Finite Group Databasebeta

← #11777390

Subgroups — #11777390

Order 1152.

391 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 391 conjugacy classes of subgroups — too many to draw. Only its 102 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×#4838C211yesmaximal, characteristic, complemented
2C4×#3713C211yesmaximal, characteristic
3C3⋊C8×D12C211yesmaximal, characteristic, complemented
4#10589345C211yesmaximal, characteristic, complemented
5C3×#4483C211yesmaximal, characteristic, complemented
6#10589081C211yesmaximal, characteristic, complemented
7#10589078C211yesmaximal, characteristic, complemented
8#70862—31nomaximal
9#68152—31nomaximal
10C2×C3×ΓL(1,𝔽25)—21no—
11C3×C4×D12C2211yescharacteristic
12C3×C4×D12C2211yescharacteristic
13C2×#3713C411yescharacteristic
14C2×D3×C3⋊C8—21no—
15C32×C4⋊C8C2211yescharacteristic
16C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
17C4×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×(C2×D3)⋊C8—21no—
19C3×C4×C3⋊C8C2211yescharacteristic
20C3×C4×C3⋊C8C2211yescharacteristic
21#63576C411yescharacteristic
22#63562C411yescharacteristic
23#63562C411yescharacteristic
24(C2×D3)⋊(C3⋊C8)—21no—
25C3×#436—31no—
26C4×#213—31no—
27C4×#213—31no—
28D4×C3⋊C8—31no—
29#4838D311yescharacteristic, complemented
30C8×D12—31no—
31C3×D4⋊C8—31no—
32D4⋊(C3⋊C8)—31no—
33#4483D311yescharacteristic, complemented
34#4479—31no—
35#4479—31no—
36#4479—61no—
37#4459—31no—
38#4455—31no—
39#4454—31no—
40C2×C3×D12C2×C411yescharacteristic
41C2×C3×D12C2×C411yescharacteristic
42C2×C3×C4×D3—21no—
43C2×C3×C4×D3—21no—
44C2×C32×C8—21no—
45C32×C42C2311yescharacteristic
46C2×C3⋊(C3⋊C8)—21no—
47C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
48C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
49C3×(C2×D3)⋊C4—21no—
50C3×(C2×D3)⋊C4—21no—
51C3×C4⋊Dic3C2×C411yescharacteristic
52C3×C4⋊Dic3C2×C411yescharacteristic
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8D411yescharacteristic
55C2×C3×C3⋊C8D411yescharacteristic
56C3×ΓL(1,𝔽25)—42no—
57#3713—22no—
58D3×C3⋊C8—42no—
59#1581—91noSylow
60C2×C3×M16—61no—
61C3×C4×D4—31no—
62C3×C4×D4—31no—
63C2×#213—31no—
64C2×#213—31no—
65C22×C3⋊C8—61no—
66C2×ΓL(1,𝔽25)—21no—
67C2×D3×C8—61no—
68C4×D12C2×D311yescharacteristic
69C4×D12C2×D311yescharacteristic
70C3×C4⋊C8—21no—
71C3×C4⋊C8C2×D311yescharacteristic
72C3×C4⋊C8C2×D311yescharacteristic
73C3×C22⋊C8—61no—
74C3×C4×C8—31no—
75C3×C4×C8—31no—
76#832—31no—
77#832—31no—
78#830—61no—
79(C2×D3)⋊C8—21no—
80(C2×D3)⋊C8—61no—
81#809—31no—
82#809—31no—
83#807—31no—
84#807—31no—
85C4⋊(C3⋊C8)—31no—
86C4⋊(C3⋊C8)—31no—
87C4⋊(C3⋊C8)—61no—
88C4×C3⋊C8—31no—
89C4×C3⋊C8—31no—
90C4×C3⋊C8—61no—
91C4×C3⋊C8C2×D311yescharacteristic
92C4×C3⋊C8C2×D311yescharacteristic
93C22×C3×D3—21no—
94C22×C3×D3—21no—
95C2×C32×C4C22×C411yescharacteristic
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4#4111yescharacteristic
98C2×C3×Dic3—21no—
99C2×C3×Dic3—21no—
100C3×D12—21no—
101C3×D12—21no—
102C3×D12—21no—
103C3×D12M1612yescomplemented
104C3×C4×D3—41no—
105C3×C4×D3—41no—
106C3×C4×D3—41no—
107C3×C4×D3—41no—
108C32×C8—41no—
109C3⋊(C3⋊C8)—21no—
110C3⋊(C3⋊C8)—21no—
111C3⋊(C3⋊C8)—41no—
112C3×C3⋊C8—21no—
113C3×C3⋊C8—41no—
114C3×C3⋊C8D812yescomplemented
115C4×D8—91no—
116#436—31no—
117C8×D4—91no—
118#335—91no—
119D4⋊C8—31no—
120D4⋊C8—91no—
121#322—91no—
122C2×C3×D4—31no—
123C2×C3×D4—31no—
124C22×C3×C4—61no—
125C22×C3×C4—61no—
126C2×D12C4×D311yescharacteristic
127C2×D12C4×D311yescharacteristic
128C2×C4×D3—21no—
129C2×C4×D3—21no—
130C3×M16—122no—
131C2×C3×C8—21no—
132C2×C3×C8—21no—
133C2×C3×C8—31no—
134C2×C3×C8—31no—
135C2×C3×C8—41no—
136C2×C3×C8—61no—
137C3×C4⋊C4—31no—
138C3×C4⋊C4—31no—
139C3×C22⋊C4—61no—
140C3×C22⋊C4—61no—
141C3×C42—21no—
142C3×C42C22×D311yescharacteristic
143C3×C42C22×D311yescharacteristic
144#213—62no—
145#213—62no—
146(C2×D3)⋊C4—21no—
147(C2×D3)⋊C4—21no—
148C4⋊Dic3C4×D311yescharacteristic
149C4⋊Dic3C4×D311yescharacteristic
150C2×C3⋊C8—21no—
151C2×C3⋊C8—31no—
152C2×C3⋊C8—31no—
153C2×C3⋊C8—31no—
154C2×C3⋊C8—31no—
155C2×C3⋊C8—61no—
156C2×C3⋊C8—61no—
157C2×C3⋊C8—61no—
158C2×C3⋊C8—61no—
159C2×C3⋊C8—121no—
160C2×C3⋊C8—122no—
161C2×C3⋊C8#6711yescharacteristic
162C2×C3⋊C8#6711yescharacteristic
163ΓL(1,𝔽25)—42no—
164D3×C8—122no—
165C22×C32C4×D411yescharacteristic
166C2×C3×D3—22no—
167C2×C3×D3—41no—
168C2×C3×D3—41no—
169C2×C3×D3—41no—
170C2×C3×D3—41no—
171C2×C3×D3—41no—
172C32×C4—21no—
173C32×C4C2×M1611yescharacteristic
174C32×C4#13111yescharacteristic
175C32×C4C2×D811yescharacteristic
176C32×C4#13511yescharacteristic
177C3×Dic3—41no—
178C3×Dic3—41no—
179C2×D8—91no—
180C2×M16—61no—
181C22×C8—181no—
182C4×D4—31no—
183C4×D4—31no—
184#107—91no—
185C4⋊C8—91no—
186C4⋊C8D3211yescharacteristic
187#102—91no—
188#102—91no—
189C22⋊C8—61no—
190C22⋊C8—181no—
191C4×C8—31no—
192C4×C8—31no—
193C4×C8—91no—
194C23×C3—61no—
195C23×C3—61no—
196C22×D3—21no—
197C22×D3—21no—
198C3×D4—32no—
199C3×D4—61no—
200C3×D4—61no—
201C3×D4—61no—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4—21no—
205C2×C3×C4—61no—
206C2×C3×C4—61no—
207C2×C3×C4—121no—
208C2×C3×C4—121no—
209C2×C3×C4—121no—
210C2×C3×C4—121no—
211C2×C3×C4C2×C4×D311yescharacteristic
212C2×C3×C4C2×C4×D311yescharacteristic
213C2×C3×C4#23511yescharacteristic
214C2×C3×C4D3×D411yescharacteristic
215C2×C3×C4#23711yescharacteristic
216C2×C3×C4C2×#6711yescharacteristic
217C2×Dic3—21no—
218C2×Dic3—21no—
219D12—21no—
220D12—21no—
221D12—21no—
222D12ΓL(1,𝔽25)12yescomplemented
223C4×D3—41no—
224C4×D3—41no—
225C4×D3—41no—
226C4×D3—41no—
227C3×C8—32no—
228C3×C8—41no—
229C3×C8—41no—
230C3×C8—61no—
231C3×C8—81no—
232C3×C8—121no—
233C3⋊C8—21no—
234C3⋊C8—41no—
235C3⋊C8—62no—
236C3⋊C8—61no—
237C3⋊C8—61no—
238C3⋊C8—61no—
239C3⋊C8—61no—
240C3⋊C8—121no—
241C3⋊C8—121no—
242C3⋊C8—121no—
243C3⋊C8—241no—
244C3⋊C8#21312yescomplemented
245C2×C32#43511yescharacteristic
246C2×C32C4×D811yescharacteristic
247C2×C32#44411yescharacteristic
248C3×D3—42no—
249C3×D3—81no—
250C2×D4—31no—
251C2×D4—31no—
252C22×C4—61no—
253C22×C4—61no—
254D8—182no—
255M16—122no—
256C2×C8—21no—
257C2×C8—31no—
258C2×C8—31no—
259C2×C8—61no—
260C2×C8—91no—
261C2×C8—91no—
262C2×C8—181no—
263C2×C8—362no—
264C4⋊C4—31no—
265C4⋊C4—31no—
266C22⋊C4—61no—
267C22⋊C4—61no—
268C42C2×D3211yescharacteristic
269C22×C3—21no—
270C22×C3—62no—
271C22×C3—121no—
272C22×C3—121no—
273C22×C3—121no—
274C22×C3—121no—
275C22×C3—121no—
276C22×C3#67⋊C411yescharacteristic
277C22×C3C4×#6711yescharacteristic
278C2×D3—22no—
279C2×D3—41no—
280C2×D3—41no—
281C2×D3—41no—
282C2×D3—41no—
283C2×D3—41no—
284C3×C4—21no—
285C3×C4—21no—
286C3×C4—21no—
287C3×C4—21no—
288C3×C4—21no—
289C3×C4—21no—
290C3×C4—41no—
291C3×C4—121no—
292C3×C4—121no—
293C3×C4C2×ΓL(1,𝔽25)11yescharacteristic
294C3×C4D3×M1611yescharacteristic
295C3×C4#90711yescharacteristic
296C3×C4#90711yescharacteristic
297C3×C4D3×D811yescharacteristic
298C3×C4#91611yescharacteristic
299C3×C4C2×#21311yescharacteristic
300C3×C4#95011yescharacteristic
301Dic3—41no—
302Dic3—41no—
303C32#158111yescharacteristic, complemented, Sylow
304C23—61no—
305C23—61no—
306D4—32no—
307D4—61no—
308D4—61no—
309D4—61no—
310C2×C4—61no—
311C2×C4—61no—
312C2×C4—121no—
313C2×C4—121no—
314C2×C4—121no—
315C2×C4—121no—
316C2×C4#379511yescharacteristic
317C2×C4C4×D3211yescharacteristic
318C2×C4D3×#6711yescharacteristic
319C8—32no—
320C8—41no—
321C8—61no—
322C8—121no—
323C8—181no—
324C8—181no—
325C8—361no—
326C2×C3—21no—
327C2×C3—21no—
328C2×C3—21no—
329C2×C3—122no—
330C2×C3—241no—
331C2×C3#473011yescharacteristic
332C2×C3#475611yescharacteristic
333C2×C3#482311yescharacteristic
334C2×C3C4×#21311yescharacteristic
335C2×C3#512711yescharacteristic
336C2×C3#514511yescharacteristic
337D3—42no—
338D3—81no—
339C22—62no—
340C22—121no—
341C22—121no—
342C22—121no—
343C22—121no—
344C22—121no—
345C22#6387911yescharacteristic
346C4—21no—
347C4—121no—
348C4—121no—
349C4D3×ΓL(1,𝔽25)11yescharacteristic
350C4#6380511yescharacteristic
351C4D3×#21311yescharacteristic
352C4#6394711yescharacteristic
353C3—21no—
354C3#6815211yescharacteristic, complemented
355C3#7086211yescharacteristic, complemented
356C2—122no—
357C2—241no—
358C2#1059045211yescharacteristic
359C2#1059072411yescharacteristic
360C2#1059097611yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32C4×D4
prime radicalC2×#3713C4
cosocleC32×C42C23
hypercenterC4⋊C8D32
hypocenterC32#1581
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. C3×#4838C2semidirect
3. C3⋊C8×D12C2semidirect
4. #10589345C2semidirect
5. C3×#4483C2semidirect
6. #10589081C2semidirect
7. #10589078C2semidirect
29. #4838D3semidirect
33. #4483D3semidirect
103. C3×D12M16semidirect
114. C3×C3⋊C8D8semidirect
222. D12ΓL(1,𝔽25)semidirect
244. C3⋊C8#213semidirect
303. C32#1581semidirect
354. C3#68152semidirect
355. C3#70862semidirect

Maximal subgroups

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

subgroupindex
C3×#48382
C4×#37132
C3⋊C8×D122
#105893452
C3×#44832
#105890812
#105890782
#708623
#681523