Finite Group Databasebeta

← #11799117

Subgroups — #11799117

Order 1152.

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

normal subgroups only

This group has 363 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
1C3×#4908C211yesmaximal, characteristic, complemented
2#10590919C211yesmaximal, characteristic, complemented
3#10590886C211yesmaximal, characteristic, complemented
4#10590630C211yesmaximal, characteristic, complemented
5#10589377C211yesmaximal, characteristic, complemented
6C3×#4516C211yesmaximal, characteristic, complemented
7#10589126C211yesmaximal, characteristic, complemented
8#71514—31nomaximal
9#69263—31nomaximal
10C3×#904C2211yescharacteristic
11C2×C3×D24C2211yescharacteristic
12C2×C3×D24C2211yescharacteristic
13#63914—21no—
14C2×#3713—21no—
15#63815—21no—
16C32×M32C2211yescharacteristic
17C8×C3⋊Dic3C2211yescharacteristic
18#63639C2211yescharacteristic
19C3×#819C2211yescharacteristic
20C3×#800—21no—
21C3×D48—21no—
22#63568—21no—
23#63547—21no—
24#63545—21no—
25C3×#509—31no—
26#5196—31no—
27#5193—31no—
28#5151—31no—
29#5151—31no—
30#5147—31no—
31#4908D311yescharacteristic, complemented
32#4895—31no—
33C3×#361—31no—
34#4563—31no—
35#4516D311yescharacteristic, complemented
36#4511—31no—
37#4511—31no—
38#4511—61no—
39#4495—31no—
40C3×#235—21no—
41C2×C3×D12—21no—
42C2×C3×D12—21no—
43C2×#625—42no—
44C2×C32×C8C2311yescharacteristic
45C4×C3⋊Dic3D411yescharacteristic
46C2×C3⋊(C3⋊C8)D411yescharacteristic
47C3×#208—21no—
48C3×Dic12D411yescharacteristic, complemented
49C3×D24—21no—
50C3×D24—21no—
51C3×D24—21no—
52C3×D24—21no—
53C3×D24D411yescharacteristic, complemented
54C3×#204—21no—
55#3713—41no—
56#3713—41no—
57#3711—41no—
58D3×C3⋊C8—41no—
59C32×C16—21no—
60C3⋊(C3⋊C16)—21no—
61#2213—91noSylow
62C3×#135—31no—
63C2×C3×D8—31no—
64C2×C3×D8—31no—
65#948—61no—
66#940—61no—
67#940—61no—
68C2×#213—61no—
69C2×#213—61no—
70#907—61no—
71#904C2×D311yescharacteristic
72C2×D24C2×D311yescharacteristic
73C2×D24C2×D311yescharacteristic
74C3×SD32—61no—
75C3×D16—61no—
76C3×M32—21no—
77C3×M32C2×D311yescharacteristic
78C3×M32C2×D311yescharacteristic
79C3×#108—31no—
80#837—61no—
81#828—61no—
82#827—61no—
83#826—61no—
84#826—61no—
85#825—61no—
86#819C2×D311yescharacteristic
87C8×Dic3—31no—
88C8×Dic3—31no—
89C8×Dic3—61no—
90#812—31no—
91#812—31no—
92#812—61no—
93#800—21no—
94D48—21no—
95C22×C3×D3—41no—
96C22×C3×D3—41no—
97C2×C32×C4C2×D411yescharacteristic
98C2×C3⋊Dic3—21no—
99C3×#67—41no—
100C3×D12—21no—
101C3×D12—41no—
102C3×D12—41no—
103C3×D12—41no—
104C3×D12—41no—
105C3×C4×D3—41no—
106C3×Dic6—21no—
107#625—84no—
108C32×C8C2×D411yescharacteristic
109C32×C8#4111yescharacteristic
110C3⋊(C3⋊C8)D811yescharacteristic
111C3⋊(C3⋊C8)D811yescharacteristic
112C3×C3⋊C8—41no—
113#509—31no—
114#509—91no—
115#493—91no—
116#443—91no—
117#364—91no—
118#361—31no—
119#361—91no—
120C3×#41—61no—
121C2×C3×D4—61no—
122C2×C3×D4—61no—
123C2×#67—122no—
124C2×#67—122no—
125#235—21no—
126C2×D12—21no—
127C2×D12—21no—
128C3×Q16—31no—
129C3×SD16—61no—
130C3×D8—31no—
131C3×D8—61no—
132C3×D8—61no—
133C3×D8—61no—
134C3×D8—61no—
135C3×M16—61no—
136C2×C3×C8—21no—
137C2×C3×C8C22×D311yescharacteristic
138C2×C3×C8C22×D311yescharacteristic
139#213—121no—
140#213—121no—
141#213—121no—
142#213—121no—
143C4×Dic3—31no—
144C4×Dic3—31no—
145C4×Dic3—61no—
146#208—21no—
147#208—121no—
148C2×C3⋊C8—31no—
149C2×C3⋊C8—31no—
150C2×C3⋊C8—61no—
151C2×C3⋊C8—121no—
152Dic12#6711yescharacteristic, complemented
153D24—21no—
154D24—21no—
155D24—21no—
156D24—21no—
157D24#6711yescharacteristic, complemented
158#204—21no—
159ΓL(1,𝔽25)—121no—
160D3×C8—121no—
161C3×C16—21no—
162C3×C16—21no—
163C3×C16—41no—
164C3⋊C16—61no—
165C3⋊C16—61no—
166C3⋊C16—121no—
167C22×C32AGL(1,ℤ/8)11yescharacteristic
168C2×C3×D3—41no—
169C2×C3×D3—82no—
170C2×C3×D3—82no—
171C2×C3×D3—81no—
172C2×C3×D3—81no—
173C32×C4#12111yescharacteristic
174C32×C4C2×D811yescharacteristic
175C3⋊Dic3—22no—
176C3×Dic3—41no—
177#135—31no—
178C2×D8—31no—
179C2×D8—31no—
180C2×D8—181no—
181#131—181no—
182#127—181no—
183SD32—61no—
184SD32—181no—
185D16—61no—
186D16—181no—
187M32—91no—
188M32D3211yescharacteristic
189#108—31no—
190#104—181no—
191C4×C8—91no—
192C23×C3—121no—
193C23×C3—121no—
194C22×D3—41no—
195C22×D3—41no—
196C3×Q8—61no—
197C3×D4—61no—
198C3×D4—121no—
199C3×D4—121no—
200C3×D4—121no—
201C3×D4—121no—
202C3×D4—121no—
203C2×C3×C4—21no—
204C2×C3×C4—121no—
205C2×C3×C4D3×D411yescharacteristic
206C2×C3×C4D3×D411yescharacteristic
207#67—41no—
208#67—244no—
209#67—244no—
210C2×Dic3—61no—
211C2×Dic3—61no—
212C2×Dic3—121no—
213D12—21no—
214D12—41no—
215D12—41no—
216D12—41no—
217D12—41no—
218C4×D3—41no—
219Dic6—21no—
220C3×C8—21no—
221C3×C8—21no—
222C3×C8—121no—
223C3×C8#23511yescharacteristic
224C3×C8D3×D411yescharacteristic
225C3×C8#23711yescharacteristic
226C3×C8C2×#6711yescharacteristic
227C3⋊C8—31no—
228C3⋊C8—31no—
229C3⋊C8—31no—
230C3⋊C8—31no—
231C3⋊C8—41no—
232C3⋊C8—61no—
233C3⋊C8—61no—
234C2×C32—21no—
235C2×C32#45911yescharacteristic
236C3×D3—81no—
237C3×D3—161no—
238C3×D3—161no—
239#41—61no—
240C2×D4—61no—
241C2×D4—61no—
242C2×D4—362no—
243Q16—31no—
244SD16—61no—
245D8—31no—
246D8—61no—
247D8—61no—
248D8—61no—
249D8—61no—
250D8—361no—
251D8—361no—
252M16—61no—
253M16—361no—
254C2×C8—91no—
255C2×C8—361no—
256C2×C8C2×D3211yescharacteristic
257C42—91no—
258C16—21no—
259C16—181no—
260C22×C3—21no—
261C22×C3—121no—
262C22×C3—242no—
263C22×C3—242no—
264C22×C3—241no—
265C22×C3—241no—
266C22×C3#91111yescharacteristic
267C22×C3#91411yescharacteristic
268C2×D3—41no—
269C2×D3—82no—
270C2×D3—82no—
271C2×D3—81no—
272C2×D3—81no—
273C3×C4—21no—
274C3×C4—21no—
275C3×C4—121no—
276C3×C4#88411yescharacteristic
277C3×C4D3×D811yescharacteristic
278C3×C4D3×D811yescharacteristic
279C3×C4#93911yescharacteristic
280Dic3—41no—
281Dic3—62no—
282Dic3—62no—
283Dic3—122no—
284C32#221311yescharacteristic, complemented, Sylow
285C23—121no—
286C23—121no—
287Q8—61no—
288D4—61no—
289D4—121no—
290D4—121no—
291D4—121no—
292D4—121no—
293D4—121no—
294D4—724no—
295C2×C4—121no—
296C2×C4—181no—
297C2×C4#380211yescharacteristic
298C8—91no—
299C8—91no—
300C8—121no—
301C8#379511yescharacteristic
302C8D3×#6711yescharacteristic
303C2×C3—21no—
304C2×C3—21no—
305C2×C3—21no—
306C2×C3—41no—
307C2×C3—241no—
308C2×C3—481no—
309C2×C3—481no—
310C2×C3#478611yescharacteristic
311C2×C3#515011yescharacteristic
312D3—81no—
313D3—161no—
314D3—161no—
315C22—121no—
316C22—242no—
317C22—242no—
318C22—241no—
319C22—241no—
320C22#6379811yescharacteristic
321C4—121no—
322C4—182no—
323C4#6379711yescharacteristic
324C4#6388511yescharacteristic
325C3—21no—
326C3#6926311yescharacteristic, complemented
327C3#7151411yescharacteristic, complemented
328C2—21no—
329C2—241no—
330C2—481no—
331C2—481no—
332C2#1059074911yescharacteristic
subgroupG/H
centerC2#10590749
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC32×M32C22
socleC2×C32#459
hypercenterM32D32
hypocenterC32#2213
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ M32

Complements

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

NH ≅ G/Ntype
1. C3×#4908C2semidirect
2. #10590919C2semidirect
3. #10590886C2semidirect
4. #10590630C2semidirect
5. #10589377C2semidirect
6. C3×#4516C2semidirect
7. #10589126C2semidirect
31. #4908D3semidirect
35. #4516D3semidirect
48. C3×Dic12D4semidirect
53. C3×D24D4semidirect
152. Dic12#67semidirect
157. D24#67semidirect
284. C32#2213semidirect
326. C3#69263semidirect
327. C3#71514semidirect

Maximal subgroups

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

subgroupindex
C3×#49082
#105909192
#105908862
#105906302
#105893772
C3×#45162
#105891262
#715143
#692633