Finite Group Databasebeta

← #11800891

Subgroups — #11800891

Order 1152.

1557 conjugacy classes of subgroups.

The subgroup lattice has 401 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64086C211yesmaximal, characteristic
2C22×#3724C211yesmaximal, characteristic
3C2×#63957C211yesmaximal, characteristic
4C3×Dic3×C22⋊C4C212yesmaximal
5Dic3×#217C212yesmaximal
6C4×#3724C212yesmaximal, complemented
7#10591257C212yesmaximal, complemented
8#10591243C214yesmaximal, complemented
9#73435—32nomaximal
10C23×C3⋊Dic3C2211yescharacteristic
11C23×C3×Dic3C2212yes—
12C2×C32×C22⋊C4C2211yescharacteristic
13C2×#3757C2211yescharacteristic
14C2×#3750C2212yes—
15C2×C4×C3⋊Dic3C2212yes—
16#64086C418yescomplemented
17C2×C3×#217C2212yes—
18C2×C3×C4×Dic3C2214yes—
19C2×#3724C418yescomplemented
20C2×#3724C2212yes—
21C2×#3724C2211yescharacteristic
22C2×#3724C2211yescharacteristic
23C2×#3724C2212yes—
24#63957C418yescomplemented
25C2×Dic32C2214yes—
26C2×Dic32C2212yes—
27C3×C3⋊#95C2214yes—
28#63579C2214yes—
29C22×Dic3⋊C4—32no—
30C2×#877—32no—
31C2×#877—32no—
32C2×#877—61no—
33C3×C4×C22⋊C4—32no—
34C4×#217—32no—
35Dic3×C22⋊C4—32no—
36Dic3×C22⋊C4D312yes—
37C4×Dic3⋊C4—34no—
38C4×Dic3⋊C4—34no—
39#4649—34no—
40#4649—34no—
41C24×C32C2311yescharacteristic
42C22×C32×C4C2312yes—
43C22×C3⋊Dic3C2×C414yes—
44C22×C3⋊Dic3C2×C414yes—
45C22×C3⋊Dic3C2×C414yes—
46C22×C3⋊Dic3C2312yes—
47C22×C3⋊Dic3C2311yescharacteristic
48C22×C3⋊Dic3C2311yescharacteristic
49C22×C3×Dic3—44no—
50C22×C3×Dic3C2×C418yes—
51C22×C3×Dic3C2312yes—
52C22×C3×Dic3C2314yes—
53C22×C3×Dic3C2312yes—
54C32×C22⋊C4C2×C414yes—
55#3757C2×C414yes—
56#3750C2×C418yescomplemented
57C4×C3⋊Dic3C2×C418yescomplemented
58C3×#217C2×C418yes—
59C3×C4×Dic3—44no—
60#3724C2×C418yes—
61#3724C2×C414yes—
62#3724C2×C414yes—
63#3724C2×C418yescomplemented
64Dic32—44no—
65Dic32C2×C418yescomplemented
66#2274—91noSylow
67C23×C3×C4—32no—
68C23×Dic3—32no—
69C23×Dic3—61no—
70C23×Dic3C2×D312yes—
71C2×C3×C22⋊C4—21no—
72C2×C3×C22⋊C4—32no—
73C2×C3×C22⋊C4C2×D312yes—
74C2×C3×C42—34no—
75C2×#217—32no—
76C2×#217—61no—
77C2×#217C2×D312yes—
78C2×Dic3⋊C4—34no—
79C2×Dic3⋊C4—316no—
80C2×Dic3⋊C4—32no—
81C2×Dic3⋊C4—32no—
82C2×Dic3⋊C4—34no—
83C2×Dic3⋊C4—32no—
84C2×Dic3⋊C4—32no—
85C2×Dic3⋊C4—62no—
86C2×C4×Dic3—34no—
87C2×C4×Dic3—34no—
88C2×C4×Dic3—34no—
89C2×C4×Dic3—34no—
90C2×C4×Dic3—62no—
91C2×C4×Dic3C2×D314yes—
92#877—316no—
93#877—316no—
94#877—68no—
95C3×#95—34no—
96C3⋊#95—34no—
97C3⋊#95—34no—
98C3⋊#95C2×D314yes—
99C23×C32—22no—
100C23×C32—22no—
101C23×C32C22×C412yes—
102C23×C32C22×C412yes—
103C23×C32C22×C412yes—
104C23×C32C2411yescharacteristic
105C2×C32×C4—22no—
106C2×C32×C4—22no—
107C2×C32×C4C22×C414yes—
108C2×C3⋊Dic3—22no—
109C2×C3⋊Dic3—22no—
110C2×C3⋊Dic3C42116yescomplemented
111C2×C3⋊Dic3C22×C414yes—
112C2×C3⋊Dic3C22×C412yes—
113C2×C3⋊Dic3C22×C412yes—
114C2×C3⋊Dic3C22×C412yes—
115C2×C3⋊Dic3C22×C412yes—
116C2×C3⋊Dic3C22×C412yes—
117C2×C3⋊Dic3C22×C412yes—
118C2×C3×Dic3—24no—
119C2×C3×Dic3—24no—
120C2×C3×Dic3—24no—
121C2×C3×Dic3—24no—
122C2×C3×Dic3—48no—
123C2×C3×Dic3C22×C418yes—
124C2×C3×Dic3C22×C414yes—
125C2×C3×Dic3C22×C414yes—
126C2×#117—91no—
127C2×#117—91no—
128C22×C4⋊C4—91no—
129C4×C4⋊C4—92no—
130C4×C4⋊C4—94no—
131C4×C4⋊C4—92no—
132C4×C22⋊C4—32no—
133C4×C22⋊C4—92no—
134C24×C3—21no—
135C24×C3C22×D312yes—
136C22×C3×C4—22no—
137C22×C3×C4—32no—
138C22×C3×C4—34no—
139C22×C3×C4—32no—
140C22×C3×C4—38no—
141C22×C3×C4—124no—
142C22×C3×C4C22×D314yes—
143C22×Dic3—38no—
144C22×Dic3—38no—
145C22×Dic3—38no—
146C22×Dic3—32no—
147C22×Dic3—32no—
148C22×Dic3—34no—
149C22×Dic3—44no—
150C22×Dic3—64no—
151C22×Dic3—61no—
152C22×Dic3—61no—
153C22×Dic3—64no—
154C22×Dic3—64no—
155C22×Dic3—62no—
156C22×Dic3C4×D318yes—
157C22×Dic3C22×D312yes—
158C22×Dic3C22×D314yes—
159C22×Dic3C22×D312yes—
160C3×C22⋊C4—24no—
161C3×C22⋊C4—38no—
162C3×C22⋊C4C4×D318yes—
163C3×C42—124no—
164#217—38no—
165#217—64no—
166#217C4×D318yes—
167Dic3⋊C4—316no—
168Dic3⋊C4—316no—
169Dic3⋊C4—38no—
170Dic3⋊C4—38no—
171Dic3⋊C4—38no—
172Dic3⋊C4—38no—
173Dic3⋊C4—68no—
174C4×Dic3—316no—
175C4×Dic3—316no—
176C4×Dic3—44no—
177C4×Dic3—68no—
178C4×Dic3—124no—
179C4×Dic3—124no—
180C22×C32—22no—
181C22×C32—22no—
182C22×C32—24no—
183C22×C32—24no—
184C22×C32C2×C4214yes—
185C22×C32C23×C411yescharacteristic
186C22×C32C23×C411yescharacteristic
187C22×C32C23×C411yescharacteristic
188C22×C32H(5,𝔽2)12yes—
189C22×C322−1+412yes—
190C32×C4—24no—
191C3⋊Dic3—24no—
192C3⋊Dic3C2×C4214yes—
193C3⋊Dic3C2×C4214yes—
194C3×Dic3—24no—
195C3×Dic3—24no—
196C3×Dic3—28no—
197C23×C4—32no—
198C23×C4—91no—
199#117—98no—
200#117—98no—
201C2×C4⋊C4—91no—
202C2×C4⋊C4—92no—
203C2×C4⋊C4—91no—
204C2×C4⋊C4—98no—
205C2×C4⋊C4—92no—
206C2×C4⋊C4—92no—
207C2×C22⋊C4—32no—
208C2×C22⋊C4—91no—
209C2×C22⋊C4D3211yescharacteristic
210C2×C42—34no—
211C2×C42—92no—
212C2×C42—92no—
213C2×C42—94no—
214#95—34no—
215#95—94no—
216C23×C3—24no—
217C23×C3—24no—
218C23×C3—21no—
219C23×C3—22no—
220C23×C3—22no—
221C23×C3—22no—
222C23×C3—42no—
223C23×C3—42no—
224C23×C3C2×C4×D314yes—
225C23×C3C2×C4×D314yes—
226C23×C3C2×C4×D314yes—
227C23×C3C23×D312yes—
228C2×C3×C4—24no—
229C2×C3×C4—24no—
230C2×C3×C4—24no—
231C2×C3×C4—38no—
232C2×C3×C4—34no—
233C2×C3×C4—34no—
234C2×C3×C4—42no—
235C2×C3×C4—42no—
236C2×C3×C4—64no—
237C2×C3×C4—64no—
238C2×C3×C4—64no—
239C2×C3×C4—64no—
240C2×C3×C4—128no—
241C2×C3×C4C2×C4×D318yes—
242C2×Dic3—24no—
243C2×Dic3—24no—
244C2×Dic3—24no—
245C2×Dic3—24no—
246C2×Dic3—332no—
247C2×Dic3—34no—
248C2×Dic3—34no—
249C2×Dic3—34no—
250C2×Dic3—34no—
251C2×Dic3—34no—
252C2×Dic3—34no—
253C2×Dic3—38no—
254C2×Dic3—48no—
255C2×Dic3—616no—
256C2×Dic3—62no—
257C2×Dic3—62no—
258C2×Dic3—62no—
259C2×Dic3—62no—
260C2×Dic3—62no—
261C2×Dic3—62no—
262C2×Dic3—64no—
263C2×Dic3—64no—
264C2×Dic3—64no—
265C2×Dic3—122no—
266C2×Dic3—122no—
267C2×Dic3C2×C4×D318yes—
268C2×Dic3C2×C4×D314yes—
269C2×Dic3C2×C4×D314yes—
270C2×C32—24no—
271C2×C32C22×C4211yescharacteristic
272C2×C32#51811yescharacteristic
273C2×C32#51911yescharacteristic
274C2×C32#52012yes—
275C2×C32#52012yes—
276C24C2×D3211yescharacteristic
277C22×C4—32no—
278C22×C4—34no—
279C22×C4—32no—
280C22×C4—38no—
281C22×C4—91no—
282C22×C4—91no—
283C22×C4—94no—
284C22×C4—94no—
285C22×C4—94no—
286C22×C4—92no—
287C22×C4—124no—
288C22×C4C2×D3212yes—
289C4⋊C4—94no—
290C4⋊C4—98no—
291C4⋊C4—94no—
292C4⋊C4—98no—
293C4⋊C4—98no—
294C22⋊C4—38no—
295C22⋊C4—94no—
296C22⋊C4#62414yes—
297C42—98no—
298C42—98no—
299C42—124no—
300C42—364no—
301C22×C3—24no—
302C22×C3—24no—
303C22×C3—28no—
304C22×C3—28no—
305C22×C3—21no—
306C22×C3—21no—
307C22×C3—22no—
308C22×C3—22no—
309C22×C3—21no—
310C22×C3—24no—
311C22×C3—44no—
312C22×C3—42no—
313C22×C3—44no—
314C22×C3—42no—
315C22×C3C42×D318yes—
316C22×C3C22×C4×D312yes—
317C22×C3C22×C4×D312yes—
318C22×C3C22×C4×D312yes—
319C22×C3#100414yes—
320C22×C3#101014yes—
321C3×C4—28no—
322C3×C4—44no—
323C3×C4—64no—
324C3×C4—64no—
325C3×C4—68no—
326Dic3—24no—
327Dic3—24no—
328Dic3—28no—
329Dic3—38no—
330Dic3—38no—
331Dic3—64no—
332Dic3—64no—
333Dic3—68no—
334Dic3—124no—
335C32#227411yescharacteristic, complemented, Sylow
336C23—22no—
337C23—22no—
338C23C4×D3212yes—
339C23C4×D3212yes—
340C23C2×#62412yes—
341C23C22×D3211yescharacteristic
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—38no—
345C2×C4—34no—
346C2×C4—34no—
347C2×C4—64no—
348C2×C4—64no—
349C2×C4—64no—
350C2×C4—64no—
351C2×C4—92no—
352C2×C4—92no—
353C2×C4—92no—
354C2×C4—92no—
355C2×C4—92no—
356C2×C4—92no—
357C2×C4—916no—
358C2×C4—94no—
359C2×C4—128no—
360C2×C4—182no—
361C2×C4—182no—
362C2×C4C2×#62414yes—
363C2×C3—28no—
364C2×C3—22no—
365C2×C3—21no—
366C2×C3—21no—
367C2×C3—22no—
368C2×C3—21no—
369C2×C3—44no—
370C2×C3C2×C42×D312yes—
371C2×C3#548612yes—
372C2×C3#551612yes—
373C2×C3#554614yes—
374C2×C3#554614yes—
375C22—24no—
376C22—22no—
377C22—24no—
378C22—22no—
379C22C4×#62414yes—
380C22C2×C4×D3211yescharacteristic
381C22C2×C4×D3211yescharacteristic
382C22#6430912yes—
383C22#6431312yes—
384C22C22×#62411yescharacteristic
385C4—24no—
386C4—68no—
387C4—64no—
388C4—64no—
389C4—94no—
390C4—94no—
391C4—184no—
392C3—21no—
393C3#7343512yescomplemented
394C2—24no—
395C2#1059405112yes—
396C2#1059418111yescharacteristic
397C2#1059424511yescharacteristic
398C2C2×C4×#62411yescharacteristic
399C2#1059521912yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC2×C32C22×C42
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC24×C32C23
hypercenterC2×C22⋊C4D32
hypocenterC32#2274
LCSG ▷ C2×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. #10591257C2semidirect
8. #10591243C2semidirect
16. #64086C4semidirect
19. C2×#3724C4semidirect
24. #63957C4semidirect
56. #3750C2×C4semidirect
57. C4×C3⋊Dic3C2×C4semidirect
63. #3724C2×C4semidirect
65. Dic32C2×C4semidirect
110. C2×C3⋊Dic3C42semidirect
335. C32#2274semidirect
393. C3#73435semidirect

Maximal subgroups

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

subgroupindex
C2×#640862
C22×#37242
C2×#639572
C3×Dic3×C22⋊C42
Dic3×#2172
C4×#37242
#105912572
#105912432
#734353