Finite Group Databasebeta

← #11781857

Subgroups — #11781857

Order 1152.

380 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 86 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#10592540C211yesmaximal, characteristic
2#10590338C211yesmaximal, characteristic
3#10590303C211yesmaximal, characteristic, complemented
4#10590300C211yesmaximal, characteristic
5C3×#4481C211yesmaximal, characteristic, complemented
6C3×#4479C211yesmaximal, characteristic, complemented
7#10589094C211yesmaximal, characteristic, complemented
8#68583—31nomaximal
9#68500—31nomaximal
10C2×#3744—21no—
11C4×C4⋊(C3⋊D3)C2211yescharacteristic
12#64078C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C2×#3712—21no—
15C32×C4⋊C8C2211yescharacteristic
16#63643—21no—
17C3×C4⋊(C3⋊C8)C2211yescharacteristic
18C3×C4⋊(C3⋊C8)C2211yescharacteristic
19C3×C4×C3⋊C8C2211yescharacteristic
20#63573—21no—
21#63573—21no—
22#63573—21no—
23#63564—21no—
24#63557—21no—
25#5084—31no—
26#5080—31no—
27#4842—31no—
28#4841—31no—
29#4841—31no—
30#4841—61no—
31#4838—31no—
32#4688—31no—
33#4680—31no—
34C3×#335—31no—
35C3×#333—31no—
36#4486—31no—
37#4482—31no—
38#4481D311yescharacteristic, complemented
39#4479D311yescharacteristic, 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
50#3744—42no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3—21no—
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8D411yescharacteristic
56C2×C3×C3⋊C8D411yescharacteristic
57#3712—42no—
58#1691—91noSylow
59C3×C4⋊Q8—31no—
60C2×#204—61no—
61C2×#204—61no—
62C2×#204—62no—
63C2×ΓL(1,𝔽25)—61no—
64C2×ΓL(1,𝔽25)—61no—
65C4×D12—31no—
66C4×D12—31no—
67C4×D12—61no—
68#869—31no—
69#869—31no—
70#869—61no—
71#869C2×D311yescharacteristic
72C3×C4⋊C8—21no—
73C3×C4⋊C8—31no—
74C3×C4⋊C8—31no—
75C3×C4⋊C8C2×D311yescharacteristic
76C3×C4⋊C8C2×D311yescharacteristic
77C3×C4×C8—31no—
78#821—61no—
79(C2×D3)⋊C8—61no—
80(C2×D3)⋊C8—61no—
81#817—61no—
82#817—61no—
83#817—61no—
84#816—61no—
85#816—61no—
86#816—62no—
87#809—61no—
88#808—61no—
89#808—61no—
90#808—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)—21no—
102C4×C3⋊D3—41no—
103C4×C3⋊D3—41no—
104#634—41no—
105#634—41no—
106C2×C3×Dic3—41no—
107C3×Dic6—81no—
108C32×C8—41no—
109C3×C3⋊C8—21no—
110C3×C3⋊C8—41no—
111C3×C3⋊C8—41no—
112C3×C3⋊C8SD1612yescomplemented
113#498—91no—
114#476—91no—
115#461—91no—
116#436—91no—
117#335—31no—
118#333—31no—
119#332—91no—
120C2×C3×Q8—61no—
121C2×D12—31no—
122C2×D12—31no—
123C2×D12—61no—
124C2×C4×D3—61no—
125C2×C4×D3—61no—
126C2×C4×D3—121no—
127C2×Dic6—21no—
128C2×Dic6—62no—
129C2×Dic6—61no—
130C2×Dic6—61no—
131C2×C3×C8—22no—
132C2×C3×C8—21no—
133C2×C3×C8—21no—
134C2×C3×C8—31no—
135C2×C3×C8—31no—
136C2×C3×C8—61no—
137C2×C3×C8—61no—
138C3×C4⋊C4—61no—
139C3×C4⋊C4—61no—
140C3×C42—21no—
141C3×C42C22×D311yescharacteristic
142C3×C42C22×D311yescharacteristic
143(C2×D3)⋊C4—61no—
144(C2×D3)⋊C4—61no—
145(C2×D3)⋊C4—121no—
146C4⋊Dic3—21no—
147C4⋊Dic3—21no—
148C4⋊Dic3—31no—
149C4⋊Dic3—31no—
150C4⋊Dic3—61no—
151C4⋊Dic3—61no—
152C4⋊Dic3—61no—
153C4⋊Dic3—61no—
154C4⋊Dic3—61no—
155C4⋊Dic3—121no—
156C4⋊Dic3—121no—
157C2×C3⋊C8—21no—
158C2×C3⋊C8—21no—
159C2×C3⋊C8D1211yescharacteristic
160C2×C3⋊C8D1211yescharacteristic
161#204—124no—
162#204—122no—
163#204—122no—
164ΓL(1,𝔽25)—122no—
165ΓL(1,𝔽25)—122no—
166C22×C32#12111yescharacteristic
167C2×C3⋊D3—41no—
168C2×C3⋊D3—41no—
169C2×C3⋊D3—41no—
170C32×C4—21no—
171C32×C4C2×SD1611yescharacteristic
172C32×C4AGL(1,ℤ/8)11yescharacteristic
173C32×C4#13711yescharacteristic
174C32×C4#13711yescharacteristic
175C3⋊Dic3—41no—
176C3⋊Dic3—81no—
177C3×Dic3—81no—
178C2×SD16—181no—
179C2×M16—181no—
180C4⋊Q8—31no—
181C4⋊Q8—91no—
182C4×D4—91no—
183#106—181no—
184#106—181no—
185#106—181no—
186C4⋊C8—31no—
187C4⋊C8—31no—
188C4⋊C8D3211yescharacteristic
189#103—181no—
190#102—181no—
191C22⋊C8—181no—
192C4×C8—31no—
193C22×D3—61no—
194C22×D3—61no—
195C22×D3—121no—
196C3×Q8—241no—
197C2×C3×C4—21no—
198C2×C3×C4—21no—
199C2×C3×C4—21no—
200C2×C3×C4—121no—
201C2×C3×C4C2×D1211yescharacteristic
202C2×C3×C4#23511yescharacteristic
203C2×C3×C4D3×D411yescharacteristic
204C2×C3×C4D3×D411yescharacteristic
205C2×C3×C4D3×D411yescharacteristic
206C2×C3×C4#23911yescharacteristic
207C2×Dic3—41no—
208C2×Dic3—61no—
209C2×Dic3—61no—
210C2×Dic3—121no—
211C2×Dic3—122no—
212C2×Dic3—121no—
213C2×Dic3—121no—
214D12—62no—
215D12—61no—
216D12—61no—
217D12—61no—
218D12—61no—
219D12—121no—
220C4×D3—121no—
221C4×D3—121no—
222C4×D3—121no—
223C4×D3—121no—
224C4×D3—241no—
225C4×D3—241no—
226Dic6—81no—
227Dic6—122no—
228Dic6—122no—
229Dic6—121no—
230Dic6—121no—
231Dic6—121no—
232Dic6—121no—
233C3×C8—32no—
234C3×C8—42no—
235C3×C8—41no—
236C3×C8—41no—
237C3×C8—61no—
238C3×C8—121no—
239C3×C8—121no—
240C3⋊C8—21no—
241C3⋊C8—41no—
242C3⋊C8—41no—
243C3⋊C8#20412yescomplemented
244C2×C32#46111yescharacteristic
245C2×C32#46811yescharacteristic
246C2×C32#47111yescharacteristic
247C3⋊D3—81no—
248C2×Q8—61no—
249C2×Q8—181no—
250C2×D4—91no—
251C22×C4—181no—
252SD16—362no—
253M16—362no—
254C2×C8—21no—
255C2×C8—31no—
256C2×C8—31no—
257C2×C8—61no—
258C2×C8—61no—
259C4⋊C4—61no—
260C4⋊C4—61no—
261C4⋊C4—91no—
262C4⋊C4—181no—
263C4⋊C4—181no—
264C22⋊C4—181no—
265C42C2×D3211yescharacteristic
266C22×C3—21no—
267C22×C3#88411yescharacteristic
268C22×C3#89511yescharacteristic
269C2×D3—122no—
270C2×D3—121no—
271C2×D3—121no—
272C2×D3—121no—
273C2×D3—121no—
274C2×D3—121no—
275C2×D3—121no—
276C2×D3—241no—
277C2×D3—241no—
278C3×C4—21no—
279C3×C4—21no—
280C3×C4—21no—
281C3×C4—21no—
282C3×C4—21no—
283C3×C4—21no—
284C3×C4—41no—
285C3×C4—241no—
286C3×C4C2×#20411yescharacteristic
287C3×C4#90911yescharacteristic
288C3×C4#91111yescharacteristic
289C3×C4D3×SD1611yescharacteristic
290C3×C4#91411yescharacteristic
291C3×C4#91811yescharacteristic
292C3×C4#91811yescharacteristic
293C3×C4#91811yescharacteristic
294Dic3—81no—
295Dic3—121no—
296Dic3—121no—
297Dic3—241no—
298Dic3—242no—
299Dic3—241no—
300Dic3—241no—
301C32#169111yescharacteristic, complemented, Sylow
302C23—181no—
303Q8—241no—
304Q8—361no—
305Q8—361no—
306D4—181no—
307D4—181no—
308C2×C4—121no—
309C2×C4—181no—
310C2×C4—361no—
311C2×C4—361no—
312C2×C4—361no—
313C2×C4#379911yescharacteristic
314C2×C4D3×D1211yescharacteristic
315C2×C4#381111yescharacteristic
316C8—32no—
317C8—41no—
318C8—61no—
319C8—121no—
320C8—121no—
321C2×C3—21no—
322C2×C3—21no—
323C2×C3—21no—
324C2×C3#474811yescharacteristic
325C2×C3#481211yescharacteristic
326C2×C3#481811yescharacteristic
327C2×C3#484111yescharacteristic
328C2×C3#488611yescharacteristic
329C2×C3#489811yescharacteristic
330D3—242no—
331D3—241no—
332D3—241no—
333C22—361no—
334C22—361no—
335C22—361no—
336C22#6391011yescharacteristic
337C4—21no—
338C4—241no—
339C4—361no—
340C4—721no—
341C4D3×#20411yescharacteristic
342C4#6380111yescharacteristic
343C4#6393711yescharacteristic
344C4#6394511yescharacteristic
345C3—21no—
346C3#6850011yescharacteristic, complemented
347C3#6858311yescharacteristic, complemented
348C2—721no—
349C2#1059052211yescharacteristic
350C2#1059076011yescharacteristic
351C2#1059098911yescharacteristic
subgroupG/H
centerC22#63910
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. #10590303C2semidirect
5. C3×#4481C2semidirect
6. C3×#4479C2semidirect
7. #10589094C2semidirect
38. #4481D3semidirect
39. #4479D3semidirect
112. C3×C3⋊C8SD16semidirect
243. C3⋊C8#204semidirect
301. C32#1691semidirect
346. C3#68500semidirect
347. C3#68583semidirect

Maximal subgroups

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

subgroupindex
#105925402
#105903382
#105903032
#105903002
C3×#44812
C3×#44792
#105890942
#685833
#685003