Finite Group Databasebeta

← #11773223

Subgroups — #11773223

Order 1152.

1836 conjugacy classes of subgroups.

The subgroup lattice has 375 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×C4⋊C4C211yesmaximal, characteristic
2C22×C4×C3⋊Dic3C211yesmaximal, characteristic
3C2×#63658C211yesmaximal, characteristic
4C2×#63658C212yesmaximal
5C2×#63658C212yesmaximal
6#71564—34nomaximal
7C23×C32×C4C2211yescharacteristic
8C23×C32×C4C2211yescharacteristic
9C23×C32×C4C2211yescharacteristic
10C23×C3⋊Dic3C2212yes—
11C23×C3⋊Dic3C2212yes—
12C2×C32×C4⋊C4—22no—
13C2×C32×C4⋊C4—22no—
14C2×C32×C4⋊C4C414yescomplemented
15C2×C4×C3⋊Dic3—22no—
16C2×C4×C3⋊Dic3—24no—
17#63658—22no—
18#63658—24no—
19#63658C418yescomplemented
20C22×C3×C4⋊C4D314yes—
21C22×C4×Dic3—34no—
22C2×C3⋊#95—38no—
23C2×C3⋊#95—38no—
24C2×C3⋊#95—34no—
25C24×C32C2311yescharacteristic
26C22×C32×C4—22no—
27C22×C32×C4—21no—
28C22×C32×C4—21no—
29C22×C32×C4—22no—
30C22×C32×C4—22no—
31C22×C32×C4—21no—
32C22×C32×C4—21no—
33C22×C32×C4—22no—
34C22×C32×C4—22no—
35C22×C32×C4C2×C412yes—
36C22×C32×C4C2×C414yes—
37C22×C32×C4C2×C412yes—
38C22×C32×C4C2×C412yes—
39C22×C32×C4D412yes—
40C22×C32×C4D412yes—
41C22×C3⋊Dic3—22no—
42C22×C3⋊Dic3—22no—
43C22×C3⋊Dic3—22no—
44C22×C3⋊Dic3—22no—
45C22×C3⋊Dic3—22no—
46C22×C3⋊Dic3—22no—
47C22×C3⋊Dic3—22no—
48C22×C3⋊Dic3—22no—
49C22×C3⋊Dic3—22no—
50C22×C3⋊Dic3—22no—
51C22×C3⋊Dic3C2×C414yes—
52C22×C3⋊Dic3C2×C414yes—
53C22×C3⋊Dic3D414yes—
54C22×C3⋊Dic3Q814yes—
55C32×C4⋊C4—28no—
56C4×C3⋊Dic3—28no—
57#1436—91noSylow
58C23×C3×C4C2×D314yes—
59C23×C3×C4C2×D314yes—
60C23×C3×C4C2×D314yes—
61C23×Dic3—38no—
62C23×Dic3—38no—
63C2×C3×C4⋊C4—28no—
64C2×C3×C4⋊C4—28no—
65C2×C3×C4⋊C4Dic3116yescomplemented
66C2×C4×Dic3—616no—
67C2×C4×Dic3—68no—
68C3⋊#95—332no—
69C3⋊#95—616no—
70C3⋊#95—68no—
71C23×C32C22×C412yes—
72C23×C32C22×C411yescharacteristic
73C23×C32C2×D412yes—
74C23×C32C2×D411yescharacteristic
75C23×C32C2×D411yescharacteristic
76C23×C32C2×Q812yes—
77C23×C32#4112yes—
78C23×C32#4112yes—
79C23×C32#4112yes—
80C2×C32×C4—22no—
81C2×C32×C4—22no—
82C2×C32×C4—24no—
83C2×C32×C4—24no—
84C2×C32×C4—24no—
85C2×C32×C4—22no—
86C2×C32×C4—24no—
87C2×C32×C4—22no—
88C2×C32×C4—22no—
89C2×C32×C4—24no—
90C2×C32×C4—41no—
91C2×C32×C4—42no—
92C2×C32×C4—41no—
93C2×C32×C4C4214yescomplemented
94C2×C32×C4C22⋊C414yes—
95C2×C3⋊Dic3—24no—
96C2×C3⋊Dic3—24no—
97C2×C3⋊Dic3—24no—
98C2×C3⋊Dic3—24no—
99C2×C3⋊Dic3—24no—
100C2×C3⋊Dic3—24no—
101C2×C3⋊Dic3—24no—
102C2×C3⋊Dic3—24no—
103C2×C3⋊Dic3—24no—
104C2×C3⋊Dic3—42no—
105C2×C3⋊Dic3—42no—
106C2×C3⋊Dic3—42no—
107C2×C3⋊Dic3—42no—
108C2×C3⋊Dic3C4⋊C418yescomplemented
109C22×C4⋊C4C3⋊D311yescharacteristic
110C22×C42—91no—
111C2×#95—92no—
112C2×#95—92no—
113C2×#95—91no—
114C24×C3C22×D314yes—
115C22×C3×C4—28no—
116C22×C3×C4—28no—
117C22×C3×C4—28no—
118C22×C3×C4—24no—
119C22×C3×C4—24no—
120C22×C3×C4—28no—
121C22×C3×C4—28no—
122C22×C3×C4—24no—
123C22×C3×C4—24no—
124C22×C3×C4C4×D3116yes—
125C22×C3×C4C2×Dic318yes—
126C22×C3×C4C2×Dic318yes—
127C22×C3×C4C2×Dic318yes—
128C22×C3×C4#6718yes—
129C22×C3×C4#6718yes—
130C22×Dic3—316no—
131C22×Dic3—316no—
132C22×Dic3—316no—
133C22×Dic3—316no—
134C22×Dic3—68no—
135C22×Dic3—68no—
136C22×Dic3—68no—
137C22×Dic3—68no—
138C22×Dic3—68no—
139C22×Dic3—68no—
140C22×Dic3—68no—
141C22×Dic3—68no—
142C22×Dic3—68no—
143C22×Dic3—68no—
144C3×C4⋊C4—232no—
145C4×Dic3—632no—
146C22×C32C2×C4211yescharacteristic
147C22×C32C2×C22⋊C411yescharacteristic
148C22×C32C2×C4⋊C412yes—
149C22×C32#11712yes—
150C22×C32#11711yescharacteristic
151C22×C32C4×D412yes—
152C22×C32C4×D412yes—
153C22×C32C4×D412yes—
154C22×C32C4×D412yes—
155C22×C32C4×Q812yes—
156C22×C32C4×Q812yes—
157C22×C32#12011yescharacteristic
158C22×C32#12112yes—
159C22×C32C22⋊Q812yes—
160C22×C32C22⋊Q812yes—
161C22×C32#12312yes—
162C22×C32#12311yescharacteristic
163C22×C32#12411yescharacteristic
164C22×C32#12512yes—
165C22×C32#12612yes—
166C22×C32C4⋊Q811yescharacteristic
167C32×C4—24no—
168C32×C4—24no—
169C32×C4—42no—
170C3⋊Dic3—28no—
171C3⋊Dic3—44no—
172C23×C4—92no—
173C23×C4—92no—
174C23×C4C2×C3⋊D311yescharacteristic
175C23×C4C2×C3⋊D311yescharacteristic
176C23×C4C2×C3⋊D311yescharacteristic
177C2×C4⋊C4—22no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4C3⋊Dic314yescomplemented
180C2×C42—184no—
181C2×C42—182no—
182#95—98no—
183#95—184no—
184#95—182no—
185C23×C3C2×C4×D318yes—
186C23×C3#23518yes—
187C23×C3D3×D418yes—
188C23×C3#23718yes—
189C23×C3D3×Q818yes—
190C23×C3#23918yes—
191C23×C3C22×Dic314yes—
192C23×C3C2×#6714yes—
193C23×C3C2×#6714yes—
194C2×C3×C4—28no—
195C2×C3×C4—216no—
196C2×C3×C4—216no—
197C2×C3×C4—216no—
198C2×C3×C4—28no—
199C2×C3×C4—28no—
200C2×C3×C4—216no—
201C2×C3×C4—28no—
202C2×C3×C4—216no—
203C2×C3×C4—28no—
204C2×C3×C4—44no—
205C2×C3×C4—44no—
206C2×C3×C4—48no—
207C2×C3×C4C4×Dic3116yescomplemented
208C2×C3×C4#217116yes—
209C2×Dic3—332no—
210C2×Dic3—616no—
211C2×Dic3—616no—
212C2×Dic3—616no—
213C2×Dic3—616no—
214C2×Dic3—616no—
215C2×Dic3—616no—
216C2×Dic3—616no—
217C2×Dic3—616no—
218C2×Dic3—616no—
219C2×Dic3—128no—
220C2×Dic3—128no—
221C2×Dic3—128no—
222C2×Dic3—128no—
223C2×C32C4×C22⋊C411yescharacteristic
224C2×C32C4×C4⋊C412yes—
225C2×C32#38512yes—
226C2×C32#38611yescharacteristic
227C2×C32#38712yes—
228C2×C32#38712yes—
229C2×C32#38812yes—
230C2×C32#38912yes—
231C2×C32#39111yescharacteristic
232C24C22×C3⋊D311yescharacteristic
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—94no—
243C22×C4—94no—
244C22×C4—94no—
245C22×C4—94no—
246C22×C4—182no—
247C22×C4—182no—
248C22×C4—182no—
249C22×C4—182no—
250C22×C4—182no—
251C22×C4—182no—
252C22×C4—182no—
253C22×C4—182no—
254C22×C4—182no—
255C22×C4—182no—
256C22×C4C4×C3⋊D314yes—
257C22×C4C2×C3⋊Dic312yes—
258C22×C4C2×C3⋊Dic312yes—
259C22×C4C2×C3⋊Dic312yes—
260C22×C4#63812yes—
261C22×C4#63812yes—
262C4⋊C4—28no—
263C42—188no—
264C22×C3#88718yes—
265C22×C3#88918yes—
266C22×C3D3×C4⋊C418yes—
267C22×C3#89218yes—
268C22×C3#89318yes—
269C22×C3#89418yes—
270C22×C3#89618yes—
271C22×C3#89818yes—
272C22×C3C2×C4×Dic314yes—
273C22×C3#92614yes—
274C22×C3C4×#6718yes—
275C22×C3C4×#6718yes—
276C22×C3D4×Dic318yes—
277C22×C3#93514yes—
278C22×C3#93714yes—
279C22×C3#93918yes—
280C22×C3#94414yes—
281C22×C3Q8×Dic318yes—
282C22×C3#94618yes—
283C22×C3#94714yes—
284C22×C3C2×#21714yes—
285C3×C4—216no—
286C3×C4—216no—
287C3×C4—48no—
288Dic3—632no—
289Dic3—1216no—
290C32#143611yescharacteristic, complemented, Sylow
291C23C2×C4×C3⋊D312yes—
292C23#382812yes—
293C23D4×C3⋊D312yes—
294C23#383012yes—
295C23Q8×C3⋊D312yes—
296C23#383212yes—
297C23C22×C3⋊Dic311yescharacteristic
298C23C2×#63811yescharacteristic
299C23C2×#63811yescharacteristic
300C2×C4—22no—
301C2×C4—24no—
302C2×C4—24no—
303C2×C4—24no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—24no—
307C2×C4—22no—
308C2×C4—24no—
309C2×C4—22no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—42no—
313C2×C4—98no—
314C2×C4—184no—
315C2×C4—184no—
316C2×C4—184no—
317C2×C4—184no—
318C2×C4—184no—
319C2×C4—184no—
320C2×C4—184no—
321C2×C4—184no—
322C2×C4—184no—
323C2×C4—362no—
324C2×C4—362no—
325C2×C4—362no—
326C2×C4—362no—
327C2×C4C4×C3⋊Dic314yescomplemented
328C2×C4#375714yes—
329C2×C3Dic3×C4⋊C418yes—
330C2×C3#497618yes—
331C2×C3#497818yes—
332C2×C3#498018yes—
333C2×C3#498918yes—
334C2×C3#499018yes—
335C2×C3C4×#21714yes—
336C2×C3#522014yes—
337C2×C3#522914yes—
338C22#6409612yes—
339C22#6409812yes—
340C22C4⋊C4×C3⋊D312yes—
341C22#6410112yes—
342C22#6410212yes—
343C22#6410312yes—
344C22#6410512yes—
345C22#6410712yes—
346C22C2×C4×C3⋊Dic311yescharacteristic
347C22#6413511yescharacteristic
348C22C4×#63812yes—
349C22C4×#63812yes—
350C22D4×C3⋊Dic312yes—
351C22#6414411yescharacteristic
352C22#6414611yescharacteristic
353C22#6414812yes—
354C22#6415311yescharacteristic
355C22Q8×C3⋊Dic312yes—
356C22#6415512yes—
357C22#6415611yescharacteristic
358C22C2×#375711yescharacteristic
359C4—24no—
360C4—24no—
361C4—42no—
362C4—188no—
363C4—364no—
364C3#7156414yescomplemented
365C2C4⋊C4×C3⋊Dic312yes—
366C2#1059267512yes—
367C2#1059267712yes—
368C2#1059267912yes—
369C2#1059268812yes—
370C2#1059268912yes—
371C2C4×#375711yescharacteristic
372C2#1059291911yescharacteristic
373C2#1059292811yescharacteristic
subgroupG/H
center, FrattiniC24C22×C3⋊D3
commutatorC22×C32C2×C42
FittingC22×C32×C4⋊C4C2
socle, prime radical, cosocleC24×C32C23
hypercenterC22×C4⋊C4C3⋊D3
hypocenterC32#1436
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C24 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
14. C2×C32×C4⋊C4C4semidirect
19. #63658C4semidirect
65. C2×C3×C4⋊C4Dic3semidirect
93. C2×C32×C4C42semidirect
108. C2×C3⋊Dic3C4⋊C4semidirect
179. C2×C4⋊C4C3⋊Dic3semidirect
207. C2×C3×C4C4×Dic3semidirect
290. C32#1436semidirect
327. C2×C4C4×C3⋊Dic3semidirect
364. C3#71564semidirect

Maximal subgroups

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

subgroupindex
C22×C32×C4⋊C42
C22×C4×C3⋊Dic32
C2×#636582
#715643