Finite Group Databasebeta

← #11901750

Subgroups — #11901750

Order 1152.

3120 conjugacy classes of subgroups.

The subgroup lattice has 411 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#532C211yesmaximal, characteristic, complemented
2#10596299C212yesmaximal, complemented
3#41×C3⋊Dic3C212yesmaximal, complemented
4#10596202C212yesmaximal, complemented
5#10596190C212yesmaximal, complemented
6#10596153C214yesmaximal, complemented
7#10596088C214yesmaximal, complemented
8#10596073C214yesmaximal, complemented
9#10596009C218yesmaximal, complemented
10C2×#64081C211yesmaximal, characteristic, complemented
11#10595941C211yesmaximal, characteristic, complemented
12#86236—34nomaximal
13C2×C32×#41C2212yes—
14C22×C4×C3⋊D3C2211yescharacteristic
15C32×C4⋊Q8C2211yescharacteristic, complemented
16C32×#127C2211yescharacteristic, complemented
17C32×#124C2212yescomplemented
18C32×#121C2214yes—
19C32×C4×D4C2214yescomplemented
20C2×C32×C42C2211yescharacteristic
21#64155C2214yes—
22Q8×C3⋊Dic3C2214yescomplemented
23#64148C2218yes—
24#64147C2214yes—
25#64146C2214yes—
26#64144C2214yes—
27#64144C2218yescomplemented
28D4×C3⋊Dic3C2218yes—
29D4×C3⋊Dic3C2214yescomplemented
30C4×#638C2218yes—
31C2×#3752C2212yes—
32#64135C2212yes—
33#64135C2214yescomplemented
34#64133C2214yes—
35C2×#3750C2212yes—
36C2×C4×C3⋊Dic3C2211yescharacteristic
37C2×C4×C3⋊Dic3C2214yescomplemented
38#64107C2218yes—
39#64098C2218yescomplemented
40#64095C2218yes—
41#64094C2218yes—
42#64088C2218yescomplemented
43#64087C2218yescomplemented
44#64081C2212yes—
45#64081C2212yes—
46#64081C2214yes—
47#64079C2212yescomplemented
48#64078C2212yescomplemented
49C4×#634C2214yescomplemented
50C3×#532D314yescomplemented
51#5828—38no—
52Dic3×#41—38no—
53#5731—38no—
54#5719—38no—
55#5682—316no—
56#5617—316no—
57#5602—316no—
58#5538—332no—
59C2×#872—34no—
60#5470—34no—
61C23×C3⋊D3C2311yescharacteristic
62C32×#41—28no—
63C2×C32×Q8C2312yes—
64C2×C32×D4C2314yes—
65C2×C32×D4C2312yes—
66C2×C32×D4C2314yes—
67C22×C32×C4C2314yes—
68C22×C32×C4C2312yes—
69C22×C32×C4C2311yescharacteristic
70C2×#638C2318yes—
71C22×C3⋊Dic3C2311yescharacteristic
72C22×C3⋊Dic3C2318yes—
73C22×C3⋊Dic3C2312yes—
74C2×C4×C3⋊D3—24no—
75C2×C4×C3⋊D3C2312yes—
76C2×C4×C3⋊D3C2312yes—
77C2×#634C2314yes—
78C32×C4⋊C4C2314yes—
79C32×C22⋊C4C2318yes—
80C32×C42C2312yes—
81C32×C42C2311yescharacteristic
82C32×C42C2311yescharacteristic
83#3757C2318yes—
84#3757C2318yes—
85#3757C2314yes—
86#3752C2314yes—
87#3752C2314yes—
88#3752C2318yes—
89C4⋊(C3⋊Dic3)C2314yes—
90C4⋊(C3⋊Dic3)C2314yes—
91C4⋊(C3⋊Dic3)C2318yes—
92#3750C2318yes—
93#3750C2314yes—
94#3750C2314yes—
95#3750C2318yes—
96C4×C3⋊Dic3C2314yes—
97C4×C3⋊Dic3C2312yes—
98C4×C3⋊Dic3C2312yes—
99C4×C3⋊Dic3C2318yes—
100#3455—91noSylow
101C2×C3×#41C2×D318yes—
102C22×C4×D3—34no—
103C3×C4⋊Q8C2×D314yescomplemented
104C3×#127C2×D314yescomplemented
105C3×#124C2×D318yescomplemented
106C3×#121C2×D3116yes—
107C3×C4×D4C2×D3116yescomplemented
108C2×C3×C42C2×D314yes—
109#946—316no—
110Q8×Dic3—316no—
111#939—332no—
112#938—316no—
113#937—316no—
114#935—332no—
115#935—316no—
116D4×Dic3—316no—
117D4×Dic3—332no—
118C4×#67—332no—
119C2×(C2×D3)⋊C4—38no—
120#926—38no—
121#926—316no—
122#924—316no—
123C2×Dic3⋊C4—38no—
124C2×C4×Dic3—34no—
125C2×C4×Dic3—316no—
126#898—332no—
127#889—332no—
128#886—332no—
129#885—332no—
130#879—332no—
131#878—332no—
132#872—38no—
133#872—38no—
134#872—316no—
135#870—38no—
136#869—38no—
137C4×Dic6—316no—
138C23×C32C2414yes—
139C23×C32C2411yescharacteristic
140C22×C3⋊D3—22no—
141C22×C3⋊D3—42no—
142C22×C3⋊D3C2412yes—
143C32×Q8—24no—
144C32×D4—28no—
145C32×D4—24no—
146C32×D4—44no—
147C2×C32×C4—28no—
148C2×C32×C4—42no—
149C2×C32×C4#4114yes—
150C2×C32×C4C2414yes—
151C2×C32×C4C2412yes—
152C2×C32×C4C2412yes—
153C2×C32×C4C2411yescharacteristic
154C2×C32×C4C2411yescharacteristic
155#638—48no—
156C2×C3⋊Dic3—22no—
157C2×C3⋊Dic3—48no—
158C2×C3⋊Dic3—42no—
159C2×C3⋊Dic3C2414yes—
160C2×C3⋊Dic3C2418yes—
161C2×C3⋊Dic3C2412yes—
162C4×C3⋊D3—24no—
163C4×C3⋊D3—24no—
164#634—44no—
165#542—94no—
166#541—92no—
167#540—92no—
168#539—94no—
169#538—94no—
170#533—91no—
171#532C3⋊D311yescharacteristic, complemented
172#529—98no—
173#525—92no—
174C4×#41—92no—
175C2×#117—91no—
176C23×D3—34no—
177C3×#41—232no—
178C2×C3×Q8C22×D318yes—
179C2×C3×D4C22×D3116yes—
180C2×C3×D4C22×D318yes—
181C2×C3×D4C22×D3116yes—
182C22×C3×C4C22×D3116yes—
183C22×C3×C4C22×D318yes—
184C22×C3×C4C22×D314yes—
185C2×#67—332no—
186C22×Dic3—34no—
187C22×Dic3—332no—
188C22×Dic3—38no—
189C2×C4×D3—38no—
190C2×C4×D3—38no—
191C2×C4×D3—616no—
192C2×Dic6—316no—
193C3×C4⋊C4C22×D3116yes—
194C3×C22⋊C4C22×D3132yes—
195C3×C42C22×D318yes—
196C3×C42C22×D314yes—
197C3×C42C22×D314yes—
198#217—332no—
199#217—332no—
200#217—316no—
201(C2×D3)⋊C4—316no—
202(C2×D3)⋊C4—316no—
203(C2×D3)⋊C4—332no—
204C4⋊Dic3—316no—
205C4⋊Dic3—316no—
206C4⋊Dic3—332no—
207Dic3⋊C4—332no—
208Dic3⋊C4—316no—
209Dic3⋊C4—316no—
210Dic3⋊C4—332no—
211C4×Dic3—316no—
212C4×Dic3—38no—
213C4×Dic3—38no—
214C4×Dic3—332no—
215C22×C32—22no—
216C22×C32—24no—
217C22×C32—28no—
218C22×C32C2×#4112yes—
219C22×C32C2511yescharacteristic
220C2×C3⋊D3—22no—
221C2×C3⋊D3—24no—
222C2×C3⋊D3—44no—
223C32×C4—24no—
224C32×C4—22no—
225C32×C4—22no—
226C32×C4C2×#4112yes—
227C32×C4C2×#4112yes—
228C3⋊Dic3—22no—
229C3⋊Dic3—28no—
230C3⋊Dic3—24no—
231C2×#41C2×C3⋊D312yes—
232C23×C4—91no—
233C4⋊Q8—92no—
234C4⋊Q8C2×C3⋊D311yescharacteristic, complemented
235#127C2×C3⋊D311yescharacteristic, complemented
236#126—98no—
237#126—98no—
238#125—98no—
239#125—92no—
240#124—98no—
241#124C2×C3⋊D312yescomplemented
242#123—94no—
243#123—98no—
244#123—98no—
245C22⋊Q8—94no—
246C22⋊Q8—94no—
247C22⋊Q8—98no—
248#121—94no—
249#121—98no—
250#121C2×C3⋊D314yes—
251#120—94no—
252C4×Q8—94no—
253C4×Q8—94no—
254C4×D4—98no—
255C4×D4—94no—
256C4×D4—98no—
257C4×D4C2×C3⋊D314yescomplemented
258#117—92no—
259#117—94no—
260#117—94no—
261#117—92no—
262#117—92no—
263C2×C4⋊C4—92no—
264C2×C22⋊C4—92no—
265C2×C42—91no—
266C2×C42—94no—
267C2×C42C2×C3⋊D311yescharacteristic
268C23×C3C23×D3116yes—
269C23×C3C23×D314yes—
270C22×D3—38no—
271C22×D3—68no—
272C22×D3—128no—
273C3×Q8—216no—
274C3×D4—232no—
275C3×D4—216no—
276C3×D4—416no—
277C2×C3×C4—232no—
278C2×C3×C4—48no—
279C2×C3×C4#237116yes—
280C2×C3×C4C23×D3116yes—
281C2×C3×C4C23×D318yes—
282C2×C3×C4C23×D318yes—
283C2×C3×C4C23×D314yes—
284C2×C3×C4C23×D314yes—
285#67—1232no—
286C2×Dic3—316no—
287C2×Dic3—332no—
288C2×Dic3—38no—
289C2×Dic3—68no—
290C2×Dic3—1232no—
291C2×Dic3—128no—
292C4×D3—616no—
293C4×D3—616no—
294Dic6—1216no—
295C2×C32—22no—
296C2×C32—44no—
297C2×C32C22×#4111yescharacteristic
298C2×C32#58512yes—
299C3⋊D3—42no—
300C24—91no—
301#41—28no—
302C2×Q8—94no—
303C2×Q8C22×C3⋊D312yes—
304C2×D4—98no—
305C2×D4C22×C3⋊D314yes—
306C2×D4C22×C3⋊D312yes—
307C2×D4C22×C3⋊D314yes—
308C22×C4—91no—
309C22×C4—92no—
310C22×C4—98no—
311C22×C4—92no—
312C22×C4—92no—
313C22×C4—184no—
314C22×C4C22×C3⋊D314yes—
315C22×C4C22×C3⋊D312yes—
316C22×C4C22×C3⋊D311yescharacteristic
317C4⋊C4—94no—
318C4⋊C4—94no—
319C4⋊C4—94no—
320C4⋊C4—98no—
321C4⋊C4—98no—
322C4⋊C4—98no—
323C4⋊C4—94no—
324C4⋊C4C22×C3⋊D314yes—
325C22⋊C4—94no—
326C22⋊C4—98no—
327C22⋊C4—98no—
328C22⋊C4—94no—
329C22⋊C4—94no—
330C22⋊C4—98no—
331C22⋊C4C22×C3⋊D318yes—
332C42—92no—
333C42—98no—
334C42—92no—
335C42—94no—
336C42C22×C3⋊D311yescharacteristic
337C42C22×C3⋊D311yescharacteristic
338C42C22×C3⋊D312yes—
339C22×C3—28no—
340C22×C3—216no—
341C22×C3—232no—
342C22×C3C2×#23718yes—
343C22×C3C24×D314yes—
344C2×D3—68no—
345C2×D3—616no—
346C2×D3—1216no—
347C3×C4—216no—
348C3×C4—28no—
349C3×C4—28no—
350C3×C4C2×#23718yes—
351C3×C4C2×#23718yes—
352Dic3—68no—
353Dic3—632no—
354Dic3—616no—
355C32#345511yescharacteristic, complemented, Sylow
356C23—92no—
357C23—182no—
358C23—362no—
359C23C23×C3⋊D314yes—
360C23C23×C3⋊D311yescharacteristic
361Q8—24no—
362Q8—364no—
363D4—28no—
364D4—24no—
365D4—44no—
366D4—368no—
367C2×C4—28no—
368C2×C4—42no—
369C2×C4—94no—
370C2×C4—98no—
371C2×C4—92no—
372C2×C4—182no—
373C2×C4—184no—
374C2×C4—184no—
375C2×C4—362no—
376C2×C4—368no—
377C2×C4#383014yes—
378C2×C4C23×C3⋊D314yes—
379C2×C4C23×C3⋊D312yes—
380C2×C4C23×C3⋊D312yes—
381C2×C4C23×C3⋊D311yescharacteristic
382C2×C4C23×C3⋊D311yescharacteristic
383C2×C3—28no—
384C2×C3—416no—
385C2×C3C22×#23714yes—
386C2×C3#596418yes—
387D3—128no—
388C22—22no—
389C22—24no—
390C22—28no—
391C22—182no—
392C22—184no—
393C22—364no—
394C22C2×#383012yes—
395C22C24×C3⋊D311yescharacteristic
396C4—24no—
397C4—22no—
398C4—22no—
399C4—182no—
400C4—184no—
401C4—188no—
402C4C2×#383012yes—
403C4C2×#383012yes—
404C3#8623614yescomplemented
405C2—22no—
406C2—44no—
407C2—362no—
408C2C22×#383011yescharacteristic
409C2#1059675612yes—
subgroupG/H
centerC2×C4C23×C3⋊D3
commutator, socle, cosocleC22×C32C25
FrattiniC22C24×C3⋊D3
FittingC32×#532C2
hypercenter#532C3⋊D3
hypocenterC32#3455
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ #532

Complements

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

NH ≅ G/Ntype
1. C32×#532C2semidirect
2. #10596299C2semidirect
3. #41×C3⋊Dic3C2semidirect
4. #10596202C2semidirect
5. #10596190C2semidirect
6. #10596153C2semidirect
7. #10596088C2semidirect
8. #10596073C2semidirect
9. #10596009C2semidirect
10. C2×#64081C2semidirect
11. #10595941C2semidirect
15. C32×C4⋊Q8C22semidirect
16. C32×#127C22semidirect
17. C32×#124C22semidirect
19. C32×C4×D4C22semidirect
22. Q8×C3⋊Dic3C22semidirect
27. #64144C22semidirect
29. D4×C3⋊Dic3C22semidirect
33. #64135C22semidirect
37. C2×C4×C3⋊Dic3C22semidirect
39. #64098C22semidirect
42. #64088C22semidirect
43. #64087C22semidirect
47. #64079C22semidirect
48. #64078C22semidirect
49. C4×#634C22semidirect
50. C3×#532D3semidirect
103. C3×C4⋊Q8C2×D3semidirect
104. C3×#127C2×D3semidirect
105. C3×#124C2×D3semidirect
107. C3×C4×D4C2×D3semidirect
171. #532C3⋊D3semidirect
234. C4⋊Q8C2×C3⋊D3semidirect
235. #127C2×C3⋊D3semidirect
241. #124C2×C3⋊D3semidirect
257. C4×D4C2×C3⋊D3semidirect
355. C32#3455semidirect
404. C3#86236semidirect

Maximal subgroups

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

subgroupindex
C32×#5322
#105962992
#41×C3⋊Dic32
#105962022
#105961902
#105961532
#105960882
#105960732
#105960092
C2×#640812
#105959412
#862363