Finite Group Databasebeta

← #11901753

Subgroups — #11901753

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
1C2×C32×#117C211yesmaximal, characteristic, complemented
2#10596262C212yesmaximal, complemented
3#10596006C212yesmaximal, complemented
4#10596005C214yesmaximal, complemented
5#10595999C218yesmaximal, complemented
6#10595989C212yesmaximal, complemented
7#10595986C214yesmaximal, complemented
8#10595965C214yesmaximal, complemented
9#10595948C211yesmaximal, characteristic, complemented
10C4×#3828C212yesmaximal, complemented
11#10595941C211yesmaximal, characteristic, complemented
12#85738—34nomaximal
13C23×C32×C4C2211yescharacteristic
14C2×#3828C2212yes—
15C32×#117C2212yes—
16C32×#117C2214yes—
17C32×#117C2212yes—
18C2×C32×C4⋊C4C2212yes—
19C2×C32×C22⋊C4C2212yes—
20C2×C32×C42C2211yescharacteristic
21C2×C32×C42C2211yescharacteristic
22#64162C2214yes—
23#64139C2214yes—
24#64139C2214yes—
25#64138C2214yes—
26C4×#638C2218yes—
27C4×#638C2218yes—
28#64135C2212yes—
29#64133C2214yes—
30#64133C2214yes—
31#64107C2218yescomplemented
32#64105C2218yescomplemented
33#64103C2218yescomplemented
34#64098C2218yescomplemented
35#64094C2218yes—
36#64093C2218yes—
37#64092C2218yes—
38#64088C2218yes—
39#64084C2212yescomplemented
40#64083C2211yescharacteristic, complemented
41C4×C4⋊(C3⋊D3)C2214yescomplemented
42C4×C4⋊(C3⋊D3)C2214yescomplemented
43#64081C2214yescomplemented
44C42×C3⋊D3C2214yescomplemented
45#64079C2212yescomplemented
46#64078C2212yescomplemented
47#64078C2211yescharacteristic, complemented
48C4×#634C2214yescomplemented
49C4×#634C2214yescomplemented
50C2×C3×#117D314yescomplemented
51#5791—38no—
52#5535—38no—
53#5534—316no—
54#5528—332no—
55#5518—38no—
56#5515—316no—
57#5494—316no—
58#5477—34no—
59C4×#235—38no—
60#5470—34no—
61C24×C32C2311yescharacteristic
62C22×C32×C4—24no—
63C22×C32×C4C2312yes—
64C22×C32×C4C2312yes—
65C22×C32×C4C2311yescharacteristic
66C22×C32×C4C2312yes—
67C22×C32×C4C2312yes—
68C22×C32×C4C2311yescharacteristic
69C2×#638C2314yes—
70C2×#638C2318yes—
71#3828—28no—
72C2×C4⋊(C3⋊D3)C2312yes—
73C2×C4⋊(C3⋊D3)C2314yes—
74C2×C4×C3⋊D3C2314yes—
75C2×C4×C3⋊D3C2318yes—
76C2×#634C2312yes—
77C2×#634C2314yes—
78C32×C4⋊C4C2314yes—
79C32×C4⋊C4C2314yes—
80C32×C22⋊C4C2314yes—
81C32×C22⋊C4C2314yes—
82C32×C42C2312yes—
83C32×C42C2312yes—
84C32×C42C2311yescharacteristic
85C32×C42C2311yescharacteristic
86C32×C42C2312yes—
87#3757C2318yes—
88#3757C2314yes—
89#3752C2318yes—
90#3752C2318yes—
91#3752C2318yes—
92C4⋊(C3⋊Dic3)C2314yes—
93C4⋊(C3⋊Dic3)C2314yes—
94C4⋊(C3⋊Dic3)C2314yes—
95#3750C2318yes—
96#3750C2318yes—
97#3750C2318yes—
98C4×C3⋊Dic3C2314yes—
99C4×C3⋊Dic3C2318yes—
100#3455—91noSylow
101C23×C3×C4C2×D314yes—
102C2×#235—38no—
103C3×#117C2×D318yes—
104C3×#117C2×D3116yes—
105C3×#117C2×D318yes—
106C2×C3×C4⋊C4C2×D318yes—
107C2×C3×C22⋊C4C2×D318yes—
108C2×C3×C42C2×D314yes—
109C2×C3×C42C2×D314yes—
110#953—316no—
111#930—316no—
112#930—316no—
113#929—316no—
114C4×#67—332no—
115C4×#67—332no—
116#926—38no—
117#924—316no—
118#924—316no—
119#898—332no—
120#896—332no—
121#894—332no—
122#889—332no—
123#885—332no—
124#884—332no—
125#883—332no—
126#879—332no—
127#875—38no—
128#874—34no—
129C4×D12—316no—
130C4×D12—316no—
131#872—316no—
132C42×D3—316no—
133#870—38no—
134#869—38no—
135#869—34no—
136C4×Dic6—316no—
137C4×Dic6—316no—
138C23×C32—22no—
139C23×C32—42no—
140C23×C32C2412yes—
141C23×C32C2411yescharacteristic
142C22×C3⋊D3C2414yes—
143C2×C32×C4—22no—
144C2×C32×C4—24no—
145C2×C32×C4—24no—
146C2×C32×C4—42no—
147C2×C32×C4—42no—
148C2×C32×C4#4114yes—
149C2×C32×C4C2414yes—
150C2×C32×C4C2412yes—
151C2×C32×C4C2412yes—
152C2×C32×C4C2412yes—
153C2×C32×C4C2411yescharacteristic
154C2×C32×C4C2411yescharacteristic
155#638—28no—
156#638—48no—
157C2×C3⋊Dic3C2414yes—
158C2×C3⋊Dic3C2418yes—
159C4⋊(C3⋊D3)—24no—
160C4⋊(C3⋊D3)—44no—
161C4×C3⋊D3—28no—
162C4×C3⋊D3—48no—
163#634—24no—
164#634—44no—
165#542—94no—
166#541—92no—
167#540—92no—
168#539—94no—
169#538—94no—
170#533—91no—
171#532—91no—
172#529—98no—
173#525—92no—
174C4×#41—92no—
175C2×#117C3⋊D311yescharacteristic, complemented
176C24×C3C22×D314yes—
177C22×C3×C4—216no—
178C22×C3×C4C22×D318yes—
179C22×C3×C4C22×D318yes—
180C22×C3×C4C22×D314yes—
181C22×C3×C4C22×D318yes—
182C22×C3×C4C22×D318yes—
183C22×C3×C4C22×D314yes—
184C2×#67—316no—
185C2×#67—332no—
186#235—632no—
187C2×D12—38no—
188C2×D12—316no—
189C2×C4×D3—316no—
190C2×C4×D3—332no—
191C2×Dic6—38no—
192C2×Dic6—316no—
193C3×C4⋊C4C22×D3116yes—
194C3×C4⋊C4C22×D3116yes—
195C3×C22⋊C4C22×D3116yes—
196C3×C22⋊C4C22×D3116yes—
197C3×C42C22×D318yes—
198C3×C42C22×D318yes—
199C3×C42C22×D314yes—
200C3×C42C22×D314yes—
201C3×C42C22×D318yes—
202#217—332no—
203#217—316no—
204(C2×D3)⋊C4—332no—
205(C2×D3)⋊C4—332no—
206(C2×D3)⋊C4—332no—
207C4⋊Dic3—316no—
208C4⋊Dic3—316no—
209C4⋊Dic3—316no—
210Dic3⋊C4—332no—
211Dic3⋊C4—332no—
212Dic3⋊C4—332no—
213C4×Dic3—316no—
214C4×Dic3—332no—
215C22×C32—22no—
216C22×C32—22no—
217C22×C32—24no—
218C22×C32—44no—
219C22×C32C2×#4112yes—
220C22×C32C2511yescharacteristic
221C2×C3⋊D3—24no—
222C2×C3⋊D3—28no—
223C32×C4—22no—
224C32×C4—22no—
225C32×C4—24no—
226C32×C4—22no—
227C32×C4C2×#4112yes—
228C32×C4C2×#4112yes—
229C3⋊Dic3—24no—
230C3⋊Dic3—28no—
231C2×#41—92no—
232C23×C4C2×C3⋊D311yescharacteristic
233C4⋊Q8—91no—
234C4⋊Q8—92no—
235#127—91no—
236#126—98no—
237#126—98no—
238#125—98no—
239#125—92no—
240#124—98no—
241#124—92no—
242#123—94no—
243#123—98no—
244#123—98no—
245C22⋊Q8—94no—
246C22⋊Q8—94no—
247C22⋊Q8—98no—
248#121—94no—
249#121—94no—
250#121—98no—
251#120—94no—
252C4×Q8—94no—
253C4×Q8—94no—
254C4×D4—98no—
255C4×D4—98no—
256C4×D4—94no—
257C4×D4—94no—
258#117—92no—
259#117—94no—
260#117C2×C3⋊D314yes—
261#117C2×C3⋊D312yes—
262#117C2×C3⋊D312yes—
263C2×C4⋊C4C2×C3⋊D312yes—
264C2×C22⋊C4C2×C3⋊D312yes—
265C2×C42—94no—
266C2×C42C2×C3⋊D311yescharacteristic
267C2×C42C2×C3⋊D311yescharacteristic
268C23×C3—28no—
269C23×C3—48no—
270C23×C3C23×D318yes—
271C23×C3C23×D314yes—
272C22×D3—316no—
273C2×C3×C4—28no—
274C2×C3×C4—216no—
275C2×C3×C4—216no—
276C2×C3×C4—48no—
277C2×C3×C4—48no—
278C2×C3×C4#235116yes—
279C2×C3×C4C23×D3116yes—
280C2×C3×C4C23×D318yes—
281C2×C3×C4C23×D318yes—
282C2×C3×C4C23×D318yes—
283C2×C3×C4C23×D314yes—
284C2×C3×C4C23×D314yes—
285#67—632no—
286#67—1232no—
287C2×Dic3—316no—
288C2×Dic3—332no—
289D12—616no—
290D12—1216no—
291C4×D3—632no—
292C4×D3—1232no—
293Dic6—616no—
294Dic6—1216no—
295C2×C32—22no—
296C2×C32—42no—
297C2×C32C22×#4111yescharacteristic
298C2×C32#58512yes—
299C3⋊D3—44no—
300C24C22×C3⋊D311yescharacteristic
301#41—188no—
302C2×Q8—92no—
303C2×Q8—94no—
304C2×D4—94no—
305C2×D4—98no—
306C2×D4—92no—
307C2×D4—94no—
308C22×C4—24no—
309C22×C4—94no—
310C22×C4—98no—
311C22×C4C22×C3⋊D311yescharacteristic
312C22×C4C22×C3⋊D312yes—
313C22×C4C22×C3⋊D312yes—
314C22×C4C22×C3⋊D312yes—
315C22×C4C22×C3⋊D312yes—
316C22×C4C22×C3⋊D311yescharacteristic
317C4⋊C4—94no—
318C4⋊C4—98no—
319C4⋊C4—94no—
320C4⋊C4—98no—
321C4⋊C4—98no—
322C4⋊C4—94no—
323C4⋊C4C22×C3⋊D314yes—
324C4⋊C4C22×C3⋊D314yes—
325C22⋊C4—94no—
326C22⋊C4—98no—
327C22⋊C4—98no—
328C22⋊C4—98no—
329C22⋊C4—98no—
330C22⋊C4C22×C3⋊D314yes—
331C22⋊C4C22×C3⋊D314yes—
332C42—98no—
333C42—94no—
334C42C22×C3⋊D312yes—
335C42C22×C3⋊D311yescharacteristic
336C42C22×C3⋊D311yescharacteristic
337C42C22×C3⋊D312yes—
338C42C22×C3⋊D312yes—
339C22×C3—28no—
340C22×C3—28no—
341C22×C3—216no—
342C22×C3—416no—
343C22×C3C2×#23518yes—
344C22×C3C24×D314yes—
345C2×D3—616no—
346C2×D3—632no—
347C3×C4—28no—
348C3×C4—28no—
349C3×C4—216no—
350C3×C4—28no—
351C3×C4C2×#23518yes—
352C3×C4C2×#23518yes—
353Dic3—616no—
354Dic3—632no—
355C32#345511yescharacteristic, complemented, Sylow
356C23—22no—
357C23—42no—
358C23—94no—
359C23C23×C3⋊D312yes—
360C23C23×C3⋊D311yescharacteristic
361Q8—184no—
362Q8—364no—
363D4—188no—
364D4—184no—
365D4—364no—
366D4—368no—
367C2×C4—22no—
368C2×C4—24no—
369C2×C4—24no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—94no—
373C2×C4—98no—
374C2×C4—188no—
375C2×C4—368no—
376C2×C4#382814yes—
377C2×C4C23×C3⋊D314yes—
378C2×C4C23×C3⋊D312yes—
379C2×C4C23×C3⋊D312yes—
380C2×C4C23×C3⋊D312yes—
381C2×C4C23×C3⋊D311yescharacteristic
382C2×C4C23×C3⋊D311yescharacteristic
383C2×C3—28no—
384C2×C3—48no—
385C2×C3C22×#23514yes—
386C2×C3#596418yes—
387D3—1216no—
388C22—22no—
389C22—22no—
390C22—24no—
391C22—44no—
392C22—184no—
393C22—188no—
394C22C2×#382812yes—
395C22C24×C3⋊D311yescharacteristic
396C4—22no—
397C4—24no—
398C4—22no—
399C4—22no—
400C4—184no—
401C4—188no—
402C4C2×#382812yes—
403C4C2×#382812yes—
404C3#8573814yescomplemented
405C2—22no—
406C2—42no—
407C2—364no—
408C2C22×#382811yescharacteristic
409C2#1059675612yes—
subgroupG/H
centerC2×C4C23×C3⋊D3
commutator, socle, cosocleC22×C32C25
FrattiniC22C24×C3⋊D3
FittingC2×C32×#117C2
hypercenterC2×#117C3⋊D3
hypocenterC32#3455
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. C2×C32×#117C2semidirect
2. #10596262C2semidirect
3. #10596006C2semidirect
4. #10596005C2semidirect
5. #10595999C2semidirect
6. #10595989C2semidirect
7. #10595986C2semidirect
8. #10595965C2semidirect
9. #10595948C2semidirect
10. C4×#3828C2semidirect
11. #10595941C2semidirect
31. #64107C22semidirect
32. #64105C22semidirect
33. #64103C22semidirect
34. #64098C22semidirect
39. #64084C22semidirect
40. #64083C22semidirect
41. C4×C4⋊(C3⋊D3)C22semidirect
42. C4×C4⋊(C3⋊D3)C22semidirect
43. #64081C22semidirect
44. C42×C3⋊D3C22semidirect
45. #64079C22semidirect
46. #64078C22semidirect
47. #64078C22semidirect
48. C4×#634C22semidirect
49. C4×#634C22semidirect
50. C2×C3×#117D3semidirect
175. C2×#117C3⋊D3semidirect
355. C32#3455semidirect
404. C3#85738semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1172
#105962622
#105960062
#105960052
#105959992
#105959892
#105959862
#105959652
#105959482
C4×#38282
#105959412
#857383