Finite Group Databasebeta

← #11873381

Subgroups — #11873381

Order 1152.

922 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 922 conjugacy classes of subgroups — too many to draw. Only its 131 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#10594008C211yesmaximal, characteristic
2#10593909C211yesmaximal, characteristic, complemented
3C4×#3787C211yesmaximal, characteristic, complemented
4#10593366C214yesmaximal, complemented
5#10593365C214yesmaximal, complemented
6#10593348C214yesmaximal, complemented
7C2×#3802—21no—
8C2×#3802—21no—
9C2×#3802C2212yes—
10C2×#3797—21no—
11C2×#3787C2212yes—
12C42×C3⋊D3C2211yescharacteristic
13C3×#874—21no—
14C3×#869—21no—
15#63919—21no—
16#63919C2212yescomplemented
17#63914—21no—
18#63914C2212yes—
19#63914C2212yes—
20#63900—21no—
21#63900C2212yes—
22#63873C2212yescomplemented
23C4×#622C2212yescomplemented
24C4×#622C2212yescomplemented
25#63739C22116yescomplemented
26D3×C4⋊Q8—61no—
27D3×#127—61no—
28C22×D32—22no—
29C2×C4×C3⋊D3D411yescharacteristic
30C2×C4×C3⋊D3D411yescharacteristic
31C2×C4×C3⋊D3C2311yescharacteristic
32C2×C3×D12—22no—
33C2×C3×D12—22no—
34C2×C3×D12—22no—
35C2×C3×Dic6—22no—
36C2×#627—22no—
37C2×#625—22no—
38C2×#625—22no—
39C2×#625C2314yes—
40C2×#624—22no—
41#3802—28no—
42#3802—44no—
43#3802—44no—
44#3797—44no—
45C2×#622C2314yes—
46#3787—24no—
47C32×C42D411yescharacteristic
48C4×C3⋊Dic3D411yescharacteristic
49C4×C3⋊Dic3C2311yescharacteristic
50C4×C3⋊Dic3C2311yescharacteristic
51C3×C4⋊Dic3—22no—
52C3×C4⋊Dic3—22no—
53#3724—22no—
54#3724C2314yes—
55C2×#486—91nomaximal, Sylow
56C2×D3×Q8—62no—
57C2×D3×D4—62no—
58C2×D3×D4—62no—
59C2×D3×D4—62no—
60C3×C4⋊Q8—61no—
61C3×#127—61no—
62#944—62no—
63#940—62no—
64#940—62no—
65#940—62no—
66D3×C4⋊C4—62no—
67D3×C4⋊C4—62no—
68#888—62no—
69#888—62no—
70#874—21no—
71C42×D3—61no—
72C42×D3—61no—
73#869—21no—
74C22×C3⋊D3C2×D411yescharacteristic
75C22×C3×D3—24no—
76C2×D32—44no—
77C2×D32—44no—
78C2×D32—44no—
79C2×C32×C4C2×D411yescharacteristic
80C2×C32×C4C2×D411yescharacteristic
81C2×C32×C4C2×D411yescharacteristic
82C2×C3⋊Dic3C2×D411yescharacteristic
83C2×C3⋊Dic3C2×D411yescharacteristic
84C2×C3⋊Dic3C2411yescharacteristic
85C4×C3⋊D3D814yes—
86C4×C3⋊D3SD1614yes—
87C4×C3⋊D3#4114yes—
88C2×C3×Dic3—24no—
89C3×D12—44no—
90C3×D12—44no—
91C3×D12—44no—
92C3×Dic6—44no—
93#627—44no—
94#625—28no—
95#625—44no—
96#625—44no—
97#624—44no—
98#622—24no—
99C2×C4⋊Q8—91no—
100C2×#127—91no—
101#486—94no—
102#486—94no—
103C2×#102—94no—
104C2×C4×C8—91no—
105C23×D3—64no—
106C2×C3×Q8—62no—
107C2×C3×D4—62no—
108C2×C3×D4—62no—
109C2×C3×D4—62no—
110C2×#67—64no—
111C2×#67—64no—
112C2×#67—64no—
113D3×Q8—128no—
114D3×D4—128no—
115D3×D4—128no—
116D3×D4—128no—
117C2×D12—22no—
118C2×D12—22no—
119C2×D12—22no—
120C2×C4×D3—61no—
121C2×C4×D3—61no—
122C2×C4×D3—61no—
123C2×C4×D3—61no—
124C2×C4×D3—61no—
125C2×C4×D3—61no—
126C2×C4×D3—64no—
127C2×Dic6—22no—
128C2×Dic6—64no—
129C3×C4⋊C4—62no—
130C3×C4⋊C4—62no—
131C3×C42—21no—
132C3×C42—21no—
133C4⋊Dic3—22no—
134C4⋊Dic3—22no—
135Dic3⋊C4—64no—
136Dic3⋊C4—64no—
137C4×Dic3—61no—
138C4×Dic3—61no—
139C4×Dic3—61no—
140C4×Dic3—61no—
141C4×Dic3—61no—
142C4×Dic3—61no—
143C22×C32C22×D411yescharacteristic
144C2×C3⋊D3#12412yes—
145C2×C3⋊D3C2×D812yes—
146C2×C3⋊D3C2×SD1612yes—
147C2×C3×D3—44no—
148C2×C3×D3—44no—
149C2×C3×D3—44no—
150D32—88no—
151C32×C4#12412yes—
152C32×C4C2×D812yes—
153C32×C4C2×SD1612yes—
154C3⋊Dic3C2×D812yes—
155C3⋊Dic3C2×SD1612yes—
156C3⋊Dic3C2×#4112yes—
157C3×Dic3—44no—
158C22×Q8—181no—
159C22×D4—92no—
160C22×D4—181no—
161C22×D4—181no—
162C22×C8—92no—
163C4⋊Q8—61no—
164C4⋊Q8—92no—
165C4⋊Q8—92no—
166C4⋊Q8—181no—
167#127—61no—
168#127—92no—
169#127—92no—
170#127—181no—
171C2×C4⋊C4—92no—
172C2×C4⋊C4—181no—
173C2×C42—91no—
174#102—916no—
175C4×C8—92no—
176C4×C8—92no—
177C23×C3—64no—
178C22×D3—24no—
179C22×D3—61no—
180C22×D3—61no—
181C22×D3—128no—
182C22×D3—128no—
183C22×D3—128no—
184C3×Q8—124no—
185C3×D4—124no—
186C3×D4—124no—
187C3×D4—124no—
188C2×C3×C4—21no—
189C2×C3×C4—21no—
190C2×C3×C4—21no—
191C2×C3×C4—21no—
192C2×C3×C4—21no—
193C2×C3×C4—21no—
194C2×C3×C4—64no—
195#67—128no—
196#67—128no—
197#67—128no—
198C2×Dic3—24no—
199C2×Dic3—61no—
200C2×Dic3—61no—
201C2×Dic3—61no—
202C2×Dic3—61no—
203C2×Dic3—61no—
204C2×Dic3—61no—
205D12—44no—
206D12—44no—
207D12—44no—
208C4×D3—64no—
209C4×D3—64no—
210C4×D3—64no—
211C4×D3—64no—
212C4×D3—64no—
213C4×D3—64no—
214C4×D3—128no—
215Dic6—44no—
216Dic6—128no—
217C2×C32C2×#12411yescharacteristic
218C2×C32C22×D811yescharacteristic
219C2×C32C22×SD1611yescharacteristic
220C3⋊D3#48614yescomplemented
221C3×D3—84no—
222C24—182no—
223C2×Q8—62no—
224C2×Q8—182no—
225C2×Q8—364no—
226C2×D4—62no—
227C2×D4—62no—
228C2×D4—62no—
229C2×D4—94no—
230C2×D4—188no—
231C2×D4—182no—
232C2×D4—182no—
233C2×D4—364no—
234C2×D4—364no—
235C22×C4—91no—
236C22×C4—91no—
237C22×C4—91no—
238C22×C4—182no—
239C2×C8—94no—
240C2×C8—184no—
241C4⋊C4—62no—
242C4⋊C4—62no—
243C4⋊C4—94no—
244C4⋊C4—182no—
245C42—91no—
246C42—91no—
247C42—91no—
248C42GO+(4,𝔽2)11yescharacteristic
249C22×C3—21no—
250C22×C3—21no—
251C22×C3—124no—
252C22×C3—124no—
253C22×C3—124no—
254C2×D3—44no—
255C2×D3—44no—
256C2×D3—44no—
257C2×D3—62no—
258C2×D3—62no—
259C2×D3—62no—
260C2×D3—62no—
261C2×D3—62no—
262C2×D3—62no—
263C2×D3—2416no—
264C3×C4—22no—
265C3×C4—22no—
266C3×C4—22no—
267C3×C4—22no—
268C3×C4—22no—
269C3×C4—22no—
270C3×C4—124no—
271Dic3—44no—
272Dic3—62no—
273Dic3—62no—
274Dic3—62no—
275Dic3—62no—
276Dic3—62no—
277Dic3—62no—
278C32C2×#48611yescharacteristic, complemented, Sylow
279C23—64no—
280C23—91no—
281C23—364no—
282C23—364no—
283C23—364no—
284Q8—124no—
285Q8—364no—
286D4—124no—
287D4—124no—
288D4—124no—
289D4—188no—
290D4—364no—
291D4—364no—
292C2×C4—64no—
293C2×C4—91no—
294C2×C4—91no—
295C2×C4—91no—
296C2×C4—94no—
297C2×C4—94no—
298C2×C4—94no—
299C2×C4—364no—
300C2×C4C2×GO+(4,𝔽2)11yescharacteristic
301C2×C4C2×GO+(4,𝔽2)11yescharacteristic
302C2×C4C2×GO+(4,𝔽2)11yescharacteristic
303C8—184no—
304C2×C3—21no—
305C2×C3—21no—
306C2×C3—21no—
307C2×C3—21no—
308C2×C3—21no—
309C2×C3—21no—
310C2×C3—244no—
311D3—64no—
312D3—64no—
313D3—84no—
314C22—92no—
315C22—92no—
316C22—92no—
317C22—124no—
318C22—124no—
319C22—124no—
320C22—728no—
321C22C22×GO+(4,𝔽2)11yescharacteristic
322C4—92no—
323C4—92no—
324C4—92no—
325C4—124no—
326C4#6422112yes—
327C4#6422512yes—
328C4#6422712yes—
329C3—21no—
330C3—21no—
331C2—94no—
332C2—244no—
333C2C2×#6422111yescharacteristic
334C2C2×#6422511yescharacteristic
335C2C2×#6422711yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FittingC32×C42D4
socleC22×C32C22×D4
prime radical#10594008C2
hypercenterC42GO+(4,𝔽2)
hypocenterC32C2×#486
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
2. #10593909C2semidirect
3. C4×#3787C2semidirect
4. #10593366C2semidirect
5. #10593365C2semidirect
6. #10593348C2semidirect
16. #63919C22semidirect
22. #63873C22semidirect
23. C4×#622C22semidirect
24. C4×#622C22semidirect
25. #63739C22semidirect
220. C3⋊D3#486semidirect
278. C32C2×#486semidirect

Maximal subgroups

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

subgroupindex
#105940082
#105939092
C4×#37872
#105933662
#105933652
#105933482
C2×#4869