Finite Group Databasebeta

← #11887400

Subgroups — #11887400

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#10596025C211yesmaximal, characteristic, complemented
2#10593982C211yesmaximal, characteristic, complemented
3C3×C4×#213C211yesmaximal, characteristic, complemented
4C3×#5009C211yesmaximal, characteristic, complemented
5#10591457C211yesmaximal, characteristic, complemented
6#10591456C211yesmaximal, characteristic, complemented
7#10591424C211yesmaximal, characteristic, complemented
8#10591416C211yesmaximal, characteristic, complemented
9#10590509C211yesmaximal, characteristic, complemented
10#10590507C211yesmaximal, characteristic, complemented
11#10590451C211yesmaximal, characteristic, complemented
12#10590444C211yesmaximal, characteristic, complemented
13#10590366C211yesmaximal, characteristic, complemented
14#10590327C211yesmaximal, characteristic, complemented
15#10590293C211yesmaximal, characteristic, complemented
16#81187—31nomaximal
17#79609—31nomaximal
18C2×#3830C2211yescharacteristic
19C2×D4×C3⋊D3C2211yescharacteristic
20C32×C4×D4C2211yescharacteristic
21#64139—21no—
22C2×#3752—21no—
23#64106C2211yescharacteristic
24#64104C2211yescharacteristic
25#64095—21no—
26#64091—21no—
27#64084C2211yescharacteristic
28C4×C4⋊(C3⋊D3)C2211yescharacteristic
29C2×C3×#213C2211yescharacteristic
30C3×C4×D12C2211yescharacteristic, complemented
31C3×#870C2211yescharacteristic, complemented
32#63916C2211yescharacteristic
33#63916C2211yescharacteristic, complemented
34#63910—21no—
35#63904—21no—
36#63900C2211yescharacteristic
37#63861—21no—
38#63850—21no—
39#63849C2211yescharacteristic, complemented
40C2×#3716C2211yescharacteristic, complemented
41C2×#3714C2211yescharacteristic
42C2×#3710C2211yescharacteristic
43C2×#3710C2211yescharacteristic, complemented
44C3×#832C2211yescharacteristic
45C3×#832C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#809C2211yescharacteristic, complemented
48C3×#808C2211yescharacteristic, complemented
49C3×#807C2211yescharacteristic, complemented
50C3×#807C2211yescharacteristic, complemented
51C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
52C3×C4×C3⋊C8C2211yescharacteristic, complemented
53#63567C2211yescharacteristic, complemented
54#63567C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63564C2211yescharacteristic
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59#63557C2211yescharacteristic
60#63557C2211yescharacteristic, complemented
61#5695—31no—
62#5558—31no—
63#5554—31no—
64#5554—31no—
65#5554—61no—
66C3×#478—31no—
67C3×C4×D8—31no—
68#5158—31no—
69#5156—31no—
70#5068—31no—
71#5016—31no—
72C4×#213D311yescharacteristic, complemented
73#5009D311yescharacteristic, complemented
74#4885—31no—
75#4884—31no—
76#4884—31no—
77#4883—31no—
78#4866—31no—
79#4864—31no—
80#4844—31no—
81#4834—31no—
82#4781—31no—
83#4778—31no—
84#4775—31no—
85#4773—31no—
86#4772—31no—
87#4772—31no—
88D3×#102—31no—
89D3×#102—31no—
90#4697—31no—
91C8×D12—31no—
92C23×C3⋊D3—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4—21no—
95C2×#638—21no—
96C2×#638—21no—
97C22×C3⋊Dic3—21no—
98#3830—22no—
99#3830—41no—
100D4×C3⋊D3—22no—
101D4×C3⋊D3—41no—
102C2×C4⋊(C3⋊D3)—21no—
103C2×C4⋊(C3⋊D3)D411yescharacteristic
104C2×C4⋊(C3⋊D3)C2311yescharacteristic
105C2×C4×C3⋊D3C2311yescharacteristic
106C2×C4×C3⋊D3C2311yescharacteristic
107C2×#634C2311yescharacteristic
108C2×C3×D12C2311yescharacteristic
109C2×C3×C4×D3—21no—
110C2×#626—21no—
111C2×#626—21no—
112C2×#624—21no—
113C32×C4⋊C4C2311yescharacteristic
114C32×C22⋊C4—21no—
115C32×C42C2311yescharacteristic
116#3752—21no—
117#3752—21no—
118#3752—21no—
119#3752—21no—
120#3752D411yescharacteristic
121#3752D411yescharacteristic
122C4⋊(C3⋊Dic3)—21no—
123C4⋊(C3⋊Dic3)D411yescharacteristic
124C3×#213—22no—
125C3×(C2×D3)⋊C4—21no—
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135#3724—21no—
136#3722—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139Dic32—21no—
140#3716—41no—
141#3714—41no—
142#3710—41no—
143#3710—41no—
144#3297—91noSylow
145C2×#237—31no—
146C2×#237—31no—
147C2×#237—61no—
148C2×D3×D4—31no—
149C2×D3×D4—31no—
150C2×D3×D4—61no—
151C2×C3×D8—31no—
152C3×#125—31no—
153C3×C4×D4—21no—
154C3×C4×D4—31no—
155C3×C4×D4C2×D311yescharacteristic
156C3×C4×D4C2×D311yescharacteristic
157#938—31no—
158#938—31no—
159C2×#214—31no—
160C2×#213—31no—
161C2×#213C2×D311yescharacteristic
162#930—61no—
163#930—61no—
164#930—62no—
165#929—61no—
166C4×#67—61no—
167C2×(C2×D3)⋊C4—61no—
168C2×(C2×D3)⋊C4—61no—
169C2×(C2×D3)⋊C4—62no—
170C2×D24—31no—
171C2×#204—31no—
172C2×D3×C8—31no—
173C2×D3×C8—31no—
174C2×D3×C8—31no—
175C2×D3×C8—31no—
176#898—61no—
177#897—31no—
178#897—31no—
179#897—61no—
180#895—31no—
181#895—31no—
182#895—31no—
183#895—31no—
184#895—61no—
185#895—61no—
186#894—61no—
187#893—61no—
188#892—31no—
189#892—31no—
190D3×C4⋊C4—31no—
191D3×C4⋊C4—31no—
192#886—61no—
193#886—61no—
194#886—62no—
195#884—61no—
196#882—61no—
197#882—61no—
198#882—62no—
199#879—61no—
200#875—31no—
201#875—31no—
202#875—61no—
203C4×D12—31no—
204C4×D12—31no—
205C4×D12—61no—
206C4×D12C2×D311yescharacteristic, complemented
207#870C2×D311yescharacteristic, complemented
208C3×#107—31no—
209C3×#107—31no—
210C3×#106—31no—
211C3×C4⋊C8—31no—
212C3×#102—31no—
213C3×#102—31no—
214C3×#102—31no—
215C3×#102—31no—
216C3×C4×C8—31no—
217#832C2×D311yescharacteristic
218#832C2×D311yescharacteristic
219#832C2×D311yescharacteristic
220#821—31no—
221#821—31no—
222#821—31no—
223(C2×D3)⋊C8—31no—
224(C2×D3)⋊C8—31no—
225(C2×D3)⋊C8—31no—
226(C2×D3)⋊C8—31no—
227#816—31no—
228#816—31no—
229#816—31no—
230#810—31no—
231#810—31no—
232#810—31no—
233#809—31no—
234#809—31no—
235#809—31no—
236#809C2×D311yescharacteristic, complemented
237#808C2×D311yescharacteristic, complemented
238#807C2×D311yescharacteristic, complemented
239#807C2×D311yescharacteristic, complemented
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×D4—21no—
251C32×D4#4112yes—
252C2×C32×C4—21no—
253C2×C32×C4—81no—
254C2×C32×C4C2×D411yescharacteristic
255C2×C32×C4C2×D411yescharacteristic
256C2×C32×C4C2411yescharacteristic
257#638—42no—
258#638—42no—
259C2×C3⋊Dic3—21no—
260C2×C3⋊Dic3—42no—
261C2×C3⋊Dic3C2×D411yescharacteristic
262C2×C3⋊Dic3C2×D411yescharacteristic
263C4⋊(C3⋊D3)—22no—
264C4⋊(C3⋊D3)—21no—
265C4⋊(C3⋊D3)—21no—
266C4⋊(C3⋊D3)—81no—
267C4×C3⋊D3—21no—
268C4×C3⋊D3—21no—
269C4×C3⋊D3—21no—
270C4×C3⋊D3—21no—
271#634—21no—
272#634—21no—
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—91no—
289#484—91no—
290#482—91no—
291#478—31no—
292#466—91no—
293#465—91no—
294#463—91no—
295#449—91no—
296#447—91no—
297C4×D8—31no—
298C8×D4—91no—
299#416—91no—
300C2×#102—91no—
301C23×D3—61no—
302C23×D3—61no—
303C23×D3—62no—
304C2×C3×D4—21no—
305C2×C3×D4—31no—
306C2×C3×D4C22×D311yescharacteristic
307C2×C3×D4C22×D311yescharacteristic
308C22×C3×C4—22no—
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—61no—
312C2×#67—61no—
313C2×#67—61no—
314C2×#67—61no—
315C2×#67—61no—
316C2×#67—61no—
317C2×#67—61no—
318C2×#67—62no—
319C2×#67—62no—
320C22×Dic3—61no—
321C22×Dic3—61no—
322C22×Dic3—62no—
323#237—62no—
324#237—62no—
325#237—122no—
326#237—121no—
327#237—121no—
328#237—122no—
329D3×D4—62no—
330D3×D4—62no—
331D3×D4—122no—
332D3×D4—121no—
333D3×D4—121no—
334D3×D4—122no—
335C2×D12—31no—
336C2×D12—31no—
337C2×D12—31no—
338C2×D12—31no—
339C2×D12—61no—
340C2×D12—61no—
341C2×D12—61no—
342C2×D12—61no—
343C2×D12—61no—
344C2×D12—62no—
345C2×D12—61no—
346C2×D12C22×D311yescharacteristic
347C2×C4×D3—21no—
348C2×C4×D3—31no—
349C2×C4×D3—31no—
350C2×C4×D3—31no—
351C2×C4×D3—31no—
352C2×C4×D3—61no—
353C2×C4×D3—61no—
354C2×C4×D3—61no—
355C2×C4×D3—61no—
356C2×Dic6—31no—
357C2×Dic6—31no—
358C2×Dic6—61no—
359C3×D8—62no—
360C2×C3×C8—31no—
361C2×C3×C8—31no—
362C2×C3×C8—31no—
363C2×C3×C8—31no—
364C3×C4⋊C4—21no—
365C3×C4⋊C4—31no—
366C3×C4⋊C4—31no—
367C3×C4⋊C4—31no—
368C3×C4⋊C4—61no—
369C3×C4⋊C4—61no—
370C3×C4⋊C4C22×D311yescharacteristic
371C3×C4⋊C4C22×D311yescharacteristic
372C3×C22⋊C4—22no—
373C3×C22⋊C4—21no—
374C3×C22⋊C4—21no—
375C3×C22⋊C4—61no—
376C3×C42—21no—
377C3×C42C22×D311yescharacteristic
378C3×C42C22×D311yescharacteristic
379#217—61no—
380#217—61no—
381#214—121no—
382#213—22no—
383#213—121no—
384(C2×D3)⋊C4—21no—
385(C2×D3)⋊C4—31no—
386(C2×D3)⋊C4—31no—
387(C2×D3)⋊C4—31no—
388(C2×D3)⋊C4—31no—
389(C2×D3)⋊C4—61no—
390(C2×D3)⋊C4—61no—
391(C2×D3)⋊C4—61no—
392(C2×D3)⋊C4—61no—
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—62no—
400(C2×D3)⋊C4—62no—
401(C2×D3)⋊C4—62no—
402(C2×D3)⋊C4—62no—
403(C2×D3)⋊C4—61no—
404(C2×D3)⋊C4—61no—
405(C2×D3)⋊C4—61no—
406(C2×D3)⋊C4—61no—
407C4⋊Dic3—31no—
408C4⋊Dic3—31no—
409C4⋊Dic3—61no—
410C4⋊Dic3—61no—
411C4⋊Dic3—61no—
412C4⋊Dic3—62no—
413C4⋊Dic3C22×D311yescharacteristic
414C4⋊Dic3C22×D311yescharacteristic
415C4⋊Dic3C22×D311yescharacteristic
416Dic3⋊C4—21no—
417Dic3⋊C4—21no—
418Dic3⋊C4—61no—
419Dic3⋊C4—61no—
420C4×Dic3—61no—
421C4×Dic3—61no—
422C2×C3⋊C8C22×D311yescharacteristic
423C2×C3⋊C8C22×D311yescharacteristic
424C2×C3⋊C8C22×D311yescharacteristic
425C2×C3⋊C8C22×D311yescharacteristic
426D24—121no—
427#204—121no—
428D3×C8—121no—
429D3×C8—121no—
430D3×C8—121no—
431D3×C8—121no—
432C22×C32—22no—
433C22×C32—41no—
434C22×C32—41no—
435C22×C32C22×D411yescharacteristic
436C2×C3⋊D3—21no—
437C2×C3⋊D3—21no—
438C2×C3⋊D3—21no—
439C2×C3⋊D3—21no—
440C2×C3⋊D3—21no—
441C2×C3⋊D3—41no—
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—91no—
463C2×D8—31no—
464C2×D8—91no—
465C22×C8—91no—
466C22×C8—91no—
467#126—181no—
468#125—31no—
469#124—91no—
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—181no—
482C4×D4D3211yescharacteristic
483#117—91no—
484C2×C4⋊C4—91no—
485C2×C22⋊C4—181no—
486#107—31no—
487#107—31no—
488#106—31no—
489C4⋊C8—31no—
490#103—91no—
491#103—91no—
492#103—91no—
493#102—31no—
494#102—31no—
495#102—31no—
496#102—31no—
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×D4—22no—
527C3×D4—21no—
528C3×D4—21no—
529C3×D4—22no—
530C3×D4—61no—
531C3×D4—61no—
532C3×D4#23512yes—
533C3×D4#23912yes—
534C2×C3×C4—22no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—61no—
541C2×C3×C4—61no—
542C2×C3×C4—61no—
543C2×C3×C4—81no—
544C2×C3×C4—81no—
545C2×C3×C4—82no—
546C2×C3×C4—241no—
547C2×C3×C4D3×D411yescharacteristic
548C2×C3×C4D3×D411yescharacteristic
549C2×C3×C4D3×D411yescharacteristic
550C2×C3×C4D3×D411yescharacteristic
551C2×C3×C4C23×D311yescharacteristic
552C2×C3×C4C23×D311yescharacteristic
553#67—122no—
554#67—122no—
555#67—122no—
556#67—122no—
557#67—122no—
558#67—124no—
559#67—124no—
560#67—241no—
561C2×Dic3—21no—
562C2×Dic3—21no—
563C2×Dic3—21no—
564C2×Dic3—31no—
565C2×Dic3—31no—
566C2×Dic3—31no—
567C2×Dic3—31no—
568C2×Dic3—61no—
569C2×Dic3—61no—
570C2×Dic3—62no—
571C2×Dic3—61no—
572C2×Dic3—61no—
573C2×Dic3—122no—
574C2×Dic3—122no—
575C2×Dic3—124no—
576D12—21no—
577D12—21no—
578D12—62no—
579D12—62no—
580D12—61no—
581D12—61no—
582D12—61no—
583D12—61no—
584D12—121no—
585D12—121no—
586D12—122no—
587D12—122no—
588D12—241no—
589D12—241no—
590D12—242no—
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—241no—
606C4×D3—241no—
607Dic6—61no—
608Dic6—61no—
609Dic6—61no—
610Dic6—61no—
611Dic6—121no—
612Dic6—121no—
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—42no—
622C2×C32#54611yescharacteristic
623C2×C32C2×#13511yescharacteristic
624C2×C32#57611yescharacteristic
625C3⋊D3—22no—
626C3⋊D3—41no—
627C3⋊D3—81no—
628C3×D3—81no—
629C24—181no—
630#41—182no—
631#41—361no—
632C2×Q8—91no—
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—21no—
645C22×C4—61no—
646C22×C4—91no—
647C22×C4—91no—
648C22×C4—181no—
649C22×C4—181no—
650SD16—361no—
651D8—62no—
652D8—361no—
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—181no—
666C4⋊C4—181no—
667C4⋊C4C2×D3211yescharacteristic
668C22⋊C4—21no—
669C22⋊C4—61no—
670C22⋊C4—91no—
671C22⋊C4—91no—
672C22⋊C4—181no—
673C22⋊C4—181no—
674C22⋊C4—181no—
675C22⋊C4—181no—
676C22⋊C4—181no—
677C22⋊C4—181no—
678C22⋊C4—181no—
679C42—181no—
680C42C2×D3211yescharacteristic
681C22×C3—24no—
682C22×C3—22no—
683C22×C3—22no—
684C22×C3—21no—
685C22×C3—42no—
686C22×C3—42no—
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—61no—
707C2×D3—61no—
708C2×D3—61no—
709C2×D3—61no—
710C2×D3—61no—
711C2×D3—61no—
712C2×D3—121no—
713C2×D3—121no—
714C2×D3—121no—
715C2×D3—121no—
716C2×D3—121no—
717C2×D3—122no—
718C2×D3—122no—
719C2×D3—122no—
720C2×D3—121no—
721C2×D3—121no—
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×C4C2×#23511yescharacteristic
744C3×C4C2×#23911yescharacteristic
745C3×C4#100911yescharacteristic
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—181no—
769Q8—181no—
770D4—21no—
771D4—61no—
772D4—61no—
773D4—182no—
774D4—181no—
775D4—181no—
776D4—362no—
777D4—362no—
778D4—362no—
779D4—721no—
780D4—721no—
781D4#379912yes—
782C2×C4—21no—
783C2×C4—61no—
784C2×C4—61no—
785C2×C4—61no—
786C2×C4—81no—
787C2×C4—91no—
788C2×C4—91no—
789C2×C4—181no—
790C2×C4—181no—
791C2×C4—181no—
792C2×C4—181no—
793C2×C4—181no—
794C2×C4—241no—
795C2×C4—362no—
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—44no—
808C2×C3—42no—
809C2×C3—42no—
810C2×C3—241no—
811C2×C3#555011yescharacteristic
812C2×C3#563011yescharacteristic
813C2×C3#575711yescharacteristic
814C2×C3D3×#13511yescharacteristic
815C2×C3D3×#13511yescharacteristic
816C2×C3#577411yescharacteristic
817D3—62no—
818D3—62no—
819D3—81no—
820D3—122no—
821D3—121no—
822D3—121no—
823D3—241no—
824D3—242no—
825D3—241no—
826D3—241no—
827C22—22no—
828C22—41no—
829C22—41no—
830C22—92no—
831C22—121no—
832C22—121no—
833C22—121no—
834C22—181no—
835C22—181no—
836C22—181no—
837C22—181no—
838C22—181no—
839C22—361no—
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—
853C4C2×#379911yescharacteristic
854C4#6430811yescharacteristic
855C3—21no—
856C3#7960911yescharacteristic, complemented
857C3#8118711yescharacteristic, complemented
858C2—42no—
859C2—182no—
860C2—241no—
861C2—361no—
862C2—721no—
863C2#1059501811yescharacteristic
864C2#1059510211yescharacteristic
865C2#1059545911yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
hypercenterC4×D4D32
hypocenterC32#3297
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #10596025C2semidirect
2. #10593982C2semidirect
3. C3×C4×#213C2semidirect
4. C3×#5009C2semidirect
5. #10591457C2semidirect
6. #10591456C2semidirect
7. #10591424C2semidirect
8. #10591416C2semidirect
9. #10590509C2semidirect
10. #10590507C2semidirect
11. #10590451C2semidirect
12. #10590444C2semidirect
13. #10590366C2semidirect
14. #10590327C2semidirect
15. #10590293C2semidirect
30. C3×C4×D12C22semidirect
31. C3×#870C22semidirect
33. #63916C22semidirect
39. #63849C22semidirect
40. C2×#3716C22semidirect
43. C2×#3710C22semidirect
47. C3×#809C22semidirect
48. C3×#808C22semidirect
49. C3×#807C22semidirect
50. C3×#807C22semidirect
51. C3×C4⋊(C3⋊C8)C22semidirect
52. C3×C4×C3⋊C8C22semidirect
53. #63567C22semidirect
54. #63567C22semidirect
55. #63567C22semidirect
60. #63557C22semidirect
72. C4×#213D3semidirect
73. #5009D3semidirect
206. C4×D12C2×D3semidirect
207. #870C2×D3semidirect
236. #809C2×D3semidirect
237. #808C2×D3semidirect
238. #807C2×D3semidirect
239. #807C2×D3semidirect
240. C4⋊(C3⋊C8)C2×D3semidirect
241. C4×C3⋊C8C2×D3semidirect
759. C32#3297semidirect
856. C3#79609semidirect
857. C3#81187semidirect

Maximal subgroups

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

subgroupindex
#105960252
#105939822
C3×C4×#2132
C3×#50092
#105914572
#105914562
#105914242
#105914162
#105905092
#105905072
#105904512
#105904442
#105903662
#105903272
#105902932
#811873
#796093