Finite Group Databasebeta

← #11781356

Subgroups — #11781356

Order 1152.

386 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 84 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#10592545C211yesmaximal, characteristic
2#10590379C211yesmaximal, characteristic
3#10590327C211yesmaximal, characteristic
4#10590288C211yesmaximal, characteristic, complemented
5C3×#4482C211yesmaximal, characteristic, complemented
6C3×#4480C211yesmaximal, characteristic, complemented
7#10589094C211yesmaximal, characteristic, complemented
8#68539—31nomaximal
9#68445—31nomaximal
10C4×C4⋊(C3⋊D3)C2211yescharacteristic
11#64078C2211yescharacteristic
12C3×#869C2211yescharacteristic
13C2×#3717—21no—
14C2×#3710—21no—
15C32×C4⋊C8C2211yescharacteristic
16#63648—21no—
17#63645—21no—
18C3×C4⋊(C3⋊C8)C2211yescharacteristic
19C3×C4⋊(C3⋊C8)C2211yescharacteristic
20C3×C4×C3⋊C8C2211yescharacteristic
21#63567—21no—
22#63567—21no—
23#63566—21no—
24#63557—21no—
25#5093—31no—
26#5083—31no—
27#4846—31no—
28#4846—31no—
29#4846—61no—
30#4841—31no—
31#4834—31no—
32C8×D12—31no—
33#4681—31no—
34C3×#334—31no—
35C3×#332—31no—
36#4486—31no—
37#4482—31no—
38#4482D311yescharacteristic, complemented
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#3717—42no—
57#3710—42no—
58#1679—91noSylow
59C3×C4⋊Q8—31no—
60C2×#215—61no—
61C2×#204—61no—
62C2×D3×C8—61no—
63C2×D3×C8—61no—
64C4×D12—31no—
65C4×D12—31no—
66C4×D12—61no—
67#869—31no—
68#869—31no—
69#869—61no—
70#869C2×D311yescharacteristic
71C3×C4⋊C8—21no—
72C3×C4⋊C8—31no—
73C3×C4⋊C8—31no—
74C3×C4⋊C8C2×D311yescharacteristic
75C3×C4⋊C8C2×D311yescharacteristic
76C3×C4×C8—31no—
77#835—61no—
78#821—61no—
79#821—61no—
80#821—62no—
81(C2×D3)⋊C8—61no—
82(C2×D3)⋊C8—61no—
83#818—61no—
84#818—61no—
85#818—62no—
86#816—61no—
87#816—61no—
88#816—61no—
89#810—61no—
90#810—61no—
91C4⋊(C3⋊C8)C2×D311yescharacteristic
92C4⋊(C3⋊C8)C2×D311yescharacteristic
93C4×C3⋊C8C2×D311yescharacteristic
94C22×C3⋊D3—21no—
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4#4111yescharacteristic
98C2×C3⋊Dic3—21no—
99C2×C3⋊Dic3—41no—
100C4⋊(C3⋊D3)—21no—
101C4⋊(C3⋊D3)SD1612yes—
102C4×C3⋊D3—41no—
103C4×C3⋊D3—41no—
104#634—41no—
105#634—41no—
106C2×C3×Dic3—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—31no—
119#332—31no—
120#332—91no—
121C2×C3×Q8—61no—
122C2×D12—31no—
123C2×D12—31no—
124C2×D12—61no—
125C2×C4×D3—61no—
126C2×C4×D3—61no—
127C2×C4×D3—121no—
128C2×Dic6—21no—
129C2×Dic6—61no—
130C2×Dic6—61no—
131C2×Dic6—121no—
132C2×C3×C8—22no—
133C2×C3×C8—21no—
134C2×C3×C8—21no—
135C2×C3×C8—31no—
136C2×C3×C8—31no—
137C2×C3×C8—61no—
138C2×C3×C8—61no—
139C3×C4⋊C4—61no—
140C3×C4⋊C4—61no—
141C3×C42—21no—
142C3×C42C22×D311yescharacteristic
143C3×C42C22×D311yescharacteristic
144#215—122no—
145(C2×D3)⋊C4—61no—
146(C2×D3)⋊C4—61no—
147(C2×D3)⋊C4—121no—
148C4⋊Dic3—21no—
149C4⋊Dic3—21no—
150C4⋊Dic3—31no—
151C4⋊Dic3—31no—
152C4⋊Dic3—61no—
153C4⋊Dic3—62no—
154C4⋊Dic3—61no—
155C4⋊Dic3—61no—
156C4⋊Dic3—61no—
157C4⋊Dic3—61no—
158C4⋊Dic3—121no—
159C2×C3⋊C8—21no—
160C2×C3⋊C8—21no—
161C2×C3⋊C8D1211yescharacteristic
162C2×C3⋊C8D1211yescharacteristic
163#204—122no—
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—91no—
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—31no—
193C22×D3—61no—
194C22×D3—61no—
195C22×D3—121no—
196C3×Q8—121no—
197C3×Q8—121no—
198C2×C3×C4—21no—
199C2×C3×C4—21no—
200C2×C3×C4—21no—
201C2×C3×C4—121no—
202C2×C3×C4C2×D1211yescharacteristic
203C2×C3×C4#23511yescharacteristic
204C2×C3×C4D3×D411yescharacteristic
205C2×C3×C4D3×D411yescharacteristic
206C2×C3×C4D3×D411yescharacteristic
207C2×C3×C4#23911yescharacteristic
208C2×Dic3—41no—
209C2×Dic3—61no—
210C2×Dic3—61no—
211C2×Dic3—121no—
212C2×Dic3—122no—
213C2×Dic3—121no—
214C2×Dic3—121no—
215D12—32no—
216D12—32no—
217D12—62no—
218D12—61no—
219D12—61no—
220D12—121no—
221C4×D3—121no—
222C4×D3—121no—
223C4×D3—121no—
224C4×D3—121no—
225C4×D3—241no—
226C4×D3—241no—
227Dic6—41no—
228Dic6—41no—
229Dic6—121no—
230Dic6—121no—
231Dic6—121no—
232Dic6—121no—
233Dic6—241no—
234Dic6—241no—
235C3×C8—42no—
236C3×C8—41no—
237C3×C8—41no—
238C3×C8—61no—
239C3×C8—61no—
240C3×C8—121no—
241C3×C8—121no—
242C3⋊C8—21no—
243C3⋊C8—21no—
244C3⋊C8—41no—
245C3⋊C8—41no—
246C2×C32#46311yescharacteristic
247C2×C32#46511yescharacteristic
248C2×C32#47311yescharacteristic
249C3⋊D3—42no—
250C2×Q8—61no—
251C2×Q8—181no—
252C2×D4—91no—
253C22×C4—181no—
254SD16—362no—
255C2×C8—21no—
256C2×C8—31no—
257C2×C8—31no—
258C2×C8—61no—
259C2×C8—61no—
260C2×C8—362no—
261C4⋊C4—61no—
262C4⋊C4—61no—
263C4⋊C4—91no—
264C4⋊C4—181no—
265C4⋊C4—181no—
266C22⋊C4—181no—
267C42C2×D3211yescharacteristic
268C22×C3—21no—
269C22×C3#88411yescharacteristic
270C22×C3#89511yescharacteristic
271C2×D3—62no—
272C2×D3—62no—
273C2×D3—122no—
274C2×D3—121no—
275C2×D3—121no—
276C2×D3—121no—
277C2×D3—121no—
278C2×D3—241no—
279C2×D3—241no—
280C3×C4—21no—
281C3×C4—21no—
282C3×C4—21no—
283C3×C4—21no—
284C3×C4—21no—
285C3×C4—21no—
286C3×C4—41no—
287C3×C4—241no—
288C3×C4#90411yescharacteristic
289C3×C4#90811yescharacteristic
290C3×C4#91211yescharacteristic
291C3×C4D3×SD1611yescharacteristic
292C3×C4D3×SD1611yescharacteristic
293C3×C4#91411yescharacteristic
294C3×C4#91611yescharacteristic
295C3×C4#91911yescharacteristic
296Dic3—81no—
297Dic3—121no—
298Dic3—121no—
299Dic3—241no—
300Dic3—242no—
301Dic3—241no—
302Dic3—241no—
303C32#167911yescharacteristic, complemented, Sylow
304C23—181no—
305Q8—121no—
306Q8—121no—
307Q8—361no—
308Q8—361no—
309D4—92no—
310D4—181no—
311C2×C4—121no—
312C2×C4—181no—
313C2×C4—361no—
314C2×C4—361no—
315C2×C4—361no—
316C2×C4#379911yescharacteristic
317C2×C4D3×D1211yescharacteristic
318C2×C4#381111yescharacteristic
319C8—41no—
320C8—61no—
321C8—61no—
322C8—121no—
323C8—121no—
324C2×C3—21no—
325C2×C3—21no—
326C2×C3—21no—
327C2×C3#475511yescharacteristic
328C2×C3#477811yescharacteristic
329C2×C3#481911yescharacteristic
330C2×C3#484411yescharacteristic
331C2×C3#486411yescharacteristic
332C2×C3#489611yescharacteristic
333D3—122no—
334D3—122no—
335D3—242no—
336C22—182no—
337C22—361no—
338C22—361no—
339C22#6391011yescharacteristic
340C4—21no—
341C4—241no—
342C4—361no—
343C4—721no—
344C4#6379411yescharacteristic
345C4#6380811yescharacteristic
346C4#6393611yescharacteristic
347C4#6394011yescharacteristic
348C3—21no—
349C3#6844511yescharacteristic, complemented
350C3#6853911yescharacteristic, complemented
351C2—362no—
352C2#1059050711yescharacteristic
353C2#1059077011yescharacteristic
354C2#1059099211yescharacteristic
subgroupG/H
centerC22#63910
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. #10590288C2semidirect
5. C3×#4482C2semidirect
6. C3×#4480C2semidirect
7. #10589094C2semidirect
38. #4482D3semidirect
39. #4480D3semidirect
303. C32#1679semidirect
349. C3#68445semidirect
350. C3#68539semidirect

Maximal subgroups

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

subgroupindex
#105925452
#105903792
#105903272
#105902882
C3×#44822
C3×#44802
#105890942
#685393
#684453