Finite Group Databasebeta

← #25007104

Subgroups — #25007104

Order 11008.

428 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 83 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#19140172C211yesmaximal, characteristic
2#19134334C211yesmaximal, characteristic
3#19132626C212yesmaximal, complemented
4#19132602C212yesmaximal, complemented
5C43×#1464C211yesmaximal, characteristic
6C22×#10621877—21no—
7C2×C4×Dic86C411yescharacteristic
8#14582829C2211yescharacteristic
9#14582824C411yescharacteristic
10#14582819C2211yescharacteristic
11#14582811C411yescharacteristic
12#14582787—21no—
13#14582783—21no—
14#14582780—21no—
15#14582772—21no—
16#14582767C411yescharacteristic
17#14582668—21no—
18#14582668C2212yes—
19C2×#117×C43C2211yescharacteristic
20C43×#432—21no—
21C43×#324C2212yes—
22C43×#323—21no—
23C22×Dic86C2×C411yescharacteristic
24C2×#10621877—24no—
25C2×#10621877—22no—
26C2×#10621877—41no—
27C2×#10621877—42no—
28C22×C43⋊C8—41no—
29C4×Dic86—41no—
30C4×Dic86—41no—
31C2×C4⋊Dic43C2×C411yescharacteristic
32C2×Dic43⋊C4—21no—
33C2×Dic43⋊C4—21no—
34C2×Dic43⋊C4—21no—
35C2×C22⋊Dic43—21no—
36C2×C22⋊Dic43—21no—
37C2×C4×Dic43—21no—
38C43⋊#95—21no—
39C43⋊#95—21no—
40C43⋊#95—21no—
41C43⋊#95—21no—
42C43⋊#95—21no—
43C43⋊#95—21no—
44C43⋊#95C2×C411yescharacteristic
45C43⋊#95C2×C411yescharacteristic
46C23×C4×C43D411yescharacteristic
47#117×C43—41no—
48#117×C43—41no—
49C2×C4⋊C4×C43D411yescharacteristic
50C2×C4⋊C4×C43C2311yescharacteristic
51C2×C22⋊C4×C43C2×C411yescharacteristic
52C2×C22⋊C4×C43D411yescharacteristic
53C2×C42×C43C2×C411yescharacteristic
54C2×C42×C43D411yescharacteristic
55C4⋊C8×C43—41no—
56C22⋊C8×C43—22no—
57#97×C43—41no—
58C24×C43C22⋊C411yescharacteristic
59C22×C4×C43—21no—
60C22×C4×C43—21no—
61C22×C4×C43—21no—
62C22×C4×C43—21no—
63C22×C4×C43—22no—
64C22×C4×C43C22⋊C411yescharacteristic
65C22×C4×C43C22⋊C411yescharacteristic
66C22×C4×C43C22⋊C411yescharacteristic
67C22×C4×C43C22×C411yescharacteristic
68C22×C4×C43C2×D411yescharacteristic
69C22×C4×C43C2×D411yescharacteristic
70C22×Dic43—21no—
71C22×Dic43—21no—
72C22×Dic43—21no—
73C22×Dic43—21no—
74C2×Dic86—41no—
75C2×Dic86—42no—
76C2×C8×C43—42no—
77C4⋊C4×C43—41no—
78C4⋊C4×C43—41no—
79C22⋊C4×C43—41no—
80C22⋊C4×C43—41no—
81C42×C43—21no—
82C42×C43—21no—
83C42×C43—21no—
84C42×C43—21no—
85C22⋊Dic43—42no—
86C22⋊Dic43—42no—
87C4⋊Dic43—41no—
88Dic43⋊C4—42no—
89Dic43⋊C4—41no—
90Dic43⋊C4—41no—
91Dic43⋊C4—41no—
92Dic43⋊C4—41no—
93C4×Dic43—42no—
94#10621877—24no—
95#10621877—44no—
96#10621877—42no—
97C2×C43⋊C8—44no—
98C2×C43⋊C8—42no—
99C23×C43—21no—
100C23×C43—21no—
101C23×C43—41no—
102C23×C43—41no—
103C23×C43#10412yes—
104C23×C43C2×C22⋊C411yescharacteristic
105C2×C4×C43—22no—
106C2×C4×C43—22no—
107C2×C4×C43—22no—
108C2×C4×C43—22no—
109C2×C4×C43—21no—
110C2×C4×C43—21no—
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—41no—
118C2×C4×C43—41no—
119C2×C4×C43—41no—
120C2×C4×C43—41no—
121C2×C4×C43#9911yescharacteristic
122C2×C4×C43#9911yescharacteristic
123C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
124C2×C4×C43#13711yescharacteristic
125C2×Dic43—22no—
126C2×Dic43—41no—
127C2×Dic43—41no—
128C2×Dic43—41no—
129C2×Dic43—41no—
130C2×Dic43—41no—
131C2×Dic43—41no—
132C2×Dic43—41no—
133C2×Dic43—41no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137Dic86—42no—
138Dic86—42no—
139C8×C43—82no—
140C43⋊C8—44no—
141#11763—431nomaximal, Sylow
142C22×C43—21no—
143C22×C43—21no—
144C22×C43—22no—
145C22×C43—42no—
146C22×C43—41no—
147C22×C43—41no—
148C22×C43—81no—
149C22×C43C2×#9911yescharacteristic
150C22×C43#41711yescharacteristic
151C22×C43C2×#10411yescharacteristic
152C4×C43—21no—
153C4×C43—21no—
154C4×C43—21no—
155C4×C43—21no—
156C4×C43—41no—
157C4×C43—41no—
158C4×C43—41no—
159C4×C43—41no—
160Dic43—42no—
161Dic43—81no—
162Dic43—81no—
163Dic43—81no—
164#2599—431no—
165#1742—431no—
166#1464D4311yescharacteristic
167#1354—432no—
168#1346—432no—
169C2×C43—21no—
170C2×C43—21no—
171C2×C43—42no—
172C2×C43#150411yescharacteristic
173C2×C43#212011yescharacteristic
174C2×C43#213511yescharacteristic
175C22×M16—861no—
176C2×C4×Q8—431no—
177C2×#117C2×D4311yescharacteristic
178#432—21no—
179#398—431no—
180#397—431no—
181#395—431no—
182#393—431no—
183#388—861no—
184#387—861no—
185#387—861no—
186#385—861no—
187#383—431no—
188#343—432no—
189#343—861no—
190#324C2×D4312yes—
191#323—21no—
192C43#1176311yescharacteristic, complemented, Sylow
193C22×Q8—431no—
194C23×C4D17211yescharacteristic
195C2×M16—864no—
196C2×M16—862no—
197C2×M16—1721no—
198C2×M16—1722no—
199C22×C8—1721no—
200C4×Q8—1721no—
201C4×Q8—1721no—
202#117—41no—
203#117—41no—
204C2×C4⋊C4—431no—
205C2×C4⋊C4—861no—
206C2×C4⋊C4—861no—
207C2×C4⋊C4—861no—
208C2×C4⋊C4D17211yescharacteristic
209C2×C4⋊C4C22×D4311yescharacteristic
210C2×C22⋊C4—861no—
211C2×C22⋊C4—861no—
212C2×C22⋊C4C4×D4311yescharacteristic
213C2×C22⋊C4C22⋊D4311yescharacteristic
214C2×C42—861no—
215C2×C42C4×D4311yescharacteristic
216C2×C42C22⋊D4311yescharacteristic
217C4⋊C8—41no—
218C22⋊C8—22no—
219#97—41no—
220#95—431no—
221#95—431no—
222#95—861no—
223#95—861no—
224#95—861no—
225#95—861no—
226#95—861no—
227#95—861no—
228C24(C2×D43)⋊C411yescharacteristic
229C2×Q8—1721no—
230C2×Q8—1722no—
231C22×C4—22no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—861no—
237C22×C4—861no—
238C22×C4—861no—
239C22×C4—861no—
240C22×C4(C2×D43)⋊C411yescharacteristic
241C22×C4(C2×D43)⋊C411yescharacteristic
242C22×C4(C2×D43)⋊C411yescharacteristic
243C22×C4C2×C4×D4311yescharacteristic
244C22×C4C2×D17211yescharacteristic
245C22×C4C2×C22⋊D4311yescharacteristic
246M16—864no—
247M16—1724no—
248M16—1722no—
249C2×C8—42no—
250C2×C8—1724no—
251C2×C8—1722no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—1721no—
255C4⋊C4—1722no—
256C4⋊C4—1721no—
257C4⋊C4—1721no—
258C4⋊C4—1721no—
259C4⋊C4—1721no—
260C22⋊C4—41no—
261C22⋊C4—41no—
262C22⋊C4—1722no—
263C22⋊C4—1722no—
264C42—21no—
265C42—21no—
266C42—21no—
267C42—21no—
268C42—1722no—
269C23—21no—
270C23—21no—
271C23—41no—
272C23—41no—
273C23#1306325112yes—
274C23C2×(C2×D43)⋊C411yescharacteristic
275Q8—1722no—
276Q8—1722no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—862no—
294C2×C4—1721no—
295C2×C4—1721no—
296C2×C4—1721no—
297C2×C4—1721no—
298C2×C4—1721no—
299C2×C4—1721no—
300C2×C4—1721no—
301C2×C4—1721no—
302C2×C4—1721no—
303C2×C4—1721no—
304C2×C4—1721no—
305C2×C4#1306323911yescharacteristic
306C2×C4#1306323911yescharacteristic
307C2×C4#1306335311yescharacteristic
308C2×C4#1306335811yescharacteristic
309C8—82no—
310C8—1724no—
311C22—21no—
312C22—21no—
313C22—22no—
314C22—42no—
315C22—41no—
316C22—41no—
317C22—81no—
318C22C2×#1306323911yescharacteristic
319C22#1458290111yescharacteristic
320C22C2×#1306325111yescharacteristic
321C4—21no—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—3441no—
330C4—3441no—
331C4—3441no—
332C4—1722no—
333C2—21no—
334C2—21no—
335C2—42no—
336C2#1913310011yescharacteristic
337C2#1913623411yescharacteristic
338C2#1913628911yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1464C2
socleC22×C43C2×#99
prime radicalC24×C43C22⋊C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1464D43
hypocenterC43#11763
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1464

Complements

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

NH ≅ G/Ntype
3. #19132626C2semidirect
4. #19132602C2semidirect
192. C43#11763semidirect

Maximal subgroups

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

subgroupindex
#191401722
#191343342
#191326262
#191326022
C43×#14642
#1176343