Finite Group Databasebeta

← #11781345

Subgroups — #11781345

Order 1152.

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

normal subgroups only

This group has 364 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×#5087C211yesmaximal, characteristic
2C3×#5079C211yesmaximal, characteristic, complemented
3#10590363C211yesmaximal, characteristic
4C3⋊C8×D12C211yesmaximal, characteristic
5#10589413C211yesmaximal, characteristic, complemented
6#10589097C211yesmaximal, characteristic, complemented
7#10589093C211yesmaximal, characteristic, complemented
8#71232—31nomaximal
9#71102—31nomaximal
10C32×C4⋊Q8C2211yescharacteristic
11C3×C4×D12C2211yescharacteristic
12C3×#869C2211yescharacteristic
13C2×#3715—21no—
14C2×D3×C3⋊C8—21no—
15C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
16C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
17C3×#835—21no—
18C3×#835—21no—
19C3×#809—21no—
20C3×#807—21no—
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4×C3⋊C8C2211yescharacteristic
23#63565—21no—
24(C2×D3)⋊(C3⋊C8)—21no—
25C3×#487—31no—
26C3×#474—31no—
27#5087D311yescharacteristic
28#5083—31no—
29#5079D311yescharacteristic, complemented
30#5019—31no—
31D4×C3⋊C8—31no—
32C8×D12—31no—
33#4547—31no—
34#4547—31no—
35#4547—31no—
36#4547—61no—
37#4482—31no—
38#4480—31no—
39#4457—31no—
40C2×C32×Q8—21no—
41C2×C3×D12D411yescharacteristic
42C2×C3×C4×D3—21no—
43C2×C3×Dic6—21no—
44C32×C4⋊C4—21no—
45C32×C4⋊C4—21no—
46C32×C42C2311yescharacteristic
47C2×C3⋊(C3⋊C8)—21no—
48C2×C3⋊(C3⋊C8)—21no—
49C3×(C2×D3)⋊C4—21no—
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3D411yescharacteristic
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8D411yescharacteristic
55C2×C3×C3⋊C8D411yescharacteristic
56#3715—42no—
57D3×C3⋊C8—42no—
58#1679—91noSylow
59C3×C4⋊Q8—21no—
60C3×C4⋊Q8—31no—
61C3×C4⋊Q8C2×D311yescharacteristic
62C3×C4⋊Q8C2×D311yescharacteristic
63C3×C4×D4—31no—
64C2×#215—61no—
65C2×#214—61no—
66C22×C3⋊C8—61no—
67C2×D3×C8—61no—
68C4×D12C2×D311yescharacteristic
69#869C2×D311yescharacteristic
70C3×#107—61no—
71C3×C4⋊C8—31no—
72C3×#103—61no—
73C3×#103—61no—
74C3×#102—61no—
75C3×C4×C8—31no—
76#835—21no—
77#835—21no—
78#835—61no—
79#830—61no—
80(C2×D3)⋊C8—61no—
81#810—61no—
82#809—21no—
83#807—21no—
84C4⋊(C3⋊C8)—31no—
85C4⋊(C3⋊C8)—31no—
86C4⋊(C3⋊C8)—31no—
87C4⋊(C3⋊C8)—31no—
88C4⋊(C3⋊C8)—61no—
89C4⋊(C3⋊C8)—61no—
90C4⋊(C3⋊C8)C2×D311yescharacteristic
91C4×C3⋊C8C2×D311yescharacteristic
92C22×C3×D3—21no—
93C32×Q8—41no—
94C32×Q8—41no—
95C2×C32×C4—41no—
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4C2×D411yescharacteristic
98C2×C32×C4#4111yescharacteristic
99C2×C3×Dic3—21no—
100C2×C3×Dic3—41no—
101C3×D12—21no—
102C3×D12SD1612yes—
103C3×C4×D3—41no—
104C3×C4×D3—41no—
105C3×Dic6—41no—
106C3×Dic6—41no—
107C3⋊(C3⋊C8)—41no—
108C3⋊(C3⋊C8)—41no—
109C3×C3⋊C8—21no—
110C3×C3⋊C8—21no—
111C3×C3⋊C8—41no—
112#487—31no—
113#474—31no—
114#461—91no—
115C8×D4—91no—
116#334—91no—
117#332—91no—
118#332—91no—
119C2×C3×Q8—21no—
120C2×C3×Q8—21no—
121C2×C3×Q8—41no—
122C2×C3×Q8—61no—
123C2×C3×D4—31no—
124C22×C3×C4—61no—
125C2×D12#6711yescharacteristic
126C2×C4×D3—21no—
127C2×Dic6—21no—
128C2×C3×C8—31no—
129C2×C3×C8—31no—
130C2×C3×C8—61no—
131C3×C4⋊C4—22no—
132C3×C4⋊C4—21no—
133C3×C4⋊C4—21no—
134C3×C4⋊C4—21no—
135C3×C4⋊C4—21no—
136C3×C4⋊C4—31no—
137C3×C4⋊C4—41no—
138C3×C4⋊C4—61no—
139C3×C4⋊C4—61no—
140C3×C22⋊C4—61no—
141C3×C42—21no—
142C3×C42C22×D311yescharacteristic
143C3×C42C22×D311yescharacteristic
144#215—122no—
145#214—122no—
146(C2×D3)⋊C4—21no—
147C4⋊Dic3—21no—
148C4⋊Dic3—21no—
149C4⋊Dic3#6711yescharacteristic
150C2×C3⋊C8—21no—
151C2×C3⋊C8—61no—
152C2×C3⋊C8—61no—
153C2×C3⋊C8—61no—
154C2×C3⋊C8—61no—
155C2×C3⋊C8—121no—
156C2×C3⋊C8—121no—
157C2×C3⋊C8—122no—
158C2×C3⋊C8#6711yescharacteristic
159C2×C3⋊C8#6711yescharacteristic
160D3×C8—122no—
161C22×C32#12111yescharacteristic
162C2×C3×D3—22no—
163C2×C3×D3—41no—
164C2×C3×D3—41no—
165C32×C4—21no—
166C32×C4—81no—
167C32×C4C2×SD1611yescharacteristic
168C32×C4#13511yescharacteristic
169C32×C4#13511yescharacteristic
170C32×C4AGL(1,ℤ/8)11yescharacteristic
171C3×Dic3—41no—
172C3×Dic3—81no—
173C2×SD16—181no—
174C22×C8—181no—
175C4⋊Q8—31no—
176C4⋊Q8D3211yescharacteristic
177C4×D4—31no—
178#107—61no—
179C4⋊C8—31no—
180C4⋊C8—91no—
181C4⋊C8—91no—
182#103—61no—
183#103—61no—
184#103—181no—
185#102—61no—
186C22⋊C8—181no—
187C4×C8—31no—
188C23×C3—61no—
189C22×D3—21no—
190C3×Q8—41no—
191C3×Q8—41no—
192C3×Q8—41no—
193C3×Q8—41no—
194C3×Q8—81no—
195C3×Q8—81no—
196C3×Q8—121no—
197C3×Q8—121no—
198C3×D4—32no—
199C3×D4—61no—
200C2×C3×C4—21no—
201C2×C3×C4—21no—
202C2×C3×C4—21no—
203C2×C3×C4—42no—
204C2×C3×C4—41no—
205C2×C3×C4—41no—
206C2×C3×C4—61no—
207C2×C3×C4—121no—
208C2×C3×C4—121no—
209C2×C3×C4—121no—
210C2×C3×C4D3×D411yescharacteristic
211C2×C3×C4D3×D411yescharacteristic
212C2×C3×C4#23711yescharacteristic
213C2×C3×C4#23711yescharacteristic
214C2×C3×C4C2×#6711yescharacteristic
215C2×C3×C4C2×#6711yescharacteristic
216C2×Dic3—21no—
217C2×Dic3—41no—
218D12—21no—
219D12#21512yes—
220C4×D3—41no—
221C4×D3—41no—
222Dic6—41no—
223Dic6—41no—
224C3×C8—61no—
225C3×C8—61no—
226C3×C8—121no—
227C3⋊C8—21no—
228C3⋊C8—21no—
229C3⋊C8—41no—
230C3⋊C8—121no—
231C3⋊C8—121no—
232C3⋊C8—121no—
233C3⋊C8—121no—
234C3⋊C8—241no—
235C3⋊C8—241no—
236C2×C32#46311yescharacteristic
237C2×C32#46511yescharacteristic
238C2×C32#47311yescharacteristic
239C3×D3—42no—
240C2×Q8—21no—
241C2×Q8—61no—
242C2×D4—31no—
243C22×C4—61no—
244SD16—362no—
245C2×C8—31no—
246C2×C8—31no—
247C2×C8—61no—
248C2×C8—181no—
249C2×C8—181no—
250C2×C8—362no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—31no—
254C4⋊C4—61no—
255C4⋊C4—61no—
256C22⋊C4—61no—
257C42C2×D3211yescharacteristic
258C22×C3—21no—
259C22×C3—62no—
260C22×C3—121no—
261C22×C3—121no—
262C22×C3#93811yescharacteristic
263C22×C3#93911yescharacteristic
264C2×D3—22no—
265C2×D3—41no—
266C2×D3—41no—
267C3×C4—21no—
268C3×C4—21no—
269C3×C4—21no—
270C3×C4—21no—
271C3×C4—21no—
272C3×C4—21no—
273C3×C4—41no—
274C3×C4—82no—
275C3×C4—81no—
276C3×C4—81no—
277C3×C4—121no—
278C3×C4—241no—
279C3×C4#91111yescharacteristic
280C3×C4#91211yescharacteristic
281C3×C4D3×SD1611yescharacteristic
282C3×C4#91611yescharacteristic
283C3×C4C2×#21511yescharacteristic
284C3×C4#94911yescharacteristic
285C3×C4#95011yescharacteristic
286C3×C4#95011yescharacteristic
287Dic3—41no—
288Dic3—81no—
289C32#167911yescharacteristic, complemented, Sylow
290C23—61no—
291Q8—41no—
292Q8—41no—
293Q8—121no—
294Q8—121no—
295D4—32no—
296D4—61no—
297C2×C4—41no—
298C2×C4—61no—
299C2×C4—121no—
300C2×C4—121no—
301C2×C4—121no—
302C2×C4#380511yescharacteristic
303C2×C4D3×#6711yescharacteristic
304C2×C4D3×#6711yescharacteristic
305C8—61no—
306C8—61no—
307C8—121no—
308C8—361no—
309C8—361no—
310C2×C3—21no—
311C2×C3—21no—
312C2×C3—21no—
313C2×C3—122no—
314C2×C3#504811yescharacteristic
315C2×C3#505711yescharacteristic
316C2×C3#515311yescharacteristic
317C2×C3#517111yescharacteristic
318C2×C3#519211yescharacteristic
319C2×C3#520411yescharacteristic
320D3—42no—
321C22—62no—
322C22—121no—
323C22—121no—
324C22#6397011yescharacteristic
325C4—21no—
326C4—81no—
327C4—121no—
328C4—241no—
329C4#6392511yescharacteristic
330C4#6393311yescharacteristic
331C4D3×#21511yescharacteristic
332C4#6394711yescharacteristic
333C3—21no—
334C3#7110211yescharacteristic, complemented
335C3#7123211yescharacteristic, complemented
336C2—122no—
337C2#1059143111yescharacteristic
338C2#1059163411yescharacteristic
339C2#1059164111yescharacteristic
subgroupG/H
centerC22#63970
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
2. C3×#5079C2semidirect
5. #10589413C2semidirect
6. #10589097C2semidirect
7. #10589093C2semidirect
29. #5079D3semidirect
289. C32#1679semidirect
334. C3#71102semidirect
335. C3#71232semidirect

Maximal subgroups

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

subgroupindex
C3×#50872
C3×#50792
#105903632
C3⋊C8×D122
#105894132
#105890972
#105890932
#712323
#711023