Finite Group Databasebeta

← #25007423

Subgroups — #25007423

Order 11008.

382 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 87 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
1#19134591C211yesmaximal, characteristic, complemented
2#19132939C211yesmaximal, characteristic, complemented
3#19132625C212yesmaximal, complemented
4#19132598C212yesmaximal
5C43×#2632C211yesmaximal, characteristic
6#14582956—21no—
7#14582923—21no—
8C2×#13063244—21no—
9#14582668C2212yes—
10#14582625—21no—
11#14582625C2212yes—
12C2×#124×C43C411yescharacteristic
13C2×C4×Q8×C43C2211yescharacteristic
14C43×#399—21no—
15C43×#395C411yescharacteristic
16C43×#395C2211yescharacteristic
17C43×#394C411yescharacteristic
18C43×#394C2211yescharacteristic
19C43×#393—21no—
20C43×#388—21no—
21C43×#388—21no—
22C43×#383C411yescharacteristic
23C2×#10621877—22no—
24C4⋊(C43⋊C8)—41no—
25C4⋊(C43⋊C8)—41no—
26C4⋊(C43⋊C8)—41no—
27#13063244—42no—
28C22⋊(C43⋊C8)—22no—
29#13063236—41no—
30C22×Q8×C43C2×C411yescharacteristic
31C22×Q8×C43D411yescharacteristic
32C22×D4×C43C2×C411yescharacteristic
33#124×C43—41no—
34#124×C43—41no—
35C4×Q8×C43—41no—
36C4×Q8×C43—41no—
37C2×C4⋊C4×C43—21no—
38C2×C4⋊C4×C43—21no—
39C2×C4⋊C4×C43C2×C411yescharacteristic
40C2×C4⋊C4×C43D411yescharacteristic
41C2×C4⋊C4×C43C2311yescharacteristic
42C2×C22⋊C4×C43—21no—
43C2×C22⋊C4×C43—21no—
44C2×C22⋊C4×C43—21no—
45C2×C22⋊C4×C43—21no—
46C2×C22⋊C4×C43—21no—
47C2×C22⋊C4×C43—21no—
48C2×C42×C43C2×C411yescharacteristic
49C2×C42×C43D411yescharacteristic
50C2×C42×C43D411yescharacteristic
51#95×C43—21no—
52#95×C43—21no—
53#95×C43—21no—
54#95×C43—21no—
55#95×C43C2×C411yescharacteristic
56#95×C43C2×C411yescharacteristic
57C24×C43—21no—
58C2×Q8×C43—21no—
59C2×Q8×C43—21no—
60C2×Q8×C43—41no—
61C2×Q8×C43—41no—
62C2×Q8×C43—41no—
63C2×Q8×C43—81no—
64C2×D4×C43—41no—
65C2×D4×C43—81no—
66C22×C4×C43—21no—
67C22×C4×C43—21no—
68C22×C4×C43—21no—
69C22×C4×C43C22⋊C411yescharacteristic
70C22×C4×C43C22⋊C411yescharacteristic
71C22×C4×C43C22⋊C411yescharacteristic
72C22×C4×C43C22⋊C411yescharacteristic
73C22×C4×C43C22×C411yescharacteristic
74C22×C4×C43C2×D411yescharacteristic
75C22×C4×C43C2×D411yescharacteristic
76C4⋊C4×C43—41no—
77C4⋊C4×C43—41no—
78C4⋊C4×C43—41no—
79C4⋊C4×C43—81no—
80C4⋊C4×C43—81no—
81C22⋊C4×C43—42no—
82C22⋊C4×C43—42no—
83C22⋊C4×C43—41no—
84C22⋊C4×C43—41no—
85C22⋊C4×C43—41no—
86C22⋊C4×C43—41no—
87C22⋊C4×C43—81no—
88C22⋊C4×C43—81no—
89C42×C43—21no—
90C42×C43—21no—
91C42×C43—21no—
92C42×C43—21no—
93C42×C43—21no—
94C42×C43—21no—
95#10621877—42no—
96#10621877—42no—
97C2×C43⋊C8—42no—
98C2×C43⋊C8—42no—
99C23×C43—41no—
100C23×C43—41no—
101C23×C43—41no—
102C23×C43—41no—
103C23×C43—41no—
104C23×C43—41no—
105C23×C43—41no—
106C23×C43C2×C22⋊C411yescharacteristic
107Q8×C43—42no—
108Q8×C43—42no—
109Q8×C43—82no—
110D4×C43—82no—
111C2×C4×C43—21no—
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
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—41no—
130C2×C4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43—41no—
135C2×C4×C43#9911yescharacteristic
136C2×C4×C43#9911yescharacteristic
137C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C43#13711yescharacteristic
139C43⋊C8—82no—
140C43⋊C8—82no—
141#11833—431nomaximal, Sylow
142C22×C43—21no—
143C22×C43—21no—
144C22×C43—81no—
145C22×C43—81no—
146C22×C43—81no—
147C22×C43—81no—
148C22×C43—81no—
149C22×C43—81no—
150C22×C43—81no—
151C22×C43C2×#9911yescharacteristic
152C22×C43#41711yescharacteristic
153C22×C43#42111yescharacteristic
154C4×C43—21no—
155C4×C43—21no—
156C4×C43—21no—
157C4×C43—21no—
158C4×C43—41no—
159C4×C43—41no—
160C4×C43—41no—
161C4×C43—41no—
162C4×C43—41no—
163C4×C43—81no—
164C4×C43—81no—
165C4×C43—81no—
166#2632D4311yescharacteristic
167#1801—431no—
168#1467—431no—
169#1354—432no—
170#1345—432no—
171C2×C43—21no—
172C2×C43—21no—
173C2×C43—161no—
174C2×C43#151311yescharacteristic
175C2×C43#212211yescharacteristic
176C2×C43#213311yescharacteristic
177C2×#124Dic4311yescharacteristic
178C2×C4×Q8C2×D4311yescharacteristic
179#432—861no—
180#423—861no—
181C2×#101—861no—
182#399—21no—
183#395Dic4311yescharacteristic
184#395C2×D4311yescharacteristic
185#394Dic4311yescharacteristic
186#394C2×D4311yescharacteristic
187#393—21no—
188#388—21no—
189#388—21no—
190#383Dic4311yescharacteristic
191#343—432no—
192#324—432no—
193#324—861no—
194C43#1183311yescharacteristic, complemented, Sylow
195C22×Q8C2×Dic4311yescharacteristic
196C22×Q8C22⋊D4311yescharacteristic
197C22×D4C2×Dic4311yescharacteristic
198C2×M16—862no—
199#124—41no—
200#124—41no—
201C4×Q8—41no—
202C4×Q8—41no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4C2×Dic4311yescharacteristic
206C2×C4⋊C4C22⋊D4311yescharacteristic
207C2×C4⋊C4C22×D4311yescharacteristic
208C2×C22⋊C4—21no—
209C2×C22⋊C4—21no—
210C2×C22⋊C4—21no—
211C2×C22⋊C4—21no—
212C2×C22⋊C4—21no—
213C2×C22⋊C4—21no—
214C2×C42C2×Dic4311yescharacteristic
215C2×C42C22⋊D4311yescharacteristic
216C2×C42C22⋊D4311yescharacteristic
217C4⋊C8—1721no—
218C4⋊C8—1721no—
219C4⋊C8—1721no—
220#101—1722no—
221C22⋊C8—862no—
222#97—1721no—
223#95—21no—
224#95—21no—
225#95—21no—
226#95—21no—
227#95C2×Dic4311yescharacteristic
228#95C2×Dic4311yescharacteristic
229C24—21no—
230C2×Q8—21no—
231C2×Q8—21no—
232C2×Q8—41no—
233C2×Q8—41no—
234C2×Q8—41no—
235C2×Q8—81no—
236C2×D4—41no—
237C2×D4—81no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4C22⋊Dic4311yescharacteristic
242C22×C4C22⋊Dic4311yescharacteristic
243C22×C4C22⋊Dic4311yescharacteristic
244C22×C4C22⋊Dic4311yescharacteristic
245C22×C4C22×Dic4311yescharacteristic
246C22×C4C2×C22⋊D4311yescharacteristic
247C22×C4C2×C22⋊D4311yescharacteristic
248M16—1722no—
249M16—1722no—
250C2×C8—1722no—
251C2×C8—1722no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—81no—
256C4⋊C4—81no—
257C22⋊C4—42no—
258C22⋊C4—42no—
259C22⋊C4—41no—
260C22⋊C4—41no—
261C22⋊C4—41no—
262C22⋊C4—41no—
263C22⋊C4—81no—
264C22⋊C4—81no—
265C42—21no—
266C42—21no—
267C42—21no—
268C42—21no—
269C42—21no—
270C42—21no—
271C23—41no—
272C23—41no—
273C23—41no—
274C23—41no—
275C23—41no—
276C23—41no—
277C23—41no—
278C23C2×C22⋊Dic4311yescharacteristic
279Q8—42no—
280Q8—42no—
281Q8—82no—
282D4—82no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
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—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4#1306324011yescharacteristic
308C2×C4#1306324011yescharacteristic
309C2×C4#1306335011yescharacteristic
310C2×C4#1306335511yescharacteristic
311C8—3442no—
312C8—3442no—
313C22—21no—
314C22—21no—
315C22—81no—
316C22—81no—
317C22—81no—
318C22—81no—
319C22—81no—
320C22—81no—
321C22—81no—
322C22C2×#1306324011yescharacteristic
323C22#1458290011yescharacteristic
324C22#1458291611yescharacteristic
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—81no—
335C4—81no—
336C4—81no—
337C2—21no—
338C2—21no—
339C2—161no—
340C2#1913313811yescharacteristic
341C2#1913624511yescharacteristic
342C2#1913628411yescharacteristic
subgroupG/H
centerC22C2×#13063240
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#2632C2
socleC22×C43C2×#99
prime radicalC22×D4×C43C2×C4
cosocleC2×C4⋊C4×C43C23
hypercenter#2632D43
hypocenterC43#11833
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2632

Complements

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

NH ≅ G/Ntype
1. #19134591C2semidirect
2. #19132939C2semidirect
3. #19132625C2semidirect
194. C43#11833semidirect

Maximal subgroups

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

subgroupindex
#191345912
#191329392
#191326252
#191325982
C43×#26322
#1183343