Finite Group Databasebeta

← #11781860

Subgroups — #11781860

Order 1152.

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

normal subgroups only

This group has 381 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#10592537C211yesmaximal, characteristic
2#10590379C211yesmaximal, characteristic
3#10590309C211yesmaximal, characteristic, complemented
4#10590300C211yesmaximal, characteristic
5C3×#4486C211yesmaximal, characteristic, complemented
6C3×#4481C211yesmaximal, characteristic, complemented
7#10589100C211yesmaximal, characteristic, complemented
8#68500—31nomaximal
9#68450—31nomaximal
10C2×#3743—21no—
11C4×C4⋊(C3⋊D3)C2211yescharacteristic
12C3×#869C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C2×#3717—21no—
15C32×C4⋊C8C2211yescharacteristic
16#63647—21no—
17C4×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×C4⋊(C3⋊C8)C2211yescharacteristic
19C3×C4⋊(C3⋊C8)C2211yescharacteristic
20#63574—21no—
21#63574—21no—
22#63573—21no—
23#63566—21no—
24#63564—21no—
25#5084—31no—
26#5083—31no—
27#5080—31no—
28#5080—31no—
29#4842—31no—
30#4841—31no—
31#4838—31no—
32#4838—31no—
33#4838—61no—
34C3×#333—31no—
35C3×#332—31no—
36#4486D311yescharacteristic, complemented
37#4481D311yescharacteristic, complemented
38#4479—31no—
39#4479—31no—
40C2×C4⋊(C3⋊D3)D411yescharacteristic
41C2×C4×C3⋊D3—21no—
42C2×C3×Dic6—21no—
43C2×C3×Dic6—21no—
44C2×C32×C8—21no—
45C32×C42C2311yescharacteristic
46#3752—21no—
47C4⋊(C3⋊Dic3)D411yescharacteristic
48C2×C3⋊(C3⋊C8)D411yescharacteristic
49C2×C3⋊(C3⋊C8)D411yescharacteristic
50#3743—42no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3—21no—
54C3×C4⋊Dic3—21no—
55C2×C3×C3⋊C8—21no—
56C2×C3×C3⋊C8—21no—
57#3717—42no—
58#1691—91noSylow
59C3×C4⋊Q8—31no—
60C3×C4⋊Q8—31no—
61C2×#215—61no—
62C2×#204—61no—
63C2×ΓL(1,𝔽25)—61no—
64C2×ΓL(1,𝔽25)—61no—
65C2×ΓL(1,𝔽25)—62no—
66C4×D12—31no—
67C4×D12—31no—
68C4×D12—61no—
69#869C2×D311yescharacteristic
70#869C2×D311yescharacteristic
71C3×C4⋊C8—21no—
72C3×C4⋊C8—31no—
73C3×C4⋊C8—31no—
74C3×C4⋊C8C2×D311yescharacteristic
75C3×C4⋊C8C2×D311yescharacteristic
76#835—61no—
77#821—61no—
78(C2×D3)⋊C8—61no—
79(C2×D3)⋊C8—61no—
80(C2×D3)⋊C8—62no—
81#817—61no—
82#816—61no—
83#809—61no—
84#808—61no—
85#808—61no—
86#808—61no—
87#808—61no—
88#808—61no—
89C4⋊(C3⋊C8)C2×D311yescharacteristic
90C4⋊(C3⋊C8)C2×D311yescharacteristic
91C4×C3⋊C8—31no—
92C4×C3⋊C8—31no—
93C4×C3⋊C8—61no—
94C22×C3⋊D3—21no—
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4#4111yescharacteristic
98C2×C3⋊Dic3—21no—
99C4⋊(C3⋊D3)—21no—
100C4⋊(C3⋊D3)—21no—
101C4×C3⋊D3—41no—
102C4×C3⋊D3—41no—
103C2×C3×Dic3—41no—
104C2×C3×Dic3—41no—
105C3×Dic6—41no—
106C3×Dic6—41no—
107C3×Dic6—81no—
108C32×C8—41no—
109C3⋊(C3⋊C8)—21no—
110C3⋊(C3⋊C8)SD1612yescomplemented
111C3×C3⋊C8—41no—
112C3×C3⋊C8—41no—
113#498—91no—
114#476—91no—
115#461—91no—
116#436—91no—
117#335—91no—
118#333—31no—
119#332—31no—
120C2×C3×Q8—61no—
121C2×C3×Q8—61no—
122C2×D12—31no—
123C2×D12—31no—
124C2×D12—61no—
125C2×C4×D3—62no—
126C2×C4×D3—61no—
127C2×C4×D3—61no—
128C2×Dic6—21no—
129C2×Dic6—21no—
130C2×C3×C8—22no—
131C2×C3×C8—21no—
132C2×C3×C8—21no—
133C2×C3×C8—61no—
134C2×C3×C8—61no—
135C3×C4⋊C4—61no—
136C3×C4⋊C4—61no—
137C3×C4⋊C4—61no—
138C3×C4⋊C4—61no—
139C3×C42—21no—
140C3×C42C22×D311yescharacteristic
141C3×C42C22×D311yescharacteristic
142#215—122no—
143(C2×D3)⋊C4—62no—
144(C2×D3)⋊C4—61no—
145(C2×D3)⋊C4—61no—
146C4⋊Dic3—21no—
147C4⋊Dic3—21no—
148C4⋊Dic3—21no—
149C4⋊Dic3—21no—
150C4⋊Dic3—31no—
151C4⋊Dic3—31no—
152C4⋊Dic3—61no—
153C2×C3⋊C8—21no—
154C2×C3⋊C8—21no—
155C2×C3⋊C8—31no—
156C2×C3⋊C8—31no—
157C2×C3⋊C8—31no—
158C2×C3⋊C8—31no—
159C2×C3⋊C8—61no—
160C2×C3⋊C8—61no—
161#204—122no—
162ΓL(1,𝔽25)—122no—
163ΓL(1,𝔽25)—122no—
164ΓL(1,𝔽25)—124no—
165C22×C32#12111yescharacteristic
166C2×C3⋊D3—41no—
167C2×C3⋊D3—41no—
168C2×C3⋊D3—41no—
169C32×C4—21no—
170C32×C4C2×SD1611yescharacteristic
171C32×C4AGL(1,ℤ/8)11yescharacteristic
172C32×C4#13711yescharacteristic
173C32×C4#13711yescharacteristic
174C3⋊Dic3—41no—
175C3×Dic3—81no—
176C3×Dic3—81no—
177C2×SD16—181no—
178C2×M16—181no—
179C4⋊Q8—31no—
180C4⋊Q8—31no—
181C4×D4—91no—
182#106—181no—
183#106—181no—
184#106—181no—
185C4⋊C8—31no—
186C4⋊C8—31no—
187C4⋊C8D3211yescharacteristic
188#103—181no—
189#102—181no—
190C22⋊C8—181no—
191C4×C8—91no—
192C22×D3—62no—
193C22×D3—61no—
194C22×D3—61no—
195C3×Q8—121no—
196C3×Q8—121no—
197C3×Q8—241no—
198C2×C3×C4—21no—
199C2×C3×C4—21no—
200C2×C3×C4—21no—
201C2×C3×C4—121no—
202C2×C3×C4—121no—
203C2×C3×C4#23511yescharacteristic
204C2×C3×C4#23511yescharacteristic
205C2×C3×C4D3×D411yescharacteristic
206C2×C3×C4D3×D411yescharacteristic
207C2×C3×C4D3×D411yescharacteristic
208C2×C3×C4D3×D411yescharacteristic
209C2×Dic3—41no—
210C2×Dic3—41no—
211C2×Dic3—62no—
212C2×Dic3—61no—
213C2×Dic3—61no—
214D12—61no—
215D12—61no—
216D12—61no—
217D12—61no—
218D12—121no—
219D12—121no—
220C4×D3—122no—
221C4×D3—122no—
222C4×D3—121no—
223C4×D3—121no—
224C4×D3—121no—
225C4×D3—121no—
226Dic6—41no—
227Dic6—41no—
228Dic6—81no—
229C3×C8—42no—
230C3×C8—41no—
231C3×C8—41no—
232C3×C8—121no—
233C3×C8—121no—
234C3⋊C8—32no—
235C3⋊C8—32no—
236C3⋊C8—41no—
237C3⋊C8—41no—
238C3⋊C8—62no—
239C3⋊C8—61no—
240C3⋊C8—61no—
241C3⋊C8—121no—
242C2×C32#46111yescharacteristic
243C2×C32#46811yescharacteristic
244C2×C32#47111yescharacteristic
245C3⋊D3—81no—
246C2×Q8—61no—
247C2×Q8—61no—
248C2×D4—91no—
249C22×C4—181no—
250SD16—362no—
251M16—362no—
252C2×C8—21no—
253C2×C8—61no—
254C2×C8—61no—
255C2×C8—91no—
256C2×C8—91no—
257C4⋊C4—61no—
258C4⋊C4—61no—
259C4⋊C4—61no—
260C4⋊C4—61no—
261C4⋊C4—91no—
262C22⋊C4—181no—
263C42C2×D3211yescharacteristic
264C22×C3—21no—
265C22×C3#88411yescharacteristic
266C22×C3#88411yescharacteristic
267C2×D3—122no—
268C2×D3—122no—
269C2×D3—122no—
270C2×D3—121no—
271C2×D3—121no—
272C2×D3—121no—
273C2×D3—121no—
274C2×D3—121no—
275C2×D3—121no—
276C3×C4—21no—
277C3×C4—21no—
278C3×C4—21no—
279C3×C4—21no—
280C3×C4—21no—
281C3×C4—21no—
282C3×C4—41no—
283C3×C4—241no—
284C3×C4—241no—
285C3×C4#91111yescharacteristic
286C3×C4D3×SD1611yescharacteristic
287C3×C4D3×SD1611yescharacteristic
288C3×C4#91411yescharacteristic
289C3×C4#91511yescharacteristic
290C3×C4#91811yescharacteristic
291C3×C4#91811yescharacteristic
292C3×C4#91811yescharacteristic
293Dic3—81no—
294Dic3—81no—
295Dic3—122no—
296Dic3—121no—
297Dic3—121no—
298C32#169111yescharacteristic, complemented, Sylow
299C23—181no—
300Q8—121no—
301Q8—121no—
302Q8—241no—
303D4—181no—
304D4—181no—
305C2×C4—121no—
306C2×C4—121no—
307C2×C4—181no—
308C2×C4—361no—
309C2×C4—361no—
310C2×C4#379811yescharacteristic
311C2×C4#380211yescharacteristic
312C2×C4#381111yescharacteristic
313C8—41no—
314C8—92no—
315C8—121no—
316C8—121no—
317C8—181no—
318C2×C3—21no—
319C2×C3—21no—
320C2×C3—21no—
321C2×C3#474811yescharacteristic
322C2×C3#475411yescharacteristic
323C2×C3#478011yescharacteristic
324C2×C3#481211yescharacteristic
325C2×C3#481811yescharacteristic
326C2×C3#481811yescharacteristic
327D3—242no—
328D3—241no—
329D3—241no—
330C22—361no—
331C22—361no—
332C22—361no—
333C22#6391211yescharacteristic
334C4—21no—
335C4—241no—
336C4—241no—
337C4—361no—
338C4#6379811yescharacteristic
339C4#6381111yescharacteristic
340C4#6393011yescharacteristic
341C4#6394511yescharacteristic
342C3—21no—
343C3#6845011yescharacteristic, complemented
344C3#6850011yescharacteristic, complemented
345C2—721no—
346C2#1059056511yescharacteristic
347C2#1059084211yescharacteristic
348C2#1059099111yescharacteristic
subgroupG/H
centerC22#63912
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#121
prime radicalC2×C4⋊(C3⋊D3)D4
hypercenterC4⋊C8D32
hypocenterC32#1691
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
3. #10590309C2semidirect
5. C3×#4486C2semidirect
6. C3×#4481C2semidirect
7. #10589100C2semidirect
36. #4486D3semidirect
37. #4481D3semidirect
110. C3⋊(C3⋊C8)SD16semidirect
298. C32#1691semidirect
343. C3#68450semidirect
344. C3#68500semidirect

Maximal subgroups

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

subgroupindex
#105925372
#105903792
#105903092
#105903002
C3×#44862
C3×#44812
#105891002
#685003
#684503