Finite Group Databasebeta

← #24990233

Subgroups — #24990233

Order 11008.

466 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#13063240C211yesmaximal, characteristic
2#19132933C211yesmaximal, characteristic
3#19132481C212yesmaximal, complemented
4#19132447C212yesmaximal, complemented
5C43×#2357C211yesmaximal, characteristic
6C2×#13063240—21no—
7#14582863C2212yes—
8C4×C22⋊Dic43C2212yes—
9#14582666—21no—
10#14582625—21no—
11#14582623—21no—
12C2×C4×D4×C43C2211yescharacteristic
13C43×#390—21no—
14C43×#388—21no—
15C43×#388—21no—
16C43×#382C411yescharacteristic, complemented
17C43×#381C411yescharacteristic, complemented
18C43×#381C2211yescharacteristic
19C4×C4⋊C4×C43—21no—
20C4×C4⋊C4×C43C411yescharacteristic, complemented
21C4×C22⋊C4×C43C411yescharacteristic, complemented
22C4×C22⋊C4×C43C2211yescharacteristic
23C2×#10621877—22no—
24C2×C22⋊Dic43—22no—
25C2×C4×Dic43—22no—
26#13063240—24no—
27C22⋊(C43⋊C8)—22no—
28C22⋊(C43⋊C8)—22no—
29C43⋊#95—22no—
30C22×D4×C43D411yescharacteristic
31C23×C4×C43C2×C411yescharacteristic
32C23×C4×C43C2311yescharacteristic
33C4×D4×C43—22no—
34C4×D4×C43—22no—
35C2×C4⋊C4×C43—21no—
36C2×C4⋊C4×C43—21no—
37C2×C4⋊C4×C43D411yescharacteristic
38C2×C22⋊C4×C43—21no—
39C2×C22⋊C4×C43—21no—
40C2×C22⋊C4×C43—21no—
41C2×C22⋊C4×C43—21no—
42C2×C22⋊C4×C43D411yescharacteristic
43C2×C22⋊C4×C43D411yescharacteristic
44C2×C42×C43—21no—
45C2×C42×C43—21no—
46C2×C42×C43—21no—
47C2×C42×C43C2×C411yescharacteristic
48#95×C43—21no—
49#95×C43—21no—
50#95×C43—21no—
51#95×C43C2×C411yescharacteristic
52#95×C43C2×C411yescharacteristic
53#95×C43C2×C411yescharacteristic
54#95×C43C2×C411yescharacteristic
55C24×C43C22⋊C411yescharacteristic
56C24×C43C2×D411yescharacteristic
57C2×D4×C43—22no—
58C2×D4×C43—22no—
59C2×D4×C43—41no—
60C22×C4×C43—21no—
61C22×C4×C43—21no—
62C22×C4×C43—21no—
63C22×C4×C43—21no—
64C22×C4×C43—21no—
65C22×C4×C43—21no—
66C22×C4×C43—81no—
67C22×C4×C43—81no—
68C22×C4×C43C22⋊C411yescharacteristic
69C22×C4×C43C22⋊C411yescharacteristic
70C22×C4×C43C22⋊C411yescharacteristic
71C22×C4×C43C22×C411yescharacteristic
72C22×C4×C43C2×D411yescharacteristic
73C22×C4×C43#4112yes—
74C22×C4×C43#4112yes—
75C22×Dic43—42no—
76C4⋊C4×C43—22no—
77C4⋊C4×C43—42no—
78C4⋊C4×C43—42no—
79C22⋊C4×C43—22no—
80C22⋊C4×C43—22no—
81C22⋊C4×C43—42no—
82C22⋊C4×C43—42no—
83C22⋊C4×C43—81no—
84C22⋊C4×C43—81no—
85C42×C43—21no—
86C42×C43—21no—
87C42×C43—42no—
88C42×C43—81no—
89C42×C43—81no—
90C22⋊Dic43—24no—
91C22⋊Dic43—42no—
92C4×Dic43—82no—
93#10621877—82no—
94C2×C43⋊C8—42no—
95C23×C43—21no—
96C23×C43—21no—
97C23×C43—21no—
98C23×C43—21no—
99C23×C43—21no—
100C23×C43—41no—
101C23×C43—41no—
102C23×C43—41no—
103C23×C43—41no—
104C23×C43C2×C22⋊C411yescharacteristic
105C23×C43#12312yes—
106D4×C43—44no—
107C2×C4×C43—21no—
108C2×C4×C43—21no—
109C2×C4×C43—22no—
110C2×C4×C43—21no—
111C2×C4×C43—21no—
112C2×C4×C43—42no—
113C2×C4×C43—42no—
114C2×C4×C43—41no—
115C2×C4×C43—41no—
116C2×C4×C43—41no—
117C2×C4×C43—41no—
118C2×C4×C43—41no—
119C2×C4×C43—41no—
120C2×C4×C43—41no—
121C2×C4×C43—41no—
122C2×C4×C43—41no—
123C2×C4×C43—41no—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—81no—
130C2×C4×C43—81no—
131C2×C4×C43#10412yes—
132C2×C4×C43#11711yescharacteristic
133C2×C4×C43#11711yescharacteristic
134C2×C4×C43#12312yes—
135C2×Dic43—44no—
136C2×Dic43—82no—
137C2×Dic43—82no—
138C43⋊C8—82no—
139#8778—431nomaximal, Sylow
140C22×C43—21no—
141C22×C43—21no—
142C22×C43—22no—
143C22×C43—22no—
144C22×C43—22no—
145C22×C43—41no—
146C22×C43—41no—
147C22×C43—41no—
148C22×C43—81no—
149C22×C43—81no—
150C22×C43—81no—
151C22×C43—81no—
152C22×C43#38111yescharacteristic
153C22×C43C2×#10411yescharacteristic
154C22×C43#42111yescharacteristic
155C4×C43—22no—
156C4×C43—22no—
157C4×C43—21no—
158C4×C43—21no—
159C4×C43—42no—
160C4×C43—41no—
161C4×C43—41no—
162C4×C43—81no—
163C4×C43—81no—
164C4×C43—81no—
165Dic43—84no—
166#2357D4311yescharacteristic
167C4×#99—431no—
168#1465—431no—
169#1297—432no—
170#1284—432no—
171C2×C43—21no—
172C2×C43—21no—
173C2×C43—42no—
174C2×C43—81no—
175C2×C43#182611yescharacteristic
176C2×C43#182711yescharacteristic
177C2×C43#182811yescharacteristic
178C2×C4×D4C2×D4311yescharacteristic
179C2×#99—861no—
180#407—432no—
181#390—21no—
182#388—21no—
183#388—21no—
184#382Dic4311yescharacteristic, complemented
185#381Dic4311yescharacteristic, complemented
186#381C2×D4311yescharacteristic
187C4×C4⋊C4—21no—
188C4×C4⋊C4Dic4311yescharacteristic, complemented
189C4×C22⋊C4—432no—
190C4×C22⋊C4Dic4311yescharacteristic, complemented
191C4×C22⋊C4C2×D4311yescharacteristic
192#342—861no—
193#324—861no—
194#323—861no—
195C43#877811yescharacteristic, complemented, Sylow
196C22×D4C22⋊D4311yescharacteristic
197C23×C4C2×Dic4311yescharacteristic
198C23×C4C22×D4311yescharacteristic
199C2×M16—862no—
200C4×D4—22no—
201C4×D4—22no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4C22⋊D4311yescharacteristic
205C2×C22⋊C4—21no—
206C2×C22⋊C4—21no—
207C2×C22⋊C4—21no—
208C2×C22⋊C4—21no—
209C2×C22⋊C4—862no—
210C2×C22⋊C4C22⋊D4311yescharacteristic
211C2×C22⋊C4C22⋊D4311yescharacteristic
212C2×C42—21no—
213C2×C42—21no—
214C2×C42—21no—
215C2×C42—862no—
216C2×C42C2×Dic4311yescharacteristic
217#99—864no—
218C22⋊C8—862no—
219C22⋊C8—862no—
220#95—21no—
221#95—21no—
222#95—21no—
223#95—862no—
224#95C2×Dic4311yescharacteristic
225#95C2×Dic4311yescharacteristic
226#95C2×Dic4311yescharacteristic
227#95C2×Dic4311yescharacteristic
228C24C22⋊Dic4311yescharacteristic
229C24C2×C22⋊D4311yescharacteristic
230C2×D4—22no—
231C2×D4—22no—
232C2×D4—41no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—81no—
240C22×C4—81no—
241C22×C4—1722no—
242C22×C4C22⋊Dic4311yescharacteristic
243C22×C4C22⋊Dic4311yescharacteristic
244C22×C4C22⋊Dic4311yescharacteristic
245C22×C4#1062189812yes—
246C22×C4#1062189812yes—
247C22×C4C22×Dic4311yescharacteristic
248C22×C4C2×C22⋊D4311yescharacteristic
249M16—3442no—
250C2×C8—1722no—
251C4⋊C4—22no—
252C4⋊C4—42no—
253C4⋊C4—42no—
254C22⋊C4—22no—
255C22⋊C4—22no—
256C22⋊C4—42no—
257C22⋊C4—42no—
258C22⋊C4—81no—
259C22⋊C4—81no—
260C22⋊C4—864no—
261C22⋊C4—1722no—
262C42—21no—
263C42—21no—
264C42—42no—
265C42—81no—
266C42—81no—
267C42—3442no—
268C23—21no—
269C23—21no—
270C23—21no—
271C23—21no—
272C23—21no—
273C23—41no—
274C23—41no—
275C23—41no—
276C23—41no—
277C23C2×C22⋊Dic4311yescharacteristic
278C23#1306330812yes—
279D4—44no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—22no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—41no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—81no—
303C2×C4—81no—
304C2×C4—3442no—
305C2×C4—3442no—
306C2×C4—1724no—
307C2×C4#1306325212yes—
308C2×C4#1306328411yescharacteristic
309C2×C4#1306328411yescharacteristic
310C2×C4#1306330812yes—
311C8—3442no—
312C22—21no—
313C22—21no—
314C22—22no—
315C22—22no—
316C22—22no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22—81no—
321C22—81no—
322C22—81no—
323C22—81no—
324C22#1458276211yescharacteristic
325C22C2×#1306325211yescharacteristic
326C22#1458291611yescharacteristic
327C4—22no—
328C4—22no—
329C4—21no—
330C4—21no—
331C4—42no—
332C4—41no—
333C4—41no—
334C4—81no—
335C4—81no—
336C4—81no—
337C4—3444no—
338C2—21no—
339C2—21no—
340C2—42no—
341C2—81no—
342C2#1913469411yescharacteristic
343C2#1913469911yescharacteristic
344C2#1913470311yescharacteristic
subgroupG/H
centerC22#14582762
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#2357C2
socleC22×C43#381
prime radicalC22×D4×C43D4
cosocleC23×C4×C43C23
hypercenter#2357D43
hypocenterC43#8778
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2357

Complements

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

NH ≅ G/Ntype
3. #19132481C2semidirect
4. #19132447C2semidirect
16. C43×#382C4semidirect
17. C43×#381C4semidirect
20. C4×C4⋊C4×C43C4semidirect
21. C4×C22⋊C4×C43C4semidirect
184. #382Dic43semidirect
185. #381Dic43semidirect
188. C4×C4⋊C4Dic43semidirect
190. C4×C22⋊C4Dic43semidirect
195. C43#8778semidirect

Maximal subgroups

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

subgroupindex
C4×#130632402
#191329332
#191324812
#191324472
C43×#23572
#877843