Finite Group Databasebeta

← C2×#10596096 #11901545

Subgroups — C2×#10596096 #11901545

Order 1152.

3012 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C22⋊Q8C211yesmaximal, characteristic
2C2×Q8×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C2×#64153C211yesmaximal, characteristic, complemented
4C2×#64135C211yesmaximal, characteristic
5C2×#64133C211yesmaximal, characteristic
6#10596096C2116yesmaximal, direct product factor
7C2×#64099C212yesmaximal, complemented
8C2×#64099C211yesmaximal, characteristic, complemented
9C2×#64098C212yesmaximal, complemented
10C2×#64096C211yesmaximal, characteristic, complemented
11C2×#64088C212yesmaximal
12C2×#64088C212yesmaximal
13C2×#5625—34nomaximal
14C22×C32×Q8C2211yescharacteristic
15C23×C32×C4C2211yescharacteristic
16C22×#634C2211yescharacteristic
17C32×C22⋊Q8C2218yes—
18C2×C32×C4⋊C4C2211yescharacteristic
19C2×C32×C4⋊C4C2212yes—
20C2×C32×C22⋊C4C2212yes—
21C2×#3757C2212yes—
22C2×#3757C2211yescharacteristic
23C2×#3757C2211yescharacteristic
24Q8×C3⋊Dic3C2218yescomplemented
25#64153C2218yescomplemented
26#64135C2218yes—
27C2×C4⋊(C3⋊Dic3)C2212yes—
28C2×C4⋊(C3⋊Dic3)C2212yes—
29C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
30C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
31C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
32#64133C2218yes—
33C2×#3750C2212yes—
34C2×#3750C2212yes—
35C2×#3750C2212yes—
36C2×#3750C2212yes—
37C2×#3750C2212yes—
38C2×C4×C3⋊Dic3C2212yes—
39C2×C4×C3⋊Dic3C2212yes—
40C2×C4×C3⋊Dic3C2211yescharacteristic
41C2×C4×C3⋊Dic3C2211yescharacteristic
42#64099C22116yescomplemented
43#64099C2218yescomplemented
44#64098C22116yescomplemented
45#64096C2218yescomplemented
46#64088C22116yes—
47#64088C22116yes—
48C2×C3×C22⋊Q8D314yes—
49C2×Q8×Dic3—34no—
50C2×#944—34no—
51C2×#926—34no—
52C2×#924—34no—
53#5625—364no—
54C2×#890—38no—
55C2×#890—34no—
56C2×#889—38no—
57C2×#887—34no—
58C2×#879—38no—
59C2×#879—38no—
60C24×C32C2311yescharacteristic
61C2×C32×Q8—24no—
62C2×C32×Q8C2314yes—
63C22×C32×C4—24no—
64C22×C32×C4C2311yescharacteristic
65C22×C32×C4C2314yes—
66C22×C32×C4C2312yes—
67C22×C32×C4C2312yes—
68C22×C32×C4C2311yescharacteristic
69C22×C3⋊Dic3C2312yes—
70C22×C3⋊Dic3C2311yescharacteristic
71C22×C3⋊Dic3C2311yescharacteristic
72C22×C3⋊Dic3C2311yescharacteristic
73C22×C3⋊Dic3C2312yes—
74C22×C3⋊Dic3C2311yescharacteristic
75C2×#634—24no—
76C2×#634C2314yes—
77C32×C4⋊C4C2314yes—
78C32×C4⋊C4C2318yes—
79C32×C22⋊C4C2318yes—
80#3757C2318yes—
81#3757C2314yes—
82#3757C2314yes—
83C4⋊(C3⋊Dic3)C2318yes—
84C4⋊(C3⋊Dic3)C2318yes—
85C4⋊(C3⋊Dic3)C2314yes—
86C4⋊(C3⋊Dic3)C2314yes—
87C4⋊(C3⋊Dic3)C2314yes—
88#3750C2318yes—
89#3750C2318yes—
90#3750C2318yes—
91#3750C2318yes—
92#3750C2318yes—
93C4×C3⋊Dic3C2318yes—
94C4×C3⋊Dic3C2318yes—
95C4×C3⋊Dic3C2314yes—
96C4×C3⋊Dic3C2314yes—
97C2×#541—91noSylow
98C22×C3×Q8C2×D314yes—
99C23×C3×C4C2×D314yes—
100C22×Dic6—34no—
101C3×C22⋊Q8C2×D3132yes—
102C2×C3×C4⋊C4C2×D314yes—
103C2×C3×C4⋊C4C2×D318yes—
104C2×C3×C22⋊C4C2×D318yes—
105C2×#217—38no—
106C2×#217—34no—
107C2×#217—34no—
108Q8×Dic3—332no—
109#944—332no—
110#926—332no—
111C2×C4⋊Dic3—38no—
112C2×C4⋊Dic3—38no—
113C2×C4⋊Dic3—34no—
114C2×C4⋊Dic3—34no—
115C2×C4⋊Dic3—34no—
116#924—332no—
117C2×Dic3⋊C4—38no—
118C2×Dic3⋊C4—38no—
119C2×Dic3⋊C4—38no—
120C2×Dic3⋊C4—38no—
121C2×Dic3⋊C4—38no—
122C2×C4×Dic3—38no—
123C2×C4×Dic3—38no—
124C2×C4×Dic3—34no—
125C2×C4×Dic3—34no—
126#890—364no—
127#890—332no—
128#889—364no—
129#887—332no—
130#879—364no—
131#879—364no—
132C23×C32—22no—
133C23×C32—22no—
134C23×C32—22no—
135C23×C32C2412yes—
136C23×C32C2411yescharacteristic
137C32×Q8—28no—
138C2×C32×C4—22no—
139C2×C32×C4—24no—
140C2×C32×C4—24no—
141C2×C32×C4—28no—
142C2×C32×C4#4114yes—
143C2×C32×C4C2414yes—
144C2×C32×C4C2414yes—
145C2×C32×C4C2412yes—
146C2×C32×C4C2412yes—
147C2×C3⋊Dic3—24no—
148C2×C3⋊Dic3—22no—
149C2×C3⋊Dic3—24no—
150C2×C3⋊Dic3—22no—
151C2×C3⋊Dic3—22no—
152C2×C3⋊Dic3—22no—
153C2×C3⋊Dic3C2412yes—
154C2×C3⋊Dic3C2412yes—
155C2×C3⋊Dic3C2412yes—
156C2×C3⋊Dic3C2414yes—
157C2×C3⋊Dic3C2414yes—
158C2×C3⋊Dic3C2412yes—
159#634—28no—
160#541—916no—
161C2×C4⋊Q8—91no—
162C2×#126—92no—
163C2×#126—92no—
164C2×#125—92no—
165C2×#125—91no—
166C2×#125—92no—
167C2×C22⋊Q8—91no—
168C2×C22⋊Q8C3⋊D311yescharacteristic
169C2×C4×Q8—91no—
170C2×C4×Q8—91no—
171C2×#117—91no—
172C24×C3C22×D314yes—
173C2×C3×Q8—216no—
174C2×C3×Q8C22×D3116yes—
175C22×C3×C4—216no—
176C22×C3×C4C22×D318yes—
177C22×C3×C4C22×D318yes—
178C22×C3×C4C22×D314yes—
179C22×C3×C4C22×D3116yes—
180C22×C3×C4C22×D314yes—
181C22×Dic3—34no—
182C22×Dic3—34no—
183C22×Dic3—34no—
184C22×Dic3—38no—
185C22×Dic3—38no—
186C22×Dic3—34no—
187C2×Dic6—316no—
188C2×Dic6—616no—
189C3×C4⋊C4C22×D3116yes—
190C3×C4⋊C4C22×D3132yes—
191C3×C22⋊C4C22×D3132yes—
192#217—332no—
193#217—316no—
194#217—316no—
195C4⋊Dic3—332no—
196C4⋊Dic3—332no—
197C4⋊Dic3—316no—
198C4⋊Dic3—316no—
199C4⋊Dic3—316no—
200Dic3⋊C4—332no—
201Dic3⋊C4—332no—
202Dic3⋊C4—332no—
203Dic3⋊C4—332no—
204Dic3⋊C4—332no—
205C4×Dic3—332no—
206C4×Dic3—332no—
207C4×Dic3—316no—
208C4×Dic3—316no—
209C22×C32—22no—
210C22×C32—22no—
211C22×C32—22no—
212C22×C32—44no—
213C22×C32C2×#4112yes—
214C22×C322−1+412yes—
215C22×C322−1+412yes—
216C22×C32C2511yescharacteristic
217C32×C4—22no—
218C32×C4—24no—
219C32×C4—24no—
220C32×C4C2×#4114yes—
221C3⋊Dic3—24no—
222C3⋊Dic3—22no—
223C3⋊Dic3—24no—
224C3⋊Dic3—22no—
225C3⋊Dic3—22no—
226C3⋊Dic3—22no—
227C22×Q8—91no—
228C22×Q8C2×C3⋊D311yescharacteristic
229C23×C4C2×C3⋊D311yescharacteristic
230C4⋊Q8—98no—
231#126—916no—
232#126—916no—
233#125—916no—
234#125—98no—
235#125—916no—
236C22⋊Q8—98no—
237C22⋊Q8C2×C3⋊D318yes—
238C4×Q8—98no—
239C4×Q8—98no—
240#117—98no—
241C2×C4⋊C4—91no—
242C2×C4⋊C4—91no—
243C2×C4⋊C4—91no—
244C2×C4⋊C4—92no—
245C2×C4⋊C4—92no—
246C2×C4⋊C4—92no—
247C2×C4⋊C4—92no—
248C2×C4⋊C4—92no—
249C2×C4⋊C4—92no—
250C2×C4⋊C4—92no—
251C2×C4⋊C4C2×C3⋊D311yescharacteristic
252C2×C4⋊C4C2×C3⋊D312yes—
253C2×C22⋊C4—91no—
254C2×C22⋊C4—91no—
255C2×C22⋊C4—92no—
256C2×C22⋊C4C2×C3⋊D312yes—
257C2×C42—91no—
258C2×C42—91no—
259C2×C42—92no—
260C2×C42—92no—
261C23×C3—28no—
262C23×C3—28no—
263C23×C3—28no—
264C23×C3C23×D318yes—
265C23×C3C23×D314yes—
266C3×Q8—232no—
267C2×C3×C4—28no—
268C2×C3×C4—216no—
269C2×C3×C4—216no—
270C2×C3×C4—232no—
271C2×C3×C4#237116yes—
272C2×C3×C4C23×D3116yes—
273C2×C3×C4C23×D3116yes—
274C2×C3×C4C23×D318yes—
275C2×C3×C4C23×D318yes—
276C2×Dic3—38no—
277C2×Dic3—38no—
278C2×Dic3—38no—
279C2×Dic3—316no—
280C2×Dic3—316no—
281C2×Dic3—38no—
282C2×Dic3—616no—
283C2×Dic3—68no—
284C2×Dic3—616no—
285C2×Dic3—68no—
286C2×Dic3—68no—
287C2×Dic3—68no—
288Dic6—632no—
289C2×C32—42no—
290C2×C32#54114yescomplemented
291C2×C32C22×#4111yescharacteristic
292C2×C32C2×2−1+411yescharacteristic
293C2×C32C2×2−1+411yescharacteristic
294C24C22×C3⋊D311yescharacteristic
295C2×Q8—24no—
296C2×Q8—94no—
297C2×Q8—184no—
298C2×Q8C22×C3⋊D314yes—
299C22×C4—24no—
300C22×C4—91no—
301C22×C4—91no—
302C22×C4—91no—
303C22×C4—92no—
304C22×C4—91no—
305C22×C4—92no—
306C22×C4C22×C3⋊D314yes—
307C22×C4C22×C3⋊D312yes—
308C22×C4C22×C3⋊D312yes—
309C22×C4C22×C3⋊D311yescharacteristic
310C22×C4C22×C3⋊D311yescharacteristic
311C4⋊C4—94no—
312C4⋊C4—94no—
313C4⋊C4—94no—
314C4⋊C4—98no—
315C4⋊C4—98no—
316C4⋊C4—98no—
317C4⋊C4—98no—
318C4⋊C4—98no—
319C4⋊C4—98no—
320C4⋊C4—98no—
321C4⋊C4C22×C3⋊D314yes—
322C4⋊C4C22×C3⋊D318yes—
323C22⋊C4—94no—
324C22⋊C4—94no—
325C22⋊C4—98no—
326C22⋊C4C22×C3⋊D318yes—
327C42—94no—
328C42—94no—
329C42—98no—
330C42—98no—
331C22×C3—28no—
332C22×C3—28no—
333C22×C3—28no—
334C22×C3—416no—
335C22×C3C2×#23718yes—
336C22×C3#100718yes—
337C22×C3#101018yes—
338C22×C3C24×D314yes—
339C3×C4—28no—
340C3×C4—216no—
341C3×C4—216no—
342C3×C4C2×#237116yes—
343Dic3—616no—
344Dic3—68no—
345Dic3—616no—
346Dic3—68no—
347Dic3—68no—
348Dic3—68no—
349C32C2×#54111yescharacteristic, complemented, Sylow
350C23—22no—
351C23—22no—
352C23—22no—
353C23C23×C3⋊D312yes—
354C23C23×C3⋊D311yescharacteristic
355Q8—28no—
356Q8—188no—
357C2×C4—22no—
358C2×C4—24no—
359C2×C4—24no—
360C2×C4—28no—
361C2×C4—92no—
362C2×C4—92no—
363C2×C4—92no—
364C2×C4—94no—
365C2×C4—92no—
366C2×C4—94no—
367C2×C4—184no—
368C2×C4—182no—
369C2×C4—182no—
370C2×C4—184no—
371C2×C4—182no—
372C2×C4—182no—
373C2×C4#383014yes—
374C2×C4C23×C3⋊D314yes—
375C2×C4C23×C3⋊D314yes—
376C2×C4C23×C3⋊D312yes—
377C2×C4C23×C3⋊D312yes—
378C2×C3—48no—
379C2×C3#5625116yescomplemented
380C2×C3C22×#23714yes—
381C2×C3C2×#100714yes—
382C2×C3C2×#101014yes—
383C22—22no—
384C22—22no—
385C22—22no—
386C22—44no—
387C22C2×#383012yes—
388C22#6436412yes—
389C22#6436712yes—
390C22C24×C3⋊D311yescharacteristic
391C4—22no—
392C4—24no—
393C4—24no—
394C4—184no—
395C4—182no—
396C4—182no—
397C4—184no—
398C4—182no—
399C4—182no—
400C4C2×#383014yes—
401C3C2×#562514yescomplemented
402C2—42no—
403C2#1059609614yesdirect product factor
404C2C22×#383011yescharacteristic
405C2C2×#6436411yescharacteristic
406C2C2×#6436711yescharacteristic
subgroupG/H
centerC23C23×C3⋊D3
commutator, cosocleC22×C32C25
FrattiniC22C24×C3⋊D3
FittingC2×C32×C22⋊Q8C2
socleC23×C32C24
prime radicalC24×C32C23
hypercenterC2×C22⋊Q8C3⋊D3
hypocenterC32C2×#541
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×Q8×C3⋊Dic3C2semidirect
3. C2×#64153C2semidirect
6. #10596096C2direct (N × H)
7. C2×#64099C2semidirect
8. C2×#64099C2semidirect
9. C2×#64098C2semidirect
10. C2×#64096C2semidirect
24. Q8×C3⋊Dic3C22semidirect
25. #64153C22semidirect
42. #64099C22semidirect
43. #64099C22semidirect
44. #64098C22semidirect
45. #64096C22semidirect
290. C2×C32#541semidirect
349. C32C2×#541semidirect
379. C2×C3#5625semidirect
401. C3C2×#5625semidirect
403. C2#10596096direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×C22⋊Q82
C2×Q8×C3⋊Dic32
C2×#641532
C2×#641352
C2×#641332
#105960962
C2×#640992
C2×#640982
C2×#640962
C2×#640882
C2×#56253