Finite Group Databasebeta

← #11774343

Subgroups — #11774343

Order 1152.

645 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 645 conjugacy classes of subgroups — too many to draw. Only its 122 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
1C4×Q8×C3⋊D3C211yesmaximal, characteristic
2#10590297C211yesmaximal, characteristic
3#10590256C211yesmaximal, characteristic
4C3×#4535C212yesmaximal, complemented
5#10589085C212yesmaximal, complemented
6#68231—32nomaximal
7C2×Q8×C3⋊D3C411yescharacteristic
8C32×C4×Q8C2211yescharacteristic
9Q8×C3⋊Dic3C411yescharacteristic
10C4⋊C4×C3⋊D3—21no—
11C4⋊C4×C3⋊D3C411yescharacteristic
12#64096—21no—
13#64096C411yescharacteristic
14C42×C3⋊D3—21no—
15C42×C3⋊D3C2211yescharacteristic
16C4×#634—21no—
17C4×#634C2211yescharacteristic
18C3×C4⋊(C3⋊C8)C2212yes—
19C3×C4×C3⋊C8C2212yes—
20#63572—21no—
21#63557—21no—
22#63557—21no—
23#63553—21no—
24C4×D3×Q8—32no—
25C4×D3×Q8—61no—
26#4833—32no—
27#4685—32no—
28C3×Q8⋊C8—32no—
29#4535D312yescomplemented
30#4484—32no—
31#4456—32no—
32C2×C32×Q8C2×C411yescharacteristic
33Q8×C3⋊D3—22no—
34Q8×C3⋊D3C814yescomplemented
35C2×C4×C3⋊D3—21no—
36C2×C4×C3⋊D3—21no—
37C2×C4×C3⋊D3C2×C411yescharacteristic
38C2×C4×C3⋊D3D411yescharacteristic
39C2×C4×C3⋊D3D411yescharacteristic
40C2×#634—21no—
41C2×#634C2×C411yescharacteristic
42C32×C4⋊C4—21no—
43C32×C4⋊C4C2×C411yescharacteristic
44C32×C42—21no—
45C32×C42C2311yescharacteristic
46C4⋊(C3⋊Dic3)—21no—
47C4⋊(C3⋊Dic3)C2×C411yescharacteristic
48#3750—21no—
49#3750—21no—
50#3750—21no—
51C4×C3⋊Dic3—21no—
52C4×C3⋊Dic3—21no—
53C4×C3⋊Dic3—21no—
54C4×C3⋊Dic3C2×C411yescharacteristic
55C4×C3⋊Dic3D411yescharacteristic
56C4×C3⋊Dic3D411yescharacteristic
57C2×C3×C3⋊C8—22no—
58C2×C3×C3⋊C8—22no—
59#1479—91noSylow
60C2×D3×Q8—32no—
61C2×D3×Q8—61no—
62C3×C4×Q8—21no—
63C3×C4×Q8C2×D312yes—
64Q8×Dic3—32no—
65Q8×Dic3—61no—
66D3×C4⋊C4—32no—
67D3×C4⋊C4—61no—
68D3×C4⋊C4—62no—
69D3×C4⋊C4—62no—
70#887—32no—
71#887—61no—
72#887—62no—
73#887—62no—
74C42×D3—32no—
75C42×D3—61no—
76C42×D3—62no—
77C42×D3—62no—
78C4×Dic6—32no—
79C4×Dic6—61no—
80C4×Dic6—62no—
81C4×Dic6—62no—
82C3×C4⋊C8—32no—
83C3×C4×C8—32no—
84(C2×D3)⋊C8—62no—
85(C2×D3)⋊C8—62no—
86Dic3⋊C8—62no—
87C8×Dic3—62no—
88C4⋊(C3⋊C8)C2×D312yes—
89C4×C3⋊C8C2×D312yes—
90C22×C3⋊D3C22⋊C411yescharacteristic
91C32×Q8—21no—
92C32×Q8C2×C812yes—
93C2×C32×C4—21no—
94C2×C32×C4—21no—
95C2×C32×C4C22×C411yescharacteristic
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4C2×D411yescharacteristic
98C2×C3⋊Dic3—21no—
99C2×C3⋊Dic3—21no—
100C2×C3⋊Dic3C22⋊C411yescharacteristic
101C2×C3⋊Dic3C22⋊C411yescharacteristic
102C2×C3⋊Dic3C22⋊C411yescharacteristic
103C4×C3⋊D3—24no—
104C4×C3⋊D3—22no—
105C4×C3⋊D3—41no—
106C4×C3⋊D3—42no—
107C4×C3⋊D3C2×C812yes—
108C4×C3⋊D3M1612yes—
109#634—21no—
110#634—24no—
111#634C2×C812yes—
112C3×C3⋊C8—42no—
113C3×C3⋊C8—42no—
114C2×C4×Q8—91no—
115#431—91no—
116#431—91no—
117Q8⋊C8—32no—
118Q8⋊C8—92no—
119C2×C3×Q8—21no—
120C2×C3×Q8C4×D312yes—
121D3×Q8—38no—
122D3×Q8—64no—
123D3×Q8—64no—
124D3×Q8—64no—
125C2×C4×D3—32no—
126C2×C4×D3—32no—
127C2×C4×D3—32no—
128C2×C4×D3—61no—
129C2×C4×D3—61no—
130C2×C4×D3—61no—
131C2×C4×D3—62no—
132C2×C4×D3—62no—
133C2×C4×D3—62no—
134C2×C4×D3—62no—
135C2×Dic6—32no—
136C2×Dic6—61no—
137C2×Dic6—62no—
138C2×Dic6—62no—
139C2×C3×C8—62no—
140C2×C3×C8—62no—
141C3×C4⋊C4—22no—
142C3×C4⋊C4—22no—
143C3×C4⋊C4—21no—
144C3×C4⋊C4C4×D312yes—
145C3×C42—22no—
146C3×C42—22no—
147C3×C42—21no—
148C3×C42C22×D312yes—
149C4⋊Dic3—32no—
150C4⋊Dic3—61no—
151C4⋊Dic3—62no—
152C4⋊Dic3—62no—
153Dic3⋊C4—62no—
154Dic3⋊C4—62no—
155Dic3⋊C4—62no—
156Dic3⋊C4—62no—
157Dic3⋊C4—62no—
158Dic3⋊C4—62no—
159C4×Dic3—32no—
160C4×Dic3—32no—
161C4×Dic3—32no—
162C4×Dic3—61no—
163C4×Dic3—61no—
164C4×Dic3—61no—
165C4×Dic3—62no—
166C4×Dic3—62no—
167C4×Dic3—62no—
168C4×Dic3—62no—
169C4×Dic3—62no—
170C4×Dic3—62no—
171C2×C3⋊C8—22no—
172C2×C3⋊C8—22no—
173C22×C32C2×C22⋊C411yescharacteristic
174C2×C3⋊D3—21no—
175C2×C3⋊D3—21no—
176C2×C3⋊D3C22⋊C812yes—
177C32×C4—22no—
178C32×C4—21no—
179C32×C4—41no—
180C32×C4C22×C811yescharacteristic
181C32×C4C2×M1611yescharacteristic
182C32×C4#13712yes—
183C3⋊Dic3—22no—
184C3⋊Dic3—21no—
185C3⋊Dic3—21no—
186C3⋊Dic3—41no—
187C3⋊Dic3C22⋊C812yes—
188C22×Q8—91no—
189C4×Q8—91no—
190C4×Q8—91no—
191C4×Q8—91no—
192C4×Q8—181no—
193C4×Q8—181no—
194C4×Q8D3211yescharacteristic
195C2×C4⋊C4—91no—
196C2×C4⋊C4—181no—
197C2×C42—91no—
198C2×C42—181no—
199C4⋊C8—32no—
200C4⋊C8—181no—
201C22⋊C8—181no—
202C22⋊C8—181no—
203C4×C8—32no—
204C4×C8—181no—
205C22×D3—32no—
206C22×D3—61no—
207C3×Q8—22no—
208C3×Q8—22no—
209C3×Q8—22no—
210C3×Q8D3×C814yes—
211C2×C3×C4—22no—
212C2×C3×C4—22no—
213C2×C3×C4—22no—
214C2×C3×C4—22no—
215C2×C3×C4—21no—
216C2×C3×C4—21no—
217C2×C3×C4—21no—
218C2×C3×C4C2×C4×D312yes—
219C2×C3×C4D3×D412yes—
220C2×C3×C4D3×D412yes—
221C2×Dic3—32no—
222C2×Dic3—32no—
223C2×Dic3—32no—
224C2×Dic3—61no—
225C2×Dic3—61no—
226C2×Dic3—61no—
227C2×Dic3—62no—
228C2×Dic3—62no—
229C2×Dic3—62no—
230C2×Dic3—62no—
231C4×D3—34no—
232C4×D3—34no—
233C4×D3—62no—
234C4×D3—62no—
235C4×D3—68no—
236C4×D3—64no—
237C4×D3—68no—
238C4×D3—62no—
239C4×D3—62no—
240C4×D3—122no—
241C4×D3—122no—
242C4×D3—124no—
243C4×D3—124no—
244Dic6—34no—
245Dic6—62no—
246Dic6—68no—
247Dic6—68no—
248Dic6—62no—
249Dic6—62no—
250C3×C8—122no—
251C3×C8—122no—
252C3⋊C8—42no—
253C3⋊C8—42no—
254C2×C32C2×C22⋊C811yescharacteristic
255C2×C32#41911yescharacteristic
256C2×C32#42111yescharacteristic
257C3⋊D3—22no—
258C2×Q8—94no—
259C2×Q8—91no—
260C2×Q8—181no—
261C2×Q8—182no—
262C2×Q8#62411yescharacteristic
263C22×C4—91no—
264C22×C4—91no—
265C22×C4—91no—
266C22×C4—181no—
267C22×C4—181no—
268C2×C8—62no—
269C2×C8—62no—
270C4⋊C4—21no—
271C4⋊C4—91no—
272C4⋊C4—181no—
273C4⋊C4—181no—
274C4⋊C4—181no—
275C4⋊C4—181no—
276C4⋊C4#62411yescharacteristic
277C42—21no—
278C42—91no—
279C42—91no—
280C42—91no—
281C42—181no—
282C42—181no—
283C42—181no—
284C42C2×D3211yescharacteristic
285C22×C3—21no—
286C22×C3D3×C22⋊C412yes—
287C2×D3—34no—
288C2×D3—62no—
289C2×D3—62no—
290C2×D3—62no—
291C2×D3—62no—
292C2×D3—62no—
293C3×C4—24no—
294C3×C4—24no—
295C3×C4—22no—
296C3×C4—21no—
297C3×C4—21no—
298C3×C4—22no—
299C3×C4—41no—
300C3×C4—42no—
301C3×C4—42no—
302C3×C4C2×D3×C812yes—
303C3×C4D3×M1612yes—
304C3×C4#91512yes—
305C3×C4#91812yes—
306Dic3—34no—
307Dic3—62no—
308Dic3—64no—
309Dic3—62no—
310Dic3—64no—
311Dic3—62no—
312Dic3—62no—
313Dic3—121no—
314Dic3—122no—
315Dic3—122no—
316C32#147911yescharacteristic, complemented, Sylow
317C23—91no—
318Q8—21no—
319Q8—92no—
320Q8—184no—
321Q8—181no—
322Q8#371012yes—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—91no—
326C2×C4—92no—
327C2×C4—92no—
328C2×C4—91no—
329C2×C4—91no—
330C2×C4—184no—
331C2×C4—181no—
332C2×C4—182no—
333C2×C4—181no—
334C2×C4—361no—
335C2×C4—362no—
336C2×C4C2×#62411yescharacteristic
337C2×C4#381111yescharacteristic
338C2×C4#381111yescharacteristic
339C8—122no—
340C8—122no—
341C2×C3—21no—
342C2×C3—21no—
343C2×C3—21no—
344C2×C3D3×C22⋊C812yes—
345C2×C3#480212yes—
346C2×C3#482112yes—
347D3—64no—
348D3—64no—
349C22—92no—
350C22—181no—
351C22—181no—
352C22#6397411yescharacteristic
353C4—22no—
354C4—21no—
355C4—41no—
356C4—92no—
357C4—181no—
358C4—182no—
359C4—181no—
360C4—361no—
361C4C2×#371011yescharacteristic
362C4#6381811yescharacteristic
363C4#6395112yes—
364C3—21no—
365C3#6823112yescomplemented
366C2—182no—
367C2#1059115211yescharacteristic
368C2#1059156211yescharacteristic
369C2#1059167211yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC32×C4C22×C8
FrattiniC42C2×D32
FittingC32×C4×Q8C22
socleC22×C32C2×C22⋊C4
prime radicalC22×C3⋊D3C22⋊C4
cosocleC32×C42C23
hypercenterC4×Q8D32
hypocenterC32#1479
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
4. C3×#4535C2semidirect
5. #10589085C2semidirect
29. #4535D3semidirect
34. Q8×C3⋊D3C8semidirect
316. C32#1479semidirect
365. C3#68231semidirect

Maximal subgroups

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

subgroupindex
C4×Q8×C3⋊D32
#105902972
#105902562
C3×#45352
#105890852
#682313