Finite Group Databasebeta

← #11773883

Subgroups — #11773883

Order 1152.

616 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 616 conjugacy classes of subgroups — too many to draw. Only its 63 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
1C2×#63883C211yesmaximal, characteristic
2#10593803C211yesmaximal, characteristic
3#10591159C211yesmaximal, characteristic
4#10590028C214yesmaximal, complemented
5C22×C4×C3⋊D3C2211yescharacteristic
6C22×#624C411yescharacteristic
7C22×#624C411yescharacteristic
8C2×#3788—21no—
9C2×C3×Dic3⋊C4—21no—
10C2×Dic3⋊Dic3—21no—
11#63883—21no—
12#63883—21no—
13#63883C412yes—
14#63883C2212yes—
15C2×#3712—21no—
16C22⋊#622—21no—
17#63778C2212yes—
18C3×#830—21no—
19#63557C2212yes—
20C2×D3×C4⋊C4—61no—
21#4726—61no—
22C23×C3⋊D3C2×C411yescharacteristic
23C22×C32×C4D411yescharacteristic
24C22×C3⋊Dic3D411yescharacteristic
25C2×C4×C3⋊D3—42no—
26C2×C4×C3⋊D3C2×C411yescharacteristic
27C2×C4×C3⋊D3D411yescharacteristic
28C2×C4×C3⋊D3D411yescharacteristic
29C2×C4×C3⋊D3C2311yescharacteristic
30C22×C3×Dic3—21no—
31C22×C3×Dic3—21no—
32C2×#624—21no—
33C2×#624—24no—
34C2×#624—21no—
35C2×#624—42no—
36C2×#624C2×C412yes—
37C2×#624C2×C412yes—
38C2×#622—22no—
39#3788—42no—
40C3×Dic3⋊C4—22no—
41C3×Dic3⋊C4—22no—
42C2×C3×C3⋊C8—22no—
43Dic3⋊Dic3—22no—
44Dic3⋊Dic3—22no—
45#3712—42no—
46#1463—91nomaximal, Sylow
47C22×C4×D3—61no—
48C22×C4×D3—61no—
49C22×C4×D3—61no—
50C22×C4×D3—61no—
51C2×C3×C4⋊C4—61no—
52C2×C4⋊Dic3—61no—
53C2×Dic3⋊C4—21no—
54C2×Dic3⋊C4—61no—
55C2×ΓL(1,𝔽25)—62no—
56D3×C4⋊C4—62no—
57D3×C4⋊C4—62no—
58D3×C4⋊C4—62no—
59D3×C4⋊C4—62no—
60C3×C22⋊C8—61no—
61#830—21no—
62(C2×D3)⋊C8—62no—
63C23×C32C22⋊C411yescharacteristic
64C22×C3⋊D3—22no—
65C22×C3⋊D3—22no—
66C22×C3⋊D3—22no—
67C22×C3⋊D3C22⋊C411yescharacteristic
68C22×C3⋊D3C22×C411yescharacteristic
69C2×C32×C4—41no—
70C2×C32×C4C22⋊C411yescharacteristic
71C2×C32×C4C2×D411yescharacteristic
72C2×C3⋊Dic3—41no—
73C2×C3⋊Dic3C22⋊C411yescharacteristic
74C2×C3⋊Dic3C2×D411yescharacteristic
75C4×C3⋊D3—22no—
76C4×C3⋊D3—22no—
77C4×C3⋊D3—41no—
78C4×C3⋊D3—41no—
79C2×C3×Dic3—24no—
80C2×C3×Dic3—22no—
81C2×C3×Dic3—22no—
82C2×C3×Dic3—42no—
83#624—24no—
84#624—22no—
85#624—42no—
86#624—42no—
87#624M1614yescomplemented
88#622—42no—
89C3×C3⋊C8—42no—
90C22×C4⋊C4—91no—
91#407—91no—
92#407—91no—
93#324—94no—
94C23×D3—61no—
95C23×D3—61no—
96C22×C3×C4—21no—
97C22×C3×C4—21no—
98C22×C3×C4—61no—
99C22×C3×C4—61no—
100C22×Dic3—21no—
101C22×Dic3—21no—
102C22×Dic3—61no—
103C22×Dic3—61no—
104C2×C4×D3—62no—
105C2×C4×D3—61no—
106C2×C4×D3—62no—
107C2×C4×D3—61no—
108C2×C4×D3—61no—
109C2×C4×D3—61no—
110C2×C4×D3—61no—
111C2×C4×D3—61no—
112C2×C4×D3—61no—
113C2×C4×D3—61no—
114C2×C4×D3—62no—
115C2×C4×D3—68no—
116C2×C4×D3—62no—
117C2×C4×D3—124no—
118C2×C4×D3—124no—
119C2×C4×D3—124no—
120C2×C3×C8—62no—
121C3×C4⋊C4—62no—
122C3×C4⋊C4—62no—
123C4⋊Dic3—62no—
124C4⋊Dic3—62no—
125Dic3⋊C4—22no—
126Dic3⋊C4—22no—
127Dic3⋊C4—62no—
128Dic3⋊C4—62no—
129C2×C3⋊C8—22no—
130ΓL(1,𝔽25)—124no—
131C22×C32—21no—
132C22×C32—21no—
133C22×C32#10112yes—
134C22×C32C2×C22⋊C411yescharacteristic
135C2×C3⋊D3—28no—
136C2×C3⋊D3—21no—
137C2×C3⋊D3—21no—
138C2×C3⋊D3—21no—
139C2×C3⋊D3—21no—
140C2×C3⋊D3#9912yes—
141C2×C3⋊D3C2×M1612yes—
142C32×C4—21no—
143C32×C4—21no—
144C3⋊Dic3—21no—
145C3⋊Dic3—21no—
146C3×Dic3—24no—
147C3×Dic3—42no—
148C23×C4—91no—
149C23×C4—91no—
150C23×C4—91no—
151C2×M16—181no—
152C2×M16—181no—
153C2×C4⋊C4—61no—
154C2×C4⋊C4—92no—
155C2×C4⋊C4—92no—
156C2×C4⋊C4—181no—
157C2×C4⋊C4—181no—
158C2×C4⋊C4—181no—
159C22⋊C8—61no—
160C22⋊C8—92no—
161C22⋊C8—92no—
162C22⋊C8—181no—
163C23×C3—21no—
164C23×C3—21no—
165C22×D3—61no—
166C22×D3—61no—
167C22×D3—61no—
168C22×D3—61no—
169C22×D3—64no—
170C22×D3—64no—
171C22×D3—64no—
172C22×D3—122no—
173C22×D3—122no—
174C22×D3—122no—
175C2×C3×C4—21no—
176C2×C3×C4—21no—
177C2×C3×C4—21no—
178C2×C3×C4—21no—
179C2×C3×C4—42no—
180C2×C3×C4—42no—
181C2×C3×C4—62no—
182C2×C3×C4—64no—
183C2×C3×C4—62no—
184C2×C3×C4—122no—
185C2×Dic3—22no—
186C2×Dic3—24no—
187C2×Dic3—22no—
188C2×Dic3—42no—
189C2×Dic3—61no—
190C2×Dic3—61no—
191C2×Dic3—61no—
192C2×Dic3—61no—
193C2×Dic3—122no—
194C2×Dic3—122no—
195C4×D3—64no—
196C4×D3—64no—
197C4×D3—68no—
198C4×D3—64no—
199C4×D3—122no—
200C4×D3—122no—
201C4×D3—122no—
202C4×D3—124no—
203C4×D3—124no—
204C4×D3—122no—
205C4×D3—122no—
206C4×D3—122no—
207C4×D3—122no—
208C3×C8—122no—
209C3⋊C8—42no—
210C2×C32—22no—
211C2×C32#40711yescharacteristic
212C2×C32C2×#9911yescharacteristic
213C2×C32C2×#10111yescharacteristic
214C3⋊D3—22no—
215C3⋊D3—22no—
216C24—91no—
217C22×C4—61no—
218C22×C4—61no—
219C22×C4—92no—
220C22×C4—92no—
221C22×C4—91no—
222C22×C4—91no—
223C22×C4—91no—
224C22×C4—91no—
225C22×C4—91no—
226C22×C4—184no—
227C22×C4—181no—
228C22×C4—181no—
229C22×C4—362no—
230C22×C4—362no—
231C22×C4GO+(4,𝔽2)11yescharacteristic
232M16—362no—
233M16—362no—
234C2×C8—62no—
235C2×C8—182no—
236C4⋊C4—62no—
237C4⋊C4—62no—
238C4⋊C4—182no—
239C4⋊C4—182no—
240C22×C3—22no—
241C22×C3—22no—
242C22×C3—21no—
243C22×C3—21no—
244C22×C3—22no—
245C22×C3—22no—
246C22×C3—41no—
247C22×C3—41no—
248C2×D3—62no—
249C2×D3—62no—
250C2×D3—62no—
251C2×D3—62no—
252C2×D3—62no—
253C2×D3—62no—
254C2×D3—616no—
255C2×D3—62no—
256C2×D3—62no—
257C2×D3—121no—
258C2×D3—121no—
259C2×D3—121no—
260C2×D3—121no—
261C2×D3—128no—
262C3×C4—22no—
263C3×C4—41no—
264C3×C4—41no—
265C3×C4—41no—
266C3×C4—64no—
267C3×C4—122no—
268Dic3—24no—
269Dic3—42no—
270Dic3—62no—
271Dic3—121no—
272Dic3—121no—
273Dic3—121no—
274C32#146311yescharacteristic, complemented, Sylow
275C23—91no—
276C23—91no—
277C23—182no—
278C23—182no—
279C23—182no—
280C23D32⋊C411yescharacteristic
281C2×C4—41no—
282C2×C4—64no—
283C2×C4—62no—
284C2×C4—62no—
285C2×C4—94no—
286C2×C4—91no—
287C2×C4—91no—
288C2×C4—122no—
289C2×C4—182no—
290C2×C4—182no—
291C2×C4—182no—
292C2×C4—184no—
293C2×C4—361no—
294C2×C4—361no—
295C2×C4—362no—
296C2×C4—362no—
297C2×C4—361no—
298C2×C4D32⋊C411yescharacteristic
299C2×C4C2×GO+(4,𝔽2)11yescharacteristic
300C8—122no—
301C8—362no—
302C2×C3—24no—
303C2×C3—21no—
304C2×C3—21no—
305C2×C3—21no—
306C2×C3—21no—
307C2×C3—21no—
308C2×C3—21no—
309C2×C3—42no—
310D3—64no—
311D3—64no—
312D3—122no—
313D3—122no—
314C22—21no—
315C22—21no—
316C22—92no—
317C22—92no—
318C22—188no—
319C22—181no—
320C22—181no—
321C22—181no—
322C22—181no—
323C22#6372812yes—
324C22C2×D32⋊C411yescharacteristic
325C4—21no—
326C4—21no—
327C4—64no—
328C4—122no—
329C4—181no—
330C4—181no—
331C3—21no—
332C3—21no—
333C2—22no—
334C2—182no—
335C2—182no—
336C2#1059330711yescharacteristic
337C2C2×#6372811yescharacteristic
338C2#1059349011yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC22×C3⋊D3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3C2×C4
cosocleC2×C4×C3⋊D3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1463
LCSG ▷ C22×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #10590028C2semidirect
87. #624M16semidirect
274. C32#1463semidirect

Maximal subgroups

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

subgroupindex
C2×#638832
#105938032
#105911592
#105900282
#14639