Finite Group Databasebeta

← #11781362

Subgroups — #11781362

Order 1152.

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

normal subgroups only

This group has 392 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#10592540C211yesmaximal, characteristic
2#10590327C211yesmaximal, characteristic
3#10590313C211yesmaximal, characteristic
4#10590287C211yesmaximal, characteristic, complemented
5C3×#4486C211yesmaximal, characteristic, complemented
6C3×#4480C211yesmaximal, characteristic, complemented
7#10589094C211yesmaximal, characteristic, complemented
8#68539—31nomaximal
9#68444—31nomaximal
10C2×#3744—21no—
11C4×C4⋊(C3⋊D3)C2211yescharacteristic
12#64078C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C2×#3710—21no—
15C32×C4⋊C8C2211yescharacteristic
16#63643—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#4841—31no—
29#4841—31no—
30#4841—61no—
31#4834—31no—
32C8×D12—31no—
33#4681—31no—
34C3×#334—31no—
35C3×#332—31no—
36#4486—31no—
37#4486D311yescharacteristic, complemented
38#4482—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
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#3710—42no—
58#1679—91noSylow
59C3×C4⋊Q8—31no—
60C2×#204—61no—
61C2×#204—61no—
62C2×#204—62no—
63C2×D3×C8—61no—
64C2×D3×C8—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#835—61no—
79#835—61no—
80#821—61no—
81(C2×D3)⋊C8—61no—
82(C2×D3)⋊C8—61no—
83#818—61no—
84#816—61no—
85#816—61no—
86#816—62no—
87#816—61no—
88#816—61no—
89#809—61no—
90#807—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—62no—
130C2×Dic6—61no—
131C2×Dic6—61no—
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(C2×D3)⋊C4—61no—
145(C2×D3)⋊C4—61no—
146(C2×D3)⋊C4—121no—
147C4⋊Dic3—21no—
148C4⋊Dic3—21no—
149C4⋊Dic3—31no—
150C4⋊Dic3—31no—
151C4⋊Dic3—61no—
152C4⋊Dic3—61no—
153C4⋊Dic3—61no—
154C4⋊Dic3—61no—
155C4⋊Dic3—61no—
156C4⋊Dic3—121no—
157C4⋊Dic3—121no—
158C2×C3⋊C8—21no—
159C2×C3⋊C8—21no—
160C2×C3⋊C8D1211yescharacteristic
161C2×C3⋊C8D1211yescharacteristic
162#204—122no—
163#204—122no—
164#204—124no—
165D3×C8—122no—
166D3×C8—122no—
167C22×C32#12111yescharacteristic
168C2×C3⋊D3—22no—
169C2×C3⋊D3—41no—
170C2×C3⋊D3—41no—
171C32×C4—21no—
172C32×C4C2×SD1611yescharacteristic
173C32×C4#13511yescharacteristic
174C32×C4#13511yescharacteristic
175C32×C4AGL(1,ℤ/8)11yescharacteristic
176C3⋊Dic3—41no—
177C3⋊Dic3—81no—
178C3×Dic3—81no—
179C2×SD16—181no—
180C22×C8—181no—
181C4⋊Q8—31no—
182C4⋊Q8—91no—
183C4×D4—91no—
184#107—181no—
185C4⋊C8—31no—
186C4⋊C8—31no—
187C4⋊C8D3211yescharacteristic
188#103—181no—
189#103—181no—
190#103—181no—
191#102—181no—
192C22⋊C8—181no—
193C4×C8—31no—
194C22×D3—61no—
195C22×D3—61no—
196C22×D3—121no—
197C3×Q8—121no—
198C3×Q8—121no—
199C2×C3×C4—21no—
200C2×C3×C4—21no—
201C2×C3×C4—21no—
202C2×C3×C4—121no—
203C2×C3×C4C2×D1211yescharacteristic
204C2×C3×C4#23511yescharacteristic
205C2×C3×C4D3×D411yescharacteristic
206C2×C3×C4D3×D411yescharacteristic
207C2×C3×C4D3×D411yescharacteristic
208C2×C3×C4#23911yescharacteristic
209C2×Dic3—41no—
210C2×Dic3—61no—
211C2×Dic3—61no—
212C2×Dic3—121no—
213C2×Dic3—122no—
214C2×Dic3—121no—
215C2×Dic3—121no—
216D12—32no—
217D12—32no—
218D12—62no—
219D12—61no—
220D12—61no—
221D12—121no—
222C4×D3—121no—
223C4×D3—121no—
224C4×D3—121no—
225C4×D3—121no—
226C4×D3—241no—
227C4×D3—241no—
228Dic6—41no—
229Dic6—41no—
230Dic6—122no—
231Dic6—122no—
232Dic6—121no—
233Dic6—121no—
234Dic6—121no—
235Dic6—121no—
236C3×C8—42no—
237C3×C8—41no—
238C3×C8—41no—
239C3×C8—61no—
240C3×C8—61no—
241C3×C8—121no—
242C3×C8—121no—
243C3⋊C8—21no—
244C3⋊C8—21no—
245C3⋊C8—41no—
246C3⋊C8—41no—
247C2×C32#46311yescharacteristic
248C2×C32#46511yescharacteristic
249C2×C32#47311yescharacteristic
250C3⋊D3—42no—
251C2×Q8—61no—
252C2×Q8—181no—
253C2×D4—91no—
254C22×C4—181no—
255SD16—362no—
256C2×C8—21no—
257C2×C8—31no—
258C2×C8—31no—
259C2×C8—61no—
260C2×C8—61no—
261C2×C8—362no—
262C4⋊C4—61no—
263C4⋊C4—61no—
264C4⋊C4—91no—
265C4⋊C4—181no—
266C4⋊C4—181no—
267C22⋊C4—181no—
268C42C2×D3211yescharacteristic
269C22×C3—21no—
270C22×C3#88411yescharacteristic
271C22×C3#89511yescharacteristic
272C2×D3—62no—
273C2×D3—62no—
274C2×D3—122no—
275C2×D3—121no—
276C2×D3—121no—
277C2×D3—121no—
278C2×D3—121no—
279C2×D3—241no—
280C2×D3—241no—
281C3×C4—21no—
282C3×C4—21no—
283C3×C4—21no—
284C3×C4—21no—
285C3×C4—21no—
286C3×C4—21no—
287C3×C4—41no—
288C3×C4—241no—
289C3×C4#90411yescharacteristic
290C3×C4#90811yescharacteristic
291C3×C4#91111yescharacteristic
292C3×C4D3×SD1611yescharacteristic
293C3×C4D3×SD1611yescharacteristic
294C3×C4#91611yescharacteristic
295C3×C4#91611yescharacteristic
296C3×C4#91911yescharacteristic
297Dic3—81no—
298Dic3—121no—
299Dic3—121no—
300Dic3—241no—
301Dic3—242no—
302Dic3—241no—
303Dic3—241no—
304C32#167911yescharacteristic, complemented, Sylow
305C23—181no—
306Q8—121no—
307Q8—121no—
308Q8—361no—
309Q8—361no—
310D4—92no—
311D4—181no—
312C2×C4—121no—
313C2×C4—181no—
314C2×C4—361no—
315C2×C4—361no—
316C2×C4—361no—
317C2×C4#379911yescharacteristic
318C2×C4D3×D1211yescharacteristic
319C2×C4#381111yescharacteristic
320C8—41no—
321C8—61no—
322C8—61no—
323C8—121no—
324C8—121no—
325C2×C3—21no—
326C2×C3—21no—
327C2×C3—21no—
328C2×C3#475511yescharacteristic
329C2×C3#478711yescharacteristic
330C2×C3#480711yescharacteristic
331C2×C3#484411yescharacteristic
332C2×C3#486411yescharacteristic
333C2×C3#489611yescharacteristic
334D3—122no—
335D3—122no—
336D3—242no—
337C22—182no—
338C22—361no—
339C22—361no—
340C22#6391011yescharacteristic
341C4—21no—
342C4—241no—
343C4—361no—
344C4—721no—
345C4#6379511yescharacteristic
346C4#6380611yescharacteristic
347C4#6393011yescharacteristic
348C4#6395011yescharacteristic
349C3—21no—
350C3#6844411yescharacteristic, complemented
351C3#6853911yescharacteristic, complemented
352C2—362no—
353C2#1059052311yescharacteristic
354C2#1059086011yescharacteristic
355C2#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. #10590287C2semidirect
5. C3×#4486C2semidirect
6. C3×#4480C2semidirect
7. #10589094C2semidirect
37. #4486D3semidirect
39. #4480D3semidirect
304. C32#1679semidirect
350. C3#68444semidirect
351. C3#68539semidirect

Maximal subgroups

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

subgroupindex
#105925402
#105903272
#105903132
#105902872
C3×#44862
C3×#44802
#105890942
#685393
#684443