Finite Group Databasebeta

← #25006125

Subgroups — #25006125

Order 11008.

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

normal subgroups only

This group has 380 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#19138879C211yesmaximal, characteristic
2#19132926C211yesmaximal, characteristic
3#19132906C211yesmaximal, characteristic
4#19132544C211yesmaximal, characteristic
5#19132542C211yesmaximal, characteristic
6#19132525C211yesmaximal, characteristic
7C43×#1317C211yesmaximal, characteristic
8C2×#13063281C2211yescharacteristic
9C22×Dic43⋊C4C411yescharacteristic
10#14582953—21no—
11#14582949—21no—
12#14582840—21no—
13#14582833—21no—
14#14582782—21no—
15#14582781—21no—
16#14582774C411yescharacteristic
17#14582771C2211yescharacteristic
18#14582762C411yescharacteristic
19#14582760C411yescharacteristic
20#14582624—21no—
21#14582624—21no—
22#14582623C2211yescharacteristic
23#14582623C2211yescharacteristic
24C43×#381C2211yescharacteristic
25C43×#323C2211yescharacteristic
26C43×#323C2211yescharacteristic
27C23×Dic43C2×C411yescharacteristic
28C23×Dic43C2×C411yescharacteristic
29#13063281—41no—
30#13063281—41no—
31C2×C4⋊Dic43—21no—
32C2×Dic43⋊C4—21no—
33C2×Dic43⋊C4—21no—
34C2×Dic43⋊C4—21no—
35C2×Dic43⋊C4—41no—
36C2×Dic43⋊C4—41no—
37C2×Dic43⋊C4D411yescharacteristic
38C2×Dic43⋊C4D411yescharacteristic
39C2×C22⋊Dic43C2×C411yescharacteristic
40C2×C22⋊Dic43C2×C411yescharacteristic
41C2×C4×Dic43D411yescharacteristic
42C2×C4×Dic43D411yescharacteristic
43Dic43⋊C8—41no—
44Dic43⋊C8—41no—
45C22⋊(C43⋊C8)—21no—
46C22⋊(C43⋊C8)—21no—
47#13063235—41no—
48C8×Dic43—41no—
49C43⋊#95—21no—
50C43⋊#95—21no—
51C43⋊#95—21no—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C43⋊#95—21no—
55C23×C4×C43C2×C411yescharacteristic
56C2×C22⋊C4×C43C2×C411yescharacteristic
57C2×C22⋊C4×C43C2311yescharacteristic
58C22⋊C8×C43—21no—
59C22⋊C8×C43—21no—
60#95×C43—21no—
61#95×C43—21no—
62C24×C43C22×C411yescharacteristic
63C22×C4×C43—21no—
64C22×C4×C43—21no—
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43—41no—
68C22×C4×C43—41no—
69C22×C4×C43C2×D411yescharacteristic
70C22×C4×C43C2×D411yescharacteristic
71C22×Dic43—21no—
72C22×Dic43—21no—
73C22×Dic43—21no—
74C22×Dic43—21no—
75C22×Dic43—21no—
76C22×Dic43—21no—
77C22×Dic43—41no—
78C22×Dic43—41no—
79C22×Dic43—42no—
80C22×Dic43C22⋊C411yescharacteristic
81C22×Dic43C22⋊C411yescharacteristic
82C22×Dic43C22⋊C411yescharacteristic
83C22×Dic43C22⋊C411yescharacteristic
84C2×C8×C43—41no—
85C2×C8×C43—41no—
86C22⋊C4×C43—41no—
87C22⋊C4×C43—41no—
88C22⋊Dic43—21no—
89C22⋊Dic43—21no—
90C22⋊Dic43—41no—
91C4⋊Dic43—42no—
92Dic43⋊C4—41no—
93Dic43⋊C4—41no—
94Dic43⋊C4—42no—
95Dic43⋊C4—42no—
96Dic43⋊C4—41no—
97Dic43⋊C4—41no—
98C4×Dic43—21no—
99C4×Dic43—21no—
100C4×Dic43—21no—
101C4×Dic43—21no—
102C2×C43⋊C8—41no—
103C2×C43⋊C8—41no—
104C23×C43—21no—
105C23×C43—21no—
106C23×C43—41no—
107C23×C43—41no—
108C23×C43C2×C22⋊C411yescharacteristic
109C23×C43#13111yescharacteristic
110C23×C43#13111yescharacteristic
111C2×C4×C43—21no—
112C2×C4×C43—21no—
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—41no—
120C2×C4×C43—41no—
121C2×C4×C43—81no—
122C2×C4×C43—81no—
123C2×Dic43—21no—
124C2×Dic43—21no—
125C2×Dic43—22no—
126C2×Dic43—21no—
127C2×Dic43—21no—
128C2×Dic43—21no—
129C2×Dic43—21no—
130C2×Dic43—21no—
131C2×Dic43—41no—
132C2×Dic43—41no—
133C2×Dic43—41no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C2×Dic43—42no—
137C2×Dic43—41no—
138C2×Dic43—41no—
139C2×Dic43—41no—
140C2×Dic43—42no—
141C2×Dic43—41no—
142C2×Dic43—41no—
143C2×Dic43—41no—
144C2×Dic43#9911yescharacteristic
145C2×Dic43#9911yescharacteristic
146C8×C43—81no—
147C8×C43—81no—
148C43⋊C8—81no—
149C43⋊C8—81no—
150#11544—431nomaximal, Sylow
151C22×C43—21no—
152C22×C43—21no—
153C22×C43—21no—
154C22×C43—21no—
155C22×C43—41no—
156C22×C43—41no—
157C22×C43—42no—
158C22×C43—41no—
159C22×C43—41no—
160C22×C43#40811yescharacteristic
161C22×C43C2×#9911yescharacteristic
162C22×C43#41311yescharacteristic
163C4×C43—41no—
164C4×C43—41no—
165C4×C43—81no—
166C4×C43—81no—
167Dic43—21no—
168Dic43—21no—
169Dic43—41no—
170Dic43—42no—
171Dic43—41no—
172Dic43—41no—
173Dic43—81no—
174#2484—431no—
175#1464—431no—
176#1458—431no—
177#1326—431no—
178#1326—431no—
179#1317—431no—
180#1317D4311yescharacteristic
181C2×C43—21no—
182C2×C43—21no—
183C2×C43—41no—
184C2×C43—41no—
185C2×C43#146811yescharacteristic
186C2×C43#212011yescharacteristic
187C2×C43#212311yescharacteristic
188C2×#117—431no—
189C22×C4⋊C4—431no—
190#432—861no—
191#431—861no—
192#400—861no—
193#398—861no—
194#387—861no—
195#387—861no—
196#385—431no—
197#385—431no—
198#381—431no—
199#381—431no—
200#381C2×D4311yescharacteristic
201#324—861no—
202#324—861no—
203#323—431no—
204#323—431no—
205#323C2×D4311yescharacteristic
206#323C2×D4311yescharacteristic
207C43#1154411yescharacteristic, complemented, Sylow
208C23×C4—431no—
209C23×C4—431no—
210C23×C4C4×D4311yescharacteristic
211#117—1721no—
212#117—1721no—
213C2×C4⋊C4—431no—
214C2×C4⋊C4—431no—
215C2×C4⋊C4—861no—
216C2×C4⋊C4—861no—
217C2×C4⋊C4—861no—
218C2×C4⋊C4—861no—
219C2×C4⋊C4—1721no—
220C2×C4⋊C4—1721no—
221C2×C22⋊C4—431no—
222C2×C22⋊C4—431no—
223C2×C22⋊C4C4×D4311yescharacteristic
224C2×C22⋊C4C22×D4311yescharacteristic
225C2×C42—431no—
226C2×C42—431no—
227C4⋊C8—1721no—
228C4⋊C8—1721no—
229C22⋊C8—21no—
230C22⋊C8—21no—
231C22⋊C8—861no—
232C22⋊C8—861no—
233#97—1721no—
234C4×C8—1721no—
235#95—21no—
236#95—21no—
237#95—861no—
238#95—861no—
239#95—861no—
240#95—861no—
241#95—861no—
242#95—861no—
243C24C2×C4×D4311yescharacteristic
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—41no—
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—1722no—
262C22×C4—1721no—
263C22×C4D4×D4311yescharacteristic
264C22×C4D4×D4311yescharacteristic
265C2×C8—41no—
266C2×C8—41no—
267C2×C8—1721no—
268C2×C8—1721no—
269C4⋊C4—1721no—
270C4⋊C4—1721no—
271C4⋊C4—1721no—
272C4⋊C4—1721no—
273C4⋊C4—1722no—
274C4⋊C4—1722no—
275C4⋊C4—1722no—
276C22⋊C4—41no—
277C22⋊C4—41no—
278C22⋊C4—861no—
279C22⋊C4—861no—
280C22⋊C4—1721no—
281C42—861no—
282C42—861no—
283C42—861no—
284C42—861no—
285C23—21no—
286C23—21no—
287C23—41no—
288C23—41no—
289C23C22⋊C4×D4311yescharacteristic
290C23#1306333111yescharacteristic
291C23#1306333311yescharacteristic
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—81no—
303C2×C4—81no—
304C2×C4—431no—
305C2×C4—431no—
306C2×C4—861no—
307C2×C4—861no—
308C2×C4—862no—
309C2×C4—861no—
310C2×C4—861no—
311C2×C4—861no—
312C2×C4—861no—
313C2×C4—861no—
314C2×C4—1721no—
315C2×C4—1721no—
316C2×C4—1721no—
317C2×C4—1721no—
318C2×C4—1721no—
319C2×C4—1721no—
320C2×C4—1721no—
321C2×C4—1721no—
322C2×C4—1722no—
323C2×C4—1721no—
324C2×C4—1721no—
325C2×C4—1721no—
326C2×C4—1722no—
327C8—81no—
328C8—81no—
329C8—3441no—
330C8—3441no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—42no—
338C22—41no—
339C22—41no—
340C22#1458286411yescharacteristic
341C22#99×D4311yescharacteristic
342C22#1458288011yescharacteristic
343C4—41no—
344C4—41no—
345C4—81no—
346C4—81no—
347C4—861no—
348C4—861no—
349C4—3441no—
350C4—1721no—
351C4—1722no—
352C4—1721no—
353C4—1721no—
354C2—21no—
355C2—21no—
356C2—41no—
357C2—41no—
358C2#1913294011yescharacteristic
359C2#1913623511yescharacteristic
360C2#1913624711yescharacteristic
subgroupG/H
centerC22#99×D43
commutator, prime radicalC24×C43C22×C4
FrattiniC2×C22⋊C4C22×D43
FittingC43×#1317C2
socleC22×C43C2×#99
cosocleC2×C22⋊C4×C43C23
hypercenter#1317D43
hypocenterC43#11544
LCSG ▷ C24×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1317

Complements

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

NH ≅ G/Ntype
207. C43#11544semidirect

Maximal subgroups

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

subgroupindex
#191388792
#191329262
#191329062
#191325442
#191325422
#191325252
C43×#13172
#1154443