Finite Group Databasebeta

← #25007311

Subgroups — #25007311

Order 11008.

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

normal subgroups only

This group has 402 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#19137862C211yesmaximal, characteristic
2#19134671C211yesmaximal, characteristic
3#19132926C211yesmaximal, characteristic
4#19132620C211yesmaximal, characteristic
5#19132618C211yesmaximal, characteristic
6#19132616C211yesmaximal, characteristic
7C43×#1351C211yesmaximal, characteristic
8C2×Q8×Dic43C411yescharacteristic, complemented
9C2×#13063281C2211yescharacteristic
10#14582953—21no—
11#14582839C411yescharacteristic, complemented
12#14582835C2211yescharacteristic
13#14582833—21no—
14#14582822—21no—
15#14582818C411yescharacteristic, complemented
16#14582760—21no—
17#14582750—21no—
18#14582750C411yescharacteristic, complemented
19C22⋊C4×Dic43—21no—
20#14582666C2211yescharacteristic
21#14582665—21no—
22#14582624—21no—
23#14582623C2211yescharacteristic
24C43×#393C2211yescharacteristic
25C43×#342C2211yescharacteristic
26C43×#323C2211yescharacteristic
27C23×Dic43D411yescharacteristic
28Q8×Dic43—41no—
29Q8×Dic43—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×Dic43—21no—
44C2×C4×Dic43C2×C411yescharacteristic
45C2×C4×Dic43D411yescharacteristic
46Dic43⋊C8—41no—
47C22⋊(C43⋊C8)—21no—
48#13063235—41no—
49C43⋊#95—21no—
50C43⋊#95—21no—
51C43⋊#95—21no—
52C43⋊#95—41no—
53C43⋊#95—41no—
54C43⋊#95C2×C411yescharacteristic
55C22×Q8×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
63C2×Q8×C43—42no—
64C2×Q8×C43—41no—
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43—41no—
68C22×C4×C43C22×C411yescharacteristic
69C22×C4×C43C2×D411yescharacteristic
70C22×Dic43—21no—
71C22×Dic43—21no—
72C22×Dic43—21no—
73C22×Dic43—21no—
74C22×Dic43—21no—
75C22×Dic43—21no—
76C22×Dic43—41no—
77C22×Dic43—41no—
78C22×Dic43C22⋊C411yescharacteristic
79C22×Dic43C22⋊C411yescharacteristic
80C22×Dic43C22⋊C411yescharacteristic
81C22×Dic43C22⋊C411yescharacteristic
82C2×C8×C43—41no—
83C22⋊C4×C43—41no—
84C22⋊C4×C43—41no—
85C22⋊C4×C43—42no—
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—42no—
98C4×Dic43—21no—
99C4×Dic43—21no—
100C4×Dic43—21no—
101C4×Dic43—21no—
102C4×Dic43—42no—
103C4×Dic43—41no—
104C4×Dic43—41no—
105C2×C43⋊C8—41no—
106C23×C43—21no—
107C23×C43—21no—
108C23×C43—41no—
109C23×C43—41no—
110C23×C43C2×C22⋊C411yescharacteristic
111C23×C43#13711yescharacteristic
112C23×C43#13711yescharacteristic
113Q8×C43—42no—
114Q8×C43—42no—
115C2×C4×C43—22no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—41no—
119C2×C4×C43—41no—
120C2×C4×C43—41no—
121C2×C4×C43—41no—
122C2×C4×C43—41no—
123C2×C4×C43—41no—
124C2×C4×C43—41no—
125C2×C4×C43—81no—
126C2×C4×C43—81no—
127C2×C4×C43—81no—
128C2×Dic43—21no—
129C2×Dic43—21no—
130C2×Dic43—22no—
131C2×Dic43—21no—
132C2×Dic43—21no—
133C2×Dic43—21no—
134C2×Dic43—21no—
135C2×Dic43—21no—
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—41no—
145C2×Dic43—41no—
146C2×Dic43—41no—
147C2×Dic43—81no—
148C2×Dic43—81no—
149C2×Dic43—81no—
150C2×Dic43#9911yescharacteristic
151C2×Dic43#9911yescharacteristic
152C8×C43—81no—
153C43⋊C8—81no—
154#11810—431nomaximal, Sylow
155C22×C43—21no—
156C22×C43—21no—
157C22×C43—21no—
158C22×C43—21no—
159C22×C43—41no—
160C22×C43—41no—
161C22×C43—41no—
162C22×C43—41no—
163C22×C43—81no—
164C22×C43C2×#9911yescharacteristic
165C22×C43#41911yescharacteristic
166C22×C43#42111yescharacteristic
167C4×C43—42no—
168C4×C43—41no—
169C4×C43—41no—
170C4×C43—81no—
171C4×C43—161no—
172Dic43—21no—
173Dic43—21no—
174Dic43—42no—
175Dic43—41no—
176Dic43—41no—
177Dic43—41no—
178Dic43—81no—
179Dic43—161no—
180#2396—431no—
181#1820—431no—
182#1464—431no—
183#1352—431no—
184#1352—431no—
185#1351—431no—
186#1351D4311yescharacteristic
187C2×C43—21no—
188C2×C43—21no—
189C2×C43—41no—
190C2×C43—41no—
191C2×C43#151111yescharacteristic
192C2×C43#212011yescharacteristic
193C2×C43#212611yescharacteristic
194C2×C4×Q8—431no—
195C2×#117—431no—
196#432—861no—
197#400—431no—
198#399—431no—
199#398—861no—
200#396—861no—
201#395—431no—
202#393C2×D4311yescharacteristic
203#381—861no—
204C4×C4⋊C4—431no—
205C4×C4⋊C4—861no—
206C4×C22⋊C4—861no—
207#342—431no—
208#342—861no—
209#342C2×D4311yescharacteristic
210#324—861no—
211#323—431no—
212#323C2×D4311yescharacteristic
213C43#1181011yescharacteristic, complemented, Sylow
214C22×Q8C4×D4311yescharacteristic
215C23×C4—431no—
216C4×Q8—1721no—
217C4×Q8—1721no—
218#117—1721no—
219#117—1721no—
220C2×C4⋊C4—431no—
221C2×C4⋊C4—431no—
222C2×C4⋊C4—431no—
223C2×C4⋊C4—861no—
224C2×C4⋊C4—861no—
225C2×C4⋊C4—861no—
226C2×C4⋊C4—861no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4—21no—
229C2×C22⋊C4—431no—
230C2×C22⋊C4—861no—
231C2×C22⋊C4—861no—
232C2×C22⋊C4C22×D4311yescharacteristic
233C2×C42—431no—
234C2×C42—431no—
235C2×C42—861no—
236C2×C42—861no—
237C4⋊C8—1721no—
238C22⋊C8—21no—
239C22⋊C8—861no—
240#97—1721no—
241#95—21no—
242#95—431no—
243#95—861no—
244#95—861no—
245#95—861no—
246#95—1721no—
247#95—1721no—
248#95C4×D4311yescharacteristic
249C24D4×D4311yescharacteristic
250C2×Q8—42no—
251C2×Q8—41no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—41no—
255C22×C4—431no—
256C22×C4—431no—
257C22×C4—431no—
258C22×C4—431no—
259C22×C4—861no—
260C22×C4—861no—
261C22×C4—861no—
262C22×C4—861no—
263C22×C4—861no—
264C22×C4—861no—
265C22×C4—1721no—
266C22×C4—1721no—
267C22×C4C2×C4×D4311yescharacteristic
268C22×C4D4×D4311yescharacteristic
269C2×C8—41no—
270C2×C8—1721no—
271C4⋊C4—1721no—
272C4⋊C4—1721no—
273C4⋊C4—1721no—
274C4⋊C4—1722no—
275C4⋊C4—1722no—
276C4⋊C4—1722no—
277C4⋊C4—1722no—
278C22⋊C4—41no—
279C22⋊C4—42no—
280C22⋊C4—41no—
281C22⋊C4—41no—
282C22⋊C4—1721no—
283C22⋊C4—1722no—
284C22⋊C4—1721no—
285C22⋊C4—1721no—
286C42—861no—
287C42—861no—
288C42—861no—
289C42—861no—
290C42—1721no—
291C42—1721no—
292C42—1722no—
293C23—21no—
294C23—21no—
295C23—41no—
296C23—41no—
297C23C22⋊C4×D4311yescharacteristic
298C23#1306335411yescharacteristic
299C23#1306335711yescharacteristic
300Q8—42no—
301Q8—42no—
302C2×C4—22no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—431no—
316C2×C4—431no—
317C2×C4—861no—
318C2×C4—861no—
319C2×C4—862no—
320C2×C4—861no—
321C2×C4—861no—
322C2×C4—861no—
323C2×C4—861no—
324C2×C4—861no—
325C2×C4—3441no—
326C2×C4—3441no—
327C2×C4—3441no—
328C2×C4—1721no—
329C2×C4—1721no—
330C2×C4—1721no—
331C2×C4—1721no—
332C2×C4—1721no—
333C2×C4—1721no—
334C2×C4—1721no—
335C2×C4—1721no—
336C2×C4—1721no—
337C2×C4—1721no—
338C2×C4—1721no—
339C8—81no—
340C8—3441no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—81no—
350C22#99×D4311yescharacteristic
351C22#1458290611yescharacteristic
352C22#1458291411yescharacteristic
353C4—41no—
354C4—42no—
355C4—41no—
356C4—81no—
357C4—161no—
358C4—861no—
359C4—861no—
360C4—3441no—
361C4—1722no—
362C4—1721no—
363C4—1721no—
364C4—1721no—
365C4—6881no—
366C2—21no—
367C2—21no—
368C2—41no—
369C2—41no—
370C2#1913312611yescharacteristic
371C2#1913623311yescharacteristic
372C2#1913625911yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C22⋊C4C22×D43
FittingC43×#1351C2
socleC22×C43C2×#99
prime radicalC24×C43C2×D4
cosocleC2×C22⋊C4×C43C23
hypercenter#1351D43
hypocenterC43#11810
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1351

Complements

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

NH ≅ G/Ntype
8. C2×Q8×Dic43C4semidirect
11. #14582839C4semidirect
15. #14582818C4semidirect
18. #14582750C4semidirect
213. C43#11810semidirect

Maximal subgroups

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

subgroupindex
#191378622
#191346712
#191329262
#191326202
#191326182
#191326162
C43×#13512
#1181043