Finite Group Databasebeta

← C4×#63936 #11859993

Subgroups — C4×#63936 #11859993

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×#3830C211yesmaximal, characteristic, complemented
2C2×#63936C211yesmaximal, characteristic
3C4×#3796C211yesmaximal, characteristic, complemented
4C3×C4×#214C211yesmaximal, characteristic, complemented
5C3×C4×#213C211yesmaximal, characteristic, complemented
6#10591445C211yesmaximal, characteristic, complemented
7#10591435C211yesmaximal, characteristic, complemented
8#10591424C211yesmaximal, characteristic, complemented
9#10590611C211yesmaximal, characteristic, complemented
10#10590574C211yesmaximal, characteristic, complemented
11#10590482C211yesmaximal, characteristic, complemented
12#10590460C211yesmaximal, characteristic, complemented
13C4×#3719C211yesmaximal, characteristic, complemented
14C4×#3716C211yesmaximal, characteristic, complemented
15C4×#3710C211yesmaximal, characteristic, complemented
16C4×#916—31nomaximal
17C4×#912—31nomaximal
18C2×#3830C2211yescharacteristic
19C2×#3796C2211yescharacteristic
20C32×C4×D4C2211yescharacteristic
21D4×C3⋊Dic3C2211yescharacteristic
22C4×#638—21no—
23C2×C4×C3⋊Dic3—21no—
24#64101C2211yescharacteristic
25#64096C2211yescharacteristic
26#64090—21no—
27#64086—21no—
28C42×C3⋊D3C2211yescharacteristic
29C4×#634C2211yescharacteristic
30C2×C3×#214C2211yescharacteristic
31C2×C3×#213C2211yescharacteristic
32C3×C4×D12C2211yescharacteristic
33C3×C4×Dic6C2211yescharacteristic
34#63936C418yesdirect product factor
35C4×#626—21no—
36#63898C2211yescharacteristic
37#63881—21no—
38#63878—21no—
39C4×D3×Dic3—21no—
40#63849C2211yescharacteristic
41#63843C2211yescharacteristic
42C2×#3719C2211yescharacteristic
43C2×#3716C2211yescharacteristic
44C2×#3710C2211yescharacteristic
45C2×#3710C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#810C2211yescharacteristic
49C3×#809C2211yescharacteristic
50C3×#808C2211yescharacteristic
51C3×#807C2211yescharacteristic
52C3×C4×C3⋊C8C2211yescharacteristic
53C3×C4×C3⋊C8C2211yescharacteristic
54#63575C2211yescharacteristic
55#63573C2211yescharacteristic
56#63567C2211yescharacteristic
57#63567C2211yescharacteristic
58#63566C2211yescharacteristic
59#63563C2211yescharacteristic
60#63553C2211yescharacteristic
61#63553C2211yescharacteristic
62C2×#916—31no—
63C2×#912—31no—
64C4×#239—31no—
65C4×#237—31no—
66C4×#237—31no—
67C4×#237—31no—
68C4×#237—61no—
69C3×C4×SD16—31no—
70C3×C4×D8—31no—
71Dic3×SD16—31no—
72Dic3×D8—31no—
73C4×#216—31no—
74C4×#214—31no—
75C4×#214D311yescharacteristic, complemented
76C4×#213D311yescharacteristic, complemented
77#4880—31no—
78#4873—31no—
79#4860—31no—
80#4852—31no—
81#4804—31no—
82#4790—31no—
83#4772—31no—
84#4772—31no—
85#4772—31no—
86#4758—31no—
87#4758—31no—
88#4756—31no—
89C4×Dic12—31no—
90C4×#204—31no—
91C4×D3×C8—31no—
92C4×D3×C8—31no—
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4—21no—
95C2×#638—21no—
96C22×C3⋊Dic3—21no—
97C22×C3⋊Dic3—21no—
98#3830—22no—
99#3830C2×C414yescomplemented
100C2×C4×C3⋊D3D411yescharacteristic
101C2×C4×C3⋊D3D411yescharacteristic
102C2×C4×C3⋊D3C2311yescharacteristic
103C2×#634C2311yescharacteristic
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⋊C4C2311yescharacteristic
113C32×C22⋊C4—21no—
114C32×C42C2311yescharacteristic
115#3757—21no—
116#3752—21no—
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118#3750—21no—
119#3750—21no—
120C4×C3⋊Dic3—21no—
121C4×C3⋊Dic3—21no—
122C4×C3⋊Dic3—21no—
123C4×C3⋊Dic3D411yescharacteristic
124C4×C3⋊Dic3D411yescharacteristic
125C4×C3⋊Dic3C2311yescharacteristic
126C3×#214C2×C414yescomplemented
127C3×#213C2×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#3719C2×C414yescomplemented
143#3716C2×C414yescomplemented
144#3710—22no—
145#3710C2×C414yescomplemented
146C4×#135—91noSylow
147C2×#239—31no—
148C2×#237—31no—
149C2×#237—31no—
150C2×#237—31no—
151C2×#237—61no—
152C2×C3×SD16—31no—
153C2×C3×D8—31no—
154C3×C4×Q8—31no—
155C3×C4×D4—21no—
156C3×C4×D4—31no—
157C3×C4×D4C2×D311yescharacteristic
158C3×C4×D4C2×D311yescharacteristic
159Q8×Dic3—31no—
160C2×#216—31no—
161D4×Dic3—31no—
162D4×Dic3—31no—
163D4×Dic3—31no—
164D4×Dic3—61no—
165C2×#214—31no—
166C2×#214C2×D311yescharacteristic
167C2×#213C2×D311yescharacteristic
168C4×#67—61no—
169C4×#67—61no—
170C4×#67—61no—
171C4×#67—62no—
172C2×C4×Dic3—61no—
173C2×C4×Dic3—61no—
174C2×C4×Dic3—61no—
175C2×C4×Dic3—62no—
176#916—38no—
177#912—38no—
178C2×Dic12—31no—
179C2×#204—31no—
180C2×D3×C8—31no—
181C2×D3×C8—31no—
182C2×D3×C8—31no—
183C2×D3×C8—31no—
184#893—31no—
185#893—61no—
186#892—31no—
187#892—31no—
188#892—31no—
189#892—31no—
190#892—61no—
191#892—61no—
192#887—31no—
193#887—31no—
194#887—31no—
195#887—61no—
196#67⋊C4—61no—
197#67⋊C4—61no—
198#67⋊C4—61no—
199#67⋊C4—62no—
200#877—61no—
201#877—61no—
202#877—61no—
203#877—62no—
204C4×D12—61no—
205C4×D12C2×D311yescharacteristic
206C42×D3—31no—
207C42×D3—31no—
208C42×D3—61no—
209C42×D3—61no—
210C4×Dic6—31no—
211C4×Dic6—31no—
212C4×Dic6—61no—
213C4×Dic6C2×D311yescharacteristic
214C3×#107—31no—
215C3×#106—31no—
216C3×#103—31no—
217C3×#102—31no—
218C3×#102—31no—
219C3×#102—31no—
220C3×C4×C8—31no—
221C3×C4×C8—31no—
222#835—31no—
223#832—31no—
224#832C2×D311yescharacteristic
225#832C2×D311yescharacteristic
226#821—31no—
227#818—31no—
228#817—31no—
229#816—31no—
230#816—31no—
231#816—31no—
232C8×Dic3—31no—
233C8×Dic3—31no—
234C8×Dic3—31no—
235C8×Dic3—31no—
236#810—31no—
237#810—31no—
238#810C2×D311yescharacteristic
239#809C2×D311yescharacteristic
240#808—31no—
241#808C2×D311yescharacteristic
242#807—31no—
243#807C2×D311yescharacteristic
244C4×C3⋊C8C2×D311yescharacteristic
245C4×C3⋊C8C2×D311yescharacteristic
246C23×C32—21no—
247C22×C3⋊D3C2×D411yescharacteristic
248C22×C3×D3—21no—
249C32×D4—21no—
250C32×D4C22×C412yes—
251C2×C32×C4—21no—
252C2×C32×C4—42no—
253C2×C32×C4C2×D411yescharacteristic
254C2×C32×C4C2×D411yescharacteristic
255C2×C32×C4C2411yescharacteristic
256#638—24no—
257C2×C3⋊Dic3—21no—
258C2×C3⋊Dic3—24no—
259C2×C3⋊Dic3—21no—
260C2×C3⋊Dic3—42no—
261C2×C3⋊Dic3C2×D411yescharacteristic
262C2×C3⋊Dic3C2×D411yescharacteristic
263C2×C3⋊Dic3C2×D411yescharacteristic
264C4×C3⋊D3—22no—
265C4×C3⋊D3—22no—
266C4×C3⋊D3C22×C412yes—
267C4×C3⋊D3#4112yes—
268#634—21no—
269#634C22×C412yes—
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—91no—
289C4×Q16—91no—
290C4×SD16—31no—
291C4×SD16—91no—
292C4×SD16—91no—
293C4×SD16—91no—
294C4×D8—31no—
295C4×D8—91no—
296#427—91no—
297#416—91no—
298#416—91no—
299C2×C4×C8—91no—
300C2×C3×Q8—31no—
301C2×C3×D4—21no—
302C2×C3×D4—31no—
303C2×C3×D4C22×D311yescharacteristic
304C2×C3×D4C22×D311yescharacteristic
305C22×C3×C4—22no—
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—61no—
309C2×#67—61no—
310C2×#67—61no—
311C2×#67—61no—
312C2×#67—62no—
313C22×Dic3—61no—
314C22×Dic3—61no—
315C22×Dic3—61no—
316C22×Dic3—61no—
317C22×Dic3—61no—
318C22×Dic3—61no—
319C22×Dic3—62no—
320C22×Dic3—62no—
321#239—34no—
322#239—62no—
323#237—34no—
324#237—34no—
325#237—34no—
326#237—64no—
327#237—62no—
328#237—62no—
329#237—62no—
330#237—64no—
331C2×D12—61no—
332C2×D12C22×D311yescharacteristic
333C2×C4×D3—21no—
334C2×C4×D3—31no—
335C2×C4×D3—31no—
336C2×C4×D3—31no—
337C2×C4×D3—31no—
338C2×C4×D3—31no—
339C2×C4×D3—31no—
340C2×C4×D3—61no—
341C2×C4×D3—61no—
342C2×C4×D3—61no—
343C2×C4×D3—61no—
344C2×C4×D3—61no—
345C2×Dic6—31no—
346C2×Dic6—31no—
347C2×Dic6—61no—
348C2×Dic6C22×D311yescharacteristic
349C3×SD16—34no—
350C3×D8—34no—
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—61no—
359C3×C4⋊C4C22×D311yescharacteristic
360C3×C4⋊C4C22×D311yescharacteristic
361C3×C22⋊C4—22no—
362C3×C22⋊C4—21no—
363C3×C22⋊C4—21no—
364C3×C22⋊C4—61no—
365C3×C42—21no—
366C3×C42—61no—
367C3×C42C22×D311yescharacteristic
368C3×C42C22×D311yescharacteristic
369#217—61no—
370#217—61no—
371#217—61no—
372#217—62no—
373#216—34no—
374#214—34no—
375#214C4×D314yescomplemented
376#213C4×D314yescomplemented
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—62no—
384C4⋊Dic3—31no—
385C4⋊Dic3—31no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3C22×D311yescharacteristic
389C4⋊Dic3C22×D311yescharacteristic
390Dic3⋊C4—21no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—62no—
395Dic3⋊C4—62no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398C4×Dic3—21no—
399C4×Dic3—31no—
400C4×Dic3—31no—
401C4×Dic3—31no—
402C4×Dic3—31no—
403C4×Dic3—31no—
404C4×Dic3—31no—
405C4×Dic3—61no—
406C4×Dic3—61no—
407C4×Dic3—61no—
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—62no—
417C4×Dic3—62no—
418C4×Dic3—62no—
419C4×Dic3—61no—
420C4×Dic3—61no—
421C2×C3⋊C8C22×D311yescharacteristic
422C2×C3⋊C8C22×D311yescharacteristic
423C2×C3⋊C8C22×D311yescharacteristic
424C2×C3⋊C8C22×D311yescharacteristic
425Dic12—34no—
426#204—34no—
427D3×C8—34no—
428D3×C8—34no—
429D3×C8—62no—
430D3×C8—62no—
431C22×C32—22no—
432C22×C32—41no—
433C22×C32—41no—
434C22×C32C22×D411yescharacteristic
435C2×C3⋊D3—21no—
436C2×C3⋊D3—21no—
437C2×C3⋊D3C4×D412yes—
438C2×C3×D3—22no—
439C2×C3×D3—41no—
440C2×C3×D3—41no—
441C32×C4—21no—
442C32×C4—41no—
443C32×C4#13512yescomplemented
444C32×C4C23×C411yescharacteristic
445C32×C4C2×#4111yescharacteristic
446C3⋊Dic3—22no—
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—91no—
458C2×SD16—31no—
459C2×SD16—91no—
460C2×D8—31no—
461C22×C8—91no—
462C22×C8—91no—
463C4×Q8—31no—
464C4×Q8—91no—
465C4×Q8—91no—
466C4×Q8—91no—
467C4×D4—31no—
468C4×D4—91no—
469C4×D4—91no—
470C4×D4—181no—
471C4×D4—181no—
472C4×D4—181no—
473C4×D4—181no—
474C4×D4D3211yescharacteristic
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—91no—
488#103—91no—
489#103—91no—
490#102—31no—
491#102—31no—
492#102—31no—
493#102—91no—
494C4×C8—31no—
495C4×C8—31no—
496C4×C8—91no—
497C4×C8—91no—
498C23×C3—22no—
499C23×C3—21no—
500C23×C3—21no—
501C23×C3—61no—
502C22×D3—21no—
503C22×D3—31no—
504C22×D3—31no—
505C22×D3—61no—
506C3×Q8—32no—
507C3×Q8—61no—
508C3×D4—22no—
509C3×D4—21no—
510C3×D4—21no—
511C3×D4—22no—
512C3×D4—32no—
513C3×D4—61no—
514C3×D4C2×C4×D312yes—
515C3×D4C2×C4×D312yes—
516C2×C3×C4—22no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—44no—
523C2×C3×C4—42no—
524C2×C3×C4—42no—
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—
536#67—64no—
537#67—64no—
538#67—68no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—31no—
543C2×Dic3—31no—
544C2×Dic3—31no—
545C2×Dic3—31no—
546C2×Dic3—31no—
547C2×Dic3—31no—
548C2×Dic3—61no—
549C2×Dic3—61no—
550C2×Dic3—61no—
551C2×Dic3—64no—
552C2×Dic3—64no—
553C2×Dic3—64no—
554C2×Dic3—62no—
555C2×Dic3—68no—
556C2×Dic3—61no—
557C2×Dic3—61no—
558C2×Dic3—62no—
559C2×Dic3—61no—
560C2×Dic3—61no—
561C2×Dic3—122no—
562C2×Dic3—122no—
563C2×Dic3—122no—
564C2×Dic3—124no—
565D12—21no—
566D12—64no—
567D12C2×C4×D312yes—
568C4×D3—32no—
569C4×D3—32no—
570C4×D3—32no—
571C4×D3—32no—
572C4×D3—42no—
573C4×D3—62no—
574C4×D3—62no—
575C4×D3—62no—
576C4×D3—62no—
577C4×D3—64no—
578C4×D3—62no—
579C4×D3—62no—
580C4×D3—122no—
581C4×D3—122no—
582C4×D3—122no—
583Dic6—21no—
584Dic6—32no—
585Dic6—32no—
586Dic6—62no—
587Dic6—62no—
588Dic6—61no—
589Dic6—61no—
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×C32—42no—
600C2×C32C2×C4×D411yescharacteristic
601C2×C32C2×#13511yescharacteristic
602C2×C32C2×#13511yescharacteristic
603C3⋊D3—22no—
604C3×D3—42no—
605#41—94no—
606#41—94no—
607#41—182no—
608#41—182no—
609C2×Q8—31no—
610C2×Q8—91no—
611C2×D4—31no—
612C2×D4—181no—
613C2×D4—181no—
614C2×D4C2×D3211yescharacteristic
615C22×C4—21no—
616C22×C4—61no—
617C22×C4—91no—
618C22×C4—91no—
619C22×C4—91no—
620C22×C4—181no—
621C22×C4—181no—
622C22×C4—181no—
623C22×C4—181no—
624Q16—94no—
625SD16—34no—
626SD16—94no—
627D8—34no—
628C2×C8—31no—
629C2×C8—31no—
630C2×C8—31no—
631C2×C8—31no—
632C2×C8—94no—
633C2×C8—182no—
634C4⋊C4—31no—
635C4⋊C4—31no—
636C4⋊C4—61no—
637C4⋊C4—91no—
638C4⋊C4—181no—
639C4⋊C4—181no—
640C4⋊C4—181no—
641C4⋊C4C2×D3211yescharacteristic
642C22⋊C4—21no—
643C22⋊C4—61no—
644C22⋊C4—181no—
645C22⋊C4—181no—
646C22⋊C4—181no—
647C22⋊C4—181no—
648C42—61no—
649C42—91no—
650C42—91no—
651C42—91no—
652C42—181no—
653C42—181no—
654C42—181no—
655C42—181no—
656C42—181no—
657C42C2×D3211yescharacteristic
658C22×C3—24no—
659C22×C3—22no—
660C22×C3—22no—
661C22×C3—21no—
662C22×C3—42no—
663C22×C3—42no—
664C22×C3—41no—
665C22×C3—41no—
666C22×C3—41no—
667C22×C3—41no—
668C22×C3—62no—
669C22×C3—121no—
670C22×C3—121no—
671C22×C3C2×D3×D411yescharacteristic
672C22×C3C2×D3×D411yescharacteristic
673C2×D3—22no—
674C2×D3—32no—
675C2×D3—32no—
676C2×D3—41no—
677C2×D3—41no—
678C2×D3—62no—
679C2×D3—61no—
680C2×D3—61no—
681C2×D3—61no—
682C2×D3—61no—
683C2×D3—121no—
684C2×D3—121no—
685C3×C4—21no—
686C3×C4—21no—
687C3×C4—21no—
688C3×C4—21no—
689C3×C4—22no—
690C3×C4—41no—
691C3×C4—42no—
692C3×C4—41no—
693C3×C4—41no—
694C3×C4—62no—
695C3×C4—121no—
696C3×C4—121no—
697C3×C4#91212yescomplemented
698C3×C4#91612yescomplemented
699C3×C4C22×C4×D311yescharacteristic
700C3×C4C22×C4×D311yescharacteristic
701C3×C4D3×#4111yescharacteristic
702C3×C4D3×#4111yescharacteristic
703Dic3—22no—
704Dic3—32no—
705Dic3—32no—
706Dic3—32no—
707Dic3—32no—
708Dic3—41no—
709Dic3—41no—
710Dic3—62no—
711Dic3—62no—
712Dic3—64no—
713Dic3—61no—
714Dic3—61no—
715Dic3—62no—
716Dic3—62no—
717Dic3—121no—
718Dic3—122no—
719Dic3—121no—
720Dic3—121no—
721C32C4×#13511yescharacteristic, complemented, Sylow
722C23—21no—
723C23—61no—
724C23—91no—
725Q8—32no—
726Q8—61no—
727Q8—92no—
728Q8—181no—
729D4—21no—
730D4—32no—
731D4—61no—
732D4—184no—
733D4—184no—
734D4C4×D3212yes—
735C2×C4—21no—
736C2×C4—42no—
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—181no—
750C2×C4—182no—
751C2×C4—181no—
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—44no—
765C2×C3—42no—
766C2×C3—42no—
767C2×C3—122no—
768C2×C3C4×D3×D411yescharacteristic
769C2×C3C4×D3×D411yescharacteristic
770C2×C3C2×#91211yescharacteristic
771C2×C3C2×#91611yescharacteristic
772C2×C3D3×#13511yescharacteristic
773C2×C3D3×#13511yescharacteristic
774D3—42no—
775D3—62no—
776D3—62no—
777D3—122no—
778C22—22no—
779C22—41no—
780C22—41no—
781C22—62no—
782C22—92no—
783C22—121no—
784C22—121no—
785C22—181no—
786C22—181no—
787C22C2×#381111yescharacteristic
788C4—21no—
789C4—41no—
790C4—62no—
791C4—92no—
792C4—92no—
793C4—121no—
794C4—121no—
795C4—181no—
796C4—182no—
797C4—361no—
798C4#6393612yesdirect product factor
799C4C2×C4×D3211yescharacteristic
800C4#6430611yescharacteristic
801C3—21no—
802C3C4×#91211yescharacteristic, complemented
803C3C4×#91611yescharacteristic, complemented
804C2—42no—
805C2—122no—
806C2—182no—
807C2C4×#381111yescharacteristic
808C2C2×#6393611yescharacteristic
809C2#1059545911yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×#63936C2
cosocleC2×C32×C4C24
hypercenterC4×D4D32
hypocenterC32C4×#135
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C4×#3830C2semidirect
3. C4×#3796C2semidirect
4. C3×C4×#214C2semidirect
5. C3×C4×#213C2semidirect
6. #10591445C2semidirect
7. #10591435C2semidirect
8. #10591424C2semidirect
9. #10590611C2semidirect
10. #10590574C2semidirect
11. #10590482C2semidirect
12. #10590460C2semidirect
13. C4×#3719C2semidirect
14. C4×#3716C2semidirect
15. C4×#3710C2semidirect
34. #63936C4direct (N × H)
75. C4×#214D3semidirect
76. C4×#213D3semidirect
99. #3830C2×C4semidirect
111. #3796C2×C4semidirect
126. C3×#214C2×C4semidirect
127. C3×#213C2×C4semidirect
142. #3719C2×C4semidirect
143. #3716C2×C4semidirect
145. #3710C2×C4semidirect
375. #214C4×D3semidirect
376. #213C4×D3semidirect
443. C32×C4#135semidirect
450. C3⋊Dic3#135semidirect
697. C3×C4#912semidirect
698. C3×C4#916semidirect
721. C32C4×#135semidirect
798. C4#63936direct (N × H)
802. C3C4×#912semidirect
803. C3C4×#916semidirect

Maximal subgroups

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

subgroupindex
C4×#38302
C2×#639362
C4×#37962
C3×C4×#2142
C3×C4×#2132
#105914452
#105914352
#105914242
#105906112
#105905742
#105904822
#105904602
C4×#37192
C4×#37162
C4×#37102
C4×#9163
C4×#9123