Finite Group Databasebeta

← #11774507

Subgroups — #11774507

Order 1152.

595 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 595 conjugacy classes of subgroups — too many to draw. Only its 100 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#10593972C211yesmaximal, characteristic
2C4×#3743C211yesmaximal, characteristic, complemented
3#10590256C211yesmaximal, characteristic, complemented
4C3×#4459C212yesmaximal, complemented
5#10589080C212yesmaximal, complemented
6#68171—32nomaximal
7C2×#3798—21no—
8C2×#3743—21no—
9C42×C3⋊D3C2211yescharacteristic
10C3×C4×D12C2212yes—
11#63919C411yescharacteristic
12#63916C412yes—
13#63915—21no—
14#63914C411yescharacteristic
15#63912—21no—
16C4×#625—21no—
17C32×C4×C8C2211yescharacteristic
18#63642—21no—
19C4×C3⋊(C3⋊C8)C2211yescharacteristic
20C3×C4⋊(C3⋊C8)C2212yes—
21#63557—21no—
22#63553—21no—
23#5548—32no—
24#4833—32no—
25C4×ΓL(1,𝔽25)—32no—
26C4×ΓL(1,𝔽25)—61no—
27C3×D4⋊C8—32no—
28D4⋊(C3⋊C8)—32no—
29#4483—32no—
30#4459D312yescomplemented
31C2×C4×C3⋊D3C2×C411yescharacteristic
32C2×C4×C3⋊D3D411yescharacteristic
33C2×C4×C3⋊D3D411yescharacteristic
34C2×C3×D12C2×C412yes—
35C2×C3×C4×D3—22no—
36C2×#627—21no—
37C2×#626—22no—
38C2×#625—21no—
39C2×#625—21no—
40#3798—44no—
41C2×C32×C8—21no—
42C32×C42C2311yescharacteristic
43C4×C3⋊Dic3C2×C411yescharacteristic
44C4×C3⋊Dic3D411yescharacteristic
45C4×C3⋊Dic3D411yescharacteristic
46C2×C3⋊(C3⋊C8)—21no—
47#3743—24no—
48C3×(C2×D3)⋊C4—22no—
49C3×C4⋊Dic3C2×C412yes—
50C2×C3×C3⋊C8—22no—
51#3724—21no—
52(C2×D3)⋊Dic3—22no—
53#1484—91noSylow
54C2×#235—62no—
55C3×C4×D4—32no—
56#940—32no—
57#938—32no—
58C4×#67—62no—
59C2×ΓL(1,𝔽25)—62no—
60C2×ΓL(1,𝔽25)—62no—
61#895—32no—
62#888—32no—
63#885—62no—
64#884—62no—
65C4×D12C2×D312yes—
66C42×D3—32no—
67C42×D3—61no—
68C3×C4⋊C8—32no—
69C3×C4×C8—21no—
70C3×C4×C8C2×D312yes—
71(C2×D3)⋊C8—62no—
72#815—62no—
73#815—62no—
74C8×Dic3—62no—
75C4⋊(C3⋊C8)C2×D312yes—
76C4×C3⋊C8—32no—
77C4×C3⋊C8—61no—
78C22×C3⋊D3C22⋊C411yescharacteristic
79C22×C3×D3—22no—
80C2×C32×C4C22×C411yescharacteristic
81C2×C32×C4C2×D411yescharacteristic
82C2×C32×C4C2×D411yescharacteristic
83C2×C3⋊Dic3C22⋊C411yescharacteristic
84C2×C3⋊Dic3C22⋊C411yescharacteristic
85C2×C3⋊Dic3C22⋊C411yescharacteristic
86C4×C3⋊D3—22no—
87C4×C3⋊D3—22no—
88C4×C3⋊D3—22no—
89C2×C3×Dic3—22no—
90C3×D12—22no—
91C3×D12—22no—
92C3×C4×D3—42no—
93C3×C4×D3—42no—
94#627—42no—
95#626—44no—
96#625—42no—
97#625—42no—
98C32×C8—22no—
99C3⋊(C3⋊C8)—22no—
100C3×C3⋊C8—42no—
101#532—91no—
102#431—91no—
103C4×M16—91no—
104D4⋊C8—32no—
105D4⋊C8—92no—
106C2×C3×D4—32no—
107C22×C3×C4—62no—
108C2×#67—62no—
109C2×#67—62no—
110C2×#67—62no—
111#235—124no—
112#235—124no—
113C2×D12—62no—
114C2×D12C4×D312yes—
115C2×C4×D3—22no—
116C2×C4×D3—32no—
117C2×C4×D3—32no—
118C2×C4×D3—32no—
119C2×C4×D3—61no—
120C2×C4×D3—61no—
121C2×C4×D3—61no—
122C2×Dic6—62no—
123C2×C3×C8—22no—
124C2×C3×C8—22no—
125C2×C3×C8—62no—
126C3×C4⋊C4—32no—
127C3×C22⋊C4—62no—
128C3×C42—21no—
129C3×C42C22×D312yes—
130#217—62no—
131(C2×D3)⋊C4—22no—
132(C2×D3)⋊C4—62no—
133C4⋊Dic3C4×D312yes—
134Dic3⋊C4—62no—
135C4×Dic3—32no—
136C4×Dic3—32no—
137C4×Dic3—32no—
138C4×Dic3—61no—
139C4×Dic3—61no—
140C4×Dic3—61no—
141C2×C3⋊C8—22no—
142C2×C3⋊C8—62no—
143C2×C3⋊C8—62no—
144ΓL(1,𝔽25)—68no—
145ΓL(1,𝔽25)—68no—
146C22×C32C2×C22⋊C411yescharacteristic
147C2×C3⋊D3—21no—
148C2×C3⋊D3—21no—
149C2×C3⋊D3—21no—
150C2×C3×D3—42no—
151C2×C3×D3—42no—
152C2×C3×D3—42no—
153C32×C4—21no—
154C32×C4#13112yes—
155C32×C4AGL(1,ℤ/8)12yes—
156C3⋊Dic3—21no—
157C3⋊Dic3—21no—
158C3⋊Dic3#10412yes—
159C3×Dic3—42no—
160C2×#41—181no—
161C2×M16—181no—
162C4⋊Q8—91no—
163#127—91no—
164#124—181no—
165#121—92no—
166#121—181no—
167C4×D4—32no—
168C4×D4—181no—
169C2×C42—91no—
170C4⋊C8—32no—
171C22⋊C8—181no—
172#97—181no—
173C4×C8—91no—
174C4×C8—181no—
175C4×C8D3211yescharacteristic
176C23×C3—62no—
177C22×D3—22no—
178C22×D3—32no—
179C22×D3—61no—
180C3×D4—62no—
181C3×D4—62no—
182C2×C3×C4—21no—
183C2×C3×C4—21no—
184C2×C3×C4—21no—
185C2×C3×C4—62no—
186C2×C3×C4—122no—
187C2×C3×C4—122no—
188C2×C3×C4C2×C4×D312yes—
189C2×C3×C4D3×D412yes—
190C2×C3×C4D3×D412yes—
191#67—124no—
192#67—124no—
193#67—124no—
194C2×Dic3—22no—
195C2×Dic3—32no—
196C2×Dic3—32no—
197C2×Dic3—32no—
198C2×Dic3—61no—
199C2×Dic3—61no—
200C2×Dic3—61no—
201D12—22no—
202D12—22no—
203D12—124no—
204C4×D3—42no—
205C4×D3—42no—
206C4×D3—64no—
207C4×D3—64no—
208C4×D3—62no—
209C4×D3—62no—
210C4×D3—62no—
211C4×D3—62no—
212C4×D3—122no—
213C4×D3—122no—
214Dic6—124no—
215C3×C8—24no—
216C3×C8—24no—
217C3×C8—122no—
218C3⋊C8—42no—
219C3⋊C8—64no—
220C3⋊C8—64no—
221C2×C32#40811yescharacteristic
222C2×C32#41811yescharacteristic
223C2×C32C2×#10411yescharacteristic
224C3⋊D3—41no—
225C3×D3—82no—
226#41—364no—
227C2×Q8—181no—
228C2×D4—32no—
229C2×D4—182no—
230C2×D4—181no—
231C2×D4—181no—
232C22×C4—62no—
233C22×C4—91no—
234C22×C4—91no—
235C22×C4—91no—
236M16—184no—
237C2×C8—21no—
238C2×C8—62no—
239C2×C8—181no—
240C4⋊C4—32no—
241C4⋊C4—181no—
242C22⋊C4—62no—
243C22⋊C4—182no—
244C42—91no—
245C42—91no—
246C42—91no—
247C42C2×D3211yescharacteristic
248C22×C3—21no—
249C22×C3—122no—
250C22×C3—122no—
251C22×C3—122no—
252C22×C3D3×C22⋊C412yes—
253C2×D3—42no—
254C2×D3—42no—
255C2×D3—42no—
256C2×D3—62no—
257C2×D3—62no—
258C2×D3—62no—
259C2×D3—62no—
260C2×D3—121no—
261C2×D3—121no—
262C3×C4—22no—
263C3×C4—22no—
264C3×C4—22no—
265C3×C4—22no—
266C3×C4—122no—
267C3×C4#90112yes—
268C3×C4#90712yes—
269C3×C4#91112yes—
270C3×C4#91412yes—
271Dic3—34no—
272Dic3—42no—
273Dic3—62no—
274Dic3—62no—
275Dic3—62no—
276Dic3—121no—
277Dic3—121no—
278C32#148411yescharacteristic, complemented, Sylow
279C23—62no—
280C23—91no—
281Q8—362no—
282D4—62no—
283D4—62no—
284D4—362no—
285D4—364no—
286D4—362no—
287C2×C4—62no—
288C2×C4—91no—
289C2×C4—91no—
290C2×C4—91no—
291C2×C4—122no—
292C2×C4—122no—
293C2×C4—182no—
294C2×C4—182no—
295C2×C4—182no—
296C2×C4C4×D3211yescharacteristic
297C2×C4#380211yescharacteristic
298C2×C4#381111yescharacteristic
299C8—22no—
300C8—122no—
301C8—182no—
302C2×C3—21no—
303C2×C3—21no—
304C2×C3—21no—
305C2×C3—242no—
306C2×C3#472712yes—
307C2×C3#477012yes—
308C2×C3D3×#10412yes—
309D3—82no—
310D3—122no—
311D3—122no—
312C22—122no—
313C22—122no—
314C22—122no—
315C22—181no—
316C22—181no—
317C22—181no—
318C22#6392111yescharacteristic
319C4—21no—
320C4—92no—
321C4—122no—
322C4—181no—
323C4—181no—
324C4#6379812yes—
325C4#6380412yes—
326C3—21no—
327C3#6817112yescomplemented
328C2—242no—
329C2—361no—
330C2#1059039311yescharacteristic
331C2#1059094111yescharacteristic
332C2#1059095911yescharacteristic
subgroupG/H
centerC2×C4#3802
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4×C8C22
socleC22×C32C2×C22⋊C4
prime radical#10593972C2
cosocleC32×C42C23
hypercenterC4×C8D32
hypocenterC32#1484
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
2. C4×#3743C2semidirect
3. #10590256C2semidirect
4. C3×#4459C2semidirect
5. #10589080C2semidirect
30. #4459D3semidirect
278. C32#1484semidirect
327. C3#68171semidirect

Maximal subgroups

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

subgroupindex
#105939722
C4×#37432
#105902562
C3×#44592
#105890802
#681713