Finite Group Databasebeta

← #11868754

Subgroups — #11868754

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×Q8×C3⋊Dic3C211yesmaximal, characteristic
2#10595050C211yesmaximal, characteristic
3C3×#5225C212yesmaximal
4#10591631C212yesmaximal, complemented
5#10591630C212yesmaximal, complemented
6#10591615C214yesmaximal, complemented
7#10591131C212yesmaximal
8#10591120C211yesmaximal, characteristic
9#78949—32nomaximal
10C22×C32×Q8C2211yescharacteristic
11Q8×C3⋊Dic3—21no—
12Q8×C3⋊Dic3—21no—
13Q8×C3⋊Dic3C2212yes—
14Q8×C3⋊Dic3C2212yes—
15C2×C4⋊(C3⋊Dic3)—21no—
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×C4×C3⋊Dic3—21no—
18C2×C4×C3⋊Dic3C2211yescharacteristic
19C3×#926C2212yes—
20C2×C3×#208C2212yes—
21#63982—21no—
22#63982—21no—
23#63919C2211yescharacteristic
24#63919C2211yescharacteristic
25C4×#627—21no—
26C4×#627—21no—
27#63872C2212yes—
28C3×#835C2214yes—
29C3×#835C2214yes—
30#63575C2214yes—
31#63573C2214yes—
32#63572C2212yes—
33#63572C2212yes—
34C2×Q8×Dic3—32no—
35C2×Q8×Dic3—61no—
36#5517—32no—
37C3×#419—32no—
38#5225D312yes—
39#5121—32no—
40#5118—32no—
41#4995—32no—
42#4799—34no—
43#4796—34no—
44#4793—34no—
45#4791—34no—
46C2×C32×Q8—21no—
47C2×C32×Q8—22no—
48C2×C32×Q8Q814yescomplemented
49C2×C32×Q8C2312yes—
50C22×C32×C4—21no—
51C22×C32×C4C2311yescharacteristic
52C22×C3⋊Dic3—21no—
53C22×C3⋊Dic3D411yescharacteristic
54C22×C3⋊Dic3D411yescharacteristic
55C2×#627—21no—
56C2×#627—21no—
57C4⋊(C3⋊Dic3)—21no—
58C4⋊(C3⋊Dic3)—22no—
59C4⋊(C3⋊Dic3)—22no—
60C4⋊(C3⋊Dic3)C2312yes—
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×C3×Q8—21no—
79C22×C3×Q8C2×D312yes—
80C2×C3×M16—32no—
81C3×#117—32no—
82Q8×Dic3—34no—
83Q8×Dic3—34no—
84Q8×Dic3—62no—
85Q8×Dic3—62no—
86Q8×Dic3—62no—
87Q8×Dic3—62no—
88Q8×Dic3—62no—
89Q8×Dic3—62no—
90#926C2×D312yes—
91C2×C4⋊Dic3—32no—
92C2×C4⋊Dic3—61no—
93C2×C4⋊Dic3—62no—
94C2×C4⋊Dic3—62no—
95C2×C4×Dic3—32no—
96C2×C4×Dic3—61no—
97C2×C4×Dic3—62no—
98C2×C4×Dic3—62no—
99C2×#208C2×D312yes—
100#890—32no—
101#890—32no—
102#888—32no—
103#888—32no—
104#878—62no—
105#878—62no—
106C4×Dic6—62no—
107C4×Dic6—62no—
108C3×#103—34no—
109C3×#103—34no—
110#835C2×D314yes—
111#835C2×D314yes—
112#818—34no—
113#817—34no—
114Dic3⋊C8—34no—
115Dic3⋊C8—34no—
116#808—34no—
117#807—34no—
118C23×C32C2×D411yescharacteristic
119C32×Q8—24no—
120C32×Q8—22no—
121C32×Q8C2×Q814yes—
122C2×C32×C4—24no—
123C2×C32×C4—22no—
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×Q812yes—
126C2×C32×C4#4112yes—
127C2×C32×C4C2411yescharacteristic
128C2×C3⋊Dic3—22no—
129C2×C3⋊Dic3—22no—
130C2×C3⋊Dic3—41no—
131C2×C3⋊Dic3—42no—
132C2×C3⋊Dic3C2×D411yescharacteristic
133C2×C3⋊Dic3C2×D411yescharacteristic
134C2×C3⋊Dic3C2×D411yescharacteristic
135C2×C3⋊Dic3C2×D411yescharacteristic
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—92no—
147#423—91no—
148#419—32no—
149C2×C3×Q8—22no—
150C2×C3×Q8—24no—
151C2×C3×Q8—22no—
152C2×C3×Q8—24no—
153C2×C3×Q8—24no—
154C2×C3×Q8—22no—
155C2×C3×Q8Dic618yescomplemented
156C2×C3×Q8C22×D314yes—
157C22×C3×C4—22no—
158C22×C3×C4—22no—
159C22×C3×C4—21no—
160C22×C3×C4C22×D312yes—
161C22×Dic3—32no—
162C22×Dic3—32no—
163C22×Dic3—61no—
164C22×Dic3—61no—
165C22×Dic3—62no—
166C22×Dic3—62no—
167C2×Dic6—62no—
168C2×Dic6—62no—
169C3×M16—64no—
170C2×C3×C8—34no—
171C3×C4⋊C4—32no—
172C3×C4⋊C4—32no—
173C3×C22⋊C4—62no—
174C3×C42—62no—
175#217—22no—
176C4⋊Dic3—34no—
177C4⋊Dic3—62no—
178C4⋊Dic3—62no—
179C4⋊Dic3—62no—
180C4⋊Dic3—64no—
181C4⋊Dic3—64no—
182C4⋊Dic3—64no—
183C4⋊Dic3—64no—
184C4⋊Dic3—62no—
185C4⋊Dic3—62no—
186C4⋊Dic3C22×D312yes—
187C4⋊Dic3C22×D312yes—
188Dic3⋊C4—62no—
189Dic3⋊C4—62no—
190Dic3⋊C4—62no—
191Dic3⋊C4—62no—
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—24no—
212C32×C4C22⋊Q812yes—
213C32×C4C22×Q811yescharacteristic
214C32×C4C2×#4111yescharacteristic
215C3⋊Dic3—21no—
216C3⋊Dic3—21no—
217C3⋊Dic3—21no—
218C3⋊Dic3—42no—
219C3⋊Dic3#13712yes—
220C3×Dic3—42no—
221C3×Dic3—42no—
222C22×Q8D3211yescharacteristic
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—91no—
237C2×C4⋊C4—181no—
238C2×C42—91no—
239C2×C42—181no—
240#107—94no—
241#106—94no—
242C4⋊C8—92no—
243C4⋊C8—92no—
244#103—34no—
245#103—34no—
246C23×C3—21no—
247C23×C3D3×D412yes—
248C3×Q8—24no—
249C3×Q8—28no—
250C3×Q8—28no—
251C3×Q8—24no—
252C3×Q8—24no—
253C3×Q8C2×Dic618yes—
254C2×C3×C4—24no—
255C2×C3×C4—28no—
256C2×C3×C4—28no—
257C2×C3×C4—24no—
258C2×C3×C4—21no—
259C2×C3×C4—22no—
260C2×C3×C4—22no—
261C2×C3×C4—21no—
262C2×C3×C4—62no—
263C2×C3×C4—62no—
264C2×C3×C4C2×Dic614yes—
265C2×C3×C4D3×D412yes—
266C2×C3×C4#23714yes—
267C2×C3×C4C23×D312yes—
268C2×Dic3—22no—
269C2×Dic3—22no—
270C2×Dic3—32no—
271C2×Dic3—32no—
272C2×Dic3—32no—
273C2×Dic3—32no—
274C2×Dic3—61no—
275C2×Dic3—61no—
276C2×Dic3—61no—
277C2×Dic3—61no—
278C2×Dic3—64no—
279C2×Dic3—64no—
280C2×Dic3—64no—
281C2×Dic3—64no—
282C2×Dic3—122no—
283C2×Dic3—122no—
284C2×Dic3—124no—
285C2×Dic3—124no—
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—22no—
295C2×Q8—21no—
296C2×Q8—181no—
297C2×Q8—181no—
298C2×Q8#62714yescomplemented
299C2×Q8C2×D3212yes—
300C22×C4—21no—
301C22×C4—91no—
302C22×C4—91no—
303C22×C4—181no—
304C22×C4C2×D3211yescharacteristic
305M16—64no—
306C2×C8—34no—
307C4⋊C4—32no—
308C4⋊C4—32no—
309C4⋊C4—92no—
310C4⋊C4—182no—
311C4⋊C4—182no—
312C4⋊C4—182no—
313C4⋊C4—182no—
314C4⋊C4—181no—
315C4⋊C4—181no—
316C4⋊C4—181no—
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#87814yes—
332C22×C3C2×D3×D412yes—
333C3×C4—28no—
334C3×C4—28no—
335C3×C4—21no—
336C3×C4—21no—
337C3×C4—22no—
338C3×C4—122no—
339C3×C4—122no—
340C3×C4#87814yes—
341C3×C4C22×Dic612yes—
342C3×C4C2×#23712yes—
343Dic3—34no—
344Dic3—42no—
345Dic3—42no—
346Dic3—62no—
347Dic3—62no—
348Dic3—62no—
349Dic3—62no—
350Dic3—62no—
351Dic3—121no—
352Dic3—121no—
353Dic3—124no—
354Dic3—124no—
355C32#307811yescharacteristic, complemented, Sylow
356C23#381111yescharacteristic
357Q8—22no—
358Q8—24no—
359Q8—362no—
360Q8—362no—
361Q8C2×#62714yes—
362C2×C4—22no—
363C2×C4—24no—
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—361no—
373C2×C4—362no—
374C2×C4#380512yes—
375C2×C4C2×#62712yes—
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×#87812yes—
385C2×C3D3×#13712yes—
386C2×C3#577712yes—
387C22—21no—
388C22—21no—
389C22#6398212yes—
390C22C2×#381111yescharacteristic
391C4—24no—
392C4—92no—
393C4—122no—
394C4—122no—
395C4—181no—
396C4—181no—
397C4—181no—
398C4—362no—
399C4#6398212yes—
400C4C2×#380511yescharacteristic
401C4C22×#62711yescharacteristic
402C3—21no—
403C3#7894912yescomplemented
404C2—22no—
405C2#1059532211yescharacteristic
406C2#1059532311yescharacteristic
407C2C2×#6398211yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
prime radicalC23×C32C2×D4
hypercenterC22×Q8D32
hypocenterC32#3078
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
4. #10591631C2semidirect
5. #10591630C2semidirect
6. #10591615C2semidirect
48. C2×C32×Q8Q8semidirect
155. C2×C3×Q8Dic6semidirect
298. C2×Q8#627semidirect
355. C32#3078semidirect
403. C3#78949semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×C3⋊Dic32
#105950502
C3×#52252
#105916312
#105916302
#105916152
#105911312
#105911202
#789493