no—
300C2×#102—91no—
301C23×D3—61no—
302C23×D3—61no—
303C23×D3—62no—
304C2×C3×Q8—21no—
305C2×C3×Q8C22×D311yescharacteristic
306C2×C3×Q8C22×D311yescharacteristic
307C2×C3×D4—21no—
308C2×C3×D4—31no—
309C2×C3×D4C22×D311yescharacteristic
310C2×C3×D4C22×D311yescharacteristic
311C22×C3×C4—61no—
312C2×#67—61no—
313C2×#67—61no—
314C2×#67—61no—
315C2×#67—61no—
316C2×#67—62no—
317C2×#67—61no—
318C2×#67—61no—
319C2×#67—62no—
320#239—62no—
321#239—62no—
322#239—122no—
323#239—121no—
324#239—121no—
325#239—122no—
326D3×D4—62no—
327D3×D4—62no—
328D3×D4—122no—
329D3×D4—121no—
330D3×D4—121no—
331D3×D4—122no—
332C2×D12—31no—
333C2×D12—31no—
334C2×D12—31no—
335C2×D12—31no—
336C2×D12—61no—
337C2×D12—61no—
338C2×D12—61no—
339C2×D12—61no—
340C2×D12—62no—
341C2×D12—61no—
342C2×D12—61no—
343C2×D12C22×D311yescharacteristic
344C2×C4×D3—21no—
345C2×C4×D3—31no—
346C2×C4×D3—31no—
347C2×C4×D3—31no—
348C2×C4×D3—31no—
349C2×C4×D3—61no—
350C2×C4×D3—61no—
351C2×C4×D3—61no—
352C2×C4×D3—61no—
353C2×C4×D3—62no—
354C2×C4×D3—61no—
355C2×C4×D3—61no—
356C2×C4×D3—62no—
357C2×C4×D3—61no—
358C2×C4×D3—61no—
359C3×SD16—121no—
360C3×D8—121no—
361C2×C3×C8—31no—
362C2×C3×C8—31no—
363C2×C3×C8—31no—
364C2×C3×C8—31no—
365C3×C4⋊C4—31no—
366C3×C4⋊C4—31no—
367C3×C4⋊C4—31no—
368C3×C4⋊C4—61no—
369C3×C4⋊C4—61no—
370C3×C22⋊C4—22no—
371C3×C22⋊C4—22no—
372C3×C22⋊C4—21no—
373C3×C22⋊C4—21no—
374C3×C22⋊C4—21no—
375C3×C22⋊C4—21no—
376C3×C22⋊C4—61no—
377C3×C42—21no—
378C3×C42C22×D311yescharacteristic
379C3×C42C22×D311yescharacteristic
380#217—61no—
381#217—61no—
382#217—61no—
383#217—61no—
384#217—62no—
385#215—41no—
386#213—41no—
387#213—62no—
388(C2×D3)⋊C4—21no—
389(C2×D3)⋊C4—31no—
390(C2×D3)⋊C4—31no—
391(C2×D3)⋊C4—31no—
392(C2×D3)⋊C4—31no—
393(C2×D3)⋊C4—61no—
394(C2×D3)⋊C4—61no—
395(C2×D3)⋊C4—61no—
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—62no—
402(C2×D3)⋊C4—62no—
403(C2×D3)⋊C4—61no—
404(C2×D3)⋊C4—61no—
405C4⋊Dic3—31no—
406C4⋊Dic3—31no—
407C4⋊Dic3—31no—
408C4⋊Dic3—31no—
409C4⋊Dic3—61no—
410C4⋊Dic3—61no—
411C4⋊Dic3C22×D311yescharacteristic
412C4⋊Dic3C22×D311yescharacteristic
413C4⋊Dic3C22×D311yescharacteristic
414Dic3⋊C4—21no—
415Dic3⋊C4—21no—
416Dic3⋊C4—61no—
417Dic3⋊C4—61no—
418Dic3⋊C4—61no—
419Dic3⋊C4—61no—
420Dic3⋊C4—62no—
421C4×Dic3—61no—
422C4×Dic3—61no—
423C2×C3⋊C8C22×D311yescharacteristic
424C2×C3⋊C8C22×D311yescharacteristic
425C2×C3⋊C8C22×D311yescharacteristic
426C2×C3⋊C8C22×D311yescharacteristic
427D24—62no—
428D3×C8—121no—
429D3×C8—121no—
430D3×C8—121no—
431D3×C8—121no—
432C22×C32—41no—
433C22×C32—41no—
434C22×C32—41no—
435C22×C32C22×D411yescharacteristic
436C2×C3⋊D3—22no—
437C2×C3⋊D3—21no—
438C2×C3⋊D3—21no—
439C2×C3⋊D3—21no—
440C2×C3⋊D3—21no—
441C2×C3⋊D3—21no—
442C2×C3⋊D3—41no—
443C2×C3⋊D3—41no—
444C2×C3⋊D3—84no—
445C2×C3⋊D3#13512yes—
446C2×C3×D3—41no—
447C2×C3×D3—41no—
448C2×C3×D3—41no—
449C32×C4—21no—
450C32×C4—21no—
451C32×C4—41no—
452C32×C4C2×#4111yescharacteristic
453C32×C4H(5,𝔽2)11yescharacteristic
454C3⋊Dic3—21no—
455C3⋊Dic3—21no—
456C3⋊Dic3—41no—
457C3×Dic3—41no—
458C3×Dic3—41no—
459C3×Dic3—41no—
460C2×#41—91no—
461C22×D4—91no—
462C2×SD16—31no—
463C2×D8—31no—
464C2×D8—91no—
465C22×C8—91no—
466C22×C8—91no—
467#126—181no—
468#125—31no—
469#124D3211yescharacteristic
470#123—181no—
471#123—181no—
472C22⋊Q8—91no—
473#121—91no—
474#121—91no—
475#121—91no—
476#121—181no—
477#121—181no—
478#120—181no—
479C4×D4—31no—
480C4×D4—91no—
481C4×D4—91no—
482C4×D4—181no—
483#117—91no—
484C2×C4⋊C4—91no—
485C2×C22⋊C4—181no—
486#107—91no—
487#107—91no—
488#106—91no—
489C4⋊C8—31no—
490#103—31no—
491#103—31no—
492#103—31no—
493#102—31no—
494#102—31no—
495#102—31no—
496#102—91no—
497#102—91no—
498#102—91no—
499#102—91no—
500C22⋊C8—91no—
501C22⋊C8—91no—
502C4×C8—31no—
503C23×C3—22no—
504C23×C3—21no—
505C23×C3—21no—
506C23×C3—61no—
507C22×D3—21no—
508C22×D3—31no—
509C22×D3—31no—
510C22×D3—31no—
511C22×D3—31no—
512C22×D3—61no—
513C22×D3—61no—
514C22×D3—62no—
515C22×D3—61no—
516C22×D3—61no—
517C22×D3—122no—
518C22×D3—122no—
519C22×D3—122no—
520C22×D3—122no—
521C22×D3—124no—
522C22×D3—124no—
523C22×D3—241no—
524C22×D3—241no—
525C22×D3—242no—
526C3×Q8—21no—
527C3×Q8—21no—
528C3×Q8—21no—
529C3×Q8—21no—
530C3×Q8—41no—
531C3×Q8—41no—
532C3×D4—21no—
533C3×D4—21no—
534C3×D4—21no—
535C3×D4—21no—
536C3×D4—41no—
537C3×D4—41no—
538C3×D4—61no—
539C3×D4—61no—
540C2×C3×C4—22no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—61no—
547C2×C3×C4—61no—
548C2×C3×C4—61no—
549C2×C3×C4—241no—
550C2×C3×C4D3×D411yescharacteristic
551C2×C3×C4D3×D411yescharacteristic
552C2×C3×C4D3×D411yescharacteristic
553C2×C3×C4D3×D411yescharacteristic
554C2×C3×C4C23×D311yescharacteristic
555C2×C3×C4C23×D311yescharacteristic
556#67—122no—
557#67—122no—
558#67—122no—
559#67—124no—
560#67—241no—
561#67—241no—
562#67—241no—
563#67—242no—
564C2×Dic3—21no—
565C2×Dic3—21no—
566C2×Dic3—21no—
567C2×Dic3—31no—
568C2×Dic3—31no—
569C2×Dic3—31no—
570C2×Dic3—31no—
571C2×Dic3—61no—
572C2×Dic3—61no—
573C2×Dic3—62no—
574C2×Dic3—61no—
575C2×Dic3—61no—
576D12—21no—
577D12—21no—
578D12—32no—
579D12—32no—
580D12—62no—
581D12—62no—
582D12—62no—
583D12—62no—
584D12—61no—
585D12—61no—
586D12—122no—
587D12—122no—
588D12—122no—
589D12—124no—
590D12—122no—
591D12—241no—
592C4×D3—61no—
593C4×D3—61no—
594C4×D3—61no—
595C4×D3—61no—
596C4×D3—61no—
597C4×D3—61no—
598C4×D3—61no—
599C4×D3—61no—
600C4×D3—81no—
601C4×D3—121no—
602C4×D3—121no—
603C4×D3—121no—
604C4×D3—121no—
605C4×D3—122no—
606C4×D3—122no—
607C4×D3—124no—
608C4×D3—241no—
609C4×D3—241no—
610C4×D3—241no—
611C4×D3—241no—
612C4×D3—242no—
613C3×C8—61no—
614C3×C8—61no—
615C3×C8—61no—
616C3×C8—61no—
617C3⋊C8—21no—
618C3⋊C8—21no—
619C3⋊C8—21no—
620C3⋊C8—21no—
621C2×C32—81no—
622C2×C32#54611yescharacteristic
623C2×C32C2×#13511yescharacteristic
624C2×C32#57611yescharacteristic
625C3⋊D3—22no—
626C3⋊D3—42no—
627C3⋊D3—41no—
628C3×D3—81no—
629C24—181no—
630#41—182no—
631#41—361no—
632C2×Q8C2×D3211yescharacteristic
633C2×D4—31no—
634C2×D4—91no—
635C2×D4—91no—
636C2×D4—181no—
637C2×D4—181no—
638C2×D4—181no—
639C2×D4—181no—
640C2×D4—182no—
641C2×D4—181no—
642C2×D4—361no—
643C2×D4C2×D3211yescharacteristic
644C22×C4—61no—
645C22×C4—91no—
646C22×C4—91no—
647C22×C4—181no—
648C22×C4—181no—
649C22×C4—181no—
650SD16—121no—
651D8—121no—
652D8—182no—
653C2×C8—31no—
654C2×C8—31no—
655C2×C8—31no—
656C2×C8—31no—
657C2×C8—361no—
658C2×C8—361no—
659C4⋊C4—31no—
660C4⋊C4—31no—
661C4⋊C4—31no—
662C4⋊C4—61no—
663C4⋊C4—61no—
664C4⋊C4—91no—
665C4⋊C4—91no—
666C4⋊C4—181no—
667C4⋊C4—181no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—61no—
671C22⋊C4—91no—
672C22⋊C4—91no—
673C22⋊C4—181no—
674C22⋊C4—181no—
675C22⋊C4—181no—
676C22⋊C4—181no—
677C22⋊C4—181no—
678C22⋊C4—181no—
679C42—181no—
680C42C2×D3211yescharacteristic
681C22×C3—21no—
682C22×C3—42no—
683C22×C3—42no—
684C22×C3—42no—
685C22×C3—41no—
686C22×C3—41no—
687C22×C3—41no—
688C22×C3—41no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—121no—
692C22×C3—121no—
693C22×C3—121no—
694C22×C3C2×D3×D411yescharacteristic
695C22×C3C2×D3×D411yescharacteristic
696C2×D3—32no—
697C2×D3—32no—
698C2×D3—41no—
699C2×D3—41no—
700C2×D3—41no—
701C2×D3—62no—
702C2×D3—61no—
703C2×D3—61no—
704C2×D3—61no—
705C2×D3—61no—
706C2×D3—64no—
707C2×D3—61no—
708C2×D3—62no—
709C2×D3—61no—
710C2×D3—61no—
711C2×D3—61no—
712C2×D3—61no—
713C2×D3—61no—
714C2×D3—62no—
715C2×D3—121no—
716C2×D3—121no—
717C2×D3—121no—
718C2×D3—121no—
719C2×D3—121no—
720C2×D3—122no—
721C2×D3—122no—
722C2×D3—121no—
723C2×D3—121no—
724C2×D3—121no—
725C2×D3—121no—
726C2×D3—244no—
727C2×D3—244no—
728C2×D3—248no—
729C3×C4—21no—
730C3×C4—21no—
731C3×C4—21no—
732C3×C4—21no—
733C3×C4—21no—
734C3×C4—21no—
735C3×C4—41no—
736C3×C4—41no—
737C3×C4—42no—
738C3×C4—41no—
739C3×C4—41no—
740C3×C4—121no—
741C3×C4—121no—
742C3×C4—121no—
743C3×C4#100411yescharacteristic
744C3×C4D3×#4111yescharacteristic
745C3×C4D3×#4111yescharacteristic
746C3×C4#100911yescharacteristic
747Dic3—41no—
748Dic3—41no—
749Dic3—41no—
750Dic3—61no—
751Dic3—61no—
752Dic3—61no—
753Dic3—61no—
754Dic3—121no—
755Dic3—121no—
756Dic3—122no—
757Dic3—121no—
758Dic3—121no—
759C32#329711yescharacteristic, complemented, Sylow
760C23—21no—
761C23—61no—
762C23—91no—
763C23—91no—
764C23—181no—
765C23—362no—
766C23—362no—
767C23—721no—
768Q8—21no—
769Q8—21no—
770D4—21no—
771D4—21no—
772D4—61no—
773D4—61no—
774D4—92no—
775D4—182no—
776D4—181no—
777D4—362no—
778D4—362no—
779D4—362no—
780D4—721no—
781D4—721no—
782C2×C4—21no—
783C2×C4—61no—
784C2×C4—61no—
785C2×C4—61no—
786C2×C4—91no—
787C2×C4—91no—
788C2×C4—181no—
789C2×C4—181no—
790C2×C4—181no—
791C2×C4—181no—
792C2×C4—181no—
793C2×C4—241no—
794C2×C4—362no—
795C2×C4—721no—
796C2×C4—721no—
797C2×C4#381111yescharacteristic
798C2×C4#381111yescharacteristic
799C2×C4C22×D3211yescharacteristic
800C8—61no—
801C8—61no—
802C8—61no—
803C8—61no—
804C2×C3—21no—
805C2×C3—21no—
806C2×C3—21no—
807C2×C3—82no—
808C2×C3—81no—
809C2×C3—81no—
810C2×C3—241no—
811C2×C3#561211yescharacteristic
812C2×C3#567611yescharacteristic
813C2×C3D3×#13511yescharacteristic
814C2×C3D3×#13511yescharacteristic
815C2×C3#576911yescharacteristic
816C2×C3#577411yescharacteristic
817D3—62no—
818D3—62no—
819D3—81no—
820D3—122no—
821D3—124no—
822D3—121no—
823D3—122no—
824D3—121no—
825D3—122no—
826D3—241no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—92no—
831C22—121no—
832C22—121no—
833C22—121no—
834C22—181no—
835C22—181no—
836C22—181no—
837C22—181no—
838C22—181no—
839C22—182no—
840C22—361no—
841C22—361no—
842C22—724no—
843C22C2×#381111yescharacteristic
844C4—21no—
845C4—21no—
846C4—41no—
847C4—121no—
848C4—121no—
849C4—121no—
850C4—181no—
851C4—181no—
852C4—361no—
853C4#6431211yescharacteristic
854C4#6431411yescharacteristic
855C3—21no—
856C3#8055911yescharacteristic, complemented
857C3#8165311yescharacteristic, complemented
858C2—81no—
859C2—182no—
860C2—241no—
861C2—361no—
862C2—362no—
863C2#1059524311yescharacteristic
864C2#1059545911yescharacteristic
865C2#1059546111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#124C22
socleC22×C32C22×D4
hypercenter#124D32
hypocenterC32#3297
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #10596147C2semidirect
2. #10593982C2semidirect
3. C3×#5057C2semidirect
4. C3×#5056C2semidirect
5. #10591593C2semidirect
6. #10591591C2semidirect
7. #10591560C2semidirect
8. #10591555C2semidirect
9. #10591456C2semidirect
10. #10591455C2semidirect
11. #10591425C2semidirect
12. #10591416C2semidirect
13. C4×#3714C2semidirect
14. #10590327C2semidirect
15. #10590308C2semidirect
29. C2×C3×#215C22semidirect
31. C3×C4×D12C22semidirect
32. C3×#870C22semidirect
34. #63916C22semidirect
40. #63849C22semidirect
43. C2×#3710C22semidirect
44. C3×#835C22semidirect
45. C3×#835C22semidirect
46. C3×#835C22semidirect
50. C3×C4⋊(C3⋊C8)C22semidirect
51. C3×C4×C3⋊C8C22semidirect
52. #63575C22semidirect
53. #63575C22semidirect
54. #63573C22semidirect
58. #63563C22semidirect
60. #63557C22semidirect
73. #5057D3semidirect
74. #5056D3semidirect
161. C2×#215C2×D3semidirect
206. C4×D12C2×D3semidirect
207. #870C2×D3semidirect
216. #835C2×D3semidirect
217. #835C2×D3semidirect
218. #835C2×D3semidirect
240. C4⋊(C3⋊C8)C2×D3semidirect
241. C4×C3⋊C8C2×D3semidirect
759. C32#3297semidirect
856. C3#80559semidirect
857. C3#81653semidirect

Maximal subgroups

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

subgroupindex
#105961472
#105939822
C3×#50572
C3×#50562
#105915932
#105915912
#105915602
#105915552
#105914562
#105914552
#105914252
#105914162
C4×#37142
#105903272
#105903082
#816533
#805593