Finite Group Databasebeta

← C8×#3796 #11861558

Subgroups — C8×#3796 #11861558

Order 1152.

993 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3796C211yesmaximal, characteristic
2C4×C8×C3⋊D3C211yesmaximal, characteristic, complemented
3C3×C8×D12C211yesmaximal, characteristic, complemented
4C3×C8×Dic6C211yesmaximal, characteristic, complemented
5#10590906C212yesmaximal, complemented
6C8×#626C212yesmaximal, complemented
7#10590656C212yesmaximal, complemented
8D3×C8×Dic3C212yesmaximal, complemented
9#10590329C211yesmaximal, characteristic, complemented
10#10590256C211yesmaximal, characteristic, complemented
11#10590250C211yesmaximal, characteristic, complemented
12C8×#239—31nomaximal
13C8×#237—31nomaximal
14C2×#3796C411yescharacteristic
15C2×C8×C3⋊D3C2211yescharacteristic
16C2×C8×C3⋊D3C2211yescharacteristic
17C42×C3⋊D3C2211yescharacteristic
18C2×C3×D3×C8C2212yes—
19C3×C4×D12C2211yescharacteristic
20C3×C4×Dic6C2211yescharacteristic
21C4×#626C2212yes—
22#63898C411yescharacteristic
23#63881C412yes—
24#63878C412yes—
25C4×D3×Dic3C2212yes—
26#63849C411yescharacteristic
27#63843C411yescharacteristic
28C2×D3×C3⋊C8C2212yes—
29C32×C4×C8C2211yescharacteristic
30C8×C3⋊Dic3C2211yescharacteristic
31C8×C3⋊Dic3C2211yescharacteristic
32C4×C3⋊(C3⋊C8)C2211yescharacteristic
33C3×(C2×D3)⋊C8C2212yes—
34C3×Dic3⋊C8C2212yes—
35C3×C8×Dic3C2212yes—
36C3×C4⋊(C3⋊C8)C2211yescharacteristic
37C3×C4⋊(C3⋊C8)C2211yescharacteristic
38Dic3⋊(C3⋊C8)C2212yes—
39#63557C2212yes—
40(C2×D3)⋊(C3⋊C8)C2212yes—
41#63553C2212yes—
42Dic3×C3⋊C8C2212yes—
43C4×#239—31no—
44C4×#237—31no—
45C3×C8×Q8—31no—
46C3×C8×D4—31no—
47C8×#67—32no—
48C2×C8×Dic3—32no—
49Q8×C3⋊C8—31no—
50D4×C3⋊C8—31no—
51#4834—31no—
52#4834—32no—
53#4833—32no—
54#4833—31no—
55#4833—31no—
56#4830—31no—
57#67⋊C8—32no—
58#4718—32no—
59C8×D12—32no—
60C8×D12D311yescharacteristic, complemented
61C4×D3×C8—32no—
62C4×D3×C8—31no—
63C4×D3×C8—31no—
64C4×D3×C8—61no—
65C8×Dic6D311yescharacteristic, complemented
66C2×C4×C3⋊D3C2×C411yescharacteristic
67C2×C4×C3⋊D3C2×C411yescharacteristic
68C2×C4×C3⋊D3C2311yescharacteristic
69C2×C3×D12C2×C411yescharacteristic
70C2×C3×C4×D3C2312yes—
71C2×C3×Dic6C2×C411yescharacteristic
72C2×#626C2×C412yes—
73C2×D3×Dic3C2×C412yes—
74C2×D3×Dic3C2×C412yes—
75#3796C818yesdirect product factor
76C2×C32×C8C2311yescharacteristic
77C2×C32×C8C2311yescharacteristic
78C32×C42C2311yescharacteristic
79C4×C3⋊Dic3C2×C411yescharacteristic
80C4×C3⋊Dic3C2×C411yescharacteristic
81C4×C3⋊Dic3C2311yescharacteristic
82C2×C3⋊(C3⋊C8)C2311yescharacteristic
83C2×C3⋊(C3⋊C8)C2311yescharacteristic
84C8×C3⋊D3—22no—
85C8×C3⋊D3—22no—
86C3×(C2×D3)⋊C4C2×C412yes—
87C3×C4⋊Dic3C2×C411yescharacteristic
88C3×C4⋊Dic3C2×C411yescharacteristic
89C3×Dic3⋊C4C2×C412yes—
90C3×C4×Dic3C2312yes—
91C2×C3×C3⋊C8C2312yes—
92C2×C3×C3⋊C8C2312yes—
93C3×D3×C8—24no—
94Dic3⋊Dic3C2×C412yes—
95#3722C2×C412yes—
96(C2×D3)⋊Dic3C2×C412yes—
97Dic32C2×C412yes—
98Dic32C2×C412yes—
99D3×C3⋊C8—24no—
100C8×#41—91noSylow
101C2×#239—31no—
102C2×#237—31no—
103C22×C3×C8—32no—
104C3×C4×Q8—31no—
105C3×C4×D4—31no—
106Q8×Dic3—31no—
107D4×Dic3—31no—
108C4×#67—32no—
109C2×C4×Dic3—32no—
110C22×C3⋊C8—32no—
111C2×D3×C8—32no—
112C2×D3×C8—31no—
113C2×D3×C8—31no—
114C2×D3×C8—31no—
115C2×D3×C8—31no—
116C2×D3×C8—61no—
117C2×D3×C8—61no—
118C2×D3×C8C2×D312yes—
119#893—31no—
120#893—32no—
121#892—32no—
122#892—31no—
123#892—31no—
124#887—31no—
125#67⋊C4—32no—
126#877—32no—
127C4×D12—32no—
128C4×D12C2×D311yescharacteristic
129C42×D3—32no—
130C42×D3—31no—
131C42×D3—31no—
132C42×D3—61no—
133C4×Dic6C2×D311yescharacteristic
134C3×C4⋊C8—32no—
135C3×C4⋊C8—31no—
136C3×C4⋊C8—31no—
137C3×C22⋊C8—32no—
138C3×C4×C8—21no—
139C3×C4×C8—32no—
140C3×C4×C8C2×D311yescharacteristic
141C3×C4×C8C2×D311yescharacteristic
142#830—32no—
143(C2×D3)⋊C8—32no—
144(C2×D3)⋊C8—32no—
145(C2×D3)⋊C8—32no—
146(C2×D3)⋊C8C2×D312yes—
147Dic3⋊C8—32no—
148Dic3⋊C8C2×D312yes—
149C8×Dic3—31no—
150C8×Dic3—31no—
151C8×Dic3—31no—
152C8×Dic3—31no—
153C8×Dic3—32no—
154C8×Dic3—32no—
155C8×Dic3—32no—
156C8×Dic3—61no—
157C8×Dic3—61no—
158C8×Dic3C2×D312yes—
159C4⋊(C3⋊C8)—32no—
160C4⋊(C3⋊C8)C2×D311yescharacteristic
161C4⋊(C3⋊C8)C2×D311yescharacteristic
162C4×C3⋊C8—31no—
163C4×C3⋊C8—31no—
164C4×C3⋊C8—32no—
165C4×C3⋊C8—61no—
166C22×C3⋊D3C22×C411yescharacteristic
167C22×C3×D3C22×C412yes—
168C2×C32×C4C22×C411yescharacteristic
169C2×C32×C4C22×C411yescharacteristic
170C2×C32×C4C2411yescharacteristic
171C2×C3⋊Dic3C22×C411yescharacteristic
172C2×C3⋊Dic3C22×C411yescharacteristic
173C2×C3⋊Dic3C22×C411yescharacteristic
174C4×C3⋊D3—21no—
175C4×C3⋊D3—21no—
176C4×C3⋊D3—22no—
177C4×C3⋊D3C2×C814yescomplemented
178C2×C3×Dic3C22×C412yes—
179C2×C3×Dic3C22×C412yes—
180C2×C3×Dic3C22×C412yes—
181C3×D12C2×C814yescomplemented
182C3×C4×D3—22no—
183C3×C4×D3—22no—
184C3×Dic6C2×C814yescomplemented
185#626C2×C818yescomplemented
186D3×Dic3—24no—
187D3×Dic3C2×C818yescomplemented
188C32×C8—21no—
189C32×C8#4112yescomplemented
190C3⋊(C3⋊C8)—21no—
191C3⋊(C3⋊C8)#4112yescomplemented
192C3×C3⋊C8—22no—
193C3×C3⋊C8—22no—
194C4×#41—91no—
195C8×Q8—31no—
196C8×Q8—91no—
197C8×D4—31no—
198C8×D4—92no—
199C8×D4—92no—
200C8×D4—91no—
201#431—92no—
202#431—91no—
203C2×C4×C8—92no—
204C2×C4×C8—91no—
205C2×C3×Q8—31no—
206C2×C3×D4—31no—
207C22×C3×C4—32no—
208C2×#67—32no—
209C22×Dic3—32no—
210C22×Dic3—32no—
211#239—38no—
212#237—38no—
213C2×D12—32no—
214C2×D12C4×D311yescharacteristic
215C2×C4×D3—32no—
216C2×C4×D3—31no—
217C2×C4×D3—31no—
218C2×C4×D3—32no—
219C2×C4×D3—31no—
220C2×C4×D3—31no—
221C2×C4×D3—31no—
222C2×C4×D3—31no—
223C2×C4×D3—61no—
224C2×C4×D3—61no—
225C2×C4×D3—61no—
226C2×C4×D3C22×D312yes—
227C2×Dic6C4×D311yescharacteristic
228C2×C3×C8—21no—
229C2×C3×C8—21no—
230C2×C3×C8—32no—
231C2×C3×C8—32no—
232C2×C3×C8—64no—
233C2×C3×C8C22×D311yescharacteristic
234C2×C3×C8C22×D311yescharacteristic
235C2×C3×C8C22×D311yescharacteristic
236C2×C3×C8C22×D311yescharacteristic
237C3×C4⋊C4—31no—
238C3×C4⋊C4—32no—
239C3×C4⋊C4—31no—
240C3×C22⋊C4—32no—
241C3×C42—21no—
242C3×C42—32no—
243C3×C42C22×D311yescharacteristic
244C3×C42C22×D311yescharacteristic
245#217—32no—
246(C2×D3)⋊C4—32no—
247(C2×D3)⋊C4—32no—
248(C2×D3)⋊C4—32no—
249(C2×D3)⋊C4C4×D312yes—
250C4⋊Dic3—32no—
251C4⋊Dic3C4×D311yescharacteristic
252C4⋊Dic3C4×D311yescharacteristic
253Dic3⋊C4—32no—
254Dic3⋊C4C4×D312yes—
255C4×Dic3—31no—
256C4×Dic3—31no—
257C4×Dic3—31no—
258C4×Dic3—31no—
259C4×Dic3—31no—
260C4×Dic3—31no—
261C4×Dic3—32no—
262C4×Dic3—32no—
263C4×Dic3—32no—
264C4×Dic3—32no—
265C4×Dic3—61no—
266C4×Dic3—61no—
267C4×Dic3—61no—
268C4×Dic3C22×D312yes—
269C2×C3⋊C8—31no—
270C2×C3⋊C8—31no—
271C2×C3⋊C8—31no—
272C2×C3⋊C8—31no—
273C2×C3⋊C8—61no—
274C2×C3⋊C8—61no—
275C2×C3⋊C8—64no—
276C2×C3⋊C8C22×D312yes—
277C2×C3⋊C8C22×D312yes—
278D3×C8—24no—
279D3×C8—62no—
280D3×C8—62no—
281D3×C8—64no—
282D3×C8—64no—
283D3×C8—64no—
284D3×C8—62no—
285D3×C8—62no—
286C22×C32C23×C411yescharacteristic
287C2×C3⋊D3—21no—
288C2×C3⋊D3—21no—
289C2×C3⋊D3C22×C812yes—
290C2×C3×D3—22no—
291C2×C3×D3—22no—
292C2×C3×D3C22×C814yes—
293C32×C4—21no—
294C32×C4C22×C812yes—
295C32×C4C2×#4111yescharacteristic
296C32×C4C2×#4111yescharacteristic
297C3⋊Dic3—21no—
298C3⋊Dic3C22×C812yes—
299C3⋊Dic3#13112yes—
300C3×Dic3—22no—
301C3×Dic3—22no—
302C3×Dic3C22×C814yes—
303C2×#41—91no—
304C22×C8—32no—
305C22×C8—92no—
306C22×C8—91no—
307C22×C8—91no—
308C4×Q8—31no—
309C4×Q8—91no—
310C4×D4—31no—
311C4×D4—92no—
312C4×D4—92no—
313C4×D4—91no—
314#117—92no—
315#117—91no—
316C2×C42—92no—
317C2×C42—91no—
318C4⋊C8—32no—
319C4⋊C8—31no—
320C4⋊C8—31no—
321C4⋊C8—92no—
322C22⋊C8—32no—
323C22⋊C8—92no—
324C22⋊C8—92no—
325C4×C8—32no—
326C4×C8—92no—
327C4×C8—92no—
328C4×C8—91no—
329C4×C8—91no—
330C4×C8—91no—
331C4×C8D3211yescharacteristic
332C23×C3—32no—
333C22×D3—31no—
334C22×D3—31no—
335C22×D3—61no—
336C22×D3C2×C4×D312yes—
337C3×Q8—34no—
338C3×D4—34no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—32no—
343C2×C3×C4—32no—
344C2×C3×C4—32no—
345C2×C3×C4—62no—
346C2×C3×C4—62no—
347C2×C3×C4C2×C4×D311yescharacteristic
348C2×C3×C4C2×C4×D311yescharacteristic
349C2×C3×C4C2×C4×D311yescharacteristic
350C2×C3×C4C2×C4×D311yescharacteristic
351C2×C3×C4C23×D311yescharacteristic
352C2×C3×C4C23×D311yescharacteristic
353#67—38no—
354C2×Dic3—31no—
355C2×Dic3—31no—
356C2×Dic3—31no—
357C2×Dic3—31no—
358C2×Dic3—38no—
359C2×Dic3—31no—
360C2×Dic3—31no—
361C2×Dic3—61no—
362C2×Dic3—61no—
363C2×Dic3—61no—
364C2×Dic3—64no—
365C2×Dic3C2×C4×D312yes—
366C2×Dic3C2×C4×D312yes—
367C2×Dic3C2×C4×D312yes—
368D12—38no—
369D12D3×C814yescomplemented
370C4×D3—22no—
371C4×D3—22no—
372C4×D3—38no—
373C4×D3—34no—
374C4×D3—34no—
375C4×D3—64no—
376C4×D3—62no—
377C4×D3—62no—
378C4×D3—64no—
379C4×D3—62no—
380C4×D3—62no—
381C4×D3—64no—
382C4×D3—61no—
383C4×D3—61no—
384C4×D3—61no—
385C4×D3—61no—
386Dic6D3×C814yescomplemented
387C3×C8—22no—
388C3×C8—21no—
389C3×C8—21no—
390C3×C8—22no—
391C3×C8—62no—
392C3×C8—62no—
393C3×C8#23712yescomplemented
394C3×C8#23912yescomplemented
395C3⋊C8—22no—
396C3⋊C8—22no—
397C3⋊C8—32no—
398C3⋊C8—32no—
399C3⋊C8—62no—
400C3⋊C8—62no—
401C3⋊C8—61no—
402C3⋊C8—61no—
403C2×C32C4×#4111yescharacteristic
404C2×C32C23×C811yescharacteristic
405C2×C32C2×#13111yescharacteristic
406C3⋊D3—22no—
407C3×D3—24no—
408#41—98no—
409C2×Q8—31no—
410C2×D4—31no—
411C2×D4—92no—
412C22×C4—32no—
413C22×C4—92no—
414C22×C4—92no—
415C22×C4—91no—
416C22×C4—91no—
417C22×C4—91no—
418C2×C8—32no—
419C2×C8—32no—
420C2×C8—64no—
421C2×C8—91no—
422C2×C8—91no—
423C2×C8—182no—
424C2×C8—184no—
425C2×C8—182no—
426C2×C8C2×D3211yescharacteristic
427C2×C8C2×D3211yescharacteristic
428C4⋊C4—31no—
429C4⋊C4—32no—
430C4⋊C4—31no—
431C4⋊C4—92no—
432C22⋊C4—32no—
433C22⋊C4—92no—
434C22⋊C4—92no—
435C42—32no—
436C42—92no—
437C42—92no—
438C42—91no—
439C42—91no—
440C42—91no—
441C42C2×D3211yescharacteristic
442C22×C3—21no—
443C22×C3—34no—
444C22×C3—62no—
445C22×C3—62no—
446C22×C3C22×C4×D311yescharacteristic
447C22×C3C22×C4×D311yescharacteristic
448C2×D3—22no—
449C2×D3—22no—
450C2×D3—32no—
451C2×D3—32no—
452C2×D3—62no—
453C2×D3—62no—
454C2×D3—62no—
455C2×D3—61no—
456C2×D3—61no—
457C2×D3—61no—
458C2×D3—61no—
459C2×D3C2×D3×C814yes—
460C3×C4—22no—
461C3×C4—21no—
462C3×C4—21no—
463C3×C4—21no—
464C3×C4—22no—
465C3×C4—21no—
466C3×C4—34no—
467C3×C4—62no—
468C3×C4—62no—
469C3×C4C2×D3×C812yes—
470C3×C4C2×D3×C812yes—
471C3×C4C2×#23711yescharacteristic
472C3×C4C2×#23911yescharacteristic
473C3×C4D3×#4111yescharacteristic
474C3×C4D3×#4111yescharacteristic
475Dic3—22no—
476Dic3—22no—
477Dic3—32no—
478Dic3—32no—
479Dic3—32no—
480Dic3—32no—
481Dic3—62no—
482Dic3—62no—
483Dic3—62no—
484Dic3—61no—
485Dic3—61no—
486Dic3C2×D3×C814yes—
487C32C8×#4111yescharacteristic, complemented, Sylow
488C23—32no—
489C23—91no—
490Q8—34no—
491D4—34no—
492D4—98no—
493C2×C4—32no—
494C2×C4—32no—
495C2×C4—32no—
496C2×C4—62no—
497C2×C4—62no—
498C2×C4—98no—
499C2×C4—91no—
500C2×C4—91no—
501C2×C4—94no—
502C2×C4—91no—
503C2×C4—182no—
504C2×C4—184no—
505C2×C4—181no—
506C2×C4—181no—
507C2×C4C4×D3211yescharacteristic
508C2×C4C4×D3211yescharacteristic
509C2×C4C22×D3211yescharacteristic
510C8—21no—
511C8—62no—
512C8—62no—
513C8—92no—
514C8—181no—
515C8#379612yesdirect product factor
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—64no—
520C2×C3C4×#23711yescharacteristic
521C2×C3C4×#23911yescharacteristic
522C2×C3C22×D3×C811yescharacteristic
523C2×C3C22×D3×C811yescharacteristic
524C2×C3D3×#13111yescharacteristic
525C2×C3D3×#13111yescharacteristic
526D3—24no—
527D3—64no—
528D3—62no—
529D3—62no—
530C22—34no—
531C22—62no—
532C22—62no—
533C22—92no—
534C22—181no—
535C22—181no—
536C22C2×C4×D3211yescharacteristic
537C4—21no—
538C4—34no—
539C4—62no—
540C4—62no—
541C4—92no—
542C4—92no—
543C4—181no—
544C4D32×C812yes—
545C4C2×#379611yescharacteristic
546C4#6430611yescharacteristic
547C3—21no—
548C3C8×#23711yescharacteristic, complemented
549C3C8×#23911yescharacteristic, complemented
550C2—64no—
551C2—182no—
552C2C4×#379611yescharacteristic
553C2C2×D32×C811yescharacteristic
554C2#1059466911yescharacteristic
subgroupG/H
centerC2×C8C2×D32
commutatorC2×C32C23×C8
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C23×C4
prime radicalC2×#3796C4
cosocleC2×C32×C4C24
hypercenterC4×C8D32
hypocenterC32C8×#41
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C8 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. C4×C8×C3⋊D3C2semidirect
3. C3×C8×D12C2semidirect
4. C3×C8×Dic6C2semidirect
5. #10590906C2semidirect
6. C8×#626C2semidirect
7. #10590656C2semidirect
8. D3×C8×Dic3C2semidirect
9. #10590329C2semidirect
10. #10590256C2semidirect
11. #10590250C2semidirect
60. C8×D12D3semidirect
65. C8×Dic6D3semidirect
75. #3796C8direct (N × H)
177. C4×C3⋊D3C2×C8semidirect
181. C3×D12C2×C8semidirect
184. C3×Dic6C2×C8semidirect
185. #626C2×C8semidirect
187. D3×Dic3C2×C8semidirect
189. C32×C8#41semidirect
191. C3⋊(C3⋊C8)#41semidirect
369. D12D3×C8semidirect
386. Dic6D3×C8semidirect
393. C3×C8#237semidirect
394. C3×C8#239semidirect
487. C32C8×#41semidirect
515. C8#3796direct (N × H)
548. C3C8×#237semidirect
549. C3C8×#239semidirect

Maximal subgroups

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

subgroupindex
C4×#37962
C4×C8×C3⋊D32
C3×C8×D122
C3×C8×Dic62
#105909062
C8×#6262
#105906562
D3×C8×Dic32
#105903292
#105902562
#105902502
C8×#2393
C8×#2373