Finite Group Databasebeta

← #11774716

Subgroups — #11774716

Order 1152.

653 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 653 conjugacy classes of subgroups — too many to draw. Only its 112 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
2C4×#3712C211yesmaximal, characteristic
3#10590260C211yesmaximal, characteristic
4C3×#4535C212yesmaximal, complemented
5#10589085C212yesmaximal, complemented
6#68239—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
18C2×#3712—21no—
19C3×C4⋊(C3⋊C8)C2212yes—
20C3×C4×C3⋊C8C2212yes—
21#63557—21no—
22#63555—21no—
23#63555—21no—
24C4×D3×Q8—32no—
25C4×D3×Q8—61no—
26#4835—32no—
27C4×ΓL(1,𝔽25)—32no—
28C3×Q8⋊C8—32no—
29#4535D312yescomplemented
30#4484—32no—
31#4456—32no—
32C2×C32×Q8C2×C411yescharacteristic
33Q8×C3⋊D3—22no—
34Q8×C3⋊D3—22no—
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#3712—24no—
60#1491—91noSylow
61C2×D3×Q8—32no—
62C2×D3×Q8—61no—
63C3×C4×Q8—21no—
64C3×C4×Q8C2×D312yes—
65Q8×Dic3—32no—
66Q8×Dic3—61no—
67C2×ΓL(1,𝔽25)—62no—
68D3×C4⋊C4—32no—
69D3×C4⋊C4—61no—
70D3×C4⋊C4—62no—
71D3×C4⋊C4—62no—
72#887—32no—
73#887—61no—
74#887—62no—
75#887—62no—
76C42×D3—32no—
77C42×D3—61no—
78C42×D3—62no—
79C42×D3—62no—
80C4×Dic6—32no—
81C4×Dic6—61no—
82C4×Dic6—62no—
83C4×Dic6—62no—
84C3×C4⋊C8—32no—
85C3×C4×C8—32no—
86(C2×D3)⋊C8—62no—
87#815—62no—
88#815—62no—
89C4⋊(C3⋊C8)C2×D312yes—
90C4×C3⋊C8C2×D312yes—
91C22×C3⋊D3C22⋊C411yescharacteristic
92C32×Q8—21no—
93C32×Q8M1612yescomplemented
94C2×C32×C4—21no—
95C2×C32×C4—21no—
96C2×C32×C4C22×C411yescharacteristic
97C2×C32×C4C2×D411yescharacteristic
98C2×C32×C4C2×D411yescharacteristic
99C2×C3⋊Dic3—21no—
100C2×C3⋊Dic3—21no—
101C2×C3⋊Dic3C22⋊C411yescharacteristic
102C2×C3⋊Dic3C22⋊C411yescharacteristic
103C2×C3⋊Dic3C22⋊C411yescharacteristic
104C4×C3⋊D3—24no—
105C4×C3⋊D3—21no—
106C4×C3⋊D3—21no—
107C4×C3⋊D3—22no—
108C4×C3⋊D3—22no—
109C4×C3⋊D3—42no—
110#634—24no—
111#634—21no—
112#634M1612yescomplemented
113C3×C3⋊C8—24no—
114C3×C3⋊C8—42no—
115C2×C4×Q8—91no—
116#432—91no—
117C4×M16—91no—
118Q8⋊C8—32no—
119Q8⋊C8—92no—
120C2×C3×Q8—21no—
121C2×C3×Q8C4×D312yes—
122D3×Q8—64no—
123D3×Q8—64no—
124D3×Q8—64no—
125D3×Q8—64no—
126C2×C4×D3—32no—
127C2×C4×D3—32no—
128C2×C4×D3—32no—
129C2×C4×D3—61no—
130C2×C4×D3—61no—
131C2×C4×D3—61no—
132C2×C4×D3—62no—
133C2×C4×D3—62no—
134C2×C4×D3—62no—
135C2×C4×D3—62no—
136C2×Dic6—32no—
137C2×Dic6—61no—
138C2×Dic6—62no—
139C2×Dic6—62no—
140C2×C3×C8—62no—
141C2×C3×C8—62no—
142C3×C4⋊C4—22no—
143C3×C4⋊C4—22no—
144C3×C4⋊C4—21no—
145C3×C4⋊C4C4×D312yes—
146C3×C42—22no—
147C3×C42—22no—
148C3×C42—21no—
149C3×C42C22×D312yes—
150C4⋊Dic3—32no—
151C4⋊Dic3—61no—
152C4⋊Dic3—62no—
153C4⋊Dic3—62no—
154Dic3⋊C4—62no—
155Dic3⋊C4—62no—
156Dic3⋊C4—62no—
157Dic3⋊C4—62no—
158Dic3⋊C4—62no—
159Dic3⋊C4—62no—
160C4×Dic3—32no—
161C4×Dic3—32no—
162C4×Dic3—32no—
163C4×Dic3—61no—
164C4×Dic3—61no—
165C4×Dic3—61no—
166C4×Dic3—62no—
167C4×Dic3—62no—
168C4×Dic3—62no—
169C4×Dic3—62no—
170C4×Dic3—62no—
171C4×Dic3—62no—
172C2×C3⋊C8—22no—
173C2×C3⋊C8—22no—
174ΓL(1,𝔽25)—68no—
175C22×C32C2×C22⋊C411yescharacteristic
176C2×C3⋊D3—21no—
177C2×C3⋊D3—21no—
178C2×C3⋊D3#10412yes—
179C32×C4—22no—
180C32×C4—21no—
181C32×C4—41no—
182C32×C4C2×M1611yescharacteristic
183C32×C4C2×M1611yescharacteristic
184C32×C4#13712yes—
185C3⋊Dic3—21no—
186C3⋊Dic3—22no—
187C3⋊Dic3—21no—
188C3⋊Dic3—21no—
189C3⋊Dic3—41no—
190C22×Q8—91no—
191C2×M16—181no—
192C4×Q8—91no—
193C4×Q8—91no—
194C4×Q8—91no—
195C4×Q8—181no—
196C4×Q8—181no—
197C4×Q8D3211yescharacteristic
198C2×C4⋊C4—91no—
199C2×C4⋊C4—181no—
200C2×C42—91no—
201C2×C42—181no—
202C4⋊C8—32no—
203C22⋊C8—181no—
204#97—181no—
205#97—181no—
206C4×C8—32no—
207C22×D3—32no—
208C22×D3—61no—
209C3×Q8—22no—
210C3×Q8—22no—
211C3×Q8—22no—
212C3×Q8ΓL(1,𝔽25)14yescomplemented
213C2×C3×C4—22no—
214C2×C3×C4—22no—
215C2×C3×C4—22no—
216C2×C3×C4—22no—
217C2×C3×C4—21no—
218C2×C3×C4—21no—
219C2×C3×C4—21no—
220C2×C3×C4C2×C4×D312yes—
221C2×C3×C4D3×D412yes—
222C2×C3×C4D3×D412yes—
223C2×Dic3—32no—
224C2×Dic3—32no—
225C2×Dic3—32no—
226C2×Dic3—61no—
227C2×Dic3—61no—
228C2×Dic3—61no—
229C2×Dic3—62no—
230C2×Dic3—62no—
231C2×Dic3—62no—
232C2×Dic3—62no—
233C4×D3—64no—
234C4×D3—64no—
235C4×D3—68no—
236C4×D3—68no—
237C4×D3—62no—
238C4×D3—62no—
239C4×D3—62no—
240C4×D3—62no—
241C4×D3—62no—
242C4×D3—62no—
243C4×D3—122no—
244C4×D3—124no—
245C4×D3—124no—
246Dic6—34no—
247Dic6—62no—
248Dic6—68no—
249Dic6—68no—
250Dic6—62no—
251Dic6—62no—
252C3×C8—64no—
253C3×C8—122no—
254C3⋊C8—24no—
255C3⋊C8—42no—
256C2×C32#40711yescharacteristic
257C2×C32#41911yescharacteristic
258C2×C32C2×#10411yescharacteristic
259C3⋊D3—22no—
260C2×Q8—91no—
261C2×Q8—181no—
262C2×Q8—182no—
263C2×Q8—182no—
264C2×Q8#62411yescharacteristic
265C22×C4—91no—
266C22×C4—91no—
267C22×C4—91no—
268C22×C4—181no—
269C22×C4—181no—
270M16—184no—
271C2×C8—62no—
272C2×C8—62no—
273C4⋊C4—21no—
274C4⋊C4—91no—
275C4⋊C4—181no—
276C4⋊C4—181no—
277C4⋊C4—181no—
278C4⋊C4—181no—
279C4⋊C4#62411yescharacteristic
280C42—21no—
281C42—91no—
282C42—91no—
283C42—91no—
284C42—181no—
285C42—181no—
286C42—181no—
287C42C2×D3211yescharacteristic
288C22×C3—21no—
289C22×C3D3×C22⋊C412yes—
290C2×D3—34no—
291C2×D3—62no—
292C2×D3—62no—
293C2×D3—62no—
294C2×D3—62no—
295C2×D3—62no—
296C3×C4—24no—
297C3×C4—24no—
298C3×C4—22no—
299C3×C4—21no—
300C3×C4—21no—
301C3×C4—22no—
302C3×C4—41no—
303C3×C4—42no—
304C3×C4—42no—
305C3×C4C2×ΓL(1,𝔽25)12yes—
306C3×C4D3×M1612yes—
307C3×C4#91512yes—
308C3×C4#91812yes—
309Dic3—62no—
310Dic3—64no—
311Dic3—62no—
312Dic3—64no—
313Dic3—62no—
314Dic3—62no—
315Dic3—62no—
316Dic3—121no—
317Dic3—122no—
318Dic3—122no—
319C32#149111yescharacteristic, complemented, Sylow
320C23—91no—
321Q8—21no—
322Q8—92no—
323Q8—184no—
324Q8—181no—
325Q8#371212yescomplemented
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—91no—
329C2×C4—91no—
330C2×C4—91no—
331C2×C4—182no—
332C2×C4—184no—
333C2×C4—181no—
334C2×C4—181no—
335C2×C4—181no—
336C2×C4—182no—
337C2×C4—181no—
338C2×C4—362no—
339C2×C4C2×#62411yescharacteristic
340C2×C4#381111yescharacteristic
341C2×C4#381111yescharacteristic
342C8—64no—
343C8—122no—
344C2×C3—21no—
345C2×C3—21no—
346C2×C3—21no—
347C2×C3#472612yes—
348C2×C3#480212yes—
349C2×C3D3×#10412yes—
350D3—64no—
351D3—64no—
352C22—92no—
353C22—181no—
354C22—181no—
355C22#6397411yescharacteristic
356C4—22no—
357C4—21no—
358C4—41no—
359C4—181no—
360C4—181no—
361C4—182no—
362C4—181no—
363C4—361no—
364C4#6381811yescharacteristic
365C4C2×#371211yescharacteristic
366C4#6395112yes—
367C3—21no—
368C3#6823912yescomplemented
369C2—182no—
370C2#1059115911yescharacteristic
371C2#1059156211yescharacteristic
372C2#1059167111yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4×Q8C22
socleC22×C32C2×C22⋊C4
prime radicalC22×C3⋊D3C22⋊C4
cosocleC32×C42C23
hypercenterC4×Q8D32
hypocenterC32#1491
LCSG ▷ C2×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
93. C32×Q8M16semidirect
112. #634M16semidirect
212. C3×Q8ΓL(1,𝔽25)semidirect
319. C32#1491semidirect
325. Q8#3712semidirect
368. C3#68239semidirect

Maximal subgroups

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

subgroupindex
C4×Q8×C3⋊D32
C4×#37122
#105902602
C3×#45352
#105890852
#682393