Finite Group Databasebeta

← #25065818

Subgroups — #25065818

Order 11008.

702 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C8×#10621898C211yesmaximal, characteristic
2#19143160C212yesmaximal
3#19133365C212yesmaximal, complemented
4#19133364C214yesmaximal, complemented
5#19133351C211yesmaximal, characteristic, complemented
6#19133349C212yesmaximal, complemented
7#334×D43C212yesmaximal, complemented
8C2×C43×#334C211yesmaximal, characteristic, complemented
9C2×#13063331—22no—
10C4×#10621898C2211yescharacteristic
11C8×Dic86C411yescharacteristic
12C8×Dic86C411yescharacteristic
13C8×D172C411yescharacteristic
14C8×D172C411yescharacteristic
15C8×C22⋊D43C412yes—
16C8×C22⋊D43C412yes—
17#14582952C2211yescharacteristic
18#14582950C2212yes—
19#14582925—22no—
20#14582924—24no—
21#14582923C2212yes—
22#14582921C2214yes—
23C4⋊C8×D43C2214yes—
24C4×C8×D43C2212yes—
25#14582650C2212yes—
26#14582650C2212yes—
27#14582649C2214yes—
28#14582649C2214yes—
29C2×C4⋊C8×C43C2212yes—
30C2×C4×C8×C43C2211yescharacteristic
31C43×#334C2211yescharacteristic
32C43×#334C2211yescharacteristic
33C43×#334C2212yes—
34C2×#10621898D411yescharacteristic
35#13063331—48no—
36C2×#10621877—22no—
37C2×#10621872—24no—
38C2×C8×D43—24no—
39C2×C8×D43C2×C412yes—
40C2×C8×D43C2×C412yes—
41C4×Dic86C2×C411yescharacteristic
42C4×Dic86Q811yescharacteristic
43C4×D172C2×C411yescharacteristic
44C4×D172Q811yescharacteristic
45C4×C22⋊D43C2×C412yes—
46C4×C22⋊D43Q812yes—
47#13063284D411yescharacteristic
48#13063282D412yes—
49C42×D43C2312yes—
50C4⋊(C43⋊C8)—22no—
51C4⋊(C43⋊C8)C2×C411yescharacteristic
52C4⋊(C43⋊C8)C2×C411yescharacteristic
53C4⋊(C43⋊C8)C2314yes—
54Dic43⋊C8—24no—
55Dic43⋊C8—24no—
56Dic43⋊C8C2×C412yes—
57Dic43⋊C8C2×C412yes—
58C22⋊(C43⋊C8)C2×C412yes—
59(C2×D43)⋊C8C2×C412yes—
60(C2×D43)⋊C8C2×C412yes—
61C4×C43⋊C8C2312yes—
62C8×Dic43C2×C412yes—
63C8×Dic43C2×C412yes—
64C22×C8×C43—22no—
65C22×C8×C43C2×C411yescharacteristic
66C22×C8×C43C2×C411yescharacteristic
67C2×C42×C43C2311yescharacteristic
68C4⋊C8×C43—22no—
69C4⋊C8×C43C2312yes—
70C4⋊C8×C43C2312yes—
71C4×C8×C43C2×C411yescharacteristic
72C4×C8×C43C2×C411yescharacteristic
73C4×C8×C43C2311yescharacteristic
74C4×C8×C43C2311yescharacteristic
75C22×C4×C43C22×C411yescharacteristic
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43C2×Q811yescharacteristic
78C2×C22⋊D43C4⋊C412yes—
79#10621898SD1618yes—
80C2×D172C4⋊C411yescharacteristic
81C2×C4×D43C22×C412yes—
82C2×C4×D43C2×D412yes—
83C2×C4×D43C2×Q812yes—
84C2×Dic86C4⋊C411yescharacteristic
85C2×C8×C43—22no—
86C2×C8×C43—22no—
87C2×C8×C43—22no—
88C2×C8×C43—41no—
89C2×C8×C43—44no—
90C2×C8×C43C22×C411yescharacteristic
91C2×C8×C43C22×C411yescharacteristic
92C2×C8×C43C22×C411yescharacteristic
93C2×C8×C43C22×C411yescharacteristic
94C42×C43C22×C411yescharacteristic
95C42×C43C2×D411yescharacteristic
96C42×C43C2×Q811yescharacteristic
97C42×C43C2411yescharacteristic
98C22⋊Dic43C4⋊C412yes—
99(C2×D43)⋊C4C4⋊C412yes—
100(C2×D43)⋊C4C4⋊C412yes—
101C4⋊Dic43C4⋊C411yescharacteristic
102C4⋊Dic43C4⋊C411yescharacteristic
103Dic43⋊C4C4⋊C412yes—
104Dic43⋊C4C4⋊C412yes—
105C4×Dic43C22×C412yes—
106C4×Dic43C2×D412yes—
107C4×Dic43C2×Q812yes—
108#10621877—44no—
109C2×C43⋊C8—24no—
110C2×C43⋊C8C22×C412yes—
111C2×C43⋊C8C22×C412yes—
112#10621872—48no—
113C8×D43—24no—
114C8×D43—42no—
115C8×D43—48no—
116C23×C43C2×C4⋊C411yescharacteristic
117C22×D43C2×C4⋊C412yes—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—41no—
121C2×C4×C43C2×C4⋊C411yescharacteristic
122C2×C4×C43C2×C4⋊C411yescharacteristic
123C2×C4×C43C2×C4⋊C411yescharacteristic
124C2×C4×C43C2×SD1614yes—
125C2×C4×C43C23×C411yescharacteristic
126C2×C4×C43C22×D411yescharacteristic
127C2×C4×C43C22×Q811yescharacteristic
128C22⋊D43#10618yes—
129C2×Dic43C2×C4⋊C412yes—
130C2×Dic43C2×C4⋊C412yes—
131C2×Dic43C2×C4⋊C412yes—
132D172#10614yes—
133C4×D43—22no—
134C4×D43—22no—
135C4×D43—42no—
136C4×D43C2×SD1618yes—
137Dic86#10614yes—
138C8×C43—21no—
139C8×C43—21no—
140C8×C43—21no—
141C8×C43—42no—
142C8×C43—42no—
143C8×C43#13112yescomplemented
144C43⋊C8—22no—
145C43⋊C8—22no—
146C43⋊C8—44no—
147#17826—431nomaximal, Sylow
148C22×C43—21no—
149C22×C43—21no—
150C22×C43C2×#10612yes—
151C22×C43C22×C4⋊C411yescharacteristic
152C2×D43—22no—
153C2×D43—22no—
154C2×D43C2×#10614yes—
155C4×C43—21no—
156C4×C43—21no—
157C4×C43—21no—
158C4×C43C2×#10612yes—
159C4×C43C2×#13111yescharacteristic
160C4×C43#56811yescharacteristic
161C4×C43C22×SD1612yes—
162Dic43—22no—
163Dic43—22no—
164Dic43C2×#10614yes—
165C8×#41—431no—
166#2906—432no—
167#1570—432no—
168#1570—434no—
169#1566—431no—
170#1566—432no—
171C2×#334—432no—
172C2×#334D4311yescharacteristic, complemented
173C2×C43—22no—
174C2×C43#290611yescharacteristic
175C2×C43C22×#10611yescharacteristic
176C2×C43#291611yescharacteristic
177D43—24no—
178C2×#131—862no—
179C4×#41—431no—
180C8×Q8—431no—
181C8×Q8—431no—
182C8×D4—432no—
183C8×D4—432no—
184C8×D4—431no—
185C8×D4—431no—
186#431—431no—
187#431—432no—
188#424—864no—
189#424—862no—
190#423—432no—
191#423—434no—
192C2×C4⋊C8—434no—
193C2×C4⋊C8C2×D4312yes—
194C2×C4×C8—432no—
195C2×C4×C8C2×D4311yescharacteristic
196#334—434no—
197#334—434no—
198#334—432no—
199#334—432no—
200#334C2×D4311yescharacteristic
201#334C2×D4311yescharacteristic
202#334C2×D4312yes—
203C43#1782611yescharacteristic, complemented, Sylow
204C2×#41—431no—
205#131—1728no—
206C2×M16—864no—
207C2×M16—862no—
208C22×C8—22no—
209C22×C8—432no—
210C22×C8—432no—
211C22×C8—864no—
212C22×C8C4×D4311yescharacteristic
213C22×C8C4×D4311yescharacteristic
214C4×Q8—431no—
215C4×Q8—431no—
216C4×D4—432no—
217C4×D4—432no—
218C4×D4—431no—
219C4×D4—431no—
220#117—431no—
221#117—432no—
222C2×C42—432no—
223C2×C42C22×D4311yescharacteristic
224C4⋊C8—22no—
225C4⋊C8—432no—
226C4⋊C8—432no—
227C4⋊C8—431no—
228C4⋊C8—431no—
229C4⋊C8—434no—
230C4⋊C8—864no—
231C4⋊C8—864no—
232C4⋊C8—862no—
233C4⋊C8C22×D4312yes—
234C4⋊C8C22×D4312yes—
235C22⋊C8—432no—
236C22⋊C8—432no—
237C22⋊C8—432no—
238C4×C8—432no—
239C4×C8—432no—
240C4×C8—432no—
241C4×C8C4×D4311yescharacteristic
242C4×C8C4×D4311yescharacteristic
243C4×C8C22×D4311yescharacteristic
244C4×C8C22×D4311yescharacteristic
245#41—438no—
246C2×Q8—431no—
247C2×D4—432no—
248C2×D4—431no—
249C22×C4—432no—
250C22×C4—432no—
251C22×C4—432no—
252C22×C4C2×C4×D4311yescharacteristic
253C22×C4D4×D4311yescharacteristic
254C22×C4Q8×D4311yescharacteristic
255M16—1728no—
256M16—1724no—
257C2×C8—22no—
258C2×C8—22no—
259C2×C8—22no—
260C2×C8—41no—
261C2×C8—44no—
262C2×C8—432no—
263C2×C8—432no—
264C2×C8—864no—
265C2×C8—864no—
266C2×C8—1722no—
267C2×C8—1728no—
268C2×C8C2×C4×D4311yescharacteristic
269C2×C8C2×C4×D4311yescharacteristic
270C2×C8C2×C4×D4311yescharacteristic
271C2×C8C2×C4×D4311yescharacteristic
272C4⋊C4—432no—
273C4⋊C4—432no—
274C4⋊C4—431no—
275C4⋊C4—431no—
276C22⋊C4—432no—
277C22⋊C4—432no—
278C22⋊C4—432no—
279C42—432no—
280C42—432no—
281C42—432no—
282C42C2×C4×D4311yescharacteristic
283C42D4×D4311yescharacteristic
284C42Q8×D4311yescharacteristic
285C42C23×D4311yescharacteristic
286C23—432no—
287C23C4⋊C4×D4311yescharacteristic
288Q8—434no—
289D4—438no—
290D4—434no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—41no—
294C2×C4—432no—
295C2×C4—438no—
296C2×C4—432no—
297C2×C4—432no—
298C2×C4—862no—
299C2×C4—862no—
300C2×C4—1722no—
301C2×C4C4⋊C4×D4311yescharacteristic
302C2×C4C4⋊C4×D4311yescharacteristic
303C2×C4C4⋊C4×D4311yescharacteristic
304C2×C4SD16×D4314yes—
305C2×C4C22×C4×D4311yescharacteristic
306C2×C4C2×D4×D4311yescharacteristic
307C2×C4C2×Q8×D4311yescharacteristic
308C8—21no—
309C8—21no—
310C8—21no—
311C8—42no—
312C8—42no—
313C8—862no—
314C8—862no—
315C8—1724no—
316C8#1306333112yescomplemented
317C22—21no—
318C22—21no—
319C22—434no—
320C22—862no—
321C22—862no—
322C22#106×D4312yes—
323C22C2×C4⋊C4×D4311yescharacteristic
324C4—21no—
325C4—21no—
326C4—21no—
327C4—434no—
328C4—862no—
329C4—862no—
330C4#106×D4312yes—
331C4C2×#1306333111yescharacteristic
332C4#1458366511yescharacteristic
333C4C2×SD16×D4312yes—
334C2—22no—
335C2—864no—
336C2#1914316011yescharacteristic
337C2C2×#106×D4311yescharacteristic
338C2#1914320311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC2×C43×#334C2
socleC22×C43C22×C4⋊C4
prime radicalC2×#10621898D4
cosocleC42×C43C24
hypercenterC2×#334D43
hypocenterC43#17826
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×#334

Complements

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

NH ≅ G/Ntype
3. #19133365C2semidirect
4. #19133364C2semidirect
5. #19133351C2semidirect
6. #19133349C2semidirect
7. #334×D43C2semidirect
8. C2×C43×#334C2semidirect
143. C8×C43#131semidirect
172. C2×#334D43semidirect
203. C43#17826semidirect
316. C8#13063331semidirect

Maximal subgroups

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

subgroupindex
C8×#106218982
#191431602
#191333652
#191333642
#191333512
#191333492
#334×D432
C2×C43×#3342
#1782643