Finite Group Databasebeta

← #25007720

Subgroups — #25007720

Order 11008.

580 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 580 conjugacy classes of subgroups — too many to draw. Only its 99 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#19137960C211yesmaximal, characteristic
2#19132916C211yesmaximal, characteristic
3#19132615C214yesmaximal, complemented
4C43×#1799C211yesmaximal, characteristic
5C23×Dic86C411yescharacteristic, complemented
6C2×#13063304—21no—
7#14582952—21no—
8#14582819C412yescomplemented
9#14582811C2212yes—
10#14582805—21no—
11#14582779—21no—
12#14582771—21no—
13#14582759C411yescharacteristic, complemented
14#14582623—21no—
15#14582623C2212yes—
16C2×C4×D4×C43C2211yescharacteristic
17C2×#99×C43—21no—
18C43×#380—21no—
19C43×#342C2212yes—
20C22×Dic86—21no—
21C22×Dic86—44no—
22C22×Dic86—41no—
23C22×Dic86—41no—
24C22×Dic86C2×C412yes—
25C23×Dic43—21no—
26#13063304—44no—
27C2×C4⋊Dic43—21no—
28C2×Dic43⋊C4—22no—
29C2×C22⋊Dic43—21no—
30C2×C22⋊Dic43—22no—
31C4⋊(C43⋊C8)—41no—
32C22⋊(C43⋊C8)—22no—
33C4×C43⋊C8—41no—
34C43⋊#95—22no—
35C43⋊#95—22no—
36C43⋊#95C2×C412yes—
37C22×D4×C43D411yescharacteristic
38C23×C4×C43C2×C411yescharacteristic
39C23×C4×C43D411yescharacteristic
40C4×D4×C43—41no—
41C4×D4×C43—41no—
42C2×C4⋊C4×C43—41no—
43C2×C4⋊C4×C43C2×C411yescharacteristic
44C2×C22⋊C4×C43—22no—
45C2×C22⋊C4×C43D411yescharacteristic
46C2×C22⋊C4×C43C2311yescharacteristic
47C2×C42×C43D411yescharacteristic
48#99×C43—42no—
49#95×C43—41no—
50C24×C43C22⋊C411yescharacteristic
51C24×C43C2×D411yescharacteristic
52C2×D4×C43—41no—
53C2×D4×C43—41no—
54C2×D4×C43SD1612yes—
55C2×D4×C43Q1612yes—
56C22×C4×C43—21no—
57C22×C4×C43—21no—
58C22×C4×C43—21no—
59C22×C4×C43—21no—
60C22×C4×C43—42no—
61C22×C4×C43—42no—
62C22×C4×C43—42no—
63C22×C4×C43C22⋊C411yescharacteristic
64C22×C4×C43C22⋊C411yescharacteristic
65C22×C4×C43C22⋊C411yescharacteristic
66C22×C4×C43C22×C411yescharacteristic
67C22×C4×C43C2×D411yescharacteristic
68C22×Dic43—22no—
69C22×Dic43—22no—
70C22×Dic43—42no—
71C22×Dic43—44no—
72C2×Dic86—24no—
73C2×Dic86—42no—
74C2×Dic86—48no—
75C2×Dic86—44no—
76C2×Dic86—41no—
77C2×Dic86—41no—
78C2×Dic86—42no—
79C2×Dic86—44no—
80C2×Dic86—44no—
81C4⋊C4×C43—41no—
82C4⋊C4×C43—82no—
83C22⋊C4×C43—41no—
84C22⋊C4×C43—41no—
85C22⋊C4×C43—42no—
86C22⋊C4×C43—42no—
87C42×C43—21no—
88C42×C43—21no—
89C22⋊Dic43—42no—
90C22⋊Dic43—44no—
91C4⋊Dic43—42no—
92Dic43⋊C4—44no—
93C2×C43⋊C8—42no—
94C23×C43—21no—
95C23×C43—21no—
96C23×C43—21no—
97C23×C43—21no—
98C23×C43—41no—
99C23×C43—41no—
100C23×C43—41no—
101C23×C43—41no—
102C23×C43#10312yes—
103C23×C43C2×C22⋊C411yescharacteristic
104C23×C43C2×SD1611yescharacteristic
105C23×C43C2×Q1611yescharacteristic
106D4×C43—42no—
107D4×C43—42no—
108C2×C4×C43—21no—
109C2×C4×C43—21no—
110C2×C4×C43—22no—
111C2×C4×C43—21no—
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—42no—
115C2×C4×C43—42no—
116C2×C4×C43—42no—
117C2×C4×C43—41no—
118C2×C4×C43—41no—
119C2×C4×C43—41no—
120C2×C4×C43—81no—
121C2×C4×C43—82no—
122C2×C4×C43—82no—
123C2×C4×C43—82no—
124C2×C4×C43#9911yescharacteristic
125C2×C4×C43#9911yescharacteristic
126C2×C4×C43#10312yes—
127C2×Dic43—24no—
128C2×Dic43—42no—
129C2×Dic43—48no—
130C2×Dic43—42no—
131C2×Dic43—42no—
132C2×Dic43—42no—
133C2×Dic43—42no—
134Dic86—44no—
135Dic86—44no—
136Dic86—44no—
137Dic86—44no—
138C43⋊C8—82no—
139#11898—431nomaximal, Sylow
140C22×C43—21no—
141C22×C43—21no—
142C22×C43—22no—
143C22×C43—21no—
144C22×C43—21no—
145C22×C43—42no—
146C22×C43—41no—
147C22×C43—41no—
148C22×C43—42no—
149C22×C43—41no—
150C22×C43—41no—
151C22×C43—41no—
152C22×C43—41no—
153C22×C43—81no—
154C22×C43C2×#9911yescharacteristic
155C22×C43C2×#10311yescharacteristic
156C22×C43#42111yescharacteristic
157C4×C43—21no—
158C4×C43—22no—
159C4×C43—41no—
160C4×C43—41no—
161C4×C43—41no—
162C4×C43—162no—
163C4×C43AΣL(1,𝔽16)12yes—
164Dic43—44no—
165Dic43—82no—
166#2409—431no—
167#1799D4311yescharacteristic
168#1460—431no—
169#1351—434no—
170C2×C43—21no—
171C2×C43—21no—
172C2×C43—41no—
173C2×C43—42no—
174C2×C43—41no—
175C2×C43#152011yescharacteristic
176C2×C43C2×AΣL(1,𝔽16)11yescharacteristic
177C2×C43#212911yescharacteristic
178C23×Q8—431no—
179C2×C22⋊Q8—861no—
180C2×C4×D4C2×D4311yescharacteristic
181#431—861no—
182C2×#99—21no—
183#395—432no—
184#393—432no—
185#391—861no—
186#386—861no—
187#385—861no—
188#380—21no—
189#380—431no—
190#342C2×D4312yes—
191#323—432no—
192#323—861no—
193C43#1189811yescharacteristic, complemented, Sylow
194C22×Q8—432no—
195C22×Q8—861no—
196C22×Q8—1721no—
197C22×Q8—1721no—
198C22×Q8—1724no—
199C22×D4C22⋊D4311yescharacteristic
200C23×C4—861no—
201C23×C4C4×D4311yescharacteristic
202C23×C4C22⋊D4311yescharacteristic
203C22⋊Q8—1724no—
204C4×D4—41no—
205C4×D4—41no—
206C2×C4⋊C4—41no—
207C2×C4⋊C4—862no—
208C2×C4⋊C4—861no—
209C2×C4⋊C4C4×D4311yescharacteristic
210C2×C22⋊C4—22no—
211C2×C22⋊C4—861no—
212C2×C22⋊C4—862no—
213C2×C22⋊C4D17211yescharacteristic
214C2×C22⋊C4C22×D4311yescharacteristic
215C2×C42D17211yescharacteristic
216C4⋊C8—1721no—
217#99—42no—
218C22⋊C8—862no—
219C4×C8—1721no—
220#95—41no—
221#95—432no—
222#95—862no—
223#95—862no—
224C24(C2×D43)⋊C411yescharacteristic
225C24C2×C22⋊D4311yescharacteristic
226C2×Q8—864no—
227C2×Q8—1722no—
228C2×Q8—1722no—
229C2×Q8—1724no—
230C2×Q8—1724no—
231C2×Q8—1728no—
232C2×Q8—1724no—
233C2×Q8—1721no—
234C2×Q8—1721no—
235C2×D4—41no—
236C2×D4—41no—
237C2×D4#1062188312yes—
238C2×D4#1062188512yes—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—42no—
244C22×C4—42no—
245C22×C4—42no—
246C22×C4—862no—
247C22×C4—862no—
248C22×C4—1724no—
249C22×C4—1722no—
250C22×C4(C2×D43)⋊C411yescharacteristic
251C22×C4(C2×D43)⋊C411yescharacteristic
252C22×C4(C2×D43)⋊C411yescharacteristic
253C22×C4C2×C4×D4311yescharacteristic
254C22×C4C2×D17211yescharacteristic
255C2×C8—1722no—
256C4⋊C4—41no—
257C4⋊C4—82no—
258C4⋊C4—1722no—
259C4⋊C4—1724no—
260C22⋊C4—41no—
261C22⋊C4—41no—
262C22⋊C4—42no—
263C22⋊C4—42no—
264C22⋊C4—1724no—
265C22⋊C4—1722no—
266C42—21no—
267C42—21no—
268C23—21no—
269C23—21no—
270C23—21no—
271C23—21no—
272C23—41no—
273C23—41no—
274C23—41no—
275C23—41no—
276C23#1306324812yes—
277C23C2×(C2×D43)⋊C411yescharacteristic
278C23C2×#1062188311yescharacteristic
279C23C2×#1062188511yescharacteristic
280Q8—1724no—
281Q8—1724no—
282Q8—1724no—
283Q8—1724no—
284D4—42no—
285D4—42no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—22no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—81no—
299C2×C4—82no—
300C2×C4—82no—
301C2×C4—82no—
302C2×C4—864no—
303C2×C4—1722no—
304C2×C4—1722no—
305C2×C4—1722no—
306C2×C4—1722no—
307C2×C4—1728no—
308C2×C4—1722no—
309C2×C4#1306323911yescharacteristic
310C2×C4#1306323911yescharacteristic
311C2×C4#1306324812yes—
312C8—3442no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—22no—
317C22—21no—
318C22—42no—
319C22—41no—
320C22—41no—
321C22—42no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—81no—
327C22C2×#1306323911yescharacteristic
328C22C2×#1306324811yescharacteristic
329C22#1458291711yescharacteristic
330C4—21no—
331C4—22no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—162no—
336C4—3442no—
337C4—1724no—
338C4#1458268512yes—
339C2—21no—
340C2—21no—
341C2—41no—
342C2—42no—
343C2—41no—
344C2#1913316611yescharacteristic
345C2C2×#1458268511yescharacteristic
346C2#1913626911yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C22⋊C4C22×D43
FittingC43×#1799C2
socleC22×C43C2×#99
prime radicalC22×D4×C43D4
cosocleC2×C22⋊C4×C43C23
hypercenter#1799D43
hypocenterC43#11898
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1799

Complements

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

NH ≅ G/Ntype
3. #19132615C2semidirect
5. C23×Dic86C4semidirect
8. #14582819C4semidirect
13. #14582759C4semidirect
193. C43#11898semidirect

Maximal subgroups

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

subgroupindex
#191379602
#191329162
#191326152
C43×#17992
#1189843