Finite Group Databasebeta

← #11789968

Subgroups — #11789968

Order 1152.

366 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 57 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×C8×#157C211yesmaximal, characteristic, complemented
2#10593349C211yesmaximal, characteristic
3C2×#63731C211yesmaximal, characteristic
4#10590958C211yesmaximal, characteristic
5#10590701C211yesmaximal, characteristic, complemented
6#10590051C211yesmaximal, characteristic, complemented
7#10590047C211yesmaximal, characteristic, complemented
8C2×#3798C2211yescharacteristic
9C2×C4×#157C2211yescharacteristic
10C2×#3787C2211yescharacteristic
11C2×C8×C3⋊D3C2211yescharacteristic
12#63874C2211yescharacteristic
13C2×#3712C2211yescharacteristic
14C2×#3712C2211yescharacteristic
15C8×#157—22no—
16#63740C411yescharacteristic, complemented
17#63740C411yescharacteristic, complemented
18#63739C411yescharacteristic, complemented
19#63739C411yescharacteristic, complemented
20#63731—22no—
21C3×(C2×D3)⋊C8—21no—
22C3×Dic3⋊C8—21no—
23Dic3⋊(C3⋊C8)—21no—
24(C2×D3)⋊(C3⋊C8)—21no—
25#4839—61no—
26#4727—61no—
27C22×#157—21no—
28C2×C4×C3⋊D3C2311yescharacteristic
29C2×C3×C4×D3—21no—
30C2×#627C2×C411yescharacteristic
31C2×#626—21no—
32C2×#625C2×C411yescharacteristic
33#3798—21no—
34#3798—21no—
35#3798—21no—
36#3798—21no—
37C2×#622C2×C411yescharacteristic
38C2×#622C2×C411yescharacteristic
39C4×#157—21no—
40C4×#157D412yes—
41#3787—21no—
42#3787—21no—
43C2×C32×C8D411yescharacteristic
44C2×C3⋊(C3⋊C8)D411yescharacteristic
45C8×C3⋊D3—21no—
46C8×C3⋊D3—21no—
47C3×C4×Dic3—21no—
48C2×C3×C3⋊C8—21no—
49C2×C3×C3⋊C8—21no—
50#3724C2×C411yescharacteristic
51#3724C2×C411yescharacteristic
52#3722—21no—
53#3712—21no—
54#3712—21no—
55#3712—21no—
56#3712—21no—
57#1937—91nomaximal, Sylow
58C2×#235—61no—
59C2×ΓL(1,𝔽25)—61no—
60C2×ΓL(1,𝔽25)—61no—
61C2×D3×C8—61no—
62C2×D3×C8—61no—
63#872—61no—
64C3×C4⋊C8—61no—
65C3×C22⋊C8—61no—
66#830—61no—
67(C2×D3)⋊C8—21no—
68(C2×D3)⋊C8—61no—
69Dic3⋊C8—21no—
70Dic3⋊C8—61no—
71C4⋊(C3⋊C8)—61no—
72C22×C3⋊D3#4111yescharacteristic
73C22×C3×D3—21no—
74C2×#157—22no—
75C2×#157—22no—
76C2×#157—22no—
77C2×C32×C4C2×D411yescharacteristic
78C2×C3⋊Dic3C22×C411yescharacteristic
79C4×C3⋊D3C2×D411yescharacteristic
80C4×C3⋊D3#4111yescharacteristic
81C4×C3⋊D3#4111yescharacteristic
82C4×C3⋊D3#4111yescharacteristic
83C2×C3×Dic3—21no—
84C2×C3×Dic3—21no—
85C2×C3×Dic3—21no—
86C3×C4×D3—41no—
87C3×C4×D3—41no—
88#627—21no—
89#627—21no—
90#626—41no—
91#626—41no—
92#625—21no—
93#625—21no—
94#622—21no—
95#622—21no—
96C32×C8—21no—
97C3⋊(C3⋊C8)—21no—
98C3×C3⋊C8—41no—
99C3×C3⋊C8—41no—
100#424—91no—
101C2×#104—91no—
102#416—91no—
103#408—91no—
104C2×C4×C8—91no—
105#341—91no—
106#339—91no—
107C22×C3×C4—61no—
108C2×#67—61no—
109C2×#67—61no—
110#235—121no—
111#235—121no—
112#235—121no—
113#235—121no—
114C2×D12—61no—
115C2×C4×D3—21no—
116C2×C4×D3—61no—
117C2×C4×D3—61no—
118C2×Dic6—61no—
119C2×C3×C8—21no—
120C2×C3×C8—21no—
121C2×C3×C8—61no—
122C2×C3×C8—61no—
123C3×C42—61no—
124(C2×D3)⋊C4—61no—
125(C2×D3)⋊C4—61no—
126Dic3⋊C4—61no—
127Dic3⋊C4—61no—
128C4×Dic3—21no—
129C2×C3⋊C8—21no—
130C2×C3⋊C8—21no—
131C2×C3⋊C8—61no—
132C2×C3⋊C8—61no—
133ΓL(1,𝔽25)—121no—
134ΓL(1,𝔽25)—121no—
135ΓL(1,𝔽25)—121no—
136ΓL(1,𝔽25)—121no—
137D3×C8—121no—
138D3×C8—121no—
139D3×C8—121no—
140D3×C8—121no—
141C22×C32C4×D411yescharacteristic
142C2×C3⋊D3—21no—
143C2×C3⋊D3—21no—
144C2×C3⋊D3#12311yescharacteristic
145C2×C3⋊D3#12611yescharacteristic
146C2×C3×D3—41no—
147C2×C3×D3—41no—
148C2×C3×D3—41no—
149#157—24no—
150C32×C4#12111yescharacteristic
151C32×C4#12411yescharacteristic
152C3⋊Dic3#11711yescharacteristic
153C3⋊Dic3C4×D411yescharacteristic
154C3×Dic3—41no—
155C3×Dic3—41no—
156C3×Dic3—41no—
157C2×#41—91no—
158C2×M16—91no—
159C2×M16—91no—
160C22×C8—91no—
161C22×C8—91no—
162#117—91no—
163C2×C42—91no—
164C4⋊C8—61no—
165C4⋊C8—181no—
166#104—182no—
167#103—91no—
168#103—91no—
169#102—91no—
170#102—91no—
171C22⋊C8—61no—
172C22⋊C8—181no—
173C4×C8—182no—
174C23×C3—61no—
175C22×D3—21no—
176C22×D3—61no—
177C22×D3—61no—
178C2×C3×C4—21no—
179C2×C3×C4—21no—
180C2×C3×C4—61no—
181C2×C3×C4—61no—
182C2×C3×C4—61no—
183C2×C3×C4—121no—
184C2×C3×C4—121no—
185#67—121no—
186#67—121no—
187#67—121no—
188#67—121no—
189C2×Dic3—21no—
190C2×Dic3—21no—
191C2×Dic3—21no—
192C2×Dic3—61no—
193C2×Dic3—61no—
194D12—121no—
195D12—121no—
196C4×D3—41no—
197C4×D3—41no—
198C4×D3—61no—
199C4×D3—61no—
200C4×D3—61no—
201C4×D3—61no—
202C4×D3—61no—
203C4×D3—61no—
204C4×D3—61no—
205C4×D3—61no—
206Dic6—121no—
207Dic6—121no—
208C3×C8—41no—
209C3×C8—41no—
210C3×C8—121no—
211C3×C8—121no—
212C3⋊C8—41no—
213C3⋊C8—41no—
214C3⋊C8—121no—
215C3⋊C8—121no—
216C2×C32#38811yescharacteristic
217C2×C32#44311yescharacteristic
218C2×C32#44311yescharacteristic
219C3⋊D3—21no—
220C3⋊D3—21no—
221C3×D3—81no—
222#41—181no—
223#41—181no—
224#41—181no—
225#41—181no—
226C2×Q8—91no—
227C2×D4—91no—
228C2×D4—181no—
229C22×C4—61no—
230C22×C4—91no—
231C22×C4—181no—
232M16—181no—
233M16—181no—
234M16—181no—
235M16—181no—
236C2×C8—61no—
237C2×C8—61no—
238C2×C8—91no—
239C2×C8—91no—
240C2×C8—91no—
241C2×C8—181no—
242C2×C8—181no—
243C2×C8—181no—
244C2×C8—181no—
245C2×C8GO+(4,𝔽2)11yescharacteristic
246C4⋊C4—91no—
247C4⋊C4—91no—
248C22⋊C4—181no—
249C42—61no—
250C42—92no—
251C42—181no—
252C22×C3—21no—
253C22×C3—21no—
254C22×C3—121no—
255C22×C3—121no—
256C22×C3—121no—
257C2×D3—41no—
258C2×D3—41no—
259C2×D3—41no—
260C2×D3—61no—
261C2×D3—61no—
262C2×D3—61no—
263C2×D3—61no—
264C2×D3—121no—
265C2×D3—121no—
266C2×D3—121no—
267C2×D3—121no—
268C3×C4—21no—
269C3×C4—21no—
270C3×C4—21no—
271C3×C4—21no—
272C3×C4—121no—
273C3×C4—121no—
274C3×C4—121no—
275Dic3—41no—
276Dic3—41no—
277Dic3—41no—
278Dic3—61no—
279Dic3—61no—
280Dic3—61no—
281Dic3—61no—
282C32#193711yescharacteristic, complemented, Sylow
283C23—61no—
284C23—91no—
285Q8—181no—
286Q8—181no—
287D4—181no—
288D4—181no—
289D4—361no—
290D4—361no—
291C2×C4—61no—
292C2×C4—61no—
293C2×C4—61no—
294C2×C4—91no—
295C2×C4—91no—
296C2×C4—91no—
297C2×C4—91no—
298C2×C4—91no—
299C2×C4—121no—
300C2×C4—121no—
301C2×C4—182no—
302C2×C4—182no—
303C2×C4—182no—
304C2×C4C2×GO+(4,𝔽2)11yescharacteristic
305C8—21no—
306C8—121no—
307C8—121no—
308C8—181no—
309C8—181no—
310C8—181no—
311C2×C3—21no—
312C2×C3—21no—
313C2×C3—21no—
314C2×C3—21no—
315C2×C3—21no—
316C2×C3—21no—
317C2×C3—241no—
318D3—81no—
319D3—121no—
320D3—121no—
321D3—121no—
322D3—121no—
323C22—91no—
324C22—91no—
325C22—121no—
326C22—121no—
327C22—121no—
328C22—181no—
329C22—181no—
330C22C4×GO+(4,𝔽2)11yescharacteristic
331C4—91no—
332C4—91no—
333C4—121no—
334C4—121no—
335C4—121no—
336C4—184no—
337C4#6422111yescharacteristic
338C4#6424211yescharacteristic
339C3—21no—
340C3—21no—
341C2—181no—
342C2—181no—
343C2—241no—
344C2#1059329711yescharacteristic
345C2#1059329911yescharacteristic
346C2#1059340011yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC2×C32×C8D4
socleC22×C32C4×D4
prime radicalC2×#3798C22
cosocleC2×C4×C3⋊D3C23
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#1937
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
1. C2×C8×#157C2semidirect
5. #10590701C2semidirect
6. #10590051C2semidirect
7. #10590047C2semidirect
16. #63740C4semidirect
17. #63740C4semidirect
18. #63739C4semidirect
19. #63739C4semidirect
282. C32#1937semidirect

Maximal subgroups

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

subgroupindex
C2×C8×#1572
#105933492
C2×#637312
#105909582
#105907012
#105900512
#105900472
#19379