Finite Group Databasebeta

← #25249198

Subgroups — #25249198

Order 11008.

822 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583307C212yesmaximal
2C2×#14583306C212yesmaximal
3#19142971C211yesmaximal, characteristic
4#19142957C211yesmaximal, characteristic
5#19134762C212yesmaximal
6#19134760C212yesmaximal
7#19134759C211yesmaximal, characteristic
8#19134757C211yesmaximal, characteristic
9#19134757C211yesmaximal, characteristic
10C4×#13063235C211yesmaximal, characteristic
11C43×#1846C211yesmaximal, characteristic
12C2×#13063324C2212yes—
13C2×#13063316C2212yes—
14#14583307—28no—
15#14583306—28no—
16C2×#13063259C2212yes—
17C2×#13063258C2212yes—
18C2×#13063258C2212yes—
19C2×#13063257C2212yes—
20C2×#13063256C2212yes—
21C2×#13063256C2212yes—
22C2×#13063235C2211yescharacteristic
23C2×#13063235C2211yescharacteristic
24C2×#13063235C2211yescharacteristic
25C2×#13063235C2211yescharacteristic
26C2×C4×C43⋊C8C2211yescharacteristic
27#14582803—24no—
28#14582796—24no—
29#14582768C2212yes—
30#14582765C2211yescharacteristic
31#14582765C2211yescharacteristic
32#14582764C2212yes—
33C42×Dic43C2211yescharacteristic
34C2×#107×C43C2212yes—
35C2×#106×C43C2212yes—
36C2×C4×C8×C43C2211yescharacteristic
37C43×#382C2211yescharacteristic
38C43×#382C2211yescharacteristic
39C22×Dic86—22no—
40C22×C43⋊C8C2311yescharacteristic
41C22×C43⋊C8C2311yescharacteristic
42#13063324—24no—
43#13063324—24no—
44#13063316—24no—
45#13063316—24no—
46C2×C4⋊Dic43—22no—
47C2×C4⋊Dic43C2312yes—
48C2×C4⋊Dic43C2312yes—
49C2×Dic43⋊C4—22no—
50C2×Dic43⋊C4—24no—
51C2×Dic43⋊C4—22no—
52C2×C4×Dic43D414yes—
53C2×C4×Dic43C2311yescharacteristic
54C2×C4×Dic43C2311yescharacteristic
55#13063259—24no—
56#13063258—24no—
57#13063258—24no—
58#13063257—24no—
59#13063256—24no—
60#13063256—24no—
61#13063235D414yes—
62#13063235D414yes—
63#13063235Q814yescomplemented
64#13063235Q814yescomplemented
65C4×C43⋊C8Q814yescomplemented
66C43⋊#95—22no—
67C43⋊#95—22no—
68C43⋊#95—24no—
69C22×C8×C43C2311yescharacteristic
70C22×C8×C43C2311yescharacteristic
71C2×C4⋊C4×C43C2312yes—
72C2×C4⋊C4×C43C2312yes—
73C2×C42×C43C2311yescharacteristic
74#107×C43—24no—
75#106×C43—24no—
76C4×C8×C43Q814yescomplemented
77#95×C43—22no—
78#95×C43—22no—
79C22×C4×C43—22no—
80C22×C4×C43—22no—
81C22×C4×C43C2×D412yes—
82C22×C4×C43C2411yescharacteristic
83C22×Dic43—22no—
84C22×Dic43—22no—
85C22×Dic43C2×D412yes—
86C22×Dic43C2×D412yes—
87C2×Dic86—48no—
88C2×Dic86—44no—
89C2×C8×C43C2×D412yes—
90C2×C8×C43C2×D412yes—
91C2×C8×C43C2×Q812yes—
92C2×C8×C43C2×Q812yes—
93C2×C8×C43C2×Q812yes—
94C2×C8×C43C2×Q812yes—
95C4⋊C4×C43—22no—
96C4⋊C4×C43—22no—
97C4⋊C4×C43—22no—
98C4⋊C4×C43—22no—
99C42×C43C2×Q812yes—
100C42×C43C2×Q812yes—
101C4⋊Dic43—22no—
102C4⋊Dic43—22no—
103C4⋊Dic43—22no—
104C4⋊Dic43—22no—
105C4⋊Dic43—44no—
106Dic43⋊C4—48no—
107Dic43⋊C4—44no—
108Dic43⋊C4—44no—
109C4×Dic43—44no—
110C4×Dic43C2×D412yes—
111C4×Dic43C2×D412yes—
112C4×Dic43C2×Q812yes—
113C4×Dic43C2×Q812yes—
114C2×C43⋊C8C2×D412yes—
115C2×C43⋊C8C2×D412yes—
116C2×C43⋊C8C2×Q812yes—
117C2×C43⋊C8C2×Q812yes—
118C2×C43⋊C8C2×Q812yes—
119C2×C43⋊C8C2×Q812yes—
120C23×C43C22×D411yescharacteristic
121C2×C4×C43—24no—
122C2×C4×C43—42no—
123C2×C4×C43—42no—
124C2×C4×C43—44no—
125C2×C4×C43—44no—
126C2×C4×C43C4⋊Q814yes—
127C2×C4×C43C22×D411yescharacteristic
128C2×C4×C43C22×D411yescharacteristic
129C2×C4×C43C22×Q811yescharacteristic
130C2×C4×C43C22×Q811yescharacteristic
131C2×C4×C43C22×Q811yescharacteristic
132C2×C4×C43C22×Q811yescharacteristic
133C2×Dic43—24no—
134C2×Dic43—24no—
135C2×Dic43—42no—
136C2×Dic43—42no—
137C2×Dic43—44no—
138C2×Dic43—44no—
139C2×Dic43#12714yes—
140C2×Dic43C4⋊Q814yes—
141Dic86—88no—
142C8×C43C4⋊Q814yes—
143C8×C43C4⋊Q814yes—
144C43⋊C8C4⋊Q814yes—
145C43⋊C8C4⋊Q814yes—
146#33317—431nomaximal, Sylow
147C22×C43C2×#12711yescharacteristic
148C22×C43C2×C4⋊Q811yescharacteristic
149C22×C43C2×C4⋊Q811yescharacteristic
150C22×C43#57514yes—
151C4×C43—24no—
152C4×C43—82no—
153C4×C43—82no—
154C4×C43C2×C4⋊Q811yescharacteristic
155C4×C43C2×C4⋊Q811yescharacteristic
156C4×C43C2×C4⋊Q811yescharacteristic
157C4×C43C2×C4⋊Q811yescharacteristic
158Dic43—24no—
159Dic43—24no—
160Dic43—82no—
161Dic43—82no—
162C2×#501—432no—
163C2×#501—432no—
164#2862—431no—
165#2859—431no—
166#1847—432no—
167#1847—432no—
168#1846—431no—
169#1846—431no—
170#1846—431no—
171#1846D4311yescharacteristic
172C4×#97—431no—
173C2×C43#286811yescharacteristic
174C2×C43#315312yes—
175C2×C43#316212yes—
176C2×C43#316612yes—
177C2×C4⋊Q8—432no—
178C2×#125—432no—
179#501—868no—
180#501—868no—
181C2×#107—432no—
182C2×#107—432no—
183C2×#107—432no—
184C2×#107C2×D4312yes—
185C2×#106—432no—
186C2×#106—432no—
187C2×#106—432no—
188C2×#106C2×D4312yes—
189C2×#97—431no—
190C2×#97—431no—
191C2×#97—431no—
192C2×#97—431no—
193C2×C4×C8—431no—
194C2×C4×C8C2×D4311yescharacteristic
195#391—864no—
196#389—864no—
197#384—432no—
198#382—432no—
199#382—431no—
200#382—431no—
201#382C2×D4311yescharacteristic
202#382C2×D4311yescharacteristic
203C43—431no—
204C43#3331711yescharacteristic, complemented, Sylow
205C22×Q8—862no—
206C22×C8—431no—
207C22×C8—431no—
208C22×C8C22×D4311yescharacteristic
209C22×C8C22×D4311yescharacteristic
210C4⋊Q8—864no—
211C4⋊Q8—864no—
212#125—864no—
213#125—864no—
214C2×C4⋊C4—432no—
215C2×C4⋊C4—432no—
216C2×C4⋊C4—862no—
217C2×C4⋊C4—862no—
218C2×C4⋊C4—862no—
219C2×C4⋊C4—864no—
220C2×C4⋊C4C22×D4312yes—
221C2×C4⋊C4C22×D4312yes—
222C2×C42—431no—
223C2×C42—431no—
224C2×C42—434no—
225C2×C42C22×D4311yescharacteristic
226#107—24no—
227#107—864no—
228#107—864no—
229#107—864no—
230#106—24no—
231#106—864no—
232#106—864no—
233#106—864no—
234#97—434no—
235#97—434no—
236#97—434no—
237#97—434no—
238C4×C8—434no—
239C4×C8Dic8614yescomplemented
240#95—22no—
241#95—22no—
242#95—864no—
243#95—862no—
244#95—862no—
245C2×Q8—1724no—
246C2×Q8—1728no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—432no—
250C22×C4—432no—
251C22×C4—862no—
252C22×C4—862no—
253C22×C4D4×D4312yes—
254C22×C4C23×D4311yescharacteristic
255C2×C8—432no—
256C2×C8—432no—
257C2×C8—432no—
258C2×C8—432no—
259C2×C8—432no—
260C2×C8—432no—
261C2×C8C2×Dic8612yes—
262C2×C8C2×Dic8612yes—
263C2×C8D4×D4312yes—
264C2×C8D4×D4312yes—
265C2×C8Q8×D4312yes—
266C2×C8Q8×D4312yes—
267C4⋊C4—22no—
268C4⋊C4—22no—
269C4⋊C4—22no—
270C4⋊C4—22no—
271C4⋊C4—862no—
272C4⋊C4—862no—
273C4⋊C4—862no—
274C4⋊C4—862no—
275C4⋊C4—1724no—
276C4⋊C4—1724no—
277C4⋊C4—1724no—
278C4⋊C4—1728no—
279C42—432no—
280C42—432no—
281C42—432no—
282C42—432no—
283C42—1724no—
284C42C2×Dic8612yes—
285C42Q8×D4312yes—
286C23C2×D4×D4311yescharacteristic
287Q8—3448no—
288C2×C4—24no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—44no—
292C2×C4—44no—
293C2×C4—434no—
294C2×C4—434no—
295C2×C4—864no—
296C2×C4—864no—
297C2×C4—1722no—
298C2×C4—1722no—
299C2×C4—1724no—
300C2×C4—1724no—
301C2×C4#1306332414yes—
302C2×C4C2×D4×D4311yescharacteristic
303C2×C4C2×D4×D4311yescharacteristic
304C2×C4C2×Q8×D4311yescharacteristic
305C2×C4C2×Q8×D4311yescharacteristic
306C2×C4C2×Q8×D4311yescharacteristic
307C2×C4C22×Dic8611yescharacteristic
308C8—434no—
309C8—434no—
310C8#1306332414yes—
311C8#1306332414yes—
312C22#127×D4311yescharacteristic
313C22C4⋊Q8×D4311yescharacteristic
314C22C2×#1306332411yescharacteristic
315C22#1458369614yes—
316C4—24no—
317C4—82no—
318C4—82no—
319C4—864no—
320C4—864no—
321C4—3442no—
322C4—3442no—
323C4C4⋊Q8×D4311yescharacteristic
324C4C4⋊Q8×D4311yescharacteristic
325C4C2×#1306332411yescharacteristic
326C4C2×#1306332411yescharacteristic
327C2#1914299211yescharacteristic
328C2#1914505612yes—
329C2#1914511812yes—
330C2#1914514312yes—
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1846C2
socle, prime radicalC23×C43C22×D4
hypercenter#1846D43
hypocenterC43#33317
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1846

Complements

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

NH ≅ G/Ntype
63. #13063235Q8semidirect
64. #13063235Q8semidirect
65. C4×C43⋊C8Q8semidirect
76. C4×C8×C43Q8semidirect
204. C43#33317semidirect
239. C4×C8Dic86semidirect

Maximal subgroups

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

subgroupindex
C2×#145833072
C2×#145833062
#191429712
#191429572
#191347622
#191347602
#191347592
#191347572
C4×#130632352
C43×#18462
#3331743