Finite Group Databasebeta

← #11868759

Subgroups — #11868759

Order 1152.

901 conjugacy classes of subgroups.

The subgroup lattice has 409 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64096C211yesmaximal, characteristic
2#10595050C211yesmaximal, characteristic
3C3×#4964C212yesmaximal
4#10591120C211yesmaximal, characteristic
5#10591107C212yesmaximal
6#10590434C214yesmaximal, complemented
7#10590432C212yesmaximal, complemented
8#10590431C212yesmaximal, complemented
9#79245—32nomaximal
10C22×#634C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×#3750—21no—
13C2×C4×C3⋊Dic3—21no—
14C2×C4×C3⋊Dic3C2211yescharacteristic
15#64096—21no—
16#64096—21no—
17#64096C2212yes—
18#64096C2212yes—
19C3×#926C2212yes—
20C2×C3×#208C2212yes—
21#63982—21no—
22#63982—21no—
23#63919C2211yescharacteristic
24#63919C2211yescharacteristic
25C4×#627—21no—
26C4×#627—21no—
27#63872C2212yes—
28C3×#808C2214yes—
29C3×#807C2214yes—
30#63572C2212yes—
31#63572C2212yes—
32#63567C2214yes—
33#63567C2214yes—
34#5517—32no—
35C2×#887—32no—
36C2×#887—61no—
37C3×#428—32no—
38#5120—32no—
39#5118—32no—
40#5004—32no—
41#4964D312yes—
42#4877—34no—
43#4875—34no—
44#4857—34no—
45#4854—34no—
46C22×C32×C4—21no—
47C22×C32×C4C2311yescharacteristic
48C22×C3⋊Dic3—21no—
49C22×C3⋊Dic3D411yescharacteristic
50C22×C3⋊Dic3D411yescharacteristic
51C2×#634—21no—
52C2×#634—22no—
53C2×#634Q814yescomplemented
54C2×#634C2312yes—
55C2×#627—21no—
56C2×#627—21no—
57C32×C4⋊C4—21no—
58C32×C4⋊C4C2312yes—
59#3750—22no—
60#3750—22no—
61C4×C3⋊Dic3—22no—
62C4×C3⋊Dic3—22no—
63C4×C3⋊Dic3D411yescharacteristic
64C4×C3⋊Dic3D411yescharacteristic
65C4×C3⋊Dic3C2311yescharacteristic
66C4×C3⋊Dic3C2311yescharacteristic
67C3×#217—22no—
68C3×C4⋊Dic3C2312yes—
69C3×C4⋊Dic3C2312yes—
70C3×C4×Dic3—22no—
71C3×#208—24no—
72C2×C3×C3⋊C8C2314yes—
73#3724—21no—
74#3724—21no—
75Dic3⋊Dic3—22no—
76Dic3⋊Dic3—22no—
77#3078—91noSylow
78C22×Dic6—32no—
79C22×Dic6—61no—
80C2×C3×M16—32no—
81C3×#117—32no—
82C2×C3×C4⋊C4—21no—
83C2×C3×C4⋊C4C2×D312yes—
84#926C2×D312yes—
85C2×Dic3⋊C4—62no—
86C2×Dic3⋊C4—62no—
87C2×C4×Dic3—32no—
88C2×C4×Dic3—61no—
89C2×C4×Dic3—62no—
90C2×C4×Dic3—62no—
91C2×#208C2×D312yes—
92#890—32no—
93#890—32no—
94#888—32no—
95#888—32no—
96#887—34no—
97#887—34no—
98#887—62no—
99#887—62no—
100#887—62no—
101#887—62no—
102#887—62no—
103#887—62no—
104#878—62no—
105#878—62no—
106C4×Dic6—62no—
107C4×Dic6—62no—
108C3×#107—34no—
109C3×#106—34no—
110#816—34no—
111#816—34no—
112Dic3⋊C8—34no—
113Dic3⋊C8—34no—
114#810—34no—
115#810—34no—
116#808C2×D314yes—
117#807C2×D314yes—
118C23×C32C2×D411yescharacteristic
119C2×C32×C4—22no—
120C2×C32×C4—42no—
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×Q812yes—
123C2×C32×C4#4112yes—
124C2×C32×C4C2411yescharacteristic
125C2×C3⋊Dic3—24no—
126C2×C3⋊Dic3—22no—
127C2×C3⋊Dic3—22no—
128C2×C3⋊Dic3—41no—
129C2×C3⋊Dic3C2×D411yescharacteristic
130C2×C3⋊Dic3C2×D411yescharacteristic
131C2×C3⋊Dic3C2×D411yescharacteristic
132C2×C3⋊Dic3C2×D411yescharacteristic
133#634—24no—
134#634—22no—
135#634C2×Q814yes—
136C2×C3×Dic3—22no—
137C2×C3×Dic3—22no—
138#627—42no—
139#627—42no—
140C3×C3⋊C8—24no—
141#533—91no—
142C2×C4×Q8—91no—
143#479—94no—
144#477—92no—
145#475—92no—
146#428—32no—
147#423—91no—
148#419—92no—
149C22×C3×C4—22no—
150C22×C3×C4—22no—
151C22×C3×C4—21no—
152C22×C3×C4C22×D312yes—
153C22×Dic3—32no—
154C22×Dic3—32no—
155C22×Dic3—61no—
156C22×Dic3—61no—
157C22×Dic3—62no—
158C22×Dic3—62no—
159C2×Dic6—38no—
160C2×Dic6—34no—
161C2×Dic6—62no—
162C2×Dic6—64no—
163C2×Dic6—62no—
164C2×Dic6—64no—
165C2×Dic6—64no—
166C2×Dic6—62no—
167C2×Dic6—62no—
168C2×Dic6—62no—
169C3×M16—64no—
170C2×C3×C8—34no—
171C3×C4⋊C4—22no—
172C3×C4⋊C4—22no—
173C3×C4⋊C4—22no—
174C3×C4⋊C4—32no—
175C3×C4⋊C4—32no—
176C3×C4⋊C4C22×D314yes—
177C3×C22⋊C4—62no—
178C3×C42—62no—
179#217—22no—
180C4⋊Dic3—62no—
181C4⋊Dic3—62no—
182C4⋊Dic3C22×D312yes—
183C4⋊Dic3C22×D312yes—
184Dic3⋊C4—62no—
185Dic3⋊C4—62no—
186Dic3⋊C4—62no—
187Dic3⋊C4—62no—
188Dic3⋊C4—64no—
189Dic3⋊C4—64no—
190Dic3⋊C4—64no—
191Dic3⋊C4—64no—
192C4×Dic3—22no—
193C4×Dic3—32no—
194C4×Dic3—32no—
195C4×Dic3—32no—
196C4×Dic3—32no—
197C4×Dic3—61no—
198C4×Dic3—61no—
199C4×Dic3—61no—
200C4×Dic3—61no—
201C4×Dic3—64no—
202C4×Dic3—64no—
203C4×Dic3—64no—
204C4×Dic3—64no—
205#208—24no—
206C2×C3⋊C8C22×D314yes—
207C22×C32—21no—
208C22×C32—21no—
209C22×C32C22⋊Q812yes—
210C22×C32C22×D411yescharacteristic
211C32×C4—42no—
212C32×C4C22⋊Q812yes—
213C32×C4C22×Q811yescharacteristic
214C32×C4C2×#4111yescharacteristic
215C3⋊Dic3—24no—
216C3⋊Dic3—21no—
217C3⋊Dic3—21no—
218C3⋊Dic3—21no—
219C3⋊Dic3#13712yes—
220C3×Dic3—42no—
221C3×Dic3—42no—
222C22×Q8—91no—
223C2×M16—32no—
224C4⋊Q8—91no—
225C4⋊Q8—91no—
226#125—92no—
227C22⋊Q8—181no—
228C22⋊Q8—181no—
229C4×Q8—92no—
230C4×Q8—92no—
231C4×Q8—181no—
232C4×Q8—181no—
233C4×Q8—181no—
234C4×Q8—181no—
235#117—32no—
236C2×C4⋊C4—181no—
237C2×C4⋊C4D3211yescharacteristic
238C2×C42—91no—
239C2×C42—181no—
240#107—34no—
241#106—34no—
242C4⋊C8—92no—
243C4⋊C8—92no—
244#103—94no—
245#103—94no—
246C23×C3—21no—
247C23×C3D3×D412yes—
248C2×C3×C4—24no—
249C2×C3×C4—24no—
250C2×C3×C4—21no—
251C2×C3×C4—22no—
252C2×C3×C4—22no—
253C2×C3×C4—21no—
254C2×C3×C4—44no—
255C2×C3×C4—44no—
256C2×C3×C4—62no—
257C2×C3×C4—62no—
258C2×C3×C4#23514yes—
259C2×C3×C4D3×D412yes—
260C2×C3×C4D3×Q814yes—
261C2×C3×C4C23×D312yes—
262C2×Dic3—22no—
263C2×Dic3—22no—
264C2×Dic3—32no—
265C2×Dic3—32no—
266C2×Dic3—32no—
267C2×Dic3—32no—
268C2×Dic3—61no—
269C2×Dic3—61no—
270C2×Dic3—61no—
271C2×Dic3—61no—
272C2×Dic3—64no—
273C2×Dic3—64no—
274C2×Dic3—68no—
275C2×Dic3—64no—
276C2×Dic3—68no—
277C2×Dic3—64no—
278C2×Dic3—122no—
279C2×Dic3—122no—
280Dic6—38no—
281Dic6—64no—
282Dic6—64no—
283Dic6—68no—
284Dic6—68no—
285Dic6—64no—
286Dic6—124no—
287Dic6—124no—
288C3×C8—64no—
289C3⋊C8—24no—
290C2×C32—22no—
291C2×C32C2×C22⋊Q811yescharacteristic
292C2×C32C2×#13711yescharacteristic
293C2×C32#57511yescharacteristic
294C2×Q8—92no—
295C2×Q8—94no—
296C2×Q8—181no—
297C2×Q8—181no—
298C2×Q8—182no—
299C2×Q8—181no—
300C22×C4—21no—
301C22×C4—91no—
302C22×C4—91no—
303C22×C4—181no—
304C22×C4C2×D3211yescharacteristic
305M16—64no—
306C2×C8—34no—
307C4⋊C4—21no—
308C4⋊C4—32no—
309C4⋊C4—32no—
310C4⋊C4—182no—
311C4⋊C4—182no—
312C4⋊C4—182no—
313C4⋊C4—182no—
314C4⋊C4—181no—
315C4⋊C4—181no—
316C4⋊C4C2×D3212yes—
317C22⋊C4—62no—
318C42—62no—
319C42—91no—
320C42—91no—
321C42—91no—
322C42—91no—
323C42—182no—
324C42—182no—
325C22×C3—22no—
326C22×C3—22no—
327C22×C3—22no—
328C22×C3—22no—
329C22×C3—21no—
330C22×C3—22no—
331C22×C3#89614yes—
332C22×C3C2×D3×D412yes—
333C3×C4—21no—
334C3×C4—21no—
335C3×C4—22no—
336C3×C4—44no—
337C3×C4—44no—
338C3×C4—122no—
339C3×C4—122no—
340C3×C4#89614yes—
341C3×C4C2×#23512yes—
342C3×C4C2×D3×Q812yes—
343Dic3—34no—
344Dic3—42no—
345Dic3—42no—
346Dic3—62no—
347Dic3—68no—
348Dic3—62no—
349Dic3—68no—
350Dic3—62no—
351Dic3—62no—
352Dic3—62no—
353Dic3—121no—
354Dic3—121no—
355C32#307811yescharacteristic, complemented, Sylow
356C23#381111yescharacteristic
357Q8—94no—
358Q8—182no—
359Q8—184no—
360Q8—362no—
361Q8—362no—
362C2×C4—22no—
363C2×C4—42no—
364C2×C4—62no—
365C2×C4—62no—
366C2×C4—91no—
367C2×C4—91no—
368C2×C4—91no—
369C2×C4—91no—
370C2×C4—182no—
371C2×C4—182no—
372C2×C4—184no—
373C2×C4—361no—
374C2×C4#379712yes—
375C2×C4#379812yes—
376C2×C4#381111yescharacteristic
377C2×C4C22×D3211yescharacteristic
378C8—64no—
379C2×C3—24no—
380C2×C3—24no—
381C2×C3—21no—
382C2×C3—21no—
383C2×C3—21no—
384C2×C3C2×#89612yes—
385C2×C3#577312yes—
386C2×C3D3×#13712yes—
387C22—21no—
388C22—21no—
389C22#6386512yes—
390C22C2×#381111yescharacteristic
391C4—42no—
392C4—92no—
393C4—122no—
394C4—122no—
395C4—181no—
396C4—181no—
397C4—184no—
398C4—181no—
399C4#6386512yes—
400C4C2×#379711yescharacteristic
401C4C2×#379811yescharacteristic
402C3—21no—
403C3#7924512yescomplemented
404C2—22no—
405C2C2×#6386511yescharacteristic
406C2#1059510111yescharacteristic
407C2#1059532211yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
prime radicalC23×C32C2×D4
hypercenterC2×C4⋊C4D32
hypocenterC32#3078
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
6. #10590434C2semidirect
7. #10590432C2semidirect
8. #10590431C2semidirect
53. C2×#634Q8semidirect
355. C32#3078semidirect
403. C3#79245semidirect

Maximal subgroups

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

subgroupindex
C2×#640962
#105950502
C3×#49642
#105911202
#105911072
#105904342
#105904322
#105904312
#792453