Finite Group Databasebeta

← #11920436

Subgroups — #11920436

Order 1152.

530 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 530 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×2−1+4⋊C9C211yesmaximal, characteristic
2C22×#3688C211yesmaximal, characteristic, complemented
3#10589527C212yesmaximal, complemented
4#10589522C211yesmaximal, characteristic, complemented
5#10589521C212yesmaximal, complemented
6#84117—31nomaximal
72−1+4⋊C9—22no—
8C2×#41⋊C9C2211yescharacteristic
9C22×Q8⋊C9C2211yescharacteristic
10C22×Q8⋊C9C2211yescharacteristic
11C2×#3688—22no—
12C2×#3688C2212yes—
13#63497—41nomaximal
14#63421C2212yes—
15C2×C3×2−1+4D311yescharacteristic
16#5825—31no—
17C2×#951—31no—
18C22×#216—31no—
19#5239—32no—
20#5239—32no—
21#5234—31no—
22#5233—31no—
23#5228—32no—
24#5228—32no—
25#5225—31no—
26C2×D4×C9—41no—
27C22×Dic9—41no—
28#41⋊C9—21no—
29C2×Q8⋊C9—21no—
30C2×Q8⋊C9D412yes—
31C2×Q8⋊C9C2311yescharacteristic
32#3688—22no—
33#3676—42no—
34#3676—41no—
35Dic9⋊C4—42no—
36#3011—91noSylow
37C3×2−1+4—22no—
38C3×2−1+4—62no—
39C2×C3×#41—31no—
40C2×C3×#41—31no—
41C2×C3×#41—31no—
42C2×C3×#41C2×D311yescharacteristic
43C22×C3×Q8—31no—
44C22×C3×Q8C2×D311yescharacteristic
45C22×C3×Q8C2×D311yescharacteristic
46C22×Dic6—31no—
47#951—64no—
48#944—61no—
49C2×#216—32no—
50C2×#216—32no—
51C2×#216—32no—
52C2×#216—62no—
53C2×#216—62no—
54#936—61no—
55#935—61no—
56#935—61no—
57C2×#214—32no—
58#926—31no—
59#924—32no—
60#924—32no—
61C2×#208—31no—
62C22×C3⋊C8—31no—
63#835—32no—
64#835—32no—
65#835—32no—
66#832—32no—
67#830—32no—
68#830—32no—
69C23×C9—41no—
70C23×C9—41no—
71D4×C9—82no—
72C2×C4×C9—41no—
73C2×Dic9—42no—
74C2×Dic9—42no—
75C2×Dic9—82no—
76Q8⋊C9C2×D411yescharacteristic
77C2×2−1+4D911yescharacteristic
78C2×#137—91no—
79C22×Q16—91no—
80#536—91no—
81#452—92no—
82#452—92no—
83#451—92no—
84#451—92no—
85#419—91no—
86#416—91no—
87#408—91no—
88C3×#41—21no—
89C3×#41—34no—
90C3×#41—62no—
91C3×#41—62no—
92C3×#41—62no—
93C3×#41—62no—
94C3×#41—62no—
95C3×#41—61no—
96C2×C3×Q8—21no—
97C2×C3×Q8—31no—
98C2×C3×Q8—31no—
99C2×C3×Q8—31no—
100C2×C3×Q8—32no—
101C2×C3×Q8—62no—
102C2×C3×Q8—62no—
103C2×C3×Q8—61no—
104C2×C3×Q8#6712yes—
105C2×C3×Q8C22×D311yescharacteristic
106C2×C3×D4—31no—
107C2×C3×D4—31no—
108C2×C3×D4—31no—
109C2×C3×D4S411yescharacteristic
110C22×C3×C4—31no—
111C22×C3×C4—31no—
112C22×C3×C4—31no—
113C22×C3×C4—61no—
114C22×Dic3—61no—
115C2×Dic6—32no—
116C2×Dic6—62no—
117C2×Dic6—62no—
118C2×Dic6—61no—
119#217—62no—
120#217—62no—
121#217—61no—
122#216—64no—
123#216—62no—
124#216—64no—
125#216—62no—
126#214—64no—
127C4⋊Dic3—32no—
128Dic3⋊C4—62no—
129Dic3⋊C4—62no—
130C4×Dic3—61no—
131#208—62no—
132C2×C3⋊C8—32no—
133C2×C3⋊C8—32no—
134C2×C3⋊C8—62no—
135C22×C9—42no—
136C22×C9—41no—
137C22×C9—82no—
138C22×C9—81no—
139C22×C9—82no—
140C4×C9—81no—
141Dic9—82no—
142Dic9—82no—
1432−1+4—22no—
1442−1+4—62no—
145C2×#41—31no—
146C2×#41—31no—
147C2×#41—31no—
148C2×#41C2×D911yescharacteristic
149C22×Q8—31no—
150C22×Q8—91no—
151C22×Q8C2×D911yescharacteristic
152C22×Q8C2×D911yescharacteristic
153#137—184no—
154C2×Q16—92no—
155C2×Q16—92no—
156C2×Q16—92no—
157C2×Q16—182no—
158C2×Q16—182no—
159C2×SD16—92no—
160C2×M16—91no—
161C22×C8—91no—
162C4⋊Q8—181no—
163#124—181no—
164#123—181no—
165#123—181no—
166C22⋊Q8—92no—
167C22⋊Q8—92no—
168#117—91no—
169#103—92no—
170#103—92no—
171#103—92no—
172#102—92no—
173C22⋊C8—92no—
174C22⋊C8—92no—
175C23×C3—31no—
176C23×C3C2×S411yescharacteristic
177C23×C3C2×S411yescharacteristic
178C3×Q8—32no—
179C3×Q8—31no—
180C3×Q8—32no—
181C3×Q8—62no—
182C3×Q8—61no—
183C3×Q8—61no—
184C3×Q8C2×#6711yescharacteristic
185C3×D4—22no—
186C3×D4—32no—
187C3×D4—62no—
188C3×D4—61no—
189C3×D4—62no—
190C2×C3×C4—32no—
191C2×C3×C4—32no—
192C2×C3×C4—31no—
193C2×C3×C4—31no—
194C2×C3×C4—31no—
195C2×C3×C4—61no—
196C2×C3×C4—61no—
197C2×C3×C4—61no—
198C2×C3×C4—61no—
199C2×C3×C4—64no—
200C2×C3×C4C2×S411yescharacteristic
201C2×Dic3—62no—
202C2×Dic3—62no—
203C2×Dic3—122no—
204Dic6—62no—
205Dic6—62no—
206Dic6—122no—
207C3⋊C8—62no—
208C3⋊C8—62no—
209C2×C9—42no—
210C2×C9—41no—
211C2×C9—82no—
212C2×C9—161no—
213#41—21no—
214#41—34no—
215#41—62no—
216#41—62no—
217#41—62no—
218#41—62no—
219#41—62no—
220#41—61no—
221C2×Q8—21no—
222C2×Q8—31no—
223C2×Q8—31no—
224C2×Q8—31no—
225C2×Q8—32no—
226C2×Q8—62no—
227C2×Q8—62no—
228C2×Q8—61no—
229C2×Q8—92no—
230C2×Q8—181no—
231C2×Q8—182no—
232C2×Q8—182no—
233C2×Q8#61112yes—
234C2×Q8C22×D911yescharacteristic
235C2×D4—31no—
236C2×D4—31no—
237C2×D4—31no—
238C2×D4(C22⋊C9)⋊C211yescharacteristic
239C22×C4—31no—
240C22×C4—31no—
241C22×C4—31no—
242C22×C4—61no—
243C22×C4—181no—
244Q16—184no—
245Q16—182no—
246Q16—184no—
247Q16—182no—
248SD16—184no—
249M16—182no—
250C2×C8—92no—
251C2×C8—92no—
252C2×C8—182no—
253C4⋊C4—92no—
254C4⋊C4—182no—
255C4⋊C4—182no—
256C22⋊C4—182no—
257C22⋊C4—181no—
258C22⋊C4—182no—
259C42—181no—
260C22×C3—22no—
261C22×C3—22no—
262C22×C3—21no—
263C22×C3—62no—
264C22×C3—61no—
265C22×C3GL(2,ℤ/4)12yes—
266C22×C3C22×S411yescharacteristic
267C3×C4—21no—
268C3×C4—31no—
269C3×C4—31no—
270C3×C4—32no—
271C3×C4—61no—
272Dic3—122no—
273Dic3—122no—
274C9—41noSylow
275C23—31no—
276C23C2×(C22⋊C9)⋊C211yescharacteristic
277C23C2×(C22⋊C9)⋊C211yescharacteristic
278Q8—32no—
279Q8—31no—
280Q8—32no—
281Q8—62no—
282Q8—61no—
283Q8—61no—
284Q8—182no—
285Q8—182no—
286Q8—362no—
287Q8C2×#61111yescharacteristic
288D4—22no—
289D4—32no—
290D4—62no—
291D4—61no—
292D4—62no—
293C2×C4—31no—
294C2×C4—31no—
295C2×C4—32no—
296C2×C4—32no—
297C2×C4—31no—
298C2×C4—61no—
299C2×C4—61no—
300C2×C4—61no—
301C2×C4—61no—
302C2×C4—64no—
303C2×C4—182no—
304C2×C4—182no—
305C2×C4—362no—
306C2×C4C2×(C22⋊C9)⋊C211yescharacteristic
307C8—182no—
308C8—182no—
309C2×C3—22no—
310C2×C3—41no—
311C2×C3—121no—
312C2×C3#592712yes—
313C2×C3C2×GL(2,ℤ/4)11yescharacteristic
314C22—22no—
315C22—22no—
316C22—21no—
317C22—62no—
318C22—61no—
319C22#6369412yes—
320C22C22×(C22⋊C9)⋊C211yescharacteristic
321C4—21no—
322C4—31no—
323C4—31no—
324C4—32no—
325C4—61no—
326C4—362no—
327C4—362no—
328C3#8553511yescharacteristic
329C2—22no—
330C2—41no—
331C2—121no—
332C2#1059310212yes—
333C2C2×#6369411yescharacteristic
subgroupG/H
centerC22C22×(C22⋊C9)⋊C2
commutator, cosocleC2×Q8⋊C9C23
Frattini, socleC22×C3C22×S4
Fitting, prime radicalC2×C3×2−1+4D3
hypercenterC2×D4(C22⋊C9)⋊C2
hypocenterQ8⋊C9C2×D4
LCSG ▷ C2×Q8⋊C9 ▷ Q8⋊C9
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. C22×#3688C2semidirect
3. #10589527C2semidirect
4. #10589522C2semidirect
5. #10589521C2semidirect

Maximal subgroups

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

subgroupindex
C2×2−1+4⋊C92
C22×#36882
#105895272
#105895222
#105895212
#841173
#634974