Finite Group Databasebeta

← #11802682

Subgroups — #11802682

Order 1152.

1733 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3797C211yesmaximal, characteristic
2C2×#64081C211yesmaximal, characteristic
3C2×#63849C211yesmaximal, characteristic
4C3×#4929C212yesmaximal, complemented
5#10591371C214yesmaximal
6#10591236C214yesmaximal, complemented
7#10591221C212yesmaximal, complemented
8#76610—32nomaximal
9C22×C4×C3⋊D3C2211yescharacteristic
10C22×C3×Dic6C2212yes—
11C22×#627C2212yes—
12C22×#624C2212yes—
13C2×#3797—24no—
14C2×#3797—24no—
15C2×#3797C418yescomplemented
16C2×C32×C42C2211yescharacteristic
17C2×#3752C2212yes—
18C2×#3750C2212yes—
19C2×C4×C3⋊Dic3C2211yescharacteristic
20#64081—24no—
21C2×C3×C4⋊Dic3C2212yes—
22C2×#3722C2212yes—
23C2×Dic32C2212yes—
24#63849—24no—
25C3×C3⋊#95C2218yes—
26#63579C2218yes—
27C22×D3×Q8—32no—
28C2×#892—32no—
29C2×#872—32no—
30C2×#872—61no—
31C3×#391—32no—
32#5229—32no—
33#4973—32no—
34#4929D312yescomplemented
35#4664—38no—
36#4646—38no—
37C23×C3⋊D3C2311yescharacteristic
38C22×C32×C4C2312yes—
39C22×C32×C4C2311yescharacteristic
40C22×C3⋊Dic3C2312yes—
41C22×C3⋊Dic3C2311yescharacteristic
42C2×C4×C3⋊D3C2×C414yes—
43C2×C4×C3⋊D3D414yes—
44C2×C4×C3⋊D3D414yes—
45C22×C3×Dic3C2314yes—
46C22×C3×Dic3C2314yes—
47C2×C3×Dic6—24no—
48C2×C3×Dic6—24no—
49C2×C3×Dic6C2×C418yes—
50C2×#627—24no—
51C2×#627—24no—
52C2×#627C2×C418yes—
53C2×#624—24no—
54C2×#624—24no—
55C2×#624C2×C418yes—
56#3797—232no—
57C32×C42—22no—
58#3752—24no—
59#3750—24no—
60C4×C3⋊Dic3—22no—
61C3×C4⋊Dic3—24no—
62#3722—24no—
63Dic32—24no—
64#2310—91noSylow
65C22×C3×Q8—32no—
66C2×D3×Q8—316no—
67C2×D3×Q8—68no—
68C2×D3×Q8—68no—
69C22×C4×D3—32no—
70C22×C4×D3—34no—
71C22×C4×D3—61no—
72C22×Dic6—34no—
73C22×Dic6C2×D312yes—
74C2×C3×C4⋊C4—32no—
75C2×C3×C42—21no—
76C2×C3×C42C2×D312yes—
77C2×(C2×D3)⋊C4—34no—
78C2×(C2×D3)⋊C4—34no—
79C2×(C2×D3)⋊C4—62no—
80C2×C4⋊Dic3C2×D312yes—
81C2×Dic3⋊C4—34no—
82C2×Dic3⋊C4—62no—
83C2×C4×Dic3—32no—
84C2×C4×Dic3—34no—
85C2×C4×Dic3—61no—
86#892—68no—
87#872—68no—
88#872—68no—
89C3×#95—38no—
90C3⋊#95—38no—
91C3⋊#95—38no—
92C3⋊#95C2×D318yes—
93C23×C32C2411yescharacteristic
94C22×C3⋊D3—24no—
95C22×C3⋊D3C22×C412yes—
96C22×C3⋊D3C2×D412yes—
97C22×C3⋊D3C2×D412yes—
98C2×C32×C4—22no—
99C2×C32×C4—24no—
100C2×C32×C4C22×C412yes—
101C2×C32×C4C2×D412yes—
102C2×C32×C4C2×D412yes—
103C2×C3⋊Dic3—22no—
104C2×C3⋊Dic3—24no—
105C2×C3⋊Dic3C22×C412yes—
106C2×C3⋊Dic3C2×D412yes—
107C2×C3⋊Dic3C2×D412yes—
108C4×C3⋊D3C22⋊C4116yes—
109C2×C3×Dic3—24no—
110C2×C3×Dic3—24no—
111C2×C3×Dic3—24no—
112C2×C3×Dic3—28no—
113C2×C3×Dic3C22×C418yes—
114C3×Dic6—216no—
115#627—216no—
116#624—216no—
117C23×Q8—91no—
118C2×#117—91no—
119C2×#117—91no—
120#391—32no—
121#391—94no—
122#391—92no—
123#381—94no—
124C23×D3—32no—
125C23×D3—61no—
126C2×C3×Q8—38no—
127C2×C3×Q8—64no—
128C2×C3×Q8—64no—
129C22×C3×C4—21no—
130C22×C3×C4—22no—
131C22×C3×C4—34no—
132C22×C3×C4—34no—
133C22×C3×C4C22×D314yes—
134C22×C3×C4C22×D312yes—
135C22×Dic3—32no—
136C22×Dic3—34no—
137C22×Dic3—61no—
138C22×Dic3—62no—
139C22×Dic3C22×D314yes—
140C22×Dic3C22×D314yes—
141D3×Q8—664no—
142C2×C4×D3—38no—
143C2×C4×D3—38no—
144C2×C4×D3—38no—
145C2×C4×D3—316no—
146C2×C4×D3—64no—
147C2×C4×D3—64no—
148C2×C4×D3—64no—
149C2×C4×D3—68no—
150C2×C4×D3—68no—
151C2×Dic6—24no—
152C2×Dic6—24no—
153C2×Dic6—316no—
154C2×Dic6—68no—
155C2×Dic6—68no—
156C2×Dic6C4×D318yes—
157C3×C4⋊C4—64no—
158C3×C42—24no—
159C3×C42—24no—
160(C2×D3)⋊C4—68no—
161(C2×D3)⋊C4—68no—
162(C2×D3)⋊C4—68no—
163C4⋊Dic3—24no—
164Dic3⋊C4—68no—
165Dic3⋊C4—68no—
166C4×Dic3—68no—
167C4×Dic3—64no—
168C4×Dic3—64no—
169C22×C32C23×C411yescharacteristic
170C22×C32C22×D411yescharacteristic
171C22×C32C22×D411yescharacteristic
172C22×C322−1+414yes—
173C2×C3⋊D3—24no—
174C2×C3⋊D3—24no—
175C2×C3⋊D3—24no—
176C2×C3⋊D3C2×C22⋊C414yes—
177C32×C4—42no—
178C32×C4C2×C22⋊C414yes—
179C3⋊Dic3—42no—
180C3⋊Dic3C2×C22⋊C414yes—
181C3×Dic3—28no—
182C3×Dic3—44no—
183C22×Q8—32no—
184C22×Q8—92no—
185C22×Q8—98no—
186C22×Q8—184no—
187C22×Q8—184no—
188C23×C4—92no—
189C23×C4—91no—
190#117—184no—
191#117—184no—
192C2×C4⋊C4—32no—
193C2×C4⋊C4—92no—
194C2×C22⋊C4—92no—
195C2×C22⋊C4—92no—
196C2×C42—92no—
197C2×C42—91no—
198C2×C42D3211yescharacteristic
199#95—38no—
200#95—98no—
201C23×C3—21no—
202C23×C3C23×D312yes—
203C22×D3—34no—
204C22×D3—34no—
205C22×D3—34no—
206C22×D3—62no—
207C22×D3—62no—
208C22×D3—62no—
209C22×D3—64no—
210C22×D3—64no—
211C22×D3—124no—
212C3×Q8—616no—
213C2×C3×C4—24no—
214C2×C3×C4—24no—
215C2×C3×C4—24no—
216C2×C3×C4—24no—
217C2×C3×C4—22no—
218C2×C3×C4—22no—
219C2×C3×C4—22no—
220C2×C3×C4—38no—
221C2×C3×C4—44no—
222C2×C3×C4—64no—
223C2×C3×C4—64no—
224C2×C3×C4—64no—
225C2×C3×C4—68no—
226C2×C3×C4C2×C4×D314yes—
227C2×C3×C4D3×D414yes—
228C2×C3×C4D3×D414yes—
229C2×Dic3—24no—
230C2×Dic3—24no—
231C2×Dic3—24no—
232C2×Dic3—28no—
233C2×Dic3—34no—
234C2×Dic3—34no—
235C2×Dic3—34no—
236C2×Dic3—62no—
237C2×Dic3—62no—
238C2×Dic3—62no—
239C2×Dic3—64no—
240C2×Dic3—64no—
241C2×Dic3—64no—
242C2×Dic3—64no—
243C2×Dic3—124no—
244C2×Dic3C2×C4×D318yes—
245C4×D3—332no—
246C4×D3—616no—
247C4×D3—632no—
248Dic6—216no—
249Dic6—632no—
250C2×C32C22×C22⋊C411yescharacteristic
251C2×C32#51912yes—
252C2×C32#53612yes—
253C2×C32#53612yes—
254C3⋊D3—24no—
255C24—91no—
256C2×Q8—38no—
257C2×Q8—64no—
258C2×Q8—64no—
259C2×Q8—98no—
260C2×Q8—184no—
261C2×Q8—184no—
262C2×Q8—1832no—
263C22×C4—34no—
264C22×C4—34no—
265C22×C4—98no—
266C22×C4—91no—
267C22×C4—94no—
268C22×C4—94no—
269C22×C4—94no—
270C22×C4—92no—
271C22×C4—184no—
272C22×C4—184no—
273C22×C4C2×D3212yes—
274C22×C4C2×D3211yescharacteristic
275C4⋊C4—64no—
276C4⋊C4—184no—
277C22⋊C4—184no—
278C22⋊C4—184no—
279C42—22no—
280C42—184no—
281C42—182no—
282C22×C3—24no—
283C22×C3—21no—
284C22×C3—21no—
285C22×C3—21no—
286C22×C3C22×C4×D312yes—
287C22×C3C2×D3×D412yes—
288C22×C3C2×D3×D412yes—
289C22×C3#100714yes—
290C22×C3#101014yes—
291C2×D3—38no—
292C2×D3—64no—
293C2×D3—64no—
294C2×D3—64no—
295C2×D3—68no—
296C2×D3—68no—
297C2×D3—124no—
298C2×D3—124no—
299C2×D3—124no—
300C3×C4—24no—
301C3×C4—44no—
302C3×C4—44no—
303C3×C4—68no—
304C3×C4—124no—
305C3×C4D3×C22⋊C418yes—
306Dic3—28no—
307Dic3—38no—
308Dic3—44no—
309Dic3—64no—
310Dic3—124no—
311Dic3—124no—
312C32#231011yescharacteristic, complemented, Sylow
313C23—92no—
314C23—92no—
315C23—92no—
316C23—184no—
317C23C22×D3211yescharacteristic
318Q8—616no—
319Q8—1816no—
320C2×C4—24no—
321C2×C4—22no—
322C2×C4—38no—
323C2×C4—64no—
324C2×C4—64no—
325C2×C4—68no—
326C2×C4—64no—
327C2×C4—92no—
328C2×C4—92no—
329C2×C4—92no—
330C2×C4—916no—
331C2×C4—1816no—
332C2×C4—184no—
333C2×C4—182no—
334C2×C4C4×D3212yes—
335C2×C4#380212yes—
336C2×C4#381112yes—
337C2×C3—22no—
338C2×C3—22no—
339C2×C3—21no—
340C2×C3—22no—
341C2×C3C2×D3×C22⋊C412yes—
342C2×C3#557214yes—
343C2×C3#562814yes—
344C2×C3#567512yes—
345C2×C3#572412yes—
346D3—68no—
347D3—124no—
348C22—94no—
349C22—184no—
350C22—184no—
351C22—184no—
352C22#6429714yes—
353C22C2×C4×D3211yescharacteristic
354C22C2×#380211yescharacteristic
355C22C2×#381111yescharacteristic
356C4—42no—
357C4—68no—
358C4—94no—
359C4—124no—
360C4—362no—
361C4#6392114yes—
362C3—21no—
363C3#7661012yescomplemented
364C2—184no—
365C2#1059384812yes—
366C2#1059390812yes—
367C2#1059480512yes—
368C2C2×#6392111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenterC2×C42D32
hypocenterC32#2310
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
4. C3×#4929C2semidirect
6. #10591236C2semidirect
7. #10591221C2semidirect
15. C2×#3797C4semidirect
34. #4929D3semidirect
312. C32#2310semidirect
363. C3#76610semidirect

Maximal subgroups

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

subgroupindex
C22×#37972
C2×#640812
C2×#638492
C3×#49292
#105913712
#105912362
#105912212
#766103