Finite Group Databasebeta

← #11781447

Subgroups — #11781447

Order 1152.

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

normal subgroups only

This group has 424 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#10592782C211yesmaximal, characteristic, complemented
2C3×#5088C211yesmaximal, characteristic, complemented
3#10590355C211yesmaximal, characteristic
4#10590327C211yesmaximal, characteristic, complemented
5C3×#4547C211yesmaximal, characteristic, complemented
6#10589099C211yesmaximal, characteristic, complemented
7#10589090C211yesmaximal, characteristic, complemented
8#71201—31nomaximal
9#68446—31nomaximal
10C32×C4⋊Q8C2211yescharacteristic
11C2×#3755—21no—
12C4×C4⋊(C3⋊D3)C2211yescharacteristic
13C3×#874C2211yescharacteristic
14C2×#3714—21no—
15C2×#3710—21no—
16#63662—21no—
17C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
18C3×#809—21no—
19C3×#809—21no—
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4×C3⋊C8C2211yescharacteristic
23#63563—21no—
24#63557—21no—
25C3×#486—31no—
26#5088D311yescharacteristic, complemented
27#5083—31no—
28#5083—31no—
29#5083—61no—
30#5072—31no—
31#4843—31no—
32#4834—31no—
33C8×D12—31no—
34C3×#332—31no—
35#4547D311yescharacteristic, complemented
36#4544—31no—
37#4485—31no—
38#4479—31no—
39#4458—31no—
40C2×C32×Q8—21no—
41C2×C4⋊(C3⋊D3)D411yescharacteristic
42C2×C4×C3⋊D3—21no—
43C2×C3×D12—21no—
44C2×C3×D12—21no—
45C2×C3×D12—21no—
46C32×C4⋊C4—21no—
47C32×C4⋊C4—21no—
48C32×C42C2311yescharacteristic
49#3755—42no—
50#3752—21no—
51C4⋊(C3⋊Dic3)D411yescharacteristic
52C2×C3⋊(C3⋊C8)—21no—
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8D411yescharacteristic
56C2×C3×C3⋊C8D411yescharacteristic
57#3714—42no—
58#3710—42no—
59#1681—91noSylow
60C3×C4⋊Q8—21no—
61C3×C4⋊Q8C2×D311yescharacteristic
62C3×C4⋊Q8C2×D311yescharacteristic
63C3×#127—31no—
64C2×#215—61no—
65C2×#215—61no—
66C2×#215—62no—
67C2×#213—61no—
68C2×D24—61no—
69C2×D3×C8—61no—
70C2×D3×C8—61no—
71#874C2×D311yescharacteristic
72C4×D12—31no—
73C4×D12—31no—
74C4×D12—61no—
75C3×C4⋊C8—31no—
76C3×C4⋊C8—31no—
77C3×#102—61no—
78C3×#102—61no—
79C3×C4×C8—31no—
80#835—61no—
81#835—61no—
82#835—62no—
83#832—61no—
84#821—61no—
85(C2×D3)⋊C8—61no—
86(C2×D3)⋊C8—61no—
87#809—21no—
88#809—21no—
89C4⋊(C3⋊C8)—31no—
90C4⋊(C3⋊C8)—31no—
91C4⋊(C3⋊C8)—61no—
92C4⋊(C3⋊C8)C2×D311yescharacteristic
93C4⋊(C3⋊C8)C2×D311yescharacteristic
94C4×C3⋊C8C2×D311yescharacteristic
95C22×C3⋊D3—21no—
96C22×C3×D3—41no—
97C32×Q8—41no—
98C32×Q8—41no—
99C2×C32×C4—41no—
100C2×C32×C4C2×D411yescharacteristic
101C2×C32×C4C2×D411yescharacteristic
102C2×C32×C4#4111yescharacteristic
103C2×C3⋊Dic3—21no—
104C4⋊(C3⋊D3)—21no—
105C4⋊(C3⋊D3)D812yes—
106C4×C3⋊D3—41no—
107C4×C3⋊D3—41no—
108C3×D12—41no—
109C3×D12—41no—
110C3×D12—41no—
111C3×D12—41no—
112C3×D12—81no—
113C3⋊(C3⋊C8)—41no—
114C3×C3⋊C8—21no—
115C3×C3⋊C8—21no—
116C3×C3⋊C8—41no—
117C3×C3⋊C8—41no—
118#486—31no—
119#461—91no—
120#459—91no—
121C8×D4—91no—
122#335—91no—
123#332—31no—
124#331—91no—
125C2×C3×Q8—22no—
126C2×C3×Q8—21no—
127C2×C3×Q8—21no—
128C2×C3×D4—61no—
129C2×C3×D4—61no—
130C2×C3×D4—61no—
131C2×D12—21no—
132C2×D12—21no—
133C2×D12—21no—
134C2×D12—31no—
135C2×D12—31no—
136C2×D12—61no—
137C2×C4×D3—61no—
138C2×C4×D3—61no—
139C2×C4×D3—121no—
140C2×C3×C8—31no—
141C2×C3×C8—31no—
142C2×C3×C8—61no—
143C2×C3×C8—61no—
144C3×C4⋊C4—21no—
145C3×C4⋊C4—21no—
146C3×C4⋊C4—21no—
147C3×C4⋊C4—21no—
148C3×C4⋊C4—41no—
149C3×C4⋊C4—41no—
150C3×C42—21no—
151C3×C42C22×D311yescharacteristic
152C3×C42C22×D311yescharacteristic
153#215—122no—
154#215—122no—
155#215—124no—
156#213—122no—
157(C2×D3)⋊C4—61no—
158(C2×D3)⋊C4—61no—
159(C2×D3)⋊C4—121no—
160C4⋊Dic3—31no—
161C4⋊Dic3—31no—
162C4⋊Dic3—61no—
163C2×C3⋊C8—21no—
164C2×C3⋊C8—21no—
165C2×C3⋊C8—62no—
166C2×C3⋊C8—61no—
167C2×C3⋊C8—61no—
168C2×C3⋊C8#6711yescharacteristic
169C2×C3⋊C8#6711yescharacteristic
170D24—122no—
171D3×C8—122no—
172D3×C8—122no—
173C22×C32#12111yescharacteristic
174C2×C3⋊D3—22no—
175C2×C3⋊D3—41no—
176C2×C3⋊D3—41no—
177C2×C3×D3—81no—
178C2×C3×D3—81no—
179C2×C3×D3—81no—
180C32×C4—21no—
181C32×C4—81no—
182C32×C4C2×D811yescharacteristic
183C32×C4#13511yescharacteristic
184C32×C4#13511yescharacteristic
185C32×C4AGL(1,ℤ/8)11yescharacteristic
186C3⋊Dic3—41no—
187C2×SD16—181no—
188C2×D8—181no—
189C22×C8—181no—
190C4⋊Q8D3211yescharacteristic
191#127—31no—
192C4×D4—91no—
193C4⋊C8—31no—
194C4⋊C8—31no—
195C4⋊C8—91no—
196#103—181no—
197#102—61no—
198#102—61no—
199#102—181no—
200C22⋊C8—181no—
201C4×C8—31no—
202C23×C3—121no—
203C22×D3—41no—
204C22×D3—61no—
205C22×D3—61no—
206C22×D3—121no—
207C3×Q8—42no—
208C3×Q8—42no—
209C3×Q8—41no—
210C3×Q8—41no—
211C3×Q8—41no—
212C3×Q8—41no—
213C3×D4—121no—
214C3×D4—121no—
215C3×D4—121no—
216C3×D4—121no—
217C3×D4—241no—
218C2×C3×C4—21no—
219C2×C3×C4—21no—
220C2×C3×C4—21no—
221C2×C3×C4—42no—
222C2×C3×C4—41no—
223C2×C3×C4—41no—
224C2×C3×C4#23511yescharacteristic
225C2×C3×C4D3×D411yescharacteristic
226C2×C3×C4D3×D411yescharacteristic
227C2×C3×C4D3×D411yescharacteristic
228C2×C3×C4#23711yescharacteristic
229C2×C3×C4C2×#6711yescharacteristic
230C2×Dic3—61no—
231C2×Dic3—61no—
232C2×Dic3—121no—
233D12—32no—
234D12—32no—
235D12—41no—
236D12—41no—
237D12—41no—
238D12—41no—
239D12—62no—
240D12—61no—
241D12—61no—
242D12—81no—
243D12—121no—
244C4×D3—121no—
245C4×D3—121no—
246C4×D3—121no—
247C4×D3—121no—
248C4×D3—241no—
249C4×D3—241no—
250C3×C8—61no—
251C3×C8—61no—
252C3×C8—121no—
253C3×C8—121no—
254C3⋊C8—21no—
255C3⋊C8—21no—
256C3⋊C8—41no—
257C3⋊C8—41no—
258C3⋊C8—122no—
259C3⋊C8—121no—
260C3⋊C8—121no—
261C2×C32#46311yescharacteristic
262C2×C32#46611yescharacteristic
263C2×C32#47111yescharacteristic
264C3⋊D3—42no—
265C3×D3—161no—
266C2×Q8—21no—
267C2×D4—61no—
268C2×D4—61no—
269C2×D4—61no—
270C2×D4—91no—
271C22×C4—181no—
272SD16—362no—
273D8—362no—
274C2×C8—31no—
275C2×C8—31no—
276C2×C8—61no—
277C2×C8—61no—
278C2×C8—181no—
279C2×C8—362no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—91no—
283C22⋊C4—181no—
284C42C2×D3211yescharacteristic
285C22×C3—21no—
286C22×C3—241no—
287C22×C3—241no—
288C22×C3—241no—
289C22×C3#88411yescharacteristic
290C22×C3#93811yescharacteristic
291C2×D3—62no—
292C2×D3—62no—
293C2×D3—81no—
294C2×D3—81no—
295C2×D3—81no—
296C2×D3—122no—
297C2×D3—121no—
298C2×D3—121no—
299C2×D3—121no—
300C2×D3—121no—
301C2×D3—241no—
302C2×D3—241no—
303C3×C4—21no—
304C3×C4—21no—
305C3×C4—21no—
306C3×C4—21no—
307C3×C4—21no—
308C3×C4—21no—
309C3×C4—41no—
310C3×C4—82no—
311C3×C4—81no—
312C3×C4—81no—
313C3×C4D3×D811yescharacteristic
314C3×C4D3×D811yescharacteristic
315C3×C4#91211yescharacteristic
316C3×C4#91411yescharacteristic
317C3×C4#91611yescharacteristic
318C3×C4#91911yescharacteristic
319C3×C4#94911yescharacteristic
320C3×C4#95011yescharacteristic
321Dic3—121no—
322Dic3—121no—
323Dic3—241no—
324C32#168111yescharacteristic, complemented, Sylow
325C23—121no—
326C23—181no—
327Q8—41no—
328Q8—41no—
329D4—92no—
330D4—121no—
331D4—121no—
332D4—121no—
333D4—121no—
334D4—181no—
335D4—241no—
336C2×C4—41no—
337C2×C4—181no—
338C2×C4—361no—
339C2×C4—361no—
340C2×C4#380411yescharacteristic
341C2×C4D3×#6711yescharacteristic
342C2×C4#381111yescharacteristic
343C8—61no—
344C8—61no—
345C8—121no—
346C8—121no—
347C8—361no—
348C2×C3—21no—
349C2×C3—21no—
350C2×C3—21no—
351C2×C3—481no—
352C2×C3#475411yescharacteristic
353C2×C3#477511yescharacteristic
354C2×C3#481911yescharacteristic
355C2×C3#505711yescharacteristic
356C2×C3#515711yescharacteristic
357C2×C3#517711yescharacteristic
358D3—122no—
359D3—122no—
360D3—161no—
361D3—242no—
362C22—182no—
363C22—241no—
364C22—241no—
365C22—241no—
366C22—361no—
367C22—361no—
368C22#6395811yescharacteristic
369C4—21no—
370C4—81no—
371C4—361no—
372C4#6392611yescharacteristic
373C4#6393611yescharacteristic
374C4#6393911yescharacteristic
375C4#6394911yescharacteristic
376C3—21no—
377C3#6844611yescharacteristic, complemented
378C3#7120111yescharacteristic, complemented
379C2—362no—
380C2—481no—
381C2#1059145511yescharacteristic
382C2#1059154211yescharacteristic
383C2#1059156811yescharacteristic
subgroupG/H
centerC22#63958
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socleC22×C32#121
prime radical#10590355C2
hypercenterC4⋊Q8D32
hypocenterC32#1681
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
1. #10592782C2semidirect
2. C3×#5088C2semidirect
4. #10590327C2semidirect
5. C3×#4547C2semidirect
6. #10589099C2semidirect
7. #10589090C2semidirect
26. #5088D3semidirect
35. #4547D3semidirect
324. C32#1681semidirect
377. C3#68446semidirect
378. C3#71201semidirect

Maximal subgroups

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

subgroupindex
#105927822
C3×#50882
#105903552
#105903272
C3×#45472
#105890992
#105890902
#712013
#684463