Finite Group Databasebeta

← #11777963

Subgroups — #11777963

Order 1152.

413 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 413 conjugacy classes of subgroups — too many to draw. Only its 96 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#10592537C211yesmaximal, characteristic, complemented
2C4×#3714C211yesmaximal, characteristic
3#10590339C211yesmaximal, characteristic, complemented
4C3×#4483C211yesmaximal, characteristic, complemented
5C3×#4480C211yesmaximal, characteristic, complemented
6#10589082C211yesmaximal, characteristic, complemented
7#10589078C211yesmaximal, characteristic, complemented
8#68525—31nomaximal
9#68163—31nomaximal
10C2×#3743—21no—
11C4×C4⋊(C3⋊D3)C2211yescharacteristic
12C3×C4×D12C2211yescharacteristic
13C2×#3714C411yescharacteristic
14C2×#3711—21no—
15C32×C4⋊C8C2211yescharacteristic
16#63647—21no—
17C4×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×C4⋊(C3⋊C8)C2211yescharacteristic
19C3×C4×C3⋊C8C2211yescharacteristic
20C3×C4×C3⋊C8C2211yescharacteristic
21#63575C411yescharacteristic
22#63564C411yescharacteristic
23#63563C411yescharacteristic
24(C2×D3)⋊(C3⋊C8)—21no—
25C4×#213—31no—
26#5012—31no—
27#4838—31no—
28#4838—31no—
29#4838—31no—
30#4838—61no—
31C4×D24—31no—
32C3×#334—31no—
33C3×D4⋊C8—31no—
34#4483—31no—
35#4483D311yescharacteristic, complemented
36#4480D311yescharacteristic, complemented
37#4459—31no—
38#4455—31no—
39#4454—31no—
40C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
41C2×C4×C3⋊D3—21no—
42C2×C3×D12C2×C411yescharacteristic
43C2×C3×C4×D3—21no—
44C2×C32×C8—21no—
45C32×C42C2311yescharacteristic
46#3752—21no—
47C4⋊(C3⋊Dic3)C2×C411yescharacteristic
48C2×C3⋊(C3⋊C8)D411yescharacteristic
49C2×C3⋊(C3⋊C8)D411yescharacteristic
50#3743—42no—
51C3×(C2×D3)⋊C4—21no—
52C3×C4⋊Dic3C2×C411yescharacteristic
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8C2×C411yescharacteristic
56C2×C3×C3⋊C8C2×C411yescharacteristic
57#3714—22no—
58#3711—42no—
59#1594—91noSylow
60C3×C4×D4—31no—
61C2×#213—31no—
62C2×#208—61no—
63C2×D24—31no—
64C2×ΓL(1,𝔽25)—61no—
65C2×ΓL(1,𝔽25)—61no—
66C2×ΓL(1,𝔽25)—61no—
67C2×ΓL(1,𝔽25)—62no—
68C4×D12—31no—
69C4×D12—31no—
70C4×D12—61no—
71C4×D12C2×D311yescharacteristic
72C3×C4⋊C8—21no—
73C3×C4⋊C8—31no—
74C3×C4⋊C8C2×D311yescharacteristic
75C3×C4⋊C8C2×D311yescharacteristic
76C3×C4×C8—31no—
77C3×C4×C8—31no—
78#832—31no—
79#830—61no—
80#821—31no—
81#821—31no—
82(C2×D3)⋊C8—61no—
83(C2×D3)⋊C8—61no—
84(C2×D3)⋊C8—61no—
85(C2×D3)⋊C8—62no—
86#818—31no—
87#809—31no—
88#807—31no—
89C4⋊(C3⋊C8)C2×D311yescharacteristic
90C4×C3⋊C8—31no—
91C4×C3⋊C8—31no—
92C4×C3⋊C8—61no—
93C4×C3⋊C8C2×D311yescharacteristic
94C4×C3⋊C8C2×D311yescharacteristic
95C22×C3⋊D3—21no—
96C22×C3×D3—21no—
97C2×C32×C4C22×C411yescharacteristic
98C2×C32×C4C2×D411yescharacteristic
99C2×C32×C4#4111yescharacteristic
100C2×C3⋊Dic3—21no—
101C4⋊(C3⋊D3)—21no—
102C4⋊(C3⋊D3)—21no—
103C4×C3⋊D3—41no—
104C4×C3⋊D3—41no—
105C2×C3×Dic3—21no—
106C3×D12—21no—
107C3×D12—21no—
108C3×C4×D3—41no—
109C3×C4×D3—41no—
110C32×C8—41no—
111C3⋊(C3⋊C8)—21no—
112C3⋊(C3⋊C8)—21no—
113C3×C3⋊C8—21no—
114C3×C3⋊C8—41no—
115C3×C3⋊C8—41no—
116C3×C3⋊C8M1612yescomplemented
117C4×D8—91no—
118#436—91no—
119#436—91no—
120#334—31no—
121D4⋊C8—31no—
122D4⋊C8—91no—
123#322—91no—
124C2×C3×D4—31no—
125C22×C3×C4—61no—
126C2×D12—31no—
127C2×D12—31no—
128C2×D12—61no—
129C2×D12C4×D311yescharacteristic
130C2×C4×D3—21no—
131C2×C4×D3—62no—
132C2×C4×D3—61no—
133C2×C4×D3—61no—
134C2×C3×C8—22no—
135C2×C3×C8—21no—
136C2×C3×C8—21no—
137C2×C3×C8—31no—
138C2×C3×C8—31no—
139C2×C3×C8—61no—
140C2×C3×C8—61no—
141C3×C4⋊C4—31no—
142C3×C22⋊C4—61no—
143C3×C42—21no—
144C3×C42C22×D311yescharacteristic
145C3×C42C22×D311yescharacteristic
146#213—62no—
147(C2×D3)⋊C4—21no—
148(C2×D3)⋊C4—62no—
149(C2×D3)⋊C4—61no—
150(C2×D3)⋊C4—61no—
151C4⋊Dic3—31no—
152C4⋊Dic3—31no—
153C4⋊Dic3—61no—
154C4⋊Dic3C4×D311yescharacteristic
155#208—122no—
156C2×C3⋊C8—21no—
157C2×C3⋊C8—21no—
158C2×C3⋊C8—31no—
159C2×C3⋊C8—31no—
160C2×C3⋊C8—31no—
161C2×C3⋊C8—31no—
162C2×C3⋊C8—61no—
163C2×C3⋊C8—61no—
164C2×C3⋊C8C4×D311yescharacteristic
165C2×C3⋊C8C4×D311yescharacteristic
166D24—62no—
167ΓL(1,𝔽25)—124no—
168ΓL(1,𝔽25)—122no—
169ΓL(1,𝔽25)—122no—
170ΓL(1,𝔽25)—122no—
171C22×C32C4×D411yescharacteristic
172C2×C3⋊D3—41no—
173C2×C3⋊D3—41no—
174C2×C3⋊D3—41no—
175C2×C3×D3—41no—
176C2×C3×D3—41no—
177C2×C3×D3—41no—
178C32×C4—21no—
179C32×C4C2×M1611yescharacteristic
180C32×C4#13111yescharacteristic
181C32×C4AGL(1,ℤ/8)11yescharacteristic
182C32×C4AGL(1,ℤ/8)11yescharacteristic
183C3⋊Dic3—41no—
184C3×Dic3—41no—
185C2×D8—91no—
186C2×M16—181no—
187C2×M16—181no—
188C4×D4—31no—
189C4×D4—91no—
190#107—91no—
191C4⋊C8—31no—
192C4⋊C8D3211yescharacteristic
193#102—91no—
194#102—91no—
195C22⋊C8—181no—
196C22⋊C8—181no—
197C4×C8—31no—
198C4×C8—31no—
199C4×C8—91no—
200C23×C3—61no—
201C22×D3—21no—
202C22×D3—62no—
203C22×D3—61no—
204C22×D3—61no—
205C3×D4—61no—
206C3×D4—61no—
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×C4×D311yescharacteristic
214C2×C3×C4C2×C4×D311yescharacteristic
215C2×C3×C4D3×D411yescharacteristic
216C2×C3×C4D3×D411yescharacteristic
217C2×C3×C4#23711yescharacteristic
218C2×C3×C4#23911yescharacteristic
219C2×Dic3—21no—
220C2×Dic3—62no—
221C2×Dic3—61no—
222C2×Dic3—61no—
223D12—21no—
224D12—21no—
225D12—61no—
226D12—61no—
227D12—61no—
228D12—61no—
229D12—121no—
230D12—121no—
231C4×D3—41no—
232C4×D3—41no—
233C4×D3—122no—
234C4×D3—122no—
235C4×D3—121no—
236C4×D3—121no—
237C4×D3—121no—
238C4×D3—121no—
239C3×C8—32no—
240C3×C8—42no—
241C3×C8—41no—
242C3×C8—41no—
243C3×C8—61no—
244C3×C8—121no—
245C3×C8—121no—
246C3⋊C8—21no—
247C3⋊C8—41no—
248C3⋊C8—41no—
249C3⋊C8—62no—
250C3⋊C8—61no—
251C3⋊C8—61no—
252C3⋊C8—61no—
253C3⋊C8—61no—
254C3⋊C8—121no—
255C3⋊C8ΓL(1,𝔽25)12yescomplemented
256C2×C32#43611yescharacteristic
257C2×C32#44211yescharacteristic
258C2×C32#44411yescharacteristic
259C3⋊D3—81no—
260C3×D3—81no—
261C2×D4—31no—
262C2×D4—91no—
263C22×C4—61no—
264C22×C4—181no—
265D8—182no—
266M16—362no—
267M16—362no—
268C2×C8—21no—
269C2×C8—31no—
270C2×C8—31no—
271C2×C8—61no—
272C2×C8—61no—
273C2×C8—91no—
274C2×C8—91no—
275C4⋊C4—31no—
276C4⋊C4—91no—
277C22⋊C4—61no—
278C22⋊C4—181no—
279C42C2×D3211yescharacteristic
280C22×C3—21no—
281C22×C3—121no—
282C22×C3—121no—
283C22×C3—121no—
284C22×C3#67⋊C411yescharacteristic
285C22×C3#89311yescharacteristic
286C2×D3—41no—
287C2×D3—41no—
288C2×D3—41no—
289C2×D3—122no—
290C2×D3—122no—
291C2×D3—122no—
292C2×D3—121no—
293C2×D3—121no—
294C2×D3—121no—
295C2×D3—121no—
296C2×D3—121no—
297C2×D3—121no—
298C3×C4—21no—
299C3×C4—21no—
300C3×C4—21no—
301C3×C4—21no—
302C3×C4—21no—
303C3×C4—21no—
304C3×C4—41no—
305C3×C4—121no—
306C3×C4C2×ΓL(1,𝔽25)11yescharacteristic
307C3×C4#90111yescharacteristic
308C3×C4D3×M1611yescharacteristic
309C3×C4#90711yescharacteristic
310C3×C4#91111yescharacteristic
311C3×C4#91411yescharacteristic
312C3×C4#91411yescharacteristic
313C3×C4#91411yescharacteristic
314Dic3—41no—
315Dic3—122no—
316Dic3—121no—
317Dic3—121no—
318C32#159411yescharacteristic, complemented, Sylow
319C23—61no—
320C23—181no—
321D4—61no—
322D4—61no—
323D4—181no—
324D4—181no—
325C2×C4—61no—
326C2×C4—121no—
327C2×C4—121no—
328C2×C4—181no—
329C2×C4—361no—
330C2×C4—361no—
331C2×C4#379611yescharacteristic
332C2×C4C4×D3211yescharacteristic
333C2×C4#381111yescharacteristic
334C8—32no—
335C8—41no—
336C8—61no—
337C8—121no—
338C8—121no—
339C8—181no—
340C8—181no—
341C2×C3—21no—
342C2×C3—21no—
343C2×C3—21no—
344C2×C3—241no—
345C2×C3#472911yescharacteristic
346C2×C3#478511yescharacteristic
347C2×C3#482311yescharacteristic
348C2×C3#483811yescharacteristic
349C2×C3#486911yescharacteristic
350C2×C3#489411yescharacteristic
351D3—81no—
352D3—242no—
353D3—241no—
354D3—241no—
355C22—121no—
356C22—121no—
357C22—121no—
358C22—361no—
359C22—361no—
360C22—361no—
361C22#6388111yescharacteristic
362C4—21no—
363C4—121no—
364C4—361no—
365C4D3×ΓL(1,𝔽25)11yescharacteristic
366C4#6380411yescharacteristic
367C4#6393711yescharacteristic
368C4#6394111yescharacteristic
369C3—21no—
370C3#6816311yescharacteristic, complemented
371C3#6852511yescharacteristic, complemented
372C2—241no—
373C2—721no—
374C2#1059046211yescharacteristic
375C2#1059073211yescharacteristic
376C2#1059097811yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32C4×D4
prime radicalC2×#3714C4
cosocleC32×C42C23
hypercenterC4⋊C8D32
hypocenterC32#1594
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4⋊C8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #10592537C2semidirect
3. #10590339C2semidirect
4. C3×#4483C2semidirect
5. C3×#4480C2semidirect
6. #10589082C2semidirect
7. #10589078C2semidirect
35. #4483D3semidirect
36. #4480D3semidirect
116. C3×C3⋊C8M16semidirect
255. C3⋊C8ΓL(1,𝔽25)semidirect
318. C32#1594semidirect
370. C3#68163semidirect
371. C3#68525semidirect

Maximal subgroups

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

subgroupindex
#105925372
C4×#37142
#105903392
C3×#44832
C3×#44802
#105890822
#105890782
#685253
#681633