Finite Group Databasebeta

← #11781446

Subgroups — #11781446

Order 1152.

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

normal subgroups only

This group has 423 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#10592787C211yesmaximal, characteristic, complemented
2C3×#5083C211yesmaximal, characteristic, complemented
3#10590349C211yesmaximal, characteristic
4#10590329C211yesmaximal, characteristic, complemented
5C3×#4547C211yesmaximal, characteristic, complemented
6#10589100C211yesmaximal, characteristic, complemented
7#10589091C211yesmaximal, characteristic, complemented
8#71039—31nomaximal
9#68446—31nomaximal
10C32×C4⋊Q8C2211yescharacteristic
11#64083C2211yescharacteristic
12C2×C3×#215—21no—
13C3×C4×D12C2211yescharacteristic
14C2×#3714—21no—
15C2×D3×C3⋊C8—21no—
16#63636—21no—
17#63636—21no—
18C4×C3⋊(C3⋊C8)C2211yescharacteristic
19C3×#835—21no—
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23#63564—21no—
24(C2×D3)⋊(C3⋊C8)—21no—
25C3×#461—31no—
26#5088—31no—
27#5088—31no—
28#5088—61no—
29#5083D311yescharacteristic, complemented
30#5015—31no—
31D4×C3⋊C8—31no—
32#4843—31no—
33#4834—31no—
34C3×#332—31no—
35#4547D311yescharacteristic, complemented
36#4485—31no—
37#4485—31no—
38#4479—31no—
39#4479—31no—
40C2×C32×Q8—21no—
41C2×C4⋊(C3⋊D3)—21no—
42C2×C4⋊(C3⋊D3)—21no—
43C2×C4⋊(C3⋊D3)—21no—
44C2×C3×D12D411yescharacteristic
45C2×C3×C4×D3—21no—
46C32×C4⋊C4—21no—
47C32×C4⋊C4—21no—
48C32×C42C2311yescharacteristic
49C2×C3⋊(C3⋊C8)D411yescharacteristic
50C2×C3⋊(C3⋊C8)D411yescharacteristic
51C3×#215—42no—
52C3×(C2×D3)⋊C4—21no—
53C3×C4⋊Dic3D411yescharacteristic
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8—21no—
56C2×C3×C3⋊C8—21no—
57#3714—42no—
58D3×C3⋊C8—42no—
59#1681—91noSylow
60C2×C3×SD16—61no—
61C3×C4⋊Q8—21no—
62C3×C4⋊Q8C2×D311yescharacteristic
63C3×C4⋊Q8C2×D311yescharacteristic
64C3×C4×D4—31no—
65C2×#215—21no—
66C2×#213—61no—
67C22×C3⋊C8—61no—
68C2×D24—61no—
69C2×D3×C8—61no—
70#874—31no—
71#874—31no—
72#874—61no—
73C4×D12C2×D311yescharacteristic
74C3×C4⋊C8—31no—
75C3×C4⋊C8—31no—
76C3×C4⋊C8—31no—
77C3×#103—61no—
78#835—21no—
79#830—61no—
80#821—61no—
81(C2×D3)⋊C8—61no—
82#809—61no—
83#809—61no—
84#809—61no—
85#809—61no—
86#809—61no—
87#809—62no—
88#809—62no—
89C4⋊(C3⋊C8)C2×D311yescharacteristic
90C4⋊(C3⋊C8)C2×D311yescharacteristic
91C4⋊(C3⋊C8)C2×D311yescharacteristic
92C4×C3⋊C8—31no—
93C4×C3⋊C8—31no—
94C4×C3⋊C8—61no—
95C22×C3⋊D3—41no—
96C22×C3×D3—21no—
97C32×Q8—41no—
98C32×Q8—41no—
99C2×C32×C4—41no—
100C2×C32×C4C2×D411yescharacteristic
101C2×C32×C4C2×D411yescharacteristic
102C2×C32×C4#4111yescharacteristic
103C4⋊(C3⋊D3)—41no—
104C4⋊(C3⋊D3)—41no—
105C4⋊(C3⋊D3)—41no—
106C4⋊(C3⋊D3)—41no—
107C4⋊(C3⋊D3)—81no—
108C2×C3×Dic3—21no—
109C3×D12—21no—
110C3×D12D812yes—
111C3×C4×D3—41no—
112C3×C4×D3—41no—
113C3⋊(C3⋊C8)—21no—
114C3⋊(C3⋊C8)—21no—
115C3×C3⋊C8—41no—
116C3×C3⋊C8—41no—
117C3×C3⋊C8—41no—
118#486—91no—
119#461—31no—
120#459—91no—
121C8×D4—91no—
122#335—91no—
123#332—31no—
124#331—91no—
125C2×C3×Q8—21no—
126C2×C3×Q8—21no—
127C2×C3×Q8—41no—
128C2×C3×D4—31no—
129C22×C3×C4—61no—
130C2×D12—62no—
131C2×D12—61no—
132C2×D12—61no—
133C2×D12—61no—
134C2×D12—61no—
135C2×D12—61no—
136C2×D12—61no—
137C2×D12—121no—
138C2×D12—121no—
139C2×D12#6711yescharacteristic
140C2×C4×D3—21no—
141C3×SD16—122no—
142C2×C3×C8—61no—
143C2×C3×C8—61no—
144C2×C3×C8—61no—
145C3×C4⋊C4—22no—
146C3×C4⋊C4—21no—
147C3×C4⋊C4—21no—
148C3×C4⋊C4—21no—
149C3×C4⋊C4—21no—
150C3×C4⋊C4—31no—
151C3×C4⋊C4—41no—
152C3×C22⋊C4—61no—
153C3×C42—21no—
154C3×C42C22×D311yescharacteristic
155C3×C42C22×D311yescharacteristic
156#215—42no—
157#213—122no—
158(C2×D3)⋊C4—21no—
159C4⋊Dic3#6711yescharacteristic
160C2×C3⋊C8—21no—
161C2×C3⋊C8—21no—
162C2×C3⋊C8—21no—
163C2×C3⋊C8—31no—
164C2×C3⋊C8—31no—
165C2×C3⋊C8—31no—
166C2×C3⋊C8—31no—
167C2×C3⋊C8—61no—
168C2×C3⋊C8—61no—
169C2×C3⋊C8—122no—
170D24—122no—
171D3×C8—122no—
172C22×C32#12111yescharacteristic
173C2×C3⋊D3—81no—
174C2×C3⋊D3—81no—
175C2×C3⋊D3—81no—
176C2×C3×D3—22no—
177C2×C3×D3—41no—
178C2×C3×D3—41no—
179C32×C4—21no—
180C32×C4—81no—
181C32×C4C2×D811yescharacteristic
182C32×C4#13511yescharacteristic
183C32×C4#13511yescharacteristic
184C32×C4AGL(1,ℤ/8)11yescharacteristic
185C3×Dic3—41no—
186C2×SD16—61no—
187C2×D8—181no—
188C22×C8—181no—
189C4⋊Q8D3211yescharacteristic
190#127—91no—
191C4×D4—31no—
192C4⋊C8—31no—
193C4⋊C8—31no—
194C4⋊C8—31no—
195#103—61no—
196#102—181no—
197#102—181no—
198#102—181no—
199C22⋊C8—181no—
200C4×C8—91no—
201C23×C3—61no—
202C22×D3—21no—
203C22×D3—122no—
204C22×D3—121no—
205C22×D3—121no—
206C3×Q8—41no—
207C3×Q8—41no—
208C3×Q8—41no—
209C3×Q8—41no—
210C3×Q8—81no—
211C3×Q8—81no—
212C3×D4—32no—
213C3×D4—61no—
214C2×C3×C4—21no—
215C2×C3×C4—21no—
216C2×C3×C4—21no—
217C2×C3×C4—42no—
218C2×C3×C4—41no—
219C2×C3×C4—41no—
220C2×C3×C4—61no—
221C2×C3×C4—121no—
222C2×C3×C4—121no—
223C2×C3×C4#23511yescharacteristic
224C2×C3×C4D3×D411yescharacteristic
225C2×C3×C4D3×D411yescharacteristic
226C2×C3×C4D3×D411yescharacteristic
227C2×C3×C4#23711yescharacteristic
228C2×C3×C4C2×#6711yescharacteristic
229C2×Dic3—21no—
230D12—21no—
231D12—122no—
232D12—122no—
233D12—121no—
234D12—121no—
235D12—121no—
236D12—121no—
237D12—121no—
238D12—121no—
239D12—121no—
240D12—121no—
241D12—241no—
242D12—241no—
243D12—241no—
244D12—241no—
245D12—242no—
246D12#21312yes—
247C4×D3—41no—
248C4×D3—41no—
249C3×C8—121no—
250C3×C8—121no—
251C3×C8—121no—
252C3⋊C8—41no—
253C3⋊C8—41no—
254C3⋊C8—41no—
255C3⋊C8—61no—
256C3⋊C8—61no—
257C3⋊C8—61no—
258C3⋊C8—61no—
259C3⋊C8—121no—
260C3⋊C8—121no—
261C2×C32#46311yescharacteristic
262C2×C32#46611yescharacteristic
263C2×C32#47111yescharacteristic
264C3⋊D3—161no—
265C3×D3—42no—
266C2×Q8—21no—
267C2×D4—31no—
268C2×D4—181no—
269C2×D4—181no—
270C2×D4—181no—
271C22×C4—61no—
272SD16—122no—
273D8—362no—
274C2×C8—61no—
275C2×C8—61no—
276C2×C8—61no—
277C2×C8—91no—
278C2×C8—91no—
279C2×C8—362no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—31no—
283C22⋊C4—61no—
284C42C2×D3211yescharacteristic
285C22×C3—21no—
286C22×C3—62no—
287C22×C3—121no—
288C22×C3—121no—
289C22×C3#88411yescharacteristic
290C22×C3#93911yescharacteristic
291C2×D3—22no—
292C2×D3—41no—
293C2×D3—41no—
294C2×D3—242no—
295C2×D3—242no—
296C2×D3—242no—
297C2×D3—241no—
298C2×D3—241no—
299C2×D3—241no—
300C2×D3—241no—
301C2×D3—241no—
302C2×D3—241no—
303C3×C4—22no—
304C3×C4—21no—
305C3×C4—21no—
306C3×C4—21no—
307C3×C4—21no—
308C3×C4—21no—
309C3×C4—21no—
310C3×C4—82no—
311C3×C4—81no—
312C3×C4—81no—
313C3×C4—121no—
314C3×C4D3×D811yescharacteristic
315C3×C4#91411yescharacteristic
316C3×C4#91411yescharacteristic
317C3×C4#91611yescharacteristic
318C3×C4#91611yescharacteristic
319C3×C4#91911yescharacteristic
320C3×C4C2×#21311yescharacteristic
321C3×C4#95011yescharacteristic
322Dic3—41no—
323C32#168111yescharacteristic, complemented, Sylow
324C23—61no—
325C23—361no—
326Q8—41no—
327Q8—41no—
328D4—32no—
329D4—61no—
330D4—361no—
331D4—361no—
332D4—361no—
333D4—361no—
334D4—721no—
335C2×C4—41no—
336C2×C4—61no—
337C2×C4—121no—
338C2×C4—121no—
339C2×C4#380411yescharacteristic
340C2×C4D3×#6711yescharacteristic
341C2×C4#381111yescharacteristic
342C8—121no—
343C8—121no—
344C8—121no—
345C8—181no—
346C8—181no—
347C2×C3—21no—
348C2×C3—21no—
349C2×C3—21no—
350C2×C3—122no—
351C2×C3#475411yescharacteristic
352C2×C3#477511yescharacteristic
353C2×C3#481911yescharacteristic
354C2×C3#503811yescharacteristic
355C2×C3#516511yescharacteristic
356C2×C3#520311yescharacteristic
357D3—42no—
358D3—482no—
359D3—481no—
360D3—481no—
361C22—62no—
362C22—121no—
363C22—121no—
364C22—721no—
365C22—721no—
366C22—721no—
367C22#6397111yescharacteristic
368C4—21no—
369C4—81no—
370C4—121no—
371C4D3×#21311yescharacteristic
372C4#6393511yescharacteristic
373C4#6394111yescharacteristic
374C4#6395011yescharacteristic
375C3—21no—
376C3#6844611yescharacteristic, complemented
377C3#7103911yescharacteristic, complemented
378C2—122no—
379C2—1441no—
380C2#1059144911yescharacteristic
381C2#1059157011yescharacteristic
382C2#1059164311yescharacteristic
subgroupG/H
centerC22#63971
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socleC22×C32#121
prime radical#10590349C2
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. #10592787C2semidirect
2. C3×#5083C2semidirect
4. #10590329C2semidirect
5. C3×#4547C2semidirect
6. #10589100C2semidirect
7. #10589091C2semidirect
29. #5083D3semidirect
35. #4547D3semidirect
323. C32#1681semidirect
376. C3#68446semidirect
377. C3#71039semidirect

Maximal subgroups

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

subgroupindex
#105927872
C3×#50832
#105903492
#105903292
C3×#45472
#105891002
#105890912
#710393
#684463