Finite Group Databasebeta

← #11781343

Subgroups — #11781343

Order 1152.

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

normal subgroups only

This group has 381 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#10592778C211yesmaximal, characteristic, complemented
2C3×#5087C211yesmaximal, characteristic
3#10590365C211yesmaximal, characteristic
4#10590329C211yesmaximal, characteristic
5C3×#4547C211yesmaximal, characteristic, complemented
6#10589098C211yesmaximal, characteristic, complemented
7#10589094C211yesmaximal, characteristic, complemented
8#71102—31nomaximal
9#68444—31nomaximal
10C32×C4⋊Q8C2211yescharacteristic
11#64078C2211yescharacteristic
12C3×C4×D12C2211yescharacteristic
13C2×#3716—21no—
14C2×D3×C3⋊C8—21no—
15#63662—21no—
16#63662—21no—
17C4×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×#809—21no—
19C3×#807—21no—
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23#63567—21no—
24(C2×D3)⋊(C3⋊C8)—21no—
25C3×#474—31no—
26#5087D311yescharacteristic
27#5079—31no—
28#5079—31no—
29#5079—61no—
30#5019—31no—
31D4×C3⋊C8—31no—
32#4841—31no—
33#4834—31no—
34C3×#332—31no—
35#4547D311yescharacteristic, complemented
36#4486—31no—
37#4482—31no—
38#4480—31no—
39#4480—31no—
40C2×C32×Q8—21no—
41C2×#634—21no—
42C2×C3×D12D411yescharacteristic
43C2×C3×C4×D3—21no—
44C32×C4⋊C4—21no—
45C32×C4⋊C4—21no—
46C32×C42C2311yescharacteristic
47C4⋊(C3⋊Dic3)—21no—
48C4⋊(C3⋊Dic3)—21no—
49C2×C3⋊(C3⋊C8)D411yescharacteristic
50C2×C3⋊(C3⋊C8)D411yescharacteristic
51C3×(C2×D3)⋊C4—21no—
52C3×C4⋊Dic3D411yescharacteristic
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8—21no—
56#3716—42no—
57D3×C3⋊C8—42no—
58#1679—91noSylow
59C3×C4⋊Q8—21no—
60C3×C4⋊Q8C2×D311yescharacteristic
61C3×C4⋊Q8C2×D311yescharacteristic
62C3×C4×D4—31no—
63C2×#214—61no—
64C22×C3⋊C8—61no—
65C2×#204—61no—
66C2×D3×C8—61no—
67C4×D12C2×D311yescharacteristic
68#869—31no—
69#869—31no—
70#869—61no—
71C3×#107—61no—
72C3×C4⋊C8—31no—
73C3×C4⋊C8—31no—
74C3×C4⋊C8—31no—
75C3×#102—61no—
76#835—61no—
77#835—61no—
78#835—61no—
79#835—61no—
80#835—62no—
81#835—62no—
82#830—61no—
83(C2×D3)⋊C8—61no—
84#816—61no—
85#810—61no—
86#809—21no—
87#807—21no—
88C4⋊(C3⋊C8)C2×D311yescharacteristic
89C4⋊(C3⋊C8)C2×D311yescharacteristic
90C4⋊(C3⋊C8)C2×D311yescharacteristic
91C4×C3⋊C8—31no—
92C4×C3⋊C8—31no—
93C4×C3⋊C8—61no—
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—41no—
102#634—41no—
103#634—41no—
104C2×C3×Dic3—21no—
105C3×D12—21no—
106C3×D12SD1612yes—
107C3×C4×D3—41no—
108C3×C4×D3—41no—
109C3⋊(C3⋊C8)—21no—
110C3⋊(C3⋊C8)—21no—
111C3×C3⋊C8—41no—
112C3×C3⋊C8—41no—
113C3×C3⋊C8—41no—
114#487—91no—
115#474—31no—
116#461—91no—
117C8×D4—91no—
118#334—91no—
119#332—31no—
120#332—91no—
121C2×C3×Q8—22no—
122C2×C3×Q8—21no—
123C2×C3×Q8—21no—
124C2×C3×D4—31no—
125C22×C3×C4—61no—
126C2×D12#6711yescharacteristic
127C2×C4×D3—21no—
128C2×Dic6—61no—
129C2×Dic6—61no—
130C2×Dic6—121no—
131C2×C3×C8—61no—
132C2×C3×C8—61no—
133C2×C3×C8—61no—
134C3×C4⋊C4—21no—
135C3×C4⋊C4—21no—
136C3×C4⋊C4—21no—
137C3×C4⋊C4—21no—
138C3×C4⋊C4—31no—
139C3×C4⋊C4—41no—
140C3×C4⋊C4—41no—
141C3×C22⋊C4—61no—
142C3×C42—21no—
143C3×C42C22×D311yescharacteristic
144C3×C42C22×D311yescharacteristic
145#214—122no—
146(C2×D3)⋊C4—21no—
147C4⋊Dic3—62no—
148C4⋊Dic3—61no—
149C4⋊Dic3—61no—
150C4⋊Dic3—61no—
151C4⋊Dic3—61no—
152C4⋊Dic3—121no—
153C4⋊Dic3#6711yescharacteristic
154C2×C3⋊C8—21no—
155C2×C3⋊C8—21no—
156C2×C3⋊C8—21no—
157C2×C3⋊C8—31no—
158C2×C3⋊C8—31no—
159C2×C3⋊C8—31no—
160C2×C3⋊C8—31no—
161C2×C3⋊C8—61no—
162C2×C3⋊C8—61no—
163C2×C3⋊C8—122no—
164#204—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—81no—
177C3×Dic3—41no—
178C2×SD16—181no—
179C22×C8—181no—
180C4⋊Q8—91no—
181C4⋊Q8D3211yescharacteristic
182C4×D4—31no—
183#107—61no—
184C4⋊C8—31no—
185C4⋊C8—31no—
186C4⋊C8—31no—
187#103—181no—
188#103—181no—
189#103—181no—
190#102—61no—
191C22⋊C8—181no—
192C4×C8—91no—
193C23×C3—61no—
194C22×D3—21no—
195C3×Q8—42no—
196C3×Q8—42no—
197C3×Q8—41no—
198C3×Q8—41no—
199C3×Q8—41no—
200C3×Q8—41no—
201C3×D4—32no—
202C3×D4—61no—
203C2×C3×C4—21no—
204C2×C3×C4—21no—
205C2×C3×C4—21no—
206C2×C3×C4—42no—
207C2×C3×C4—41no—
208C2×C3×C4—41no—
209C2×C3×C4—61no—
210C2×C3×C4—121no—
211C2×C3×C4—121no—
212C2×C3×C4#23511yescharacteristic
213C2×C3×C4D3×D411yescharacteristic
214C2×C3×C4D3×D411yescharacteristic
215C2×C3×C4D3×D411yescharacteristic
216C2×C3×C4#23711yescharacteristic
217C2×C3×C4C2×#6711yescharacteristic
218C2×Dic3—21no—
219C2×Dic3—122no—
220C2×Dic3—121no—
221C2×Dic3—121no—
222D12—21no—
223D12#21512yes—
224C4×D3—41no—
225C4×D3—41no—
226Dic6—121no—
227Dic6—121no—
228Dic6—121no—
229Dic6—121no—
230Dic6—241no—
231Dic6—241no—
232C3×C8—121no—
233C3×C8—121no—
234C3×C8—121no—
235C3⋊C8—41no—
236C3⋊C8—41no—
237C3⋊C8—41no—
238C3⋊C8—61no—
239C3⋊C8—61no—
240C3⋊C8—61no—
241C3⋊C8—61no—
242C3⋊C8—121no—
243C3⋊C8—121no—
244C2×C32#46311yescharacteristic
245C2×C32#46511yescharacteristic
246C2×C32#47311yescharacteristic
247C3×D3—42no—
248C2×Q8—21no—
249C2×Q8—181no—
250C2×D4—31no—
251C22×C4—61no—
252SD16—362no—
253C2×C8—61no—
254C2×C8—61no—
255C2×C8—61no—
256C2×C8—91no—
257C2×C8—91no—
258C2×C8—362no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—31no—
262C4⋊C4—181no—
263C4⋊C4—181no—
264C22⋊C4—61no—
265C42C2×D3211yescharacteristic
266C22×C3—21no—
267C22×C3—62no—
268C22×C3—121no—
269C22×C3—121no—
270C22×C3#88411yescharacteristic
271C22×C3#93911yescharacteristic
272C2×D3—22no—
273C2×D3—41no—
274C2×D3—41no—
275C3×C4—22no—
276C3×C4—21no—
277C3×C4—21no—
278C3×C4—21no—
279C3×C4—21no—
280C3×C4—21no—
281C3×C4—21no—
282C3×C4—82no—
283C3×C4—81no—
284C3×C4—81no—
285C3×C4—121no—
286C3×C4#91111yescharacteristic
287C3×C4#91111yescharacteristic
288C3×C4#91211yescharacteristic
289C3×C4D3×SD1611yescharacteristic
290C3×C4#91611yescharacteristic
291C3×C4#91911yescharacteristic
292C3×C4C2×#21511yescharacteristic
293C3×C4#95011yescharacteristic
294Dic3—41no—
295Dic3—242no—
296Dic3—241no—
297Dic3—241no—
298C32#167911yescharacteristic, complemented, Sylow
299C23—61no—
300Q8—41no—
301Q8—41no—
302Q8—361no—
303Q8—361no—
304D4—32no—
305D4—61no—
306C2×C4—41no—
307C2×C4—61no—
308C2×C4—121no—
309C2×C4—121no—
310C2×C4—361no—
311C2×C4#380411yescharacteristic
312C2×C4D3×#6711yescharacteristic
313C2×C4#381111yescharacteristic
314C8—121no—
315C8—121no—
316C8—121no—
317C8—181no—
318C8—181no—
319C2×C3—21no—
320C2×C3—21no—
321C2×C3—21no—
322C2×C3—122no—
323C2×C3#475511yescharacteristic
324C2×C3#478711yescharacteristic
325C2×C3#480711yescharacteristic
326C2×C3#504811yescharacteristic
327C2×C3#515311yescharacteristic
328C2×C3#520411yescharacteristic
329D3—42no—
330C22—62no—
331C22—121no—
332C22—121no—
333C22#6397111yescharacteristic
334C4—21no—
335C4—81no—
336C4—121no—
337C4—721no—
338C4#6392711yescharacteristic
339C4#6393611yescharacteristic
340C4D3×#21511yescharacteristic
341C4#6394911yescharacteristic
342C3—21no—
343C3#6844411yescharacteristic, complemented
344C3#7110211yescharacteristic, complemented
345C2—122no—
346C2#1059143411yescharacteristic
347C2#1059158511yescharacteristic
348C2#1059164411yescharacteristic
subgroupG/H
centerC22#63971
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socleC22×C32#121
prime radicalC2×C3×D12D4
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
1. #10592778C2semidirect
5. C3×#4547C2semidirect
6. #10589098C2semidirect
7. #10589094C2semidirect
35. #4547D3semidirect
298. C32#1679semidirect
343. C3#68444semidirect
344. C3#71102semidirect

Maximal subgroups

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

subgroupindex
#105927782
C3×#50872
#105903652
#105903292
C3×#45472
#105890982
#105890942
#711023
#684443