Finite Group Databasebeta

← #11781451

Subgroups — #11781451

Order 1152.

396 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 88 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
1C3×#4843C211yesmaximal, characteristic
2#10590365C211yesmaximal, characteristic, complemented
3C3⋊C8×D12C211yesmaximal, characteristic, complemented
4#10590273C211yesmaximal, characteristic, complemented
5#10589348C211yesmaximal, characteristic, complemented
6C3×#4479C211yesmaximal, characteristic, complemented
7#10589090C211yesmaximal, characteristic, complemented
8#71007—31nomaximal
9#68580—31nomaximal
10#64078C2211yescharacteristic
11C2×C3×D24—21no—
12C3×#874C2211yescharacteristic
13C3×C4×D12C2211yescharacteristic
14C2×#3716—21no—
15C2×D3×C3⋊C8—21no—
16C32×C4⋊C8C2211yescharacteristic
17C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
18C3×#821—21no—
19C3×C4⋊(C3⋊C8)C2211yescharacteristic
20C3×C4×C3⋊C8C2211yescharacteristic
21#63567—21no—
22#63563—21no—
23#63563—21no—
24(C2×D3)⋊(C3⋊C8)—21no—
25C3×#459—31no—
26#5070—31no—
27#5019—31no—
28D4×C3⋊C8—31no—
29#4843D311yescharacteristic
30#4841—31no—
31#4694—31no—
32C8×D12—31no—
33C3×#335—31no—
34#4544—31no—
35#4485—31no—
36#4482—31no—
37#4482—31no—
38#4482—61no—
39#4479D311yescharacteristic, complemented
40C2×#634—21no—
41C2×C3×D12—21no—
42C2×C3×D12—21no—
43C2×C3×D12—21no—
44C2×C3×D12D411yescharacteristic
45C2×C3×C4×D3—21no—
46C2×C32×C8—21no—
47C32×C42C2311yescharacteristic
48C4⋊(C3⋊Dic3)—21no—
49C4⋊(C3⋊Dic3)—21no—
50C2×C3⋊(C3⋊C8)—21no—
51C3×(C2×D3)⋊C4—21no—
52C3×C4⋊Dic3D411yescharacteristic
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8D411yescharacteristic
55C2×C3×C3⋊C8D411yescharacteristic
56C3×D24—42no—
57#3716—42no—
58D3×C3⋊C8—42no—
59#1681—91noSylow
60C2×C3×D8—61no—
61C3×#127—31no—
62C3×C4×D4—31no—
63C2×#214—61no—
64C22×C3⋊C8—61no—
65C2×D24—21no—
66C2×#204—61no—
67C2×D3×C8—61no—
68#874C2×D311yescharacteristic
69C4×D12C2×D311yescharacteristic
70#869—31no—
71#869—31no—
72#869—61no—
73C3×C4⋊C8—21no—
74C3×C4⋊C8—31no—
75C3×C4⋊C8C2×D311yescharacteristic
76C3×C4⋊C8C2×D311yescharacteristic
77C3×#102—61no—
78C3×C4×C8—31no—
79#832—61no—
80#832—61no—
81#830—61no—
82#821—21no—
83#821—61no—
84#821—61no—
85(C2×D3)⋊C8—61no—
86#816—61no—
87#810—61no—
88C4⋊(C3⋊C8)—31no—
89C4⋊(C3⋊C8)—31no—
90C4⋊(C3⋊C8)—61no—
91C4⋊(C3⋊C8)C2×D311yescharacteristic
92C4×C3⋊C8C2×D311yescharacteristic
93C22×C3×D3—21no—
94C22×C3×D3—41no—
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4#4111yescharacteristic
98C2×C3⋊Dic3—41no—
99#634—41no—
100#634—41no—
101C2×C3×Dic3—21no—
102C3×D12—21no—
103C3×D12—41no—
104C3×D12—41no—
105C3×D12—41no—
106C3×D12—41no—
107C3×D12—81no—
108C3×D12D812yes—
109C3×C4×D3—41no—
110C3×C4×D3—41no—
111C32×C8—41no—
112C3⋊(C3⋊C8)—41no—
113C3×C3⋊C8—21no—
114C3×C3⋊C8—21no—
115C3×C3⋊C8—41no—
116#486—91no—
117#461—91no—
118#459—31no—
119C8×D4—91no—
120#335—31no—
121#332—91no—
122#331—91no—
123C2×C3×D4—31no—
124C2×C3×D4—61no—
125C2×C3×D4—61no—
126C2×C3×D4—61no—
127C22×C3×C4—61no—
128C2×D12—21no—
129C2×D12—21no—
130C2×D12—21no—
131C2×D12#6711yescharacteristic
132C2×C4×D3—21no—
133C2×Dic6—61no—
134C2×Dic6—61no—
135C2×Dic6—121no—
136C3×D8—122no—
137C2×C3×C8—21no—
138C2×C3×C8—21no—
139C2×C3×C8—31no—
140C2×C3×C8—31no—
141C2×C3×C8—41no—
142C2×C3×C8—61no—
143C3×C4⋊C4—31no—
144C3×C22⋊C4—61no—
145C3×C42—21no—
146C3×C42C22×D311yescharacteristic
147C3×C42C22×D311yescharacteristic
148#214—122no—
149(C2×D3)⋊C4—21no—
150C4⋊Dic3—62no—
151C4⋊Dic3—61no—
152C4⋊Dic3—61no—
153C4⋊Dic3—61no—
154C4⋊Dic3—61no—
155C4⋊Dic3—121no—
156C4⋊Dic3#6711yescharacteristic
157C2×C3⋊C8—21no—
158C2×C3⋊C8—61no—
159C2×C3⋊C8—61no—
160C2×C3⋊C8—121no—
161C2×C3⋊C8—122no—
162C2×C3⋊C8D1211yescharacteristic
163C2×C3⋊C8D1211yescharacteristic
164D24—42no—
165#204—122no—
166D3×C8—122no—
167C22×C32#12111yescharacteristic
168C2×C3×D3—22no—
169C2×C3×D3—41no—
170C2×C3×D3—41no—
171C2×C3×D3—81no—
172C2×C3×D3—81no—
173C2×C3×D3—81no—
174C32×C4—21no—
175C32×C4C2×D811yescharacteristic
176C32×C4#13511yescharacteristic
177C32×C4#13511yescharacteristic
178C32×C4AGL(1,ℤ/8)11yescharacteristic
179C3⋊Dic3—81no—
180C3×Dic3—41no—
181C2×SD16—181no—
182C2×D8—61no—
183C22×C8—181no—
184C4⋊Q8—91no—
185#127—31no—
186C4×D4—31no—
187C4⋊C8—31no—
188C4⋊C8—91no—
189C4⋊C8D3211yescharacteristic
190#103—181no—
191#102—61no—
192#102—181no—
193#102—181no—
194C22⋊C8—181no—
195C4×C8—31no—
196C23×C3—61no—
197C23×C3—121no—
198C22×D3—21no—
199C22×D3—41no—
200C3×D4—32no—
201C3×D4—61no—
202C3×D4—121no—
203C3×D4—121no—
204C3×D4—121no—
205C3×D4—121no—
206C3×D4—241no—
207C2×C3×C4—21no—
208C2×C3×C4—21no—
209C2×C3×C4—21no—
210C2×C3×C4—61no—
211C2×C3×C4—121no—
212C2×C3×C4—121no—
213C2×C3×C4C2×D1211yescharacteristic
214C2×C3×C4D3×D411yescharacteristic
215C2×C3×C4D3×D411yescharacteristic
216C2×C3×C4#23711yescharacteristic
217C2×C3×C4#23911yescharacteristic
218C2×C3×C4C2×#6711yescharacteristic
219C2×Dic3—21no—
220C2×Dic3—122no—
221C2×Dic3—121no—
222C2×Dic3—121no—
223D12—21no—
224D12—41no—
225D12—41no—
226D12—41no—
227D12—41no—
228D12—81no—
229D12#21312yes—
230C4×D3—41no—
231C4×D3—41no—
232Dic6—121no—
233Dic6—121no—
234Dic6—121no—
235Dic6—121no—
236Dic6—241no—
237Dic6—241no—
238C3×C8—41no—
239C3×C8—41no—
240C3×C8—61no—
241C3×C8—61no—
242C3×C8—81no—
243C3×C8—121no—
244C3⋊C8—21no—
245C3⋊C8—21no—
246C3⋊C8—41no—
247C3⋊C8—121no—
248C3⋊C8—121no—
249C3⋊C8—241no—
250C2×C32#46311yescharacteristic
251C2×C32#46611yescharacteristic
252C2×C32#47111yescharacteristic
253C3×D3—42no—
254C3×D3—161no—
255C2×Q8—181no—
256C2×D4—31no—
257C2×D4—61no—
258C2×D4—61no—
259C2×D4—61no—
260C22×C4—61no—
261SD16—362no—
262D8—122no—
263C2×C8—21no—
264C2×C8—31no—
265C2×C8—31no—
266C2×C8—61no—
267C2×C8—181no—
268C2×C8—362no—
269C4⋊C4—31no—
270C4⋊C4—181no—
271C4⋊C4—181no—
272C22⋊C4—61no—
273C42C2×D3211yescharacteristic
274C22×C3—21no—
275C22×C3—62no—
276C22×C3—121no—
277C22×C3—121no—
278C22×C3—241no—
279C22×C3—241no—
280C22×C3—241no—
281C22×C3#89511yescharacteristic
282C22×C3#93911yescharacteristic
283C2×D3—22no—
284C2×D3—41no—
285C2×D3—41no—
286C2×D3—81no—
287C2×D3—81no—
288C2×D3—81no—
289C3×C4—21no—
290C3×C4—21no—
291C3×C4—21no—
292C3×C4—21no—
293C3×C4—21no—
294C3×C4—21no—
295C3×C4—41no—
296C3×C4—121no—
297C3×C4#90411yescharacteristic
298C3×C4#90811yescharacteristic
299C3×C4D3×D811yescharacteristic
300C3×C4#91111yescharacteristic
301C3×C4#91211yescharacteristic
302C3×C4#91911yescharacteristic
303C3×C4C2×#21311yescharacteristic
304C3×C4#95011yescharacteristic
305Dic3—41no—
306Dic3—242no—
307Dic3—241no—
308Dic3—241no—
309C32#168111yescharacteristic, complemented, Sylow
310C23—61no—
311C23—121no—
312Q8—361no—
313Q8—361no—
314D4—32no—
315D4—61no—
316D4—121no—
317D4—121no—
318D4—121no—
319D4—121no—
320D4—241no—
321C2×C4—61no—
322C2×C4—121no—
323C2×C4—121no—
324C2×C4—361no—
325C2×C4#379611yescharacteristic
326C2×C4D3×D1211yescharacteristic
327C2×C4D3×#6711yescharacteristic
328C8—41no—
329C8—61no—
330C8—61no—
331C8—121no—
332C8—361no—
333C2×C3—21no—
334C2×C3—21no—
335C2×C3—21no—
336C2×C3—122no—
337C2×C3—481no—
338C2×C3#484411yescharacteristic
339C2×C3#488311yescharacteristic
340C2×C3#489811yescharacteristic
341C2×C3#503811yescharacteristic
342C2×C3#515311yescharacteristic
343C2×C3#520011yescharacteristic
344D3—42no—
345D3—161no—
346C22—62no—
347C22—121no—
348C22—121no—
349C22—241no—
350C22—241no—
351C22—241no—
352C22#6388611yescharacteristic
353C4—21no—
354C4—121no—
355C4—721no—
356C4#6379511yescharacteristic
357C4#6380711yescharacteristic
358C4D3×#21311yescharacteristic
359C4#6394911yescharacteristic
360C3—21no—
361C3#6858011yescharacteristic, complemented
362C3#7100711yescharacteristic, complemented
363C2—122no—
364C2—481no—
365C2#1059057611yescharacteristic
366C2#1059075511yescharacteristic
367C2#1059098611yescharacteristic
subgroupG/H
centerC22#63886
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#121
prime radicalC3×#4843C2
hypercenterC4⋊C8D32
hypocenterC32#1681
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
2. #10590365C2semidirect
3. C3⋊C8×D12C2semidirect
4. #10590273C2semidirect
5. #10589348C2semidirect
6. C3×#4479C2semidirect
7. #10589090C2semidirect
39. #4479D3semidirect
309. C32#1681semidirect
361. C3#68580semidirect
362. C3#71007semidirect

Maximal subgroups

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

subgroupindex
C3×#48432
#105903652
C3⋊C8×D122
#105902732
#105893482
C3×#44792
#105890902
#710073
#685803