Finite Group Databasebeta

← #11775280

Subgroups — #11775280

Order 1152.

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

normal subgroups only

This group has 456 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
1#10594963C211yesmaximal, characteristic
2#10593804C211yesmaximal, characteristic, complemented
3C4×#3724C211yesmaximal, characteristic, complemented
4#10590072C212yesmaximal, complemented
5#10590071C212yesmaximal
6C2×C4×C3⋊Dic3C2211yescharacteristic
7C3×#929—21no—
8C2×C3×C4×Dic3—21no—
9#63982C2211yescharacteristic
10#63980C2211yescharacteristic
11#67⋊Dic3—21no—
12C2×#3724—21no—
13#63915C411yescharacteristic, complemented
14#63902C411yescharacteristic, complemented
15#63878—21no—
16#63870C411yescharacteristic, complemented
17#63862—21no—
18#63838C411yescharacteristic, complemented
19C22⋊#622C2212yes—
20#63779—21no—
21#63777—21no—
22#63579C2212yes—
23#5649—61no—
24C4×Dic3⋊C4—61no—
25C22×C32×C4D411yescharacteristic
26C22×C3⋊Dic3D411yescharacteristic
27C22×C3⋊Dic3C2311yescharacteristic
28C2×C3×#67—21no—
29C22×C3×Dic3—22no—
30C2×#627C2×C411yescharacteristic
31C2×#625C2×C411yescharacteristic
32C2×D3×Dic3—21no—
33C2×#622—22no—
34C4×C3⋊Dic3C2×C411yescharacteristic
35C4×C3⋊Dic3C2×C411yescharacteristic
36C4×C3⋊Dic3D411yescharacteristic
37C4×C3⋊Dic3D411yescharacteristic
38C3×#217—21no—
39C3×(C2×D3)⋊C4—21no—
40C3×(C2×D3)⋊C4—21no—
41C3×Dic3⋊C4—21no—
42C3×Dic3⋊C4—21no—
43C3×C4×Dic3—42no—
44#3724—24no—
45#3724C2×C411yescharacteristic
46#3724C2×C411yescharacteristic
47Dic3⋊Dic3—21no—
48Dic3⋊Dic3—21no—
49(C2×D3)⋊Dic3—21no—
50(C2×D3)⋊Dic3—21no—
51Dic32—21no—
52#1509—91nomaximal, Sylow
53C3×#123—61no—
54C2×C3×C42—61no—
55#939—61no—
56D4×Dic3—61no—
57#929—21no—
58C2×Dic3⋊C4—62no—
59C2×C4×Dic3—21no—
60C2×C4×Dic3—61no—
61C2×C4×Dic3—61no—
62#898—61no—
63#892—61no—
64#889—61no—
65#887—61no—
66#885—61no—
67#67⋊C4—61no—
68#67⋊C4—61no—
69#879—61no—
70#878—61no—
71#877—61no—
72C3⋊#95—62no—
73C23×C32C2×D411yescharacteristic
74C22×C3×D3—21no—
75C2×C32×C4—21no—
76C2×C32×C4—21no—
77C2×C32×C4C22⋊C411yescharacteristic
78C2×C32×C4C22⋊C411yescharacteristic
79C2×C3⋊Dic3—22no—
80C2×C3⋊Dic3—41no—
81C2×C3⋊Dic3C22⋊C411yescharacteristic
82C2×C3⋊Dic3C22⋊C411yescharacteristic
83C2×C3⋊Dic3C22×C411yescharacteristic
84C2×C3⋊Dic3C2×D411yescharacteristic
85C3×#67—41no—
86C3×#67—41no—
87C2×C3×Dic3—24no—
88C2×C3×Dic3—21no—
89C2×C3×Dic3—21no—
90C2×C3×Dic3—21no—
91C2×C3×Dic3—42no—
92C2×C3×Dic3—42no—
93#627—41no—
94#625—41no—
95D3×Dic3—42no—
96#622—42no—
97#529—91no—
98#432—91no—
99C4×C4⋊C4—91no—
100#328—92no—
101#327—92no—
102C2×C3×D4—61no—
103C22×C3×C4—21no—
104C22×C3×C4—21no—
105C22×C3×C4—62no—
106C2×#67—21no—
107C2×#67—61no—
108C22×Dic3—22no—
109C22×Dic3—61no—
110C22×Dic3—61no—
111C22×Dic3—61no—
112C22×Dic3—61no—
113C22×Dic3—61no—
114C2×C4×D3—61no—
115C2×Dic6—61no—
116C3×C4⋊C4—61no—
117C3×C4⋊C4—61no—
118C3×C22⋊C4—61no—
119C3×C22⋊C4—61no—
120C3×C22⋊C4—61no—
121C3×C42—122no—
122#217—21no—
123#217—61no—
124#217—61no—
125(C2×D3)⋊C4—21no—
126(C2×D3)⋊C4—21no—
127(C2×D3)⋊C4—61no—
128(C2×D3)⋊C4—61no—
129C4⋊Dic3—61no—
130C4⋊Dic3—61no—
131Dic3⋊C4—21no—
132Dic3⋊C4—21no—
133Dic3⋊C4—61no—
134Dic3⋊C4—61no—
135Dic3⋊C4—61no—
136Dic3⋊C4—61no—
137Dic3⋊C4—68no—
138C4×Dic3—42no—
139C4×Dic3—61no—
140C4×Dic3—61no—
141C4×Dic3—61no—
142C4×Dic3—61no—
143C4×Dic3—61no—
144C4×Dic3—61no—
145C4×Dic3—61no—
146C4×Dic3—61no—
147C4×Dic3—61no—
148C4×Dic3—61no—
149C22×C32—21no—
150C22×C32—21no—
151C22×C32C2×C22⋊C411yescharacteristic
152C22×C32AGL(1,ℤ/8)11yescharacteristic
153C22×C32#13711yescharacteristic
154C2×C3×D3—41no—
155C2×C3×D3—41no—
156C2×C3×D3—41no—
157C32×C4—21no—
158C32×C4—21no—
159C3⋊Dic3—21no—
160C3⋊Dic3—21no—
161C3⋊Dic3—21no—
162C3⋊Dic3#10412yes—
163C3×Dic3—44no—
164C3×Dic3—41no—
165C3×Dic3—41no—
166C3×Dic3—41no—
167#126—181no—
168#125—91no—
169#124—91no—
170#123—61no—
171C22⋊Q8—91no—
172#121—91no—
173C4×Q8—91no—
174C4×D4—91no—
175C4×D4—181no—
176#117—181no—
177C2×C4⋊C4—181no—
178C2×C42—61no—
179C2×C42—91no—
180C4⋊C8—181no—
181C22⋊C8—92no—
182#97—181no—
183#95—92no—
184C23×C3—21no—
185C23×C3—21no—
186C23×C3—61no—
187C22×D3—21no—
188C3×D4—121no—
189C3×D4—121no—
190C2×C3×C4—22no—
191C2×C3×C4—22no—
192C2×C3×C4—21no—
193C2×C3×C4—21no—
194C2×C3×C4—21no—
195C2×C3×C4—21no—
196C2×C3×C4—41no—
197C2×C3×C4—41no—
198C2×C3×C4—61no—
199C2×C3×C4—61no—
200C2×C3×C4—61no—
201C2×C3×C4—64no—
202C2×C3×C4—122no—
203C2×C3×C4—122no—
204#67—41no—
205#67—41no—
206#67—122no—
207C2×Dic3—21no—
208C2×Dic3—21no—
209C2×Dic3—21no—
210C2×Dic3—24no—
211C2×Dic3—42no—
212C2×Dic3—42no—
213C2×Dic3—61no—
214C2×Dic3—61no—
215C2×Dic3—61no—
216C2×Dic3—61no—
217C2×Dic3—61no—
218C2×Dic3—61no—
219C2×Dic3—61no—
220C2×Dic3—61no—
221C2×Dic3—64no—
222C2×Dic3—122no—
223C2×Dic3—122no—
224C2×Dic3—122no—
225C2×Dic3—122no—
226C4×D3—122no—
227Dic6—122no—
228C2×C32—21no—
229C2×C32—21no—
230C2×C32#41011yescharacteristic
231C2×C32#41711yescharacteristic
232C2×C32C2×#10411yescharacteristic
233C3×D3—81no—
234C2×Q8—91no—
235C2×D4—61no—
236C2×D4—91no—
237C22×C4—62no—
238C22×C4—91no—
239C22×C4—91no—
240C22×C4—181no—
241C22×C4GO+(4,𝔽2)11yescharacteristic
242C2×C8—182no—
243C4⋊C4—61no—
244C4⋊C4—61no—
245C4⋊C4—91no—
246C4⋊C4—91no—
247C4⋊C4—181no—
248C4⋊C4—181no—
249C4⋊C4—184no—
250C22⋊C4—61no—
251C22⋊C4—61no—
252C22⋊C4—61no—
253C22⋊C4—181no—
254C22⋊C4—181no—
255C42—91no—
256C42—91no—
257C42—91no—
258C42—91no—
259C42—122no—
260C42—181no—
261C22×C3—22no—
262C22×C3—22no—
263C22×C3—21no—
264C22×C3—21no—
265C22×C3—21no—
266C22×C3—21no—
267C22×C3—21no—
268C22×C3—21no—
269C22×C3—41no—
270C22×C3—41no—
271C22×C3—121no—
272C22×C3—121no—
273C22×C3—121no—
274C2×D3—41no—
275C2×D3—41no—
276C2×D3—41no—
277C3×C4—22no—
278C3×C4—22no—
279C3×C4—41no—
280C3×C4—41no—
281C3×C4—121no—
282C3×C4—121no—
283C3×C4—124no—
284C3×C4—121no—
285Dic3—41no—
286Dic3—44no—
287Dic3—41no—
288Dic3—41no—
289Dic3—62no—
290Dic3—62no—
291Dic3—62no—
292Dic3—62no—
293Dic3—121no—
294Dic3—121no—
295Dic3—121no—
296Dic3—121no—
297C32#150911yescharacteristic, complemented, Sylow
298C23—61no—
299C23C2×GO+(4,𝔽2)11yescharacteristic
300Q8—361no—
301D4—121no—
302D4—121no—
303D4—361no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—64no—
307C2×C4—61no—
308C2×C4—61no—
309C2×C4—61no—
310C2×C4—91no—
311C2×C4—91no—
312C2×C4—91no—
313C2×C4—91no—
314C2×C4—122no—
315C2×C4—122no—
316C2×C4—182no—
317C2×C4—362no—
318C2×C4—361no—
319C2×C4D32⋊C411yescharacteristic
320C2×C4D32⋊C411yescharacteristic
321C8—362no—
322C2×C3—22no—
323C2×C3—22no—
324C2×C3—21no—
325C2×C3—21no—
326C2×C3—21no—
327C2×C3—21no—
328C2×C3—21no—
329C2×C3—21no—
330C2×C3—41no—
331C2×C3—41no—
332C2×C3—241no—
333D3—81no—
334C22—21no—
335C22—21no—
336C22—121no—
337C22—121no—
338C22—121no—
339C22C2×D32⋊C411yescharacteristic
340C22#6423611yescharacteristic
341C22#6423911yescharacteristic
342C4—21no—
343C4—21no—
344C4—92no—
345C4—124no—
346C4—121no—
347C4—121no—
348C4—121no—
349C4—181no—
350C4—181no—
351C4—181no—
352C3—21no—
353C3—21no—
354C2—21no—
355C2—21no—
356C2—241no—
357C2#1059334511yescharacteristic
358C2#1059338011yescharacteristic
359C2#1059349611yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC23C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radical#63980C22
cosocleC22×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1509
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. #10593804C2semidirect
3. C4×#3724C2semidirect
4. #10590072C2semidirect
13. #63915C4semidirect
14. #63902C4semidirect
16. #63870C4semidirect
18. #63838C4semidirect
297. C32#1509semidirect

Maximal subgroups

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

subgroupindex
#105949632
#105938042
C4×#37242
#105900722
#105900712
#15099