Finite Group Databasebeta

← #25065885

Subgroups — #25065885

Order 11008.

616 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143716C212yesmaximal
2C8×#10621898C211yesmaximal, characteristic
3#19133383C212yesmaximal, complemented
4#19133379C214yesmaximal, complemented
5#19133355C212yesmaximal, complemented
6#19133351C211yesmaximal, characteristic, complemented
7#334×D43C212yesmaximal, complemented
8C43×#1564C211yesmaximal, characteristic, complemented
9C4×#10621898C2211yescharacteristic
10#14583029—22no—
11C8×Dic86C411yescharacteristic
12C8×Dic86C411yescharacteristic
13#14582973—24no—
14C8×D172—22no—
15C8×D172C411yescharacteristic
16C8×D172C411yescharacteristic
17C8×C22⋊D43C412yes—
18C8×C22⋊D43C412yes—
19#14582955C2214yes—
20#14582952C2211yescharacteristic
21#14582950C2212yes—
22#14582923C2212yes—
23C4⋊C8×D43C2214yes—
24C4×C8×D43C2212yes—
25#14582651C2214yes—
26#14582650C2212yes—
27#14582650C2212yes—
28#14582649C2214yes—
29C43×#431C2212yes—
30C2×C4×C8×C43C2211yescharacteristic
31C43×#335C2212yes—
32C43×#334C2211yescharacteristic
33C43×#334C2211yescharacteristic
34C2×#10621898Q811yescharacteristic
35C2×#10621877—22no—
36C2×C8×D43—24no—
37C2×C8×D43C2×C412yes—
38C2×C8×D43C2×C412yes—
39C4×Dic86C2×C411yescharacteristic
40C4×Dic86D411yescharacteristic
41C4×D172C2×C411yescharacteristic
42C4×D172D411yescharacteristic
43C4×C22⋊D43C2×C412yes—
44C4×C22⋊D43D412yes—
45#13063284Q811yescharacteristic
46#13063282Q812yes—
47C42×D43C2312yes—
48C4⋊(C43⋊C8)—22no—
49C4⋊(C43⋊C8)C2×C411yescharacteristic
50C4⋊(C43⋊C8)C2×C411yescharacteristic
51C4⋊(C43⋊C8)C2314yes—
52Dic43⋊C8—24no—
53Dic43⋊C8C2×C412yes—
54Dic43⋊C8C2×C412yes—
55C22⋊(C43⋊C8)C2×C412yes—
56(C2×D43)⋊C8—24no—
57(C2×D43)⋊C8C2×C412yes—
58(C2×D43)⋊C8C2×C412yes—
59#13063235—24no—
60C4×C43⋊C8C2312yes—
61C8×Dic43C2×C412yes—
62C8×Dic43C2×C412yes—
63C22×C8×C43C2×C411yescharacteristic
64C22×C8×C43C2×C411yescharacteristic
65C2×C42×C43C2311yescharacteristic
66C4⋊C8×C43C2312yes—
67C4⋊C8×C43C2312yes—
68C22⋊C8×C43—22no—
69C4×C8×C43—22no—
70C4×C8×C43C2×C411yescharacteristic
71C4×C8×C43C2×C411yescharacteristic
72C4×C8×C43C2311yescharacteristic
73C4×C8×C43C2311yescharacteristic
74C22×C4×C43C22×C411yescharacteristic
75C22×C4×C43C2×D411yescharacteristic
76C22×C4×C43C2×Q811yescharacteristic
77C2×C22⋊D43C4⋊C412yes—
78#10621898—24no—
79C2×D172C4⋊C411yescharacteristic
80C2×C4×D43C22×C412yes—
81C2×C4×D43C2×D412yes—
82C2×C4×D43C2×Q812yes—
83C2×Dic86C4⋊C411yescharacteristic
84C2×C8×C43—22no—
85C2×C8×C43—22no—
86C2×C8×C43—22no—
87C2×C8×C43—41no—
88C2×C8×C43C22×C411yescharacteristic
89C2×C8×C43C22×C411yescharacteristic
90C2×C8×C43C22×C411yescharacteristic
91C2×C8×C43C22×C411yescharacteristic
92C42×C43C22×C411yescharacteristic
93C42×C43C2×D411yescharacteristic
94C42×C43C2×Q811yescharacteristic
95C42×C43C2411yescharacteristic
96C22⋊Dic43C4⋊C412yes—
97(C2×D43)⋊C4C4⋊C412yes—
98(C2×D43)⋊C4C4⋊C412yes—
99C4⋊Dic43C4⋊C411yescharacteristic
100C4⋊Dic43C4⋊C411yescharacteristic
101Dic43⋊C4C4⋊C412yes—
102Dic43⋊C4C4⋊C412yes—
103C4×Dic43C22×C412yes—
104C4×Dic43C2×D412yes—
105C4×Dic43C2×Q812yes—
106#10621877—82no—
107C2×C43⋊C8—24no—
108C2×C43⋊C8C22×C412yes—
109C2×C43⋊C8C22×C412yes—
110C8×D43—24no—
111C8×D43—42no—
112C8×D43—84no—
113C23×C43C2×C4⋊C411yescharacteristic
114C22×D43C2×C4⋊C412yes—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—22no—
118C2×C4×C43—22no—
119C2×C4×C43C2×C4⋊C411yescharacteristic
120C2×C4×C43C2×C4⋊C411yescharacteristic
121C2×C4×C43C2×C4⋊C411yescharacteristic
122C2×C4×C43C23×C411yescharacteristic
123C2×C4×C43C22×D411yescharacteristic
124C2×C4×C43C22×Q811yescharacteristic
125C22⋊D43—24no—
126C2×Dic43C2×C4⋊C412yes—
127C2×Dic43C2×C4⋊C412yes—
128C2×Dic43C2×C4⋊C412yes—
129D172#10814yes—
130C4×D43—24no—
131C4×D43—22no—
132C4×D43—22no—
133C4×D43—24no—
134Dic86—22no—
135C8×C43—21no—
136C8×C43—21no—
137C8×C43—21no—
138C8×C43—42no—
139C8×C43—42no—
140C8×C43#13112yes—
141C43⋊C8—22no—
142C43⋊C8—22no—
143C43⋊C8—44no—
144#17834—431nomaximal, Sylow
145C22×C43—21no—
146C22×C43—21no—
147C22×C43—21no—
148C22×C43C22×C4⋊C411yescharacteristic
149C2×D43—22no—
150C2×D43—22no—
151C2×D43C2×#10814yes—
152C4×C43—21no—
153C4×C43—21no—
154C4×C43—21no—
155C4×C43C2×#10812yes—
156C4×C43C2×#13111yescharacteristic
157C4×C43#56811yescharacteristic
158C4×C43#57712yes—
159Dic43—22no—
160Dic43—22no—
161Dic43—22no—
162#2990—432no—
163C8×#41—431no—
164#1574—432no—
165#1573—434no—
166#1568—432no—
167#1566—431no—
168#1564D4311yescharacteristic, complemented
169C2×#334—432no—
170C2×C43—41no—
171C2×C43#290611yescharacteristic
172C2×C43#291211yescharacteristic
173C2×C43C22×#10811yescharacteristic
174D43—24no—
175C4×#41—431no—
176#446—862no—
177C8×Q8—431no—
178C8×Q8—431no—
179#435—864no—
180C8×D4—432no—
181C8×D4—432no—
182C8×D4—431no—
183C8×D4—431no—
184C8×D4—862no—
185#432—434no—
186#431—431no—
187#431—432no—
188#431C2×D4312yes—
189#423—432no—
190C2×C4⋊C8—434no—
191C2×C4×C8—432no—
192C2×C4×C8C2×D4311yescharacteristic
193#335—434no—
194#335C2×D4312yes—
195#334—434no—
196#334—432no—
197#334—432no—
198#334C2×D4311yescharacteristic
199#334C2×D4311yescharacteristic
200C43#1783411yescharacteristic, complemented, Sylow
201C2×#41—431no—
202C2×M16—862no—
203C22×C8—432no—
204C22×C8—432no—
205C22×C8—864no—
206C22×C8C4×D4311yescharacteristic
207C22×C8C4×D4311yescharacteristic
208C4×Q8—431no—
209C4×Q8—431no—
210C4×D4—432no—
211C4×D4—432no—
212C4×D4—431no—
213C4×D4—431no—
214#117—431no—
215#117—432no—
216C2×C42—432no—
217C2×C42C22×D4311yescharacteristic
218C4⋊C8—432no—
219C4⋊C8—432no—
220C4⋊C8—431no—
221C4⋊C8—431no—
222C4⋊C8—434no—
223C4⋊C8—864no—
224C4⋊C8—862no—
225C4⋊C8C22×D4312yes—
226C4⋊C8C22×D4312yes—
227C22⋊C8—22no—
228C22⋊C8—432no—
229C22⋊C8—432no—
230C22⋊C8—432no—
231C22⋊C8—864no—
232#97—864no—
233C4×C8—22no—
234C4×C8—432no—
235C4×C8—432no—
236C4×C8—432no—
237C4×C8C4×D4311yescharacteristic
238C4×C8C4×D4311yescharacteristic
239C4×C8C22×D4311yescharacteristic
240C4×C8C22×D4311yescharacteristic
241#41—864no—
242C2×Q8—431no—
243C2×D4—432no—
244C2×D4—431no—
245C22×C4—432no—
246C22×C4—432no—
247C22×C4—432no—
248C22×C4C2×C4×D4311yescharacteristic
249C22×C4D4×D4311yescharacteristic
250C22×C4Q8×D4311yescharacteristic
251M16—3442no—
252C2×C8—22no—
253C2×C8—22no—
254C2×C8—22no—
255C2×C8—41no—
256C2×C8—432no—
257C2×C8—432no—
258C2×C8—864no—
259C2×C8—864no—
260C2×C8—3444no—
261C2×C8—1722no—
262C2×C8C2×C4×D4311yescharacteristic
263C2×C8C2×C4×D4311yescharacteristic
264C2×C8C2×C4×D4311yescharacteristic
265C2×C8C2×C4×D4311yescharacteristic
266C4⋊C4—432no—
267C4⋊C4—432no—
268C4⋊C4—431no—
269C4⋊C4—431no—
270C22⋊C4—432no—
271C22⋊C4—432no—
272C22⋊C4—432no—
273C42—432no—
274C42—432no—
275C42—432no—
276C42C2×C4×D4311yescharacteristic
277C42D4×D4311yescharacteristic
278C42Q8×D4311yescharacteristic
279C42C23×D4311yescharacteristic
280C23—432no—
281C23C4⋊C4×D4311yescharacteristic
282Q8—862no—
283D4—434no—
284D4—864no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—432no—
290C2×C4—432no—
291C2×C4—432no—
292C2×C4—864no—
293C2×C4—862no—
294C2×C4—862no—
295C2×C4—864no—
296C2×C4C4⋊C4×D4311yescharacteristic
297C2×C4C4⋊C4×D4311yescharacteristic
298C2×C4C4⋊C4×D4311yescharacteristic
299C2×C4C22×C4×D4311yescharacteristic
300C2×C4C2×D4×D4311yescharacteristic
301C2×C4C2×Q8×D4311yescharacteristic
302C8—21no—
303C8—21no—
304C8—21no—
305C8—42no—
306C8—42no—
307C8—862no—
308C8—862no—
309C8—1724no—
310C8#1306333112yes—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—434no—
315C22—862no—
316C22—862no—
317C22C2×C4⋊C4×D4311yescharacteristic
318C4—21no—
319C4—21no—
320C4—21no—
321C4—862no—
322C4—862no—
323C4—862no—
324C4#108×D4312yes—
325C4C2×#1306333111yescharacteristic
326C4#1458366511yescharacteristic
327C4#1458370612yes—
328C2—41no—
329C2—864no—
330C2#1914316011yescharacteristic
331C2#1914318711yescharacteristic
332C2C2×#108×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1564C2
socleC22×C43C22×C4⋊C4
prime radicalC2×#10621898Q8
cosocleC42×C43C24
hypercenter#1564D43
hypocenterC43#17834
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1564

Complements

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

NH ≅ G/Ntype
3. #19133383C2semidirect
4. #19133379C2semidirect
5. #19133355C2semidirect
6. #19133351C2semidirect
7. #334×D43C2semidirect
8. C43×#1564C2semidirect
168. #1564D43semidirect
200. C43#17834semidirect

Maximal subgroups

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

subgroupindex
#191437162
C8×#106218982
#191333832
#191333792
#191333552
#191333512
#334×D432
C43×#15642
#1783443