Finite Group Databasebeta

← #24994300

Subgroups — #24994300

Order 11008.

432 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 95 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#19143679C211yesmaximal, characteristic
2#19139810C211yesmaximal, characteristic
3#19133313C211yesmaximal, characteristic
4#19133311C211yesmaximal, characteristic
5#19132938C211yesmaximal, characteristic
6#19132451C211yesmaximal, characteristic
7C43×#1285C211yesmaximal, characteristic
8C2×#13063325C2211yescharacteristic
9C2×C4×Dic86C2211yescharacteristic
10#14583028—22no—
11#14583027—22no—
12#14582956C2211yescharacteristic
13#14582956C2211yescharacteristic
14#14582953—21no—
15#14582949—21no—
16#14582839—21no—
17#14582839—21no—
18#14582805C412yes—
19#14582804—21no—
20#14582804—21no—
21#14582765C412yes—
22#14582646—22no—
23#14582644—22no—
24#14582624—21no—
25#14582624—21no—
26C43×#432C2211yescharacteristic
27C43×#432C2211yescharacteristic
28C4×C4⋊C4×C43C2211yescharacteristic
29C22×Dic86—21no—
30C22×Dic86C2×C411yescharacteristic
31#13063325—21no—
32#13063325—21no—
33#13063325—21no—
34#13063325—21no—
35C4×Dic86—21no—
36C4×Dic86—21no—
37C4×Dic86—21no—
38C4×Dic86—21no—
39C2×C4⋊Dic43—21no—
40C2×C4⋊Dic43C2×C412yes—
41C2×C4⋊Dic43C2×C411yescharacteristic
42C2×Dic43⋊C4D411yescharacteristic
43C2×Dic43⋊C4D411yescharacteristic
44C2×C4×Dic43D411yescharacteristic
45C2×C4×Dic43D411yescharacteristic
46C4⋊(C43⋊C8)—21no—
47C4⋊(C43⋊C8)D412yes—
48Dic43⋊C8—22no—
49Dic43⋊C8—22no—
50C22⋊(C43⋊C8)—21no—
51C22⋊(C43⋊C8)—21no—
52#13063236—21no—
53#13063236—21no—
54#13063235—22no—
55C8×Dic43—22no—
56C43⋊#95—22no—
57C43⋊#95—22no—
58C43⋊#95—22no—
59C43⋊#95—22no—
60C2×C4⋊C4×C43—21no—
61C2×C42×C43C2×C412yes—
62C2×C42×C43C2311yescharacteristic
63C4⋊C8×C43—21no—
64C4⋊C8×C43D412yes—
65C22⋊C8×C43—21no—
66C22⋊C8×C43—21no—
67#97×C43—21no—
68#97×C43—21no—
69#95×C43—21no—
70C22×C4×C43—22no—
71C22×C4×C43C22×C411yescharacteristic
72C22×C4×C43C2×D411yescharacteristic
73C22×C4×C43C2×D411yescharacteristic
74C22×Dic43—22no—
75C22×Dic43C22⋊C411yescharacteristic
76C22×Dic43C22⋊C411yescharacteristic
77C22×Dic43C22⋊C411yescharacteristic
78C22×Dic43C22⋊C411yescharacteristic
79C2×Dic86—21no—
80C2×Dic86—21no—
81C2×Dic86—22no—
82C2×Dic86—41no—
83C2×Dic86—44no—
84C2×Dic86—41no—
85C2×Dic86—41no—
86C2×C8×C43—22no—
87C2×C8×C43—41no—
88C4⋊C4×C43—42no—
89C42×C43—42no—
90C42×C43C2×D411yescharacteristic
91C42×C43C2×D411yescharacteristic
92C42×C43#4111yescharacteristic
93C42×C43#4111yescharacteristic
94C4⋊Dic43—21no—
95C4⋊Dic43—21no—
96C4⋊Dic43—22no—
97C4⋊Dic43—22no—
98C4⋊Dic43—41no—
99C4⋊Dic43—41no—
100Dic43⋊C4—21no—
101Dic43⋊C4—21no—
102Dic43⋊C4—21no—
103Dic43⋊C4—21no—
104C4×Dic43—21no—
105C4×Dic43—21no—
106C4×Dic43—21no—
107C4×Dic43—21no—
108C2×C43⋊C8—22no—
109C2×C43⋊C8—41no—
110C23×C43C2×C22⋊C411yescharacteristic
111C2×C4×C43—21no—
112C2×C4×C43—21no—
113C2×C4×C43—22no—
114C2×C4×C43—41no—
115C2×C4×C43—42no—
116C2×C4×C43—42no—
117C2×C4×C43—42no—
118C2×C4×C43C4×D411yescharacteristic
119C2×C4×C43C4×D411yescharacteristic
120C2×C4×C43#12011yescharacteristic
121C2×C4×C43#12111yescharacteristic
122C2×C4×C43#12111yescharacteristic
123C2×C4×C43#12311yescharacteristic
124C2×Dic43—21no—
125C2×Dic43—21no—
126C2×Dic43—21no—
127C2×Dic43—21no—
128C2×Dic43—21no—
129C2×Dic43—21no—
130C2×Dic43—21no—
131C2×Dic43—41no—
132C2×Dic43—41no—
133C2×Dic43—44no—
134C2×Dic43—42no—
135C2×Dic43#10112yes—
136Dic86—42no—
137Dic86—42no—
138Dic86—82no—
139Dic86—82no—
140C8×C43—42no—
141C8×C43—81no—
142C43⋊C8—42no—
143C43⋊C8—81no—
144#9456—431nomaximal, Sylow
145C22×C43—21no—
146C22×C43—21no—
147C22×C43#38611yescharacteristic
148C22×C43C2×#10111yescharacteristic
149C22×C43#41311yescharacteristic
150C4×C43—21no—
151C4×C43—21no—
152C4×C43—21no—
153C4×C43—21no—
154C4×C43—21no—
155C4×C43—82no—
156C4×C43#45412yes—
157Dic43—22no—
158Dic43—41no—
159Dic43—41no—
160Dic43—41no—
161Dic43—82no—
162#2983—431no—
163#2568—431no—
164#1556—431no—
165#1556—431no—
166#1467—431no—
167#1285—431no—
168#1285D4311yescharacteristic
169C2×C43—21no—
170C2×C43—21no—
171C2×C43#188811yescharacteristic
172C2×C43#190111yescharacteristic
173C2×C43#190911yescharacteristic
174C2×C4⋊Q8—431no—
175C2×C4×Q8—431no—
176#446—862no—
177#446—862no—
178#432—431no—
179#432—431no—
180#432—861no—
181#432C2×D4311yescharacteristic
182#432C2×D4311yescharacteristic
183#431—861no—
184#400—861no—
185#400—861no—
186#391—432no—
187#391—861no—
188#391—861no—
189#382—432no—
190C4×C4⋊C4C2×D4311yescharacteristic
191#332—862no—
192#332—862no—
193#324—861no—
194#324—861no—
195C43#945611yescharacteristic, complemented, Sylow
196C22×Q8—431no—
197C22×Q8—861no—
198C4⋊Q8—861no—
199C4⋊Q8—861no—
200C4⋊Q8—861no—
201C4⋊Q8—861no—
202C4×Q8—861no—
203C4×Q8—861no—
204C4×Q8—861no—
205C4×Q8—861no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—431no—
208C2×C4⋊C4—431no—
209C2×C4⋊C4—431no—
210C2×C4⋊C4—432no—
211C2×C4⋊C4—861no—
212C2×C42—431no—
213C2×C42—431no—
214C2×C42C4×D4312yes—
215C2×C42C22×D4311yescharacteristic
216C4⋊C8—21no—
217C4⋊C8—432no—
218C4⋊C8—862no—
219C4⋊C8—862no—
220C4⋊C8—861no—
221C4⋊C8D17212yes—
222C22⋊C8—21no—
223C22⋊C8—21no—
224C22⋊C8—861no—
225C22⋊C8—861no—
226#97—21no—
227#97—21no—
228#97—862no—
229#97—861no—
230#97—861no—
231C4×C8—862no—
232#95—21no—
233#95—862no—
234#95—862no—
235#95—862no—
236#95—862no—
237C2×Q8—862no—
238C2×Q8—861no—
239C2×Q8—861no—
240C2×Q8—1721no—
241C2×Q8—1724no—
242C2×Q8—1721no—
243C2×Q8—1721no—
244C22×C4—22no—
245C22×C4—431no—
246C22×C4—431no—
247C22×C4—431no—
248C22×C4—431no—
249C22×C4—862no—
250C22×C4C2×C4×D4311yescharacteristic
251C22×C4D4×D4311yescharacteristic
252C22×C4D4×D4311yescharacteristic
253C2×C8—22no—
254C2×C8—41no—
255C2×C8—862no—
256C2×C8—1721no—
257C4⋊C4—42no—
258C4⋊C4—861no—
259C4⋊C4—861no—
260C4⋊C4—861no—
261C4⋊C4—861no—
262C4⋊C4—861no—
263C4⋊C4—861no—
264C4⋊C4—862no—
265C4⋊C4—862no—
266C4⋊C4—1721no—
267C4⋊C4—1721no—
268C42—42no—
269C42—861no—
270C42—861no—
271C42—861no—
272C42—861no—
273C42C2×D17211yescharacteristic
274C42#1062189811yescharacteristic
275C42D4×D4311yescharacteristic
276C42#1062190211yescharacteristic
277C23C22⋊C4×D4311yescharacteristic
278Q8—3442no—
279Q8—3442no—
280Q8—1722no—
281Q8—1722no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—22no—
285C2×C4—41no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—432no—
290C2×C4—861no—
291C2×C4—861no—
292C2×C4—861no—
293C2×C4—861no—
294C2×C4—861no—
295C2×C4—861no—
296C2×C4—861no—
297C2×C4—1724no—
298C2×C4—1722no—
299C2×C4—1721no—
300C2×C4—1721no—
301C2×C4#1306328711yescharacteristic
302C2×C4C4×D17211yescharacteristic
303C2×C4#1306329511yescharacteristic
304C2×C4#1306329811yescharacteristic
305C2×C4#1306330011yescharacteristic
306C2×C4#1306331011yescharacteristic
307C8—42no—
308C8—81no—
309C8—3441no—
310C8—1722no—
311C22—21no—
312C22—21no—
313C22#1458277711yescharacteristic
314C22#101×D4311yescharacteristic
315C22#1458288011yescharacteristic
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—21no—
321C4—82no—
322C4—862no—
323C4—3442no—
324C4—1721no—
325C4—1721no—
326C4—1721no—
327C4#1458307312yes—
328C2—21no—
329C2—21no—
330C2#1913499711yescharacteristic
331C2#1913506211yescharacteristic
332C2#1913511611yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1285C2
socleC22×C43#386
prime radicalC23×C43C2×C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1285D43
hypocenterC43#9456
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1285

Complements

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

NH ≅ G/Ntype
195. C43#9456semidirect

Maximal subgroups

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

subgroupindex
#191436792
#191398102
#191333132
#191333112
#191329382
#191324512
C43×#12852
#945643