Finite Group Databasebeta

← #25006277

Subgroups — #25006277

Order 11008.

424 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 83 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#19139938C211yesmaximal, characteristic
2#19132933C211yesmaximal, characteristic
3#19132544C212yesmaximal, complemented
4#19132542C212yesmaximal, complemented
5C43×#1460C211yesmaximal, characteristic
6C22×Dic43⋊C4C411yescharacteristic
7#14582863—21no—
8#14582832—21no—
9#14582822—21no—
10#14582783—21no—
11#14582779C411yescharacteristic
12#14582779C411yescharacteristic
13#14582772—21no—
14#14582771C2211yescharacteristic
15#14582771C2211yescharacteristic
16#14582759C411yescharacteristic
17#14582625—21no—
18#14582623C2212yes—
19C2×C4×D4×C43C2211yescharacteristic
20C43×#431—21no—
21C43×#323—21no—
22C43×#323C2212yes—
23C23×Dic43C2×C411yescharacteristic
24C23×Dic43C2×C411yescharacteristic
25C2×#10621877—41no—
26C2×C4⋊Dic43—21no—
27C2×Dic43⋊C4—21no—
28C2×Dic43⋊C4—21no—
29C2×Dic43⋊C4—21no—
30C2×Dic43⋊C4—21no—
31C2×Dic43⋊C4—41no—
32C2×Dic43⋊C4—41no—
33C2×C22⋊Dic43—21no—
34C2×C22⋊Dic43—21no—
35C2×C22⋊Dic43C2×C411yescharacteristic
36C2×C22⋊Dic43C2×C411yescharacteristic
37C22⋊(C43⋊C8)—22no—
38C22⋊(C43⋊C8)—41no—
39C43⋊#95—21no—
40C43⋊#95—21no—
41C43⋊#95—21no—
42C43⋊#95—21no—
43C43⋊#95—21no—
44C22×D4×C43C2×C411yescharacteristic
45C23×C4×C43C2×C411yescharacteristic
46C23×C4×C43D411yescharacteristic
47C4×D4×C43—41no—
48C4×D4×C43—41no—
49C2×C4⋊C4×C43D411yescharacteristic
50C2×C22⋊C4×C43D411yescharacteristic
51C2×C22⋊C4×C43C2311yescharacteristic
52C2×C42×C43D411yescharacteristic
53C4⋊C8×C43—41no—
54C22⋊C8×C43—22no—
55C4×C8×C43—41no—
56C24×C43C22⋊C411yescharacteristic
57C24×C43C22×C411yescharacteristic
58C2×D4×C43—22no—
59C2×D4×C43—22no—
60C2×D4×C43—41no—
61C22×C4×C43—21no—
62C22×C4×C43—21no—
63C22×C4×C43—21no—
64C22×C4×C43—21no—
65C22×C4×C43—81no—
66C22×C4×C43—81no—
67C22×C4×C43C22⋊C411yescharacteristic
68C22×C4×C43C22⋊C411yescharacteristic
69C22×C4×C43C22⋊C411yescharacteristic
70C22×C4×C43C2×D411yescharacteristic
71C22×C4×C43C2×D411yescharacteristic
72C22×Dic43—21no—
73C22×Dic43—21no—
74C22×Dic43—21no—
75C22×Dic43—21no—
76C22×Dic43—41no—
77C22×Dic43—41no—
78C22×Dic43—42no—
79C22×Dic43—81no—
80C2×C8×C43—42no—
81C4⋊C4×C43—41no—
82C22⋊C4×C43—41no—
83C22⋊C4×C43—41no—
84C42×C43—21no—
85C42×C43—21no—
86C22⋊Dic43—22no—
87C22⋊Dic43—22no—
88C22⋊Dic43—42no—
89C22⋊Dic43—81no—
90C4⋊Dic43—81no—
91Dic43⋊C4—42no—
92Dic43⋊C4—42no—
93Dic43⋊C4—41no—
94Dic43⋊C4—41no—
95Dic43⋊C4—81no—
96#10621877—82no—
97C2×C43⋊C8—42no—
98C23×C43—21no—
99C23×C43—21no—
100C23×C43—21no—
101C23×C43—21no—
102C23×C43—21no—
103C23×C43—41no—
104C23×C43—41no—
105C23×C43—41no—
106C23×C43—41no—
107C23×C43C2×C22⋊C411yescharacteristic
108C23×C43#13112yes—
109D4×C43—44no—
110C2×C4×C43—21no—
111C2×C4×C43—21no—
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—41no—
116C2×C4×C43—42no—
117C2×C4×C43—41no—
118C2×C4×C43—41no—
119C2×C4×C43—41no—
120C2×C4×C43—81no—
121C2×C4×C43—81no—
122C2×C4×C43—81no—
123C2×C4×C43#9911yescharacteristic
124C2×C4×C43#9911yescharacteristic
125C2×C4×C43#10112yes—
126C2×Dic43—22no—
127C2×Dic43—41no—
128C2×Dic43—42no—
129C2×Dic43—41no—
130C2×Dic43—42no—
131C2×Dic43—41no—
132C2×Dic43—41no—
133C2×Dic43—41no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137C2×Dic43—41no—
138C2×Dic43—41no—
139C2×Dic43—41no—
140C2×Dic43—82no—
141C8×C43—82no—
142C43⋊C8—82no—
143#11577—431nomaximal, Sylow
144C22×C43—21no—
145C22×C43—21no—
146C22×C43—22no—
147C22×C43—42no—
148C22×C43—42no—
149C22×C43—42no—
150C22×C43—41no—
151C22×C43—41no—
152C22×C43—41no—
153C22×C43—41no—
154C22×C43—41no—
155C22×C43—81no—
156C22×C43#40811yescharacteristic
157C22×C43C2×#9911yescharacteristic
158C22×C43C2×#10111yescharacteristic
159C4×C43—21no—
160C4×C43—21no—
161C4×C43—22no—
162C4×C43—41no—
163C4×C43—41no—
164C4×C43—41no—
165Dic43—42no—
166Dic43—81no—
167Dic43—81no—
168Dic43—81no—
169#2579—431no—
170#1465—431no—
171#1460D4311yescharacteristic
172#1326—432no—
173#1326—432no—
174C2×C43—21no—
175C2×C43—21no—
176C2×C43—42no—
177C2×C43—81no—
178C2×C43#147211yescharacteristic
179C2×C43#212011yescharacteristic
180C2×C43#212111yescharacteristic
181C2×C4×D4C2×D4311yescharacteristic
182C22×C4⋊C4—431no—
183#431—21no—
184#407—861no—
185#398—861no—
186#396—861no—
187#387—861no—
188#386—431no—
189#386—431no—
190#385—431no—
191#385—431no—
192#385—861no—
193#380—431no—
194#324—861no—
195#323—21no—
196#323—432no—
197#323C2×D4312yes—
198C43#1157711yescharacteristic, complemented, Sylow
199C22×D4C4×D4311yescharacteristic
200C23×C4—431no—
201C23×C4—431no—
202C23×C4C4×D4311yescharacteristic
203C23×C4D17211yescharacteristic
204C2×M16—1721no—
205C4×D4—41no—
206C4×D4—41no—
207C2×C4⋊C4—861no—
208C2×C4⋊C4—861no—
209C2×C4⋊C4—861no—
210C2×C4⋊C4—861no—
211C2×C4⋊C4—861no—
212C2×C4⋊C4—1721no—
213C2×C4⋊C4—1721no—
214C2×C4⋊C4D17211yescharacteristic
215C2×C22⋊C4—431no—
216C2×C22⋊C4—431no—
217C2×C22⋊C4—861no—
218C2×C22⋊C4—861no—
219C2×C22⋊C4C22⋊D4311yescharacteristic
220C2×C22⋊C4C22×D4311yescharacteristic
221C2×C42C22⋊D4311yescharacteristic
222C4⋊C8—41no—
223C22⋊C8—22no—
224C22⋊C8—862no—
225C22⋊C8—1721no—
226C4×C8—41no—
227#95—861no—
228#95—861no—
229#95—861no—
230#95—861no—
231#95—861no—
232C24(C2×D43)⋊C411yescharacteristic
233C24C2×C4×D4311yescharacteristic
234C2×D4—22no—
235C2×D4—22no—
236C2×D4—41no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—81no—
242C22×C4—81no—
243C22×C4—861no—
244C22×C4—861no—
245C22×C4—861no—
246C22×C4—861no—
247C22×C4—3441no—
248C22×C4—1722no—
249C22×C4—1721no—
250C22×C4—1721no—
251C22×C4(C2×D43)⋊C411yescharacteristic
252C22×C4(C2×D43)⋊C411yescharacteristic
253C22×C4(C2×D43)⋊C411yescharacteristic
254C22×C4C2×D17211yescharacteristic
255C22×C4C2×C22⋊D4311yescharacteristic
256M16—3442no—
257C2×C8—42no—
258C2×C8—1722no—
259C4⋊C4—41no—
260C4⋊C4—3441no—
261C4⋊C4—3441no—
262C4⋊C4—1722no—
263C4⋊C4—1722no—
264C4⋊C4—1721no—
265C4⋊C4—1721no—
266C22⋊C4—41no—
267C22⋊C4—41no—
268C22⋊C4—862no—
269C22⋊C4—862no—
270C22⋊C4—3441no—
271C22⋊C4—1722no—
272C42—21no—
273C42—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23—41no—
280C23—41no—
281C23—41no—
282C23—41no—
283C23C2×(C2×D43)⋊C411yescharacteristic
284C23#1306333112yes—
285D4—44no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—41no—
292C2×C4—42no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—862no—
300C2×C4—3442no—
301C2×C4—1721no—
302C2×C4—1721no—
303C2×C4—1721no—
304C2×C4—1721no—
305C2×C4—1721no—
306C2×C4—1721no—
307C2×C4—1721no—
308C2×C4—1721no—
309C2×C4—1721no—
310C2×C4—1721no—
311C2×C4—1722no—
312C2×C4—1721no—
313C2×C4—1722no—
314C2×C4#1306323911yescharacteristic
315C2×C4#1306323911yescharacteristic
316C2×C4#1306324312yes—
317C8—82no—
318C8—3442no—
319C22—21no—
320C22—21no—
321C22—22no—
322C22—42no—
323C22—42no—
324C22—42no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—81no—
331C22#1458286511yescharacteristic
332C22C2×#1306323911yescharacteristic
333C22C2×#1306324311yescharacteristic
334C4—22no—
335C4—21no—
336C4—21no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—3441no—
341C4—3441no—
342C4—3441no—
343C4—1722no—
344C2—21no—
345C2—21no—
346C2—42no—
347C2—81no—
348C2#1913295811yescharacteristic
349C2#1913623411yescharacteristic
350C2#1913624211yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC24×C43C22×C4
FrattiniC2×C22⋊C4C22×D43
FittingC43×#1460C2
socleC22×C43C2×#99
prime radicalC22×D4×C43C2×C4
cosocleC2×C22⋊C4×C43C23
hypercenter#1460D43
hypocenterC43#11577
LCSG ▷ C24×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1460

Complements

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

NH ≅ G/Ntype
3. #19132544C2semidirect
4. #19132542C2semidirect
198. C43#11577semidirect

Maximal subgroups

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

subgroupindex
#191399382
#191329332
#191325442
#191325422
C43×#14602
#1157743