Finite Group Databasebeta

← #25062660

Subgroups — #25062660

Order 11008.

876 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143680C211yesmaximal, characteristic, complemented
2#19143676C211yesmaximal, characteristic, complemented
3#19132964C214yesmaximal
4#19132951C214yesmaximal, complemented
5#19132919C212yesmaximal, complemented
6#19132909C212yesmaximal
7C2×C43×#541C211yesmaximal, characteristic
8#14583030—24no—
9Q8×C43⋊C8—24no—
10#14582956C2214yes—
11#14582952C2212yes—
12#14582952C2214yes—
13#14582952C2212yes—
14#14582625C2214yes—
15#14582625C2218yes—
16#14582623C2214yes—
17C43×#541—24no—
18C43×#541—24no—
19C2×C4⋊Q8×C43C411yescharacteristic
20C2×#126×C43C412yes—
21C2×#126×C43C2212yes—
22C2×#125×C43C411yescharacteristic
23C2×#125×C43C412yes—
24C2×#125×C43C2212yes—
25C2×C22⋊Q8×C43C411yescharacteristic
26C2×C22⋊Q8×C43C411yescharacteristic
27C2×C4×Q8×C43C2211yescharacteristic
28C2×C4×Q8×C43C2211yescharacteristic
29C2×#117×C43C2211yescharacteristic
30C4⋊(C43⋊C8)—22no—
31C4⋊(C43⋊C8)—24no—
32C4⋊(C43⋊C8)—22no—
33C4⋊(C43⋊C8)—24no—
34C22⋊(C43⋊C8)C2314yes—
35C22⋊(C43⋊C8)C2314yes—
36#13063236—24no—
37C4×C43⋊C8—22no—
38C4×C43⋊C8—24no—
39C4×C43⋊C8—22no—
40C22×Q8×C43C2×C411yescharacteristic
41C22×Q8×C43C2×C411yescharacteristic
42C23×C4×C43C2×C411yescharacteristic
43C4⋊Q8×C43—24no—
44#126×C43—28no—
45#126×C43—24no—
46#126×C43—24no—
47#125×C43—24no—
48#125×C43—28no—
49#125×C43—24no—
50#125×C43—24no—
51C22⋊Q8×C43—24no—
52C22⋊Q8×C43—24no—
53C4×Q8×C43—22no—
54C4×Q8×C43—22no—
55C4×Q8×C43D414yes—
56C4×Q8×C43D414yes—
57#117×C43—22no—
58#117×C43—22no—
59C2×C4⋊C4×C43C2×C411yescharacteristic
60C2×C4⋊C4×C43C2×C411yescharacteristic
61C2×C4⋊C4×C43C2×C412yes—
62C2×C4⋊C4×C43C2×C412yes—
63C2×C4⋊C4×C43C2×C412yes—
64C2×C4⋊C4×C43C2×C412yes—
65C2×C4⋊C4×C43C2×C412yes—
66C2×C4⋊C4×C43C2×C412yes—
67C2×C4⋊C4×C43C2×C411yescharacteristic
68C2×C4⋊C4×C43C2×C412yes—
69C2×C4⋊C4×C43C2311yescharacteristic
70C2×C4⋊C4×C43C2312yes—
71C2×C22⋊C4×C43C2×C411yescharacteristic
72C2×C22⋊C4×C43C2×C412yes—
73C2×C22⋊C4×C43C2×C412yes—
74C2×C22⋊C4×C43C2311yescharacteristic
75C2×C42×C43C2×C411yescharacteristic
76C2×C42×C43C2×C412yes—
77C2×C42×C43C2311yescharacteristic
78C2×C42×C43C2312yes—
79C24×C43C22×C411yescharacteristic
80C2×Q8×C43—22no—
81C2×Q8×C43—24no—
82C2×Q8×C43—24no—
83C2×Q8×C43C22⋊C414yes—
84C22×C4×C43—22no—
85C22×C4×C43—24no—
86C22×C4×C43C22×C412yes—
87C22×C4×C43C22×C411yescharacteristic
88C22×C4×C43C22×C412yes—
89C22×C4×C43C22×C411yescharacteristic
90C22×C4×C43C22×C412yes—
91C22×C4×C43C22×C411yescharacteristic
92C22×C4×C43C22×C411yescharacteristic
93C22×C4×C43C22×C412yes—
94C22×C4×C43C22×C411yescharacteristic
95C22×C4×C43C2411yescharacteristic
96C4⋊C4×C43—22no—
97C4⋊C4×C43—22no—
98C4⋊C4×C43—24no—
99C4⋊C4×C43—24no—
100C4⋊C4×C43—24no—
101C4⋊C4×C43—24no—
102C4⋊C4×C43—24no—
103C4⋊C4×C43—24no—
104C4⋊C4×C43—21no—
105C4⋊C4×C43—21no—
106C4⋊C4×C43—22no—
107C4⋊C4×C43—22no—
108C4⋊C4×C43C22⋊C414yes—
109C4⋊C4×C43C22⋊C418yes—
110C22⋊C4×C43—22no—
111C22⋊C4×C43—24no—
112C22⋊C4×C43—24no—
113C22⋊C4×C43—21no—
114C22⋊C4×C43—21no—
115C42×C43—22no—
116C42×C43—24no—
117C42×C43C2×D412yes—
118C42×C43C2×D412yes—
119C42×C43C2×D414yes—
120C42×C43C2×D414yes—
121C2×C43⋊C8—24no—
122C2×C43⋊C8—24no—
123C23×C43—21no—
124C23×C43—22no—
125C23×C43—41no—
126C23×C43—41no—
127C23×C43C23×C411yescharacteristic
128Q8×C43—28no—
129Q8×C43—44no—
130C2×C4×C43—24no—
131C2×C4×C43—21no—
132C2×C4×C43—22no—
133C2×C4×C43—21no—
134C2×C4×C43—22no—
135C2×C4×C43—21no—
136C2×C4×C43—22no—
137C2×C4×C43—24no—
138C2×C4×C43—41no—
139C2×C4×C43—42no—
140C2×C4×C43—41no—
141C2×C4×C43—44no—
142C2×C4×C43—41no—
143C2×C4×C43—42no—
144C2×C4×C43—41no—
145C2×C4×C43C2×C22⋊C412yes—
146C2×C4×C43C2×C22⋊C414yes—
147C2×C4×C43C2×C22⋊C414yes—
148C2×C4×C43C2×C22⋊C412yes—
149C2×C4×C43#13114yes—
150C2×C4×C43C22×D411yescharacteristic
151C2×C4×C43C22×D411yescharacteristic
152C43⋊C8—44no—
153C43⋊C8—44no—
154#17391—431nomaximal, Sylow
155C22×C43—21no—
156C22×C43—21no—
157C22×C43—41no—
158C22×C43—41no—
159C22×C43—41no—
160C22×C43—82no—
161C22×C43C22×C22⋊C411yescharacteristic
162C22×C43C2×#13112yes—
163C4×C43—24no—
164C4×C43—21no—
165C4×C43—21no—
166C4×C43—22no—
167C4×C43—24no—
168C4×C43—41no—
169C4×C43—42no—
170C4×C43—41no—
171C4×C43—42no—
172C4×C43—41no—
173C4×C43#40814yes—
174C2×#541D4311yescharacteristic
175#2983—431no—
176#2982—431no—
177#1473—434no—
178#1470—434no—
179#1461—432no—
180#1458—432no—
181C2×C43—22no—
182C2×C43—81no—
183C2×C43C2×#40811yescharacteristic
184C2×C43#288411yescharacteristic
185C2×C43#288911yescharacteristic
186#541—24no—
187#541—24no—
188C2×C4⋊Q8Dic4311yescharacteristic
189C2×#126Dic4312yes—
190C2×#126C2×D4312yes—
191C2×#125Dic4311yescharacteristic
192C2×#125Dic4312yes—
193C2×#125C2×D4312yes—
194C2×C22⋊Q8Dic4311yescharacteristic
195C2×C22⋊Q8Dic4311yescharacteristic
196C2×C4×Q8C2×D4311yescharacteristic
197C2×C4×Q8C2×D4311yescharacteristic
198C2×#117C2×D4311yescharacteristic
199#446—864no—
200C8×Q8—864no—
201#432—434no—
202#431—432no—
203#431—434no—
204#431—432no—
205#324—434no—
206#324—438no—
207#323—434no—
208C43#1739111yescharacteristic, complemented, Sylow
209C22×Q8C2×Dic4311yescharacteristic
210C22×Q8C2×Dic4311yescharacteristic
211C23×C4C2×Dic4311yescharacteristic
212C4⋊Q8—24no—
213#126—28no—
214#126—24no—
215#126—24no—
216#125—24no—
217#125—28no—
218#125—24no—
219#125—24no—
220C22⋊Q8—24no—
221C22⋊Q8—24no—
222C4×Q8—22no—
223C4×Q8—22no—
224C4×Q8C22⋊D4314yes—
225C4×Q8C22⋊D4314yes—
226#117—22no—
227#117—22no—
228C2×C4⋊C4C2×Dic4311yescharacteristic
229C2×C4⋊C4C2×Dic4311yescharacteristic
230C2×C4⋊C4C2×Dic4312yes—
231C2×C4⋊C4C2×Dic4312yes—
232C2×C4⋊C4C2×Dic4312yes—
233C2×C4⋊C4C2×Dic4312yes—
234C2×C4⋊C4C2×Dic4312yes—
235C2×C4⋊C4C2×Dic4312yes—
236C2×C4⋊C4C2×Dic4311yescharacteristic
237C2×C4⋊C4C2×Dic4312yes—
238C2×C4⋊C4C22×D4311yescharacteristic
239C2×C4⋊C4C22×D4312yes—
240C2×C22⋊C4C2×Dic4311yescharacteristic
241C2×C22⋊C4C2×Dic4312yes—
242C2×C22⋊C4C2×Dic4312yes—
243C2×C22⋊C4C22×D4311yescharacteristic
244C2×C42C2×Dic4311yescharacteristic
245C2×C42C2×Dic4312yes—
246C2×C42C22×D4311yescharacteristic
247C2×C42C22×D4312yes—
248C4⋊C8—862no—
249C4⋊C8—864no—
250C4⋊C8—862no—
251C4⋊C8—864no—
252C22⋊C8—434no—
253C22⋊C8—434no—
254#97—864no—
255C4×C8—862no—
256C4×C8—864no—
257C4×C8—862no—
258C24C22×Dic4311yescharacteristic
259C2×Q8—22no—
260C2×Q8—24no—
261C2×Q8—24no—
262C2×Q8C22⋊Dic4314yes—
263C22×C4—22no—
264C22×C4—24no—
265C22×C4C22×Dic4312yes—
266C22×C4C22×Dic4311yescharacteristic
267C22×C4C22×Dic4312yes—
268C22×C4C22×Dic4311yescharacteristic
269C22×C4C22×Dic4311yescharacteristic
270C22×C4C22×Dic4312yes—
271C22×C4C22×Dic4311yescharacteristic
272C22×C4C22×Dic4312yes—
273C22×C4C22×Dic4311yescharacteristic
274C22×C4C23×D4311yescharacteristic
275C2×C8—864no—
276C2×C8—864no—
277C4⋊C4—22no—
278C4⋊C4—22no—
279C4⋊C4—24no—
280C4⋊C4—24no—
281C4⋊C4—24no—
282C4⋊C4—24no—
283C4⋊C4—24no—
284C4⋊C4—24no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—22no—
288C4⋊C4—22no—
289C4⋊C4C22⋊Dic4314yes—
290C4⋊C4C22⋊Dic4318yes—
291C22⋊C4—22no—
292C22⋊C4—24no—
293C22⋊C4—24no—
294C22⋊C4—21no—
295C22⋊C4—21no—
296C42—22no—
297C42—24no—
298C42C2×C22⋊D4312yes—
299C42C2×C22⋊D4312yes—
300C42C2×C22⋊D4314yes—
301C42C2×C22⋊D4314yes—
302C23—21no—
303C23—22no—
304C23—41no—
305C23—41no—
306C23C23×Dic4311yescharacteristic
307Q8—28no—
308Q8—44no—
309C2×C4—24no—
310C2×C4—21no—
311C2×C4—22no—
312C2×C4—21no—
313C2×C4—22no—
314C2×C4—21no—
315C2×C4—22no—
316C2×C4—24no—
317C2×C4—41no—
318C2×C4—42no—
319C2×C4—41no—
320C2×C4—44no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—41no—
324C2×C4C2×C22⋊Dic4312yes—
325C2×C4C2×C22⋊Dic4314yes—
326C2×C4C2×C22⋊Dic4314yes—
327C2×C4C2×C22⋊Dic4312yes—
328C2×C4#1306333214yes—
329C2×C4C22×C22⋊D4311yescharacteristic
330C2×C4C22×C22⋊D4311yescharacteristic
331C8—1724no—
332C8—1724no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—82no—
339C22C22×C22⋊Dic4311yescharacteristic
340C22C2×#1306333212yes—
341C4—24no—
342C4—21no—
343C4—21no—
344C4—22no—
345C4—24no—
346C4—41no—
347C4—42no—
348C4—41no—
349C4—42no—
350C4—41no—
351C4#1458286614yes—
352C2—22no—
353C2—81no—
354C2C2×#1458286611yescharacteristic
355C2#1914305911yescharacteristic
356C2#1914307811yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#541C2
socleC22×C43C22×C22⋊C4
prime radicalC24×C43C22×C4
cosocleC22×C4×C43C24
hypercenterC2×#541D43
hypocenterC43#17391
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C4×Q8 ◁ C2×#541

Complements

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

NH ≅ G/Ntype
1. #19143680C2semidirect
2. #19143676C2semidirect
4. #19132951C2semidirect
5. #19132919C2semidirect
208. C43#17391semidirect

Maximal subgroups

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

subgroupindex
#191436802
#191436762
#191329642
#191329512
#191329192
#191329092
C2×C43×#5412
#1739143