Finite Group Databasebeta

← #11901960

Subgroups — #11901960

Order 1152.

2157 conjugacy classes of subgroups.

The subgroup lattice has 413 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64101C211yesmaximal, characteristic
2C3×#5500C212yesmaximal, complemented
3#10595052C212yesmaximal, complemented
4#10594981C214yesmaximal
5#10594969C212yesmaximal
6#10594810C214yesmaximal, complemented
7#10594508C214yesmaximal, complemented
8#10594448C218yesmaximal, complemented
9#10594351C214yesmaximal, complemented
10#86581—32nomaximal
11C22×C4×C3⋊D3C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×#3752C2212yes—
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C2×C4×C3⋊Dic3C2212yes—
16#64101C2214yes—
17#64101C2214yes—
18C3×#926C2214yes—
19C3×#924C2218yes—
20C3×#890C2218yescomplemented
21C3×#888C2218yescomplemented
22#63982C2218yes—
23#63974C2214yes—
24#63957C2214yes—
25#63919C2214yescomplemented
26#63918C2218yescomplemented
27#63900C2212yes—
28#63900C2212yes—
29#63895C22116yes—
30#63888C22116yes—
31C4×#624C2214yes—
32#63874C2214yes—
33#63873C2214yescomplemented
34#63870C2218yescomplemented
35#63869C2218yescomplemented
36#63849C2214yes—
37#63843C2218yescomplemented
38#63838C2218yescomplemented
39C3×#544—32no—
40#5729—38no—
41#5728—38no—
42#5689—38no—
43#5688—38no—
44#5634—38no—
45#5622—38no—
46D3×#117—34no—
47#5519—34no—
48C2×#892—32no—
49C2×#892—61no—
50#5500D312yescomplemented
51C23×C3⋊D3C2311yescharacteristic
52C22×C32×C4C2312yes—
53C22×C32×C4C2311yescharacteristic
54C22×C3⋊Dic3C2312yes—
55C22×C3⋊Dic3C2311yescharacteristic
56C2×C4×C3⋊D3Q818yescomplemented
57C2×C4×C3⋊D3C2312yes—
58C2×C4×C3⋊D3C2312yes—
59C2×C3×Dic6C2318yes—
60C2×#627C2318yes—
61C2×#624C2314yes—
62C2×#624C2314yes—
63C32×C4⋊C4C2314yes—
64#3752C2318yes—
65C4⋊(C3⋊Dic3)C2314yes—
66C4×C3⋊Dic3C2314yes—
67C4×C3⋊Dic3C2314yes—
68C3×#217C2318yes—
69C3×C4⋊Dic3C2314yes—
70C3×C4⋊Dic3C2318yes—
71C3×C4⋊Dic3C2314yes—
72C3×Dic3⋊C4C23116yes—
73C3×C4×Dic3C2318yes—
74#3724C2318yes—
75#3724C2314yes—
76#3724C2314yes—
77Dic3⋊Dic3C23116yes—
78#3722C2318yes—
79Dic32C2318yes—
80#3458—91noSylow
81C22×C4×D3—32no—
82C22×C4×D3—61no—
83C3×C4⋊Q8—38no—
84C3×#125—38no—
85C3×C22⋊Q8—38no—
86C3×#117—34no—
87C2×C3×C4⋊C4—21no—
88C2×C3×C4⋊C4C2×D312yes—
89#946—316no—
90Q8×Dic3—38no—
91#944—38no—
92C2×(C2×D3)⋊C4—34no—
93C2×(C2×D3)⋊C4—62no—
94#926C2×D314yes—
95C2×C4⋊Dic3—32no—
96C2×C4⋊Dic3—61no—
97#924C2×D318yes—
98C2×C4×Dic3—34no—
99C2×C4×Dic3—62no—
100#897—316no—
101#896—316no—
102#896—316no—
103#892—38no—
104#892—38no—
105#892—34no—
106#892—34no—
107#892—64no—
108#892—64no—
109D3×C4⋊C4—34no—
110D3×C4⋊C4—34no—
111#890—38no—
112#890C2×D318yescomplemented
113#889—316no—
114#888—38no—
115#888—38no—
116#888C2×D318yescomplemented
117#887—38no—
118#887—316no—
119D3×C22⋊C4—38no—
120#878—316no—
121#877—38no—
122#872—38no—
123C42×D3—38no—
124#870—38no—
125#869—38no—
126C23×C32C2411yescharacteristic
127C22×C3⋊D3—41no—
128C22×C3⋊D3—41no—
129C22×C3⋊D3C2×Q814yes—
130C22×C3⋊D3C2412yes—
131C2×C32×C4—42no—
132C2×C32×C4C2×Q814yes—
133C2×C32×C4C2414yes—
134C2×C32×C4C2412yes—
135C2×C3⋊Dic3—42no—
136C2×C3⋊Dic3C2×Q814yes—
137C2×C3⋊Dic3C2414yes—
138C2×C3⋊Dic3C2411yescharacteristic
139C2×C3⋊Dic3C2411yescharacteristic
140C4×C3⋊D3C2×Q818yes—
141C4×C3⋊D3C2×Q818yes—
142C2×C3×Dic3C2418yes—
143C2×C3×Dic3C2418yes—
144C3×Dic6—48no—
145#627—48no—
146#624—44no—
147#624—44no—
148#544—32no—
149#544—92no—
150#544—94no—
151#544—94no—
152#543—94no—
153#533—94no—
154#533—98no—
155C2×#117—92no—
156C2×#117—91no—
157C23×D3—32no—
158C23×D3—61no—
159C2×C3×Q8—38no—
160C22×C3×C4—21no—
161C22×C3×C4—22no—
162C22×C3×C4C22×D314yes—
163C22×C3×C4C22×D312yes—
164C22×Dic3—32no—
165C22×Dic3—34no—
166C22×Dic3—61no—
167C22×Dic3—62no—
168C2×C4×D3—316no—
169C2×C4×D3—34no—
170C2×C4×D3—34no—
171C2×C4×D3—38no—
172C2×C4×D3—38no—
173C2×C4×D3—62no—
174C2×C4×D3—62no—
175C2×C4×D3—68no—
176C2×Dic6—316no—
177C2×Dic6C22×D318yes—
178C3×C4⋊C4—24no—
179C3×C4⋊C4—38no—
180C3×C4⋊C4—316no—
181C3×C4⋊C4—34no—
182C3×C4⋊C4—34no—
183C3×C4⋊C4C22×D318yes—
184C3×C22⋊C4—38no—
185C3×C42—38no—
186#217C22×D318yes—
187(C2×D3)⋊C4—316no—
188(C2×D3)⋊C4—38no—
189(C2×D3)⋊C4—38no—
190(C2×D3)⋊C4—68no—
191C4⋊Dic3—38no—
192C4⋊Dic3—316no—
193C4⋊Dic3—64no—
194C4⋊Dic3C22×D314yes—
195C4⋊Dic3C22×D314yes—
196C4⋊Dic3C22×D318yes—
197Dic3⋊C4—316no—
198Dic3⋊C4—316no—
199Dic3⋊C4—38no—
200Dic3⋊C4—38no—
201Dic3⋊C4C22×D3116yes—
202C4×Dic3—38no—
203C4×Dic3—38no—
204C4×Dic3—38no—
205C4×Dic3—38no—
206C4×Dic3—64no—
207C4×Dic3—64no—
208C4×Dic3C22×D318yes—
209C22×C32—21no—
210C22×C32—21no—
211C22×C32C22×Q812yes—
212C22×C32C2511yescharacteristic
213C2×C3⋊D3—22no—
214C2×C3⋊D3—22no—
215C2×C3⋊D3—44no—
216C2×C3⋊D3C22×Q814yes—
217C32×C4—24no—
218C32×C4C22×Q814yes—
219C3⋊Dic3—24no—
220C3⋊Dic3C22×Q812yes—
221C3⋊Dic3C22×Q812yes—
222C3×Dic3—28no—
223C3×Dic3—28no—
224C23×C4—91no—
225C4⋊Q8—38no—
226C4⋊Q8—98no—
227C4⋊Q8—94no—
228C4⋊Q8—94no—
229#125—38no—
230#125—98no—
231#125—98no—
232C22⋊Q8—38no—
233C22⋊Q8—98no—
234C22⋊Q8—916no—
235C22⋊Q8—916no—
236C4×Q8—98no—
237C4×Q8—98no—
238#117—34no—
239#117—94no—
240#117—94no—
241#117—94no—
242#117—94no—
243#117—94no—
244C2×C4⋊C4—92no—
245C2×C4⋊C4—92no—
246C2×C4⋊C4—91no—
247C2×C4⋊C4D3211yescharacteristic
248C2×C22⋊C4—94no—
249C2×C22⋊C4—92no—
250C2×C42—94no—
251C2×C42—92no—
252C23×C3—21no—
253C23×C3C23×D312yes—
254C22×D3—34no—
255C22×D3—38no—
256C22×D3—64no—
257C22×D3—62no—
258C22×D3—122no—
259C22×D3—122no—
260C22×D3—122no—
261C22×D3—122no—
262C3×Q8—128no—
263C2×C3×C4—22no—
264C2×C3×C4—24no—
265C2×C3×C4—24no—
266C2×C3×C4—38no—
267C2×C3×C4—38no—
268C2×C3×C4—44no—
269C2×C3×C4—44no—
270C2×C3×C4D3×Q818yes—
271C2×C3×C4C23×D318yes—
272C2×C3×C4C23×D314yes—
273C2×Dic3—38no—
274C2×Dic3—32no—
275C2×Dic3—32no—
276C2×Dic3—38no—
277C2×Dic3—64no—
278C2×Dic3—61no—
279C2×Dic3—61no—
280C2×Dic3—64no—
281C2×Dic3—124no—
282C2×Dic3—124no—
283C2×Dic3C23×D318yes—
284C2×Dic3C23×D318yes—
285C4×D3—316no—
286C4×D3—316no—
287C4×D3—68no—
288C4×D3—68no—
289C4×D3—128no—
290C4×D3—128no—
291Dic6—48no—
292Dic6—1216no—
293C2×C32—22no—
294C2×C32C23×Q811yescharacteristic
295C2×C32#58511yescharacteristic
296C2×C32#58511yescharacteristic
297C3⋊D3—24no—
298C24—91no—
299C2×Q8—38no—
300C2×Q8—98no—
301C22×C4—94no—
302C22×C4—94no—
303C22×C4—91no—
304C22×C4—92no—
305C22×C4—92no—
306C22×C4—98no—
307C22×C4—92no—
308C22×C4C2×D3212yes—
309C22×C4C2×D3211yescharacteristic
310C4⋊C4—34no—
311C4⋊C4—34no—
312C4⋊C4—38no—
313C4⋊C4—316no—
314C4⋊C4—94no—
315C4⋊C4—94no—
316C4⋊C4—98no—
317C4⋊C4—916no—
318C4⋊C4—94no—
319C4⋊C4C2×D3214yes—
320C22⋊C4—38no—
321C22⋊C4—98no—
322C22⋊C4—98no—
323C42—38no—
324C42—98no—
325C42—94no—
326C42—94no—
327C22×C3—22no—
328C22×C3—22no—
329C22×C3—22no—
330C22×C3—22no—
331C22×C3—22no—
332C22×C3—21no—
333C22×C3C2×D3×Q814yes—
334C22×C3C24×D312yes—
335C2×D3—38no—
336C2×D3—64no—
337C2×D3—64no—
338C2×D3—64no—
339C2×D3—122no—
340C2×D3—122no—
341C2×D3—128no—
342C2×D3—128no—
343C3×C4—28no—
344C3×C4—24no—
345C3×C4—44no—
346C3×C4—68no—
347C3×C4—68no—
348C3×C4C2×D3×Q818yes—
349Dic3—28no—
350Dic3—28no—
351Dic3—34no—
352Dic3—34no—
353Dic3—62no—
354Dic3—62no—
355Dic3—68no—
356Dic3—124no—
357C32#345811yescharacteristic, complemented, Sylow
358C23—92no—
359C23—94no—
360C23—361no—
361C23—361no—
362C23C22×D3211yescharacteristic
363Q8—128no—
364Q8—368no—
365C2×C4—38no—
366C2×C4—38no—
367C2×C4—42no—
368C2×C4—94no—
369C2×C4—91no—
370C2×C4—91no—
371C2×C4—98no—
372C2×C4—98no—
373C2×C4—94no—
374C2×C4—364no—
375C2×C4—364no—
376C2×C4—362no—
377C2×C4#379714yes—
378C2×C4C22×D3214yes—
379C2×C4C22×D3212yes—
380C2×C3—24no—
381C2×C3—24no—
382C2×C3—21no—
383C2×C3—21no—
384C2×C3—21no—
385C2×C3C22×D3×Q812yes—
386C2×C3#596612yes—
387C2×C3#596812yes—
388D3—68no—
389D3—124no—
390C22—21no—
391C22—21no—
392C22—94no—
393C22—182no—
394C22—182no—
395C22—364no—
396C22C2×#379712yes—
397C22C23×D3211yescharacteristic
398C4—24no—
399C4—68no—
400C4—68no—
401C4—92no—
402C4—92no—
403C4—184no—
404C4C2×#379714yes—
405C3—21no—
406C3#8658112yescomplemented
407C2—22no—
408C2—184no—
409C2C22×#379711yescharacteristic
410C2#1059667911yescharacteristic
411C2#1059668911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×C4⋊C4C22
prime radicalC23×C3⋊D3C23
hypercenterC2×C4⋊C4D32
hypocenterC32#3458
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C3×#5500C2semidirect
3. #10595052C2semidirect
6. #10594810C2semidirect
7. #10594508C2semidirect
8. #10594448C2semidirect
9. #10594351C2semidirect
20. C3×#890C22semidirect
21. C3×#888C22semidirect
25. #63919C22semidirect
26. #63918C22semidirect
33. #63873C22semidirect
34. #63870C22semidirect
35. #63869C22semidirect
37. #63843C22semidirect
38. #63838C22semidirect
50. #5500D3semidirect
56. C2×C4×C3⋊D3Q8semidirect
112. #890C2×D3semidirect
116. #888C2×D3semidirect
357. C32#3458semidirect
406. C3#86581semidirect

Maximal subgroups

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

subgroupindex
C2×#641012
C3×#55002
#105950522
#105949812
#105949692
#105948102
#105945082
#105944482
#105943512
#865813