Finite Group Databasebeta

← #25006264

Subgroups — #25006264

Order 11008.

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

normal subgroups only

This group has 374 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#19139801C211yesmaximal, characteristic
2#19132937C211yesmaximal, characteristic
3#19132917C211yesmaximal, characteristic
4#19132541C211yesmaximal, characteristic
5#19132540C211yesmaximal, characteristic
6#19132540C211yesmaximal, characteristic
7C43×#1325C211yesmaximal, characteristic
8C2×#13063324C411yescharacteristic
9C2×#13063290C2211yescharacteristic
10#14582953—21no—
11#14582949—21no—
12#14582819—21no—
13#14582819—21no—
14#14582805C411yescharacteristic
15#14582804C411yescharacteristic
16#14582794—21no—
17#14582794—21no—
18#14582768C2211yescharacteristic
19C4×Dic43⋊C4C411yescharacteristic
20#14582625C2211yescharacteristic
21#14582625C2211yescharacteristic
22#14582624—21no—
23#14582624—21no—
24C43×#384C2211yescharacteristic
25C43×#324C2211yescharacteristic
26C43×#324C2211yescharacteristic
27C22×Dic86—21no—
28C22×Dic86C2×C411yescharacteristic
29#13063324—41no—
30#13063324—41no—
31#13063290—41no—
32#13063290—41no—
33C2×C4⋊Dic43C2×C411yescharacteristic
34C2×Dic43⋊C4—21no—
35C2×Dic43⋊C4—21no—
36C2×Dic43⋊C4—21no—
37C2×Dic43⋊C4—21no—
38C2×Dic43⋊C4D411yescharacteristic
39C2×Dic43⋊C4D411yescharacteristic
40C2×C4×Dic43C2×C411yescharacteristic
41C2×C4×Dic43C2×C411yescharacteristic
42C2×C4×Dic43D411yescharacteristic
43C2×C4×Dic43D411yescharacteristic
44Dic43⋊C8—41no—
45Dic43⋊C8—41no—
46C22⋊(C43⋊C8)—21no—
47C22⋊(C43⋊C8)—21no—
48#13063235—41no—
49C8×Dic43—41no—
50C43⋊#95—21no—
51C43⋊#95—21no—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C43⋊#95—21no—
55C2×C4⋊C4×C43—21no—
56C2×C4⋊C4×C43—21no—
57C2×C4⋊C4×C43C2×C411yescharacteristic
58C2×C4⋊C4×C43C2311yescharacteristic
59C2×C42×C43C2×C411yescharacteristic
60C22⋊C8×C43—21no—
61C22⋊C8×C43—21no—
62C22×C4×C43—21no—
63C22×C4×C43—21no—
64C22×C4×C43C22×C411yescharacteristic
65C22×C4×C43C2×D411yescharacteristic
66C22×C4×C43C2×D411yescharacteristic
67C22×Dic43—21no—
68C22×Dic43—21no—
69C22×Dic43C22⋊C411yescharacteristic
70C22×Dic43C22⋊C411yescharacteristic
71C22×Dic43C22⋊C411yescharacteristic
72C22×Dic43C22⋊C411yescharacteristic
73C2×Dic86—21no—
74C2×Dic86—21no—
75C2×Dic86—22no—
76C2×Dic86—41no—
77C2×Dic86—42no—
78C2×Dic86—81no—
79C2×Dic86—81no—
80C2×C8×C43—41no—
81C2×C8×C43—41no—
82C4⋊C4×C43—41no—
83C4⋊C4×C43—41no—
84C4⋊C4×C43—81no—
85C4⋊C4×C43—81no—
86C42×C43—21no—
87C42×C43—21no—
88C4⋊Dic43—41no—
89Dic43⋊C4—24no—
90Dic43⋊C4—41no—
91Dic43⋊C4—41no—
92Dic43⋊C4—41no—
93Dic43⋊C4—41no—
94Dic43⋊C4—81no—
95Dic43⋊C4—81no—
96C4×Dic43—21no—
97C4×Dic43—21no—
98C4×Dic43—21no—
99C4×Dic43—21no—
100C4×Dic43—21no—
101C4×Dic43—21no—
102C4×Dic43—21no—
103C4×Dic43—21no—
104C2×C43⋊C8—41no—
105C2×C43⋊C8—41no—
106C23×C43C2×C22⋊C411yescharacteristic
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×C43#13111yescharacteristic
120C2×C4×C43#13111yescharacteristic
121C2×Dic43—21no—
122C2×Dic43—21no—
123C2×Dic43—22no—
124C2×Dic43—22no—
125C2×Dic43—21no—
126C2×Dic43—21no—
127C2×Dic43—21no—
128C2×Dic43—21no—
129C2×Dic43—41no—
130C2×Dic43—41no—
131C2×Dic43—41no—
132C2×Dic43—41no—
133C2×Dic43—41no—
134C2×Dic43—41no—
135C2×Dic43#9911yescharacteristic
136C2×Dic43#9911yescharacteristic
137C2×Dic43#10112yes—
138Dic86—42no—
139Dic86—42no—
140Dic86—84no—
141C8×C43—81no—
142C8×C43—81no—
143C43⋊C8—81no—
144C43⋊C8—81no—
145#11574—431nomaximal, Sylow
146C22×C43—21no—
147C22×C43—21no—
148C22×C43#40811yescharacteristic
149C22×C43C2×#9911yescharacteristic
150C22×C43C2×#10111yescharacteristic
151C4×C43—21no—
152C4×C43—21no—
153C4×C43—42no—
154C4×C43—41no—
155C4×C43—41no—
156C4×C43—81no—
157Dic43—21no—
158Dic43—22no—
159Dic43—42no—
160Dic43—41no—
161Dic43—41no—
162Dic43—81no—
163Dic43#35612yes—
164#2567—431no—
165#1467—431no—
166#1461—431no—
167#1325—431no—
168#1325—431no—
169#1325—431no—
170#1325D4311yescharacteristic
171C2×C43—21no—
172C2×C43—21no—
173C2×C43#147211yescharacteristic
174C2×C43#212811yescharacteristic
175C2×C43C2×#35611yescharacteristic
176C2×C4⋊Q8—431no—
177C2×C4×Q8—431no—
178#432—861no—
179#431—861no—
180#395—861no—
181#395—861no—
182#391—431no—
183#391—431no—
184#389—861no—
185#389—861no—
186#384—431no—
187#384C2×D4311yescharacteristic
188C4×C4⋊C4—431no—
189#324—431no—
190#324—431no—
191#324—861no—
192#324—861no—
193#324C2×D4311yescharacteristic
194#324C2×D4311yescharacteristic
195C43#1157411yescharacteristic, complemented, Sylow
196C22×Q8—431no—
197C22×Q8—861no—
198C4⋊Q8—1721no—
199C4⋊Q8—1721no—
200C4×Q8—1721no—
201C4×Q8—1721no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—431no—
205C2×C4⋊C4—431no—
206C2×C4⋊C4—431no—
207C2×C4⋊C4—861no—
208C2×C4⋊C4—861no—
209C2×C4⋊C4—861no—
210C2×C4⋊C4—861no—
211C2×C4⋊C4C4×D4311yescharacteristic
212C2×C4⋊C4C22×D4311yescharacteristic
213C2×C42—431no—
214C2×C42—431no—
215C2×C42—431no—
216C2×C42—431no—
217C2×C42C4×D4311yescharacteristic
218C4⋊C8—1721no—
219C4⋊C8—1721no—
220C22⋊C8—21no—
221C22⋊C8—21no—
222C22⋊C8—861no—
223C22⋊C8—861no—
224#97—1721no—
225C4×C8—1721no—
226#95—861no—
227#95—861no—
228#95—861no—
229#95—861no—
230#95—861no—
231C2×Q8—862no—
232C2×Q8—861no—
233C2×Q8—861no—
234C2×Q8—3441no—
235C2×Q8—3441no—
236C2×Q8—1721no—
237C2×Q8—1722no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—431no—
241C22×C4—431no—
242C22×C4—431no—
243C22×C4—431no—
244C22×C4—861no—
245C22×C4—861no—
246C22×C4C2×C4×D4311yescharacteristic
247C22×C4D4×D4311yescharacteristic
248C22×C4D4×D4311yescharacteristic
249C2×C8—41no—
250C2×C8—41no—
251C2×C8—1721no—
252C2×C8—1721no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—81no—
256C4⋊C4—81no—
257C4⋊C4—864no—
258C4⋊C4—3441no—
259C4⋊C4—3441no—
260C4⋊C4—1721no—
261C4⋊C4—1721no—
262C4⋊C4—1721no—
263C4⋊C4—1721no—
264C4⋊C4—1721no—
265C42—21no—
266C42—21no—
267C42—861no—
268C42—861no—
269C42—861no—
270C42—861no—
271C42—861no—
272C42—861no—
273C42—861no—
274C42—861no—
275C23C22⋊C4×D4311yescharacteristic
276Q8—3444no—
277Q8—1722no—
278Q8—1722no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—22no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—431no—
292C2×C4—431no—
293C2×C4—432no—
294C2×C4—862no—
295C2×C4—861no—
296C2×C4—861no—
297C2×C4—862no—
298C2×C4—861no—
299C2×C4—861no—
300C2×C4—861no—
301C2×C4—861no—
302C2×C4—1721no—
303C2×C4—1721no—
304C2×C4—1721no—
305C2×C4—1721no—
306C2×C4—1721no—
307C2×C4—1721no—
308C2×C4#1306333111yescharacteristic
309C2×C4#1306333311yescharacteristic
310C8—81no—
311C8—81no—
312C8—3441no—
313C8—3441no—
314C22—21no—
315C22—21no—
316C22#1458286411yescharacteristic
317C22#99×D4311yescharacteristic
318C22#101×D4311yescharacteristic
319C4—21no—
320C4—21no—
321C4—42no—
322C4—41no—
323C4—41no—
324C4—81no—
325C4—432no—
326C4—861no—
327C4—862no—
328C4—3441no—
329C4—1722no—
330C4—1721no—
331C4—1721no—
332C2—21no—
333C2—21no—
334C2#1913295711yescharacteristic
335C2#1913626511yescharacteristic
336C2#356×D4311yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1325C2
socleC22×C43C2×#99
prime radicalC23×C43C2×C22⋊C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1325D43
hypocenterC43#11574
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1325

Complements

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

NH ≅ G/Ntype
195. C43#11574semidirect

Maximal subgroups

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

subgroupindex
#191398012
#191329372
#191329172
#191325412
#191325402
C43×#13252
#1157443