Finite Group Databasebeta

← #11887246

Subgroups — #11887246

Order 1152.

983 conjugacy classes of subgroups.

The subgroup lattice has 843 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596025C211yesmaximal, characteristic
2#10593947C211yesmaximal, characteristic, complemented
3C3×C4×#214C211yesmaximal, characteristic, complemented
4C3×#5009C211yesmaximal, characteristic, complemented
5#10591467C211yesmaximal, characteristic, complemented
6#10591466C211yesmaximal, characteristic, complemented
7#10591424C211yesmaximal, characteristic, complemented
8#10591416C211yesmaximal, characteristic, complemented
9#10590525C211yesmaximal, characteristic, complemented
10#10590523C211yesmaximal, characteristic, complemented
11#10590451C211yesmaximal, characteristic, complemented
12#10590443C211yesmaximal, characteristic, complemented
13#10590368C211yesmaximal, characteristic, complemented
14#10590327C211yesmaximal, characteristic, complemented
15#10590293C211yesmaximal, characteristic, complemented
16#81186—31nomaximal
17#79677—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×#214C2211yescharacteristic
30C3×#870C2211yescharacteristic, complemented
31C3×C4×Dic6C2211yescharacteristic, complemented
32#63900C2211yescharacteristic
33#63897—21no—
34#63871C2211yescharacteristic
35#63871C2211yescharacteristic, complemented
36#63868—21no—
37#63849C2211yescharacteristic, complemented
38#63845—21no—
39#63836—21no—
40C2×#3719C2211yescharacteristic, complemented
41C2×#3717C2211yescharacteristic
42C2×#3710C2211yescharacteristic
43C2×#3710C2211yescharacteristic, complemented
44C3×#832C2211yescharacteristic
45C3×#832C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#810C2211yescharacteristic, complemented
48C3×#808C2211yescharacteristic, complemented
49C3×#808C2211yescharacteristic, 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#5694—31no—
62#5581—31no—
63#5554—31no—
64#5554—31no—
65#5554—61no—
66C3×#478—31no—
67C3×C4×SD16—31no—
68#5173—31no—
69#5169—31no—
70#5068—31no—
71#5028—31no—
72C4×#214D311yescharacteristic, complemented
73#5009D311yescharacteristic, complemented
74#4887—31no—
75#4885—31no—
76#4866—31no—
77#4864—31no—
78#4862—31no—
79#4862—31no—
80#4845—31no—
81#4834—31no—
82#4813—31no—
83#4807—31no—
84#4783—31no—
85#4776—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×Dic6C2311yescharacteristic
109C2×#624—21no—
110C32×C4⋊C4C2311yescharacteristic
111C32×C22⋊C4—21no—
112C32×C42C2311yescharacteristic
113#3752—21no—
114#3752—21no—
115#3752—21no—
116#3752—21no—
117#3752D411yescharacteristic
118#3752D411yescharacteristic
119C4⋊(C3⋊Dic3)—21no—
120C4⋊(C3⋊Dic3)D411yescharacteristic
121C3×#214—22no—
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×C4×Dic3—21no—
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133#3724—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136#3722—21no—
137#3722—21no—
138#3722—21no—
139Dic32—21no—
140#3719—41no—
141#3717—41no—
142#3710—41no—
143#3710—41no—
144#3296—91noSylow
145C2×#237—31no—
146C2×#237—31no—
147C2×#237—61no—
148C2×D3×D4—31no—
149C2×D3×D4—31no—
150C2×D3×D4—61no—
151C2×C3×SD16—31no—
152C3×#125—31no—
153C3×C4×Q8—31no—
154C3×C4×D4—21no—
155C3×C4×D4C2×D311yescharacteristic
156C3×C4×D4C2×D311yescharacteristic
157#946—31no—
158#946—31no—
159C2×#216—31no—
160C2×#215—31no—
161C2×#214C2×D311yescharacteristic
162#930—61no—
163#930—61no—
164#930—62no—
165C2×(C2×D3)⋊C4—61no—
166C2×(C2×D3)⋊C4—61no—
167C2×(C2×D3)⋊C4—62no—
168C2×Dic12—31no—
169C2×#204—31no—
170C2×D3×C8—31no—
171C2×D3×C8—31no—
172C2×D3×C8—31no—
173C2×D3×C8—31no—
174#898—61no—
175#897—31no—
176#897—31no—
177#897—31no—
178#897—31no—
179#897—61no—
180#895—31no—
181#895—31no—
182#895—61no—
183#894—61no—
184#894—61no—
185#892—31no—
186#892—31no—
187#892—61no—
188D3×C4⋊C4—31no—
189D3×C4⋊C4—31no—
190#890—61no—
191#889—61no—
192#886—61no—
193#886—61no—
194#886—62no—
195#882—61no—
196#882—61no—
197#882—62no—
198#876—61no—
199#875—31no—
200#875—31no—
201#875—61no—
202C4×D12—31no—
203C4×D12—31no—
204C4×D12—61no—
205#872—61no—
206#870C2×D311yescharacteristic, complemented
207C4×Dic6C2×D311yescharacteristic, complemented
208C3×#107—31no—
209C3×#106—31no—
210C3×#106—31no—
211C3×C4⋊C8—31no—
212C3×#103—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#810C2×D311yescharacteristic, complemented
234#809—31no—
235#809—31no—
236#809—31no—
237#808C2×D311yescharacteristic, complemented
238#808C2×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
249C32×D4—21no—
250C32×D4#4112yes—
251C2×C32×C4—21no—
252C2×C32×C4—81no—
253C2×C32×C4C2×D411yescharacteristic
254C2×C32×C4C2×D411yescharacteristic
255C2×C32×C4C2411yescharacteristic
256#638—42no—
257#638—42no—
258C2×C3⋊Dic3—21no—
259C2×C3⋊Dic3—42no—
260C2×C3⋊Dic3C2×D411yescharacteristic
261C2×C3⋊Dic3C2×D411yescharacteristic
262C4⋊(C3⋊D3)—22no—
263C4⋊(C3⋊D3)—21no—
264C4⋊(C3⋊D3)—21no—
265C4⋊(C3⋊D3)—81no—
266C4×C3⋊D3—21no—
267C4×C3⋊D3—21no—
268C4×C3⋊D3—21no—
269C4×C3⋊D3—21no—
270#634—21no—
271#634—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C3×Dic6—21no—
277C3×Dic6—21no—
278#624—42no—
279C3×C3⋊C8—21no—
280C3×C3⋊C8—21no—
281C3×C3⋊C8—21no—
282C3×C3⋊C8—21no—
283#552—91no—
284#546—91no—
285#488—91no—
286#483—91no—
287#482—91no—
288#478—31no—
289#467—91no—
290#465—91no—
291#464—91no—
292#452—91no—
293#450—91no—
294C4×SD16—31no—
295C8×D4—91no—
296#416—91no—
297C2×#102—91no—
298C23×D3—61no—
299C23×D3—61no—
300C23×D3—62no—
301C2×C3×Q8—31no—
302C2×C3×D4—21no—
303C2×C3×D4C22×D311yescharacteristic
304C2×C3×D4C22×D311yescharacteristic
305C22×C3×C4—22no—
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C2×#67—61no—
309C2×#67—61no—
310C2×#67—61no—
311C2×#67—61no—
312C2×#67—62no—
313C2×#67—62no—
314C22×Dic3—61no—
315C22×Dic3—61no—
316C22×Dic3—62no—
317#237—62no—
318#237—62no—
319#237—122no—
320#237—121no—
321#237—121no—
322#237—122no—
323D3×D4—62no—
324D3×D4—62no—
325D3×D4—122no—
326D3×D4—121no—
327D3×D4—121no—
328D3×D4—122no—
329C2×D12—31no—
330C2×D12—31no—
331C2×D12—31no—
332C2×D12—31no—
333C2×D12—61no—
334C2×D12—61no—
335C2×D12—61no—
336C2×D12—61no—
337C2×D12—62no—
338C2×C4×D3—31no—
339C2×C4×D3—31no—
340C2×C4×D3—31no—
341C2×C4×D3—31no—
342C2×C4×D3—61no—
343C2×C4×D3—61no—
344C2×C4×D3—61no—
345C2×C4×D3—61no—
346C2×Dic6—31no—
347C2×Dic6—31no—
348C2×Dic6—61no—
349C2×Dic6C22×D311yescharacteristic
350C3×SD16—62no—
351C2×C3×C8—31no—
352C2×C3×C8—31no—
353C2×C3×C8—31no—
354C2×C3×C8—31no—
355C3×C4⋊C4—21no—
356C3×C4⋊C4—31no—
357C3×C4⋊C4—31no—
358C3×C4⋊C4—31no—
359C3×C4⋊C4—61no—
360C3×C4⋊C4—61no—
361C3×C4⋊C4—61no—
362C3×C4⋊C4C22×D311yescharacteristic
363C3×C4⋊C4C22×D311yescharacteristic
364C3×C22⋊C4—22no—
365C3×C22⋊C4—21no—
366C3×C22⋊C4—21no—
367C3×C42—21no—
368C3×C42—61no—
369C3×C42C22×D311yescharacteristic
370C3×C42C22×D311yescharacteristic
371#216—121no—
372#215—121no—
373#214—22no—
374(C2×D3)⋊C4—31no—
375(C2×D3)⋊C4—31no—
376(C2×D3)⋊C4—31no—
377(C2×D3)⋊C4—31no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—61no—
387(C2×D3)⋊C4—61no—
388(C2×D3)⋊C4—61no—
389(C2×D3)⋊C4—61no—
390(C2×D3)⋊C4—62no—
391(C2×D3)⋊C4—62no—
392(C2×D3)⋊C4—62no—
393(C2×D3)⋊C4—62no—
394(C2×D3)⋊C4—61no—
395(C2×D3)⋊C4—61no—
396(C2×D3)⋊C4—61no—
397(C2×D3)⋊C4—61no—
398C4⋊Dic3—31no—
399C4⋊Dic3—31no—
400C4⋊Dic3—61no—
401C4⋊Dic3—61no—
402C4⋊Dic3—61no—
403C4⋊Dic3—61no—
404C4⋊Dic3—61no—
405C4⋊Dic3—62no—
406C4⋊Dic3C22×D311yescharacteristic
407C4⋊Dic3C22×D311yescharacteristic
408C4⋊Dic3C22×D311yescharacteristic
409Dic3⋊C4—21no—
410Dic3⋊C4—21no—
411Dic3⋊C4—21no—
412Dic3⋊C4—61no—
413Dic3⋊C4—61no—
414Dic3⋊C4—61no—
415Dic3⋊C4—61no—
416C4×Dic3—21no—
417C4×Dic3—61no—
418C4×Dic3—61no—
419C2×C3⋊C8C22×D311yescharacteristic
420C2×C3⋊C8C22×D311yescharacteristic
421C2×C3⋊C8C22×D311yescharacteristic
422C2×C3⋊C8C22×D311yescharacteristic
423Dic12—121no—
424#204—121no—
425D3×C8—121no—
426D3×C8—121no—
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—21no—
436C2×C3⋊D3—21no—
437C2×C3⋊D3—21no—
438C2×C3⋊D3—41no—
439C2×C3⋊D3—41no—
440C2×C3⋊D3—41no—
441C2×C3⋊D3—84no—
442C2×C3⋊D3#13512yes—
443C32×C4—21no—
444C32×C4—21no—
445C32×C4—41no—
446C32×C4C2×#4111yescharacteristic
447C32×C4H(5,𝔽2)11yescharacteristic
448C3⋊Dic3—21no—
449C3⋊Dic3—21no—
450C3⋊Dic3—41no—
451C3×Dic3—41no—
452C3×Dic3—41no—
453C3×Dic3—41no—
454C3×Dic3—41no—
455C2×#41—91no—
456C22×D4—91no—
457C2×Q16—91no—
458C2×SD16—31no—
459C2×SD16—91no—
460C22×C8—91no—
461C22×C8—91no—
462#126—181no—
463#125—31no—
464#125—181no—
465#124—91no—
466#123—181no—
467#123—181no—
468C22⋊Q8—91no—
469C22⋊Q8—91no—
470C22⋊Q8—91no—
471#121—91no—
472#121—181no—
473#120—181no—
474C4×Q8—31no—
475C4×D4—91no—
476C4×D4D3211yescharacteristic
477#117—91no—
478#117—181no—
479C2×C4⋊C4—91no—
480C2×C22⋊C4—181no—
481#107—31no—
482#106—31no—
483#106—31no—
484C4⋊C8—31no—
485#103—31no—
486#103—91no—
487#103—91no—
488#103—91no—
489#102—31no—
490#102—31no—
491#102—31no—
492#102—91no—
493#102—91no—
494#102—91no—
495C22⋊C8—91no—
496C22⋊C8—91no—
497C4×C8—31no—
498C23×C3—22no—
499C23×C3—21no—
500C23×C3—21no—
501C22×D3—31no—
502C22×D3—31no—
503C22×D3—31no—
504C22×D3—31no—
505C22×D3—61no—
506C22×D3—61no—
507C22×D3—62no—
508C22×D3—61no—
509C22×D3—61no—
510C22×D3—122no—
511C22×D3—122no—
512C22×D3—122no—
513C22×D3—122no—
514C22×D3—124no—
515C22×D3—124no—
516C22×D3—241no—
517C22×D3—241no—
518C22×D3—242no—
519C3×Q8—61no—
520C3×Q8—61no—
521C3×D4—22no—
522C3×D4—21no—
523C3×D4—21no—
524C3×D4—22no—
525C3×D4#23512yes—
526C3×D4#23912yes—
527C2×C3×C4—22no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—81no—
538C2×C3×C4—81no—
539C2×C3×C4—82no—
540C2×C3×C4D3×D411yescharacteristic
541C2×C3×C4D3×D411yescharacteristic
542C2×C3×C4D3×D411yescharacteristic
543C2×C3×C4D3×D411yescharacteristic
544C2×C3×C4C23×D311yescharacteristic
545C2×C3×C4C23×D311yescharacteristic
546#67—122no—
547#67—122no—
548#67—122no—
549#67—122no—
550#67—124no—
551#67—124no—
552C2×Dic3—21no—
553C2×Dic3—21no—
554C2×Dic3—21no—
555C2×Dic3—21no—
556C2×Dic3—31no—
557C2×Dic3—31no—
558C2×Dic3—31no—
559C2×Dic3—31no—
560C2×Dic3—61no—
561C2×Dic3—61no—
562C2×Dic3—62no—
563C2×Dic3—61no—
564C2×Dic3—61no—
565C2×Dic3—122no—
566C2×Dic3—122no—
567C2×Dic3—124no—
568D12—62no—
569D12—62no—
570D12—61no—
571D12—61no—
572D12—61no—
573D12—61no—
574D12—121no—
575D12—121no—
576D12—122no—
577D12—241no—
578D12—241no—
579D12—242no—
580C4×D3—61no—
581C4×D3—61no—
582C4×D3—61no—
583C4×D3—61no—
584C4×D3—61no—
585C4×D3—61no—
586C4×D3—61no—
587C4×D3—61no—
588C4×D3—121no—
589C4×D3—121no—
590C4×D3—121no—
591C4×D3—121no—
592C4×D3—122no—
593C4×D3—122no—
594Dic6—21no—
595Dic6—21no—
596Dic6—61no—
597Dic6—61no—
598Dic6—61no—
599Dic6—61no—
600Dic6—121no—
601Dic6—121no—
602C3×C8—61no—
603C3×C8—61no—
604C3×C8—61no—
605C3×C8—61no—
606C3⋊C8—21no—
607C3⋊C8—21no—
608C3⋊C8—21no—
609C3⋊C8—21no—
610C2×C32—42no—
611C2×C32#54611yescharacteristic
612C2×C32C2×#13511yescharacteristic
613C2×C32#57711yescharacteristic
614C3⋊D3—22no—
615C3⋊D3—41no—
616C3⋊D3—81no—
617C24—181no—
618#41—182no—
619#41—361no—
620C2×Q8—31no—
621C2×Q8—91no—
622C2×D4—91no—
623C2×D4—91no—
624C2×D4—181no—
625C2×D4—181no—
626C2×D4—182no—
627C2×D4—181no—
628C2×D4—361no—
629C2×D4C2×D3211yescharacteristic
630C22×C4—21no—
631C22×C4—91no—
632C22×C4—91no—
633C22×C4—181no—
634C22×C4—181no—
635Q16—361no—
636SD16—62no—
637SD16—361no—
638C2×C8—31no—
639C2×C8—31no—
640C2×C8—31no—
641C2×C8—31no—
642C2×C8—361no—
643C2×C8—361no—
644C4⋊C4—31no—
645C4⋊C4—31no—
646C4⋊C4—31no—
647C4⋊C4—61no—
648C4⋊C4—61no—
649C4⋊C4—61no—
650C4⋊C4—91no—
651C4⋊C4—181no—
652C4⋊C4—181no—
653C4⋊C4—181no—
654C4⋊C4—181no—
655C4⋊C4C2×D3211yescharacteristic
656C22⋊C4—21no—
657C22⋊C4—91no—
658C22⋊C4—91no—
659C22⋊C4—181no—
660C22⋊C4—181no—
661C22⋊C4—181no—
662C22⋊C4—181no—
663C22⋊C4—181no—
664C22⋊C4—181no—
665C22⋊C4—181no—
666C42—61no—
667C42—181no—
668C42C2×D3211yescharacteristic
669C22×C3—24no—
670C22×C3—22no—
671C22×C3—22no—
672C22×C3—21no—
673C22×C3—42no—
674C22×C3—42no—
675C22×C3—41no—
676C22×C3—41no—
677C22×C3—41no—
678C22×C3—41no—
679C22×C3C2×D3×D411yescharacteristic
680C22×C3C2×D3×D411yescharacteristic
681C2×D3—32no—
682C2×D3—32no—
683C2×D3—62no—
684C2×D3—61no—
685C2×D3—61no—
686C2×D3—61no—
687C2×D3—61no—
688C2×D3—61no—
689C2×D3—61no—
690C2×D3—61no—
691C2×D3—61no—
692C2×D3—61no—
693C2×D3—61no—
694C2×D3—121no—
695C2×D3—121no—
696C2×D3—121no—
697C2×D3—121no—
698C2×D3—121no—
699C2×D3—122no—
700C2×D3—122no—
701C2×D3—122no—
702C2×D3—121no—
703C2×D3—121no—
704C2×D3—121no—
705C2×D3—121no—
706C2×D3—121no—
707C2×D3—121no—
708C2×D3—244no—
709C2×D3—244no—
710C2×D3—248no—
711C3×C4—21no—
712C3×C4—21no—
713C3×C4—21no—
714C3×C4—21no—
715C3×C4—21no—
716C3×C4—21no—
717C3×C4—41no—
718C3×C4—41no—
719C3×C4—42no—
720C3×C4—41no—
721C3×C4—41no—
722C3×C4—121no—
723C3×C4—121no—
724C3×C4—121no—
725C3×C4—121no—
726C3×C4C2×#23511yescharacteristic
727C3×C4C2×#23911yescharacteristic
728C3×C4#100911yescharacteristic
729C3×C4#100911yescharacteristic
730Dic3—41no—
731Dic3—41no—
732Dic3—41no—
733Dic3—41no—
734Dic3—61no—
735Dic3—61no—
736Dic3—61no—
737Dic3—61no—
738Dic3—121no—
739Dic3—121no—
740Dic3—122no—
741Dic3—121no—
742Dic3—121no—
743C32#329611yescharacteristic, complemented, Sylow
744C23—21no—
745C23—91no—
746C23—91no—
747C23—181no—
748C23—362no—
749C23—362no—
750C23—721no—
751Q8—61no—
752Q8—61no—
753Q8—181no—
754Q8—181no—
755D4—21no—
756D4—182no—
757D4—181no—
758D4—181no—
759D4—362no—
760D4—362no—
761D4—721no—
762D4#379912yes—
763C2×C4—21no—
764C2×C4—61no—
765C2×C4—61no—
766C2×C4—61no—
767C2×C4—61no—
768C2×C4—81no—
769C2×C4—91no—
770C2×C4—91no—
771C2×C4—181no—
772C2×C4—181no—
773C2×C4—181no—
774C2×C4—181no—
775C2×C4—181no—
776C2×C4—362no—
777C2×C4—362no—
778C2×C4#381111yescharacteristic
779C2×C4#381111yescharacteristic
780C2×C4C22×D3211yescharacteristic
781C8—61no—
782C8—61no—
783C8—61no—
784C8—61no—
785C2×C3—21no—
786C2×C3—21no—
787C2×C3—21no—
788C2×C3—44no—
789C2×C3—42no—
790C2×C3—42no—
791C2×C3#555011yescharacteristic
792C2×C3#563011yescharacteristic
793C2×C3#576211yescharacteristic
794C2×C3D3×#13511yescharacteristic
795C2×C3D3×#13511yescharacteristic
796C2×C3#577511yescharacteristic
797D3—62no—
798D3—62no—
799D3—122no—
800D3—121no—
801D3—121no—
802D3—241no—
803D3—242no—
804D3—241no—
805D3—241no—
806C22—22no—
807C22—41no—
808C22—41no—
809C22—92no—
810C22—181no—
811C22—181no—
812C22—181no—
813C22—181no—
814C22—181no—
815C22—361no—
816C22—361no—
817C22—361no—
818C22—724no—
819C22C2×#381111yescharacteristic
820C4—21no—
821C4—21no—
822C4—41no—
823C4—121no—
824C4—121no—
825C4—121no—
826C4—121no—
827C4—181no—
828C4—181no—
829C4—361no—
830C4C2×#379911yescharacteristic
831C4#6430811yescharacteristic
832C3—21no—
833C3#7967711yescharacteristic, complemented
834C3#8118611yescharacteristic, complemented
835C2—42no—
836C2—182no—
837C2—361no—
838C2—721no—
839C2#1059501811yescharacteristic
840C2#1059511511yescharacteristic
841C2#1059545911yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radical#10596025C2
hypercenterC4×D4D32
hypocenterC32#3296
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
2. #10593947C2semidirect
3. C3×C4×#214C2semidirect
4. C3×#5009C2semidirect
5. #10591467C2semidirect
6. #10591466C2semidirect
7. #10591424C2semidirect
8. #10591416C2semidirect
9. #10590525C2semidirect
10. #10590523C2semidirect
11. #10590451C2semidirect
12. #10590443C2semidirect
13. #10590368C2semidirect
14. #10590327C2semidirect
15. #10590293C2semidirect
30. C3×#870C22semidirect
31. C3×C4×Dic6C22semidirect
35. #63871C22semidirect
37. #63849C22semidirect
40. C2×#3719C22semidirect
43. C2×#3710C22semidirect
47. C3×#810C22semidirect
48. C3×#808C22semidirect
49. C3×#808C22semidirect
50. C3×#807C22semidirect
51. C3×C4⋊(C3⋊C8)C22semidirect
52. C3×C4×C3⋊C8C22semidirect
53. #63567C22semidirect
54. #63567C22semidirect
55. #63567C22semidirect
60. #63557C22semidirect
72. C4×#214D3semidirect
73. #5009D3semidirect
206. #870C2×D3semidirect
207. C4×Dic6C2×D3semidirect
233. #810C2×D3semidirect
237. #808C2×D3semidirect
238. #808C2×D3semidirect
239. #807C2×D3semidirect
240. C4⋊(C3⋊C8)C2×D3semidirect
241. C4×C3⋊C8C2×D3semidirect
743. C32#3296semidirect
833. C3#79677semidirect
834. C3#81186semidirect

Maximal subgroups

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

subgroupindex
#105960252
#105939472
C3×C4×#2142
C3×#50092
#105914672
#105914662
#105914242
#105914162
#105905252
#105905232
#105904512
#105904432
#105903682
#105903272
#105902932
#811863
#796773