Finite Group Databasebeta

← #25006975

Subgroups — #25006975

Order 11008.

402 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 73 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#19137885C211yesmaximal, characteristic
2#19134390C211yesmaximal, characteristic
3#19132917C211yesmaximal, characteristic
4#19132625C211yesmaximal, characteristic
5#19132602C211yesmaximal, characteristic
6#19132600C211yesmaximal, characteristic
7C43×#1354C211yesmaximal, characteristic
8C2×Q8×Dic43C411yescharacteristic
9C2×#13063290C2211yescharacteristic
10#14582949—21no—
11C2×#13063243—21no—
12M16×Dic43—21no—
13#14582832—21no—
14#14582831C411yescharacteristic
15#14582829C2211yescharacteristic
16#14582820—21no—
17#14582818C411yescharacteristic
18C4⋊C4×Dic43—21no—
19#14582750—21no—
20#14582744C411yescharacteristic
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⋊Dic43—21no—
35C2×C4⋊Dic43C2×C411yescharacteristic
36C2×Dic43⋊C4—21no—
37C2×Dic43⋊C4—21no—
38C2×Dic43⋊C4C2×C411yescharacteristic
39C2×Dic43⋊C4D411yescharacteristic
40C2×C4×Dic43—21no—
41C2×C4×Dic43—21no—
42C2×C4×Dic43C2×C411yescharacteristic
43C2×C4×Dic43D411yescharacteristic
44C2×C4×Dic43D411yescharacteristic
45Dic43⋊C8—41no—
46#13063243—24no—
47C22⋊(C43⋊C8)—21no—
48#13063235—41no—
49C8×Dic43—41no—
50C8×Dic43—41no—
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—21no—
77C2×Dic86—21no—
78C2×Dic86—22no—
79C2×Dic86—41no—
80M16×C43—22no—
81M16×C43—41no—
82C2×C8×C43—41no—
83C2×C8×C43—41no—
84C4⋊C4×C43—41no—
85C4⋊C4×C43—42no—
86C4⋊Dic43—42no—
87C4⋊Dic43—42no—
88C4⋊Dic43—41no—
89Dic43⋊C4—41no—
90Dic43⋊C4—41no—
91Dic43⋊C4—42no—
92Dic43⋊C4—41no—
93Dic43⋊C4—41no—
94C4×Dic43—24no—
95C4×Dic43—21no—
96C4×Dic43—21no—
97C4×Dic43—21no—
98C4×Dic43—21no—
99C4×Dic43—21no—
100C4×Dic43—21no—
101C4×Dic43—41no—
102C4×Dic43—41no—
103#10621877—22no—
104#10621877—41no—
105C2×C43⋊C8—41no—
106C2×C43⋊C8—41no—
107C23×C43C2×C22⋊C411yescharacteristic
108Q8×C43—42no—
109Q8×C43—42no—
110C2×C4×C43—21no—
111C2×C4×C43—21no—
112C2×C4×C43—22no—
113C2×C4×C43—22no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
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#13511yescharacteristic
123C2×C4×C43#13511yescharacteristic
124C2×Dic43—21no—
125C2×Dic43—21no—
126C2×Dic43—22no—
127C2×Dic43—22no—
128C2×Dic43—21no—
129C2×Dic43—21no—
130C2×Dic43—21no—
131C2×Dic43—21no—
132C2×Dic43—41no—
133C2×Dic43—41no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137C2×Dic43—41no—
138C2×Dic43#9911yescharacteristic
139C2×Dic43#9911yescharacteristic
140C2×Dic43#10412yes—
141Dic86—42no—
142Dic86—42no—
143C8×C43—42no—
144C8×C43—81no—
145C43⋊C8—42no—
146C43⋊C8—81no—
147#11736—431nomaximal, Sylow
148C22×C43—21no—
149C22×C43—21no—
150C22×C43C2×#9911yescharacteristic
151C22×C43#41611yescharacteristic
152C22×C43C2×#10411yescharacteristic
153C4×C43—21no—
154C4×C43—21no—
155C4×C43—42no—
156C4×C43—41no—
157C4×C43—42no—
158C4×C43—41no—
159Dic43—21no—
160Dic43—22no—
161Dic43—42no—
162Dic43—41no—
163Dic43—41no—
164Dic43—81no—
165Dic43#35612yes—
166#2399—431no—
167C4×#101—431no—
168#1461—431no—
169#1354—431no—
170#1354D4311yescharacteristic
171#1346—431no—
172#1346—431no—
173C2×C43—21no—
174C2×C43—21no—
175C2×C43#150111yescharacteristic
176C2×C43#212011yescharacteristic
177C2×C43C2×#35611yescharacteristic
178C2×C4×Q8—431no—
179C2×C4×Q8—431no—
180#431—861no—
181C2×#101—861no—
182C4×M16—861no—
183#398—431no—
184#398—431no—
185#398—861no—
186#395—431no—
187#395—861no—
188#395C2×D4311yescharacteristic
189C4×C4⋊C4—861no—
190C4×C4⋊C4—861no—
191#376—431no—
192#343—431no—
193#343C2×D4311yescharacteristic
194#324—431no—
195#324—861no—
196#324C2×D4311yescharacteristic
197C43#1173611yescharacteristic, complemented, Sylow
198C22×Q8—431no—
199C22×Q8C4×D4311yescharacteristic
200C2×M16—21no—
201C2×M16—861no—
202C4×Q8—1721no—
203C4×Q8—1721no—
204C4×Q8—1721no—
205C4×Q8—1721no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—431no—
208C2×C4⋊C4—431no—
209C2×C4⋊C4—431no—
210C2×C4⋊C4—861no—
211C2×C4⋊C4—861no—
212C2×C4⋊C4—861no—
213C2×C4⋊C4—861no—
214C2×C4⋊C4C22×D4311yescharacteristic
215C2×C42—431no—
216C2×C42—431no—
217C2×C42—431no—
218C2×C42—861no—
219C2×C42—861no—
220C4⋊C8—1721no—
221#101—864no—
222C22⋊C8—21no—
223C22⋊C8—861no—
224#97—1721no—
225C4×C8—1721no—
226C4×C8—1721no—
227#95—21no—
228#95—431no—
229#95—861no—
230#95—861no—
231#95—861no—
232#95—861no—
233#95C4×D4311yescharacteristic
234C2×Q8—42no—
235C2×Q8—41no—
236C2×Q8—862no—
237C2×Q8—861no—
238C2×Q8—861no—
239C2×Q8—1721no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—431no—
243C22×C4—431no—
244C22×C4—431no—
245C22×C4—431no—
246C22×C4—861no—
247C22×C4—861no—
248C22×C4C2×C4×D4311yescharacteristic
249C22×C4D4×D4311yescharacteristic
250C22×C4D4×D4311yescharacteristic
251M16—22no—
252M16—41no—
253M16—862no—
254M16—1721no—
255C2×C8—41no—
256C2×C8—41no—
257C2×C8—1721no—
258C2×C8—1721no—
259C4⋊C4—41no—
260C4⋊C4—42no—
261C4⋊C4—1721no—
262C4⋊C4—1721no—
263C4⋊C4—1721no—
264C4⋊C4—1722no—
265C4⋊C4—1722no—
266C4⋊C4—1722no—
267C4⋊C4—1721no—
268C4⋊C4—1721no—
269C42—861no—
270C42—861no—
271C42—861no—
272C42—861no—
273C42—861no—
274C42—861no—
275C42—864no—
276C42—1721no—
277C42—1721no—
278C23C22⋊C4×D4311yescharacteristic
279Q8—42no—
280Q8—42no—
281Q8—1722no—
282Q8—1722no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—431no—
296C2×C4—431no—
297C2×C4—432no—
298C2×C4—862no—
299C2×C4—861no—
300C2×C4—861no—
301C2×C4—862no—
302C2×C4—861no—
303C2×C4—861no—
304C2×C4—861no—
305C2×C4—861no—
306C2×C4—1721no—
307C2×C4—1721no—
308C2×C4—1721no—
309C2×C4—1721no—
310C2×C4—1721no—
311C2×C4—1721no—
312C2×C4#1306334611yescharacteristic
313C2×C4#1306334811yescharacteristic
314C8—42no—
315C8—81no—
316C8—3441no—
317C8—1722no—
318C22—21no—
319C22—21no—
320C22#99×D4311yescharacteristic
321C22#1458289411yescharacteristic
322C22#104×D4311yescharacteristic
323C4—21no—
324C4—21no—
325C4—42no—
326C4—41no—
327C4—42no—
328C4—41no—
329C4—432no—
330C4—861no—
331C4—862no—
332C4—3441no—
333C4—1722no—
334C4—1721no—
335C4—1721no—
336C2—21no—
337C2—21no—
338C2#1913308511yescharacteristic
339C2#1913623311yescharacteristic
340C2#356×D4311yescharacteristic
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#11736
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
197. C43#11736semidirect

Maximal subgroups

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

subgroupindex
#191378852
#191343902
#191329172
#191326252
#191326022
#191326002
C43×#13542
#1173643