Finite Group Databasebeta

← #11799458

Subgroups — #11799458

Order 1152.

342 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 68 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#10592859C211yesmaximal, characteristic
2C2×C3×#827C211yesmaximal, characteristic, complemented
3#10590933C211yesmaximal, characteristic, complemented
4#10590624C211yesmaximal, characteristic, complemented
5C3×#4563C211yesmaximal, characteristic, complemented
6#10589143C211yesmaximal, characteristic, complemented
7#10589130C211yesmaximal, characteristic, complemented
8#71491—31nomaximal
9#69261—31nomaximal
10C2×C32×D8C2211yescharacteristic
11#64141—21no—
12#64110C2211yescharacteristic
13C2×C3×Dic12C2211yescharacteristic
14#63833—21no—
15#63660—21no—
16#63646C2211yescharacteristic
17C3×#827—21no—
18C3×#827—21no—
19C3×#819C2211yescharacteristic
20C3×#812C2211yescharacteristic
21C2×C3×C3⋊C16C2211yescharacteristic
22#63560—21no—
23#63544—21no—
24#63542—21no—
25C2×C3×SD32—31no—
26#5192—31no—
27#5160—31no—
28#5160—31no—
29#5160—61no—
30C2×#827D311yescharacteristic, complemented
31#4907—31no—
32#4901—31no—
33#4896—31no—
34C3×#361—31no—
35#4565—31no—
36#4563D311yescharacteristic, complemented
37#4517—31no—
38#4506—31no—
39#4493—31no—
40C2×C32×D4—21no—
41#3828D411yescharacteristic
42C2×C3×Dic6—21no—
43C32×D8—21no—
44C32×D8—21no—
45C2×C32×C8C2311yescharacteristic
46#3754—41no—
47#3753—41no—
48#3748—21no—
49#3748D411yescharacteristic
50#3743—21no—
51C8×C3⋊D3—21no—
52C3×#208—21no—
53C3×Dic12—21no—
54C3×Dic12—21no—
55#3719—41no—
56#3717—41no—
57C3×C3⋊C16—21no—
58C3×C3⋊C16D411yescharacteristic
59C3×C3⋊C16D411yescharacteristic
60#2223—91noSylow
61C2×C3×Q16—31no—
62C2×C3×D8—21no—
63C2×C3×D8C2×D311yescharacteristic
64C2×C3×D8C2×D311yescharacteristic
65#942—61no—
66#932—61no—
67#932—61no—
68#932—62no—
69#909—61no—
70C2×Dic12C2×D311yescharacteristic
71#901—31no—
72#901—31no—
73#901—61no—
74C3×SD32—61no—
75C3×SD32—61no—
76C3×M32—31no—
77C2×C3×C16—31no—
78C3×#108—31no—
79#836—61no—
80#833—61no—
81#833—61no—
82#833—62no—
83#827—21no—
84#827—21no—
85#824—61no—
86#819—31no—
87#819—31no—
88#819—61no—
89#819C2×D311yescharacteristic
90#812C2×D311yescharacteristic
91C2×C3⋊C16C2×D311yescharacteristic
92#798—61no—
93#798—61no—
94D3×C16—61no—
95D3×C16—61no—
96C23×C32—41no—
97C32×D4—41no—
98C32×D4—41no—
99C2×C32×C4C2×D411yescharacteristic
100#638—21no—
101C4⋊(C3⋊D3)D811yescharacteristic
102C4×C3⋊D3—21no—
103#634D811yescharacteristic
104C2×C3×Dic3—41no—
105C3×Dic6—41no—
106C3×Dic6—41no—
107C32×C8C2×D411yescharacteristic
108C32×C8#4111yescharacteristic
109C3⋊(C3⋊C8)—21no—
110C3⋊(C3⋊C8)—41no—
111C3×C3⋊C8—41no—
112C2×SD32—31no—
113#504—91no—
114#473—91no—
115#472—91no—
116#368—91no—
117#362—91no—
118#361—31no—
119C2×C3×Q8—61no—
120C2×C3×D4—22no—
121C2×C3×D4—21no—
122C2×C3×D4—21no—
123#235—31no—
124#235—31no—
125#235—61no—
126C2×Dic6—21no—
127C3×Q16—61no—
128C3×Q16—61no—
129C3×D8—21no—
130C3×D8—21no—
131C3×D8—21no—
132C3×D8—21no—
133C3×D8—41no—
134C3×D8—41no—
135C3×M16—61no—
136C2×C3×C8—21no—
137C2×C3×C8C22×D311yescharacteristic
138C2×C3×C8C22×D311yescharacteristic
139#216—121no—
140#215—121no—
141#214—121no—
142#214—121no—
143#214—122no—
144#213—121no—
145#213—121no—
146#213—122no—
147#208—21no—
148#208—31no—
149#208—31no—
150#208—61no—
151#208—62no—
152#208—61no—
153#208—61no—
154Dic12—21no—
155Dic12—21no—
156Dic12—121no—
157#204—121no—
158ΓL(1,𝔽25)—61no—
159ΓL(1,𝔽25)—61no—
160ΓL(1,𝔽25)—121no—
161D3×C8—61no—
162D3×C8—61no—
163D3×C8—121no—
164C3×C16—31no—
165C3×C16—31no—
166C3×C16—61no—
167C3⋊C16—21no—
168C3⋊C16#6711yescharacteristic
169C3⋊C16#6711yescharacteristic
170C22×C32—81no—
171C22×C32—161no—
172C22×C32#13511yescharacteristic
173C2×C3⋊D3—21no—
174C32×C4#12111yescharacteristic
175C32×C4C2×D811yescharacteristic
176C3⋊Dic3—21no—
177C3×Dic3—81no—
178#137—181no—
179AGL(1,ℤ/8)—181no—
180C2×Q16—31no—
181C2×D8D3211yescharacteristic
182#131—91no—
183SD32—61no—
184SD32—61no—
185M32—31no—
186M32—181no—
187C2×C16—31no—
188C2×C16—181no—
189#108—31no—
190#108—91no—
191#101—181no—
192#100—181no—
193C23×C3—42no—
194C23×C3—41no—
195C23×C3—41no—
196C3×Q8—121no—
197C3×Q8—121no—
198C3×D4—42no—
199C3×D4—42no—
200C3×D4—41no—
201C3×D4—41no—
202C3×D4—41no—
203C3×D4—41no—
204C2×C3×C4—21no—
205C2×C3×C4—121no—
206C2×C3×C4D3×D411yescharacteristic
207C2×C3×C4D3×D411yescharacteristic
208#67—61no—
209#67—61no—
210#67—121no—
211C2×Dic3—41no—
212D12—31no—
213D12—31no—
214D12—61no—
215C4×D3—61no—
216C4×D3—61no—
217C4×D3—121no—
218Dic6—31no—
219Dic6—31no—
220Dic6—41no—
221Dic6—41no—
222Dic6—61no—
223C3×C8—21no—
224C3×C8—21no—
225C3×C8—121no—
226C3×C8#23511yescharacteristic
227C3×C8D3×D411yescharacteristic
228C3×C8#23711yescharacteristic
229C3×C8C2×#6711yescharacteristic
230C3⋊C8—41no—
231C3⋊C8—61no—
232C3⋊C8—61no—
233C3⋊C8—121no—
234C3⋊C8—122no—
235C3⋊C8—121no—
236C3⋊C8—121no—
237C2×C32—21no—
238C2×C32—161no—
239C2×C32#46611yescharacteristic
240C3⋊D3—41no—
241#41—91no—
242C2×Q8—61no—
243C2×D4—21no—
244Q16—61no—
245Q16—61no—
246Q16—361no—
247SD16—361no—
248SD16—361no—
249D8—21no—
250D8—21no—
251D8—361no—
252M16—61no—
253M16—91no—
254M16—181no—
255M16—181no—
256C2×C8—181no—
257C2×C8C2×D3211yescharacteristic
258C16—31no—
259C16—31no—
260C16—61no—
261C22×C3—21no—
262C22×C3—82no—
263C22×C3—81no—
264C22×C3—81no—
265C22×C3—161no—
266C22×C3—161no—
267C22×C3—162no—
268C22×C3#91211yescharacteristic
269C22×C3#91611yescharacteristic
270C2×D3—61no—
271C2×D3—61no—
272C2×D3—121no—
273C3×C4—21no—
274C3×C4—21no—
275C3×C4—241no—
276C3×C4#88411yescharacteristic
277C3×C4D3×D811yescharacteristic
278C3×C4D3×D811yescharacteristic
279C3×C4#93811yescharacteristic
280Dic3—61no—
281Dic3—61no—
282Dic3—81no—
283Dic3—121no—
284C32#222311yescharacteristic, complemented, Sylow
285C23—41no—
286Q8—91no—
287Q8—121no—
288Q8—121no—
289D4—41no—
290D4—41no—
291D4—91no—
292D4—181no—
293C2×C4—121no—
294C2×C4—181no—
295C2×C4#381111yescharacteristic
296C8—121no—
297C8—181no—
298C8—361no—
299C8#380411yescharacteristic
300C8D3×#6711yescharacteristic
301C2×C3—21no—
302C2×C3—21no—
303C2×C3—21no—
304C2×C3—41no—
305C2×C3—162no—
306C2×C3—161no—
307C2×C3—161no—
308C2×C3#477511yescharacteristic
309C2×C3#515711yescharacteristic
310D3—121no—
311D3—121no—
312D3—241no—
313C22—81no—
314C22—161no—
315C22—181no—
316C22#6393611yescharacteristic
317C4—181no—
318C4—241no—
319C4#6392611yescharacteristic
320C4#6395811yescharacteristic
321C3—21no—
322C3#6926111yescharacteristic, complemented
323C3#7149111yescharacteristic, complemented
324C2—21no—
325C2—161no—
326C2—361no—
327C2#1059145511yescharacteristic
subgroupG/H
centerC2#10591455
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC2×C32×D8C22
socleC2×C32#466
prime radical#10592859C2
hypercenterC2×D8D32
hypocenterC32#2223
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
2. C2×C3×#827C2semidirect
3. #10590933C2semidirect
4. #10590624C2semidirect
5. C3×#4563C2semidirect
6. #10589143C2semidirect
7. #10589130C2semidirect
30. C2×#827D3semidirect
36. #4563D3semidirect
284. C32#2223semidirect
322. C3#69261semidirect
323. C3#71491semidirect

Maximal subgroups

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

subgroupindex
#105928592
C2×C3×#8272
#105909332
#105906242
C3×#45632
#105891432
#105891302
#714913
#692613