Finite Group Databasebeta

← #11773476

Subgroups — #11773476

Order 1152.

894 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 894 conjugacy classes of subgroups — too many to draw. Only its 127 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×#63900C211yesmaximal, characteristic
2C2×#63781C211yesmaximal, characteristic
3C2×#63737C214yesmaximal
4#10591370C211yesmaximal, characteristic
5C23×#157C2212yes—
6C22×C4×C3⋊D3C2211yescharacteristic
7C22×#624C2212yes—
8C22×#624C2212yes—
9C2×C3×C4⋊Dic3—21no—
10C2×#3724—21no—
11#63900—22no—
12#63900C414yescomplemented
13#63781—22no—
14#63737—28no—
15C3×C3⋊#95—21no—
16#63579—21no—
17C2×D3×C4⋊C4—61no—
18D3×#95—61no—
19C23×C3⋊D3C2311yescharacteristic
20C22×#157—22no—
21C22×#157—24no—
22C22×#157—24no—
23C22×#157—22no—
24C22×#157Q814yes—
25C22×C32×C4D411yescharacteristic
26C22×C3⋊Dic3D411yescharacteristic
27C2×C4×C3⋊D3—24no—
28C2×C4×C3⋊D3C2×C412yes—
29C2×C4×C3⋊D3D412yes—
30C22×C3×Dic3—22no—
31C22×C3×Dic3—22no—
32C2×#624—24no—
33C2×#624—24no—
34C2×#624—24no—
35C2×#624—24no—
36C2×#624—22no—
37C2×#624—22no—
38C2×#624C2×C414yes—
39C2×#624D414yes—
40C3×C4⋊Dic3—24no—
41#3724—24no—
42#1445—91nomaximal, Sylow
43C22×C4×D3—61no—
44C22×C4×D3—62no—
45C22×C4×D3—62no—
46C22×C4×D3—61no—
47C2×C3×C4⋊C4—61no—
48C2×C4⋊Dic3—21no—
49C2×Dic3⋊C4—62no—
50D3×C4⋊C4—64no—
51D3×C4⋊C4—64no—
52C3×#95—61no—
53C3⋊#95—21no—
54C3⋊#95—62no—
55C23×C32C2×D411yescharacteristic
56C22×C3⋊D3C22×C411yescharacteristic
57C22×C3⋊D3C2×D412yes—
58C22×C3⋊D3C2×D411yescharacteristic
59C22×C3⋊D3C2×Q812yes—
60C22×C3⋊D3#4114yes—
61C22×C3⋊D3#4112yes—
62C22×C3⋊D3#4112yes—
63C2×#157—28no—
64C2×#157—24no—
65C2×#157—44no—
66C2×#157—42no—
67C2×#157—42no—
68C2×C32×C4—22no—
69C2×C32×C4C22⋊C412yes—
70C2×C3⋊Dic3—22no—
71C2×C3⋊Dic3C22⋊C412yes—
72C4×C3⋊D3—24no—
73C4×C3⋊D3—24no—
74C2×C3×Dic3—24no—
75C2×C3×Dic3—24no—
76C2×C3×Dic3—44no—
77C2×C3×Dic3—42no—
78C2×C3×Dic3—42no—
79#624—28no—
80#624—28no—
81#624—42no—
82#624—44no—
83#624—42no—
84C22×C4⋊C4—91no—
85C2×#95—91no—
86C2×#95—91no—
87C2×#95—94no—
88C23×D3—61no—
89C23×D3—61no—
90C22×C3×C4—21no—
91C22×C3×C4—21no—
92C22×C3×C4—62no—
93C22×C3×C4—62no—
94C22×Dic3—22no—
95C22×Dic3—22no—
96C22×Dic3—61no—
97C22×Dic3—61no—
98C2×C4×D3—62no—
99C2×C4×D3—62no—
100C2×C4×D3—64no—
101C2×C4×D3—64no—
102C2×C4×D3—62no—
103C2×C4×D3—62no—
104C2×C4×D3—68no—
105C2×C4×D3—64no—
106C2×C4×D3—64no—
107C2×C4×D3—124no—
108C2×C4×D3—124no—
109C2×C4×D3—124no—
110C2×C4×D3—124no—
111C2×C4×D3—124no—
112C3×C4⋊C4—64no—
113C4⋊Dic3—24no—
114Dic3⋊C4—68no—
115C22×C32C2×C22⋊C411yescharacteristic
116C22×C32#12112yes—
117C22×C32#12312yes—
118C22×C32#12411yescharacteristic
119C22×C32C4⋊Q811yescharacteristic
120C2×C3⋊D3#11712yes—
121C2×C3⋊D3C4×D412yes—
122C2×C3⋊D3C4×Q812yes—
123C2×C3⋊D3C22⋊Q814yes—
124C2×C3⋊D3C22⋊Q812yes—
125C2×C3⋊D3#12314yes—
126C2×C3⋊D3#12312yes—
127C2×C3⋊D3#12411yescharacteristic
128C2×C3⋊D3#12514yes—
129C2×C3⋊D3#12614yes—
130C2×C3⋊D3#12711yescharacteristic
131#157—44no—
132C32×C4—22no—
133C3⋊Dic3—22no—
134C3×Dic3—44no—
135C3×Dic3—44no—
136C23×C4—92no—
137C23×C4—92no—
138C23×C4—91no—
139C23×C4—92no—
140C2×C4⋊C4—61no—
141C2×C4⋊C4—94no—
142C2×C4⋊C4—182no—
143C2×C4⋊C4—181no—
144#95—61no—
145#95—181no—
146#95—182no—
147#95—188no—
148C23×C3—21no—
149C23×C3—21no—
150C22×D3—61no—
151C22×D3—61no—
152C22×D3—61no—
153C22×D3—62no—
154C22×D3—61no—
155C22×D3—62no—
156C22×D3—62no—
157C22×D3—62no—
158C22×D3—62no—
159C22×D3—64no—
160C22×D3—62no—
161C22×D3—62no—
162C22×D3—64no—
163C22×D3—62no—
164C2×C3×C4—24no—
165C2×C3×C4—22no—
166C2×C3×C4—22no—
167C2×C3×C4—42no—
168C2×C3×C4—64no—
169C2×C3×C4—64no—
170C2×C3×C4—122no—
171C2×C3×C4—124no—
172C2×C3×C4—122no—
173C2×Dic3—24no—
174C2×Dic3—24no—
175C2×Dic3—42no—
176C2×Dic3—44no—
177C2×Dic3—42no—
178C2×Dic3—62no—
179C2×Dic3—62no—
180C2×Dic3—64no—
181C2×Dic3—122no—
182C4×D3—68no—
183C4×D3—68no—
184C4×D3—128no—
185C4×D3—128no—
186C4×D3—124no—
187C4×D3—124no—
188C4×D3—124no—
189C4×D3—124no—
190C4×D3—128no—
191C2×C32#38111yescharacteristic
192C2×C32#39011yescharacteristic
193C2×C32#39111yescharacteristic
194C2×C32#39712yes—
195C2×C32#39812yes—
196C3⋊D3#38714yes—
197C3⋊D3#39912yes—
198C3⋊D3#40012yes—
199C24—91no—
200C22×C4—62no—
201C22×C4—62no—
202C22×C4—94no—
203C22×C4—94no—
204C22×C4—91no—
205C22×C4—92no—
206C22×C4—92no—
207C22×C4—94no—
208C22×C4—184no—
209C22×C4—182no—
210C22×C4—182no—
211C22×C4—184no—
212C22×C4—184no—
213C22×C4—184no—
214C22×C4—184no—
215C22×C4—184no—
216C22×C4—182no—
217C22×C4—182no—
218C22×C4—184no—
219C22×C4GO+(4,𝔽2)11yescharacteristic
220C4⋊C4—64no—
221C4⋊C4—184no—
222C22×C3—21no—
223C22×C3—21no—
224C22×C3—21no—
225C22×C3—21no—
226C22×C3—22no—
227C22×C3—22no—
228C22×C3—21no—
229C22×C3—21no—
230C22×C3—22no—
231C22×C3—22no—
232C2×D3—62no—
233C2×D3—62no—
234C2×D3—62no—
235C2×D3—61no—
236C2×D3—61no—
237C2×D3—62no—
238C2×D3—64no—
239C2×D3—62no—
240C2×D3—64no—
241C2×D3—62no—
242C2×D3—62no—
243C2×D3—62no—
244C2×D3—64no—
245C2×D3—64no—
246C2×D3—62no—
247C2×D3—62no—
248C2×D3—64no—
249C2×D3—61no—
250C2×D3—64no—
251C2×D3—64no—
252C2×D3—64no—
253C2×D3—61no—
254C3×C4—24no—
255C3×C4—42no—
256C3×C4—124no—
257C3×C4—124no—
258Dic3—44no—
259Dic3—44no—
260Dic3—64no—
261Dic3—122no—
262C32#144511yescharacteristic, complemented, Sylow
263C23—92no—
264C23—92no—
265C23—92no—
266C23—92no—
267C23—91no—
268C23—91no—
269C23—94no—
270C23C2×GO+(4,𝔽2)11yescharacteristic
271C2×C4—22no—
272C2×C4—64no—
273C2×C4—64no—
274C2×C4—92no—
275C2×C4—122no—
276C2×C4—124no—
277C2×C4—122no—
278C2×C4—184no—
279C2×C4—184no—
280C2×C4—188no—
281C2×C4—188no—
282C2×C4—182no—
283C2×C4—188no—
284C2×C4—184no—
285C2×C4—364no—
286C2×C4—362no—
287C2×C4—362no—
288C2×C4—364no—
289C2×C4—362no—
290C2×C4—362no—
291C2×C4D32⋊C412yes—
292C2×C3—22no—
293C2×C3—22no—
294C2×C3—21no—
295C2×C3—21no—
296C2×C3—22no—
297C2×C3—22no—
298C2×C3—21no—
299C2×C3—21no—
300C2×C3—21no—
301C2×C3—21no—
302D3—64no—
303D3—64no—
304D3—62no—
305D3—62no—
306D3—62no—
307D3—62no—
308C22—94no—
309C22—94no—
310C22—92no—
311C22—92no—
312C22—94no—
313C22—94no—
314C22—92no—
315C22—91no—
316C22—91no—
317C22—92no—
318C22—92no—
319C22#6422111yescharacteristic
320C22#6422211yescharacteristic
321C22#6423012yes—
322C22C2×D32⋊C411yescharacteristic
323C22#6423312yes—
324C4—22no—
325C4—124no—
326C4—124no—
327C4—182no—
328C4—364no—
329C3—21no—
330C3—21no—
331C2—92no—
332C2—94no—
333C2—92no—
334C2#1059333912yes—
335C2#1059334211yescharacteristic
336C2#1059340412yes—
337C2#1059340511yescharacteristic
338C2#1059348811yescharacteristic
subgroupG/H
center, FrattiniC23C2×GO+(4,𝔽2)
commutatorC22×C3⋊D3C22×C4
FittingC22×C32×C4D4
socleC23×C32C2×D4
prime radical, cosocleC23×C3⋊D3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1445
LCSG ▷ C22×C3⋊D3 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
12. #63900C4semidirect
262. C32#1445semidirect

Maximal subgroups

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

subgroupindex
C2×#639002
C2×#637812
C2×#637372
#105913702
#14459