Finite Group Databasebeta

← #11799387

Subgroups — #11799387

Order 1152.

345 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 345 conjugacy classes of subgroups — too many to draw. Only its 70 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
1C2×#63653C211yesmaximal, characteristic, complemented
2C3×#5160C211yesmaximal, characteristic, complemented
3#10590927C211yesmaximal, characteristic, complemented
4#10590622C211yesmaximal, characteristic, complemented
5C3×#4563C211yesmaximal, characteristic, complemented
6#10589144C211yesmaximal, characteristic, complemented
7#10589128C211yesmaximal, characteristic, complemented
8#71092—31nomaximal
9#69260—31nomaximal
10C2×C32×D8C2211yescharacteristic
11C2×#3745C2211yescharacteristic
12C3×#932—21no—
13C3×#901C2211yescharacteristic
14#63825—21no—
15#63653—21no—
16#63653—21no—
17C2×C3⋊(C3⋊C16)C2211yescharacteristic
18C3×#833—21no—
19C3×#819C2211yescharacteristic
20C3×#819C2211yescharacteristic
21C3×#812C2211yescharacteristic
22#63559—21no—
23#63543—21no—
24D3×C3⋊C16—21no—
25C3×#472—31no—
26#5160D311yescharacteristic, complemented
27C2×#826—31no—
28C2×#826—31no—
29C2×#826—61no—
30#5142—31no—
31#5140—31no—
32#4907—31no—
33#4897—31no—
34C3×#361—31no—
35#4563D311yescharacteristic, complemented
36#4516—31no—
37#4495—31no—
38#4493—31no—
39#4493—31no—
40C2×C32×D4—21no—
41C2×C4⋊(C3⋊D3)—21no—
42C3×#235D411yescharacteristic
43C32×D8—21no—
44C32×D8—21no—
45C2×C32×C8C2311yescharacteristic
46#3745—21no—
47#3745—21no—
48C3×#214—41no—
49C3×#213—41no—
50C3×#208—21no—
51C3×#208—21no—
52C3×#208D411yescharacteristic
53C3×ΓL(1,𝔽25)—21no—
54C3×D3×C8—21no—
55#3717—41no—
56#3714—41no—
57C3⋊(C3⋊C16)D411yescharacteristic
58C3⋊(C3⋊C16)D411yescharacteristic
59C3×C3⋊C16—21no—
60#2221—91noSylow
61C3×AGL(1,ℤ/8)—61no—
62C2×C3×D8—21no—
63C2×C3×D8C2×D311yescharacteristic
64C2×C3×D8C2×D311yescharacteristic
65C3×#131—31no—
66#949—61no—
67#932—21no—
68#908—61no—
69C2×D24—31no—
70C2×D24—31no—
71C2×D24—61no—
72#901C2×D311yescharacteristic
73C3×M32—31no—
74C3×#108—31no—
75C3×#108—31no—
76C3×#100—61no—
77#833—21no—
78#826—61no—
79#826—61no—
80#826—61no—
81#826—61no—
82#826—62no—
83#826—62no—
84#823—61no—
85#823—61no—
86#819C2×D311yescharacteristic
87#819C2×D311yescharacteristic
88#812—61no—
89#812C2×D311yescharacteristic
90C2×C3⋊C16—31no—
91C2×C3⋊C16—31no—
92C2×C3⋊C16—61no—
93C2×C3⋊C16—61no—
94#798—61no—
95D3×C16—61no—
96C23×C32—41no—
97C22×C3⋊D3—41no—
98C32×D4—41no—
99C32×D4—41no—
100C2×C32×C4C2×D411yescharacteristic
101C4⋊(C3⋊D3)—41no—
102C4⋊(C3⋊D3)—41no—
103C3×#67—21no—
104C3×D12D811yescharacteristic
105C3×C4×D3—21no—
106C3×Dic6D811yescharacteristic
107C32×C8C2×D411yescharacteristic
108C32×C8#4111yescharacteristic
109C3×C3⋊C8—21no—
110C3×C3⋊C8—41no—
111C3×C3⋊C8—41no—
112C2×D16—91no—
113#504—91no—
114#472—31no—
115#472—91no—
116#368—91no—
117#361—31no—
118#361—91no—
119C3×#41—31no—
120C2×C3×D4—21no—
121C2×C3×D4—21no—
122C2×C3×D4—41no—
123#235#6711yescharacteristic
124C2×D12—61no—
125C2×D12—61no—
126C2×D12—121no—
127C3×SD16—121no—
128C3×D8—22no—
129C3×D8—21no—
130C3×D8—21no—
131C3×D8—21no—
132C3×D8—21no—
133C3×D8—41no—
134C3×D8—121no—
135C3×M16—31no—
136C3×M16—61no—
137C3×M16—61no—
138C3×M16—61no—
139C2×C3×C8—21no—
140C2×C3×C8—61no—
141C2×C3×C8C22×D311yescharacteristic
142C2×C3×C8C22×D311yescharacteristic
143#215—121no—
144#214—41no—
145#213—41no—
146#213—121no—
147#208—21no—
148#208—21no—
149#208#6711yescharacteristic
150D24—62no—
151D24—61no—
152D24—61no—
153D24—61no—
154D24—61no—
155D24—121no—
156D24—121no—
157#204—121no—
158ΓL(1,𝔽25)—21no—
159D3×C8—21no—
160C3×C16—61no—
161C3⋊C16—21no—
162C3⋊C16—31no—
163C3⋊C16—31no—
164C3⋊C16—31no—
165C3⋊C16—31no—
166C3⋊C16—61no—
167C3⋊C16—61no—
168C22×C32—81no—
169C22×C32—161no—
170C22×C32#13511yescharacteristic
171C2×C3⋊D3—81no—
172C2×C3⋊D3—161no—
173C2×C3×D3—21no—
174C32×C4#12111yescharacteristic
175C32×C4C2×D811yescharacteristic
176C3×Dic3—21no—
177AGL(1,ℤ/8)—61no—
178AGL(1,ℤ/8)—181no—
179C2×D8—91no—
180C2×D8D3211yescharacteristic
181#131—31no—
182D16—181no—
183D16—181no—
184M32—31no—
185M32—181no—
186C2×C16—91no—
187C2×C16—181no—
188#108—31no—
189#108—31no—
190#100—61no—
191#100—181no—
192C23×C3—41no—
193C23×C3—41no—
194C23×C3—81no—
195C22×D3—121no—
196C22×D3—121no—
197C22×D3—241no—
198C3×Q8—31no—
199C3×D4—31no—
200C3×D4—42no—
201C3×D4—41no—
202C3×D4—41no—
203C3×D4—41no—
204C3×D4—41no—
205C3×D4—61no—
206C3×D4—81no—
207C2×C3×C4—21no—
208C2×C3×C4—61no—
209C2×C3×C4D3×D411yescharacteristic
210C2×C3×C4C2×#6711yescharacteristic
211#67—21no—
212D12—122no—
213D12—121no—
214D12—121no—
215D12—121no—
216D12—121no—
217D12—241no—
218D12#21311yescharacteristic
219C4×D3—21no—
220Dic6#21311yescharacteristic
221C3×C8—21no—
222C3×C8—21no—
223C3×C8—61no—
224C3×C8—121no—
225C3×C8—121no—
226C3×C8#23511yescharacteristic
227C3×C8D3×D411yescharacteristic
228C3×C8D3×D411yescharacteristic
229C3×C8#23711yescharacteristic
230C3⋊C8—21no—
231C3⋊C8—41no—
232C3⋊C8—41no—
233C2×C32—21no—
234C2×C32—161no—
235C2×C32#46611yescharacteristic
236C3⋊D3—161no—
237C3×D3—41no—
238#41—31no—
239C2×D4—21no—
240C2×D4—181no—
241SD16—121no—
242SD16—361no—
243D8—21no—
244D8—21no—
245D8—121no—
246D8—181no—
247D8—181no—
248D8—361no—
249M16—31no—
250M16—61no—
251M16—61no—
252M16—61no—
253C2×C8—61no—
254C2×C8C2×D3211yescharacteristic
255C16—61no—
256C16—91no—
257C16—91no—
258C22×C3—21no—
259C22×C3—61no—
260C22×C3—82no—
261C22×C3—81no—
262C22×C3—81no—
263C22×C3—161no—
264C22×C3—161no—
265C22×C3—162no—
266C22×C3#91611yescharacteristic
267C22×C3#95011yescharacteristic
268C2×D3—21no—
269C2×D3—242no—
270C2×D3—241no—
271C2×D3—241no—
272C2×D3—482no—
273C2×D3—481no—
274C2×D3—481no—
275C3×C4—21no—
276C3×C4—21no—
277C3×C4—61no—
278C3×C4#88411yescharacteristic
279C3×C4D3×D811yescharacteristic
280C3×C4C2×#21311yescharacteristic
281C3×C4#93911yescharacteristic
282Dic3—21no—
283C32#222111yescharacteristic, complemented, Sylow
284C23—41no—
285C23—361no—
286Q8—31no—
287D4—31no—
288D4—41no—
289D4—41no—
290D4—61no—
291D4—361no—
292D4—361no—
293C2×C4—61no—
294C2×C4D3×#6711yescharacteristic
295C8—61no—
296C8—121no—
297C8—121no—
298C8#380411yescharacteristic
299C8#381111yescharacteristic
300C2×C3—22no—
301C2×C3—21no—
302C2×C3—21no—
303C2×C3—21no—
304C2×C3—121no—
305C2×C3—162no—
306C2×C3—161no—
307C2×C3—161no—
308C2×C3#477511yescharacteristic
309C2×C3#503811yescharacteristic
310D3—41no—
311D3—482no—
312D3—481no—
313D3—481no—
314C22—61no—
315C22—81no—
316C22—161no—
317C22—721no—
318C22—1441no—
319C22#6393511yescharacteristic
320C4—61no—
321C4D3×#21311yescharacteristic
322C4#6397111yescharacteristic
323C3—21no—
324C3#6926011yescharacteristic, complemented
325C3#7109211yescharacteristic, complemented
326C2—21no—
327C2—121no—
328C2—161no—
329C2—1441no—
330C2#1059144911yescharacteristic
subgroupG/H
centerC2#10591449
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC2×C32×D8C22
socleC2×C32#466
hypercenterC2×D8D32
hypocenterC32#2221
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×#63653C2semidirect
2. C3×#5160C2semidirect
3. #10590927C2semidirect
4. #10590622C2semidirect
5. C3×#4563C2semidirect
6. #10589144C2semidirect
7. #10589128C2semidirect
26. #5160D3semidirect
35. #4563D3semidirect
283. C32#2221semidirect
324. C3#69260semidirect
325. C3#71092semidirect

Maximal subgroups

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

subgroupindex
C2×#636532
C3×#51602
#105909272
#105906222
C3×#45632
#105891442
#105891282
#710923
#692603