Finite Group Databasebeta

← #11860688

Subgroups — #11860688

Order 1152.

1225 conjugacy classes of subgroups.

The subgroup lattice has 873 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596016C211yesmaximal, characteristic, complemented
2C2×#63926C211yesmaximal, characteristic
3#10593996C211yesmaximal, characteristic, complemented
4C3×#5014C211yesmaximal, characteristic, complemented
5C3×C4×#213C211yesmaximal, characteristic, complemented
6#10591436C211yesmaximal, characteristic, complemented
7#10591435C211yesmaximal, characteristic, complemented
8#10591426C211yesmaximal, characteristic, complemented
9#10590594C211yesmaximal, characteristic, complemented
10#10590574C211yesmaximal, characteristic, complemented
11#10590462C211yesmaximal, characteristic, complemented
12#10590459C211yesmaximal, characteristic, complemented
13#10590346C211yesmaximal, characteristic, complemented
14C4×#3714C211yesmaximal, characteristic, complemented
15#10590321C211yesmaximal, characteristic, complemented
16#79867—31nomaximal
17#79588—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×#3802C2211yescharacteristic
20C32×C4×D4C2211yescharacteristic, complemented
21D4×C3⋊Dic3C2211yescharacteristic, complemented
22C4×#638—21no—
23C2×#3752—21no—
24#64102C2211yescharacteristic, complemented
25#64101C2211yescharacteristic
26#64090—21no—
27C22⋊C4×C3⋊D3—21no—
28C4×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
29#64081C2211yescharacteristic
30C2×C3×#213C2211yescharacteristic
31C2×C3×#213C2211yescharacteristic
32C3×C4×D12C2211yescharacteristic, complemented
33C3×C4×D12C2211yescharacteristic, complemented
34#63926C418yescomplemented
35D3×(C2×D3)⋊C4—21no—
36D3×(C2×D3)⋊C4—21no—
37#63898C2211yescharacteristic, complemented
38#63898C2211yescharacteristic, complemented
39#63879—21no—
40#63879—21no—
41#63849C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43C2×#3714C2211yescharacteristic
44C2×#3712C2211yescharacteristic
45C2×#3710C2211yescharacteristic
46C3×#832C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic, complemented
48C3×#809C2211yescharacteristic, complemented
49C3×#809C2211yescharacteristic, complemented
50C3×#808C2211yescharacteristic, complemented
51C3×#807C2211yescharacteristic, complemented
52C3×#803C2211yescharacteristic, complemented
53C3×C4×C3⋊C8C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56#63564C2211yescharacteristic, complemented
57#63564C2211yescharacteristic, complemented
58#63563C2211yescharacteristic, complemented
59#63563C2211yescharacteristic, complemented
60#63555C2211yescharacteristic, complemented
61#63553C2211yescharacteristic, complemented
62C2×D3×D8—31no—
63C2×D3×D8—31no—
64#5545—31no—
65#5545—31no—
66#5545—31no—
67#5545—31no—
68#5545—61no—
69C3×#442—31no—
70C3×C4×D8—31no—
71#5152—31no—
72Dic3×D8—31no—
73#5014—31no—
74#5014D311yescharacteristic, complemented
75C4×#213—31no—
76C4×#213D311yescharacteristic, complemented
77#4880—31no—
78#4872—31no—
79#4869—31no—
80#4860—31no—
81#4785—31no—
82#4785—31no—
83#4770—31no—
84#4770—31no—
85#4770—31no—
86#4770—31no—
87#4756—31no—
88#4756—31no—
89#4711—31no—
90#4708—31no—
91C4×D24—31no—
92#4689—31no—
93C23×C3⋊D3—21no—
94C22×D32—21no—
95C2×C32×D4C2311yescharacteristic
96C22×C32×C4—21no—
97C2×#638—21no—
98C22×C3⋊Dic3—21no—
99D4×C3⋊D3—22no—
100D4×C3⋊D3C2×C414yescomplemented
101C2×C4⋊(C3⋊D3)C2311yescharacteristic
102C2×C4×C3⋊D3—21no—
103C2×C4×C3⋊D3—21no—
104C2×C4×C3⋊D3C2311yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×C3×D12C2311yescharacteristic
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3—21no—
109C2×#625—21no—
110C2×D3×Dic3—21no—
111C2×D3×Dic3—21no—
112#3802—22no—
113#3802C2×C414yescomplemented
114C32×C4⋊C4C2311yescharacteristic
115C32×C22⋊C4—21no—
116C32×C42C2311yescharacteristic
117#3757—21no—
118#3752—21no—
119#3752—21no—
120#3752—21no—
121#3752D411yescharacteristic
122#3752D411yescharacteristic
123C4⋊(C3⋊Dic3)C2311yescharacteristic
124#3750D411yescharacteristic
125#3750D411yescharacteristic
126C4×C3⋊Dic3—21no—
127C4×C3⋊Dic3C2311yescharacteristic
128C3×#213C2×C414yescomplemented
129C3×#213C2×C414yescomplemented
130C3×(C2×D3)⋊C4—21no—
131C3×(C2×D3)⋊C4—21no—
132C3×C4⋊Dic3C2311yescharacteristic
133C3×C4⋊Dic3C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138#3722—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141Dic32—21no—
142#3714C2×C414yescomplemented
143#3714C2×C414yescomplemented
144#3712—22no—
145#3710C2×C414yescomplemented
146#2948—91noSylow
147C2×D3×D4—31no—
148C2×D3×D4—31no—
149C2×D3×D4—31no—
150C2×D3×D4—31no—
151C2×D3×D4—61no—
152C2×C3×D8—31no—
153C2×C3×D8—31no—
154C3×C4×D4—21no—
155C3×C4×D4—31no—
156C3×C4×D4—31no—
157C3×C4×D4C2×D311yescharacteristic, complemented
158C3×C4×D4C2×D311yescharacteristic, complemented
159D4×Dic3—31no—
160D4×Dic3—31no—
161D4×Dic3—31no—
162D4×Dic3—31no—
163D4×Dic3—61no—
164C2×#213—31no—
165C2×#213—31no—
166C2×#213C2×D311yescharacteristic
167C2×#213C2×D311yescharacteristic
168C4×#67—61no—
169C4×#67—61no—
170C4×#67—61no—
171C4×#67—61no—
172C4×#67—62no—
173C2×(C2×D3)⋊C4—61no—
174C2×(C2×D3)⋊C4—61no—
175C2×(C2×D3)⋊C4—61no—
176C2×(C2×D3)⋊C4—61no—
177C2×(C2×D3)⋊C4—62no—
178D3×D8—38no—
179D3×D8—38no—
180C2×D24—31no—
181C2×D24—31no—
182C2×ΓL(1,𝔽25)—31no—
183C2×ΓL(1,𝔽25)—31no—
184C2×D3×C8—31no—
185C2×D3×C8—31no—
186#893—31no—
187#893—31no—
188#893—31no—
189#893—31no—
190#893—61no—
191#892—31no—
192#892—31no—
193#892—31no—
194#892—31no—
195#892—61no—
196#67⋊C4—61no—
197#67⋊C4—61no—
198#67⋊C4—61no—
199#67⋊C4—61no—
200#67⋊C4—62no—
201D3×C22⋊C4—61no—
202D3×C22⋊C4—61no—
203D3×C22⋊C4—61no—
204D3×C22⋊C4—61no—
205D3×C22⋊C4—62no—
206C4×D12—31no—
207C4×D12—31no—
208C4×D12—61no—
209C4×D12C2×D311yescharacteristic, complemented
210C4×D12C2×D311yescharacteristic, complemented
211#872—31no—
212#872—31no—
213#872—61no—
214C3×#107—31no—
215C3×#106—31no—
216C3×#102—31no—
217C3×#102—31no—
218C3×#102—31no—
219C3×#102—31no—
220C3×#97—31no—
221C3×C4×C8—31no—
222#832—31no—
223#832—31no—
224#832C2×D311yescharacteristic, complemented
225#832C2×D311yescharacteristic, complemented
226#821—31no—
227#821—31no—
228#821—31no—
229#821—31no—
230#818—31no—
231#817—31no—
232#815—31no—
233#815—31no—
234C8×Dic3—31no—
235C8×Dic3—31no—
236#809—31no—
237#809—31no—
238#809C2×D311yescharacteristic, complemented
239#809C2×D311yescharacteristic, complemented
240#808—31no—
241#808C2×D311yescharacteristic, complemented
242#807—31no—
243#807C2×D311yescharacteristic, complemented
244#803C2×D311yescharacteristic, complemented
245C4×C3⋊C8C2×D311yescharacteristic, complemented
246C23×C32—21no—
247C22×C3⋊D3—21no—
248C22×C3⋊D3—24no—
249C22×C3⋊D3—81no—
250C22×C3⋊D3—81no—
251C22×C3⋊D3C2×D411yescharacteristic
252C22×C3×D3—21no—
253C22×C3×D3—21no—
254C2×D32—24no—
255C2×D32—81no—
256C2×D32—81no—
257C32×D4—21no—
258C32×D4C22×C412yes—
259C2×C32×C4—21no—
260C2×C32×C4—81no—
261C2×C32×C4C2×D411yescharacteristic
262C2×C32×C4C2×D411yescharacteristic
263C2×C32×C4C2411yescharacteristic
264#638—24no—
265C2×C3⋊Dic3—21no—
266C2×C3⋊Dic3—81no—
267C2×C3⋊Dic3C2×D411yescharacteristic
268C2×C3⋊Dic3C2×D411yescharacteristic
269C2×C3⋊Dic3C2×D411yescharacteristic
270C4⋊(C3⋊D3)—21no—
271C4⋊(C3⋊D3)C22×C412yes—
272C4×C3⋊D3—81no—
273C4×C3⋊D3—81no—
274C4×C3⋊D3C22×C412yes—
275C4×C3⋊D3#4112yes—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C3×D12—21no—
279C3×D12—21no—
280C3×D12C22×C412yes—
281C3×D12C22×C412yes—
282C3×C4×D3—81no—
283C3×C4×D3—81no—
284#625—24no—
285D3×Dic3—81no—
286D3×Dic3—81no—
287C3×C3⋊C8—21no—
288C3×C3⋊C8—21no—
289C3×C3⋊C8C22×C412yes—
290C3×C3⋊C8C22×C412yes—
291C22×D8—91no—
292#518—91no—
293#518—91no—
294#442—31no—
295#442—91no—
296#442—91no—
297#442—91no—
298C4×D8—31no—
299C4×D8—91no—
300C4×D8—91no—
301C4×D8—91no—
302#427—91no—
303#418—91no—
304#418—91no—
305#405—91no—
306C23×D3—61no—
307C23×D3—61no—
308C23×D3—61no—
309C23×D3—61no—
310C23×D3—62no—
311C2×C3×D4—21no—
312C2×C3×D4—31no—
313C2×C3×D4—31no—
314C2×C3×D4C22×D311yescharacteristic
315C2×C3×D4C22×D311yescharacteristic
316C22×C3×C4—22no—
317C22×C3×C4—21no—
318C22×C3×C4—21no—
319C22×C3×C4—61no—
320C22×C3×C4—61no—
321C2×#67—61no—
322C2×#67—61no—
323C2×#67—61no—
324C2×#67—61no—
325C2×#67—62no—
326C22×Dic3—61no—
327C22×Dic3—61no—
328C22×Dic3—61no—
329C22×Dic3—61no—
330C22×Dic3—62no—
331D3×D4—34no—
332D3×D4—34no—
333D3×D4—34no—
334D3×D4—34no—
335D3×D4—64no—
336D3×D4—62no—
337D3×D4—62no—
338D3×D4—62no—
339D3×D4—62no—
340D3×D4—64no—
341C2×D12—31no—
342C2×D12—31no—
343C2×D12—61no—
344C2×D12C22×D311yescharacteristic
345C2×D12C22×D311yescharacteristic
346C2×C4×D3—21no—
347C2×C4×D3—21no—
348C2×C4×D3—31no—
349C2×C4×D3—31no—
350C2×C4×D3—61no—
351C2×C4×D3—61no—
352C2×C4×D3—61no—
353C2×C4×D3—61no—
354C2×C4×D3—61no—
355C2×C4×D3—62no—
356C2×C4×D3—62no—
357C2×C4×D3—61no—
358C2×C4×D3—61no—
359C3×D8—34no—
360C3×D8—34no—
361C2×C3×C8—31no—
362C2×C3×C8—31no—
363C2×C3×C8—31no—
364C2×C3×C8—31no—
365C3×C4⋊C4—21no—
366C3×C4⋊C4—31no—
367C3×C4⋊C4—31no—
368C3×C4⋊C4C22×D311yescharacteristic
369C3×C4⋊C4C22×D311yescharacteristic
370C3×C22⋊C4—22no—
371C3×C22⋊C4—21no—
372C3×C22⋊C4—21no—
373C3×C22⋊C4—61no—
374C3×C22⋊C4—61no—
375C3×C42—21no—
376C3×C42C22×D311yescharacteristic
377C3×C42C22×D311yescharacteristic
378#217—61no—
379#217—61no—
380#217—61no—
381#217—61no—
382#217—62no—
383#213—34no—
384#213—34no—
385#213C4×D314yescomplemented
386#213C4×D314yescomplemented
387(C2×D3)⋊C4—21no—
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—61no—
402(C2×D3)⋊C4—61no—
403(C2×D3)⋊C4—62no—
404(C2×D3)⋊C4—62no—
405(C2×D3)⋊C4—62no—
406(C2×D3)⋊C4—61no—
407(C2×D3)⋊C4—61no—
408C4⋊Dic3—31no—
409C4⋊Dic3—31no—
410C4⋊Dic3—61no—
411C4⋊Dic3C22×D311yescharacteristic
412C4⋊Dic3C22×D311yescharacteristic
413Dic3⋊C4—31no—
414Dic3⋊C4—31no—
415Dic3⋊C4—31no—
416Dic3⋊C4—31no—
417Dic3⋊C4—61no—
418Dic3⋊C4—61no—
419C4×Dic3—31no—
420C4×Dic3—31no—
421C4×Dic3—61no—
422C4×Dic3—61no—
423C4×Dic3—61no—
424C4×Dic3—61no—
425C4×Dic3—61no—
426C4×Dic3—62no—
427C2×C3⋊C8C22×D311yescharacteristic
428C2×C3⋊C8C22×D311yescharacteristic
429C2×C3⋊C8C22×D311yescharacteristic
430C2×C3⋊C8C22×D311yescharacteristic
431D24—34no—
432D24—34no—
433ΓL(1,𝔽25)—62no—
434ΓL(1,𝔽25)—62no—
435D3×C8—34no—
436D3×C8—34no—
437C22×C32—22no—
438C22×C32—41no—
439C22×C32—41no—
440C22×C32C22×D411yescharacteristic
441C2×C3⋊D3—22no—
442C2×C3⋊D3—21no—
443C2×C3⋊D3—21no—
444C2×C3⋊D3—41no—
445C2×C3⋊D3—41no—
446C2×C3⋊D3—84no—
447C2×C3⋊D3C4×D412yes—
448C2×C3×D3—22no—
449C2×C3×D3—22no—
450C2×C3×D3—41no—
451C2×C3×D3—41no—
452C2×C3×D3—41no—
453C2×C3×D3—41no—
454D32—84no—
455C32×C4—21no—
456C32×C4—21no—
457C32×C4—41no—
458C32×C4C23×C411yescharacteristic
459C32×C4C2×#4111yescharacteristic
460C3⋊Dic3—21no—
461C3⋊Dic3—21no—
462C3⋊Dic3—41no—
463C3⋊Dic3C4×D412yes—
464C3×Dic3—41no—
465C3×Dic3—41no—
466C22×D4—91no—
467C22×D4—91no—
468C2×D8—31no—
469C2×D8—31no—
470C2×D8—91no—
471C2×D8—91no—
472C2×D8—98no—
473C2×M16—91no—
474C22×C8—91no—
475C4×D4—31no—
476C4×D4—31no—
477C4×D4—91no—
478C4×D4—91no—
479C4×D4—91no—
480C4×D4—91no—
481C4×D4—91no—
482C4×D4—181no—
483C4×D4—181no—
484C4×D4—181no—
485C4×D4—181no—
486C4×D4D3211yescharacteristic, complemented
487#117—91no—
488#117—91no—
489#117—91no—
490C2×C22⋊C4—181no—
491C2×C22⋊C4—181no—
492C2×C22⋊C4—181no—
493C2×C22⋊C4—181no—
494#107—31no—
495#107—91no—
496#106—31no—
497#106—91no—
498#102—31no—
499#102—31no—
500#102—31no—
501#102—31no—
502#102—91no—
503#102—91no—
504#102—91no—
505#102—91no—
506#97—31no—
507#97—91no—
508C4×C8—31no—
509C4×C8—91no—
510C23×C3—22no—
511C23×C3—21no—
512C23×C3—21no—
513C23×C3—61no—
514C23×C3—61no—
515C22×D3—21no—
516C22×D3—21no—
517C22×D3—31no—
518C22×D3—31no—
519C22×D3—61no—
520C22×D3—64no—
521C22×D3—64no—
522C22×D3—64no—
523C22×D3—64no—
524C22×D3—62no—
525C22×D3—61no—
526C22×D3—61no—
527C22×D3—68no—
528C22×D3—241no—
529C22×D3—241no—
530C22×D3—241no—
531C22×D3—241no—
532C22×D3—241no—
533C22×D3—241no—
534C22×D3—241no—
535C22×D3—241no—
536C22×D3—242no—
537C22×D3—242no—
538C3×D4—22no—
539C3×D4—21no—
540C3×D4—21no—
541C3×D4—22no—
542C3×D4—32no—
543C3×D4—32no—
544C3×D4—61no—
545C3×D4—61no—
546C3×D4C2×C4×D312yes—
547C3×D4C2×C4×D312yes—
548C2×C3×C4—22no—
549C2×C3×C4—21no—
550C2×C3×C4—21no—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—61no—
555C2×C3×C4—61no—
556C2×C3×C4—81no—
557C2×C3×C4—81no—
558C2×C3×C4—82no—
559C2×C3×C4—241no—
560C2×C3×C4—241no—
561C2×C3×C4D3×D411yescharacteristic
562C2×C3×C4D3×D411yescharacteristic
563C2×C3×C4D3×D411yescharacteristic
564C2×C3×C4D3×D411yescharacteristic
565C2×C3×C4C23×D311yescharacteristic
566C2×C3×C4C23×D311yescharacteristic
567#67—64no—
568#67—64no—
569#67—64no—
570#67—64no—
571#67—68no—
572C2×Dic3—21no—
573C2×Dic3—21no—
574C2×Dic3—31no—
575C2×Dic3—31no—
576C2×Dic3—31no—
577C2×Dic3—31no—
578C2×Dic3—31no—
579C2×Dic3—31no—
580C2×Dic3—61no—
581C2×Dic3—61no—
582C2×Dic3—61no—
583C2×Dic3—62no—
584C2×Dic3—61no—
585C2×Dic3—61no—
586C2×Dic3—241no—
587C2×Dic3—241no—
588C2×Dic3—241no—
589C2×Dic3—241no—
590C2×Dic3—242no—
591D12—21no—
592D12—21no—
593D12—32no—
594D12—32no—
595D12—62no—
596D12—62no—
597D12—61no—
598D12—61no—
599D12C2×C4×D312yes—
600D12C2×C4×D312yes—
601C4×D3—32no—
602C4×D3—32no—
603C4×D3—32no—
604C4×D3—32no—
605C4×D3—62no—
606C4×D3—62no—
607C4×D3—81no—
608C4×D3—81no—
609C4×D3—241no—
610C4×D3—241no—
611C4×D3—241no—
612C4×D3—241no—
613C4×D3—241no—
614C4×D3—241no—
615C4×D3—242no—
616C4×D3—242no—
617C3×C8—32no—
618C3×C8—32no—
619C3×C8—61no—
620C3×C8—61no—
621C3⋊C8—21no—
622C3⋊C8—21no—
623C3⋊C8C2×C4×D312yes—
624C3⋊C8C2×C4×D312yes—
625C2×C32—42no—
626C2×C32C2×C4×D411yescharacteristic
627C2×C32#57611yescharacteristic
628C2×C32#57611yescharacteristic
629C3⋊D3—22no—
630C3⋊D3—42no—
631C3×D3—42no—
632C3×D3—42no—
633C24—181no—
634C24—181no—
635C2×D4—31no—
636C2×D4—31no—
637C2×D4—94no—
638C2×D4—94no—
639C2×D4—91no—
640C2×D4—182no—
641C2×D4—182no—
642C2×D4—181no—
643C2×D4—181no—
644C2×D4C2×D3211yescharacteristic
645C22×C4—21no—
646C22×C4—61no—
647C22×C4—61no—
648C22×C4—91no—
649C22×C4—181no—
650C22×C4—181no—
651C22×C4—181no—
652C22×C4—181no—
653C22×C4—181no—
654D8—34no—
655D8—34no—
656D8—94no—
657D8—94no—
658M16—182no—
659C2×C8—31no—
660C2×C8—31no—
661C2×C8—31no—
662C2×C8—31no—
663C2×C8—94no—
664C4⋊C4—31no—
665C4⋊C4—31no—
666C4⋊C4—91no—
667C4⋊C4—91no—
668C4⋊C4—91no—
669C4⋊C4C2×D3211yescharacteristic
670C22⋊C4—21no—
671C22⋊C4—61no—
672C22⋊C4—61no—
673C22⋊C4—91no—
674C22⋊C4—91no—
675C22⋊C4—181no—
676C22⋊C4—181no—
677C22⋊C4—181no—
678C22⋊C4—181no—
679C22⋊C4—181no—
680C22⋊C4—181no—
681C22⋊C4—181no—
682C42—91no—
683C42—181no—
684C42—181no—
685C42C2×D3211yescharacteristic
686C22×C3—24no—
687C22×C3—22no—
688C22×C3—22no—
689C22×C3—21no—
690C22×C3—42no—
691C22×C3—42no—
692C22×C3—41no—
693C22×C3—41no—
694C22×C3—41no—
695C22×C3—41no—
696C22×C3—62no—
697C22×C3—62no—
698C22×C3—121no—
699C22×C3—121no—
700C22×C3—121no—
701C22×C3—121no—
702C22×C3C2×D3×D411yescharacteristic
703C22×C3C2×D3×D411yescharacteristic
704C2×D3—22no—
705C2×D3—22no—
706C2×D3—32no—
707C2×D3—32no—
708C2×D3—41no—
709C2×D3—41no—
710C2×D3—41no—
711C2×D3—41no—
712C2×D3—62no—
713C2×D3—61no—
714C2×D3—61no—
715C2×D3—61no—
716C2×D3—61no—
717C2×D3—64no—
718C2×D3—62no—
719C2×D3—62no—
720C2×D3—121no—
721C2×D3—121no—
722C2×D3—122no—
723C2×D3—122no—
724C2×D3—121no—
725C2×D3—121no—
726C2×D3—121no—
727C2×D3—121no—
728C2×D3—244no—
729C2×D3—244no—
730C2×D3—244no—
731C2×D3—244no—
732C2×D3—248no—
733C3×C4—21no—
734C3×C4—21no—
735C3×C4—21no—
736C3×C4—21no—
737C3×C4—21no—
738C3×C4—21no—
739C3×C4—41no—
740C3×C4—41no—
741C3×C4—42no—
742C3×C4—41no—
743C3×C4—41no—
744C3×C4—121no—
745C3×C4—121no—
746C3×C4C22×C4×D311yescharacteristic
747C3×C4C22×C4×D311yescharacteristic
748C3×C4D3×#4111yescharacteristic
749C3×C4D3×#4111yescharacteristic
750Dic3—32no—
751Dic3—32no—
752Dic3—41no—
753Dic3—41no—
754Dic3—62no—
755Dic3—61no—
756Dic3—61no—
757Dic3—61no—
758Dic3—61no—
759Dic3—121no—
760Dic3—121no—
761Dic3—122no—
762Dic3—121no—
763Dic3—121no—
764C32#294811yescharacteristic, complemented, Sylow
765C23—21no—
766C23—61no—
767C23—61no—
768C23—91no—
769C23—184no—
770C23—184no—
771C23—181no—
772C23—721no—
773C23—721no—
774C23—721no—
775C23—721no—
776D4—21no—
777D4—32no—
778D4—32no—
779D4—61no—
780D4—61no—
781D4—92no—
782D4—184no—
783D4—184no—
784D4—181no—
785D4C4×D3212yes—
786C2×C4—21no—
787C2×C4—61no—
788C2×C4—61no—
789C2×C4—81no—
790C2×C4—91no—
791C2×C4—92no—
792C2×C4—92no—
793C2×C4—91no—
794C2×C4—91no—
795C2×C4—181no—
796C2×C4—241no—
797C2×C4—241no—
798C2×C4—721no—
799C2×C4—721no—
800C2×C4—721no—
801C2×C4—721no—
802C2×C4—721no—
803C2×C4#381111yescharacteristic
804C2×C4#381111yescharacteristic
805C2×C4C22×D3211yescharacteristic
806C8—32no—
807C8—32no—
808C8—61no—
809C8—61no—
810C2×C3—21no—
811C2×C3—21no—
812C2×C3—21no—
813C2×C3—44no—
814C2×C3—42no—
815C2×C3—42no—
816C2×C3—122no—
817C2×C3—122no—
818C2×C3C4×D3×D411yescharacteristic
819C2×C3C4×D3×D411yescharacteristic
820C2×C3#575711yescharacteristic
821C2×C3#576911yescharacteristic
822C2×C3#577411yescharacteristic
823C2×C3#577411yescharacteristic
824D3—42no—
825D3—42no—
826D3—62no—
827D3—62no—
828D3—122no—
829D3—124no—
830D3—122no—
831D3—122no—
832C22—22no—
833C22—41no—
834C22—41no—
835C22—62no—
836C22—62no—
837C22—92no—
838C22—121no—
839C22—121no—
840C22—121no—
841C22—121no—
842C22—181no—
843C22—181no—
844C22—182no—
845C22—361no—
846C22—361no—
847C22—724no—
848C22—724no—
849C22C2×#381111yescharacteristic
850C4—21no—
851C4—21no—
852C4—41no—
853C4—92no—
854C4—121no—
855C4—121no—
856C4—181no—
857C4—181no—
858C4—361no—
859C4C2×C4×D3211yescharacteristic
860C4#6430611yescharacteristic
861C3—21no—
862C3#7958811yescharacteristic, complemented
863C3#7986711yescharacteristic, complemented
864C2—42no—
865C2—122no—
866C2—122no—
867C2—182no—
868C2—362no—
869C2C4×#381111yescharacteristic
870C2#1059510211yescharacteristic
871C2#1059546111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×#63926C2
cosocleC2×C32×C4C24
hypercenterC4×D4D32
hypocenterC32#2948
LCSG ▷ 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. #10596016C2semidirect
3. #10593996C2semidirect
4. C3×#5014C2semidirect
5. C3×C4×#213C2semidirect
6. #10591436C2semidirect
7. #10591435C2semidirect
8. #10591426C2semidirect
9. #10590594C2semidirect
10. #10590574C2semidirect
11. #10590462C2semidirect
12. #10590459C2semidirect
13. #10590346C2semidirect
14. C4×#3714C2semidirect
15. #10590321C2semidirect
20. C32×C4×D4C22semidirect
21. D4×C3⋊Dic3C22semidirect
24. #64102C22semidirect
28. C4×C4⋊(C3⋊D3)C22semidirect
32. C3×C4×D12C22semidirect
33. C3×C4×D12C22semidirect
34. #63926C4semidirect
37. #63898C22semidirect
38. #63898C22semidirect
46. C3×#832C22semidirect
47. C3×#832C22semidirect
48. C3×#809C22semidirect
49. C3×#809C22semidirect
50. C3×#808C22semidirect
51. C3×#807C22semidirect
52. C3×#803C22semidirect
53. C3×C4×C3⋊C8C22semidirect
54. #63575C22semidirect
55. #63573C22semidirect
56. #63564C22semidirect
57. #63564C22semidirect
58. #63563C22semidirect
59. #63563C22semidirect
60. #63555C22semidirect
61. #63553C22semidirect
74. #5014D3semidirect
76. C4×#213D3semidirect
100. D4×C3⋊D3C2×C4semidirect
113. #3802C2×C4semidirect
128. C3×#213C2×C4semidirect
129. C3×#213C2×C4semidirect
142. #3714C2×C4semidirect
143. #3714C2×C4semidirect
145. #3710C2×C4semidirect
157. C3×C4×D4C2×D3semidirect
158. C3×C4×D4C2×D3semidirect
209. C4×D12C2×D3semidirect
210. C4×D12C2×D3semidirect
224. #832C2×D3semidirect
225. #832C2×D3semidirect
238. #809C2×D3semidirect
239. #809C2×D3semidirect
241. #808C2×D3semidirect
243. #807C2×D3semidirect
244. #803C2×D3semidirect
245. C4×C3⋊C8C2×D3semidirect
385. #213C4×D3semidirect
386. #213C4×D3semidirect
486. C4×D4D32semidirect
764. C32#2948semidirect
862. C3#79588semidirect
863. C3#79867semidirect

Maximal subgroups

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

subgroupindex
#105960162
C2×#639262
#105939962
C3×#50142
C3×C4×#2132
#105914362
#105914352
#105914262
#105905942
#105905742
#105904622
#105904592
#105903462
C4×#37142
#105903212
#798673
#795883