Finite Group Databasebeta

← #11775067

Subgroups — #11775067

Order 1152.

536 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 67 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#10594929C211yesmaximal, characteristic
2#10593801C211yesmaximal, characteristic, complemented
3#10591274C211yesmaximal, characteristic, complemented
4#10590071C214yesmaximal, complemented
5C2×#3805—21no—
6C2×C4×C3⋊Dic3C2211yescharacteristic
7C3×#930—21no—
8C2×C3×C4⋊Dic3—21no—
9#63980C2212yes—
10C2×Dic32—21no—
11#63919C411yescharacteristic, complemented
12#63915—21no—
13#63914C411yescharacteristic, complemented
14#63902C412yescomplemented
15#63898—21no—
16C22⋊#622C2212yes—
17#63779—21no—
18C4×#622—21no—
19#63579C2212yes—
20#5596—61no—
21Dic3×C4⋊C4—61no—
22C22×C32×C4D411yescharacteristic
23C22×C3⋊Dic3D411yescharacteristic
24C22×C3⋊Dic3C2311yescharacteristic
25C2×C3×#67—22no—
26C22×C3×Dic3—22no—
27C2×C3×D12—21no—
28C2×#627—21no—
29C2×#625—21no—
30C2×#625C2×C412yes—
31#3805—42no—
32#3805—42no—
33C2×D3×Dic3—22no—
34C2×#622—22no—
35C4×C3⋊Dic3C2×C411yescharacteristic
36C4×C3⋊Dic3C2×C411yescharacteristic
37C4×C3⋊Dic3D411yescharacteristic
38C4×C3⋊Dic3D411yescharacteristic
39C3×(C2×D3)⋊C4—22no—
40C3×C4⋊Dic3—24no—
41C3×C4⋊Dic3—21no—
42#3724C2×C412yes—
43(C2×D3)⋊Dic3—22no—
44Dic32—42no—
45#1502—91nomaximal, Sylow
46C2×#237—62no—
47C3×#121—61no—
48C2×C3×C4⋊C4—61no—
49#940—61no—
50#939—62no—
51D4×Dic3—61no—
52#930—21no—
53C2×C4⋊Dic3—21no—
54C2×C4×Dic3—61no—
55C2×C4×Dic3—61no—
56C2×C4×Dic3—62no—
57#893—61no—
58#888—61no—
59#885—62no—
60#67⋊C4—62no—
61C3⋊#95—62no—
62C23×C32C2×D411yescharacteristic
63C22×C3×D3—22no—
64C2×C32×C4—22no—
65C2×C32×C4C22⋊C411yescharacteristic
66C2×C32×C4C22⋊C411yescharacteristic
67C2×C3⋊Dic3—41no—
68C2×C3⋊Dic3C22⋊C411yescharacteristic
69C2×C3⋊Dic3C22⋊C411yescharacteristic
70C2×C3⋊Dic3D812yes—
71C2×C3⋊Dic3SD1612yes—
72C2×C3⋊Dic3C22×C411yescharacteristic
73C2×C3⋊Dic3C2×D411yescharacteristic
74C3×#67—42no—
75C3×#67—42no—
76C2×C3×Dic3—24no—
77C2×C3×Dic3—22no—
78C2×C3×Dic3—42no—
79C2×C3×Dic3—42no—
80C3×D12—42no—
81#627—42no—
82#625—42no—
83#625—42no—
84D3×Dic3—44no—
85#622—42no—
86#532—91no—
87#431—91no—
88C4×C4⋊C4—91no—
89#327—94no—
90C2×C3×D4—61no—
91C2×C3×D4—62no—
92C22×C3×C4—21no—
93C22×C3×C4—21no—
94C22×C3×C4—62no—
95C2×#67—22no—
96C2×#67—62no—
97C2×#67—62no—
98C22×Dic3—22no—
99C22×Dic3—61no—
100C22×Dic3—61no—
101C22×Dic3—61no—
102C22×Dic3—61no—
103C22×Dic3—62no—
104#237—124no—
105#237—124no—
106C2×D12—21no—
107C2×C4×D3—62no—
108C2×Dic6—62no—
109C3×C4⋊C4—61no—
110C3×C4⋊C4—64no—
111C3×C22⋊C4—62no—
112#217—62no—
113(C2×D3)⋊C4—22no—
114(C2×D3)⋊C4—62no—
115C4⋊Dic3—21no—
116C4⋊Dic3—24no—
117Dic3⋊C4—62no—
118C4×Dic3—61no—
119C4×Dic3—61no—
120C4×Dic3—61no—
121C4×Dic3—61no—
122C4×Dic3—61no—
123C4×Dic3—61no—
124C4×Dic3—61no—
125C4×Dic3—61no—
126C4×Dic3—124no—
127C22×C32—21no—
128C22×C32—21no—
129C22×C32C2×C22⋊C411yescharacteristic
130C22×C32C2×D811yescharacteristic
131C22×C32C2×SD1611yescharacteristic
132C2×C3×D3—42no—
133C2×C3×D3—42no—
134C2×C3×D3—42no—
135C32×C4—21no—
136C32×C4#10412yes—
137C3⋊Dic3—21no—
138C3⋊Dic3—21no—
139C3⋊Dic3#10212yes—
140C3⋊Dic3#10212yes—
141C3×Dic3—44no—
142C3×Dic3—42no—
143C2×#41—181no—
144C4⋊Q8—91no—
145#127—91no—
146#124—181no—
147#121—61no—
148#121—92no—
149C4×D4—92no—
150C4×D4—181no—
151C2×C4⋊C4—61no—
152C2×C42—91no—
153C2×C42—181no—
154C4⋊C8—181no—
155C22⋊C8—92no—
156C4×C8—181no—
157#95—92no—
158C23×C3—21no—
159C23×C3—21no—
160C23×C3—62no—
161C22×D3—22no—
162C3×D4—122no—
163C3×D4—122no—
164C3×D4—122no—
165C2×C3×C4—22no—
166C2×C3×C4—22no—
167C2×C3×C4—21no—
168C2×C3×C4—21no—
169C2×C3×C4—21no—
170C2×C3×C4—21no—
171C2×C3×C4—42no—
172C2×C3×C4—62no—
173C2×C3×C4—64no—
174C2×C3×C4—122no—
175C2×C3×C4—122no—
176#67—42no—
177#67—42no—
178#67—124no—
179#67—124no—
180C2×Dic3—22no—
181C2×Dic3—24no—
182C2×Dic3—42no—
183C2×Dic3—42no—
184C2×Dic3—61no—
185C2×Dic3—61no—
186C2×Dic3—61no—
187C2×Dic3—61no—
188C2×Dic3—62no—
189C2×Dic3—62no—
190C2×Dic3—62no—
191C2×Dic3—62no—
192C2×Dic3—61no—
193C2×Dic3—61no—
194C2×Dic3—61no—
195C2×Dic3—61no—
196C2×Dic3—124no—
197C2×Dic3—122no—
198C2×Dic3—121no—
199C2×Dic3—121no—
200D12—42no—
201C4×D3—124no—
202Dic6—124no—
203C2×C32—21no—
204C2×C32—21no—
205C2×C32#41011yescharacteristic
206C2×C32C2×#10211yescharacteristic
207C2×C32C2×#10411yescharacteristic
208C3×D3—82no—
209#41—362no—
210#41—362no—
211C2×Q8—181no—
212C2×D4—62no—
213C2×D4—61no—
214C2×D4—92no—
215C2×D4—181no—
216C22×C4—62no—
217C22×C4—91no—
218C22×C4—91no—
219C22×C4—182no—
220C22×C4GO+(4,𝔽2)11yescharacteristic
221C2×C8—182no—
222C4⋊C4—64no—
223C4⋊C4—61no—
224C4⋊C4—92no—
225C22⋊C4—62no—
226C22⋊C4—182no—
227C42—91no—
228C42—91no—
229C42—91no—
230C42—91no—
231C42—362no—
232C22×C3—21no—
233C22×C3—21no—
234C22×C3—21no—
235C22×C3—21no—
236C22×C3—21no—
237C22×C3—21no—
238C22×C3—21no—
239C22×C3—21no—
240C22×C3—21no—
241C22×C3—21no—
242C22×C3—41no—
243C22×C3—41no—
244C22×C3—122no—
245C22×C3—122no—
246C22×C3—122no—
247C2×D3—42no—
248C2×D3—42no—
249C2×D3—42no—
250C3×C4—22no—
251C3×C4—22no—
252C3×C4—22no—
253C3×C4—41no—
254C3×C4—122no—
255C3×C4—124no—
256Dic3—42no—
257Dic3—44no—
258Dic3—62no—
259Dic3—62no—
260Dic3—62no—
261Dic3—62no—
262Dic3—62no—
263Dic3—121no—
264Dic3—121no—
265Dic3—121no—
266C32#150211yescharacteristic, complemented, Sylow
267C23—62no—
268C23C2×GO+(4,𝔽2)11yescharacteristic
269Q8—362no—
270D4—122no—
271D4—122no—
272D4—122no—
273D4—362no—
274D4—362no—
275C2×C4—22no—
276C2×C4—64no—
277C2×C4—62no—
278C2×C4—92no—
279C2×C4—92no—
280C2×C4—91no—
281C2×C4—91no—
282C2×C4—91no—
283C2×C4—91no—
284C2×C4—122no—
285C2×C4—122no—
286C2×C4—364no—
287C2×C4—361no—
288C2×C4D32⋊C411yescharacteristic
289C2×C4D32⋊C411yescharacteristic
290C8—362no—
291C2×C3—21no—
292C2×C3—21no—
293C2×C3—21no—
294C2×C3—21no—
295C2×C3—21no—
296C2×C3—21no—
297C2×C3—21no—
298C2×C3—21no—
299C2×C3—21no—
300C2×C3—21no—
301C2×C3—41no—
302C2×C3—41no—
303C2×C3—242no—
304D3—82no—
305C22—21no—
306C22—21no—
307C22—122no—
308C22—122no—
309C22—122no—
310C22#6422511yescharacteristic
311C22#6422711yescharacteristic
312C22C2×D32⋊C411yescharacteristic
313C4—21no—
314C4—92no—
315C4—92no—
316C4—124no—
317C4—122no—
318C4—181no—
319C4—181no—
320C4#6374112yes—
321C3—21no—
322C3—21no—
323C2—21no—
324C2—21no—
325C2—242no—
326C2#1059334611yescharacteristic
327C2#1059336511yescharacteristic
328C2C2×#6374111yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC23C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radical#10594929C2
cosocleC22×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1502
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. #10593801C2semidirect
3. #10591274C2semidirect
4. #10590071C2semidirect
11. #63919C4semidirect
13. #63914C4semidirect
14. #63902C4semidirect
266. C32#1502semidirect

Maximal subgroups

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

subgroupindex
#105949292
#105938012
#105912742
#105900712
#15029