Finite Group Databasebeta

← C2×#10589829 #11902647

Subgroups — C2×#10589829 #11902647

Order 1152.

2352 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×D9C212yesmaximal, complemented
2C2×C9×C4⋊Q8C211yesmaximal, characteristic, complemented
3C2×#63508C212yesmaximal, complemented
4#10589829C2116yesmaximal, direct product factor
5C2×#63458C214yesmaximal, complemented
6C2×#63455C212yesmaximal
7C2×#63450C212yesmaximal, complemented
8C2×C4×D36C211yesmaximal, characteristic
9C2×C4×Dic18C211yesmaximal, characteristic, complemented
10C2×#5727—31nomaximal
11C22×Q8×C9C2212yes—
12C2×Q8×D9—216no—
13C2×Q8×D9C22116yescomplemented
14C22×D36C2211yescharacteristic
15C22×C4×D9C2212yes—
16C22×C4×D9C2214yes—
17C22×Dic18C2214yes—
18C22×Dic18C2211yescharacteristic
19C9×C4⋊Q8C2218yescomplemented
20C2×C9×C4⋊C4C2212yes—
21C2×C9×C4⋊C4C2212yes—
22C2×C42×C9C2211yescharacteristic
23#63508C22116yescomplemented
24C2×(C2×D9)⋊C4C2212yes—
25C2×(C2×D9)⋊C4C2214yes—
26C2×C4⋊Dic9C2211yescharacteristic
27C2×C4⋊Dic9C2211yescharacteristic
28C2×Dic9⋊C4C2212yes—
29C2×Dic9⋊C4C2214yes—
30C2×C4×Dic9C2212yes—
31#63458C22132yescomplemented
32#63455C22116yes—
33#63450C22116yescomplemented
34C4×D36C2218yes—
35C4×Dic18C2218yescomplemented
36C22×D3×Q8—32no—
37C2×C3×C4⋊Q8D311yescharacteristic
38C2×#946—32no—
39#5727—316no—
40C2×#896—34no—
41C2×#893—32no—
42C2×#888—32no—
43C2×C4×D12—31no—
44C2×C4×Dic6—31no—
45C23×D9C2312yes—
46C2×Q8×C9—28no—
47C2×Q8×C9C2318yes—
48C22×C4×C9C2311yescharacteristic
49C22×C4×C9C2314yes—
50C22×C4×C9C2311yescharacteristic
51C22×C4×C9C2311yescharacteristic
52C22×Dic9C2312yes—
53C22×Dic9C2312yes—
54C22×Dic9C2312yes—
55Q8×D9—264no—
56C2×D36Q818yescomplemented
57C2×D36C2314yes—
58C2×C4×D9—28no—
59C2×C4×D9—216no—
60C2×C4×D9C2318yes—
61C2×C4×D9C23116yes—
62C2×Dic18—216no—
63C2×Dic18D418yescomplemented
64C2×Dic18C23116yes—
65C2×Dic18C2314yes—
66C9×C4⋊C4C2318yes—
67C9×C4⋊C4C2318yes—
68C42×C9C2314yes—
69(C2×D9)⋊C4C23116yes—
70(C2×D9)⋊C4C2318yes—
71C4⋊Dic9C2314yes—
72C4⋊Dic9C2314yes—
73Dic9⋊C4C23116yes—
74Dic9⋊C4C2318yes—
75C4×Dic9C2318yes—
76C2×D4×Q8—91noSylow
77C22×C3×Q8C2×D312yes—
78C2×D3×Q8—316no—
79C2×D3×Q8—616no—
80C22×D12—31no—
81C22×C4×D3—32no—
82C22×C4×D3—34no—
83C22×Dic6—31no—
84C22×Dic6—34no—
85C3×C4⋊Q8C2×D318yes—
86C2×C3×C4⋊C4C2×D312yes—
87C2×C3×C4⋊C4C2×D312yes—
88C2×C3×C42C2×D311yescharacteristic
89#946—316no—
90C2×(C2×D3)⋊C4—32no—
91C2×(C2×D3)⋊C4—34no—
92C2×C4⋊Dic3—31no—
93C2×C4⋊Dic3—31no—
94C2×Dic3⋊C4—32no—
95C2×Dic3⋊C4—34no—
96C2×C4×Dic3—32no—
97#896—332no—
98#893—316no—
99#888—316no—
100C4×D12—38no—
101C4×Dic6—38no—
102C23×C9C2411yescharacteristic
103C22×D9—24no—
104C22×D9—24no—
105C22×D9C2×Q818yescomplemented
106C22×D9C2414yes—
107Q8×C9—216no—
108C2×C4×C9—28no—
109C2×C4×C9—22no—
110C2×C4×C9C2×D414yes—
111C2×C4×C9C2×Q814yescomplemented
112C2×C4×C9C2412yes—
113C2×C4×C9C2418yes—
114C2×C4×C9C2412yes—
115C2×C4×C9C2412yes—
116C2×Dic9—24no—
117C2×Dic9—24no—
118C2×Dic9C2×D418yes—
119C2×Dic9C2414yes—
120C2×Dic9C2414yes—
121C2×Dic9C2414yes—
122D36C2×Q8116yescomplemented
123C4×D9—216no—
124C4×D9—232no—
125Dic18—232no—
126Dic18C2×D4116yescomplemented
127C23×Q8—92no—
128D4×Q8—916no—
129C2×C4⋊Q8—92no—
130C2×C4⋊Q8D911yescharacteristic, complemented
131C2×C22⋊Q8—92no—
132C2×C22⋊Q8—94no—
133C2×C4×Q8—91no—
134C2×C4×D4—92no—
135C2×C4×D4—91no—
136C23×D3—32no—
137C2×C3×Q8—28no—
138C2×C3×Q8C22×D318yes—
139C22×C3×C4C22×D311yescharacteristic
140C22×C3×C4C22×D314yes—
141C22×C3×C4C22×D311yescharacteristic
142C22×C3×C4C22×D311yescharacteristic
143C22×Dic3—32no—
144C22×Dic3—32no—
145C22×Dic3—32no—
146D3×Q8—664no—
147C2×D12—38no—
148C2×D12—34no—
149C2×C4×D3—38no—
150C2×C4×D3—316no—
151C2×C4×D3—616no—
152C2×C4×D3—68no—
153C2×Dic6—38no—
154C2×Dic6—34no—
155C2×Dic6—316no—
156C2×Dic6—616no—
157C3×C4⋊C4C22×D318yes—
158C3×C4⋊C4C22×D318yes—
159C3×C42C22×D314yes—
160(C2×D3)⋊C4—38no—
161(C2×D3)⋊C4—316no—
162C4⋊Dic3—34no—
163C4⋊Dic3—34no—
164Dic3⋊C4—38no—
165Dic3⋊C4—316no—
166C4×Dic3—38no—
167C22×C9C22×D412yes—
168C22×C9C22×Q812yes—
169C22×C92−1+412yes—
170C22×C9C2511yescharacteristic
171C2×D9—216no—
172C2×D9—24no—
173C2×D9—24no—
174C2×D9C22×Q818yescomplemented
175C4×C9—28no—
176C4×C9—22no—
177C4×C9C22×D414yes—
178C4×C9C22×Q814yescomplemented
179Dic9—24no—
180Dic9—24no—
181Dic9C22×D418yes—
182C22×Q8—916no—
183C22×Q8—91no—
184C22×Q8—94no—
185C22×Q8—1816no—
186C22×Q8C2×D912yes—
187C22×D4—91no—
188C23×C4—94no—
189C23×C4—92no—
190C4⋊Q8—916no—
191C4⋊Q8C2×D918yescomplemented
192C22⋊Q8—916no—
193C22⋊Q8—932no—
194C4×Q8—98no—
195C4×D4—916no—
196C4×D4—98no—
197C2×C4⋊C4—91no—
198C2×C4⋊C4—92no—
199C2×C4⋊C4—91no—
200C2×C4⋊C4—94no—
201C2×C4⋊C4C2×D912yes—
202C2×C4⋊C4C2×D912yes—
203C2×C22⋊C4—94no—
204C2×C22⋊C4—92no—
205C2×C42—92no—
206C2×C42C2×D911yescharacteristic
207C23×C3C23×D311yescharacteristic
208C22×D3—38no—
209C22×D3—34no—
210C22×D3—64no—
211C22×D3—64no—
212C3×Q8—216no—
213C2×C3×C4—28no—
214C2×C3×C4—22no—
215C2×C3×C4D3×D414yes—
216C2×C3×C4D3×Q814yes—
217C2×C3×C4C23×D312yes—
218C2×C3×C4C23×D318yes—
219C2×C3×C4C23×D312yes—
220C2×C3×C4C23×D312yes—
221C2×Dic3—38no—
222C2×Dic3—34no—
223C2×Dic3—34no—
224C2×Dic3—34no—
225C2×Dic3—64no—
226C2×Dic3—64no—
227D12—316no—
228C4×D3—632no—
229C4×D3—616no—
230Dic6—316no—
231Dic6—632no—
232C2×C9D4×Q814yescomplemented
233C2×C9C23×D411yescharacteristic
234C2×C9C23×Q811yescharacteristic
235C2×C9C2×2−1+411yescharacteristic
236D9—28no—
237C24—92no—
238C2×Q8—28no—
239C2×Q8—98no—
240C2×Q8—94no—
241C2×Q8—916no—
242C2×Q8—1816no—
243C2×Q8—1864no—
244C2×Q8C22×D918yes—
245C2×D4—98no—
246C2×D4—94no—
247C22×C4—92no—
248C22×C4—92no—
249C22×C4—92no—
250C22×C4—916no—
251C22×C4—98no—
252C22×C4—1816no—
253C22×C4—188no—
254C22×C4C22×D911yescharacteristic
255C22×C4C22×D914yes—
256C22×C4C22×D911yescharacteristic
257C22×C4C22×D911yescharacteristic
258C4⋊C4—94no—
259C4⋊C4—98no—
260C4⋊C4—94no—
261C4⋊C4—916no—
262C4⋊C4C22×D918yes—
263C4⋊C4C22×D918yes—
264C22⋊C4—916no—
265C22⋊C4—98no—
266C42—98no—
267C42C22×D914yes—
268C22×C3C2×D3×D412yes—
269C22×C3C2×D3×Q812yes—
270C22×C3#100712yes—
271C22×C3C24×D311yescharacteristic
272C2×D3—38no—
273C2×D3—64no—
274C2×D3—64no—
275C2×D3—616no—
276C3×C4—28no—
277C3×C4—22no—
278C3×C4C2×D3×D414yes—
279C3×C4C2×D3×Q814yes—
280Dic3—38no—
281Dic3—64no—
282Dic3—64no—
283C9C2×D4×Q811yescharacteristic, complemented, Sylow
284C23—94no—
285C23—98no—
286C23—184no—
287C23—184no—
288C23C23×D911yescharacteristic
289Q8—216no—
290Q8—916no—
291Q8—1832no—
292D4—916no—
293C2×C4—28no—
294C2×C4—22no—
295C2×C4—94no—
296C2×C4—98no—
297C2×C4—94no—
298C2×C4—94no—
299C2×C4—1832no—
300C2×C4—184no—
301C2×C4—184no—
302C2×C4—1816no—
303C2×C4D4×D914yes—
304C2×C4Q8×D914yescomplemented
305C2×C4C23×D912yes—
306C2×C4C23×D918yes—
307C2×C4C23×D912yes—
308C2×C4C23×D912yes—
309C2×C3#572714yes—
310C2×C3C22×D3×D411yescharacteristic
311C2×C3C22×D3×Q811yescharacteristic
312C2×C3C2×#100711yescharacteristic
313D3—68no—
314C22—98no—
315C22—184no—
316C22—184no—
317C22—1816no—
318C22C2×D4×D912yes—
319C22C2×Q8×D912yes—
320C22#6371312yes—
321C22C24×D911yescharacteristic
322C4—28no—
323C4—22no—
324C4—98no—
325C4—184no—
326C4—184no—
327C4C2×D4×D914yes—
328C4C2×Q8×D914yescomplemented
329C3C2×#572711yescharacteristic
330C2—188no—
331C2#1058982914yesdirect product factor
332C2C22×D4×D911yescharacteristic
333C2C22×Q8×D911yescharacteristic
334C2C2×#6371311yescharacteristic
subgroupG/H
centerC23C23×D9
commutator, cosocleC22×C9C25
FrattiniC22×C3C24×D3
FittingC2×C9×C4⋊Q8C2
socleC23×C3C23×D3
prime radicalC22×D36C22
hypercenterC2×C4⋊Q8D9
hypocenterC9C2×D4×Q8
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×Q8×D9C2semidirect
2. C2×C9×C4⋊Q8C2semidirect
3. C2×#63508C2semidirect
4. #10589829C2direct (N × H)
5. C2×#63458C2semidirect
7. C2×#63450C2semidirect
9. C2×C4×Dic18C2semidirect
13. C2×Q8×D9C22semidirect
19. C9×C4⋊Q8C22semidirect
23. #63508C22semidirect
31. #63458C22semidirect
33. #63450C22semidirect
35. C4×Dic18C22semidirect
56. C2×D36Q8semidirect
63. C2×Dic18D4semidirect
105. C22×D9C2×Q8semidirect
111. C2×C4×C9C2×Q8semidirect
122. D36C2×Q8semidirect
126. Dic18C2×D4semidirect
130. C2×C4⋊Q8D9semidirect
174. C2×D9C22×Q8semidirect
178. C4×C9C22×Q8semidirect
191. C4⋊Q8C2×D9semidirect
232. C2×C9D4×Q8semidirect
283. C9C2×D4×Q8semidirect
304. C2×C4Q8×D9semidirect
328. C4C2×Q8×D9semidirect
331. C2#10589829direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Q8×D92
C2×C9×C4⋊Q82
C2×#635082
#105898292
C2×#634582
C2×#634552
C2×#634502
C2×C4×D362
C2×C4×Dic182
C2×#57273