Finite Group Databasebeta

← #11774752

Subgroups — #11774752

Order 1152.

512 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 69 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#10594929C211yesmaximal, characteristic
2#10593805C211yesmaximal, characteristic, complemented
3C2×#63553C211yesmaximal, characteristic, complemented
4#10590030C214yesmaximal, complemented
5C2×#3805—21no—
6C2×#3792—21no—
7C2×C4×C3⋊Dic3C2211yescharacteristic
8C3×#930—21no—
9C22×C3×C3⋊C8—21no—
10#63980C412yes—
11#63919C411yescharacteristic
12#63915—21no—
13#63914C411yescharacteristic
14#63902C2212yes—
15#63898—21no—
16#63779C2212yes—
17C4⋊#622—21no—
18#63553—21no—
19#63553C2212yes—
20#5596—61no—
21C2×C8×Dic3—61no—
22C22×C32×C4D411yescharacteristic
23C22×C3⋊Dic3C2×C411yescharacteristic
24C22×C3⋊Dic3D411yescharacteristic
25C2×C3×#67—22no—
26C2×C3×D12—21no—
27C2×#627—21no—
28C2×#625—21no—
29C2×#625C2×C412yes—
30#3805—42no—
31#3805—42no—
32C2×D3×Dic3—22no—
33#3792—42no—
34C2×#622—22no—
35C4×C3⋊Dic3C2×C411yescharacteristic
36C4×C3⋊Dic3D411yescharacteristic
37C4×C3⋊Dic3D411yescharacteristic
38C4×C3⋊Dic3C2311yescharacteristic
39C3×(C2×D3)⋊C4—22no—
40C3×C4⋊Dic3—21no—
41C2×C3×C3⋊C8—24no—
42C2×C3×C3⋊C8—22no—
43#3724C2×C412yes—
44(C2×D3)⋊Dic3—22no—
45#1492—91nomaximal, Sylow
46C2×#237—62no—
47C22×C3×C8—61no—
48C3×#121—61no—
49#940—61no—
50#939—62no—
51D4×Dic3—61no—
52#930—21no—
53C2×C4×Dic3—61no—
54C2×C4×Dic3—61no—
55C22×C3⋊C8—21no—
56#893—61no—
57#888—61no—
58#885—62no—
59#67⋊C4—62no—
60C8×Dic3—62no—
61C8×Dic3—62no—
62C23×C32C22⋊C411yescharacteristic
63C22×C3×D3—22no—
64C2×C32×C4—22no—
65C2×C32×C4C22⋊C411yescharacteristic
66C2×C32×C4C2×D411yescharacteristic
67C2×C3⋊Dic3—22no—
68C2×C3⋊Dic3C22⋊C411yescharacteristic
69C2×C3⋊Dic3C22⋊C411yescharacteristic
70C2×C3⋊Dic3D812yes—
71C2×C3⋊Dic3SD1612yes—
72C2×C3⋊Dic3C22×C411yescharacteristic
73C2×C3⋊Dic3C2×D411yescharacteristic
74C3×#67—44no—
75C2×C3×Dic3—22no—
76C3×D12—42no—
77#627—42no—
78#625—24no—
79#625—42no—
80D3×Dic3—42no—
81D3×Dic3—42no—
82#622—42no—
83C3×C3⋊C8—24no—
84#532—91no—
85#423—91no—
86C2×C4×C8—91no—
87D4⋊C8—94no—
88C2×C3×D4—61no—
89C2×C3×D4—62no—
90C22×C3×C4—21no—
91C22×C3×C4—21no—
92C2×#67—22no—
93C2×#67—62no—
94C2×#67—62no—
95C22×Dic3—61no—
96C22×Dic3—61no—
97C22×Dic3—61no—
98C22×Dic3—61no—
99C22×Dic3—62no—
100#237—124no—
101#237—124no—
102C2×D12—21no—
103C2×C4×D3—62no—
104C2×Dic6—62no—
105C2×C3×C8—62no—
106C2×C3×C8—64no—
107C3×C4⋊C4—61no—
108C3×C22⋊C4—62no—
109#217—62no—
110(C2×D3)⋊C4—22no—
111(C2×D3)⋊C4—62no—
112C4⋊Dic3—21no—
113Dic3⋊C4—62no—
114C4×Dic3—61no—
115C4×Dic3—61no—
116C4×Dic3—61no—
117C4×Dic3—61no—
118C4×Dic3—61no—
119C4×Dic3—61no—
120C4×Dic3—61no—
121C4×Dic3—61no—
122C2×C3⋊C8—22no—
123C2×C3⋊C8—24no—
124C22×C32—21no—
125C22×C32—21no—
126C22×C32#10212yes—
127C22×C32C2×C22⋊C411yescharacteristic
128C2×C3×D3—42no—
129C2×C3×D3—42no—
130C2×C3×D3—42no—
131C32×C4—21no—
132C32×C4#10412yes—
133C3⋊Dic3—21no—
134C3⋊Dic3#10212yes—
135C3⋊Dic3#13112yes—
136C3⋊Dic3C2×D811yescharacteristic
137C3⋊Dic3C2×SD1611yescharacteristic
138C3×Dic3—42no—
139C2×#41—181no—
140C2×M16—181no—
141C22×C8—61no—
142C4⋊Q8—91no—
143#127—91no—
144#124—181no—
145#121—61no—
146#121—92no—
147C4×D4—92no—
148C4×D4—181no—
149C2×C42—91no—
150C4⋊C8—92no—
151C4⋊C8—181no—
152C4×C8—92no—
153C4×C8—181no—
154C23×C3—21no—
155C23×C3—21no—
156C23×C3—62no—
157C22×D3—22no—
158C3×D4—122no—
159C3×D4—124no—
160C2×C3×C4—22no—
161C2×C3×C4—22no—
162C2×C3×C4—21no—
163C2×C3×C4—21no—
164C2×C3×C4—21no—
165C2×C3×C4—21no—
166C2×C3×C4—42no—
167C2×C3×C4—62no—
168#67—44no—
169#67—124no—
170#67—124no—
171C2×Dic3—22no—
172C2×Dic3—61no—
173C2×Dic3—61no—
174C2×Dic3—61no—
175C2×Dic3—62no—
176C2×Dic3—62no—
177C2×Dic3—62no—
178C2×Dic3—62no—
179C2×Dic3—61no—
180C2×Dic3—61no—
181C2×Dic3—61no—
182C2×Dic3—61no—
183C2×Dic3—61no—
184C2×Dic3—64no—
185C2×Dic3—122no—
186C2×Dic3—122no—
187C2×Dic3—122no—
188D12—42no—
189C4×D3—122no—
190C4×D3—122no—
191Dic6—124no—
192C3×C8—64no—
193C3⋊C8—24no—
194C2×C32—22no—
195C2×C32#40811yescharacteristic
196C2×C32C2×#10211yescharacteristic
197C2×C32C2×#10411yescharacteristic
198C3×D3—82no—
199#41—362no—
200#41—362no—
201C2×Q8—181no—
202C2×D4—62no—
203C2×D4—61no—
204C2×D4—92no—
205C2×D4—181no—
206C22×C4—91no—
207C22×C4—91no—
208C22×C4—182no—
209C22×C4GO+(4,𝔽2)11yescharacteristic
210M16—362no—
211C2×C8—64no—
212C2×C8—62no—
213C2×C8—182no—
214C4⋊C4—61no—
215C4⋊C4—92no—
216C22⋊C4—62no—
217C22⋊C4—182no—
218C42—91no—
219C42—91no—
220C42—91no—
221C42—91no—
222C22×C3—22no—
223C22×C3—22no—
224C22×C3—21no—
225C22×C3—21no—
226C22×C3—22no—
227C22×C3—22no—
228C22×C3—41no—
229C22×C3—41no—
230C22×C3—122no—
231C22×C3—122no—
232C22×C3—122no—
233C2×D3—42no—
234C2×D3—42no—
235C2×D3—42no—
236C3×C4—21no—
237C3×C4—21no—
238C3×C4—22no—
239C3×C4—22no—
240C3×C4—41no—
241C3×C4—122no—
242Dic3—42no—
243Dic3—62no—
244Dic3—61no—
245Dic3—61no—
246Dic3—62no—
247Dic3—62no—
248Dic3—61no—
249Dic3—61no—
250Dic3—62no—
251Dic3—62no—
252Dic3—121no—
253C32#149211yescharacteristic, complemented, Sylow
254C23—62no—
255C23D32⋊C411yescharacteristic
256Q8—362no—
257D4—124no—
258D4—122no—
259D4—184no—
260D4—362no—
261C2×C4—22no—
262C2×C4—62no—
263C2×C4—91no—
264C2×C4—91no—
265C2×C4—91no—
266C2×C4—92no—
267C2×C4—92no—
268C2×C4—91no—
269C2×C4—182no—
270C2×C4—362no—
271C2×C4—362no—
272C2×C4D32⋊C411yescharacteristic
273C2×C4C2×GO+(4,𝔽2)11yescharacteristic
274C8—64no—
275C8—362no—
276C2×C3—24no—
277C2×C3—21no—
278C2×C3—21no—
279C2×C3—21no—
280C2×C3—21no—
281C2×C3—21no—
282C2×C3—21no—
283C2×C3—42no—
284C2×C3—242no—
285D3—82no—
286C22—21no—
287C22—21no—
288C22—122no—
289C22—122no—
290C22—122no—
291C22#6372912yes—
292C22C2×D32⋊C411yescharacteristic
293C4—21no—
294C4—92no—
295C4—91no—
296C4—91no—
297C4—92no—
298C4—122no—
299C4—181no—
300C4#6374112yes—
301C3—21no—
302C3—21no—
303C2—22no—
304C2—242no—
305C2#1059330811yescharacteristic
306C2C2×#6372911yescharacteristic
307C2C2×#6374111yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radical#10594929C2
cosocleC4×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1492
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. #10593805C2semidirect
3. C2×#63553C2semidirect
4. #10590030C2semidirect
253. C32#1492semidirect

Maximal subgroups

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

subgroupindex
#105949292
#105938052
C2×#635532
#105900302
#14929