Finite Group Databasebeta

← #25007487

Subgroups — #25007487

Order 11008.

382 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 69 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#19140294C211yesmaximal, characteristic
2#19134671C211yesmaximal, characteristic
3#19132906C211yesmaximal, characteristic
4#19132620C211yesmaximal, characteristic
5#19132618C211yesmaximal, characteristic
6#19132595C211yesmaximal, characteristic
7C43×#1344C211yesmaximal, characteristic
8C2×#13063316C411yescharacteristic, complemented
9C2×#13063281C2211yescharacteristic
10#14582949—21no—
11#14582839C411yescharacteristic, complemented
12#14582835C2211yescharacteristic
13#14582830C411yescharacteristic, complemented
14#14582796—21no—
15#14582792—21no—
16#14582781—21no—
17#14582771—21no—
18#14582760—21no—
19#14582744C411yescharacteristic, complemented
20#14582666C2211yescharacteristic
21#14582665—21no—
22#14582624—21no—
23#14582623C2211yescharacteristic
24C43×#397C2211yescharacteristic
25C43×#342C2211yescharacteristic
26C43×#323C2211yescharacteristic
27C23×Dic43D411yescharacteristic
28#13063316—41no—
29#13063316—41no—
30#13063281—41no—
31#13063281—41no—
32C2×C4⋊Dic43—21no—
33C2×C4⋊Dic43C2×C411yescharacteristic
34C2×Dic43⋊C4—21no—
35C2×Dic43⋊C4—21no—
36C2×Dic43⋊C4—21no—
37C2×Dic43⋊C4C2×C411yescharacteristic
38C2×Dic43⋊C4D411yescharacteristic
39C2×C22⋊Dic43—21no—
40C2×C22⋊Dic43—21no—
41C2×C22⋊Dic43D411yescharacteristic
42C2×C4×Dic43—21no—
43C2×C4×Dic43C2×C411yescharacteristic
44C2×C4×Dic43D411yescharacteristic
45Dic43⋊C8—41no—
46C22⋊(C43⋊C8)—21no—
47C8×Dic43—41no—
48C43⋊#95—21no—
49C43⋊#95—21no—
50C43⋊#95—21no—
51C43⋊#95—21no—
52C43⋊#95—41no—
53C43⋊#95—41no—
54C43⋊#95C2×C411yescharacteristic
55C2×C4⋊C4×C43C2×C411yescharacteristic
56C2×C22⋊C4×C43—21no—
57C2×C22⋊C4×C43—21no—
58C2×C22⋊C4×C43C2311yescharacteristic
59C22⋊C8×C43—21no—
60#95×C43—21no—
61#95×C43C2×C411yescharacteristic
62C24×C43C2×D411yescharacteristic
63C22×C4×C43—21no—
64C22×C4×C43—21no—
65C22×C4×C43—41no—
66C22×C4×C43C22×C411yescharacteristic
67C22×C4×C43C2×D411yescharacteristic
68C22×Dic43—21no—
69C22×Dic43—21no—
70C22×Dic43—21no—
71C22×Dic43—21no—
72C22×Dic43—21no—
73C22×Dic43—21no—
74C22×Dic43—41no—
75C22×Dic43—41no—
76C22×Dic43C22⋊C411yescharacteristic
77C22×Dic43C22⋊C411yescharacteristic
78C22×Dic43C22⋊C411yescharacteristic
79C22×Dic43C22⋊C411yescharacteristic
80C2×C8×C43—41no—
81C4⋊C4×C43—41no—
82C22⋊C4×C43—41no—
83C22⋊C4×C43—41no—
84C22⋊C4×C43—41no—
85C22⋊C4×C43—41no—
86C22⋊C4×C43—41no—
87C22⋊Dic43—41no—
88C22⋊Dic43—41no—
89C22⋊Dic43—42no—
90C22⋊Dic43—41no—
91C4⋊Dic43—42no—
92C4⋊Dic43—41no—
93Dic43⋊C4—41no—
94Dic43⋊C4—41no—
95Dic43⋊C4—42no—
96Dic43⋊C4—42no—
97Dic43⋊C4—41no—
98Dic43⋊C4—41no—
99C4×Dic43—21no—
100C4×Dic43—21no—
101C4×Dic43—21no—
102C4×Dic43—21no—
103C4×Dic43—42no—
104C2×C43⋊C8—41no—
105C23×C43—21no—
106C23×C43—21no—
107C23×C43—41no—
108C23×C43—41no—
109C23×C43C2×C22⋊C411yescharacteristic
110C23×C43#13511yescharacteristic
111C23×C43#13511yescharacteristic
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—41no—
115C2×C4×C43—41no—
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—81no—
123C2×C4×C43—81no—
124C2×C4×C43—81no—
125C2×Dic43—21no—
126C2×Dic43—21no—
127C2×Dic43—22no—
128C2×Dic43—21no—
129C2×Dic43—21no—
130C2×Dic43—21no—
131C2×Dic43—21no—
132C2×Dic43—21no—
133C2×Dic43—41no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137C2×Dic43—41no—
138C2×Dic43—41no—
139C2×Dic43—41no—
140C2×Dic43—41no—
141C2×Dic43—41no—
142C2×Dic43—41no—
143C2×Dic43—41no—
144C2×Dic43—81no—
145C2×Dic43—81no—
146C2×Dic43—81no—
147C2×Dic43#9911yescharacteristic
148C2×Dic43#9911yescharacteristic
149C8×C43—81no—
150C43⋊C8—81no—
151#11846—431nomaximal, Sylow
152C22×C43—21no—
153C22×C43—21no—
154C22×C43—21no—
155C22×C43—21no—
156C22×C43—41no—
157C22×C43—41no—
158C22×C43—41no—
159C22×C43—41no—
160C22×C43—81no—
161C22×C43C2×#9911yescharacteristic
162C22×C43#41611yescharacteristic
163C22×C43#42111yescharacteristic
164C4×C43—41no—
165C4×C43—41no—
166C4×C43—81no—
167C4×C43—81no—
168C4×C43—161no—
169Dic43—21no—
170Dic43—21no—
171Dic43—42no—
172Dic43—41no—
173Dic43—41no—
174Dic43—41no—
175Dic43—81no—
176Dic43—161no—
177#2611—431no—
178#1820—431no—
179#1458—431no—
180#1352—431no—
181#1352—431no—
182#1344—431no—
183#1344D4311yescharacteristic
184C2×C43—21no—
185C2×C43—21no—
186C2×C43—41no—
187C2×C43—41no—
188C2×C43#151611yescharacteristic
189C2×C43#212311yescharacteristic
190C2×C43#212611yescharacteristic
191C2×#125—431no—
192C2×#117—431no—
193#431—861no—
194#400—431no—
195#399—431no—
196#398—431no—
197#397C2×D4311yescharacteristic
198#389—861no—
199#388—861no—
200#387—861no—
201#385—861no—
202#381—861no—
203#376—431no—
204#342—431no—
205#342—861no—
206#342C2×D4311yescharacteristic
207#324—861no—
208#323—431no—
209#323C2×D4311yescharacteristic
210C43#1184611yescharacteristic, complemented, Sylow
211C23×C4—431no—
212#125—1721no—
213#125—1721no—
214#117—1721no—
215#117—1721no—
216C2×C4⋊C4—431no—
217C2×C4⋊C4—431no—
218C2×C4⋊C4—431no—
219C2×C4⋊C4—861no—
220C2×C4⋊C4—861no—
221C2×C4⋊C4—861no—
222C2×C4⋊C4—861no—
223C2×C4⋊C4C4×D4311yescharacteristic
224C2×C22⋊C4—21no—
225C2×C22⋊C4—21no—
226C2×C22⋊C4—431no—
227C2×C22⋊C4—861no—
228C2×C22⋊C4—861no—
229C2×C22⋊C4C22×D4311yescharacteristic
230C2×C42—431no—
231C2×C42—431no—
232C2×C42—861no—
233C4⋊C8—1721no—
234C22⋊C8—21no—
235C22⋊C8—861no—
236C4×C8—1721no—
237#95—21no—
238#95—431no—
239#95—861no—
240#95—861no—
241#95—861no—
242#95—861no—
243#95—1721no—
244#95—1721no—
245#95C4×D4311yescharacteristic
246C24D4×D4311yescharacteristic
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—41no—
250C22×C4—431no—
251C22×C4—431no—
252C22×C4—431no—
253C22×C4—431no—
254C22×C4—861no—
255C22×C4—861no—
256C22×C4—861no—
257C22×C4—861no—
258C22×C4—861no—
259C22×C4—861no—
260C22×C4—1721no—
261C22×C4—1721no—
262C22×C4C2×C4×D4311yescharacteristic
263C22×C4D4×D4311yescharacteristic
264C2×C8—41no—
265C2×C8—1721no—
266C4⋊C4—41no—
267C4⋊C4—1721no—
268C4⋊C4—1721no—
269C4⋊C4—1721no—
270C4⋊C4—1721no—
271C4⋊C4—1721no—
272C4⋊C4—1722no—
273C4⋊C4—1722no—
274C4⋊C4—1722no—
275C22⋊C4—41no—
276C22⋊C4—41no—
277C22⋊C4—41no—
278C22⋊C4—41no—
279C22⋊C4—41no—
280C22⋊C4—1721no—
281C22⋊C4—1722no—
282C22⋊C4—1721no—
283C22⋊C4—1721no—
284C42—861no—
285C42—861no—
286C42—861no—
287C42—861no—
288C42—1722no—
289C23—21no—
290C23—21no—
291C23—41no—
292C23—41no—
293C23C22⋊C4×D4311yescharacteristic
294C23#1306334411yescharacteristic
295C23#1306334611yescharacteristic
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4—431no—
310C2×C4—431no—
311C2×C4—861no—
312C2×C4—861no—
313C2×C4—862no—
314C2×C4—861no—
315C2×C4—861no—
316C2×C4—861no—
317C2×C4—861no—
318C2×C4—861no—
319C2×C4—3441no—
320C2×C4—3441no—
321C2×C4—3441no—
322C2×C4—1721no—
323C2×C4—1721no—
324C2×C4—1721no—
325C2×C4—1721no—
326C2×C4—1721no—
327C2×C4—1721no—
328C2×C4—1721no—
329C2×C4—1721no—
330C2×C4—1721no—
331C2×C4—1721no—
332C2×C4—1721no—
333C8—81no—
334C8—3441no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—81no—
344C22#99×D4311yescharacteristic
345C22#1458289211yescharacteristic
346C22#1458291411yescharacteristic
347C4—41no—
348C4—41no—
349C4—81no—
350C4—81no—
351C4—161no—
352C4—861no—
353C4—861no—
354C4—3441no—
355C4—1722no—
356C4—1721no—
357C4—1721no—
358C4—1721no—
359C4—6881no—
360C2—21no—
361C2—21no—
362C2—41no—
363C2—41no—
364C2#1913314811yescharacteristic
365C2#1913624711yescharacteristic
366C2#1913625911yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C22⋊C4C22×D43
FittingC43×#1344C2
socleC22×C43C2×#99
prime radicalC24×C43C2×D4
cosocleC2×C22⋊C4×C43C23
hypercenter#1344D43
hypocenterC43#11846
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1344

Complements

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

NH ≅ G/Ntype
8. C2×#13063316C4semidirect
11. #14582839C4semidirect
13. #14582830C4semidirect
19. #14582744C4semidirect
210. C43#11846semidirect

Maximal subgroups

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

subgroupindex
#191402942
#191346712
#191329062
#191326202
#191326182
#191325952
C43×#13442
#1184643