Finite Group Databasebeta

← #11858825

Subgroups — #11858825

Order 1152.

982 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C3⋊Dic3C211yesmaximal, characteristic
2#10593845C212yesmaximal
3#10593806C212yesmaximal, complemented
4#10593805C212yesmaximal, complemented
5#10593804C212yesmaximal, complemented
6#10593801C212yesmaximal, complemented
7C4×#3792C212yesmaximal, complemented
8#10593795C212yesmaximal, complemented
9C23×C32×C4C411yescharacteristic
10C23×C3⋊Dic3C411yescharacteristic
11C23×C3⋊Dic3C2211yescharacteristic
12C2×#3792C2214yes—
13C2×C4×C3⋊Dic3C411yescharacteristic
14C2×C4×C3⋊Dic3C411yescharacteristic
15C2×C4×C3⋊Dic3C411yescharacteristic
16C2×C4×C3⋊Dic3C411yescharacteristic
17C2×C4×C3⋊Dic3C411yescharacteristic
18C2×C4×C3⋊Dic3C411yescharacteristic
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C2×C4×C3⋊Dic3C2211yescharacteristic
21C2×C4×C3⋊Dic3C2211yescharacteristic
22C2×C4×C3⋊Dic3C2211yescharacteristic
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C2×C4×C3⋊Dic3C2211yescharacteristic
25C22⋊#622C2214yes—
26C22⋊#622C2214yes—
27#63779C2214yescomplemented
28#63777C2214yescomplemented
29C4⋊#622C2214yescomplemented
30C4×#622C2214yescomplemented
31C22×C4×Dic3—62no—
32C24×C32C2×C411yescharacteristic
33C22×C32×C4—24no—
34C22×C32×C4C2×C411yescharacteristic
35C22×C32×C4C2×C411yescharacteristic
36C22×C32×C4C2×C411yescharacteristic
37C22×C32×C4C2×C411yescharacteristic
38C22×C32×C4C2×C411yescharacteristic
39C22×C32×C4C2×C411yescharacteristic
40C22×C3⋊Dic3—24no—
41C22×C3⋊Dic3—24no—
42C22×C3⋊Dic3C2×C411yescharacteristic
43C22×C3⋊Dic3C2×C411yescharacteristic
44C22×C3⋊Dic3C2×C411yescharacteristic
45C22×C3⋊Dic3C2×C411yescharacteristic
46C22×C3⋊Dic3C2×C411yescharacteristic
47C22×C3⋊Dic3C2×C411yescharacteristic
48C22×C3⋊Dic3C2×C411yescharacteristic
49C22×C3⋊Dic3C2×C411yescharacteristic
50C22×C3⋊Dic3C2×C411yescharacteristic
51C22×C3⋊Dic3C2311yescharacteristic
52C22×C3⋊Dic3C2311yescharacteristic
53C22×C3⋊Dic3C2311yescharacteristic
54#3792—28no—
55C2×#622C2318yes—
56C4×C3⋊Dic3C2×C411yescharacteristic
57C4×C3⋊Dic3C2×C411yescharacteristic
58C4×C3⋊Dic3C2×C411yescharacteristic
59C4×C3⋊Dic3C2×C411yescharacteristic
60C4×C3⋊Dic3C2×C411yescharacteristic
61C4×C3⋊Dic3C2×C411yescharacteristic
62C4×C3⋊Dic3C2×C411yescharacteristic
63C4×C3⋊Dic3C2×C411yescharacteristic
64C4×C3⋊Dic3C2×C411yescharacteristic
65C4×C3⋊Dic3C2×C411yescharacteristic
66C4×C3⋊Dic3C2×C411yescharacteristic
67C4×C3⋊Dic3C2×C411yescharacteristic
68C4×C3⋊Dic3C2311yescharacteristic
69C4×C3⋊Dic3C2311yescharacteristic
70C4×C3⋊Dic3C2311yescharacteristic
71C4×C3⋊Dic3C2311yescharacteristic
72#2920—91nomaximal, Sylow
73C23×C3×C4—22no—
74C23×Dic3—62no—
75C23×Dic3—62no—
76C2×C4×Dic3—62no—
77C2×C4×Dic3—62no—
78C2×C4×Dic3—62no—
79C2×C4×Dic3—62no—
80C2×C4×Dic3—62no—
81C2×C4×Dic3—62no—
82C2×C4×Dic3—62no—
83C2×C4×Dic3—62no—
84C2×C4×Dic3—62no—
85C2×C4×Dic3—62no—
86C2×C4×Dic3—62no—
87C2×C4×Dic3—62no—
88C23×C32—22no—
89C23×C32—22no—
90C23×C32—22no—
91C23×C32C22×C411yescharacteristic
92C23×C32C22×C411yescharacteristic
93C23×C32C22×C411yescharacteristic
94C2×C32×C4—22no—
95C2×C32×C4—22no—
96C2×C32×C4—22no—
97C2×C32×C4—22no—
98C2×C32×C4—22no—
99C2×C32×C4M1614yescomplemented
100C2×C32×C4C22×C411yescharacteristic
101C2×C32×C4C22×C411yescharacteristic
102C2×C32×C4C22×C411yescharacteristic
103C2×C32×C4C22×C411yescharacteristic
104C2×C3⋊Dic3—22no—
105C2×C3⋊Dic3—22no—
106C2×C3⋊Dic3—22no—
107C2×C3⋊Dic3—22no—
108C2×C3⋊Dic3—22no—
109C2×C3⋊Dic3—22no—
110C2×C3⋊Dic3—22no—
111C2×C3⋊Dic3—22no—
112C2×C3⋊Dic3—22no—
113C2×C3⋊Dic3—22no—
114C2×C3⋊Dic3M1614yescomplemented
115C2×C3⋊Dic3C22×C411yescharacteristic
116C2×C3⋊Dic3C22×C411yescharacteristic
117C2×C3⋊Dic3C22×C411yescharacteristic
118C2×C3⋊Dic3C22×C411yescharacteristic
119C2×C3⋊Dic3C22×C411yescharacteristic
120C2×C3⋊Dic3C22×C411yescharacteristic
121C2×C3⋊Dic3C22×C411yescharacteristic
122C2×C3⋊Dic3#4114yes—
123C2×C3⋊Dic3C2411yescharacteristic
124#622—28no—
125C22×C42—91no—
126#432—92no—
127#432—92no—
128#431—92no—
129#431—92no—
130#423—92no—
131#407—92no—
132C4×M16—92no—
133C24×C3—22no—
134C22×C3×C4—216no—
135C22×C3×C4—22no—
136C22×C3×C4—22no—
137C22×C3×C4—22no—
138C22×C3×C4—22no—
139C22×C3×C4—22no—
140C22×C3×C4—22no—
141C22×Dic3—62no—
142C22×Dic3—62no—
143C22×Dic3—62no—
144C22×Dic3—62no—
145C22×Dic3—62no—
146C22×Dic3—62no—
147C22×Dic3—62no—
148C22×Dic3—62no—
149C22×Dic3—62no—
150C22×Dic3—62no—
151C22×Dic3—62no—
152C22×Dic3—62no—
153C22×Dic3—616no—
154C22×Dic3—616no—
155C4×Dic3—62no—
156C4×Dic3—62no—
157C4×Dic3—62no—
158C4×Dic3—62no—
159C4×Dic3—62no—
160C4×Dic3—62no—
161C4×Dic3—62no—
162C4×Dic3—62no—
163C4×Dic3—62no—
164C4×Dic3—62no—
165C4×Dic3—62no—
166C4×Dic3—62no—
167C4×Dic3—62no—
168C4×Dic3—62no—
169C4×Dic3—62no—
170C4×Dic3—62no—
171C22×C32—28no—
172C22×C32—21no—
173C22×C32—21no—
174C22×C32—21no—
175C22×C32—21no—
176C22×C32—21no—
177C22×C32—21no—
178C22×C32#11712yes—
179C22×C32C2×M1612yes—
180C22×C32C2×M1612yes—
181C22×C32C23×C411yescharacteristic
182C32×C4—21no—
183C32×C4—21no—
184C32×C4C2×M1612yes—
185C32×C4C2×M1612yes—
186C3⋊Dic3—21no—
187C3⋊Dic3—21no—
188C3⋊Dic3—21no—
189C3⋊Dic3—21no—
190C3⋊Dic3#11712yes—
191C3⋊Dic3C2×M1612yes—
192C3⋊Dic3C2×M1612yes—
193C3⋊Dic3C2×#4112yes—
194C23×C4—91no—
195C23×C4—91no—
196C23×C4#15711yescharacteristic
197C2×M16—94no—
198C2×C42—91no—
199C2×C42—91no—
200C2×C42—91no—
201C2×C42—91no—
202C2×C42—91no—
203C2×C42—91no—
204C2×C42—91no—
205C2×C42—91no—
206C2×C42—91no—
207C2×C42—91no—
208C2×C42—91no—
209C2×C42—91no—
210C4⋊C8—94no—
211C4⋊C8—94no—
212C22⋊C8—94no—
213C22⋊C8—94no—
214#97—94no—
215C4×C8—94no—
216C23×C3—28no—
217C23×C3—28no—
218C23×C3—28no—
219C23×C3—22no—
220C23×C3—22no—
221C23×C3—22no—
222C2×C3×C4—28no—
223C2×C3×C4—28no—
224C2×C3×C4—28no—
225C2×C3×C4—28no—
226C2×C3×C4—28no—
227C2×C3×C4—22no—
228C2×C3×C4—22no—
229C2×C3×C4—22no—
230C2×C3×C4—22no—
231C2×C3×C4—28no—
232C2×Dic3—68no—
233C2×Dic3—62no—
234C2×Dic3—62no—
235C2×Dic3—62no—
236C2×Dic3—62no—
237C2×Dic3—62no—
238C2×Dic3—62no—
239C2×Dic3—62no—
240C2×Dic3—68no—
241C2×Dic3—62no—
242C2×Dic3—68no—
243C2×Dic3—68no—
244C2×Dic3—68no—
245C2×Dic3—68no—
246C2×Dic3—68no—
247C2×Dic3—68no—
248C2×Dic3—68no—
249C2×Dic3—68no—
250C2×Dic3—68no—
251C2×Dic3—68no—
252C2×C32—22no—
253C2×C32—22no—
254C2×C32—22no—
255C2×C32C2×#11711yescharacteristic
256C2×C32C22×M1611yescharacteristic
257C2×C32C22×M1611yescharacteristic
258C24C2×#15711yescharacteristic
259C22×C4—24no—
260C22×C4—91no—
261C22×C4—91no—
262C22×C4—91no—
263C22×C4—91no—
264C22×C4—91no—
265C22×C4—91no—
266C22×C4—91no—
267C22×C4—91no—
268C22×C4—91no—
269C22×C4—91no—
270C22×C4—91no—
271C22×C4—91no—
272C22×C4—184no—
273C22×C4—184no—
274C22×C4C2×#15711yescharacteristic
275C22×C4C2×#15711yescharacteristic
276C22×C4C2×#15711yescharacteristic
277C22×C4C2×#15711yescharacteristic
278C22×C4C2×#15711yescharacteristic
279C22×C4C2×#15711yescharacteristic
280M16—188no—
281C2×C8—98no—
282C42—91no—
283C42—91no—
284C42—91no—
285C42—91no—
286C42—91no—
287C42—91no—
288C42—91no—
289C42—91no—
290C42—91no—
291C42—91no—
292C42—91no—
293C42—91no—
294C42—91no—
295C42—91no—
296C42—91no—
297C42—91no—
298C22×C3—24no—
299C22×C3—24no—
300C22×C3—24no—
301C22×C3—24no—
302C22×C3—24no—
303C22×C3—24no—
304C22×C3—232no—
305C22×C3—24no—
306C22×C3—24no—
307C22×C3—24no—
308C22×C3—22no—
309C3×C4—24no—
310C3×C4—24no—
311C3×C4—24no—
312C3×C4—24no—
313Dic3—64no—
314Dic3—64no—
315Dic3—64no—
316Dic3—64no—
317Dic3—64no—
318Dic3—64no—
319Dic3—64no—
320Dic3—64no—
321C32#292011yescharacteristic, complemented, Sylow
322C23—22no—
323C23—22no—
324C23—22no—
325C23C22×#15711yescharacteristic
326C23C22×#15711yescharacteristic
327C23C22×#15711yescharacteristic
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—94no—
334C2×C4—94no—
335C2×C4—91no—
336C2×C4—91no—
337C2×C4—91no—
338C2×C4—91no—
339C2×C4—91no—
340C2×C4—91no—
341C2×C4—91no—
342C2×C4—91no—
343C2×C4—182no—
344C2×C4—182no—
345C2×C4—182no—
346C2×C4—182no—
347C2×C4—182no—
348C2×C4—182no—
349C2×C4—182no—
350C2×C4—182no—
351C2×C4—182no—
352C2×C4—182no—
353C2×C4#379214yescomplemented
354C2×C4C22×#15711yescharacteristic
355C2×C4C22×#15711yescharacteristic
356C2×C4C22×#15711yescharacteristic
357C2×C4C22×#15711yescharacteristic
358C8—188no—
359C2×C3—28no—
360C2×C3—28no—
361C2×C3—28no—
362C2×C3—22no—
363C2×C3—22no—
364C2×C3—22no—
365C22—28no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22#6428312yes—
373C22#6428612yes—
374C22C2×#379212yes—
375C22C23×#15711yescharacteristic
376C4—21no—
377C4—21no—
378C4—92no—
379C4—92no—
380C4—92no—
381C4—92no—
382C4—181no—
383C4—181no—
384C4—181no—
385C4—181no—
386C4C2×#379212yes—
387C4C2×#379212yes—
388C3—22no—
389C2—22no—
390C2—22no—
391C2—22no—
392C2C2×#6428311yescharacteristic
393C2C2×#6428611yescharacteristic
394C2C22×#379211yescharacteristic
subgroupG/H
centerC2×C4C22×#157
commutator, socleC22×C32C23×C4
FrattiniC22C23×#157
FittingC23×C32×C4C4
prime radicalC24×C32C2×C4
cosocleC2×C3⋊Dic3C24
hypercenterC23×C4#157
hypocenterC32#2920
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
3. #10593806C2semidirect
4. #10593805C2semidirect
5. #10593804C2semidirect
6. #10593801C2semidirect
7. C4×#3792C2semidirect
8. #10593795C2semidirect
27. #63779C22semidirect
28. #63777C22semidirect
29. C4⋊#622C22semidirect
30. C4×#622C22semidirect
99. C2×C32×C4M16semidirect
114. C2×C3⋊Dic3M16semidirect
321. C32#2920semidirect
353. C2×C4#3792semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C3⋊Dic32
#105938452
#105938062
#105938052
#105938042
#105938012
C4×#37922
#105937952
#29209