Finite Group Databasebeta

← #11869045

Subgroups — #11869045

Order 1152.

1086 conjugacy classes of subgroups.

The subgroup lattice has 351 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595990C211yesmaximal, characteristic
2#10595987C211yesmaximal, characteristic
3C32×#427C211yesmaximal, characteristic
4C2×#63643C211yesmaximal, characteristic
5#10592801C211yesmaximal, characteristic
6#10592703C211yesmaximal, characteristic
7#10592694C211yesmaximal, characteristic
8#10592576C212yesmaximal, complemented
9#10592574C212yesmaximal, complemented
10#10592556C212yesmaximal, complemented
11#10592553C212yesmaximal, complemented
12#79198—34nomaximal
13C22×#634C2211yescharacteristic
14C22×C32×C8C2211yescharacteristic
15C32×#117C2211yescharacteristic
16C32×#117C2211yescharacteristic
17#64135C2211yescharacteristic
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C2×#3748C2211yescharacteristic
20#64099C2212yes—
21#64097C2212yes—
22#64096C2212yes—
23#64096C2212yes—
24#64087—22no—
25#64086—22no—
26#64079—21no—
27#64078—21no—
28C4×#634—21no—
29C4×#634—21no—
30C32×#107C2211yescharacteristic
31C32×#107C2211yescharacteristic
32C32×#106C2211yescharacteristic
33C32×#106C2211yescharacteristic
34#63643C2212yes—
35#63643C2212yes—
36#63641C2212yes—
37#63641C2212yes—
38#63637C2212yes—
39#63637C2212yes—
40#63635C2212yes—
41#63634C2212yes—
42#5519—34no—
43#5516—34no—
44C3×#427D314yes—
45C2×#816—34no—
46#5102—34no—
47#5004—34no—
48#4995—34no—
49#4877—38no—
50#4875—38no—
51#4857—38no—
52#4854—38no—
53C22×C32×C4C2311yescharacteristic
54C22×C3⋊Dic3—21no—
55C22×C3⋊Dic3—21no—
56C2×#634—21no—
57C2×#634—22no—
58C2×#634—22no—
59C2×#634Q814yescomplemented
60C2×#634C2312yes—
61C2×C32×C8—22no—
62C2×C32×C8C2311yescharacteristic
63C2×C32×C8C2311yescharacteristic
64C32×C4⋊C4C2311yescharacteristic
65C32×C4⋊C4C2311yescharacteristic
66C32×C4⋊C4C2311yescharacteristic
67C32×C4⋊C4C2311yescharacteristic
68C32×C22⋊C4—21no—
69C32×C22⋊C4—21no—
70C32×C42—21no—
71C32×C42—21no—
72#3757D412yes—
73C4⋊(C3⋊Dic3)—21no—
74C4⋊(C3⋊Dic3)—22no—
75C4⋊(C3⋊Dic3)D411yescharacteristic
76C4⋊(C3⋊Dic3)D411yescharacteristic
77C4⋊(C3⋊Dic3)C2312yes—
78#3750—22no—
79#3750—22no—
80#3750—22no—
81#3750—22no—
82C4×C3⋊Dic3—22no—
83C4×C3⋊Dic3—22no—
84C4×C3⋊Dic3C2312yes—
85#3748—22no—
86C2×C3⋊(C3⋊C8)C2312yes—
87#3082—91noSylow
88C22×Dic6—34no—
89C22×C3×C8C2×D314yes—
90C3×#117C2×D314yes—
91C3×#117C2×D314yes—
92#926—34no—
93C2×C4⋊Dic3—34no—
94C2×#208—34no—
95#890—38no—
96#888—38no—
97#887—38no—
98#887—38no—
99#878—68no—
100#877—68no—
101#870—64no—
102#869—64no—
103C4×Dic6—64no—
104C4×Dic6—64no—
105C3×#107C2×D314yes—
106C3×#107C2×D314yes—
107C3×#106C2×D314yes—
108C3×#106C2×D314yes—
109#816—38no—
110#816—38no—
111Dic3⋊C8—38no—
112Dic3⋊C8—38no—
113#810—38no—
114#810—38no—
115#808—38no—
116#807—38no—
117C23×C32C2×D411yescharacteristic
118C2×C32×C4—21no—
119C2×C32×C4—21no—
120C2×C32×C4—21no—
121C2×C32×C4—21no—
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×Q812yes—
124C2×C32×C4#4112yes—
125C2×C32×C4C2411yescharacteristic
126C2×C3⋊Dic3—24no—
127C2×C3⋊Dic3—22no—
128C2×C3⋊Dic3—22no—
129C2×C3⋊Dic3—81no—
130C2×C3⋊Dic3C2×D412yes—
131C2×C3⋊Dic3C2×D412yes—
132#634—24no—
133#634—22no—
134#634—82no—
135#634C2×Q814yes—
136C32×C8—21no—
137C32×C8—21no—
138C3⋊(C3⋊C8)—22no—
139#544—91no—
140#519—91no—
141#479—92no—
142#479—92no—
143#477—92no—
144#475—92no—
145#428—91no—
146#427C3⋊D311yescharacteristic
147#424—91no—
148#419—91no—
149C2×#103—91no—
150C22×C3×C4C22×D314yes—
151C22×Dic3—64no—
152C22×Dic3—64no—
153C2×Dic6—316no—
154C2×Dic6—38no—
155C2×Dic6—68no—
156C2×Dic6—64no—
157C2×Dic6—68no—
158C2×C3×C8—28no—
159C2×C3×C8C22×D314yes—
160C2×C3×C8C22×D314yes—
161C3×C4⋊C4C22×D314yes—
162C3×C4⋊C4C22×D314yes—
163C3×C4⋊C4C22×D314yes—
164C3×C4⋊C4C22×D314yes—
165C3×C22⋊C4—24no—
166C3×C22⋊C4—24no—
167C3×C42—24no—
168C3×C42—24no—
169#217—38no—
170C4⋊Dic3—34no—
171C4⋊Dic3—34no—
172C4⋊Dic3—38no—
173C4⋊Dic3—68no—
174C4⋊Dic3—64no—
175Dic3⋊C4—68no—
176Dic3⋊C4—68no—
177Dic3⋊C4—68no—
178Dic3⋊C4—68no—
179C4×Dic3—38no—
180C4×Dic3—68no—
181C4×Dic3—68no—
182#208—68no—
183C2×C3⋊C8—38no—
184C22×C32—21no—
185C22×C32—21no—
186C22×C32C22⋊Q812yes—
187C22×C32C22×D411yescharacteristic
188C32×C4—41no—
189C32×C4—41no—
190C32×C4—41no—
191C32×C4—41no—
192C32×C4C22⋊Q812yes—
193C32×C4C22×Q811yescharacteristic
194C32×C4C2×#4111yescharacteristic
195C3⋊Dic3—24no—
196C3⋊Dic3—22no—
197C3⋊Dic3—22no—
198C3⋊Dic3—42no—
199C22×Q8—91no—
200C2×M16—91no—
201C22×C8C2×C3⋊D311yescharacteristic
202C4⋊Q8—92no—
203C4⋊Q8—181no—
204#125—92no—
205#125—181no—
206C22⋊Q8—182no—
207C4×Q8—92no—
208C4×Q8—92no—
209C4×Q8—181no—
210C4×Q8—181no—
211#117—91no—
212#117—182no—
213#117C2×C3⋊D311yescharacteristic
214#117C2×C3⋊D311yescharacteristic
215C2×C4⋊C4—91no—
216#107—92no—
217#107C2×C3⋊D311yescharacteristic
218#107C2×C3⋊D311yescharacteristic
219#106—92no—
220#106C2×C3⋊D311yescharacteristic
221#106C2×C3⋊D311yescharacteristic
222C4⋊C8—92no—
223C4⋊C8—92no—
224#103—92no—
225#103—92no—
226#103—92no—
227#103—92no—
228C23×C3D3×D414yes—
229C2×C3×C4—24no—
230C2×C3×C4—24no—
231C2×C3×C4—24no—
232C2×C3×C4—24no—
233C2×C3×C4#23518yes—
234C2×C3×C4D3×D414yes—
235C2×C3×C4D3×Q818yes—
236C2×C3×C4C23×D314yes—
237C2×Dic3—38no—
238C2×Dic3—38no—
239C2×Dic3—616no—
240C2×Dic3—68no—
241C2×Dic3—68no—
242C2×Dic3—244no—
243Dic6—316no—
244Dic6—616no—
245Dic6—68no—
246Dic6—248no—
247C3×C8—24no—
248C3×C8—24no—
249C3⋊C8—68no—
250C2×C32—22no—
251C2×C32C2×C22⋊Q811yescharacteristic
252C2×C32#57711yescharacteristic
253C2×C32#57811yescharacteristic
254C2×Q8—92no—
255C2×Q8—94no—
256C2×Q8—182no—
257C2×Q8—182no—
258C2×Q8—181no—
259C22×C4—181no—
260C22×C4—181no—
261C22×C4C22×C3⋊D311yescharacteristic
262M16—182no—
263C2×C8—22no—
264C2×C8—92no—
265C2×C8C22×C3⋊D311yescharacteristic
266C2×C8C22×C3⋊D311yescharacteristic
267C4⋊C4—91no—
268C4⋊C4—91no—
269C4⋊C4—92no—
270C4⋊C4—182no—
271C4⋊C4—182no—
272C4⋊C4—182no—
273C4⋊C4—182no—
274C4⋊C4—182no—
275C4⋊C4—181no—
276C4⋊C4C22×C3⋊D311yescharacteristic
277C4⋊C4C22×C3⋊D311yescharacteristic
278C4⋊C4C22×C3⋊D311yescharacteristic
279C4⋊C4C22×C3⋊D311yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—92no—
283C42—21no—
284C42—21no—
285C42—92no—
286C42—182no—
287C42—182no—
288C22×C3—24no—
289C22×C3—24no—
290C22×C3#89618yes—
291C22×C3C2×D3×D414yes—
292C3×C4—44no—
293C3×C4—44no—
294C3×C4—44no—
295C3×C4—44no—
296C3×C4#89618yes—
297C3×C4C2×#23514yes—
298C3×C4C2×D3×Q814yes—
299Dic3—616no—
300Dic3—68no—
301Dic3—68no—
302Dic3—128no—
303C32#308211yescharacteristic, complemented, Sylow
304C23D4×C3⋊D311yescharacteristic
305Q8—94no—
306Q8—182no—
307Q8—184no—
308Q8—722no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—92no—
314C2×C4—92no—
315C2×C4—182no—
316C2×C4—184no—
317C2×C4—182no—
318C2×C4—721no—
319C2×C4#382812yes—
320C2×C4D4×C3⋊D311yescharacteristic
321C2×C4Q8×C3⋊D312yes—
322C2×C4C23×C3⋊D311yescharacteristic
323C8—21no—
324C8—21no—
325C8—182no—
326C2×C3—28no—
327C2×C3C2×#89614yes—
328C2×C3#577014yes—
329C2×C3#577114yes—
330C22—21no—
331C22—21no—
332C22#6410512yes—
333C22C2×D4×C3⋊D311yescharacteristic
334C4—41no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—184no—
339C4—182no—
340C4—182no—
341C4—362no—
342C4#6410512yes—
343C4C2×#382811yescharacteristic
344C4C2×Q8×C3⋊D311yescharacteristic
345C3#7919814yescomplemented
346C2—22no—
347C2C2×#6410511yescharacteristic
348C2#1059624111yescharacteristic
349C2#1059624211yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#427C2
socleC22×C32C22×D4
prime radicalC23×C32C2×D4
hypercenter#427C3⋊D3
hypocenterC32#3082
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #427

Complements

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

NH ≅ G/Ntype
8. #10592576C2semidirect
9. #10592574C2semidirect
10. #10592556C2semidirect
11. #10592553C2semidirect
59. C2×#634Q8semidirect
303. C32#3082semidirect
345. C3#79198semidirect

Maximal subgroups

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

subgroupindex
#105959902
#105959872
C32×#4272
C2×#636432
#105928012
#105927032
#105926942
#105925762
#105925742
#105925562
#105925532
#791983