Finite Group Databasebeta

← #11778571

Subgroups — #11778571

Order 1152.

476 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 45 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#10595044C211yesmaximal, characteristic
2#10593492C212yesmaximal, complemented
3#10591215C211yesmaximal, characteristic, complemented
4#10590202C211yesmaximal, characteristic, complemented
5#10590071C212yesmaximal, complemented
6C2×C3×#235—21no—
7C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
8C2×C3×Dic3⋊C4—21no—
9#63980—21no—
10#63980C2212yes—
11C2×#3724C2211yescharacteristic
12#63908—22no—
13#63856—22no—
14C22⋊#622C2212yes—
15#63743—22no—
16#63739—22no—
17#63579—21no—
18#63579C2211yescharacteristic
19#5833—61no—
20#4982—61no—
21C22×C32×C4D411yescharacteristic
22C22×C3⋊Dic3D411yescharacteristic
23C22×C3⋊Dic3C2311yescharacteristic
24C2×C3×#67—22no—
25C22×C3×Dic3—21no—
26C22×C3×Dic3—21no—
27C3×#235—42no—
28C3×#235—42no—
29C2×C3×D12—21no—
30C2×C3×C4×D3—22no—
31C2×C3×Dic6—21no—
32C2×#625—21no—
33C2×#625D412yes—
34C2×#622—22no—
35C4⋊(C3⋊Dic3)—22no—
36C3×Dic3⋊C4—42no—
37#3724—21no—
38#3724—22no—
39#3724D412yes—
40(C2×D3)⋊Dic3—22no—
41(C2×D3)⋊Dic3—22no—
42#1610—91nomaximal, Sylow
43C2×C3×#41—61no—
44C2×#235—21no—
45C2×C3×C4⋊C4—61no—
46#946—62no—
47#939—62no—
48#939—62no—
49#938—62no—
50#930—62no—
51C2×C4⋊Dic3—61no—
52C2×C4⋊Dic3—61no—
53#924—62no—
54C2×Dic3⋊C4—21no—
55C2×Dic3⋊C4—61no—
56C3⋊#95—61no—
57C3⋊#95—61no—
58C3⋊#95—61no—
59C23×C32C2×D411yescharacteristic
60C22×C3×D3—22no—
61C2×C32×C4—21no—
62C2×C32×C4—21no—
63C2×C32×C4D812yes—
64C2×C3⋊Dic3—21no—
65C2×C3⋊Dic3—41no—
66C2×C3⋊Dic3—41no—
67C2×C3⋊Dic3C2×D412yes—
68C3×#67—42no—
69C3×#67—42no—
70C2×C3×Dic3—22no—
71C2×C3×Dic3—22no—
72C2×C3×Dic3—41no—
73C2×C3×Dic3—41no—
74C2×C3×Dic3—41no—
75C2×C3×Dic3—41no—
76C2×C3×Dic3—41no—
77C3×D12—42no—
78C3×C4×D3—44no—
79C3×Dic6—42no—
80#625—42no—
81#625—81no—
82#622—42no—
83#537—91no—
84#480—92no—
85#398—91no—
86#327—92no—
87#324—91no—
88C3×#41—122no—
89C3×#41—122no—
90C2×C3×Q8—61no—
91C2×C3×D4—61no—
92C2×C3×D4—62no—
93C22×C3×C4—21no—
94C22×C3×C4—21no—
95C22×C3×C4—62no—
96C22×C3×C4—61no—
97C22×C3×C4—61no—
98C2×#67—22no—
99C2×#67—62no—
100C2×#67—62no—
101C22×Dic3—21no—
102C22×Dic3—21no—
103C22×Dic3—61no—
104C22×Dic3—61no—
105C22×Dic3—61no—
106C22×Dic3—61no—
107#235—42no—
108#235—42no—
109C2×D12—21no—
110C2×C4×D3—22no—
111C2×Dic6—21no—
112C3×C4⋊C4—122no—
113#217—62no—
114#217—62no—
115(C2×D3)⋊C4—62no—
116(C2×D3)⋊C4—62no—
117C4⋊Dic3—62no—
118C4⋊Dic3—62no—
119C4⋊Dic3—122no—
120Dic3⋊C4—42no—
121Dic3⋊C4—62no—
122Dic3⋊C4—62no—
123Dic3⋊C4—122no—
124C22×C32—21no—
125C22×C32—21no—
126C22×C32#12011yescharacteristic
127C22×C32C2×D811yescharacteristic
128C22×C32AGL(1,ℤ/8)11yescharacteristic
129C2×C3×D3—42no—
130C2×C3×D3—42no—
131C2×C3×D3—42no—
132C32×C4—22no—
133C3⋊Dic3—22no—
134C3⋊Dic3—41no—
135C3×Dic3—42no—
136C3×Dic3—42no—
137C3×Dic3—81no—
138C2×#41—61no—
139C22⋊Q8—182no—
140#121—92no—
141#121—182no—
142#121—181no—
143C2×C4⋊C4—61no—
144C2×C4⋊C4—91no—
145C2×C4⋊C4—91no—
146#107—182no—
147#102—182no—
148C22⋊C8—92no—
149#95—91no—
150#95—181no—
151C23×C3—21no—
152C23×C3—21no—
153C23×C3—62no—
154C22×D3—22no—
155C3×Q8—122no—
156C3×D4—122no—
157C3×D4—122no—
158C3×D4—122no—
159C2×C3×C4—21no—
160C2×C3×C4—21no—
161C2×C3×C4—22no—
162C2×C3×C4—22no—
163C2×C3×C4—22no—
164C2×C3×C4—41no—
165C2×C3×C4—41no—
166C2×C3×C4—62no—
167C2×C3×C4—62no—
168C2×C3×C4—124no—
169C2×C3×C4—121no—
170C2×C3×C4—121no—
171C2×C3×C4—121no—
172C2×C3×C4—121no—
173C2×C3×C4—121no—
174#67—42no—
175#67—42no—
176#67—242no—
177#67—242no—
178C2×Dic3—22no—
179C2×Dic3—22no—
180C2×Dic3—41no—
181C2×Dic3—41no—
182C2×Dic3—41no—
183C2×Dic3—41no—
184C2×Dic3—41no—
185C2×Dic3—62no—
186C2×Dic3—62no—
187C2×Dic3—62no—
188C2×Dic3—121no—
189C2×Dic3—121no—
190C2×Dic3—121no—
191C2×Dic3—121no—
192C2×Dic3—121no—
193C2×Dic3—241no—
194C2×Dic3—241no—
195D12—42no—
196C4×D3—44no—
197Dic6—42no—
198C2×C32—21no—
199C2×C32—21no—
200C2×C32#44711yescharacteristic
201C2×C32#45611yescharacteristic
202C2×C32#45811yescharacteristic
203C3×D3—82no—
204#41—122no—
205#41—122no—
206C2×Q8—61no—
207C2×D4—61no—
208C2×D4—62no—
209C2×D4—92no—
210C2×D4—181no—
211C22×C4—62no—
212C22×C4—61no—
213C22×C4—61no—
214C22×C4—91no—
215C22×C4—91no—
216C22×C4GO+(4,𝔽2)11yescharacteristic
217C2×C8—182no—
218C4⋊C4—92no—
219C4⋊C4—122no—
220C4⋊C4—182no—
221C4⋊C4—181no—
222C4⋊C4—182no—
223C22⋊C4—182no—
224C22⋊C4—182no—
225C22×C3—21no—
226C22×C3—21no—
227C22×C3—21no—
228C22×C3—21no—
229C22×C3—21no—
230C22×C3—21no—
231C22×C3—21no—
232C22×C3—21no—
233C22×C3—21no—
234C22×C3—21no—
235C22×C3—41no—
236C22×C3—41no—
237C22×C3—122no—
238C22×C3—122no—
239C22×C3—122no—
240C2×D3—42no—
241C2×D3—42no—
242C2×D3—42no—
243C3×C4—22no—
244C3×C4—22no—
245C3×C4—42no—
246C3×C4—122no—
247C3×C4—122no—
248C3×C4—241no—
249Dic3—42no—
250Dic3—42no—
251Dic3—81no—
252Dic3—122no—
253Dic3—122no—
254Dic3—122no—
255Dic3—241no—
256C32#161011yescharacteristic, complemented, Sylow
257C23—62no—
258C23C2×GO+(4,𝔽2)11yescharacteristic
259Q8—122no—
260D4—122no—
261D4—122no—
262D4—122no—
263D4—362no—
264D4—721no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—62no—
268C2×C4—62no—
269C2×C4—92no—
270C2×C4—124no—
271C2×C4—121no—
272C2×C4—121no—
273C2×C4—121no—
274C2×C4—121no—
275C2×C4—121no—
276C2×C4—181no—
277C2×C4—361no—
278C2×C4—361no—
279C2×C4#377412yes—
280C8—362no—
281C2×C3—21no—
282C2×C3—21no—
283C2×C3—21no—
284C2×C3—21no—
285C2×C3—21no—
286C2×C3—21no—
287C2×C3—21no—
288C2×C3—21no—
289C2×C3—21no—
290C2×C3—21no—
291C2×C3—41no—
292C2×C3—41no—
293C2×C3—242no—
294D3—82no—
295C22—21no—
296C22—21no—
297C22—122no—
298C22—122no—
299C22—122no—
300C22C2×#377411yescharacteristic
301C22#6423611yescharacteristic
302C22#6424111yescharacteristic
303C4—22no—
304C4—122no—
305C4—122no—
306C4—182no—
307C4—241no—
308C4—361no—
309C3—21no—
310C3—21no—
311C2—21no—
312C2—21no—
313C2—242no—
314C2#1059341511yescharacteristic
315C2#1059345211yescharacteristic
316C2#1059351911yescharacteristic
subgroupG/H
centerC22#64241
commutator, cosocleC22×C3⋊Dic3C23
FrattiniC23C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32#120
prime radical#10595044C2
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1610
LCSG ▷ C22×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. #10593492C2semidirect
3. #10591215C2semidirect
4. #10590202C2semidirect
5. #10590071C2semidirect
256. C32#1610semidirect

Maximal subgroups

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

subgroupindex
#105950442
#105934922
#105912152
#105902022
#105900712
#16109