Finite Group Databasebeta

← #11791412

Subgroups — #11791412

Order 1152.

562 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 562 conjugacy classes of subgroups — too many to draw. Only its 71 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
2C4×C4⋊#157C211yesmaximal, characteristic, complemented
3C2×#63731C214yesmaximal, complemented
4C4×#3712C211yesmaximal, characteristic, complemented
5C2×#3798C2212yes—
6C2×C4⋊#157—21no—
7C2×C4×#157C2212yes—
8C42×C3⋊D3C2211yescharacteristic
9C3×C4×D12—21no—
10#63919C411yescharacteristic, complemented
11#63916—21no—
12#63915C412yescomplemented
13#63914C411yescharacteristic, complemented
14#63912—21no—
15C4×#625—21no—
16C2×#3712C2212yes—
17#63781—21no—
18#63731—28no—
19C3×C4×C3⋊C8—21no—
20#63555—21no—
21#5548—61no—
22C4×ΓL(1,𝔽25)—61no—
23C22×#157—22no—
24C2×C4×C3⋊D3D411yescharacteristic
25C2×C4×C3⋊D3D411yescharacteristic
26C2×C4×C3⋊D3C2311yescharacteristic
27C2×C3×D12—21no—
28C2×C3×C4×D3—22no—
29C2×#627C2×C412yes—
30C2×#626—22no—
31C2×#625—21no—
32C2×#625C2×C412yes—
33#3798—24no—
34#3798—24no—
35C4⋊#157—24no—
36C4×#157—24no—
37C32×C42D411yescharacteristic
38C4×C3⋊Dic3C2×C411yescharacteristic
39C4×C3⋊Dic3C2×C411yescharacteristic
40C4×C3⋊Dic3D411yescharacteristic
41C3×(C2×D3)⋊C4—22no—
42C3×C4⋊Dic3—21no—
43C2×C3×C3⋊C8—22no—
44#3724—21no—
45(C2×D3)⋊Dic3—22no—
46#3712—22no—
47#3712D414yescomplemented
48#1980—91nomaximal, Sylow
49C2×#235—62no—
50C3×C4×D4—61no—
51#940—61no—
52#938—61no—
53C4×#67—62no—
54C2×ΓL(1,𝔽25)—62no—
55#895—61no—
56#888—61no—
57#885—62no—
58#884—62no—
59C4×D12—21no—
60C42×D3—61no—
61C42×D3—61no—
62C3×C4×C8—61no—
63#815—62no—
64C4×C3⋊C8—21no—
65C22×C3⋊D3C2×D411yescharacteristic
66C22×C3×D3—22no—
67C2×#157—24no—
68C2×#157—42no—
69C2×#157—42no—
70C2×C32×C4C22⋊C411yescharacteristic
71C2×C32×C4C22⋊C411yescharacteristic
72C2×C32×C4C2×D411yescharacteristic
73C2×C3⋊Dic3C22⋊C411yescharacteristic
74C2×C3⋊Dic3C22⋊C411yescharacteristic
75C2×C3⋊Dic3C22×C411yescharacteristic
76C4×C3⋊D3—22no—
77C4×C3⋊D3—41no—
78C4×C3⋊D3C2×D412yes—
79C4×C3⋊D3#4112yes—
80C2×C3×Dic3—22no—
81C3×D12—42no—
82C3×C4×D3—44no—
83#627—24no—
84#626—42no—
85#626—42no—
86#625—24no—
87#625—42no—
88C3×C3⋊C8—24no—
89#532—91no—
90C2×#104—94no—
91C4×M16—91no—
92C4×C4⋊C4—91no—
93C2×C3×D4—61no—
94C22×C3×C4—62no—
95C2×#67—62no—
96C2×#67—62no—
97C2×#67—62no—
98#235—124no—
99#235—124no—
100C2×D12—21no—
101C2×D12—62no—
102C2×C4×D3—22no—
103C2×C4×D3—61no—
104C2×C4×D3—61no—
105C2×C4×D3—61no—
106C2×C4×D3—61no—
107C2×C4×D3—61no—
108C2×C4×D3—61no—
109C2×Dic6—62no—
110C2×C3×C8—62no—
111C3×C4⋊C4—61no—
112C3×C22⋊C4—62no—
113C3×C42—21no—
114C3×C42—21no—
115#217—62no—
116(C2×D3)⋊C4—22no—
117(C2×D3)⋊C4—62no—
118C4⋊Dic3—21no—
119Dic3⋊C4—62no—
120C4×Dic3—61no—
121C4×Dic3—61no—
122C4×Dic3—61no—
123C4×Dic3—61no—
124C4×Dic3—61no—
125C4×Dic3—61no—
126C2×C3⋊C8—22no—
127ΓL(1,𝔽25)—64no—
128ΓL(1,𝔽25)—64no—
129C22×C32C2×C22⋊C411yescharacteristic
130C2×C3⋊D3—21no—
131C2×C3⋊D3—21no—
132C2×C3⋊D3#12411yescharacteristic
133C2×C3⋊D3#12711yescharacteristic
134C2×C3×D3—42no—
135C2×C3×D3—42no—
136C2×C3×D3—42no—
137#157—44no—
138C32×C4—21no—
139C32×C4#10412yescomplemented
140C32×C4#12112yes—
141C3⋊Dic3—21no—
142C3⋊Dic3—21no—
143C3⋊Dic3C4×D412yes—
144C3×Dic3—42no—
145C2×#41—92no—
146C2×M16—92no—
147C4⋊Q8—91no—
148#127—91no—
149#124—92no—
150#121—181no—
151#121—181no—
152C4×D4—61no—
153C4×D4—181no—
154C2×C4⋊C4—181no—
155C2×C42—91no—
156C2×C42—92no—
157#104—188no—
158#97—181no—
159C4×C8—61no—
160#95—181no—
161C23×C3—62no—
162C22×D3—22no—
163C22×D3—61no—
164C22×D3—61no—
165C3×D4—122no—
166C2×C3×C4—21no—
167C2×C3×C4—21no—
168C2×C3×C4—21no—
169C2×C3×C4—21no—
170C2×C3×C4—21no—
171C2×C3×C4—21no—
172C2×C3×C4—62no—
173C2×C3×C4—124no—
174#67—124no—
175#67—122no—
176#67—122no—
177#67—124no—
178C2×Dic3—22no—
179C2×Dic3—61no—
180C2×Dic3—61no—
181C2×Dic3—61no—
182C2×Dic3—61no—
183C2×Dic3—61no—
184C2×Dic3—61no—
185D12—42no—
186D12—122no—
187D12—122no—
188C4×D3—44no—
189C4×D3—62no—
190C4×D3—62no—
191C4×D3—62no—
192C4×D3—62no—
193C4×D3—122no—
194C4×D3—122no—
195C4×D3—122no—
196C4×D3—122no—
197Dic6—124no—
198C3×C8—64no—
199C3⋊C8—24no—
200C2×C32#39011yescharacteristic
201C2×C32C2×#10411yescharacteristic
202C2×C32#42111yescharacteristic
203C3⋊D3—21no—
204C3⋊D3—21no—
205C3×D3—82no—
206#41—184no—
207#41—184no—
208C2×Q8—92no—
209C2×D4—61no—
210C2×D4—92no—
211C2×D4—182no—
212C2×D4—181no—
213C22×C4—62no—
214C22×C4—91no—
215C22×C4—91no—
216C22×C4—91no—
217C22×C4—182no—
218M16—94no—
219M16—182no—
220C2×C8—62no—
221C4⋊C4—61no—
222C4⋊C4—181no—
223C4⋊C4—184no—
224C22⋊C4—62no—
225C22⋊C4—182no—
226C42—91no—
227C42—91no—
228C42—91no—
229C42—184no—
230C42GO+(4,𝔽2)11yescharacteristic
231C22×C3—21no—
232C22×C3—21no—
233C22×C3—122no—
234C22×C3—122no—
235C22×C3—122no—
236C2×D3—42no—
237C2×D3—42no—
238C2×D3—42no—
239C2×D3—61no—
240C2×D3—61no—
241C2×D3—61no—
242C2×D3—61no—
243C2×D3—121no—
244C2×D3—121no—
245C2×D3—121no—
246C2×D3—121no—
247C3×C4—22no—
248C3×C4—22no—
249C3×C4—22no—
250C3×C4—22no—
251C3×C4—22no—
252C3×C4—41no—
253C3×C4—122no—
254Dic3—42no—
255Dic3—62no—
256Dic3—62no—
257Dic3—62no—
258Dic3—121no—
259Dic3—121no—
260Dic3—121no—
261C32#198011yescharacteristic, complemented, Sylow
262C23—62no—
263C23—91no—
264Q8—184no—
265D4—122no—
266D4—184no—
267D4—362no—
268D4—362no—
269D4—362no—
270C2×C4—62no—
271C2×C4—91no—
272C2×C4—92no—
273C2×C4—92no—
274C2×C4—91no—
275C2×C4—91no—
276C2×C4—124no—
277C2×C4—182no—
278C2×C4—184no—
279C2×C4—361no—
280C2×C4—362no—
281C2×C4—362no—
282C2×C4D32⋊C411yescharacteristic
283C2×C4D32⋊C411yescharacteristic
284C2×C4C2×GO+(4,𝔽2)11yescharacteristic
285C8—64no—
286C2×C3—21no—
287C2×C3—21no—
288C2×C3—21no—
289C2×C3—21no—
290C2×C3—21no—
291C2×C3—21no—
292C2×C3—242no—
293D3—82no—
294D3—121no—
295D3—121no—
296D3—121no—
297D3—121no—
298C22—91no—
299C22—91no—
300C22—122no—
301C22—122no—
302C22—122no—
303C22—181no—
304C22—181no—
305C22C2×D32⋊C411yescharacteristic
306C4—21no—
307C4—92no—
308C4—122no—
309C4—181no—
310C4—181no—
311C4—364no—
312C4#6373112yescomplemented
313C4#6423012yes—
314C3—21no—
315C3—21no—
316C2—181no—
317C2—181no—
318C2—242no—
319C2C2×#6373111yescharacteristic
320C2#1059332411yescharacteristic
321C2#1059340511yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC32×C42D4
socleC22×C32C2×C22⋊C4
prime radical#10593972C2
cosocleC2×C4×C3⋊D3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1980
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
2. C4×C4⋊#157C2semidirect
3. C2×#63731C2semidirect
4. C4×#3712C2semidirect
10. #63919C4semidirect
12. #63915C4semidirect
13. #63914C4semidirect
47. #3712D4semidirect
139. C32×C4#104semidirect
261. C32#1980semidirect
312. C4#63731semidirect

Maximal subgroups

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

subgroupindex
#105939722
C4×C4⋊#1572
C2×#637312
C4×#37122
#19809