Finite Group Databasebeta

← #11920416

Subgroups — #11920416

Order 1152.

550 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 550 conjugacy classes of subgroups — too many to draw. Only its 61 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
1C22×#41⋊C9C211yesmaximal, characteristic
2C2×#63690C211yesmaximal, characteristic, complemented
3#10589528C211yesmaximal, characteristic, complemented
4#10589527C212yesmaximal, complemented
5#10589521C212yesmaximal, complemented
6#84084—31nomaximal
7C2×#41⋊C9—22no—
8C2×#41⋊C9C2211yescharacteristic
9C2×#41⋊C9C2211yescharacteristic
10C22×Q8⋊C9C2211yescharacteristic
11#63690—22no—
12C2×#3688C2212yescomplemented
13#63486—41nomaximal
14#63421C2212yescomplemented
15C22×C3×#41D311yescharacteristic
16C2×#951—31no—
17C2×#951—31no—
18C2×#924—31no—
19#5239—32no—
20#5239—32no—
21#5232—31no—
22#5232—31no—
23#5228—32no—
24#5218—32no—
25#5207—31no—
26C22×C4×C9—41no—
27C2×Dic18—41no—
28#41⋊C9—21no—
29#41⋊C9D412yes—
30C2×Q8⋊C9—21no—
31C2×Q8⋊C9C2311yescharacteristic
32#3688—22no—
33#3676—42no—
34C4⋊Dic9—41no—
35Dic9⋊C4—42no—
36#3007—91noSylow
37C2×C3×#41—22no—
38C2×C3×#41—31no—
39C2×C3×#41—31no—
40C2×C3×#41—62no—
41C2×C3×#41C2×D311yescharacteristic
42C2×C3×#41C2×D311yescharacteristic
43C22×C3×Q8C2×D311yescharacteristic
44C22×C3×D4—31no—
45C23×C3×C4—31no—
46C22×Dic6—31no—
47C2×#217—61no—
48#951—62no—
49#951—64no—
50#951—62no—
51C2×#216—32no—
52C2×#216—32no—
53C2×#214—32no—
54C2×#214—32no—
55C2×C4⋊Dic3—31no—
56#924—32no—
57#924—32no—
58#924—61no—
59#924—61no—
60C2×Dic3⋊C4—61no—
61C2×#208—31no—
62C2×#208—31no—
63#835—32no—
64#835—32no—
65#832—32no—
66#832—32no—
67#830—32no—
68#830—32no—
69C23×C9—41no—
70C2×C4×C9—41no—
71C2×C4×C9—41no—
72C2×C4×C9—82no—
73C2×Dic9—42no—
74C2×Dic9—42no—
75Dic18—82no—
76Q8⋊C9C2×D411yescharacteristic
77C22×#41D911yescharacteristic
78C2×#137—91no—
79C2×#137—91no—
80C2×C22⋊Q8—91no—
81#452—92no—
82#452—92no—
83#451—92no—
84#450—92no—
85#417—91no—
86#417—91no—
87#407—91no—
88C24×C3—31no—
89C3×#41—21no—
90C3×#41—32no—
91C3×#41—34no—
92C3×#41—62no—
93C3×#41—62no—
94C3×#41—61no—
95C3×#41—62no—
96C3×#41#6712yes—
97C2×C3×Q8—21no—
98C2×C3×Q8—31no—
99C2×C3×Q8—61no—
100C2×C3×Q8C22×D311yescharacteristic
101C2×C3×D4—31no—
102C2×C3×D4—31no—
103C2×C3×D4—61no—
104C2×C3×D4—62no—
105C2×C3×D4—62no—
106C22×C3×C4—31no—
107C22×C3×C4—31no—
108C22×C3×C4—31no—
109C22×C3×C4—31no—
110C22×C3×C4—31no—
111C22×C3×C4—62no—
112C22×C3×C4—62no—
113C22×C3×C4S411yescharacteristic
114C22×Dic3—61no—
115C22×Dic3—61no—
116C2×Dic6—32no—
117C2×Dic6—62no—
118C2×Dic6—62no—
119C2×Dic6—61no—
120#217—62no—
121#217—62no—
122#216—62no—
123#216—64no—
124#216—62no—
125#214—64no—
126#214—64no—
127C4⋊Dic3—32no—
128C4⋊Dic3—61no—
129Dic3⋊C4—62no—
130Dic3⋊C4—62no—
131#208—62no—
132#208—62no—
133C2×C3⋊C8—32no—
134C2×C3⋊C8—32no—
135C22×C9—42no—
136C22×C9—41no—
137C22×C9—81no—
138C22×C9—81no—
139C4×C9—42no—
140C4×C9—81no—
141Dic9—82no—
142Dic9—82no—
143C2×#41—22no—
144C2×#41—31no—
145C2×#41—31no—
146C2×#41—62no—
147C2×#41C2×D911yescharacteristic
148C2×#41C2×D911yescharacteristic
149C22×Q8—91no—
150C22×Q8C2×D911yescharacteristic
151C22×D4—31no—
152C23×C4—31no—
153#137—182no—
154#137—184no—
155#137—182no—
156C2×Q16—92no—
157C2×Q16—92no—
158C2×SD16—92no—
159C2×SD16—92no—
160C2×M16—91no—
161C2×M16—91no—
162C22⋊Q8—92no—
163C22⋊Q8—92no—
164C22⋊Q8—181no—
165C22⋊Q8—181no—
166C2×C4⋊C4—91no—
167C2×C4⋊C4—181no—
168C2×C22⋊C4—181no—
169#103—92no—
170#103—92no—
171#102—92no—
172#102—92no—
173C22⋊C8—92no—
174C22⋊C8—92no—
175C23×C3—31no—
176C23×C3—31no—
177C23×C3—62no—
178C23×C3—62no—
179C23×C3—121no—
180C23×C3C2×S411yescharacteristic
181C3×Q8—31no—
182C3×Q8—32no—
183C3×Q8—61no—
184C3×Q8C2×#6711yescharacteristic
185C3×D4—32no—
186C3×D4—32no—
187C3×D4—61no—
188C3×D4—61no—
189C3×D4—64no—
190C2×C3×C4—22no—
191C2×C3×C4—31no—
192C2×C3×C4—32no—
193C2×C3×C4—32no—
194C2×C3×C4—31no—
195C2×C3×C4—61no—
196C2×C3×C4—61no—
197C2×C3×C4—62no—
198C2×C3×C4—61no—
199C2×C3×C4—61no—
200C2×C3×C4—62no—
201C2×C3×C4C2×S411yescharacteristic
202C2×C3×C4C2×S411yescharacteristic
203C2×Dic3—62no—
204C2×Dic3—62no—
205C2×Dic3—122no—
206C2×Dic3—122no—
207Dic6—62no—
208Dic6—62no—
209Dic6—122no—
210C3⋊C8—62no—
211C3⋊C8—62no—
212C2×C9—41no—
213C2×C9—41no—
214C2×C9—41no—
215C2×C9—82no—
216C24—31no—
217#41—21no—
218#41—32no—
219#41—34no—
220#41—62no—
221#41—62no—
222#41—61no—
223#41—62no—
224#41#61112yes—
225C2×Q8—21no—
226C2×Q8—31no—
227C2×Q8—61no—
228C2×Q8—92no—
229C2×Q8—182no—
230C2×Q8—182no—
231C2×Q8—181no—
232C2×Q8C22×D911yescharacteristic
233C2×D4—31no—
234C2×D4—31no—
235C2×D4—61no—
236C2×D4—62no—
237C2×D4—62no—
238C22×C4—31no—
239C22×C4—31no—
240C22×C4—31no—
241C22×C4—31no—
242C22×C4—31no—
243C22×C4—62no—
244C22×C4—62no—
245C22×C4—181no—
246C22×C4—181no—
247C22×C4(C22⋊C9)⋊C211yescharacteristic
248Q16—182no—
249Q16—184no—
250Q16—182no—
251SD16—184no—
252SD16—184no—
253M16—182no—
254M16—182no—
255C2×C8—92no—
256C2×C8—92no—
257C4⋊C4—92no—
258C4⋊C4—182no—
259C4⋊C4—181no—
260C4⋊C4—182no—
261C22⋊C4—182no—
262C22⋊C4—182no—
263C22×C3—21no—
264C22×C3—21no—
265C22×C3—32no—
266C22×C3—61no—
267C22×C3—61no—
268C22×C3—61no—
269C22×C3—61no—
270C22×C3—61no—
271C22×C3—124no—
272C22×C3#98412yes—
273C22×C3C22×S411yescharacteristic
274C3×C4—21no—
275C3×C4—31no—
276C3×C4—31no—
277C3×C4—61no—
278C3×C4GL(2,ℤ/4)12yes—
279Dic3—122no—
280Dic3—122no—
281C9—41noSylow
282C23—31no—
283C23—31no—
284C23—62no—
285C23—62no—
286C23—121no—
287C23C2×(C22⋊C9)⋊C211yescharacteristic
288Q8—31no—
289Q8—32no—
290Q8—61no—
291Q8—182no—
292Q8—182no—
293Q8—362no—
294Q8C2×#61111yescharacteristic
295D4—32no—
296D4—32no—
297D4—61no—
298D4—61no—
299D4—64no—
300C2×C4—22no—
301C2×C4—31no—
302C2×C4—32no—
303C2×C4—32no—
304C2×C4—31no—
305C2×C4—61no—
306C2×C4—61no—
307C2×C4—62no—
308C2×C4—61no—
309C2×C4—61no—
310C2×C4—62no—
311C2×C4—182no—
312C2×C4—182no—
313C2×C4—362no—
314C2×C4—362no—
315C2×C4C2×(C22⋊C9)⋊C211yescharacteristic
316C2×C4C2×(C22⋊C9)⋊C211yescharacteristic
317C8—182no—
318C8—182no—
319C2×C3—22no—
320C2×C3—62no—
321C2×C3—121no—
322C2×C3C2×#98411yescharacteristic
323C2×C3#592311yescharacteristic
324C2×C3C2×GL(2,ℤ/4)11yescharacteristic
325C22—21no—
326C22—21no—
327C22—32no—
328C22—61no—
329C22—61no—
330C22—61no—
331C22—61no—
332C22—61no—
333C22—124no—
334C22#6369012yescomplemented
335C22C22×(C22⋊C9)⋊C211yescharacteristic
336C4—21no—
337C4—31no—
338C4—31no—
339C4—61no—
340C4—362no—
341C4—362no—
342C4#6369412yes—
343C3#8551711yescharacteristic
344C2—22no—
345C2—62no—
346C2—121no—
347C2C2×#6369011yescharacteristic
348C2#1059309811yescharacteristic
349C2C2×#6369411yescharacteristic
subgroupG/H
centerC22C22×(C22⋊C9)⋊C2
commutator, cosocleC2×Q8⋊C9C23
Frattini, socleC22×C3C22×S4
Fitting, prime radicalC22×C3×#41D3
hypercenterC22×C4(C22⋊C9)⋊C2
hypocenterQ8⋊C9C2×D4
LCSG ▷ C2×Q8⋊C9 ▷ Q8⋊C9
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×#63690C2semidirect
3. #10589528C2semidirect
4. #10589527C2semidirect
5. #10589521C2semidirect
12. C2×#3688C22semidirect
14. #63421C22semidirect
334. C22#63690semidirect

Maximal subgroups

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

subgroupindex
C22×#41⋊C92
C2×#636902
#105895282
#105895272
#105895212
#840843
#634864