Finite Group Databasebeta

← #11774500

Subgroups — #11774500

Order 1152.

583 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 583 conjugacy classes of subgroups — too many to draw. Only its 100 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#10593972C211yesmaximal, characteristic
2#10592532C211yesmaximal, characteristic, complemented
3C4×#3712C211yesmaximal, characteristic, complemented
4C3×#4483C212yesmaximal, complemented
5#10589081C212yesmaximal, complemented
6#68171—32nomaximal
7C2×#3798—21no—
8C42×C3⋊D3C2211yescharacteristic
9C3×C4×D12C2212yes—
10#63919C411yescharacteristic
11#63916C412yes—
12#63915—21no—
13#63914C411yescharacteristic
14#63912—21no—
15C4×#625—21no—
16C2×#3712—21no—
17C32×C4⋊C8C2211yescharacteristic
18#63647—21no—
19C8×C3⋊Dic3—21no—
20C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
21C3×C4×C3⋊C8C2212yes—
22#63555—21no—
23#5548—32no—
24#4833—32no—
25#4833—61no—
26C4×ΓL(1,𝔽25)—32no—
27C3×D4⋊C8—32no—
28D4⋊(C3⋊C8)—32no—
29#4483D312yescomplemented
30#4459—32no—
31C2×C4×C3⋊D3C2×C411yescharacteristic
32C2×C4×C3⋊D3D411yescharacteristic
33C2×C4×C3⋊D3D411yescharacteristic
34C2×C3×D12C2×C412yes—
35C2×C3×C4×D3—22no—
36C2×#627—21no—
37C2×#626—22no—
38C2×#625—21no—
39C2×#625—21no—
40#3798—42no—
41#3798—42no—
42C2×C32×C8—21no—
43C32×C42C2311yescharacteristic
44C4×C3⋊Dic3C2×C411yescharacteristic
45C4×C3⋊Dic3D411yescharacteristic
46C4×C3⋊Dic3D411yescharacteristic
47C2×C3⋊(C3⋊C8)—21no—
48C3×(C2×D3)⋊C4—22no—
49C3×C4⋊Dic3C2×C412yes—
50C2×C3×C3⋊C8—22no—
51#3724—21no—
52(C2×D3)⋊Dic3—22no—
53#3712—24no—
54#1484—91noSylow
55C2×#235—62no—
56C3×C4×D4—32no—
57#940—32no—
58#938—32no—
59C4×#67—62no—
60C2×ΓL(1,𝔽25)—62no—
61#895—32no—
62#888—32no—
63#885—62no—
64#884—62no—
65C4×D12C2×D312yes—
66C42×D3—32no—
67C42×D3—61no—
68C3×C4⋊C8—21no—
69C3×C4⋊C8C2×D312yes—
70C3×C4×C8—32no—
71(C2×D3)⋊C8—62no—
72(C2×D3)⋊C8—62no—
73#815—62no—
74C8×Dic3—62no—
75C8×Dic3—62no—
76C4⋊(C3⋊C8)—32no—
77C4⋊(C3⋊C8)—61no—
78C4×C3⋊C8C2×D312yes—
79C22×C3⋊D3C22⋊C411yescharacteristic
80C22×C3×D3—22no—
81C2×C32×C4C22×C411yescharacteristic
82C2×C32×C4C2×D411yescharacteristic
83C2×C32×C4C2×D411yescharacteristic
84C2×C3⋊Dic3C22⋊C411yescharacteristic
85C2×C3⋊Dic3C22⋊C411yescharacteristic
86C2×C3⋊Dic3C22⋊C411yescharacteristic
87C4×C3⋊D3—21no—
88C4×C3⋊D3—21no—
89C4×C3⋊D3—21no—
90C4×C3⋊D3—21no—
91C4×C3⋊D3—22no—
92C2×C3×Dic3—22no—
93C3×D12—22no—
94C3×D12—22no—
95C3×C4×D3—42no—
96C3×C4×D3—42no—
97#627—42no—
98#626—44no—
99#625—42no—
100#625—42no—
101C32×C8—41no—
102C3⋊(C3⋊C8)—41no—
103C3×C3⋊C8—24no—
104#532—91no—
105#431—91no—
106C4×M16—91no—
107D4⋊C8—32no—
108D4⋊C8—92no—
109C2×C3×D4—32no—
110C22×C3×C4—62no—
111C2×#67—62no—
112C2×#67—62no—
113C2×#67—62no—
114#235—124no—
115#235—124no—
116C2×D12—62no—
117C2×D12C4×D312yes—
118C2×C4×D3—22no—
119C2×C4×D3—32no—
120C2×C4×D3—32no—
121C2×C4×D3—32no—
122C2×C4×D3—61no—
123C2×C4×D3—61no—
124C2×C4×D3—61no—
125C2×Dic6—62no—
126C2×C3×C8—22no—
127C2×C3×C8—22no—
128C2×C3×C8—62no—
129C3×C4⋊C4—32no—
130C3×C22⋊C4—62no—
131C3×C42—21no—
132C3×C42C22×D312yes—
133#217—62no—
134(C2×D3)⋊C4—22no—
135(C2×D3)⋊C4—62no—
136C4⋊Dic3C4×D312yes—
137Dic3⋊C4—62no—
138C4×Dic3—32no—
139C4×Dic3—32no—
140C4×Dic3—32no—
141C4×Dic3—61no—
142C4×Dic3—61no—
143C4×Dic3—61no—
144C2×C3⋊C8—22no—
145C2×C3⋊C8—62no—
146C2×C3⋊C8—62no—
147ΓL(1,𝔽25)—68no—
148C22×C32C2×C22⋊C411yescharacteristic
149C2×C3⋊D3—21no—
150C2×C3⋊D3—21no—
151C2×C3⋊D3—21no—
152C2×C3×D3—42no—
153C2×C3×D3—42no—
154C2×C3×D3—42no—
155C32×C4—21no—
156C32×C4#13111yescharacteristic
157C32×C4#13111yescharacteristic
158C32×C4AGL(1,ℤ/8)11yescharacteristic
159C32×C4AGL(1,ℤ/8)11yescharacteristic
160C3⋊Dic3—21no—
161C3⋊Dic3—21no—
162C3⋊Dic3#10412yes—
163C3×Dic3—42no—
164C2×#41—181no—
165C2×M16—181no—
166C4⋊Q8—91no—
167#127—91no—
168#124—181no—
169#121—92no—
170#121—181no—
171C4×D4—32no—
172C4×D4—181no—
173C2×C42—91no—
174C4⋊C8—91no—
175C4⋊C8D3211yescharacteristic
176C22⋊C8—181no—
177#97—181no—
178C4×C8—32no—
179C4×C8—181no—
180C23×C3—62no—
181C22×D3—22no—
182C22×D3—32no—
183C22×D3—61no—
184C3×D4—62no—
185C3×D4—62no—
186C2×C3×C4—21no—
187C2×C3×C4—21no—
188C2×C3×C4—21no—
189C2×C3×C4—62no—
190C2×C3×C4—122no—
191C2×C3×C4—122no—
192C2×C3×C4C2×C4×D312yes—
193C2×C3×C4D3×D412yes—
194C2×C3×C4D3×D412yes—
195#67—124no—
196#67—124no—
197#67—124no—
198C2×Dic3—22no—
199C2×Dic3—32no—
200C2×Dic3—32no—
201C2×Dic3—32no—
202C2×Dic3—61no—
203C2×Dic3—61no—
204C2×Dic3—61no—
205D12—22no—
206D12—22no—
207D12—124no—
208C4×D3—42no—
209C4×D3—42no—
210C4×D3—64no—
211C4×D3—62no—
212C4×D3—62no—
213C4×D3—62no—
214C4×D3—62no—
215C4×D3—62no—
216C4×D3—62no—
217C4×D3—122no—
218C4×D3—121no—
219C4×D3—121no—
220Dic6—124no—
221C3×C8—42no—
222C3×C8—42no—
223C3×C8—64no—
224C3⋊C8—24no—
225C3⋊C8—122no—
226C3⋊C8—122no—
227C2×C32#40811yescharacteristic
228C2×C32#41811yescharacteristic
229C2×C32C2×#10411yescharacteristic
230C3⋊D3—41no—
231C3×D3—82no—
232#41—362no—
233#41—362no—
234C2×Q8—181no—
235C2×D4—32no—
236C2×D4—182no—
237C2×D4—181no—
238C2×D4—181no—
239C22×C4—62no—
240C22×C4—91no—
241C22×C4—91no—
242C22×C4—91no—
243M16—184no—
244C2×C8—21no—
245C2×C8—62no—
246C2×C8—181no—
247C4⋊C4—32no—
248C4⋊C4—181no—
249C22⋊C4—62no—
250C22⋊C4—182no—
251C42—91no—
252C42—91no—
253C42—91no—
254C42C2×D3211yescharacteristic
255C22×C3—21no—
256C22×C3—122no—
257C22×C3—122no—
258C22×C3—122no—
259C22×C3D3×C22⋊C412yes—
260C2×D3—42no—
261C2×D3—42no—
262C2×D3—42no—
263C2×D3—62no—
264C2×D3—62no—
265C2×D3—62no—
266C2×D3—62no—
267C2×D3—121no—
268C2×D3—121no—
269C3×C4—22no—
270C3×C4—21no—
271C3×C4—21no—
272C3×C4—21no—
273C3×C4—21no—
274C3×C4—41no—
275C3×C4—122no—
276C3×C4#90112yes—
277C3×C4#90712yes—
278C3×C4#91112yes—
279C3×C4#91412yes—
280Dic3—34no—
281Dic3—42no—
282Dic3—62no—
283Dic3—62no—
284Dic3—62no—
285Dic3—62no—
286Dic3—121no—
287C32#148411yescharacteristic, complemented, Sylow
288C23—62no—
289C23—91no—
290Q8—362no—
291D4—62no—
292D4—62no—
293D4—362no—
294D4—364no—
295D4—362no—
296C2×C4—62no—
297C2×C4—91no—
298C2×C4—91no—
299C2×C4—91no—
300C2×C4—122no—
301C2×C4—122no—
302C2×C4—182no—
303C2×C4—181no—
304C2×C4—181no—
305C2×C4—181no—
306C2×C4—181no—
307C2×C4C4×D3211yescharacteristic
308C2×C4#380211yescharacteristic
309C2×C4#381111yescharacteristic
310C8—41no—
311C8—64no—
312C8—361no—
313C2×C3—21no—
314C2×C3—21no—
315C2×C3—21no—
316C2×C3—242no—
317C2×C3#472712yes—
318C2×C3#477012yes—
319C2×C3D3×#10412yes—
320D3—82no—
321D3—122no—
322D3—122no—
323C22—122no—
324C22—122no—
325C22—122no—
326C22—181no—
327C22—181no—
328C22—181no—
329C22#6392111yescharacteristic
330C4—21no—
331C4—92no—
332C4—122no—
333C4—181no—
334C4—181no—
335C4#6380311yescharacteristic
336C4#6380511yescharacteristic
337C4#6392711yescharacteristic
338C4#6394111yescharacteristic
339C3—21no—
340C3#6817112yescomplemented
341C2—242no—
342C2—361no—
343C2#1059059411yescharacteristic
344C2#1059095811yescharacteristic
345C2#1059100811yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32C2×C22⋊C4
prime radical#10593972C2
cosocleC32×C42C23
hypercenterC4⋊C8D32
hypocenterC32#1484
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10592532C2semidirect
3. C4×#3712C2semidirect
4. C3×#4483C2semidirect
5. #10589081C2semidirect
29. #4483D3semidirect
287. C32#1484semidirect
340. C3#68171semidirect

Maximal subgroups

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

subgroupindex
#105939722
#105925322
C4×#37122
C3×#44832
#105890812
#681713