Finite Group Databasebeta

← #11805246

Subgroups — #11805246

Order 1152.

1225 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×#3724C211yesmaximal, characteristic
2C22⋊C4×C3⋊Dic3C211yesmaximal, characteristic
3C3×Dic3×C22⋊C4C212yesmaximal
4#10591720C211yesmaximal, characteristic
5#10591716C212yesmaximal
6C4×#3724C212yesmaximal, complemented
7#10591333C214yesmaximal, complemented
8#10591328C212yesmaximal, complemented
9#73458—32nomaximal
10C23×C3⋊Dic3C2211yescharacteristic
11C23×C3×Dic3C2212yes—
12C2×C32×C22⋊C4C2211yescharacteristic
13C2×#3757C2211yescharacteristic
14C2×C4×C3⋊Dic3C2212yes—
15C2×C3×#217C2212yes—
16C2×C3×C4×Dic3C2214yes—
17C2×#3724C418yescomplemented
18C2×#3724C2212yes—
19C2×#3724C2211yescharacteristic
20C2×#3724C2212yes—
21C2×#3724C2211yescharacteristic
22C2×Dic3⋊Dic3C2214yes—
23#63658C2212yes—
24C3×C3⋊#95C2214yes—
25#63579C2212yes—
26#63579C2214yes—
27C22×Dic3⋊C4—32no—
28C3×C4×C22⋊C4—32no—
29#5212—32no—
30#4942—32no—
31#4942—32no—
32Dic3×C22⋊C4—32no—
33Dic3×C22⋊C4—61no—
34Dic3×C22⋊C4D312yes—
35#4933—34no—
36C4×Dic3⋊C4—34no—
37#4655—34no—
38#4647—34no—
39C24×C32C2311yescharacteristic
40C22×C32×C4C2312yes—
41C22×C3⋊Dic3—24no—
42C22×C3⋊Dic3C2×C414yes—
43C22×C3⋊Dic3C2312yes—
44C22×C3⋊Dic3C2311yescharacteristic
45C22×C3⋊Dic3C2311yescharacteristic
46C22×C3×Dic3—44no—
47C22×C3×Dic3C2×C418yes—
48C22×C3×Dic3C2314yes—
49C22×C3×Dic3C2312yes—
50C22×C3×Dic3C2312yes—
51C32×C22⋊C4Q814yes—
52#3757—22no—
53C4×C3⋊Dic3—24no—
54C3×#217—24no—
55C3×C4×Dic3—44no—
56#3724—24no—
57#3724C2×C418yes—
58#3724C2×C414yes—
59#3724C2×C414yes—
60Dic3⋊Dic3—44no—
61#2345—91noSylow
62C23×C3×C4—32no—
63C23×Dic3—32no—
64C23×Dic3—61no—
65C23×Dic3C2×D312yes—
66C2×C3×C22⋊C4—21no—
67C2×C3×C22⋊C4—32no—
68C2×C3×C22⋊C4C2×D312yes—
69C2×C3×C42—34no—
70C2×#217—32no—
71C2×#217—61no—
72C2×#217C2×D312yes—
73C2×C4⋊Dic3—34no—
74C2×Dic3⋊C4—316no—
75C2×Dic3⋊C4—32no—
76C2×Dic3⋊C4—32no—
77C2×Dic3⋊C4—32no—
78C2×Dic3⋊C4—32no—
79C2×Dic3⋊C4—34no—
80C2×Dic3⋊C4—34no—
81C2×C4×Dic3—34no—
82C2×C4×Dic3—62no—
83C2×C4×Dic3C2×D314yes—
84C3×#95—34no—
85C3⋊#95—34no—
86C3⋊#95—34no—
87C3⋊#95—34no—
88C3⋊#95—34no—
89C3⋊#95—62no—
90C3⋊#95C2×D314yes—
91C23×C32—22no—
92C23×C32—22no—
93C23×C32C22×C412yes—
94C23×C32C2×Q812yes—
95C23×C32#4112yes—
96C23×C32C2411yescharacteristic
97C2×C32×C4—22no—
98C2×C32×C4—22no—
99C2×C32×C4C2×Q814yes—
100C2×C3⋊Dic3—22no—
101C2×C3⋊Dic3—22no—
102C2×C3⋊Dic3—28no—
103C2×C3⋊Dic3—22no—
104C2×C3⋊Dic3—22no—
105C2×C3⋊Dic3C22×C412yes—
106C2×C3⋊Dic3C22×C412yes—
107C2×C3⋊Dic3#4114yes—
108C2×C3×Dic3—24no—
109C2×C3×Dic3—24no—
110C2×C3×Dic3—24no—
111C2×C3×Dic3—24no—
112C2×C3×Dic3—24no—
113C2×C3×Dic3—48no—
114C2×C3×Dic3C22×C414yes—
115C2×C3×Dic3C22×C414yes—
116C22×C4⋊C4—91no—
117#389—92no—
118#387—94no—
119#380—91no—
120#380—92no—
121C4×C4⋊C4—92no—
122C4×C22⋊C4—32no—
123C4×C22⋊C4—91no—
124C24×C3—21no—
125C24×C3C22×D312yes—
126C22×C3×C4—22no—
127C22×C3×C4—32no—
128C22×C3×C4—32no—
129C22×C3×C4—38no—
130C22×C3×C4—34no—
131C22×C3×C4—124no—
132C22×C3×C4C22×D314yes—
133C22×Dic3—32no—
134C22×Dic3—38no—
135C22×Dic3—32no—
136C22×Dic3—34no—
137C22×Dic3—44no—
138C22×Dic3—61no—
139C22×Dic3—61no—
140C22×Dic3—62no—
141C22×Dic3—64no—
142C22×Dic3—68no—
143C22×Dic3—124no—
144C22×Dic3C4×D318yes—
145C22×Dic3C22×D314yes—
146C22×Dic3C22×D312yes—
147C22×Dic3C22×D312yes—
148C3×C22⋊C4—24no—
149C3×C22⋊C4—64no—
150C3×C22⋊C4Dic618yes—
151C3×C42—124no—
152#217—24no—
153#217—64no—
154#217—64no—
155C4⋊Dic3—124no—
156Dic3⋊C4—38no—
157Dic3⋊C4—38no—
158Dic3⋊C4—38no—
159Dic3⋊C4—38no—
160Dic3⋊C4—68no—
161Dic3⋊C4—124no—
162C4×Dic3—44no—
163C4×Dic3—68no—
164C4×Dic3—124no—
165C22×C32—22no—
166C22×C32—22no—
167C22×C32—24no—
168C22×C32—24no—
169C22×C32C4×Q814yes—
170C22×C32C23×C411yescharacteristic
171C22×C32C22×Q811yescharacteristic
172C22×C32C2×#4111yescharacteristic
173C22×C32C2×#4112yes—
174C22×C32H(5,𝔽2)12yes—
175C32×C4—24no—
176C3⋊Dic3—22no—
177C3⋊Dic3—42no—
178C3⋊Dic3#11714yes—
179C3×Dic3—24no—
180C3×Dic3—24no—
181C3×Dic3—44no—
182C23×C4—32no—
183C23×C4—91no—
184C2×C4⋊C4—91no—
185C2×C4⋊C4—92no—
186C2×C4⋊C4—91no—
187C2×C4⋊C4—98no—
188C2×C4⋊C4—92no—
189C2×C4⋊C4—94no—
190C2×C22⋊C4—32no—
191C2×C22⋊C4—91no—
192C2×C22⋊C4D3211yescharacteristic
193C2×C42—34no—
194C2×C42—92no—
195#95—34no—
196#95—94no—
197#95—92no—
198#95—92no—
199C23×C3—24no—
200C23×C3—24no—
201C23×C3—21no—
202C23×C3—22no—
203C23×C3—22no—
204C23×C3—22no—
205C23×C3—42no—
206C23×C3—42no—
207C23×C3C2×Dic614yes—
208C23×C3C2×C4×D314yes—
209C23×C3#23514yes—
210C23×C3C23×D312yes—
211C2×C3×C4—24no—
212C2×C3×C4—24no—
213C2×C3×C4—24no—
214C2×C3×C4—34no—
215C2×C3×C4—34no—
216C2×C3×C4—42no—
217C2×C3×C4—42no—
218C2×C3×C4—64no—
219C2×C3×C4—64no—
220C2×C3×C4—64no—
221C2×C3×C4—64no—
222C2×C3×C4—64no—
223C2×C3×C4—128no—
224C2×C3×C4C2×Dic618yes—
225C2×Dic3—24no—
226C2×Dic3—24no—
227C2×Dic3—24no—
228C2×Dic3—24no—
229C2×Dic3—24no—
230C2×Dic3—34no—
231C2×Dic3—38no—
232C2×Dic3—34no—
233C2×Dic3—48no—
234C2×Dic3—62no—
235C2×Dic3—64no—
236C2×Dic3—62no—
237C2×Dic3—616no—
238C2×Dic3—64no—
239C2×Dic3—64no—
240C2×Dic3—64no—
241C2×Dic3—64no—
242C2×Dic3—64no—
243C2×Dic3—128no—
244C2×Dic3—122no—
245C2×Dic3—122no—
246C2×Dic3—122no—
247C2×Dic3C2×C4×D314yes—
248C2×Dic3C2×C4×D314yes—
249C2×C32—24no—
250C2×C32C2×#11711yescharacteristic
251C2×C32C2×C4×Q811yescharacteristic
252C2×C32#51811yescharacteristic
253C2×C32#55312yes—
254C2×C32#55412yes—
255C24C2×D3211yescharacteristic
256C22×C4—32no—
257C22×C4—32no—
258C22×C4—38no—
259C22×C4—34no—
260C22×C4—91no—
261C22×C4—91no—
262C22×C4—94no—
263C22×C4—92no—
264C22×C4—124no—
265C22×C4—184no—
266C22×C4C2×D3212yes—
267C4⋊C4—94no—
268C4⋊C4—94no—
269C4⋊C4—98no—
270C4⋊C4—184no—
271C4⋊C4—364no—
272C22⋊C4—64no—
273C22⋊C4—182no—
274C22⋊C4#62714yes—
275C42—124no—
276C42—184no—
277C22×C3—24no—
278C22×C3—24no—
279C22×C3—28no—
280C22×C3—28no—
281C22×C3—21no—
282C22×C3—21no—
283C22×C3—22no—
284C22×C3—22no—
285C22×C3—21no—
286C22×C3—24no—
287C22×C3—42no—
288C22×C3—42no—
289C22×C3—44no—
290C22×C3—44no—
291C22×C3C4×Dic618yes—
292C22×C3C22×Dic612yes—
293C22×C3C22×C4×D312yes—
294C22×C3C2×#23512yes—
295C22×C3#100414yes—
296C22×C3D3×#4114yes—
297C3×C4—28no—
298C3×C4—44no—
299C3×C4—64no—
300C3×C4—64no—
301C3×C4—124no—
302Dic3—24no—
303Dic3—24no—
304Dic3—38no—
305Dic3—44no—
306Dic3—64no—
307Dic3—64no—
308Dic3—122no—
309Dic3—124no—
310Dic3—124no—
311C32#234511yescharacteristic, complemented, Sylow
312C23—22no—
313C23—22no—
314C23#379812yes—
315C23C4×D3212yes—
316C23C2×#62712yes—
317C23C22×D3211yescharacteristic
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—34no—
321C2×C4—34no—
322C2×C4—64no—
323C2×C4—64no—
324C2×C4—64no—
325C2×C4—64no—
326C2×C4—64no—
327C2×C4—92no—
328C2×C4—94no—
329C2×C4—92no—
330C2×C4—128no—
331C2×C4—188no—
332C2×C4—182no—
333C2×C4—182no—
334C2×C4—182no—
335C2×C4—182no—
336C2×C4C2×#62714yes—
337C2×C3—28no—
338C2×C3—21no—
339C2×C3—21no—
340C2×C3—22no—
341C2×C3—22no—
342C2×C3—21no—
343C2×C3—44no—
344C2×C3C2×C4×Dic612yes—
345C2×C3#548612yes—
346C2×C3D3×#11712yes—
347C2×C3#553914yes—
348C2×C3#554014yes—
349C22—22no—
350C22—22no—
351C22—24no—
352C22—24no—
353C22C4×#62714yes—
354C22C2×#379811yescharacteristic
355C22C2×C4×D3211yescharacteristic
356C22#6431212yes—
357C22#6431312yes—
358C22C22×#62711yescharacteristic
359C4—24no—
360C4—64no—
361C4—64no—
362C4—94no—
363C4—124no—
364C4—182no—
365C4—362no—
366C3—21no—
367C3#7345812yescomplemented
368C2—24no—
369C2#1059405211yescharacteristic
370C2#1059418111yescharacteristic
371C2#1059423112yes—
372C2C2×C4×#62711yescharacteristic
373C2#1059527412yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC24×C32C23
hypercenterC2×C22⋊C4D32
hypocenterC32#2345
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
6. C4×#3724C2semidirect
7. #10591333C2semidirect
8. #10591328C2semidirect
17. C2×#3724C4semidirect
311. C32#2345semidirect
367. C3#73458semidirect

Maximal subgroups

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

subgroupindex
C22×#37242
C22⋊C4×C3⋊Dic32
C3×Dic3×C22⋊C42
#105917202
#105917162
C4×#37242
#105913332
#105913282
#734583