Finite Group Databasebeta

← #11878896

Subgroups — #11878896

Order 1152.

879 conjugacy classes of subgroups; only the 172 normal subgroups are shown.

normal subgroups only

This group has 879 conjugacy classes of subgroups — too many to draw. Only its 172 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
1#10596199C211yesmaximal, characteristic
2#10593909C211yesmaximal, characteristic
3C3×#5092C212yesmaximal, complemented
4#10591654C214yesmaximal
5#10591633C214yesmaximal, complemented
6#10590297C211yesmaximal, characteristic
7#10590287C212yesmaximal, complemented
8#81802—32nomaximal
9C2×#3797C2212yes—
10C32×C4⋊Q8C2211yescharacteristic
11#64155C2212yes—
12Q8×C3⋊Dic3C2212yes—
13#64106—21no—
14#64101—21no—
15#64099—21no—
16#64096—21no—
17C42×C3⋊D3C2211yescharacteristic
18#64078C2211yescharacteristic
19C2×C3×#216C2218yes—
20C3×#869C2212yes—
21#63919—21no—
22#63919—21no—
23#63900—21no—
24#63900—21no—
25#63873C2212yes—
26C3×C4×C3⋊C8C2212yes—
27#63572C2212yes—
28#63566C2218yes—
29#63557C2212yes—
30#5728—32no—
31#5728—61no—
32D3×C4⋊Q8—32no—
33C3×#494—32no—
34#5186—38no—
35#5182—38no—
36#5092D312yescomplemented
37#5079—32no—
38#4685—32no—
39#4681—32no—
40C2×C32×Q8C2312yes—
41C2×C4×C3⋊D3D411yescharacteristic
42C2×C4×C3⋊D3D411yescharacteristic
43C2×C4×C3⋊D3C2311yescharacteristic
44C2×#634—21no—
45C2×C3×Dic6C2314yes—
46C2×#627—22no—
47C2×#624—22no—
48#3797—44no—
49C32×C4⋊C4—21no—
50C32×C4⋊C4—21no—
51C32×C42C2311yescharacteristic
52#3752—22no—
53C4⋊(C3⋊Dic3)—21no—
54C4⋊(C3⋊Dic3)—22no—
55C4⋊(C3⋊Dic3)C2312yes—
56#3750—22no—
57C4×C3⋊Dic3—22no—
58C4×C3⋊Dic3D411yescharacteristic
59C4×C3⋊Dic3D411yescharacteristic
60C4×C3⋊Dic3C2311yescharacteristic
61C3×#216—48no—
62C3×C4⋊Dic3—22no—
63C3×C4⋊Dic3—22no—
64C2×C3×C3⋊C8C2314yes—
65#3724—22no—
66#3724—22no—
67#3209—91noSylow
68C2×D3×Q8—34no—
69C2×C3×Q16—38no—
70C3×C4⋊Q8—21no—
71C3×C4⋊Q8—32no—
72C3×C4⋊Q8C2×D312yes—
73#946—34no—
74#946—62no—
75Q8×Dic3—34no—
76Q8×Dic3—62no—
77#944—34no—
78C2×#216C2×D318yes—
79#897—62no—
80#897—62no—
81#892—62no—
82#892—62no—
83D3×C4⋊C4—62no—
84D3×C4⋊C4—62no—
85#890—62no—
86#890—62no—
87#888—62no—
88#888—62no—
89#887—62no—
90#887—62no—
91C42×D3—32no—
92C42×D3—61no—
93#869—32no—
94#869—61no—
95#869C2×D312yes—
96C3×C4×C8—32no—
97#835—38no—
98(C2×D3)⋊C8—34no—
99#816—38no—
100Dic3⋊C8—34no—
101C4×C3⋊C8C2×D312yes—
102C22×C3⋊D3C2×D411yescharacteristic
103C32×Q8—24no—
104C2×C32×C4—22no—
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4C2411yescharacteristic
108C2×C3⋊Dic3—22no—
109C2×C3⋊Dic3C2×D411yescharacteristic
110C2×C3⋊Dic3C2×D411yescharacteristic
111C2×C3⋊Dic3C2×D411yescharacteristic
112C4×C3⋊D3—22no—
113C4×C3⋊D3—22no—
114C4×C3⋊D3Q1614yescomplemented
115#634—42no—
116C2×C3×Dic3—24no—
117C3×Dic6—28no—
118#627—44no—
119#624—44no—
120C3×C3⋊C8—24no—
121#533—91no—
122C2×C4⋊Q8—91no—
123#494—32no—
124#487—92no—
125#462—94no—
126#451—94no—
127#431—91no—
128C2×C3×Q8—22no—
129C2×C3×Q8—34no—
130C2×C3×Q8C22×D314yes—
131D3×Q8—128no—
132C2×C4×D3—32no—
133C2×C4×D3—32no—
134C2×C4×D3—32no—
135C2×C4×D3—61no—
136C2×C4×D3—61no—
137C2×C4×D3—61no—
138C2×C4×D3—64no—
139C2×Dic6—64no—
140C2×Dic6—62no—
141C2×Dic6—62no—
142C2×Dic6C22×D314yes—
143C3×Q16—128no—
144C2×C3×C8—34no—
145C3×C4⋊C4—22no—
146C3×C4⋊C4—22no—
147C3×C4⋊C4—22no—
148C3×C4⋊C4—22no—
149C3×C4⋊C4—62no—
150C3×C4⋊C4—62no—
151C3×C42—21no—
152C3×C42C22×D312yes—
153#216—48no—
154(C2×D3)⋊C4—64no—
155(C2×D3)⋊C4—64no—
156C4⋊Dic3—22no—
157C4⋊Dic3—22no—
158C4⋊Dic3—34no—
159C4⋊Dic3—62no—
160C4⋊Dic3—64no—
161C4⋊Dic3—62no—
162C4⋊Dic3—64no—
163C4⋊Dic3—62no—
164Dic3⋊C4—64no—
165Dic3⋊C4—64no—
166Dic3⋊C4—64no—
167Dic3⋊C4—64no—
168C4×Dic3—32no—
169C4×Dic3—32no—
170C4×Dic3—32no—
171C4×Dic3—61no—
172C4×Dic3—61no—
173C4×Dic3—61no—
174C4×Dic3—64no—
175C4×Dic3—64no—
176C2×C3⋊C8C22×D314yes—
177C22×C32C22×D411yescharacteristic
178C2×C3⋊D3—21no—
179C2×C3⋊D3—21no—
180C2×C3⋊D3C2×Q1612yes—
181C32×C4—42no—
182C32×C4C2×Q1612yes—
183C32×C4#13712yes—
184C32×C4H(5,𝔽2)12yes—
185C3⋊Dic3—21no—
186C3⋊Dic3—21no—
187C3⋊Dic3—42no—
188C3⋊Dic3C2×Q1612yes—
189C3×Dic3—44no—
190C22×Q8—92no—
191C2×Q16—38no—
192C4⋊Q8—32no—
193C4⋊Q8—92no—
194C4⋊Q8—91no—
195C4⋊Q8—181no—
196C4⋊Q8—181no—
197C4⋊Q8D3211yescharacteristic
198#125—181no—
199C22⋊Q8—92no—
200C22⋊Q8—181no—
201C4×Q8—92no—
202C4×Q8—181no—
203#117—181no—
204C2×C4⋊C4—181no—
205C2×C4⋊C4—181no—
206C2×C42—91no—
207C4⋊C8—92no—
208#103—98no—
209C22⋊C8—92no—
210C4×C8—32no—
211C22×D3—32no—
212C22×D3—61no—
213C3×Q8—28no—
214C3×Q8—44no—
215C3×Q8—68no—
216C2×C3×C4—24no—
217C2×C3×C4—24no—
218C2×C3×C4—21no—
219C2×C3×C4—21no—
220C2×C3×C4—21no—
221C2×C3×C4—64no—
222C2×C3×C4D3×D412yes—
223C2×C3×C4D3×D412yes—
224C2×C3×C4C23×D312yes—
225C2×Dic3—24no—
226C2×Dic3—32no—
227C2×Dic3—32no—
228C2×Dic3—32no—
229C2×Dic3—61no—
230C2×Dic3—61no—
231C2×Dic3—61no—
232C2×Dic3—64no—
233C2×Dic3—64no—
234C4×D3—38no—
235C4×D3—64no—
236C4×D3—64no—
237C4×D3—64no—
238C4×D3—122no—
239C4×D3—122no—
240C4×D3—128no—
241Dic6—28no—
242Dic6—128no—
243Dic6—124no—
244Dic6—124no—
245C3×C8—64no—
246C3⋊C8—24no—
247C2×C32#53511yescharacteristic
248C2×C32C22×Q1611yescharacteristic
249C2×C32C2×#13711yescharacteristic
250C3⋊D3—22no—
251C2×Q8—34no—
252C2×Q8—182no—
253C2×Q8—181no—
254C2×Q8—364no—
255C2×Q8C2×D3212yes—
256C22×C4—91no—
257C22×C4—91no—
258C22×C4—91no—
259C22×C4—182no—
260Q16—128no—
261C2×C8—34no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—62no—
265C4⋊C4—62no—
266C4⋊C4—92no—
267C4⋊C4—182no—
268C4⋊C4—182no—
269C4⋊C4—182no—
270C4⋊C4—182no—
271C4⋊C4—181no—
272C22⋊C4—182no—
273C42—91no—
274C42—91no—
275C42—91no—
276C42—182no—
277C42C2×D3211yescharacteristic
278C22×C3—21no—
279C22×C3C2×D3×D412yes—
280C2×D3—34no—
281C2×D3—62no—
282C2×D3—62no—
283C2×D3—62no—
284C2×D3—121no—
285C2×D3—121no—
286C3×C4—22no—
287C3×C4—22no—
288C3×C4—22no—
289C3×C4—44no—
290C3×C4—44no—
291C3×C4—124no—
292C3×C4D3×Q1614yes—
293C3×C4#91814yes—
294C3×C4#100414yes—
295Dic3—34no—
296Dic3—44no—
297Dic3—62no—
298Dic3—62no—
299Dic3—62no—
300Dic3—121no—
301Dic3—121no—
302Dic3—124no—
303Dic3—124no—
304C32#320911yescharacteristic, complemented, Sylow
305C23—91no—
306Q8—24no—
307Q8—68no—
308Q8—364no—
309Q8—362no—
310C2×C4—22no—
311C2×C4—64no—
312C2×C4—91no—
313C2×C4—94no—
314C2×C4—91no—
315C2×C4—91no—
316C2×C4—182no—
317C2×C4—182no—
318C2×C4—182no—
319C2×C4—364no—
320C2×C4#381111yescharacteristic
321C2×C4#381111yescharacteristic
322C2×C4C22×D3211yescharacteristic
323C8—64no—
324C2×C3—21no—
325C2×C3—21no—
326C2×C3—21no—
327C2×C3#571512yes—
328C2×C3C2×D3×Q1612yes—
329C2×C3C2×#91812yes—
330D3—64no—
331D3—122no—
332C22—92no—
333C22—181no—
334C22—181no—
335C22C2×#381111yescharacteristic
336C4—42no—
337C4—92no—
338C4—124no—
339C4—181no—
340C4—181no—
341C4—362no—
342C4#6394412yes—
343C4#6394512yes—
344C4#6431312yes—
345C3—21no—
346C3#8180212yescomplemented
347C2—182no—
348C2#1059530911yescharacteristic
349C2C2×#6394411yescharacteristic
350C2C2×#6394511yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenterC4⋊Q8D32
hypocenterC32#3209
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. C3×#5092C2semidirect
5. #10591633C2semidirect
7. #10590287C2semidirect
36. #5092D3semidirect
114. C4×C3⋊D3Q16semidirect
304. C32#3209semidirect
346. C3#81802semidirect

Maximal subgroups

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

subgroupindex
#105961992
#105939092
C3×#50922
#105916542
#105916332
#105902972
#105902872
#818023