Finite Group Databasebeta

← #11781344

Subgroups — #11781344

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#10592786C211yesmaximal, characteristic
2C3×#5079C211yesmaximal, characteristic, complemented
3#10590379C211yesmaximal, characteristic
4#10590327C211yesmaximal, characteristic
5C3×#4547C211yesmaximal, characteristic, complemented
6#10589097C211yesmaximal, characteristic, complemented
7#10589092C211yesmaximal, characteristic, complemented
8#71232—31nomaximal
9#68444—31nomaximal
10C32×C4⋊Q8C2211yescharacteristic
11C4×C4⋊(C3⋊D3)C2211yescharacteristic
12C3×#869C2211yescharacteristic
13C2×#3717—21no—
14C2×#3710—21no—
15#63636—21no—
16#63634—21no—
17C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
18C3×#835—21no—
19C3×#835—21no—
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4×C3⋊C8C2211yescharacteristic
23#63566—21no—
24#63557—21no—
25C3×#487—31no—
26#5087—31no—
27#5087—31no—
28#5087—61no—
29#5083—31no—
30#5079D311yescharacteristic, complemented
31#4841—31no—
32#4834—31no—
33C8×D12—31no—
34C3×#332—31no—
35#4547—31no—
36#4547D311yescharacteristic, complemented
37#4486—31no—
38#4480—31no—
39#4457—31no—
40C2×C32×Q8—21no—
41C2×C4⋊(C3⋊D3)D411yescharacteristic
42C2×C4×C3⋊D3—21no—
43C2×C3×Dic6—21no—
44C32×C4⋊C4—21no—
45C32×C4⋊C4—21no—
46C32×C42C2311yescharacteristic
47#3752—21no—
48C4⋊(C3⋊Dic3)D411yescharacteristic
49C2×C3⋊(C3⋊C8)—21no—
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—21no—
60C3×C4⋊Q8—31no—
61C3×C4⋊Q8C2×D311yescharacteristic
62C3×C4⋊Q8C2×D311yescharacteristic
63C2×#215—61no—
64C2×#204—61no—
65C2×D3×C8—61no—
66C2×D3×C8—61no—
67C4×D12—31no—
68C4×D12—31no—
69C4×D12—61no—
70#869C2×D311yescharacteristic
71C3×C4⋊C8—31no—
72C3×C4⋊C8—31no—
73C3×#103—61no—
74C3×#103—61no—
75C3×C4×C8—31no—
76#835—21no—
77#835—21no—
78#835—61no—
79(C2×D3)⋊C8—61no—
80(C2×D3)⋊C8—61no—
81#816—61no—
82#809—61no—
83#809—61no—
84#809—62no—
85#807—61no—
86#807—61no—
87#807—62no—
88C4⋊(C3⋊C8)—31no—
89C4⋊(C3⋊C8)—31no—
90C4⋊(C3⋊C8)—61no—
91C4⋊(C3⋊C8)C2×D311yescharacteristic
92C4⋊(C3⋊C8)C2×D311yescharacteristic
93C4×C3⋊C8C2×D311yescharacteristic
94C22×C3⋊D3—21no—
95C32×Q8—41no—
96C32×Q8—41no—
97C2×C32×C4—41no—
98C2×C32×C4C2×D411yescharacteristic
99C2×C32×C4C2×D411yescharacteristic
100C2×C32×C4#4111yescharacteristic
101C2×C3⋊Dic3—21no—
102C4⋊(C3⋊D3)—21no—
103C4⋊(C3⋊D3)SD1612yes—
104C4×C3⋊D3—41no—
105C4×C3⋊D3—41no—
106C2×C3×Dic3—41no—
107C3×Dic6—41no—
108C3×Dic6—41no—
109C3⋊(C3⋊C8)—41no—
110C3×C3⋊C8—21no—
111C3×C3⋊C8—21no—
112C3×C3⋊C8—41no—
113C3×C3⋊C8—41no—
114#487—31no—
115#474—91no—
116#461—91no—
117C8×D4—91no—
118#334—91no—
119#332—31no—
120#332—91no—
121C2×C3×Q8—21no—
122C2×C3×Q8—21no—
123C2×C3×Q8—41no—
124C2×C3×Q8—61no—
125C2×D12—31no—
126C2×D12—31no—
127C2×D12—61no—
128C2×C4×D3—61no—
129C2×C4×D3—61no—
130C2×C4×D3—121no—
131C2×Dic6—21no—
132C2×C3×C8—31no—
133C2×C3×C8—31no—
134C2×C3×C8—61no—
135C2×C3×C8—61no—
136C3×C4⋊C4—22no—
137C3×C4⋊C4—21no—
138C3×C4⋊C4—21no—
139C3×C4⋊C4—21no—
140C3×C4⋊C4—21no—
141C3×C4⋊C4—41no—
142C3×C4⋊C4—61no—
143C3×C4⋊C4—61no—
144C3×C42—21no—
145C3×C42C22×D311yescharacteristic
146C3×C42C22×D311yescharacteristic
147#215—122no—
148(C2×D3)⋊C4—61no—
149(C2×D3)⋊C4—61no—
150(C2×D3)⋊C4—121no—
151C4⋊Dic3—21no—
152C4⋊Dic3—21no—
153C4⋊Dic3—31no—
154C4⋊Dic3—31no—
155C4⋊Dic3—61no—
156C2×C3⋊C8—21no—
157C2×C3⋊C8—21no—
158C2×C3⋊C8—62no—
159C2×C3⋊C8—61no—
160C2×C3⋊C8—61no—
161C2×C3⋊C8#6711yescharacteristic
162C2×C3⋊C8#6711yescharacteristic
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×C4—81no—
172C32×C4C2×SD1611yescharacteristic
173C32×C4#13511yescharacteristic
174C32×C4#13511yescharacteristic
175C32×C4AGL(1,ℤ/8)11yescharacteristic
176C3⋊Dic3—41no—
177C3×Dic3—81no—
178C2×SD16—181no—
179C22×C8—181no—
180C4⋊Q8—31no—
181C4⋊Q8D3211yescharacteristic
182C4×D4—91no—
183#107—181no—
184C4⋊C8—31no—
185C4⋊C8—31no—
186C4⋊C8—91no—
187#103—61no—
188#103—61no—
189#103—181no—
190#102—181no—
191C22⋊C8—181no—
192C4×C8—31no—
193C22×D3—61no—
194C22×D3—61no—
195C22×D3—121no—
196C3×Q8—41no—
197C3×Q8—41no—
198C3×Q8—41no—
199C3×Q8—41no—
200C3×Q8—81no—
201C3×Q8—81no—
202C3×Q8—121no—
203C3×Q8—121no—
204C2×C3×C4—21no—
205C2×C3×C4—21no—
206C2×C3×C4—21no—
207C2×C3×C4—42no—
208C2×C3×C4—41no—
209C2×C3×C4—41no—
210C2×C3×C4—121no—
211C2×C3×C4#23511yescharacteristic
212C2×C3×C4D3×D411yescharacteristic
213C2×C3×C4D3×D411yescharacteristic
214C2×C3×C4D3×D411yescharacteristic
215C2×C3×C4#23711yescharacteristic
216C2×C3×C4C2×#6711yescharacteristic
217C2×Dic3—41no—
218C2×Dic3—61no—
219C2×Dic3—61no—
220C2×Dic3—121no—
221D12—32no—
222D12—32no—
223D12—62no—
224D12—61no—
225D12—61no—
226D12—121no—
227C4×D3—121no—
228C4×D3—121no—
229C4×D3—121no—
230C4×D3—121no—
231C4×D3—241no—
232C4×D3—241no—
233Dic6—41no—
234Dic6—41no—
235C3×C8—61no—
236C3×C8—61no—
237C3×C8—121no—
238C3×C8—121no—
239C3⋊C8—21no—
240C3⋊C8—21no—
241C3⋊C8—41no—
242C3⋊C8—41no—
243C3⋊C8—122no—
244C3⋊C8—121no—
245C3⋊C8—121no—
246C2×C32#46311yescharacteristic
247C2×C32#46511yescharacteristic
248C2×C32#47311yescharacteristic
249C3⋊D3—42no—
250C2×Q8—21no—
251C2×Q8—61no—
252C2×D4—91no—
253C22×C4—181no—
254SD16—362no—
255C2×C8—31no—
256C2×C8—31no—
257C2×C8—61no—
258C2×C8—61no—
259C2×C8—181no—
260C2×C8—362no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—61no—
264C4⋊C4—61no—
265C4⋊C4—91no—
266C22⋊C4—181no—
267C42C2×D3211yescharacteristic
268C22×C3—21no—
269C22×C3#88411yescharacteristic
270C22×C3#93811yescharacteristic
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—82no—
288C3×C4—81no—
289C3×C4—81no—
290C3×C4—241no—
291C3×C4#91111yescharacteristic
292C3×C4D3×SD1611yescharacteristic
293C3×C4D3×SD1611yescharacteristic
294C3×C4#91611yescharacteristic
295C3×C4#91611yescharacteristic
296C3×C4#91911yescharacteristic
297C3×C4#94911yescharacteristic
298C3×C4#95011yescharacteristic
299Dic3—81no—
300Dic3—121no—
301Dic3—121no—
302Dic3—241no—
303C32#167911yescharacteristic, complemented, Sylow
304C23—181no—
305Q8—41no—
306Q8—41no—
307Q8—121no—
308Q8—121no—
309D4—92no—
310D4—181no—
311C2×C4—41no—
312C2×C4—121no—
313C2×C4—181no—
314C2×C4—361no—
315C2×C4—361no—
316C2×C4#380411yescharacteristic
317C2×C4D3×#6711yescharacteristic
318C2×C4#381111yescharacteristic
319C8—61no—
320C8—61no—
321C8—121no—
322C8—121no—
323C8—361no—
324C2×C3—21no—
325C2×C3—21no—
326C2×C3—21no—
327C2×C3#475511yescharacteristic
328C2×C3#478711yescharacteristic
329C2×C3#480711yescharacteristic
330C2×C3#505711yescharacteristic
331C2×C3#517111yescharacteristic
332C2×C3#519211yescharacteristic
333D3—122no—
334D3—122no—
335D3—242no—
336C22—182no—
337C22—361no—
338C22—361no—
339C22#6395811yescharacteristic
340C4—21no—
341C4—81no—
342C4—241no—
343C4—361no—
344C4#6392511yescharacteristic
345C4#6393511yescharacteristic
346C4#6394011yescharacteristic
347C4#6395011yescharacteristic
348C3—21no—
349C3#6844411yescharacteristic, complemented
350C3#7123211yescharacteristic, complemented
351C2—362no—
352C2#1059143211yescharacteristic
353C2#1059154311yescharacteristic
354C2#1059159111yescharacteristic
subgroupG/H
centerC22#63958
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socleC22×C32#121
prime radicalC2×C4⋊(C3⋊D3)D4
hypercenterC4⋊Q8D32
hypocenterC32#1679
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C3×#5079C2semidirect
5. C3×#4547C2semidirect
6. #10589097C2semidirect
7. #10589092C2semidirect
30. #5079D3semidirect
36. #4547D3semidirect
303. C32#1679semidirect
349. C3#68444semidirect
350. C3#71232semidirect

Maximal subgroups

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

subgroupindex
#105927862
C3×#50792
#105903792
#105903272
C3×#45472
#105890972
#105890922
#712323
#684443