Finite Group Databasebeta

← #11782362

Subgroups — #11782362

Order 1152.

362 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 82 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#10592541C211yesmaximal, characteristic
2#10590338C211yesmaximal, characteristic
3#10590313C211yesmaximal, characteristic
4#10590287C211yesmaximal, characteristic, complemented
5C3×#4486C211yesmaximal, characteristic, complemented
6C3×#4480C211yesmaximal, characteristic, complemented
7#10589096C211yesmaximal, characteristic, complemented
8#68545—31nomaximal
9#68455—31nomaximal
10C4×C4⋊(C3⋊D3)C2211yescharacteristic
11#64078C2211yescharacteristic
12C3×#869C2211yescharacteristic
13C2×#3712—21no—
14C32×C4⋊C8C2211yescharacteristic
15#63648—21no—
16#63644—21no—
17C3×C4⋊(C3⋊C8)C2211yescharacteristic
18C3×C4⋊(C3⋊C8)C2211yescharacteristic
19C3×C4×C3⋊C8C2211yescharacteristic
20#63575—21no—
21#63566—21no—
22#63566—21no—
23#63564—21no—
24#63557—21no—
25#5087—31no—
26#5079—31no—
27#4846—31no—
28#4842—31no—
29#4842—31no—
30#4842—61no—
31#4838—31no—
32#4688—31no—
33#4681—31no—
34C3×#334—31no—
35C3×#332—31no—
36#4486D311yescharacteristic, complemented
37#4481—31no—
38#4481—31no—
39#4480D311yescharacteristic, complemented
40C2×C4⋊(C3⋊D3)D411yescharacteristic
41C2×C4×C3⋊D3—21no—
42C2×#634—21no—
43C2×C3×Dic6—21no—
44C2×C32×C8—21no—
45C32×C42C2311yescharacteristic
46#3752—21no—
47C4⋊(C3⋊Dic3)—21no—
48C4⋊(C3⋊Dic3)—21no—
49C4⋊(C3⋊Dic3)D411yescharacteristic
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3—21no—
52C2×C3×C3⋊C8—21no—
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8D411yescharacteristic
55C2×C3×C3⋊C8D411yescharacteristic
56#3712—42no—
57#1703—91noSylow
58C3×C4⋊Q8—31no—
59C2×ΓL(1,𝔽25)—61no—
60C2×ΓL(1,𝔽25)—61no—
61C4×D12—31no—
62C4×D12—31no—
63C4×D12—61no—
64#869—31no—
65#869—31no—
66#869—61no—
67#869C2×D311yescharacteristic
68C3×C4⋊C8—21no—
69C3×C4⋊C8—31no—
70C3×C4⋊C8—31no—
71C3×C4⋊C8C2×D311yescharacteristic
72C3×C4⋊C8C2×D311yescharacteristic
73C3×C4×C8—31no—
74#835—61no—
75#835—61no—
76#821—61no—
77#821—61no—
78#821—61no—
79#821—62no—
80(C2×D3)⋊C8—61no—
81(C2×D3)⋊C8—61no—
82#818—61no—
83#817—61no—
84#817—61no—
85#817—62no—
86#816—61no—
87#816—61no—
88#809—61no—
89#807—61no—
90C4⋊(C3⋊C8)C2×D311yescharacteristic
91C4⋊(C3⋊C8)C2×D311yescharacteristic
92C4×C3⋊C8C2×D311yescharacteristic
93C22×C3⋊D3—21no—
94C2×C32×C4C2×D411yescharacteristic
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4#4111yescharacteristic
97C2×C3⋊Dic3—21no—
98C2×C3⋊Dic3—41no—
99C4⋊(C3⋊D3)—21no—
100C4⋊(C3⋊D3)—21no—
101C4×C3⋊D3—41no—
102C4×C3⋊D3—41no—
103#634—81no—
104C2×C3×Dic3—41no—
105C3×Dic6—41no—
106C3×Dic6—41no—
107C32×C8—41no—
108C3×C3⋊C8—21no—
109C3×C3⋊C8—21no—
110C3×C3⋊C8—41no—
111C3×C3⋊C8—41no—
112#487—91no—
113#476—91no—
114#474—91no—
115#436—91no—
116#334—31no—
117#333—91no—
118#332—31no—
119C2×C3×Q8—61no—
120C2×D12—31no—
121C2×D12—31no—
122C2×D12—61no—
123C2×C4×D3—61no—
124C2×C4×D3—61no—
125C2×C4×D3—121no—
126C2×Dic6—21no—
127C2×Dic6—61no—
128C2×Dic6—61no—
129C2×Dic6—121no—
130C2×C3×C8—22no—
131C2×C3×C8—21no—
132C2×C3×C8—21no—
133C2×C3×C8—31no—
134C2×C3×C8—31no—
135C2×C3×C8—61no—
136C2×C3×C8—61no—
137C3×C4⋊C4—61no—
138C3×C4⋊C4—61no—
139C3×C42—21no—
140C3×C42C22×D311yescharacteristic
141C3×C42C22×D311yescharacteristic
142(C2×D3)⋊C4—61no—
143(C2×D3)⋊C4—61no—
144(C2×D3)⋊C4—121no—
145C4⋊Dic3—21no—
146C4⋊Dic3—21no—
147C4⋊Dic3—31no—
148C4⋊Dic3—31no—
149C4⋊Dic3—61no—
150C4⋊Dic3—62no—
151C4⋊Dic3—61no—
152C4⋊Dic3—61no—
153C4⋊Dic3—61no—
154C4⋊Dic3—61no—
155C4⋊Dic3—121no—
156C2×C3⋊C8—21no—
157C2×C3⋊C8—21no—
158C2×C3⋊C8D1211yescharacteristic
159C2×C3⋊C8D1211yescharacteristic
160ΓL(1,𝔽25)—122no—
161ΓL(1,𝔽25)—122no—
162C22×C32#12111yescharacteristic
163C2×C3⋊D3—41no—
164C2×C3⋊D3—41no—
165C2×C3⋊D3—41no—
166C32×C4—21no—
167C32×C4#13511yescharacteristic
168C32×C4AGL(1,ℤ/8)11yescharacteristic
169C32×C4#13711yescharacteristic
170C32×C4#13711yescharacteristic
171C3⋊Dic3—41no—
172C3⋊Dic3—81no—
173C3×Dic3—81no—
174C2×M16—181no—
175C4⋊Q8—31no—
176C4⋊Q8—91no—
177C4×D4—91no—
178#107—181no—
179#106—181no—
180C4⋊C8—31no—
181C4⋊C8—31no—
182C4⋊C8D3211yescharacteristic
183#103—181no—
184#103—181no—
185#102—181no—
186#102—181no—
187C22⋊C8—181no—
188C4×C8—31no—
189C22×D3—61no—
190C22×D3—61no—
191C22×D3—121no—
192C3×Q8—121no—
193C3×Q8—121no—
194C2×C3×C4—21no—
195C2×C3×C4—21no—
196C2×C3×C4—21no—
197C2×C3×C4—121no—
198C2×C3×C4C2×D1211yescharacteristic
199C2×C3×C4#23511yescharacteristic
200C2×C3×C4D3×D411yescharacteristic
201C2×C3×C4D3×D411yescharacteristic
202C2×C3×C4D3×D411yescharacteristic
203C2×C3×C4#23911yescharacteristic
204C2×Dic3—41no—
205C2×Dic3—61no—
206C2×Dic3—61no—
207C2×Dic3—121no—
208C2×Dic3—122no—
209C2×Dic3—121no—
210C2×Dic3—121no—
211D12—62no—
212D12—61no—
213D12—61no—
214D12—61no—
215D12—61no—
216D12—121no—
217C4×D3—121no—
218C4×D3—121no—
219C4×D3—121no—
220C4×D3—121no—
221C4×D3—241no—
222C4×D3—241no—
223Dic6—41no—
224Dic6—41no—
225Dic6—242no—
226Dic6—241no—
227Dic6—241no—
228C3×C8—42no—
229C3×C8—41no—
230C3×C8—41no—
231C3×C8—61no—
232C3×C8—61no—
233C3×C8—121no—
234C3×C8—121no—
235C3⋊C8—21no—
236C3⋊C8—21no—
237C3⋊C8—41no—
238C3⋊C8—41no—
239C2×C32#46311yescharacteristic
240C2×C32#47011yescharacteristic
241C2×C32#47111yescharacteristic
242C3⋊D3—81no—
243C2×Q8—61no—
244C2×Q8—181no—
245C2×D4—91no—
246C22×C4—181no—
247M16—362no—
248C2×C8—21no—
249C2×C8—31no—
250C2×C8—31no—
251C2×C8—61no—
252C2×C8—61no—
253C4⋊C4—61no—
254C4⋊C4—61no—
255C4⋊C4—91no—
256C4⋊C4—181no—
257C4⋊C4—181no—
258C22⋊C4—181no—
259C42C2×D3211yescharacteristic
260C22×C3—21no—
261C22×C3#88411yescharacteristic
262C22×C3#89511yescharacteristic
263C2×D3—122no—
264C2×D3—121no—
265C2×D3—121no—
266C2×D3—121no—
267C2×D3—121no—
268C2×D3—121no—
269C2×D3—121no—
270C2×D3—241no—
271C2×D3—241no—
272C3×C4—21no—
273C3×C4—21no—
274C3×C4—21no—
275C3×C4—21no—
276C3×C4—21no—
277C3×C4—21no—
278C3×C4—41no—
279C3×C4—241no—
280C3×C4#90411yescharacteristic
281C3×C4#90811yescharacteristic
282C3×C4#91111yescharacteristic
283C3×C4#91511yescharacteristic
284C3×C4#91511yescharacteristic
285C3×C4#91511yescharacteristic
286C3×C4#91611yescharacteristic
287C3×C4#91811yescharacteristic
288Dic3—81no—
289Dic3—121no—
290Dic3—121no—
291Dic3—241no—
292Dic3—242no—
293Dic3—241no—
294Dic3—241no—
295C32#170311yescharacteristic, complemented, Sylow
296C23—181no—
297Q8—121no—
298Q8—121no—
299Q8—721no—
300D4—181no—
301D4—181no—
302C2×C4—121no—
303C2×C4—181no—
304C2×C4—361no—
305C2×C4—361no—
306C2×C4—361no—
307C2×C4#379911yescharacteristic
308C2×C4D3×D1211yescharacteristic
309C2×C4#381111yescharacteristic
310C8—41no—
311C8—61no—
312C8—61no—
313C8—121no—
314C8—121no—
315C2×C3—21no—
316C2×C3—21no—
317C2×C3—21no—
318C2×C3#475411yescharacteristic
319C2×C3#478711yescharacteristic
320C2×C3#481611yescharacteristic
321C2×C3#484411yescharacteristic
322C2×C3#486711yescharacteristic
323C2×C3#489811yescharacteristic
324D3—242no—
325D3—241no—
326D3—241no—
327C22—361no—
328C22—361no—
329C22—361no—
330C22#6391011yescharacteristic
331C4—21no—
332C4—241no—
333C4—361no—
334C4—721no—
335C4#6379511yescharacteristic
336C4#6380611yescharacteristic
337C4#6393111yescharacteristic
338C4#6395111yescharacteristic
339C3—21no—
340C3#6845511yescharacteristic, complemented
341C3#6854511yescharacteristic, complemented
342C2—721no—
343C2#1059052411yescharacteristic
344C2#1059086011yescharacteristic
345C2#1059099011yescharacteristic
subgroupG/H
centerC22#63910
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#121
prime radicalC2×C4⋊(C3⋊D3)D4
hypercenterC4⋊C8D32
hypocenterC32#1703
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
4. #10590287C2semidirect
5. C3×#4486C2semidirect
6. C3×#4480C2semidirect
7. #10589096C2semidirect
36. #4486D3semidirect
39. #4480D3semidirect
295. C32#1703semidirect
340. C3#68455semidirect
341. C3#68545semidirect

Maximal subgroups

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

subgroupindex
#105925412
#105903382
#105903132
#105902872
C3×#44862
C3×#44802
#105890962
#685453
#684553