Finite Group Databasebeta

← C4×#63950 #11859999

Subgroups — C4×#63950 #11859999

Order 1152.

1155 conjugacy classes of subgroups.

The subgroup lattice has 811 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3832C211yesmaximal, characteristic, complemented
2C2×#63950C211yesmaximal, characteristic
3C4×#3796C211yesmaximal, characteristic, complemented
4C3×C4×#216C211yesmaximal, characteristic, complemented
5C3×C4×#215C211yesmaximal, characteristic, complemented
6#10591581C211yesmaximal, characteristic, complemented
7#10591571C211yesmaximal, characteristic, complemented
8#10591560C211yesmaximal, characteristic, complemented
9#10590611C211yesmaximal, characteristic, complemented
10#10590574C211yesmaximal, characteristic, complemented
11#10590483C211yesmaximal, characteristic, complemented
12#10590459C211yesmaximal, characteristic, complemented
13C4×#3717C211yesmaximal, characteristic, complemented
14C4×#3714C211yesmaximal, characteristic, complemented
15C4×#3710C211yesmaximal, characteristic, complemented
16C4×#919—31nomaximal
17C4×#916—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×#3796C2211yescharacteristic
20C32×C4×Q8C2211yescharacteristic
21Q8×C3⋊Dic3C2211yescharacteristic
22#64102—21no—
23#64102C2211yescharacteristic
24#64101—21no—
25#64101C2211yescharacteristic
26C4×C4⋊(C3⋊D3)—21no—
27C4×C4⋊(C3⋊D3)C2211yescharacteristic
28C42×C3⋊D3—21no—
29C42×C3⋊D3C2211yescharacteristic
30C2×C3×#216C2211yescharacteristic
31C2×C3×#215C2211yescharacteristic
32C3×C4×D12C2211yescharacteristic
33C3×C4×Dic6C2211yescharacteristic
34#63950C418yesdirect product factor
35C4×#626—21no—
36#63898C2211yescharacteristic
37#63881—21no—
38#63878—21no—
39C4×D3×Dic3—21no—
40#63849C2211yescharacteristic
41#63843C2211yescharacteristic
42C2×#3717C2211yescharacteristic
43C2×#3714C2211yescharacteristic
44C2×#3710C2211yescharacteristic
45C2×#3710C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#810C2211yescharacteristic
49C3×#809C2211yescharacteristic
50C3×#808C2211yescharacteristic
51C3×#807C2211yescharacteristic
52C3×C4×C3⋊C8C2211yescharacteristic
53C3×C4×C3⋊C8C2211yescharacteristic
54#63575C2211yescharacteristic
55#63573C2211yescharacteristic
56#63566C2211yescharacteristic
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59#63563C2211yescharacteristic
60#63553C2211yescharacteristic
61#63553C2211yescharacteristic
62C2×#919—31no—
63C2×#916—31no—
64C4×#239—31no—
65C4×#239—31no—
66C4×#239—31no—
67C4×#239—61no—
68C4×#237—31no—
69C3×C4×Q16—31no—
70C3×C4×SD16—31no—
71Dic3×Q16—31no—
72Dic3×SD16—31no—
73C4×#216D311yescharacteristic, complemented
74C4×#215—31no—
75C4×#215D311yescharacteristic, complemented
76C4×#213—31no—
77#4880—31no—
78#4872—31no—
79#4860—31no—
80#4852—31no—
81#4804—31no—
82#4804—31no—
83#4804—31no—
84#4790—31no—
85#4788—31no—
86#4788—31no—
87#4772—31no—
88#4756—31no—
89C4×D24—31no—
90C4×#204—31no—
91C4×D3×C8—31no—
92C4×D3×C8—31no—
93C2×C32×Q8C2311yescharacteristic
94#3832—22no—
95#3832C2×C414yescomplemented
96C2×C4⋊(C3⋊D3)—21no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3—21no—
99C2×C4×C3⋊D3—21no—
100C2×C4×C3⋊D3—21no—
101C2×C4×C3⋊D3D411yescharacteristic
102C2×C4×C3⋊D3D411yescharacteristic
103C2×C4×C3⋊D3C2311yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3—21no—
106C2×C3×Dic6C2311yescharacteristic
107C2×#626—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110#3796—22no—
111#3796C2×C414yescomplemented
112C32×C4⋊C4—21no—
113C32×C4⋊C4C2311yescharacteristic
114C32×C42—21no—
115C32×C42C2311yescharacteristic
116#3752—21no—
117#3752—21no—
118#3752—21no—
119C4⋊(C3⋊Dic3)—21no—
120C4⋊(C3⋊Dic3)C2311yescharacteristic
121C4×C3⋊Dic3—21no—
122C4×C3⋊Dic3—21no—
123C4×C3⋊Dic3D411yescharacteristic
124C4×C3⋊Dic3D411yescharacteristic
125C4×C3⋊Dic3C2311yescharacteristic
126C3×#216C2×C414yescomplemented
127C3×#215C2×C414yescomplemented
128C3×(C2×D3)⋊C4—21no—
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×Dic3⋊C4—21no—
132C3×C4×Dic3—21no—
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137Dic3⋊Dic3—21no—
138#3722—21no—
139(C2×D3)⋊Dic3—21no—
140Dic32—21no—
141Dic32—21no—
142#3717C2×C414yescomplemented
143#3714C2×C414yescomplemented
144#3710—22no—
145#3710C2×C414yescomplemented
146C4×#135—91noSylow
147C2×#239—31no—
148C2×#239—31no—
149C2×#239—31no—
150C2×#239—61no—
151C2×#237—31no—
152C2×C3×Q16—31no—
153C2×C3×SD16—31no—
154C3×C4×Q8—21no—
155C3×C4×Q8—31no—
156C3×C4×Q8C2×D311yescharacteristic
157C3×C4×Q8C2×D311yescharacteristic
158C3×C4×D4—31no—
159Q8×Dic3—31no—
160Q8×Dic3—31no—
161Q8×Dic3—31no—
162Q8×Dic3—61no—
163C2×#216C2×D311yescharacteristic
164C2×#215—31no—
165C2×#215C2×D311yescharacteristic
166D4×Dic3—31no—
167C2×#213—31no—
168C4×#67—61no—
169C2×C4×Dic3—61no—
170#919—38no—
171#916—38no—
172C2×D24—31no—
173C2×#204—31no—
174C2×D3×C8—31no—
175C2×D3×C8—31no—
176C2×D3×C8—31no—
177C2×D3×C8—31no—
178#893—31no—
179#893—31no—
180#893—31no—
181#893—61no—
182#893—61no—
183#893—61no—
184#893—61no—
185#893—62no—
186#892—31no—
187#892—31no—
188#892—31no—
189#892—31no—
190#892—61no—
191#892—61no—
192#892—61no—
193#892—61no—
194#892—62no—
195#887—31no—
196#67⋊C4—61no—
197#877—61no—
198C4×D12—31no—
199C4×D12—31no—
200C4×D12—61no—
201C4×D12—61no—
202C4×D12—61no—
203C4×D12—62no—
204C4×D12—61no—
205C4×D12C2×D311yescharacteristic
206C42×D3—31no—
207C42×D3—31no—
208C42×D3—61no—
209C42×D3—61no—
210C42×D3—61no—
211C42×D3—61no—
212C42×D3—62no—
213C4×Dic6C2×D311yescharacteristic
214C3×#107—31no—
215C3×#106—31no—
216C3×#103—31no—
217C3×#103—31no—
218C3×#103—31no—
219C3×#102—31no—
220C3×C4×C8—31no—
221C3×C4×C8—31no—
222#835—31no—
223#835C2×D311yescharacteristic
224#835C2×D311yescharacteristic
225#832—31no—
226#821—31no—
227#821—31no—
228#821—31no—
229#818—31no—
230#817—31no—
231#816—31no—
232C8×Dic3—31no—
233C8×Dic3—31no—
234C8×Dic3—31no—
235C8×Dic3—31no—
236#810C2×D311yescharacteristic
237#809—31no—
238#809—31no—
239#809C2×D311yescharacteristic
240#808—31no—
241#808C2×D311yescharacteristic
242#807—31no—
243#807C2×D311yescharacteristic
244C4×C3⋊C8C2×D311yescharacteristic
245C4×C3⋊C8C2×D311yescharacteristic
246C22×C3⋊D3—21no—
247C22×C3⋊D3C2×D411yescharacteristic
248C22×C3×D3—21no—
249C32×Q8—21no—
250C32×Q8C22×C412yes—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4C2×D411yescharacteristic
254C2×C32×C4C2×D411yescharacteristic
255C2×C32×C4C2411yescharacteristic
256C2×C3⋊Dic3—21no—
257C2×C3⋊Dic3C2×D411yescharacteristic
258C2×C3⋊Dic3C2×D411yescharacteristic
259C2×C3⋊Dic3C2×D411yescharacteristic
260C4⋊(C3⋊D3)—24no—
261C4⋊(C3⋊D3)—21no—
262C4⋊(C3⋊D3)C22×C412yes—
263C4×C3⋊D3—24no—
264C4×C3⋊D3—22no—
265C4×C3⋊D3—22no—
266C4×C3⋊D3—42no—
267C4×C3⋊D3—42no—
268C4×C3⋊D3C22×C412yes—
269C4×C3⋊D3#4112yes—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C3×D12—21no—
274C3×D12C22×C412yes—
275C3×C4×D3—42no—
276C3×Dic6—21no—
277C3×Dic6C22×C412yes—
278#626—24no—
279D3×Dic3—24no—
280D3×Dic3—42no—
281C3×C3⋊C8—21no—
282C3×C3⋊C8—21no—
283C3×C3⋊C8C22×C412yes—
284C3×C3⋊C8C22×C412yes—
285C2×#135—91no—
286C4×#41—91no—
287C4×#41—91no—
288C4×Q16—31no—
289C4×Q16—91no—
290C4×SD16—31no—
291C4×SD16—91no—
292C4×SD16—91no—
293C4×SD16—91no—
294C4×D8—91no—
295C4×D8—91no—
296#427—91no—
297#416—91no—
298#416—91no—
299C2×C4×C8—91no—
300C2×C3×Q8—21no—
301C2×C3×Q8—31no—
302C2×C3×Q8C22×D311yescharacteristic
303C2×C3×Q8C22×D311yescharacteristic
304C2×C3×D4—31no—
305C22×C3×C4—61no—
306C2×#67—61no—
307C22×Dic3—61no—
308C22×Dic3—61no—
309#239—34no—
310#239—34no—
311#239—34no—
312#239—64no—
313#239—62no—
314#239—62no—
315#239—62no—
316#239—64no—
317#237—34no—
318#237—62no—
319C2×D12—31no—
320C2×D12—31no—
321C2×D12—61no—
322C2×D12—61no—
323C2×D12—61no—
324C2×D12—62no—
325C2×D12—61no—
326C2×D12C22×D311yescharacteristic
327C2×C4×D3—21no—
328C2×C4×D3—31no—
329C2×C4×D3—31no—
330C2×C4×D3—31no—
331C2×C4×D3—31no—
332C2×C4×D3—31no—
333C2×C4×D3—31no—
334C2×C4×D3—61no—
335C2×C4×D3—61no—
336C2×C4×D3—61no—
337C2×C4×D3—61no—
338C2×C4×D3—61no—
339C2×C4×D3—61no—
340C2×C4×D3—62no—
341C2×C4×D3—61no—
342C2×C4×D3—61no—
343C2×C4×D3—61no—
344C2×C4×D3—62no—
345C2×C4×D3—62no—
346C2×C4×D3—61no—
347C2×C4×D3—61no—
348C2×Dic6C22×D311yescharacteristic
349C3×Q16—34no—
350C3×SD16—34no—
351C2×C3×C8—31no—
352C2×C3×C8—31no—
353C2×C3×C8—31no—
354C2×C3×C8—31no—
355C3×C4⋊C4—22no—
356C3×C4⋊C4—21no—
357C3×C4⋊C4—21no—
358C3×C4⋊C4—21no—
359C3×C4⋊C4—31no—
360C3×C4⋊C4—31no—
361C3×C4⋊C4—61no—
362C3×C4⋊C4C22×D311yescharacteristic
363C3×C4⋊C4C22×D311yescharacteristic
364C3×C22⋊C4—61no—
365C3×C42—22no—
366C3×C42—21no—
367C3×C42—21no—
368C3×C42—21no—
369C3×C42—61no—
370C3×C42C22×D311yescharacteristic
371C3×C42C22×D311yescharacteristic
372#217—61no—
373#216C4×D314yescomplemented
374#215—34no—
375#215C4×D314yescomplemented
376#213—34no—
377(C2×D3)⋊C4—21no—
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—62no—
386(C2×D3)⋊C4—62no—
387(C2×D3)⋊C4—62no—
388(C2×D3)⋊C4—61no—
389(C2×D3)⋊C4—61no—
390C4⋊Dic3—31no—
391C4⋊Dic3—31no—
392C4⋊Dic3—61no—
393C4⋊Dic3—61no—
394C4⋊Dic3—61no—
395C4⋊Dic3—61no—
396C4⋊Dic3—62no—
397C4⋊Dic3C22×D311yescharacteristic
398C4⋊Dic3C22×D311yescharacteristic
399Dic3⋊C4—21no—
400Dic3⋊C4—61no—
401C4×Dic3—21no—
402C4×Dic3—31no—
403C4×Dic3—31no—
404C4×Dic3—31no—
405C4×Dic3—31no—
406C4×Dic3—31no—
407C4×Dic3—31no—
408C4×Dic3—61no—
409C4×Dic3—61no—
410C4×Dic3—61no—
411C4×Dic3—61no—
412C4×Dic3—61no—
413C4×Dic3—61no—
414C4×Dic3—61no—
415C4×Dic3—61no—
416C4×Dic3—61no—
417C4×Dic3—61no—
418C4×Dic3—61no—
419C4×Dic3—62no—
420C4×Dic3—62no—
421C2×C3⋊C8C22×D311yescharacteristic
422C2×C3⋊C8C22×D311yescharacteristic
423C2×C3⋊C8C22×D311yescharacteristic
424C2×C3⋊C8C22×D311yescharacteristic
425D24—34no—
426#204—34no—
427D3×C8—34no—
428D3×C8—34no—
429D3×C8—62no—
430D3×C8—62no—
431C22×C32C22×D411yescharacteristic
432C2×C3⋊D3—22no—
433C2×C3⋊D3—21no—
434C2×C3⋊D3—21no—
435C2×C3⋊D3—41no—
436C2×C3⋊D3—41no—
437C2×C3⋊D3C4×D412yes—
438C2×C3×D3—22no—
439C2×C3×D3—41no—
440C2×C3×D3—41no—
441C32×C4—22no—
442C32×C4—21no—
443C32×C4—41no—
444C32×C4#13512yescomplemented
445C32×C4C23×C411yescharacteristic
446C32×C4C2×#4111yescharacteristic
447C3⋊Dic3—21no—
448C3⋊Dic3—41no—
449C3⋊Dic3C4×D412yes—
450C3⋊Dic3#13512yescomplemented
451C3×Dic3—22no—
452C3×Dic3—41no—
453C3×Dic3—41no—
454C2×#41—91no—
455C2×#41—91no—
456#135—98no—
457C2×Q16—31no—
458C2×SD16—31no—
459C2×SD16—91no—
460C2×D8—91no—
461C22×C8—91no—
462C22×C8—91no—
463C4×Q8—31no—
464C4×Q8—91no—
465C4×Q8—91no—
466C4×Q8D3211yescharacteristic
467C4×D4—31no—
468C4×D4—91no—
469C4×D4—91no—
470C4×D4—91no—
471C4×D4—181no—
472C4×D4—181no—
473C4×D4—181no—
474C4×D4—181no—
475#117—91no—
476#117—91no—
477#117—181no—
478#117—181no—
479C2×C42—91no—
480C2×C42—181no—
481C2×C42—181no—
482#107—31no—
483#107—91no—
484#106—31no—
485#106—91no—
486#103—31no—
487#103—31no—
488#103—31no—
489#103—91no—
490#102—31no—
491#102—91no—
492#102—91no—
493#102—91no—
494C4×C8—31no—
495C4×C8—31no—
496C4×C8—91no—
497C4×C8—91no—
498C23×C3—61no—
499C22×D3—21no—
500C22×D3—31no—
501C22×D3—31no—
502C22×D3—61no—
503C22×D3—62no—
504C22×D3—61no—
505C22×D3—61no—
506C3×Q8—22no—
507C3×Q8—21no—
508C3×Q8—21no—
509C3×Q8—22no—
510C3×Q8—32no—
511C3×Q8—61no—
512C3×Q8C2×C4×D312yes—
513C3×Q8C2×C4×D312yes—
514C3×D4—32no—
515C3×D4—61no—
516C2×C3×C4—22no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—22no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—122no—
529C2×C3×C4D3×D411yescharacteristic
530C2×C3×C4D3×D411yescharacteristic
531C2×C3×C4D3×D411yescharacteristic
532C2×C3×C4D3×D411yescharacteristic
533C2×C3×C4C23×D311yescharacteristic
534C2×C3×C4C23×D311yescharacteristic
535#67—64no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—31no—
540C2×Dic3—31no—
541C2×Dic3—31no—
542C2×Dic3—31no—
543C2×Dic3—31no—
544C2×Dic3—31no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—61no—
548C2×Dic3—64no—
549C2×Dic3—62no—
550C2×Dic3—61no—
551C2×Dic3—61no—
552C2×Dic3—122no—
553D12—21no—
554D12—32no—
555D12—32no—
556D12—62no—
557D12—64no—
558D12—64no—
559D12—68no—
560D12—62no—
561D12—64no—
562D12—61no—
563D12—61no—
564D12C2×C4×D312yes—
565C4×D3—32no—
566C4×D3—32no—
567C4×D3—32no—
568C4×D3—32no—
569C4×D3—42no—
570C4×D3—62no—
571C4×D3—62no—
572C4×D3—62no—
573C4×D3—62no—
574C4×D3—64no—
575C4×D3—64no—
576C4×D3—64no—
577C4×D3—68no—
578C4×D3—62no—
579C4×D3—62no—
580C4×D3—122no—
581C4×D3—122no—
582C4×D3—122no—
583C4×D3—122no—
584C4×D3—122no—
585C4×D3—124no—
586C4×D3—124no—
587C4×D3—122no—
588C4×D3—122no—
589Dic6—21no—
590Dic6C2×C4×D312yes—
591C3×C8—32no—
592C3×C8—32no—
593C3×C8—61no—
594C3×C8—61no—
595C3⋊C8—21no—
596C3⋊C8—21no—
597C3⋊C8C2×C4×D312yes—
598C3⋊C8C2×C4×D312yes—
599C2×C32C2×C4×D411yescharacteristic
600C2×C32C2×#13511yescharacteristic
601C2×C32C2×#13511yescharacteristic
602C3⋊D3—22no—
603C3⋊D3—42no—
604C3×D3—42no—
605#41—94no—
606#41—94no—
607#41—182no—
608#41—182no—
609C2×Q8—31no—
610C2×Q8C2×D3211yescharacteristic
611C2×D4—31no—
612C2×D4—91no—
613C2×D4—181no—
614C2×D4—181no—
615C22×C4—61no—
616C22×C4—91no—
617C22×C4—91no—
618C22×C4—91no—
619C22×C4—181no—
620C22×C4—181no—
621C22×C4—181no—
622C22×C4—181no—
623C22×C4—181no—
624Q16—34no—
625SD16—34no—
626SD16—94no—
627D8—94no—
628C2×C8—31no—
629C2×C8—31no—
630C2×C8—31no—
631C2×C8—31no—
632C2×C8—94no—
633C2×C8—182no—
634C4⋊C4—21no—
635C4⋊C4—31no—
636C4⋊C4—31no—
637C4⋊C4—61no—
638C4⋊C4—91no—
639C4⋊C4—181no—
640C4⋊C4—181no—
641C4⋊C4C2×D3211yescharacteristic
642C22⋊C4—61no—
643C22⋊C4—181no—
644C22⋊C4—181no—
645C22⋊C4—181no—
646C22⋊C4—181no—
647C22⋊C4—181no—
648C42—21no—
649C42—61no—
650C42—91no—
651C42—91no—
652C42—91no—
653C42—181no—
654C42—181no—
655C42—181no—
656C42—181no—
657C42C2×D3211yescharacteristic
658C22×C3—21no—
659C22×C3—62no—
660C22×C3—121no—
661C22×C3—121no—
662C22×C3C2×D3×D411yescharacteristic
663C22×C3C2×D3×D411yescharacteristic
664C2×D3—22no—
665C2×D3—32no—
666C2×D3—32no—
667C2×D3—41no—
668C2×D3—41no—
669C2×D3—62no—
670C2×D3—61no—
671C2×D3—61no—
672C2×D3—61no—
673C2×D3—61no—
674C2×D3—64no—
675C2×D3—62no—
676C2×D3—62no—
677C2×D3—121no—
678C2×D3—121no—
679C2×D3—122no—
680C2×D3—122no—
681C2×D3—121no—
682C2×D3—121no—
683C2×D3—121no—
684C2×D3—121no—
685C3×C4—24no—
686C3×C4—21no—
687C3×C4—21no—
688C3×C4—22no—
689C3×C4—22no—
690C3×C4—21no—
691C3×C4—21no—
692C3×C4—22no—
693C3×C4—41no—
694C3×C4—42no—
695C3×C4—41no—
696C3×C4—41no—
697C3×C4—62no—
698C3×C4—121no—
699C3×C4—121no—
700C3×C4#91612yescomplemented
701C3×C4#91912yescomplemented
702C3×C4C22×C4×D311yescharacteristic
703C3×C4C22×C4×D311yescharacteristic
704C3×C4D3×#4111yescharacteristic
705C3×C4D3×#4111yescharacteristic
706Dic3—22no—
707Dic3—32no—
708Dic3—32no—
709Dic3—32no—
710Dic3—32no—
711Dic3—41no—
712Dic3—41no—
713Dic3—62no—
714Dic3—62no—
715Dic3—61no—
716Dic3—61no—
717Dic3—121no—
718Dic3—122no—
719Dic3—121no—
720Dic3—121no—
721C32C4×#13511yescharacteristic, complemented, Sylow
722C23—61no—
723C23—91no—
724C23—181no—
725Q8—21no—
726Q8—32no—
727Q8—61no—
728Q8C4×D3212yes—
729D4—32no—
730D4—61no—
731D4—92no—
732D4—184no—
733D4—184no—
734D4—181no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—61no—
740C2×C4—91no—
741C2×C4—91no—
742C2×C4—92no—
743C2×C4—92no—
744C2×C4—91no—
745C2×C4—122no—
746C2×C4—182no—
747C2×C4—184no—
748C2×C4—184no—
749C2×C4—182no—
750C2×C4—181no—
751C2×C4—362no—
752C2×C4—362no—
753C2×C4—362no—
754C2×C4#381111yescharacteristic
755C2×C4#381111yescharacteristic
756C2×C4C22×D3211yescharacteristic
757C8—32no—
758C8—32no—
759C8—61no—
760C8—61no—
761C2×C3—21no—
762C2×C3—21no—
763C2×C3—21no—
764C2×C3—122no—
765C2×C3C4×D3×D411yescharacteristic
766C2×C3C4×D3×D411yescharacteristic
767C2×C3C2×#91611yescharacteristic
768C2×C3C2×#91911yescharacteristic
769C2×C3D3×#13511yescharacteristic
770C2×C3D3×#13511yescharacteristic
771D3—42no—
772D3—62no—
773D3—62no—
774D3—122no—
775D3—124no—
776D3—122no—
777D3—122no—
778C22—62no—
779C22—92no—
780C22—121no—
781C22—121no—
782C22—181no—
783C22—181no—
784C22—182no—
785C22—361no—
786C22—361no—
787C22C2×#381111yescharacteristic
788C4—21no—
789C4—22no—
790C4—41no—
791C4—62no—
792C4—92no—
793C4—92no—
794C4—121no—
795C4—121no—
796C4—181no—
797C4—361no—
798C4#6395012yesdirect product factor
799C4C2×C4×D3211yescharacteristic
800C4#6430611yescharacteristic
801C3—21no—
802C3C4×#91611yescharacteristic, complemented
803C3C4×#91911yescharacteristic, complemented
804C2—122no—
805C2—182no—
806C2—362no—
807C2C4×#381111yescharacteristic
808C2C2×#6395011yescharacteristic
809C2#1059545911yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC2×#63950C2
cosocleC2×C32×C4C24
hypercenterC4×Q8D32
hypocenterC32C4×#135
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C4×#3832C2semidirect
3. C4×#3796C2semidirect
4. C3×C4×#216C2semidirect
5. C3×C4×#215C2semidirect
6. #10591581C2semidirect
7. #10591571C2semidirect
8. #10591560C2semidirect
9. #10590611C2semidirect
10. #10590574C2semidirect
11. #10590483C2semidirect
12. #10590459C2semidirect
13. C4×#3717C2semidirect
14. C4×#3714C2semidirect
15. C4×#3710C2semidirect
34. #63950C4direct (N × H)
73. C4×#216D3semidirect
75. C4×#215D3semidirect
95. #3832C2×C4semidirect
111. #3796C2×C4semidirect
126. C3×#216C2×C4semidirect
127. C3×#215C2×C4semidirect
142. #3717C2×C4semidirect
143. #3714C2×C4semidirect
145. #3710C2×C4semidirect
373. #216C4×D3semidirect
375. #215C4×D3semidirect
444. C32×C4#135semidirect
450. C3⋊Dic3#135semidirect
700. C3×C4#916semidirect
701. C3×C4#919semidirect
721. C32C4×#135semidirect
798. C4#63950direct (N × H)
802. C3C4×#916semidirect
803. C3C4×#919semidirect

Maximal subgroups

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

subgroupindex
C4×#38322
C2×#639502
C4×#37962
C3×C4×#2162
C3×C4×#2152
#105915812
#105915712
#105915602
#105906112
#105905742
#105904832
#105904592
C4×#37172
C4×#37142
C4×#37102
C4×#9193
C4×#9163