Finite Group Databasebeta

← #25007344

Subgroups — #25007344

Order 11008.

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

normal subgroups only

This group has 386 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#19140407C211yesmaximal, characteristic
2#19134674C211yesmaximal, characteristic
3#19132923C211yesmaximal, characteristic
4#19132625C211yesmaximal, characteristic, complemented
5#19132623C211yesmaximal, characteristic, complemented
6#19132621C211yesmaximal, characteristic, complemented
7C43×#1354C211yesmaximal, characteristic, complemented
8C2×#13063301C411yescharacteristic
9C2×C4⋊C4×D43C2211yescharacteristic
10#14582862—21no—
11#14582861—21no—
12#14582839C411yescharacteristic
13#14582838C2211yescharacteristic
14#14582833—21no—
15#14582830—21no—
16#14582818C411yescharacteristic
17#14582770—21no—
18#14582761—21no—
19#14582758C411yescharacteristic
20#14582668C2211yescharacteristic
21#14582667—21no—
22#14582625C2211yescharacteristic
23#14582624—21no—
24C43×#395C2211yescharacteristic
25C43×#343C2211yescharacteristic
26C43×#324C2211yescharacteristic
27C22×C4×D43C2×C411yescharacteristic
28C22×C4×D43D411yescharacteristic
29C22×C4×D43D411yescharacteristic
30C2×#10621877—21no—
31C2×#10621872—41no—
32#13063301—41no—
33#13063301—41no—
34C2×C4⋊Dic43C2×C411yescharacteristic
35C2×C4⋊Dic43D411yescharacteristic
36C2×Dic43⋊C4—21no—
37C2×Dic43⋊C4—21no—
38C2×Dic43⋊C4—21no—
39C2×Dic43⋊C4C2×C411yescharacteristic
40C2×Dic43⋊C4D411yescharacteristic
41C4⋊C4×D43—41no—
42C4⋊C4×D43—41no—
43C2×(C2×D43)⋊C4—21no—
44C2×(C2×D43)⋊C4—21no—
45C22⋊(C43⋊C8)—21no—
46(C2×D43)⋊C8—41no—
47(C2×D43)⋊C8—41no—
48(C2×D43)⋊C8—41no—
49C43⋊#95—21no—
50C43⋊#95—21no—
51C43⋊#95—21no—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C43⋊#95C2×C411yescharacteristic
55C22×Q8×C43C2×C411yescharacteristic
56C2×M16×C43—21no—
57C2×C4⋊C4×C43—21no—
58C2×C4⋊C4×C43C2311yescharacteristic
59C22⋊C8×C43—21no—
60#95×C43—21no—
61#95×C43C2×C411yescharacteristic
62C23×D43C22⋊C411yescharacteristic
63C2×Q8×C43—41no—
64C2×Q8×C43—81no—
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43C22×C411yescharacteristic
68C22×C4×C43C2×D411yescharacteristic
69C22×C4×C43C2×D411yescharacteristic
70C22×Dic43—21no—
71C22×Dic43—21no—
72C22×Dic43C22⋊C411yescharacteristic
73C22×Dic43C22⋊C411yescharacteristic
74C22×Dic43C22⋊C411yescharacteristic
75C2×C4×D43—21no—
76C2×C4×D43—21no—
77C2×C4×D43—21no—
78C2×C4×D43—21no—
79C2×C4×D43—21no—
80C2×C4×D43—21no—
81C2×C4×D43—21no—
82C2×C4×D43—21no—
83C2×C4×D43—41no—
84C2×C4×D43—81no—
85C2×C4×D43—81no—
86M16×C43—41no—
87M16×C43—41no—
88C2×C8×C43—41no—
89C2×C8×C43—41no—
90C4⋊C4×C43—41no—
91C4⋊C4×C43—81no—
92(C2×D43)⋊C4—42no—
93(C2×D43)⋊C4—41no—
94(C2×D43)⋊C4—41no—
95C4⋊Dic43—41no—
96C4⋊Dic43—41no—
97Dic43⋊C4—41no—
98Dic43⋊C4—41no—
99Dic43⋊C4—42no—
100Dic43⋊C4—81no—
101Dic43⋊C4—81no—
102#10621877—41no—
103#10621877—41no—
104C2×C43⋊C8—41no—
105C2×C43⋊C8—41no—
106#10621872—82no—
107C23×C43C2×C22⋊C411yescharacteristic
108C22×D43—21no—
109C22×D43—21no—
110C22×D43—41no—
111C22×D43—41no—
112C22×D43#9911yescharacteristic
113C22×D43#9911yescharacteristic
114Q8×C43—82no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
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—41no—
126C2×C4×C43—41no—
127C2×C4×C43#13711yescharacteristic
128C2×C4×C43#13711yescharacteristic
129C2×Dic43—21no—
130C2×Dic43—21no—
131C2×Dic43—21no—
132C2×Dic43—21no—
133C2×Dic43—21no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137C2×Dic43—41no—
138C2×Dic43—42no—
139C2×Dic43—41no—
140C2×Dic43—41no—
141C4×D43—41no—
142C4×D43—41no—
143C4×D43—41no—
144C4×D43—41no—
145C4×D43—42no—
146C4×D43—81no—
147C4×D43—81no—
148C4×D43—81no—
149C8×C43—81no—
150C8×C43—81no—
151C43⋊C8—81no—
152C43⋊C8—81no—
153#11817—431nomaximal, Sylow
154C22×C43—21no—
155C22×C43—21no—
156C22×C43C2×#9911yescharacteristic
157C22×C43#41911yescharacteristic
158C22×C43#42111yescharacteristic
159C2×D43—21no—
160C2×D43—21no—
161C2×D43—21no—
162C2×D43—21no—
163C2×D43—21no—
164C2×D43—21no—
165C2×D43—42no—
166C2×D43—42no—
167C4×C43—21no—
168C4×C43—21no—
169C4×C43—41no—
170C4×C43—41no—
171C4×C43—81no—
172C4×C43—81no—
173Dic43—41no—
174Dic43—41no—
175Dic43—41no—
176Dic43—81no—
177Dic43—81no—
178#2627—431no—
179#1821—431no—
180#1463—431no—
181#1354—431no—
182#1354D4311yescharacteristic, complemented
183#1353—431no—
184#1353—431no—
185C2×C43—21no—
186C2×C43—21no—
187C2×C43#151111yescharacteristic
188C2×C43#212111yescharacteristic
189C2×C43#213311yescharacteristic
190D43—41no—
191D43—41no—
192C2×C22⋊Q8—431no—
193C22×C4⋊C4—431no—
194#407—861no—
195#407—861no—
196#400—431no—
197#400—431no—
198#398—861no—
199#398—861no—
200#395—431no—
201#395C2×D4311yescharacteristic
202#385—861no—
203#381—861no—
204#380—431no—
205#343—431no—
206#343—861no—
207#343C2×D4311yescharacteristic
208#324—431no—
209#324—861no—
210#324C2×D4311yescharacteristic
211C43#1181711yescharacteristic, complemented, Sylow
212C22×Q8C4×D4311yescharacteristic
213C23×C4—431no—
214C23×C4—431no—
215C23×C4—431no—
216C2×M16—21no—
217C2×M16—861no—
218C2×M16—1721no—
219C22⋊Q8—1721no—
220C22⋊Q8—1721no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—431no—
223C2×C4⋊C4—431no—
224C2×C4⋊C4—431no—
225C2×C4⋊C4—431no—
226C2×C4⋊C4—861no—
227C2×C4⋊C4—861no—
228C2×C4⋊C4—861no—
229C2×C4⋊C4—1721no—
230C2×C4⋊C4—1721no—
231C2×C4⋊C4C22×D4311yescharacteristic
232C2×C22⋊C4—861no—
233C2×C22⋊C4—861no—
234C22⋊C8—21no—
235C22⋊C8—861no—
236C22⋊C8—1721no—
237C22⋊C8—1721no—
238C22⋊C8—1721no—
239#95—21no—
240#95—431no—
241#95—861no—
242#95—861no—
243#95—861no—
244#95—861no—
245#95—861no—
246#95C4×D4311yescharacteristic
247C24—431no—
248C2×Q8—41no—
249C2×Q8—81no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—431no—
253C22×C4—431no—
254C22×C4—431no—
255C22×C4—861no—
256C22×C4—861no—
257C22×C4—861no—
258C22×C4—861no—
259C22×C4—861no—
260C22×C4—861no—
261C22×C4—861no—
262C22×C4—861no—
263C22×C4—861no—
264C22×C4—861no—
265C22×C4—3441no—
266C22×C4—3441no—
267C22×C4—1721no—
268C22×C4C2×C4×D4311yescharacteristic
269C22×C4D4×D4311yescharacteristic
270C22×C4D4×D4311yescharacteristic
271M16—41no—
272M16—41no—
273M16—3442no—
274M16—1721no—
275M16—1721no—
276C2×C8—41no—
277C2×C8—41no—
278C2×C8—1721no—
279C2×C8—1721no—
280C4⋊C4—41no—
281C4⋊C4—81no—
282C4⋊C4—3441no—
283C4⋊C4—3441no—
284C4⋊C4—1721no—
285C4⋊C4—1721no—
286C4⋊C4—1721no—
287C4⋊C4—1721no—
288C4⋊C4—1722no—
289C22⋊C4—1721no—
290C22⋊C4—1721no—
291C22⋊C4—1722no—
292C23—431no—
293C23—431no—
294C23—861no—
295C23—861no—
296C23—1721no—
297C23—1721no—
298C23C22⋊C4×D4311yescharacteristic
299Q8—82no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—861no—
313C2×C4—861no—
314C2×C4—861no—
315C2×C4—861no—
316C2×C4—861no—
317C2×C4—3441no—
318C2×C4—3441no—
319C2×C4—3441no—
320C2×C4—1721no—
321C2×C4—1721no—
322C2×C4—1721no—
323C2×C4—1721no—
324C2×C4—1722no—
325C2×C4—1721no—
326C2×C4—1721no—
327C2×C4—1722no—
328C2×C4—1721no—
329C2×C4—1721no—
330C2×C4—1721no—
331C2×C4—1721no—
332C2×C4#1306335411yescharacteristic
333C2×C4#1306335711yescharacteristic
334C8—81no—
335C8—81no—
336C8—3441no—
337C8—3441no—
338C22—21no—
339C22—21no—
340C22—861no—
341C22—861no—
342C22—861no—
343C22—861no—
344C22—861no—
345C22—861no—
346C22—1722no—
347C22—1722no—
348C22#99×D4311yescharacteristic
349C22#1458290611yescharacteristic
350C22#1458291411yescharacteristic
351C4—21no—
352C4—21no—
353C4—41no—
354C4—41no—
355C4—81no—
356C4—81no—
357C4—3441no—
358C4—3441no—
359C4—1721no—
360C4—1721no—
361C4—1721no—
362C2—21no—
363C2—21no—
364C2—1721no—
365C2—1721no—
366C2#1913312611yescharacteristic
367C2#1913623811yescharacteristic
368C2#1913628311yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1354C2
socleC22×C43C2×#99
prime radicalC23×D43C22⋊C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1354D43
hypocenterC43#11817
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1354

Complements

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

NH ≅ G/Ntype
4. #19132625C2semidirect
5. #19132623C2semidirect
6. #19132621C2semidirect
7. C43×#1354C2semidirect
182. #1354D43semidirect
211. C43#11817semidirect

Maximal subgroups

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

subgroupindex
#191404072
#191346742
#191329232
#191326252
#191326232
#191326212
C43×#13542
#1181743