Finite Group Databasebeta

← C8×#3805 #11861556

Subgroups — C8×#3805 #11861556

Order 1152.

993 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3805C211yesmaximal, characteristic
2C2×C8×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C3×C8×#67C212yesmaximal, complemented
4#67⋊(C3⋊C8)C212yesmaximal, complemented
5#10591061C211yesmaximal, characteristic, complemented
6C8×#627C211yesmaximal, characteristic, complemented
7#10590718C211yesmaximal, characteristic, complemented
8C8×#625C211yesmaximal, characteristic, complemented
9#10590656C212yesmaximal, complemented
10D3×C8×Dic3C212yesmaximal, complemented
11#10590645C211yesmaximal, characteristic, complemented
12C8×#237—32nomaximal
13C2×#3805C411yescharacteristic
14C22×C32×C8C2211yescharacteristic
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C3×C4×#67C2212yes—
18C2×C3×D3×C8C2212yes—
19#67⋊Dic3C412yes—
20#63957C411yescharacteristic
21C4×#627C2211yescharacteristic
22#63902C411yescharacteristic
23C4×#625C2211yescharacteristic
24#63878C412yes—
25C4×D3×Dic3C2212yes—
26#63838C411yescharacteristic
27C2×D3×C3⋊C8C2212yes—
28C8×C3⋊Dic3C2211yescharacteristic
29C8×C3⋊Dic3C2211yescharacteristic
30C8×C3⋊Dic3C2211yescharacteristic
31C8×C3⋊Dic3C2211yescharacteristic
32C3×#830C2212yes—
33C3×(C2×D3)⋊C8C2212yes—
34C3×Dic3⋊C8C2212yes—
35C3×C8×Dic3C2212yes—
36#63572C2211yescharacteristic
37#63572C2211yescharacteristic
38Dic3⋊(C3⋊C8)C2212yes—
39(C2×D3)⋊(C3⋊C8)C2212yes—
40#63553C2212yes—
41Dic3×C3⋊C8C2212yes—
42C4×#237—32no—
43C3×C8×D4—32no—
44C8×#67—32no—
45C8×#67D312yescomplemented
46C2×C8×Dic3—32no—
47C2×C8×Dic3—32no—
48C2×C8×Dic3—61no—
49D4×C3⋊C8—32no—
50#4833—32no—
51#4830—32no—
52#67⋊C8—32no—
53#67⋊C8—32no—
54#4718—32no—
55#4718—32no—
56C4×D3×C8—32no—
57C8×Dic6—32no—
58C22×C32×C4C2311yescharacteristic
59C22×C3⋊Dic3C2×C411yescharacteristic
60C22×C3⋊Dic3C2×C411yescharacteristic
61C2×C3×#67C2×C412yes—
62C2×C3×C4×D3C2312yes—
63C2×#627C2×C411yescharacteristic
64C2×#625C2×C411yescharacteristic
65#3805C818yesdirect product factor
66C2×D3×Dic3C2×C412yes—
67C2×D3×Dic3C2×C412yes—
68C2×C32×C8—22no—
69C2×C32×C8C2311yescharacteristic
70C2×C32×C8C2311yescharacteristic
71C4×C3⋊Dic3C2×C411yescharacteristic
72C4×C3⋊Dic3C2×C411yescharacteristic
73C4×C3⋊Dic3C2311yescharacteristic
74C4×C3⋊Dic3C2311yescharacteristic
75C2×C3⋊(C3⋊C8)—22no—
76C2×C3⋊(C3⋊C8)C2311yescharacteristic
77C2×C3⋊(C3⋊C8)C2311yescharacteristic
78C3×#217C2×C412yes—
79C3×(C2×D3)⋊C4C2×C412yes—
80C3×Dic3⋊C4C2×C412yes—
81C3×C4×Dic3C2312yes—
82C2×C3×C3⋊C8C2312yes—
83C2×C3×C3⋊C8C2312yes—
84C3×D3×C8—24no—
85#3724C2×C411yescharacteristic
86#3724C2×C411yescharacteristic
87Dic3⋊Dic3C2×C412yes—
88(C2×D3)⋊Dic3C2×C412yes—
89Dic32C2×C412yes—
90Dic32C2×C412yes—
91D3×C3⋊C8—24no—
92C8×#41—91noSylow
93C2×#237—32no—
94C22×C3×C8—21no—
95C22×C3×C8—32no—
96C22×C3×C8C2×D312yes—
97C3×C4×D4—32no—
98D4×Dic3—32no—
99C4×#67—32no—
100C4×#67C2×D312yes—
101C2×C4×Dic3—32no—
102C2×C4×Dic3—32no—
103C2×C4×Dic3—61no—
104C22×C3⋊C8—32no—
105C22×C3⋊C8—32no—
106C22×C3⋊C8—61no—
107C2×D3×C8—32no—
108C2×D3×C8C2×D312yes—
109#892—32no—
110#887—32no—
111#67⋊C4—32no—
112#67⋊C4—32no—
113#877—32no—
114#877—32no—
115C42×D3—32no—
116C4×Dic6—32no—
117C3×C4⋊C8—32no—
118C3×C22⋊C8—32no—
119C3×C22⋊C8—32no—
120C3×C4×C8—32no—
121#830—32no—
122#830C2×D312yes—
123(C2×D3)⋊C8—32no—
124(C2×D3)⋊C8C2×D312yes—
125Dic3⋊C8—32no—
126Dic3⋊C8—32no—
127Dic3⋊C8—32no—
128Dic3⋊C8C2×D312yes—
129C8×Dic3—32no—
130C8×Dic3—32no—
131C8×Dic3—32no—
132C8×Dic3—32no—
133C8×Dic3—32no—
134C8×Dic3—32no—
135C8×Dic3—32no—
136C8×Dic3—61no—
137C8×Dic3—61no—
138C8×Dic3—61no—
139C8×Dic3—61no—
140C8×Dic3C2×D312yes—
141C4⋊(C3⋊C8)—32no—
142C4×C3⋊C8—32no—
143C23×C32C22×C411yescharacteristic
144C22×C3×D3C22×C412yes—
145C2×C32×C4—21no—
146C2×C32×C4—21no—
147C2×C32×C4C22×C411yescharacteristic
148C2×C32×C4C2411yescharacteristic
149C2×C3⋊Dic3—22no—
150C2×C3⋊Dic3C2×C814yescomplemented
151C2×C3⋊Dic3C22×C411yescharacteristic
152C2×C3⋊Dic3C22×C411yescharacteristic
153C2×C3⋊Dic3C22×C411yescharacteristic
154C2×C3⋊Dic3C22×C411yescharacteristic
155C3×#67C2×C818yescomplemented
156C2×C3×Dic3C22×C412yes—
157C2×C3×Dic3C22×C412yes—
158C2×C3×Dic3C22×C412yes—
159C3×C4×D3—22no—
160C3×C4×D3—22no—
161#627C2×C814yescomplemented
162#625C2×C814yescomplemented
163D3×Dic3—24no—
164D3×Dic3C2×C818yescomplemented
165C32×C8—21no—
166C32×C8#4112yescomplemented
167C3⋊(C3⋊C8)—21no—
168C3⋊(C3⋊C8)#4112yescomplemented
169C3×C3⋊C8—22no—
170C3×C3⋊C8—22no—
171C4×#41—91no—
172C8×Q8—91no—
173C8×Q8—91no—
174C8×D4—32no—
175C8×D4—91no—
176C8×D4—92no—
177C8×D4—91no—
178#431—91no—
179#431—92no—
180C2×C4×C8—92no—
181C2×C4×C8—91no—
182C2×C3×D4—32no—
183C22×C3×C4—21no—
184C22×C3×C4—32no—
185C22×C3×C4C22×D312yes—
186C2×#67—32no—
187C2×#67C4×D312yes—
188C22×Dic3—32no—
189C22×Dic3—32no—
190C22×Dic3—32no—
191C22×Dic3—32no—
192C22×Dic3—61no—
193C22×Dic3—61no—
194#237—316no—
195C2×C4×D3—32no—
196C2×C4×D3—32no—
197C2×C4×D3C22×D312yes—
198C2×Dic6—32no—
199C2×C3×C8—24no—
200C2×C3×C8—24no—
201C2×C3×C8—21no—
202C2×C3×C8—21no—
203C2×C3×C8—32no—
204C2×C3×C8—32no—
205C2×C3×C8—64no—
206C2×C3×C8C22×D312yes—
207C2×C3×C8C22×D312yes—
208C3×C4⋊C4—32no—
209C3×C22⋊C4—32no—
210C3×C22⋊C4—32no—
211C3×C42—32no—
212#217—32no—
213#217C4×D312yes—
214(C2×D3)⋊C4—32no—
215(C2×D3)⋊C4C4×D312yes—
216C4⋊Dic3—32no—
217Dic3⋊C4—32no—
218Dic3⋊C4—32no—
219Dic3⋊C4—32no—
220Dic3⋊C4C4×D312yes—
221C4×Dic3—32no—
222C4×Dic3—32no—
223C4×Dic3—32no—
224C4×Dic3—32no—
225C4×Dic3—32no—
226C4×Dic3—32no—
227C4×Dic3—32no—
228C4×Dic3—32no—
229C4×Dic3—61no—
230C4×Dic3—61no—
231C4×Dic3—61no—
232C4×Dic3—61no—
233C4×Dic3C22×D312yes—
234C2×C3⋊C8—32no—
235C2×C3⋊C8—32no—
236C2×C3⋊C8—61no—
237C2×C3⋊C8—61no—
238C2×C3⋊C8—64no—
239C2×C3⋊C8—64no—
240C2×C3⋊C8—64no—
241C2×C3⋊C8C22×D312yes—
242C2×C3⋊C8C22×D312yes—
243D3×C8—24no—
244D3×C8—64no—
245C22×C32—21no—
246C22×C32—21no—
247C22×C32C22×C812yes—
248C22×C32C23×C411yescharacteristic
249C2×C3×D3—22no—
250C2×C3×D3—22no—
251C2×C3×D3C22×C814yes—
252C32×C4—21no—
253C32×C4C2×#4111yescharacteristic
254C32×C4C2×#4111yescharacteristic
255C3⋊Dic3—21no—
256C3⋊Dic3C22×C812yes—
257C3⋊Dic3C22×C812yes—
258C3⋊Dic3#13112yes—
259C3×Dic3—22no—
260C3×Dic3—22no—
261C3×Dic3C22×C814yes—
262C2×#41—91no—
263C22×C8—32no—
264C22×C8—92no—
265C22×C8—91no—
266C22×C8D3211yescharacteristic
267C4×Q8—91no—
268C4×Q8—91no—
269C4×D4—32no—
270C4×D4—91no—
271C4×D4—92no—
272C4×D4—91no—
273#117—91no—
274#117—92no—
275C2×C42—92no—
276C2×C42—91no—
277C4⋊C8—32no—
278C4⋊C8—92no—
279C4⋊C8—91no—
280C4⋊C8—91no—
281C22⋊C8—32no—
282C22⋊C8—32no—
283C22⋊C8—92no—
284C4×C8—32no—
285C4×C8—92no—
286C4×C8—92no—
287C4×C8—91no—
288C4×C8—91no—
289C4×C8—91no—
290C4×C8—91no—
291C23×C3—21no—
292C23×C3—32no—
293C23×C3C2×C4×D312yes—
294C22×D3C2×C4×D312yes—
295C3×D4—38no—
296C2×C3×C4—22no—
297C2×C3×C4—22no—
298C2×C3×C4—22no—
299C2×C3×C4—22no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—32no—
303C2×C3×C4—32no—
304C2×C3×C4—32no—
305C2×C3×C4—62no—
306C2×C3×C4—62no—
307C2×C3×C4C2×C4×D312yes—
308C2×C3×C4C23×D312yes—
309#67—38no—
310#67D3×C818yescomplemented
311C2×Dic3—38no—
312C2×Dic3—32no—
313C2×Dic3—32no—
314C2×Dic3—32no—
315C2×Dic3—38no—
316C2×Dic3—32no—
317C2×Dic3—64no—
318C2×Dic3—61no—
319C2×Dic3—61no—
320C2×Dic3—61no—
321C2×Dic3—61no—
322C2×Dic3—64no—
323C2×Dic3—64no—
324C2×Dic3—64no—
325C2×Dic3C2×C4×D312yes—
326C2×Dic3C2×C4×D312yes—
327C2×Dic3C2×C4×D312yes—
328C4×D3—22no—
329C4×D3—22no—
330C4×D3—38no—
331C4×D3—64no—
332Dic6—38no—
333C3×C8—22no—
334C3×C8—22no—
335C3×C8—22no—
336C3×C8—62no—
337C3×C8—62no—
338C3×C8#23714yescomplemented
339C3⋊C8—22no—
340C3⋊C8—22no—
341C3⋊C8—34no—
342C3⋊C8—62no—
343C3⋊C8—62no—
344C3⋊C8—62no—
345C2×C32—22no—
346C2×C32C4×#4111yescharacteristic
347C2×C32C23×C811yescharacteristic
348C2×C32C2×#13111yescharacteristic
349C3×D3—24no—
350#41—98no—
351C2×Q8—91no—
352C2×D4—32no—
353C2×D4—91no—
354C22×C4—32no—
355C22×C4—92no—
356C22×C4—92no—
357C22×C4—91no—
358C22×C4—91no—
359C22×C4C2×D3211yescharacteristic
360C2×C8—22no—
361C2×C8—32no—
362C2×C8—32no—
363C2×C8—64no—
364C2×C8—91no—
365C2×C8—91no—
366C2×C8—184no—
367C2×C8—182no—
368C2×C8C2×D3211yescharacteristic
369C2×C8C2×D3211yescharacteristic
370C4⋊C4—32no—
371C4⋊C4—91no—
372C4⋊C4—91no—
373C4⋊C4—92no—
374C22⋊C4—32no—
375C22⋊C4—32no—
376C22⋊C4—92no—
377C42—32no—
378C42—92no—
379C42—92no—
380C42—91no—
381C42—91no—
382C42—91no—
383C42—91no—
384C22×C3—22no—
385C22×C3—22no—
386C22×C3—22no—
387C22×C3—22no—
388C22×C3—22no—
389C22×C3—21no—
390C22×C3—34no—
391C22×C3—62no—
392C22×C3—62no—
393C22×C3C2×D3×C814yes—
394C22×C3C22×C4×D312yes—
395C2×D3—22no—
396C2×D3—22no—
397C2×D3C2×D3×C814yes—
398C3×C4—22no—
399C3×C4—22no—
400C3×C4—21no—
401C3×C4—21no—
402C3×C4—34no—
403C3×C4—62no—
404C3×C4—62no—
405C3×C4C2×#23712yes—
406C3×C4D3×#4112yes—
407Dic3—22no—
408Dic3—22no—
409Dic3—34no—
410Dic3—34no—
411Dic3—34no—
412Dic3—62no—
413Dic3—62no—
414Dic3—62no—
415Dic3—62no—
416Dic3—62no—
417Dic3C2×D3×C814yes—
418C32C8×#4111yescharacteristic, complemented, Sylow
419C23—32no—
420C23C4×D3211yescharacteristic
421Q8—94no—
422D4—38no—
423D4—94no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—32no—
427C2×C4—32no—
428C2×C4—32no—
429C2×C4—62no—
430C2×C4—62no—
431C2×C4—98no—
432C2×C4—94no—
433C2×C4—91no—
434C2×C4—91no—
435C2×C4—91no—
436C2×C4—91no—
437C2×C4—184no—
438C2×C4—182no—
439C2×C4C4×D3211yescharacteristic
440C2×C4C22×D3211yescharacteristic
441C8—21no—
442C8—62no—
443C8—62no—
444C8—92no—
445C8—181no—
446C8#380512yesdirect product factor
447C2×C3—24no—
448C2×C3—24no—
449C2×C3—21no—
450C2×C3—21no—
451C2×C3—21no—
452C2×C3—64no—
453C2×C3C4×#23712yes—
454C2×C3C22×D3×C812yes—
455C2×C3D3×#13112yes—
456D3—24no—
457C22—21no—
458C22—21no—
459C22—34no—
460C22—62no—
461C22—62no—
462C22D32×C812yes—
463C22C2×C4×D3211yescharacteristic
464C4—21no—
465C4—34no—
466C4—62no—
467C4—62no—
468C4—92no—
469C4—92no—
470C4—92no—
471C4—181no—
472C4#6430611yescharacteristic
473C4C2×#380511yescharacteristic
474C3—21no—
475C3C8×#23712yescomplemented
476C2—22no—
477C2—64no—
478C2C2×D32×C811yescharacteristic
479C2#1059466911yescharacteristic
480C2C4×#380511yescharacteristic
subgroupG/H
centerC2×C8C2×D32
commutatorC2×C32C23×C8
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C23×C4
prime radicalC2×#3805C4
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32C8×#41
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C8 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C2×C8×C3⋊Dic3C2semidirect
3. C3×C8×#67C2semidirect
4. #67⋊(C3⋊C8)C2semidirect
5. #10591061C2semidirect
6. C8×#627C2semidirect
7. #10590718C2semidirect
8. C8×#625C2semidirect
9. #10590656C2semidirect
10. D3×C8×Dic3C2semidirect
11. #10590645C2semidirect
45. C8×#67D3semidirect
65. #3805C8direct (N × H)
150. C2×C3⋊Dic3C2×C8semidirect
155. C3×#67C2×C8semidirect
161. #627C2×C8semidirect
162. #625C2×C8semidirect
164. D3×Dic3C2×C8semidirect
166. C32×C8#41semidirect
168. C3⋊(C3⋊C8)#41semidirect
310. #67D3×C8semidirect
338. C3×C8#237semidirect
418. C32C8×#41semidirect
446. C8#3805direct (N × H)
475. C3C8×#237semidirect

Maximal subgroups

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

subgroupindex
C4×#38052
C2×C8×C3⋊Dic32
C3×C8×#672
#67⋊(C3⋊C8)2
#105910612
C8×#6272
#105907182
C8×#6252
#105906562
D3×C8×Dic32
#105906452
C8×#2373