Finite Group Databasebeta

← #11781359

Subgroups — #11781359

Order 1152.

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

normal subgroups only

This group has 399 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#10592533C211yesmaximal, characteristic
2#10590379C211yesmaximal, characteristic
3#10590313C211yesmaximal, characteristic
4#10590290C211yesmaximal, characteristic, complemented
5C3×#4486C211yesmaximal, characteristic, complemented
6C3×#4482C211yesmaximal, characteristic, complemented
7#10589098C211yesmaximal, characteristic, complemented
8#68445—31nomaximal
9#68444—31nomaximal
10C2×C8×C3⋊D3—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#63575—21no—
21#63566—21no—
22#63565—21no—
23#63565—21no—
24#63564—21no—
25#5093—31no—
26#5087—31no—
27#5083—31no—
28#5079—31no—
29#4846—31no—
30#4841—31no—
31#4834—31no—
32#4834—31no—
33#4834—61no—
34C3×#332—31no—
35C3×#332—31no—
36#4486D311yescharacteristic, complemented
37#4482D311yescharacteristic, complemented
38#4480—31no—
39#4480—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
50C8×C3⋊D3—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#1679—91noSylow
59C3×C4⋊Q8—31no—
60C3×C4⋊Q8—31no—
61C2×#215—61no—
62C2×#204—61no—
63C2×D3×C8—61no—
64C2×D3×C8—61no—
65C2×D3×C8—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#835—61no—
78#835—61no—
79#821—61no—
80(C2×D3)⋊C8—61no—
81(C2×D3)⋊C8—61no—
82(C2×D3)⋊C8—62no—
83#818—61no—
84#816—61no—
85#810—61no—
86#810—61no—
87#809—61no—
88#807—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)SD1612yes—
101C4×C3⋊D3—41no—
102C4×C3⋊D3—41no—
103C2×C3×Dic3—41no—
104C2×C3×Dic3—41no—
105C3×Dic6—41no—
106C3×Dic6—41no—
107C3×Dic6—41no—
108C3×Dic6—41no—
109C32×C8—41no—
110C3⋊(C3⋊C8)—21no—
111C3⋊(C3⋊C8)—21no—
112C3×C3⋊C8—41no—
113C3×C3⋊C8—41no—
114#487—91no—
115#474—91no—
116#461—91no—
117C8×D4—91no—
118#334—91no—
119#332—31no—
120#332—31no—
121C2×C3×Q8—61no—
122C2×C3×Q8—61no—
123C2×D12—31no—
124C2×D12—31no—
125C2×D12—61no—
126C2×C4×D3—62no—
127C2×C4×D3—61no—
128C2×C4×D3—61no—
129C2×Dic6—21no—
130C2×Dic6—21no—
131C2×C3×C8—22no—
132C2×C3×C8—21no—
133C2×C3×C8—21no—
134C2×C3×C8—61no—
135C2×C3×C8—61no—
136C3×C4⋊C4—61no—
137C3×C4⋊C4—61no—
138C3×C4⋊C4—61no—
139C3×C4⋊C4—61no—
140C3×C42—21no—
141C3×C42C22×D311yescharacteristic
142C3×C42C22×D311yescharacteristic
143#215—122no—
144(C2×D3)⋊C4—62no—
145(C2×D3)⋊C4—61no—
146(C2×D3)⋊C4—61no—
147C4⋊Dic3—21no—
148C4⋊Dic3—21no—
149C4⋊Dic3—21no—
150C4⋊Dic3—21no—
151C4⋊Dic3—31no—
152C4⋊Dic3—31no—
153C4⋊Dic3—61no—
154C2×C3⋊C8—21no—
155C2×C3⋊C8—21no—
156C2×C3⋊C8—31no—
157C2×C3⋊C8—31no—
158C2×C3⋊C8—31no—
159C2×C3⋊C8—31no—
160C2×C3⋊C8—61no—
161C2×C3⋊C8—61no—
162#204—122no—
163D3×C8—124no—
164D3×C8—122no—
165D3×C8—122no—
166C22×C32#12111yescharacteristic
167C2×C3⋊D3—22no—
168C2×C3⋊D3—41no—
169C2×C3⋊D3—41no—
170C32×C4—21no—
171C32×C4C2×SD1611yescharacteristic
172C32×C4#13511yescharacteristic
173C32×C4#13511yescharacteristic
174C32×C4AGL(1,ℤ/8)11yescharacteristic
175C3⋊Dic3—41no—
176C3×Dic3—81no—
177C3×Dic3—81no—
178C2×SD16—181no—
179C22×C8—181no—
180C4⋊Q8—31no—
181C4⋊Q8—31no—
182C4×D4—91no—
183#107—181no—
184C4⋊C8—31no—
185C4⋊C8—31no—
186C4⋊C8D3211yescharacteristic
187#103—181no—
188#103—181no—
189#103—181no—
190#102—181no—
191C22⋊C8—181no—
192C4×C8—91no—
193C22×D3—62no—
194C22×D3—61no—
195C22×D3—61no—
196C3×Q8—121no—
197C3×Q8—121no—
198C3×Q8—121no—
199C3×Q8—121no—
200C2×C3×C4—21no—
201C2×C3×C4—21no—
202C2×C3×C4—21no—
203C2×C3×C4—121no—
204C2×C3×C4—121no—
205C2×C3×C4#23511yescharacteristic
206C2×C3×C4#23511yescharacteristic
207C2×C3×C4D3×D411yescharacteristic
208C2×C3×C4D3×D411yescharacteristic
209C2×C3×C4D3×D411yescharacteristic
210C2×C3×C4D3×D411yescharacteristic
211C2×Dic3—41no—
212C2×Dic3—41no—
213C2×Dic3—62no—
214C2×Dic3—61no—
215C2×Dic3—61no—
216D12—32no—
217D12—32no—
218D12—62no—
219D12—62no—
220D12—61no—
221D12—61no—
222C4×D3—122no—
223C4×D3—122no—
224C4×D3—121no—
225C4×D3—121no—
226C4×D3—121no—
227C4×D3—121no—
228Dic6—41no—
229Dic6—41no—
230Dic6—41no—
231Dic6—41no—
232C3×C8—42no—
233C3×C8—41no—
234C3×C8—41no—
235C3×C8—121no—
236C3×C8—121no—
237C3⋊C8—41no—
238C3⋊C8—41no—
239C3⋊C8—62no—
240C3⋊C8—61no—
241C3⋊C8—61no—
242C3⋊C8—61no—
243C3⋊C8—61no—
244C3⋊C8—121no—
245C2×C32#46311yescharacteristic
246C2×C32#46511yescharacteristic
247C2×C32#47311yescharacteristic
248C3⋊D3—42no—
249C2×Q8—61no—
250C2×Q8—61no—
251C2×D4—91no—
252C22×C4—181no—
253SD16—362no—
254C2×C8—21no—
255C2×C8—61no—
256C2×C8—61no—
257C2×C8—91no—
258C2×C8—91no—
259C2×C8—362no—
260C4⋊C4—61no—
261C4⋊C4—61no—
262C4⋊C4—61no—
263C4⋊C4—61no—
264C4⋊C4—91no—
265C22⋊C4—181no—
266C42C2×D3211yescharacteristic
267C22×C3—21no—
268C22×C3#88411yescharacteristic
269C22×C3#88411yescharacteristic
270C2×D3—64no—
271C2×D3—62no—
272C2×D3—62no—
273C2×D3—122no—
274C2×D3—122no—
275C2×D3—121no—
276C2×D3—121no—
277C2×D3—121no—
278C2×D3—121no—
279C3×C4—21no—
280C3×C4—21no—
281C3×C4—21no—
282C3×C4—21no—
283C3×C4—21no—
284C3×C4—21no—
285C3×C4—41no—
286C3×C4—241no—
287C3×C4—241no—
288C3×C4#91111yescharacteristic
289C3×C4#91211yescharacteristic
290C3×C4D3×SD1611yescharacteristic
291C3×C4D3×SD1611yescharacteristic
292C3×C4#91411yescharacteristic
293C3×C4#91611yescharacteristic
294C3×C4#91911yescharacteristic
295C3×C4#91911yescharacteristic
296Dic3—81no—
297Dic3—81no—
298Dic3—122no—
299Dic3—121no—
300Dic3—121no—
301C32#167911yescharacteristic, complemented, Sylow
302C23—181no—
303Q8—121no—
304Q8—121no—
305Q8—121no—
306Q8—121no—
307D4—92no—
308D4—181no—
309C2×C4—121no—
310C2×C4—121no—
311C2×C4—181no—
312C2×C4—361no—
313C2×C4—361no—
314C2×C4#379811yescharacteristic
315C2×C4#380211yescharacteristic
316C2×C4#381111yescharacteristic
317C8—41no—
318C8—121no—
319C8—121no—
320C8—181no—
321C8—181no—
322C2×C3—21no—
323C2×C3—21no—
324C2×C3—21no—
325C2×C3#475511yescharacteristic
326C2×C3#475511yescharacteristic
327C2×C3#477811yescharacteristic
328C2×C3#478711yescharacteristic
329C2×C3#480711yescharacteristic
330C2×C3#481911yescharacteristic
331D3—124no—
332D3—122no—
333D3—122no—
334C22—182no—
335C22—361no—
336C22—361no—
337C22#6391211yescharacteristic
338C4—21no—
339C4—241no—
340C4—241no—
341C4—361no—
342C4#6379611yescharacteristic
343C4#6381011yescharacteristic
344C4#6393711yescharacteristic
345C4#6395011yescharacteristic
346C3—21no—
347C3#6844411yescharacteristic, complemented
348C3#6844511yescharacteristic, complemented
349C2—362no—
350C2#1059054011yescharacteristic
351C2#1059084111yescharacteristic
352C2#1059099311yescharacteristic
subgroupG/H
centerC22#63912
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#121
prime radicalC2×C4⋊(C3⋊D3)D4
hypercenterC4⋊C8D32
hypocenterC32#1679
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. #10590290C2semidirect
5. C3×#4486C2semidirect
6. C3×#4482C2semidirect
7. #10589098C2semidirect
36. #4486D3semidirect
37. #4482D3semidirect
301. C32#1679semidirect
347. C3#68444semidirect
348. C3#68445semidirect

Maximal subgroups

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

subgroupindex
#105925332
#105903792
#105903132
#105902902
C3×#44862
C3×#44822
#105890982
#684453
#684443