Finite Group Databasebeta

← #24999778

Subgroups — #24999778

Order 11008.

360 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 75 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#19140244C211yesmaximal, characteristic
2#19135540C211yesmaximal, characteristic
3#19133107C211yesmaximal, characteristic
4#19132487C211yesmaximal, characteristic
5#19132459C211yesmaximal, characteristic
6#19132450C211yesmaximal, characteristic
7C43×#1515C211yesmaximal, characteristic
8#14582956C2211yescharacteristic
9C4×#10621877C2211yescharacteristic
10#14582841—21no—
11#14582820—21no—
12#14582803—21no—
13#14582803—21no—
14#14582786—21no—
15#14582782—21no—
16C4×C4⋊Dic43C2211yescharacteristic
17#14582745C2211yescharacteristic
18#14582658—21no—
19#14582658—21no—
20#14582636—21no—
21#14582636—21no—
22C43×#533C2211yescharacteristic
23C43×#432C2211yescharacteristic
24C43×#383C2211yescharacteristic
25C43×#328—21no—
26C43×#328—21no—
27C22×Dic86—21no—
28C2×#10621877—21no—
29C2×C4⋊Dic43—21no—
30C2×C4⋊Dic43—21no—
31C2×Dic43⋊C4—21no—
32C2×Dic43⋊C4—21no—
33C2×C4×Dic43—21no—
34C2×C4×Dic43D411yescharacteristic
35C2×C4×Dic43D411yescharacteristic
36C4⋊(C43⋊C8)—21no—
37C22⋊(C43⋊C8)—21no—
38#13063236—21no—
39#13063236—21no—
40C4×C43⋊C8—21no—
41C43⋊#95—21no—
42C43⋊#95—21no—
43C43⋊#95—21no—
44C43⋊#95—21no—
45C43⋊#95—21no—
46C43⋊#95—21no—
47C43⋊#95D411yescharacteristic
48C43⋊#95D411yescharacteristic
49C4⋊Q8×C43Q811yescharacteristic, complemented
50C4⋊Q8×C43Q811yescharacteristic, complemented
51#125×C43—21no—
52C22⋊Q8×C43—21no—
53C22⋊Q8×C43—21no—
54C4×Q8×C43—21no—
55C4×Q8×C43—21no—
56#117×C43—21no—
57C2×C42×C43C2311yescharacteristic
58C4⋊C8×C43—21no—
59C22⋊C8×C43—21no—
60#97×C43—21no—
61#95×C43—21no—
62#95×C43—21no—
63#95×C43D411yescharacteristic
64#95×C43D411yescharacteristic
65C2×Q8×C43—21no—
66C2×Q8×C43—21no—
67C22×C4×C43—21no—
68C22×C4×C43—21no—
69C22×C4×C43C2×D411yescharacteristic
70C22×C4×C43C2×D411yescharacteristic
71C22×C4×C43C2×D411yescharacteristic
72C22×Dic43—21no—
73C22×Dic43—21no—
74C22×Dic43—21no—
75C22×Dic43—21no—
76C2×Dic86—42no—
77C2×Dic86—42no—
78C2×Dic86—81no—
79C2×C8×C43—41no—
80C4⋊C4×C43—21no—
81C4⋊C4×C43—21no—
82C4⋊C4×C43—21no—
83C4⋊C4×C43—21no—
84C4⋊C4×C43—41no—
85C4⋊C4×C43—41no—
86C22⋊C4×C43—41no—
87C42×C43—41no—
88C42×C43C2×Q811yescharacteristic
89C42×C43#4111yescharacteristic
90C42×C43#4111yescharacteristic
91C42×C43#4111yescharacteristic
92C4⋊Dic43—42no—
93C4⋊Dic43—42no—
94Dic43⋊C4—42no—
95Dic43⋊C4—81no—
96C4×Dic43—42no—
97C4×Dic43—41no—
98C4×Dic43—41no—
99#10621877—22no—
100#10621877—41no—
101C2×C43⋊C8—41no—
102C2×C43⋊C8—41no—
103C23×C43#12011yescharacteristic
104Q8×C43—81no—
105Q8×C43—81no—
106C2×C4×C43—21no—
107C2×C4×C43—21no—
108C2×C4×C43—41no—
109C2×C4×C43—41no—
110C2×C4×C43—41no—
111C2×C4×C43—41no—
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×C43C22⋊Q811yescharacteristic
119C2×C4×C43C22⋊Q811yescharacteristic
120C2×C4×C43C22⋊Q811yescharacteristic
121C2×C4×C43#12411yescharacteristic
122C2×C4×C43#12411yescharacteristic
123C2×C4×C43#12411yescharacteristic
124C2×Dic43—22no—
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—
136Dic86—84no—
137C8×C43—81no—
138C43⋊C8—42no—
139C43⋊C8—81no—
140#10379—431nomaximal, Sylow
141C22×C43—21no—
142C22×C43—21no—
143C22×C43#39311yescharacteristic
144C22×C43#45511yescharacteristic
145C22×C43#45611yescharacteristic
146C4×C43—21no—
147C4×C43—21no—
148C4×C43—21no—
149C4×C43—21no—
150C4×C43—21no—
151C4×C43—21no—
152C4×C43—81no—
153C4×C43—81no—
154C4×C43—81no—
155C4×C43—81no—
156Dic43—42no—
157Dic43—42no—
158Dic43—81no—
159Dic43—81no—
160#2605—431no—
161#1986—431no—
162#1515D4311yescharacteristic
163#1506—431no—
164#1300—431no—
165#1288—431no—
166#1285—431no—
167C2×C43—21no—
168C2×C43—21no—
169C2×C43#202811yescharacteristic
170C2×C43#203111yescharacteristic
171C2×C43#203111yescharacteristic
172#533C2×D4311yescharacteristic
173#432—431no—
174#432C2×D4311yescharacteristic
175C4×M16—431no—
176#400—861no—
177#395—861no—
178#391—861no—
179#391—861no—
180#387—861no—
181#387—861no—
182#383C2×D4311yescharacteristic
183C4×C4⋊C4—431no—
184#376—431no—
185#339—861no—
186#339—861no—
187#328—21no—
188#328—21no—
189#328—861no—
190#328—861no—
191C43#1037911yescharacteristic, complemented, Sylow
192C22×Q8—861no—
193C2×M16—861no—
194C4⋊Q8Dic8611yescharacteristic, complemented
195C4⋊Q8Dic8611yescharacteristic, complemented
196#125—21no—
197C22⋊Q8—21no—
198C22⋊Q8—21no—
199C4×Q8—21no—
200C4×Q8—21no—
201#117—21no—
202C2×C4⋊C4—861no—
203C2×C4⋊C4—861no—
204C2×C4⋊C4—861no—
205C2×C4⋊C4—861no—
206C2×C42—431no—
207C2×C42—431no—
208C2×C42—861no—
209C2×C42C22×D4311yescharacteristic
210C4⋊C8—21no—
211C4⋊C8—861no—
212C22⋊C8—21no—
213C22⋊C8—861no—
214#97—21no—
215#97—861no—
216#97—861no—
217C4×C8—861no—
218#95—21no—
219#95—21no—
220#95—431no—
221#95—431no—
222#95—861no—
223#95—861no—
224#95—861no—
225#95—861no—
226#95—861no—
227#95—861no—
228#95C22⋊D4311yescharacteristic
229#95C22⋊D4311yescharacteristic
230C2×Q8—21no—
231C2×Q8—21no—
232C2×Q8—3441no—
233C2×Q8—1722no—
234C2×Q8—1722no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—861no—
238C22×C4—861no—
239C22×C4—861no—
240C22×C4—861no—
241C22×C4D4×D4311yescharacteristic
242C22×C4D4×D4311yescharacteristic
243C22×C4C2×C22⋊D4311yescharacteristic
244M16—862no—
245M16—1721no—
246C2×C8—41no—
247C2×C8—1721no—
248C2×C8—1721no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—3441no—
256C4⋊C4—1722no—
257C4⋊C4—1722no—
258C4⋊C4—1722no—
259C22⋊C4—41no—
260C42—41no—
261C42—1721no—
262C42—1721no—
263C42—1722no—
264C42C2×Dic8611yescharacteristic
265C42#1062189811yescharacteristic
266C42#1062190011yescharacteristic
267C42#1062190011yescharacteristic
268C23#1306329311yescharacteristic
269Q8—81no—
270Q8—81no—
271Q8—3444no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—862no—
285C2×C4—862no—
286C2×C4—1721no—
287C2×C4—1721no—
288C2×C4—1721no—
289C2×C4—1721no—
290C2×C4—1721no—
291C2×C4—1721no—
292C2×C4—1721no—
293C2×C4—1721no—
294C2×C4—1721no—
295C2×C4—1721no—
296C2×C4#1306330211yescharacteristic
297C2×C4#1306330211yescharacteristic
298C2×C4#1306330411yescharacteristic
299C2×C4#1306331111yescharacteristic
300C2×C4#1306331111yescharacteristic
301C2×C4#1306331211yescharacteristic
302C8—81no—
303C8—3441no—
304C8—1722no—
305C22—21no—
306C22—21no—
307C22#1458281111yescharacteristic
308C22#1458307511yescharacteristic
309C22#1458308011yescharacteristic
310C4—21no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—81no—
317C4—81no—
318C4—81no—
319C4—81no—
320C4—3441no—
321C4—3441no—
322C4—1722no—
323C4—1722no—
324C2—21no—
325C2—21no—
326C2#1913575411yescharacteristic
327C2#1913576511yescharacteristic
328C2#1913576911yescharacteristic
subgroupG/H
centerC22#14582811
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1515C2
socleC22×C43#393
prime radicalC23×C43#120
hypercenter#1515D43
hypocenterC43#10379
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1515

Complements

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

NH ≅ G/Ntype
49. C4⋊Q8×C43Q8semidirect
50. C4⋊Q8×C43Q8semidirect
191. C43#10379semidirect
194. C4⋊Q8Dic86semidirect
195. C4⋊Q8Dic86semidirect

Maximal subgroups

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

subgroupindex
#191402442
#191355402
#191331072
#191324872
#191324592
#191324502
C43×#15152
#1037943