Finite Group Databasebeta

← #11785224

Subgroups — #11785224

Order 1152.

550 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 550 conjugacy classes of subgroups — too many to draw. Only its 103 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×C4×#627C211yesmaximal, characteristic
2C2×C4⋊#622C211yesmaximal, characteristic
3C2×#63740C212yesmaximal
4#10591359C211yesmaximal, characteristic
5#10590075C212yesmaximal
6C22×#627C2211yescharacteristic
7C22×#622C2212yes—
8C2×C4×C3⋊Dic3C2211yescharacteristic
9C2×C3×C4⋊Dic3—21no—
10C2×C3×C4×Dic3—21no—
11C2×#3724—21no—
12C2×#3724C2212yes—
13C2×#3724C2211yescharacteristic
14C2×Dic3⋊Dic3—21no—
15C4×#627—22no—
16C4×#627C414yescomplemented
17C4⋊#622—22no—
18#63740—24no—
19C2×C4×Dic6—61no—
20#4975—61no—
21C22×C32×C4D411yescharacteristic
22C22×C3⋊Dic3D411yescharacteristic
23C22×C3⋊Dic3C2311yescharacteristic
24C22×C3×Dic3—21no—
25C22×C3×Dic3—21no—
26C22×C3×Dic3—22no—
27C2×#627—21no—
28C2×#627—21no—
29C2×#627—21no—
30C2×#627C2×C412yes—
31C2×#627D412yes—
32C2×#627Q812yes—
33C2×#622—22no—
34C2×#622—22no—
35C2×#622—22no—
36C4×C3⋊Dic3C2×C412yes—
37C4×C3⋊Dic3D412yes—
38C3×C4⋊Dic3—42no—
39C3×C4×Dic3—24no—
40#3724—21no—
41#3724—22no—
42#3724—22no—
43#3724—42no—
44#3724C2×C412yes—
45Dic3⋊Dic3—24no—
46#1803—91nomaximal, Sylow
47C22×Dic6—61no—
48C2×C3×C4⋊C4—61no—
49C2×C3×C42—61no—
50C2×C4⋊Dic3—21no—
51C2×C4⋊Dic3—61no—
52C2×Dic3⋊C4—61no—
53C2×Dic3⋊C4—62no—
54C2×Dic3⋊C4—61no—
55C2×Dic3⋊C4—62no—
56C2×C4×Dic3—21no—
57C2×C4×Dic3—61no—
58C2×C4×Dic3—61no—
59C4×Dic6—64no—
60C4×Dic6—64no—
61C23×C32C2×D411yescharacteristic
62C2×C32×C4C22⋊C412yes—
63C2×C32×C4SD1612yes—
64C2×C32×C4Q1612yes—
65C2×C3⋊Dic3—21no—
66C2×C3⋊Dic3—21no—
67C2×C3⋊Dic3C22⋊C412yes—
68C2×C3⋊Dic3C22×C411yescharacteristic
69C2×C3⋊Dic3C2×D411yescharacteristic
70C2×C3⋊Dic3C2×D411yescharacteristic
71C2×C3⋊Dic3C2×Q811yescharacteristic
72C2×C3⋊Dic3#4111yescharacteristic
73C2×C3⋊Dic3#4111yescharacteristic
74C2×C3×Dic3—22no—
75C2×C3×Dic3—22no—
76C2×C3×Dic3—22no—
77C2×C3×Dic3—22no—
78C2×C3×Dic3—41no—
79C2×C3×Dic3—41no—
80C2×C3×Dic3—42no—
81C2×C3×Dic3—42no—
82C2×C3×Dic3—42no—
83#627—22no—
84#627—22no—
85#627—22no—
86#627C4⋊C414yescomplemented
87#622—42no—
88C2×C4×Q8—91no—
89C2×C4⋊C8—91no—
90C2×#103—92no—
91#384—91no—
92#340—92no—
93C22×C3×C4—21no—
94C22×C3×C4—21no—
95C22×C3×C4—61no—
96C22×C3×C4—61no—
97C22×C3×C4—62no—
98C22×Dic3—21no—
99C22×Dic3—21no—
100C22×Dic3—22no—
101C22×Dic3—61no—
102C22×Dic3—61no—
103C22×Dic3—61no—
104C22×Dic3—61no—
105C2×Dic6—62no—
106C2×Dic6—62no—
107C2×Dic6—62no—
108C2×Dic6—62no—
109C2×Dic6—62no—
110C2×Dic6—62no—
111C3×C4⋊C4—122no—
112C3×C42—64no—
113C4⋊Dic3—42no—
114C4⋊Dic3—64no—
115Dic3⋊C4—62no—
116Dic3⋊C4—64no—
117Dic3⋊C4—62no—
118Dic3⋊C4—122no—
119Dic3⋊C4—122no—
120Dic3⋊C4—124no—
121C4×Dic3—24no—
122C4×Dic3—62no—
123C4×Dic3—62no—
124C4×Dic3—62no—
125C4×Dic3—62no—
126C22×C32C2×C22⋊C411yescharacteristic
127C22×C32#12111yescharacteristic
128C22×C32C22⋊Q811yescharacteristic
129C22×C32C2×SD1611yescharacteristic
130C22×C32C2×Q1611yescharacteristic
131C22×C32AGL(1,ℤ/8)11yescharacteristic
132C22×C32#13711yescharacteristic
133C32×C4#10314yescomplemented
134C3⋊Dic3—22no—
135C3⋊Dic3C2×C4⋊C411yescharacteristic
136C3⋊Dic3#11711yescharacteristic
137C3⋊Dic3#12111yescharacteristic
138C3⋊Dic3C22⋊Q811yescharacteristic
139C3×Dic3—24no—
140C3×Dic3—42no—
141C3×Dic3—82no—
142C22×Q8—91no—
143C22×C8—92no—
144C4×Q8—94no—
145C4×Q8—182no—
146C2×C4⋊C4—61no—
147C2×C4⋊C4—91no—
148C2×C4⋊C4—92no—
149C2×C4⋊C4—181no—
150C2×C4⋊C4—181no—
151C2×C42—61no—
152C2×C42—91no—
153C4⋊C8—182no—
154#103—184no—
155C23×C3—21no—
156C23×C3—21no—
157C2×C3×C4—22no—
158C2×C3×C4—22no—
159C2×C3×C4—22no—
160C2×C3×C4—22no—
161C2×C3×C4—22no—
162C2×C3×C4—22no—
163C2×C3×C4—62no—
164C2×C3×C4—62no—
165C2×C3×C4—62no—
166C2×C3×C4—62no—
167C2×C3×C4—121no—
168C2×C3×C4—121no—
169C2×C3×C4—122no—
170C2×C3×C4—122no—
171C2×C3×C4—122no—
172C2×Dic3—22no—
173C2×Dic3—22no—
174C2×Dic3—22no—
175C2×Dic3—22no—
176C2×Dic3—41no—
177C2×Dic3—41no—
178C2×Dic3—42no—
179C2×Dic3—42no—
180C2×Dic3—42no—
181C2×Dic3—62no—
182C2×Dic3—61no—
183C2×Dic3—61no—
184C2×Dic3—61no—
185C2×Dic3—61no—
186C2×Dic3—61no—
187C2×Dic3—61no—
188C2×Dic3—61no—
189C2×Dic3—61no—
190C2×Dic3—61no—
191C2×Dic3—61no—
192C2×Dic3—61no—
193C2×Dic3—61no—
194C2×Dic3—62no—
195C2×Dic3—62no—
196C2×Dic3—62no—
197C2×Dic3—121no—
198C2×Dic3—121no—
199Dic6—64no—
200Dic6—64no—
201Dic6—64no—
202Dic6—64no—
203C2×C32#38011yescharacteristic
204C2×C32C2×#10311yescharacteristic
205C2×C32#41711yescharacteristic
206C2×C32#46011yescharacteristic
207C2×C32#46211yescharacteristic
208C2×C32#47511yescharacteristic
209C2×C32#47711yescharacteristic
210C2×Q8—92no—
211C2×Q8—92no—
212C2×Q8—92no—
213C2×Q8—181no—
214C2×Q8—181no—
215C2×Q8—181no—
216C22×C4—61no—
217C22×C4—61no—
218C22×C4—62no—
219C22×C4—91no—
220C22×C4—91no—
221C22×C4GO+(4,𝔽2)11yescharacteristic
222C2×C8—182no—
223C2×C8—182no—
224C2×C8—182no—
225C4⋊C4—92no—
226C4⋊C4—122no—
227C4⋊C4—181no—
228C4⋊C4—184no—
229C4⋊C4—182no—
230C4⋊C4—182no—
231C4⋊C4—362no—
232C42—64no—
233C42—92no—
234C42—92no—
235C22×C3—21no—
236C22×C3—21no—
237C22×C3—21no—
238C22×C3—21no—
239C22×C3—21no—
240C22×C3—21no—
241C22×C3—21no—
242C22×C3—21no—
243C22×C3—21no—
244C22×C3—21no—
245C22×C3—21no—
246C22×C3—21no—
247C22×C3—21no—
248C22×C3—21no—
249C3×C4—24no—
250C3×C4—24no—
251C3×C4—64no—
252C3×C4—122no—
253C3×C4—242no—
254Dic3—24no—
255Dic3—42no—
256Dic3—61no—
257Dic3—61no—
258Dic3—61no—
259Dic3—61no—
260Dic3—61no—
261Dic3—61no—
262Dic3—61no—
263Dic3—61no—
264Dic3—64no—
265Dic3—82no—
266Dic3—122no—
267C32#180311yescharacteristic, complemented, Sylow
268C23C2×GO+(4,𝔽2)11yescharacteristic
269Q8—94no—
270Q8—182no—
271Q8—182no—
272Q8—182no—
273C2×C4—62no—
274C2×C4—62no—
275C2×C4—62no—
276C2×C4—62no—
277C2×C4—91no—
278C2×C4—91no—
279C2×C4—91no—
280C2×C4—91no—
281C2×C4—91no—
282C2×C4—91no—
283C2×C4—92no—
284C2×C4—121no—
285C2×C4—121no—
286C2×C4—122no—
287C2×C4—122no—
288C2×C4—122no—
289C2×C4—181no—
290C2×C4—181no—
291C2×C4D32⋊C412yes—
292C2×C4#377512yes—
293C2×C4#377612yes—
294C8—362no—
295C2×C3—21no—
296C2×C3—21no—
297C2×C3—21no—
298C2×C3—21no—
299C2×C3—21no—
300C2×C3—21no—
301C2×C3—21no—
302C2×C3—21no—
303C2×C3—21no—
304C2×C3—21no—
305C2×C3—21no—
306C2×C3—21no—
307C2×C3—21no—
308C2×C3—21no—
309C22D32⋊Q811yescharacteristic
310C22#6422411yescharacteristic
311C22#6422611yescharacteristic
312C22#6423011yescharacteristic
313C22C2×D32⋊C411yescharacteristic
314C22C2×#377511yescharacteristic
315C22C2×#377611yescharacteristic
316C4—64no—
317C4—91no—
318C4—91no—
319C4—91no—
320C4—91no—
321C4—122no—
322C4—182no—
323C4—242no—
324C4#6374014yescomplemented
325C3—21no—
326C3—21no—
327C2#1059336011yescharacteristic
328C2#1059337611yescharacteristic
329C2#1059339311yescharacteristic
330C2#1059340311yescharacteristic
331C2#1059343911yescharacteristic
332C2#1059344711yescharacteristic
333C2C2×#6374011yescharacteristic
subgroupG/H
center, FrattiniC23C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC22×C32×C4D4
socle, prime radicalC23×C32C2×D4
cosocleC22×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1803
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
16. C4×#627C4semidirect
86. #627C4⋊C4semidirect
133. C32×C4#103semidirect
267. C32#1803semidirect
324. C4#63740semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6272
C2×C4⋊#6222
C2×#637402
#105913592
#105900752
#18039