Finite Group Databasebeta

← #11781545

Subgroups — #11781545

Order 1152.

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

normal subgroups only

This group has 387 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#10590313C211yesmaximal, characteristic
3#10590300C211yesmaximal, characteristic
4#10590290C211yesmaximal, characteristic, complemented
5C3×#4482C211yesmaximal, characteristic, complemented
6C3×#4481C211yesmaximal, characteristic, complemented
7#10589100C211yesmaximal, characteristic, complemented
8#68499—31nomaximal
9#68447—31nomaximal
10C2×C8×C3⋊D3—21no—
11C4×C4⋊(C3⋊D3)C2211yescharacteristic
12C3×#869C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C32×C4⋊C8C2211yescharacteristic
15#63647—21no—
16C4×C3⋊(C3⋊C8)C2211yescharacteristic
17C3×C4⋊(C3⋊C8)C2211yescharacteristic
18C3×C4⋊(C3⋊C8)C2211yescharacteristic
19#63575—21no—
20#63573—21no—
21#63565—21no—
22#63565—21no—
23#63564—21no—
24#63564—21no—
25#5093—31no—
26#5087—31no—
27#5084—31no—
28#5079—31no—
29#4846—31no—
30#4842—31no—
31#4834—31no—
32#4834—31no—
33#4834—61no—
34C3×#333—31no—
35C3×#332—31no—
36#4482D311yescharacteristic, complemented
37#4481D311yescharacteristic, complemented
38#4479—31no—
39#4479—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#1683—91noSylow
58C3×C4⋊Q8—31no—
59C3×C4⋊Q8—31no—
60C2×D3×C8—61no—
61C2×D3×C8—61no—
62C2×D3×C8—62no—
63C4×D12—31no—
64C4×D12—31no—
65C4×D12—61no—
66#869C2×D311yescharacteristic
67#869C2×D311yescharacteristic
68C3×C4⋊C8—21no—
69C3×C4⋊C8—31no—
70C3×C4⋊C8—31no—
71C3×C4⋊C8C2×D311yescharacteristic
72C3×C4⋊C8C2×D311yescharacteristic
73#835—61no—
74#835—61no—
75#821—61no—
76#821—61no—
77(C2×D3)⋊C8—61no—
78(C2×D3)⋊C8—61no—
79(C2×D3)⋊C8—62no—
80#818—61no—
81#817—61no—
82#810—61no—
83#810—61no—
84#809—61no—
85#809—61no—
86#808—61no—
87#807—61no—
88C4⋊(C3⋊C8)C2×D311yescharacteristic
89C4⋊(C3⋊C8)C2×D311yescharacteristic
90C4×C3⋊C8—31no—
91C4×C3⋊C8—31no—
92C4×C3⋊C8—61no—
93C22×C3⋊D3—21no—
94C2×C32×C4C2×D411yescharacteristic
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4#4111yescharacteristic
97C2×C3⋊Dic3—21no—
98C4⋊(C3⋊D3)—21no—
99C4⋊(C3⋊D3)Q1612yes—
100C4×C3⋊D3—41no—
101C4×C3⋊D3—41no—
102C2×C3×Dic3—41no—
103C2×C3×Dic3—41no—
104C3×Dic6—41no—
105C3×Dic6—41no—
106C3×Dic6—81no—
107C32×C8—41no—
108C3⋊(C3⋊C8)—21no—
109C3⋊(C3⋊C8)—21no—
110C3×C3⋊C8—41no—
111C3×C3⋊C8—41no—
112#487—91no—
113#476—91no—
114#474—91no—
115C8×D4—91no—
116#335—91no—
117#333—31no—
118#332—31no—
119C2×C3×Q8—61no—
120C2×C3×Q8—61no—
121C2×D12—31no—
122C2×D12—31no—
123C2×D12—61no—
124C2×C4×D3—62no—
125C2×C4×D3—61no—
126C2×C4×D3—61no—
127C2×Dic6—21no—
128C2×Dic6—21no—
129C2×C3×C8—22no—
130C2×C3×C8—21no—
131C2×C3×C8—21no—
132C2×C3×C8—61no—
133C2×C3×C8—61no—
134C3×C4⋊C4—61no—
135C3×C4⋊C4—61no—
136C3×C4⋊C4—61no—
137C3×C4⋊C4—61no—
138C3×C42—21no—
139C3×C42C22×D311yescharacteristic
140C3×C42C22×D311yescharacteristic
141(C2×D3)⋊C4—62no—
142(C2×D3)⋊C4—61no—
143(C2×D3)⋊C4—61no—
144C4⋊Dic3—21no—
145C4⋊Dic3—21no—
146C4⋊Dic3—21no—
147C4⋊Dic3—21no—
148C4⋊Dic3—31no—
149C4⋊Dic3—31no—
150C4⋊Dic3—61no—
151C2×C3⋊C8—21no—
152C2×C3⋊C8—21no—
153C2×C3⋊C8—31no—
154C2×C3⋊C8—31no—
155C2×C3⋊C8—31no—
156C2×C3⋊C8—31no—
157C2×C3⋊C8—61no—
158C2×C3⋊C8—61no—
159D3×C8—124no—
160D3×C8—122no—
161D3×C8—122no—
162C22×C32#12111yescharacteristic
163C2×C3⋊D3—22no—
164C2×C3⋊D3—41no—
165C2×C3⋊D3—41no—
166C32×C4—21no—
167C32×C4C2×Q1611yescharacteristic
168C32×C4#13511yescharacteristic
169C32×C4#13511yescharacteristic
170C32×C4AGL(1,ℤ/8)11yescharacteristic
171C3⋊Dic3—41no—
172C3×Dic3—81no—
173C3×Dic3—81no—
174C22×C8—181no—
175C4⋊Q8—31no—
176C4⋊Q8—31no—
177C4×D4—91no—
178#107—181no—
179#106—181no—
180C4⋊C8—31no—
181C4⋊C8—31no—
182C4⋊C8D3211yescharacteristic
183#103—181no—
184#103—181no—
185#102—181no—
186#102—181no—
187C22⋊C8—181no—
188C4×C8—91no—
189C22×D3—62no—
190C22×D3—61no—
191C22×D3—61no—
192C3×Q8—121no—
193C3×Q8—121no—
194C3×Q8—241no—
195C2×C3×C4—21no—
196C2×C3×C4—21no—
197C2×C3×C4—21no—
198C2×C3×C4—121no—
199C2×C3×C4—121no—
200C2×C3×C4#23511yescharacteristic
201C2×C3×C4#23511yescharacteristic
202C2×C3×C4D3×D411yescharacteristic
203C2×C3×C4D3×D411yescharacteristic
204C2×C3×C4D3×D411yescharacteristic
205C2×C3×C4D3×D411yescharacteristic
206C2×Dic3—41no—
207C2×Dic3—41no—
208C2×Dic3—62no—
209C2×Dic3—61no—
210C2×Dic3—61no—
211D12—32no—
212D12—32no—
213D12—62no—
214D12—62no—
215D12—61no—
216D12—61no—
217C4×D3—122no—
218C4×D3—122no—
219C4×D3—121no—
220C4×D3—121no—
221C4×D3—121no—
222C4×D3—121no—
223Dic6—41no—
224Dic6—41no—
225Dic6—81no—
226C3×C8—42no—
227C3×C8—41no—
228C3×C8—41no—
229C3×C8—121no—
230C3×C8—121no—
231C3⋊C8—41no—
232C3⋊C8—41no—
233C3⋊C8—62no—
234C3⋊C8—61no—
235C3⋊C8—61no—
236C3⋊C8—61no—
237C3⋊C8—61no—
238C3⋊C8—121no—
239C2×C32#46311yescharacteristic
240C2×C32#46711yescharacteristic
241C2×C32#47111yescharacteristic
242C3⋊D3—42no—
243C2×Q8—61no—
244C2×Q8—61no—
245C2×D4—91no—
246C22×C4—181no—
247C2×C8—21no—
248C2×C8—61no—
249C2×C8—61no—
250C2×C8—91no—
251C2×C8—91no—
252C2×C8—362no—
253C4⋊C4—61no—
254C4⋊C4—61no—
255C4⋊C4—61no—
256C4⋊C4—61no—
257C4⋊C4—91no—
258C22⋊C4—181no—
259C42C2×D3211yescharacteristic
260C22×C3—21no—
261C22×C3#88411yescharacteristic
262C22×C3#88411yescharacteristic
263C2×D3—64no—
264C2×D3—62no—
265C2×D3—62no—
266C2×D3—122no—
267C2×D3—122no—
268C2×D3—121no—
269C2×D3—121no—
270C2×D3—121no—
271C2×D3—121no—
272C3×C4—21no—
273C3×C4—21no—
274C3×C4—21no—
275C3×C4—21no—
276C3×C4—21no—
277C3×C4—21no—
278C3×C4—41no—
279C3×C4—241no—
280C3×C4—241no—
281C3×C4#91111yescharacteristic
282C3×C4#91411yescharacteristic
283C3×C4#91611yescharacteristic
284C3×C4#91611yescharacteristic
285C3×C4#91611yescharacteristic
286C3×C4D3×Q1611yescharacteristic
287C3×C4D3×Q1611yescharacteristic
288C3×C4#91911yescharacteristic
289Dic3—81no—
290Dic3—81no—
291Dic3—122no—
292Dic3—121no—
293Dic3—121no—
294C32#168311yescharacteristic, complemented, Sylow
295C23—181no—
296Q8—121no—
297Q8—121no—
298Q8—241no—
299D4—92no—
300D4—181no—
301C2×C4—121no—
302C2×C4—121no—
303C2×C4—181no—
304C2×C4—361no—
305C2×C4—361no—
306C2×C4#379811yescharacteristic
307C2×C4#380211yescharacteristic
308C2×C4#381111yescharacteristic
309C8—41no—
310C8—121no—
311C8—121no—
312C8—181no—
313C8—181no—
314C2×C3—21no—
315C2×C3—21no—
316C2×C3—21no—
317C2×C3#474811yescharacteristic
318C2×C3#475411yescharacteristic
319C2×C3#478711yescharacteristic
320C2×C3#481311yescharacteristic
321C2×C3#481311yescharacteristic
322C2×C3#481911yescharacteristic
323D3—124no—
324D3—122no—
325D3—122no—
326C22—182no—
327C22—361no—
328C22—361no—
329C22#6391211yescharacteristic
330C4—21no—
331C4—241no—
332C4—241no—
333C4—361no—
334C4#6380211yescharacteristic
335C4#6380911yescharacteristic
336C4#6393711yescharacteristic
337C4#6395011yescharacteristic
338C3—21no—
339C3#6844711yescharacteristic, complemented
340C3#6849911yescharacteristic, complemented
341C2—362no—
342C2#1059054011yescharacteristic
343C2#1059085511yescharacteristic
344C2#1059099111yescharacteristic
subgroupG/H
centerC22#63912
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#121
prime radicalC2×C4⋊(C3⋊D3)D4
hypercenterC4⋊C8D32
hypocenterC32#1683
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×#4482C2semidirect
6. C3×#4481C2semidirect
7. #10589100C2semidirect
36. #4482D3semidirect
37. #4481D3semidirect
294. C32#1683semidirect
339. C3#68447semidirect
340. C3#68499semidirect

Maximal subgroups

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

subgroupindex
#105925332
#105903132
#105903002
#105902902
C3×#44822
C3×#44812
#105891002
#684993
#684473