Finite Group Databasebeta

← #11771927

Subgroups — #11771927

Order 1152.

425 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 425 conjugacy classes of subgroups — too many to draw. Only its 64 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#10592646C211yesmaximal, characteristic
2C3×#4526C211yesmaximal, characteristic
3C3×#4525C211yesmaximal, characteristic
4#67490—31nomaximal
5#67449—31nomaximal
6C22×#634C411yescharacteristic, complemented
7C2×C32×C22⋊C4C2211yescharacteristic
8C2×#3757—21no—
9C2×C3×#217—21no—
10#63658—21no—
11#63658C411yescharacteristic, complemented
12C3×#830—21no—
13#4947—31no—
14#4947—31no—
15#4947—61no—
16C3×#342—31no—
17C3×#323—31no—
18#4526D311yescharacteristic
19#4525D311yescharacteristic
20C24×C32D411yescharacteristic
21C22×C32×C4C2×C411yescharacteristic
22C22×C32×C4D411yescharacteristic
23C22×C3⋊Dic3—21no—
24C22×C3⋊Dic3—21no—
25C2×#634—41no—
26C2×#634—42no—
27C22×C3×Dic3—41no—
28C32×C22⋊C4—41no—
29#3757—42no—
30C3×#217—22no—
31C3×#217—41no—
32C2×C3×C3⋊C8—41no—
33#1351—91noSylow
34C22×Dic6—31no—
35C22×Dic6—31no—
36C22×Dic6—61no—
37C2×C3×C22⋊C4—21no—
38C2×C3×C22⋊C4—61no—
39C2×C3×C22⋊C4C2×D311yescharacteristic
40C2×C3×C22⋊C4C2×D311yescharacteristic
41C2×#217—21no—
42C2×#217—62no—
43C2×#217—61no—
44C2×#217—61no—
45C3×C22⋊C8—61no—
46C3⋊#95—31no—
47C3⋊#95—31no—
48C3⋊#95—61no—
49C3⋊#95—62no—
50C3⋊#95—61no—
51C3⋊#95—61no—
52#830—21no—
53C23×C32—21no—
54C23×C32—21no—
55C23×C32—41no—
56C23×C32—41no—
57C23×C32C22⋊C411yescharacteristic
58C23×C32SD1611yescharacteristic
59C23×C32Q1611yescharacteristic
60C2×C32×C4—21no—
61C2×C32×C4—21no—
62C2×C32×C4—41no—
63C2×C32×C4—41no—
64C2×C3⋊Dic3—22no—
65C2×C3⋊Dic3—41no—
66C2×C3⋊Dic3—41no—
67C2×C3⋊Dic3—41no—
68C2×C3⋊Dic3—41no—
69C2×C3⋊Dic3—41no—
70#634—42no—
71#634—42no—
72C2×C3×Dic3—42no—
73C2×C3×Dic3—81no—
74C2×C3×Dic3—81no—
75C3×C3⋊C8—81no—
76#393—91no—
77#342—31no—
78#323—31no—
79C24×C3—21no—
80C24×C3D1211yescharacteristic
81C24×C3#6711yescharacteristic
82C22×C3×C4—21no—
83C22×C3×C4—21no—
84C22×C3×C4—121no—
85C22×C3×C4C4×D311yescharacteristic
86C22×C3×C4C4×D311yescharacteristic
87C22×C3×C4D1211yescharacteristic
88C22×C3×C4#6711yescharacteristic
89C22×Dic3—41no—
90C22×Dic3—62no—
91C22×Dic3—61no—
92C22×Dic3—61no—
93C22×Dic3—62no—
94C22×Dic3—61no—
95C22×Dic3—61no—
96C2×Dic6—124no—
97C2×Dic6—122no—
98C2×Dic6—121no—
99C2×Dic6—121no—
100C2×Dic6—122no—
101C2×Dic6—122no—
102C2×C3×C8—121no—
103C3×C22⋊C4—41no—
104C3×C22⋊C4—41no—
105C3×C22⋊C4—42no—
106C3×C22⋊C4—62no—
107C3×C22⋊C4—121no—
108#217—22no—
109#217—41no—
110#217—122no—
111#217—122no—
112#217—124no—
113C2×C3⋊C8—41no—
114C22×C32—21no—
115C22×C32—21no—
116C22×C32—21no—
117C22×C32—21no—
118C22×C32—41no—
119C22×C32—41no—
120C22×C32—41no—
121C22×C32—41no—
122C22×C32—81no—
123C22×C32#9911yescharacteristic
124C22×C32#10311yescharacteristic
125C22×C32#10411yescharacteristic
126C32×C4—41no—
127C32×C4—41no—
128C3⋊Dic3—42no—
129C3⋊Dic3—81no—
130C3×Dic3—82no—
131C22×Q8—91no—
132C2×C22⋊C4—61no—
133C2×C22⋊C4—181no—
134C2×C22⋊C4D3211yescharacteristic
135C22⋊C8—61no—
136#95—91no—
137#95—181no—
138C23×C3—21no—
139C23×C3—21no—
140C23×C3—21no—
141C23×C3—21no—
142C23×C3—21no—
143C23×C3—21no—
144C23×C3—21no—
145C23×C3—41no—
146C23×C3—41no—
147C23×C3—41no—
148C23×C3—41no—
149C23×C3—41no—
150C23×C3—41no—
151C23×C3—42no—
152C23×C3—42no—
153C23×C3#20411yescharacteristic
154C23×C3Dic1211yescharacteristic
155C23×C3(C2×D3)⋊C411yescharacteristic
156C23×C3(C2×D3)⋊C411yescharacteristic
157C23×C3#21411yescharacteristic
158C23×C3#21611yescharacteristic
159C2×C3×C4—22no—
160C2×C3×C4—21no—
161C2×C3×C4—21no—
162C2×C3×C4—21no—
163C2×C3×C4—21no—
164C2×C3×C4—41no—
165C2×C3×C4—42no—
166C2×C3×C4—41no—
167C2×C3×C4—41no—
168C2×C3×C4—41no—
169C2×C3×C4—41no—
170C2×C3×C4—42no—
171C2×C3×C4—122no—
172C2×C3×C4—241no—
173C2×C3×C4—241no—
174C2×Dic3—42no—
175C2×Dic3—64no—
176C2×Dic3—62no—
177C2×Dic3—62no—
178C2×Dic3—81no—
179C2×Dic3—81no—
180C2×Dic3—122no—
181C2×Dic3—121no—
182C2×Dic3—121no—
183C2×Dic3—122no—
184C2×Dic3—121no—
185C2×Dic3—121no—
186C2×Dic3—122no—
187C2×Dic3—121no—
188C2×Dic3—121no—
189C2×Dic3—122no—
190C2×Dic3—121no—
191C2×Dic3—121no—
192C2×Dic3—122no—
193C2×Dic3—121no—
194C2×Dic3—121no—
195Dic6—124no—
196Dic6—124no—
197Dic6—122no—
198Dic6—122no—
199Dic6—122no—
200Dic6—122no—
201C3×C8—241no—
202C3⋊C8—81no—
203C2×C32—21no—
204C2×C32—21no—
205C2×C32—41no—
206C2×C32—41no—
207C2×C32#32811yescharacteristic
208C2×C32AΣL(1,𝔽16)11yescharacteristic
209C2×C32#35411yescharacteristic
210C24#62611yescharacteristic
211C2×Q8—361no—
212C2×Q8—362no—
213C22×C4—121no—
214C22×C4—181no—
215C22×C4—181no—
216C22×C4#62411yescharacteristic
217C22×C4#62611yescharacteristic
218C2×C8—121no—
219C22⋊C4—41no—
220C22⋊C4—62no—
221C22⋊C4—121no—
222C22⋊C4—362no—
223C22×C3—22no—
224C22×C3—22no—
225C22×C3—21no—
226C22×C3—21no—
227C22×C3—21no—
228C22×C3—21no—
229C22×C3—21no—
230C22×C3—21no—
231C22×C3—21no—
232C22×C3—21no—
233C22×C3—21no—
234C22×C3—21no—
235C22×C3—21no—
236C22×C3—41no—
237C22×C3—41no—
238C22×C3—41no—
239C22×C3—41no—
240C22×C3—41no—
241C22×C3—41no—
242C22×C3—42no—
243C22×C3—42no—
244C22×C3—41no—
245C22×C3—41no—
246C22×C3—41no—
247C22×C3—41no—
248C22×C3—81no—
249C22×C3—81no—
250C22×C3—81no—
251C22×C3—81no—
252C22×C3—82no—
253C22×C3#80511yescharacteristic
254C22×C3#80611yescharacteristic
255C22×C3#80611yescharacteristic
256C22×C3#81011yescharacteristic
257C22×C3#81611yescharacteristic
258C22×C3#82511yescharacteristic
259C3×C4—42no—
260C3×C4—41no—
261C3×C4—41no—
262C3×C4—41no—
263C3×C4—41no—
264C3×C4—81no—
265C3×C4—242no—
266Dic3—82no—
267Dic3—124no—
268Dic3—122no—
269Dic3—122no—
270Dic3—242no—
271Dic3—241no—
272Dic3—241no—
273C32#135111yescharacteristic, complemented, Sylow
274C23—21no—
275C23—21no—
276C23—41no—
277C23—41no—
278C23#371611yescharacteristic
279C23#371911yescharacteristic
280C23#372211yescharacteristic
281Q8—362no—
282Q8—362no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—122no—
288C2×C4—182no—
289C2×C4—241no—
290C2×C4—241no—
291C2×C4—361no—
292C2×C4—361no—
293C2×C4—361no—
294C2×C4—361no—
295C2×C4—361no—
296C8—241no—
297C2×C3—22no—
298C2×C3—22no—
299C2×C3—21no—
300C2×C3—21no—
301C2×C3—21no—
302C2×C3—21no—
303C2×C3—21no—
304C2×C3—21no—
305C2×C3—21no—
306C2×C3—41no—
307C2×C3—41no—
308C2×C3—41no—
309C2×C3—41no—
310C2×C3—81no—
311C2×C3—81no—
312C2×C3#445211yescharacteristic
313C2×C3#446711yescharacteristic
314C2×C3#447111yescharacteristic
315C2×C3#447311yescharacteristic
316C2×C3#447311yescharacteristic
317C2×C3#447511yescharacteristic
318C22—21no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—81no—
327C22#6356711yescharacteristic
328C22#6357011yescharacteristic
329C22#6358111yescharacteristic
330C4—41no—
331C4—41no—
332C4—242no—
333C4—362no—
334C4—721no—
335C3—21no—
336C3#6744911yescharacteristic, complemented
337C3#6749011yescharacteristic, complemented
338C2—21no—
339C2—21no—
340C2—41no—
341C2—41no—
342C2#1058915411yescharacteristic
343C2#1058917411yescharacteristic
344C2#1058918111yescharacteristic
subgroupG/H
centerC22#63581
commutatorC22×C32×C4C2×C4
Frattini, hypercenterC2×C22⋊C4D32
Fitting, cosocleC2×C32×C22⋊C4C22
socleC22×C32#99
prime radicalC24×C32D4
hypocenterC32#1351
LCSG ▷ C22×C32×C4 ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
6. C22×#634C4semidirect
11. #63658C4semidirect
273. C32#1351semidirect
336. C3#67449semidirect
337. C3#67490semidirect

Maximal subgroups

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

subgroupindex
#105926462
C3×#45262
C3×#45252
#674903
#674493