Finite Group Databasebeta

← C2×#10596049 #11900814

Subgroups — C2×#10596049 #11900814

Order 1152.

3504 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×Q8C211yesmaximal, characteristic, complemented
2C2×#64155C211yesmaximal, characteristic
3C2×#64153C211yesmaximal, characteristic, complemented
4#10596049C2116yesmaximal, direct product factor
5C2×#64106C211yesmaximal, characteristic
6C2×#64105C212yesmaximal
7C2×#64098C212yesmaximal, complemented
8C2×#64097C211yesmaximal, characteristic, complemented
9C2×#64081C212yesmaximal
10C2×C42×C3⋊D3C211yesmaximal, characteristic
11C2×C4×#634C212yesmaximal, complemented
12C2×C4×#634C211yesmaximal, characteristic, complemented
13C2×#5578—34nomaximal
14C22×C32×Q8C2211yescharacteristic
15C22×C4×C3⋊D3C2211yescharacteristic
16C22×C4×C3⋊D3C2211yescharacteristic
17C22×C4×C3⋊D3C2211yescharacteristic
18C22×#634C2212yes—
19C22×#634C2211yescharacteristic
20C32×C4×Q8C2218yescomplemented
21C2×C32×C4⋊C4C2211yescharacteristic
22C2×C32×C4⋊C4C2212yes—
23C2×C32×C42C2211yescharacteristic
24C2×C32×C42C2212yes—
25#64155C2218yes—
26#64153C2218yescomplemented
27C2×#3752C2212yes—
28C2×#3752C2212yes—
29C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
30C2×C4⋊(C3⋊Dic3)C2212yes—
31C2×#3750C2212yes—
32C2×#3750C2212yes—
33C2×#3750C2212yes—
34C2×#3750C2212yes—
35C2×#3750C2212yes—
36C2×C4×C3⋊Dic3C2211yescharacteristic
37C2×C4×C3⋊Dic3C2212yes—
38C2×C4×C3⋊Dic3C2211yescharacteristic
39C2×C4×C3⋊Dic3C2211yescharacteristic
40#64106C2218yes—
41#64105C22116yes—
42#64098C22116yescomplemented
43#64097C2218yescomplemented
44#64081C22116yes—
45C42×C3⋊D3C2218yes—
46C4×#634C22116yescomplemented
47C4×#634C2218yescomplemented
48C2×C3×C4×Q8D314yescomplemented
49C2×#946—34no—
50C2×#944—34no—
51#5578—364no—
52C2×#897—34no—
53C2×#896—38no—
54C2×#889—38no—
55C2×#888—34no—
56C2×#872—38no—
57C2×C42×D3—34no—
58C2×C4×Dic6—38no—
59C2×C4×Dic6—34no—
60C23×C3⋊D3C2311yescharacteristic
61C2×C32×Q8—24no—
62C2×C32×Q8C2314yes—
63C22×C32×C4C2312yes—
64C22×C32×C4C2311yescharacteristic
65C22×C32×C4C2312yes—
66C22×C32×C4C2311yescharacteristic
67C22×C32×C4C2311yescharacteristic
68C22×C3⋊Dic3C2312yes—
69C22×C3⋊Dic3C2312yes—
70C22×C3⋊Dic3C2311yescharacteristic
71C22×C3⋊Dic3C2311yescharacteristic
72C22×C3⋊Dic3C2311yescharacteristic
73C2×C4×C3⋊D3—24no—
74C2×C4×C3⋊D3—24no—
75C2×C4×C3⋊D3Q818yescomplemented
76C2×C4×C3⋊D3C2314yes—
77C2×C4×C3⋊D3C2314yes—
78C2×C4×C3⋊D3C2314yes—
79C2×#634—24no—
80C2×#634—28no—
81C2×#634C2318yes—
82C2×#634C2314yes—
83C32×C4⋊C4C2314yes—
84C32×C4⋊C4C2318yes—
85C32×C42C2314yes—
86C32×C42C2318yes—
87#3752C2318yes—
88#3752C2318yes—
89C4⋊(C3⋊Dic3)C2314yes—
90C4⋊(C3⋊Dic3)C2318yes—
91#3750C2318yes—
92#3750C2318yes—
93#3750C2318yes—
94#3750C2318yes—
95#3750C2318yes—
96C4×C3⋊Dic3C2314yes—
97C4×C3⋊Dic3C2318yes—
98C4×C3⋊Dic3C2314yes—
99C4×C3⋊Dic3C2314yes—
100C2×#533—91noSylow
101C22×C3×Q8C2×D314yes—
102C22×C4×D3—34no—
103C22×C4×D3—34no—
104C22×C4×D3—34no—
105C22×Dic6—38no—
106C22×Dic6—34no—
107C3×C4×Q8C2×D3132yescomplemented
108C2×C3×C4⋊C4C2×D314yes—
109C2×C3×C4⋊C4C2×D318yes—
110C2×C3×C42C2×D314yes—
111C2×C3×C42C2×D318yes—
112#946—332no—
113#944—332no—
114C2×(C2×D3)⋊C4—38no—
115C2×(C2×D3)⋊C4—38no—
116C2×C4⋊Dic3—34no—
117C2×C4⋊Dic3—38no—
118C2×Dic3⋊C4—38no—
119C2×Dic3⋊C4—38no—
120C2×Dic3⋊C4—38no—
121C2×Dic3⋊C4—38no—
122C2×Dic3⋊C4—38no—
123C2×C4×Dic3—34no—
124C2×C4×Dic3—38no—
125C2×C4×Dic3—34no—
126C2×C4×Dic3—34no—
127#897—332no—
128#896—364no—
129#889—364no—
130#888—332no—
131#872—364no—
132C42×D3—332no—
133C4×Dic6—364no—
134C4×Dic6—332no—
135C23×C32C2411yescharacteristic
136C22×C3⋊D3—22no—
137C22×C3⋊D3—22no—
138C22×C3⋊D3C2×Q814yes—
139C22×C3⋊D3C2412yes—
140C32×Q8—28no—
141C2×C32×C4—24no—
142C2×C32×C4—22no—
143C2×C32×C4—24no—
144C2×C32×C4C2×Q814yes—
145C2×C32×C4#4114yes—
146C2×C32×C4C2412yes—
147C2×C32×C4C2414yes—
148C2×C32×C4C2414yes—
149C2×C32×C4C2412yes—
150C2×C32×C4C2412yes—
151C2×C3⋊Dic3—24no—
152C2×C3⋊Dic3—24no—
153C2×C3⋊Dic3—22no—
154C2×C3⋊Dic3C2×Q814yes—
155C2×C3⋊Dic3#4114yes—
156C2×C3⋊Dic3C2412yes—
157C2×C3⋊Dic3C2414yes—
158C2×C3⋊Dic3C2414yes—
159C2×C3⋊Dic3C2412yes—
160C2×C3⋊Dic3C2412yes—
161C4×C3⋊D3—28no—
162C4×C3⋊D3—28no—
163C4×C3⋊D3C2×Q8116yescomplemented
164#634—28no—
165#634—216no—
166#533—916no—
167C2×C4⋊Q8—91no—
168C2×C4⋊Q8—91no—
169C2×#125—92no—
170C2×C22⋊Q8—91no—
171C2×C22⋊Q8—92no—
172C2×C22⋊Q8—91no—
173C2×C4×Q8—91no—
174C2×C4×Q8—92no—
175C2×C4×Q8C3⋊D311yescharacteristic, complemented
176C2×#117—92no—
177C22×C42—91no—
178C23×D3—34no—
179C2×C3×Q8—216no—
180C2×C3×Q8C22×D3116yes—
181C22×C3×C4C22×D314yes—
182C22×C3×C4C22×D318yes—
183C22×C3×C4C22×D318yes—
184C22×C3×C4C22×D314yes—
185C22×C3×C4C22×D314yes—
186C22×Dic3—34no—
187C22×Dic3—34no—
188C22×Dic3—34no—
189C22×Dic3—38no—
190C22×Dic3—38no—
191C2×C4×D3—332no—
192C2×C4×D3—316no—
193C2×C4×D3—316no—
194C2×C4×D3—316no—
195C2×C4×D3—616no—
196C2×C4×D3—616no—
197C2×Dic6—332no—
198C2×Dic6—316no—
199C2×Dic6—632no—
200C2×Dic6—616no—
201C3×C4⋊C4C22×D3116yes—
202C3×C4⋊C4C22×D3132yes—
203C3×C42C22×D3116yes—
204C3×C42C22×D3132yes—
205(C2×D3)⋊C4—332no—
206(C2×D3)⋊C4—332no—
207C4⋊Dic3—316no—
208C4⋊Dic3—332no—
209Dic3⋊C4—332no—
210Dic3⋊C4—332no—
211Dic3⋊C4—332no—
212Dic3⋊C4—332no—
213Dic3⋊C4—332no—
214C4×Dic3—316no—
215C4×Dic3—332no—
216C4×Dic3—316no—
217C4×Dic3—316no—
218C22×C32C22×Q812yes—
219C22×C32C2×#4112yes—
220C22×C32C2×#4112yes—
221C22×C32C2511yescharacteristic
222C2×C3⋊D3—28no—
223C2×C3⋊D3—22no—
224C2×C3⋊D3—22no—
225C2×C3⋊D3C22×Q814yes—
226C32×C4—24no—
227C32×C4—22no—
228C32×C4—24no—
229C32×C4C22×Q814yes—
230C32×C4C2×#4114yes—
231C3⋊Dic3—24no—
232C3⋊Dic3—24no—
233C3⋊Dic3—22no—
234C3⋊Dic3C22×Q814yes—
235C3⋊Dic3C2×#4114yes—
236C22×Q8—92no—
237C22×Q8—91no—
238C22×Q8C2×C3⋊D311yescharacteristic
239C23×C4—91no—
240C23×C4—91no—
241C23×C4—91no—
242C4⋊Q8—98no—
243C4⋊Q8—98no—
244#125—916no—
245C22⋊Q8—98no—
246C22⋊Q8—916no—
247C22⋊Q8—98no—
248C4×Q8—916no—
249C4×Q8—98no—
250C4×Q8C2×C3⋊D318yescomplemented
251#117—916no—
252C2×C4⋊C4—92no—
253C2×C4⋊C4—92no—
254C2×C4⋊C4—92no—
255C2×C4⋊C4—92no—
256C2×C4⋊C4—92no—
257C2×C4⋊C4—92no—
258C2×C4⋊C4—91no—
259C2×C4⋊C4C2×C3⋊D312yes—
260C2×C4⋊C4C2×C3⋊D311yescharacteristic
261C2×C22⋊C4—92no—
262C2×C22⋊C4—92no—
263C2×C42—91no—
264C2×C42—91no—
265C2×C42—92no—
266C2×C42—91no—
267C2×C42—98no—
268C2×C42C2×C3⋊D312yes—
269C2×C42C2×C3⋊D311yescharacteristic
270C23×C3C23×D314yes—
271C22×D3—316no—
272C22×D3—38no—
273C22×D3—68no—
274C22×D3—68no—
275C3×Q8—232no—
276C2×C3×C4—216no—
277C2×C3×C4—216no—
278C2×C3×C4—28no—
279C2×C3×C4#235116yes—
280C2×C3×C4D3×Q8116yes—
281C2×C3×C4C23×D318yes—
282C2×C3×C4C23×D3116yes—
283C2×C3×C4C23×D3116yes—
284C2×C3×C4C23×D318yes—
285C2×C3×C4C23×D318yes—
286C2×Dic3—316no—
287C2×Dic3—316no—
288C2×Dic3—38no—
289C2×Dic3—38no—
290C2×Dic3—38no—
291C2×Dic3—316no—
292C2×Dic3—316no—
293C2×Dic3—616no—
294C2×Dic3—68no—
295C2×Dic3—616no—
296C4×D3—364no—
297C4×D3—632no—
298C4×D3—632no—
299Dic6—664no—
300Dic6—632no—
301C2×C32#53314yescomplemented
302C2×C32C23×Q811yescharacteristic
303C2×C32C22×#4111yescharacteristic
304C2×C32C22×#4111yescharacteristic
305C3⋊D3—24no—
306C24—91no—
307C2×Q8—24no—
308C2×Q8—98no—
309C2×Q8—94no—
310C2×Q8—188no—
311C2×Q8—184no—
312C2×Q8C22×C3⋊D314yes—
313C22×C4—91no—
314C22×C4—91no—
315C22×C4—94no—
316C22×C4—98no—
317C22×C4—91no—
318C22×C4—92no—
319C22×C4—92no—
320C22×C4—94no—
321C22×C4—94no—
322C22×C4—184no—
323C22×C4—184no—
324C22×C4C22×C3⋊D311yescharacteristic
325C22×C4C22×C3⋊D312yes—
326C22×C4C22×C3⋊D312yes—
327C22×C4C22×C3⋊D311yescharacteristic
328C22×C4C22×C3⋊D311yescharacteristic
329C4⋊C4—98no—
330C4⋊C4—98no—
331C4⋊C4—98no—
332C4⋊C4—98no—
333C4⋊C4—98no—
334C4⋊C4—98no—
335C4⋊C4—94no—
336C4⋊C4C22×C3⋊D318yes—
337C4⋊C4C22×C3⋊D314yes—
338C22⋊C4—98no—
339C22⋊C4—98no—
340C42—94no—
341C42—94no—
342C42—94no—
343C42—98no—
344C42C22×C3⋊D314yes—
345C42C22×C3⋊D318yes—
346C22×C3C2×#23518yes—
347C22×C3C2×D3×Q818yes—
348C22×C3D3×#4118yes—
349C22×C3C24×D314yes—
350C2×D3—316no—
351C2×D3—68no—
352C2×D3—68no—
353C2×D3—632no—
354C3×C4—216no—
355C3×C4—216no—
356C3×C4—28no—
357C3×C4C2×#235116yes—
358C3×C4C2×D3×Q8116yes—
359Dic3—316no—
360Dic3—316no—
361Dic3—616no—
362Dic3—68no—
363Dic3—616no—
364C32C2×#53311yescharacteristic, complemented, Sylow
365C23—94no—
366C23—92no—
367C23—182no—
368C23—182no—
369C23C23×C3⋊D311yescharacteristic
370Q8—28no—
371Q8—1816no—
372Q8—188no—
373C2×C4—24no—
374C2×C4—22no—
375C2×C4—24no—
376C2×C4—94no—
377C2×C4—94no—
378C2×C4—92no—
379C2×C4—92no—
380C2×C4—916no—
381C2×C4—92no—
382C2×C4—94no—
383C2×C4—94no—
384C2×C4—188no—
385C2×C4—182no—
386C2×C4—184no—
387C2×C4—184no—
388C2×C4—188no—
389C2×C4#382814yes—
390C2×C4Q8×C3⋊D314yes—
391C2×C4C23×C3⋊D312yes—
392C2×C4C23×C3⋊D314yes—
393C2×C4C23×C3⋊D314yes—
394C2×C4C23×C3⋊D312yes—
395C2×C4C23×C3⋊D312yes—
396C2×C3#5578116yescomplemented
397C2×C3C22×#23514yes—
398C2×C3C22×D3×Q814yes—
399C2×C3C2×D3×#4114yes—
400D3—616no—
401C22—94no—
402C22—182no—
403C22—182no—
404C22—188no—
405C22C2×#382812yes—
406C22C2×Q8×C3⋊D312yes—
407C22#41×C3⋊D312yes—
408C22C24×C3⋊D311yescharacteristic
409C4—24no—
410C4—22no—
411C4—24no—
412C4—94no—
413C4—94no—
414C4—182no—
415C4—184no—
416C4—184no—
417C4C2×#382814yes—
418C4C2×Q8×C3⋊D314yes—
419C3C2×#557814yescomplemented
420C2—184no—
421C2#1059604914yesdirect product factor
422C2C22×#382811yescharacteristic
423C2C22×Q8×C3⋊D311yescharacteristic
424C2C2×#41×C3⋊D311yescharacteristic
subgroupG/H
centerC22×C4C22×C3⋊D3
commutator, cosocleC22×C32C25
FrattiniC22C24×C3⋊D3
FittingC2×C32×C4×Q8C2
socleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenterC2×C4×Q8C3⋊D3
hypocenterC32C2×#533
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C32×C4×Q8C2semidirect
3. C2×#64153C2semidirect
4. #10596049C2direct (N × H)
7. C2×#64098C2semidirect
8. C2×#64097C2semidirect
11. C2×C4×#634C2semidirect
12. C2×C4×#634C2semidirect
20. C32×C4×Q8C22semidirect
26. #64153C22semidirect
42. #64098C22semidirect
43. #64097C22semidirect
46. C4×#634C22semidirect
47. C4×#634C22semidirect
48. C2×C3×C4×Q8D3semidirect
75. C2×C4×C3⋊D3Q8semidirect
107. C3×C4×Q8C2×D3semidirect
163. C4×C3⋊D3C2×Q8semidirect
175. C2×C4×Q8C3⋊D3semidirect
250. C4×Q8C2×C3⋊D3semidirect
301. C2×C32#533semidirect
364. C32C2×#533semidirect
396. C2×C3#5578semidirect
419. C3C2×#5578semidirect
421. C2#10596049direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×C4×Q82
C2×#641552
C2×#641532
#105960492
C2×#641062
C2×#641052
C2×#640982
C2×#640972
C2×#640812
C2×C42×C3⋊D32
C2×C4×#6342
C2×#55783