Finite Group Databasebeta

← #11795285

Subgroups — #11795285

Order 1152.

358 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 61 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#10593412C211yesmaximal, characteristic
2#10593412C211yesmaximal, characteristic
3#10590685C211yesmaximal, characteristic
4#10590658C211yesmaximal, characteristic
5#10590182C211yesmaximal, characteristic
6#10590049C211yesmaximal, characteristic
7#10590049C211yesmaximal, characteristic
8C2×C4⋊#157C2211yescharacteristic
9C2×C4⋊#157C2211yescharacteristic
10C2×#3773—21no—
11C2×#3773—21no—
12C2×C8×C3⋊D3C2211yescharacteristic
13#63900C2211yescharacteristic
14#63900C2211yescharacteristic
15C4×#624C2211yescharacteristic
16C2×#3710C2211yescharacteristic
17#63737—21no—
18#63737—21no—
19C3×#817—21no—
20C3×Dic3⋊C8—21no—
21#63574—21no—
22Dic3⋊(C3⋊C8)—21no—
23D3×#106—61no—
24D3×C4⋊C8—61no—
25C22×#157—21no—
26C22×#157—21no—
27C2×C4×C3⋊D3C2311yescharacteristic
28C2×#624—21no—
29C2×#624—21no—
30C2×#624D411yescharacteristic
31C2×#624D411yescharacteristic
32C4⋊#157—21no—
33C4⋊#157—21no—
34C4⋊#157Q812yes—
35C4⋊#157Q812yes—
36#3773—42no—
37#3773—42no—
38C2×C32×C8D411yescharacteristic
39C2×C3⋊(C3⋊C8)D411yescharacteristic
40C8×C3⋊D3—21no—
41C8×C3⋊D3—21no—
42C3×C4⋊Dic3—21no—
43C3×C4⋊Dic3—21no—
44C3×C4×Dic3—21no—
45C2×C3×C3⋊C8—21no—
46#3724—21no—
47#3724—21no—
48Dic32—21no—
49#3710—21no—
50#3710—21no—
51#2088—91nomaximal, Sylow
52C2×D3×C8—61no—
53C2×D3×C8—61no—
54C2×D3×C8—61no—
55D3×C4⋊C4—61no—
56D3×C4⋊C4—61no—
57C42×D3—61no—
58C3×#106—61no—
59C3×C4⋊C8—61no—
60#817—21no—
61Dic3⋊C8—21no—
62Dic3⋊C8—61no—
63#808—61no—
64#808—61no—
65C4⋊(C3⋊C8)—61no—
66C22×C3⋊D3C2×D411yescharacteristic
67C2×#157—22no—
68C2×#157—22no—
69C2×#157—41no—
70C2×#157—41no—
71C2×#157—41no—
72C2×#157—41no—
73C2×C32×C4C2×D411yescharacteristic
74C2×C3⋊Dic3#4111yescharacteristic
75C4×C3⋊D3C2×Q811yescharacteristic
76C4×C3⋊D3C2×Q811yescharacteristic
77C4×C3⋊D3#4111yescharacteristic
78C4×C3⋊D3#4111yescharacteristic
79C2×C3×Dic3—21no—
80C2×C3×Dic3—21no—
81C2×C3×Dic3—41no—
82C2×C3×Dic3—41no—
83#624—21no—
84#624—21no—
85#624—21no—
86#624—41no—
87#624—41no—
88#624—41no—
89#624—41no—
90#624SD1612yes—
91C32×C8—21no—
92C3⋊(C3⋊C8)—21no—
93C3×C3⋊C8—41no—
94C2×#106—91no—
95C2×C4⋊C8—91no—
96#389—91no—
97#389—91no—
98#340—91no—
99#340—91no—
100#340—91no—
101C2×C4×D3—61no—
102C2×C4×D3—61no—
103C2×C4×D3—61no—
104C2×C4×D3—61no—
105C2×C4×D3—121no—
106C2×C4×D3—121no—
107C2×C3×C8—21no—
108C2×C3×C8—21no—
109C2×C3×C8—61no—
110C3×C4⋊C4—61no—
111C3×C4⋊C4—61no—
112C3×C42—61no—
113C4⋊Dic3—21no—
114C4⋊Dic3—21no—
115Dic3⋊C4—121no—
116Dic3⋊C4—121no—
117C4×Dic3—21no—
118C4×Dic3—61no—
119C4×Dic3—61no—
120C2×C3⋊C8—21no—
121C2×C3⋊C8—61no—
122C2×C3⋊C8—61no—
123D3×C8—62no—
124D3×C8—62no—
125D3×C8—121no—
126D3×C8—121no—
127D3×C8—121no—
128D3×C8—121no—
129C22×C32#12111yescharacteristic
130C2×C3⋊D3C22⋊Q811yescharacteristic
131C2×C3⋊D3C22⋊Q811yescharacteristic
132C2×C3⋊D3C2×SD1611yescharacteristic
133C2×C3⋊D3#13511yescharacteristic
134C2×C3⋊D3AGL(1,ℤ/8)11yescharacteristic
135C2×C3⋊D3#13711yescharacteristic
136#157—42no—
137#157—42no—
138C32×C4#12311yescharacteristic
139C32×C4C4⋊Q811yescharacteristic
140C3⋊Dic3#12511yescharacteristic
141C3⋊Dic3#12511yescharacteristic
142C3×Dic3—22no—
143C3×Dic3—41no—
144C3×Dic3—81no—
145C3×Dic3—81no—
146C22×C8—91no—
147C22×C8—91no—
148C2×C4⋊C4—91no—
149C2×C4⋊C4—91no—
150C2×C4⋊C4—91no—
151C2×C4⋊C4—91no—
152C2×C4⋊C4—181no—
153C2×C4⋊C4—181no—
154C2×C42—91no—
155#106—61no—
156#106—181no—
157C4⋊C8—61no—
158C4⋊C8—181no—
159#95—181no—
160#95—181no—
161C22×D3—61no—
162C22×D3—61no—
163C2×C3×C4—21no—
164C2×C3×C4—21no—
165C2×C3×C4—61no—
166C2×C3×C4—61no—
167C2×C3×C4—121no—
168C2×C3×C4—121no—
169C2×Dic3—21no—
170C2×Dic3—21no—
171C2×Dic3—41no—
172C2×Dic3—41no—
173C2×Dic3—61no—
174C2×Dic3—61no—
175C4×D3—62no—
176C4×D3—61no—
177C4×D3—61no—
178C4×D3—61no—
179C4×D3—61no—
180C4×D3—61no—
181C4×D3—61no—
182C4×D3—61no—
183C4×D3—61no—
184C4×D3—62no—
185C4×D3—121no—
186C4×D3—121no—
187C4×D3—241no—
188C4×D3—241no—
189C4×D3—241no—
190C4×D3—241no—
191C3×C8—22no—
192C3×C8—41no—
193C3×C8—121no—
194C3⋊C8—41no—
195C3⋊C8—62no—
196C3⋊C8—121no—
197C2×C32#39811yescharacteristic
198C2×C32#46511yescharacteristic
199C2×C32#46811yescharacteristic
200C3⋊D3#47511yescharacteristic
201C3⋊D3#47611yescharacteristic
202C3⋊D3#47811yescharacteristic
203C3⋊D3#47911yescharacteristic
204C22×C4—91no—
205C22×C4—91no—
206C22×C4—91no—
207C22×C4—181no—
208C22×C4—181no—
209C22×C4—181no—
210C22×C4—181no—
211C2×C8—61no—
212C2×C8—91no—
213C2×C8—181no—
214C2×C8—181no—
215C2×C8—181no—
216C2×C8—181no—
217C2×C8GO+(4,𝔽2)11yescharacteristic
218C4⋊C4—61no—
219C4⋊C4—61no—
220C4⋊C4—92no—
221C4⋊C4—92no—
222C4⋊C4—181no—
223C4⋊C4—181no—
224C4⋊C4—181no—
225C4⋊C4—181no—
226C4⋊C4—362no—
227C4⋊C4—362no—
228C42—61no—
229C42—181no—
230C22×C3—21no—
231C22×C3—21no—
232C2×D3—61no—
233C2×D3—61no—
234C2×D3—61no—
235C2×D3—61no—
236C2×D3—61no—
237C2×D3—61no—
238C2×D3—61no—
239C2×D3—61no—
240C2×D3—61no—
241C2×D3—61no—
242C2×D3—61no—
243C2×D3—61no—
244C3×C4—21no—
245C3×C4—21no—
246C3×C4—21no—
247C3×C4—21no—
248C3×C4—62no—
249C3×C4—121no—
250C3×C4—241no—
251C3×C4—241no—
252Dic3—22no—
253Dic3—41no—
254Dic3—61no—
255Dic3—61no—
256Dic3—61no—
257Dic3—61no—
258Dic3—81no—
259Dic3—81no—
260C32#208811yescharacteristic, complemented, Sylow
261C23—91no—
262C2×C4—61no—
263C2×C4—61no—
264C2×C4—92no—
265C2×C4—91no—
266C2×C4—91no—
267C2×C4—91no—
268C2×C4—91no—
269C2×C4—91no—
270C2×C4—121no—
271C2×C4—121no—
272C2×C4—181no—
273C2×C4—181no—
274C2×C4—181no—
275C2×C4—182no—
276C2×C4—182no—
277C2×C4—361no—
278C2×C4—361no—
279C2×C4—361no—
280C2×C4—361no—
281C2×C4—361no—
282C2×C4—361no—
283C2×C4—361no—
284C2×C4—361no—
285C2×C4C2×GO+(4,𝔽2)11yescharacteristic
286C8—21no—
287C8—121no—
288C8—181no—
289C2×C3—21no—
290C2×C3—21no—
291C2×C3—21no—
292C2×C3—21no—
293C2×C3—21no—
294C2×C3—21no—
295D3—61no—
296D3—61no—
297D3—61no—
298D3—61no—
299D3—61no—
300D3—61no—
301D3—61no—
302D3—61no—
303C22—91no—
304C22—91no—
305C22—91no—
306C22—91no—
307C22—91no—
308C22—91no—
309C22#6423011yescharacteristic
310C4—62no—
311C4—91no—
312C4—91no—
313C4—121no—
314C4—241no—
315C4—241no—
316C4—362no—
317C4—362no—
318C4#6422211yescharacteristic
319C4#6423311yescharacteristic
320C3—21no—
321C3—21no—
322C2—91no—
323C2—91no—
324C2—91no—
325C2—91no—
326C2#1059328411yescharacteristic
327C2#1059328611yescharacteristic
328C2#1059333911yescharacteristic
subgroupG/H
centerC22#64230
commutator, cosocleC2×C4×C3⋊D3C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC22×C32#121
prime radicalC22×C3⋊D3C2×D4
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#2088
LCSG ▷ C2×C4×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
260. C32#2088semidirect

Maximal subgroups

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

subgroupindex
#105934122
#105906852
#105906582
#105901822
#105900492
#20889