Finite Group Databasebeta

← #25007750

Subgroups — #25007750

Order 11008.

372 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 77 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#19139956C211yesmaximal, characteristic
2#19134590C211yesmaximal, characteristic
3#19132917C211yesmaximal, characteristic
4#19132625C211yesmaximal, characteristic
5#19132623C211yesmaximal, characteristic
6#19132621C211yesmaximal, characteristic
7C43×#1354C211yesmaximal, characteristic
8C2×Q8×Dic43C411yescharacteristic
9C2×#13063290C2211yescharacteristic
10#14582949—21no—
11#14582922—21no—
12C2×#13063243—21no—
13#14582839C411yescharacteristic
14#14582838C2211yescharacteristic
15#14582818C411yescharacteristic
16#14582803—21no—
17#14582794—21no—
18#14582786—21no—
19#14582785—21no—
20#14582763C411yescharacteristic
21#14582668C2211yescharacteristic
22#14582625C2211yescharacteristic
23#14582624—21no—
24C43×#395C2211yescharacteristic
25C43×#343C2211yescharacteristic
26C43×#324C2211yescharacteristic
27C22×Dic86D411yescharacteristic
28C2×#10621877—21no—
29Q8×Dic43—41no—
30Q8×Dic43—41no—
31#13063290—41no—
32#13063290—41no—
33C2×C4⋊Dic43—21no—
34C2×C4⋊Dic43C2×C411yescharacteristic
35C2×Dic43⋊C4—21no—
36C2×Dic43⋊C4—21no—
37C2×Dic43⋊C4C2×C411yescharacteristic
38C2×Dic43⋊C4D411yescharacteristic
39C2×C4×Dic43—21no—
40C2×C4×Dic43C2×C411yescharacteristic
41C2×C4×Dic43D411yescharacteristic
42C2×C4×Dic43D411yescharacteristic
43Dic43⋊C8—41no—
44Dic43⋊C8—41no—
45Dic43⋊C8—41no—
46#13063243—42no—
47C22⋊(C43⋊C8)—21no—
48C8×Dic43—41no—
49C43⋊#95—21no—
50C43⋊#95—21no—
51C43⋊#95—21no—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C43⋊#95—21no—
55C43⋊#95C2×C411yescharacteristic
56C22×Q8×C43C2×C411yescharacteristic
57C2×M16×C43—21no—
58C2×C4⋊C4×C43—21no—
59C2×C4⋊C4×C43C2311yescharacteristic
60C22⋊C8×C43—21no—
61#95×C43—21no—
62#95×C43C2×C411yescharacteristic
63C2×Q8×C43—42no—
64C2×Q8×C43—41no—
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43C22×C411yescharacteristic
68C22×C4×C43C2×D411yescharacteristic
69C22×C4×C43C2×D411yescharacteristic
70C22×Dic43—21no—
71C22×Dic43—21no—
72C22×Dic43C22⋊C411yescharacteristic
73C22×Dic43C22⋊C411yescharacteristic
74C22×Dic43C22⋊C411yescharacteristic
75C22×Dic43C22⋊C411yescharacteristic
76C2×Dic86—41no—
77C2×Dic86—41no—
78C2×Dic86SD1612yes—
79C2×Dic86Q1612yes—
80M16×C43—41no—
81M16×C43—41no—
82C2×C8×C43—41no—
83C2×C8×C43—41no—
84C4⋊C4×C43—41no—
85C4⋊C4×C43—42no—
86C4⋊Dic43—41no—
87C4⋊Dic43—41no—
88C4⋊Dic43—41no—
89Dic43⋊C4—41no—
90Dic43⋊C4—41no—
91Dic43⋊C4—42no—
92Dic43⋊C4—42no—
93C4×Dic43—21no—
94C4×Dic43—21no—
95C4×Dic43—21no—
96C4×Dic43—21no—
97C4×Dic43—21no—
98C4×Dic43—21no—
99C4×Dic43—42no—
100#10621877—41no—
101#10621877—41no—
102C2×C43⋊C8—41no—
103C2×C43⋊C8—41no—
104C23×C43C2×C22⋊C411yescharacteristic
105Q8×C43—42no—
106Q8×C43—42no—
107C2×C4×C43—21no—
108C2×C4×C43—21no—
109C2×C4×C43—22no—
110C2×C4×C43—21no—
111C2×C4×C43—21no—
112C2×C4×C43—41no—
113C2×C4×C43—41no—
114C2×C4×C43—41no—
115C2×C4×C43—41no—
116C2×C4×C43—41no—
117C2×C4×C43—41no—
118C2×C4×C43—41no—
119C2×C4×C43C2×SD1611yescharacteristic
120C2×C4×C43C2×Q1611yescharacteristic
121C2×Dic43—21no—
122C2×Dic43—21no—
123C2×Dic43—21no—
124C2×Dic43—21no—
125C2×Dic43—21no—
126C2×Dic43—41no—
127C2×Dic43—41no—
128C2×Dic43—41no—
129C2×Dic43—41no—
130C2×Dic43—42no—
131C2×Dic43—41no—
132C2×Dic43—41no—
133C2×Dic43#9911yescharacteristic
134C2×Dic43#9911yescharacteristic
135C2×Dic43#10312yes—
136C2×Dic43#10312yes—
137Dic86—42no—
138Dic86—42no—
139C8×C43—81no—
140C8×C43—81no—
141C43⋊C8—81no—
142C43⋊C8—81no—
143#11905—431nomaximal, Sylow
144C22×C43—21no—
145C22×C43—21no—
146C22×C43C2×#9911yescharacteristic
147C22×C43C2×#10311yescharacteristic
148C22×C43#42111yescharacteristic
149C4×C43—21no—
150C4×C43—21no—
151C4×C43—41no—
152C4×C43—42no—
153C4×C43—41no—
154C4×C43—81no—
155Dic43—21no—
156Dic43—21no—
157Dic43—22no—
158Dic43—22no—
159Dic43—41no—
160Dic43—81no—
161Dic43—81no—
162#2581—431no—
163#1801—431no—
164#1461—431no—
165#1354—431no—
166#1354D4311yescharacteristic
167#1353—431no—
168#1353—431no—
169C2×C43—21no—
170C2×C43—21no—
171C2×C43#152011yescharacteristic
172C2×C43#212011yescharacteristic
173C2×C43#213311yescharacteristic
174C2×C4×Q8—431no—
175C2×C4×Q8—431no—
176#431—861no—
177#423—861no—
178C2×#101—861no—
179#400—431no—
180#400—431no—
181#395—431no—
182#395C2×D4311yescharacteristic
183#391—861no—
184#389—861no—
185#387—861no—
186#387—861no—
187#382—431no—
188#343—431no—
189#343C2×D4311yescharacteristic
190#324—431no—
191#324—861no—
192#324C2×D4311yescharacteristic
193C43#1190511yescharacteristic, complemented, Sylow
194C22×Q8—431no—
195C22×Q8C4×D4311yescharacteristic
196C2×M16—21no—
197C2×M16—861no—
198C4×Q8—1721no—
199C4×Q8—1721no—
200C4×Q8—1721no—
201C4×Q8—1721no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—431no—
204C2×C4⋊C4—431no—
205C2×C4⋊C4—431no—
206C2×C4⋊C4—861no—
207C2×C4⋊C4—861no—
208C2×C4⋊C4—861no—
209C2×C4⋊C4C22×D4311yescharacteristic
210C2×C42—431no—
211C2×C42—431no—
212C2×C42—431no—
213C2×C42—861no—
214C4⋊C8—1721no—
215C4⋊C8—1721no—
216C4⋊C8—1721no—
217#101—1722no—
218C22⋊C8—21no—
219C22⋊C8—861no—
220C4×C8—1721no—
221#95—21no—
222#95—431no—
223#95—861no—
224#95—861no—
225#95—861no—
226#95—861no—
227#95—861no—
228#95—861no—
229#95C4×D4311yescharacteristic
230C2×Q8—42no—
231C2×Q8—41no—
232C2×Q8—432no—
233C2×Q8—432no—
234C2×Q8—1721no—
235C2×Q8—1721no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—431no—
239C22×C4—431no—
240C22×C4—431no—
241C22×C4—431no—
242C22×C4—861no—
243C22×C4—861no—
244C22×C4C2×C4×D4311yescharacteristic
245C22×C4D4×D4311yescharacteristic
246C22×C4D4×D4311yescharacteristic
247M16—41no—
248M16—41no—
249M16—1721no—
250M16—1721no—
251C2×C8—41no—
252C2×C8—41no—
253C2×C8—1721no—
254C2×C8—1721no—
255C4⋊C4—41no—
256C4⋊C4—42no—
257C4⋊C4—1721no—
258C4⋊C4—1721no—
259C4⋊C4—1721no—
260C4⋊C4—1722no—
261C4⋊C4—1721no—
262C4⋊C4—1721no—
263C4⋊C4—1722no—
264C42—861no—
265C42—861no—
266C42—861no—
267C42—861no—
268C42—861no—
269C42—861no—
270C42—1722no—
271C23C22⋊C4×D4311yescharacteristic
272Q8—42no—
273Q8—42no—
274Q8—1722no—
275Q8—1722no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—431no—
289C2×C4—431no—
290C2×C4—432no—
291C2×C4—432no—
292C2×C4—861no—
293C2×C4—861no—
294C2×C4—861no—
295C2×C4—861no—
296C2×C4—861no—
297C2×C4—1721no—
298C2×C4—1721no—
299C2×C4—1721no—
300C2×C4—1722no—
301C2×C4—1721no—
302C2×C4—1721no—
303C2×C4—1721no—
304C2×C4SD16×D4311yescharacteristic
305C2×C4Q16×D4311yescharacteristic
306C8—81no—
307C8—81no—
308C8—3441no—
309C8—3441no—
310C22—21no—
311C22—21no—
312C22#99×D4311yescharacteristic
313C22#103×D4311yescharacteristic
314C22#1458291411yescharacteristic
315C4—21no—
316C4—21no—
317C4—41no—
318C4—42no—
319C4—41no—
320C4—81no—
321C4—861no—
322C4—861no—
323C4—862no—
324C4—862no—
325C4—3441no—
326C4—3441no—
327C4—1721no—
328C2—21no—
329C2—21no—
330C2#1913316511yescharacteristic
331C2#1913623311yescharacteristic
332C2#1913628311yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1354C2
socleC22×C43C2×#99
prime radicalC23×C43C2×C22⋊C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1354D43
hypocenterC43#11905
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1354

Complements

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

NH ≅ G/Ntype
193. C43#11905semidirect

Maximal subgroups

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

subgroupindex
#191399562
#191345902
#191329172
#191326252
#191326232
#191326212
C43×#13542
#1190543