Finite Group Databasebeta

← #25006992

Subgroups — #25006992

Order 11008.

420 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 83 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#19140512C211yesmaximal, characteristic
2C4×#13063242C211yesmaximal, characteristic
3#19132626C212yesmaximal, complemented
4#19132602C212yesmaximal, complemented
5C43×#1459C211yesmaximal, characteristic
6C2×#13063304C411yescharacteristic
7C2×#13063242—21no—
8C4×#10621877—21no—
9#14582829C2211yescharacteristic
10#14582827—21no—
11#14582824C411yescharacteristic
12#14582819C2211yescharacteristic
13#14582813—21no—
14#14582811C411yescharacteristic
15#14582783—21no—
16#14582772—21no—
17#14582762C411yescharacteristic
18#14582668C2212yes—
19C2×C4×D4×C43C2211yescharacteristic
20C2×C22⋊C8×C43—21no—
21C43×#324C2212yes—
22C43×#323—21no—
23C22×Dic86C2×C411yescharacteristic
24C2×#10621877—22no—
25#13063304—41no—
26#13063304—41no—
27C2×C4⋊Dic43C2×C411yescharacteristic
28C2×Dic43⋊C4—21no—
29C2×Dic43⋊C4—21no—
30C2×Dic43⋊C4—21no—
31C2×C22⋊Dic43—21no—
32C2×C22⋊Dic43—21no—
33C2×C22⋊Dic43—21no—
34C2×C22⋊Dic43—21no—
35#13063242—24no—
36#13063236—41no—
37C4×C43⋊C8—41no—
38C43⋊#95—21no—
39C43⋊#95—21no—
40C43⋊#95—21no—
41C43⋊#95—21no—
42C43⋊#95—21no—
43C43⋊#95C2×C411yescharacteristic
44C43⋊#95C2×C411yescharacteristic
45C22×D4×C43D411yescharacteristic
46C23×C4×C43C2×C411yescharacteristic
47C23×C4×C43D411yescharacteristic
48C22×C8×C43—41no—
49C4×D4×C43—41no—
50C4×D4×C43—41no—
51C2×C4⋊C4×C43C2311yescharacteristic
52C2×C22⋊C4×C43C2×C411yescharacteristic
53C2×C22⋊C4×C43D411yescharacteristic
54C2×C42×C43D411yescharacteristic
55C22⋊C8×C43—22no—
56C22⋊C8×C43—41no—
57C24×C43C22⋊C411yescharacteristic
58C24×C43C22⋊C411yescharacteristic
59C2×D4×C43—22no—
60C2×D4×C43—22no—
61C2×D4×C43—41no—
62C22×C4×C43—21no—
63C22×C4×C43—21no—
64C22×C4×C43—21no—
65C22×C4×C43—21no—
66C22×C4×C43—81no—
67C22×C4×C43—81no—
68C22×C4×C43C22⋊C411yescharacteristic
69C22×C4×C43C22⋊C411yescharacteristic
70C22×C4×C43C22×C411yescharacteristic
71C22×C4×C43C2×D411yescharacteristic
72C22×C4×C43C2×D411yescharacteristic
73C22×Dic43—21no—
74C22×Dic43—21no—
75C22×Dic43—21no—
76C22×Dic43—21no—
77C2×Dic86—41no—
78C2×Dic86—81no—
79C2×C8×C43—42no—
80C2×C8×C43—82no—
81C4⋊C4×C43—41no—
82C22⋊C4×C43—41no—
83C22⋊C4×C43—41no—
84C42×C43—21no—
85C42×C43—21no—
86C22⋊Dic43—42no—
87C22⋊Dic43—42no—
88C22⋊Dic43—81no—
89C22⋊Dic43—81no—
90C4⋊Dic43—41no—
91Dic43⋊C4—41no—
92Dic43⋊C4—41no—
93Dic43⋊C4—42no—
94Dic43⋊C4—81no—
95#10621877—24no—
96#10621877—42no—
97C2×C43⋊C8—42no—
98C23×C43—21no—
99C23×C43—21no—
100C23×C43—21no—
101C23×C43—21no—
102C23×C43—21no—
103C23×C43—41no—
104C23×C43—41no—
105C23×C43—41no—
106C23×C43—41no—
107C23×C43#10412yes—
108C23×C43C2×C22⋊C411yescharacteristic
109D4×C43—44no—
110C2×C4×C43—21no—
111C2×C4×C43—21no—
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—41no—
116C2×C4×C43—42no—
117C2×C4×C43—41no—
118C2×C4×C43—41no—
119C2×C4×C43—41no—
120C2×C4×C43—81no—
121C2×C4×C43—81no—
122C2×C4×C43—81no—
123C2×C4×C43#9911yescharacteristic
124C2×C4×C43#9911yescharacteristic
125C2×C4×C43#13512yes—
126C2×Dic43—41no—
127C2×Dic43—41no—
128C2×Dic43—41no—
129C2×Dic43—41no—
130C2×Dic43—41no—
131C2×Dic43—41no—
132C2×Dic43—41no—
133C2×Dic43—41no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137C2×Dic43—41no—
138Dic86—82no—
139C8×C43—82no—
140C43⋊C8—44no—
141#11739—431nomaximal, Sylow
142C22×C43—21no—
143C22×C43—21no—
144C22×C43—22no—
145C22×C43—42no—
146C22×C43—41no—
147C22×C43—41no—
148C22×C43—41no—
149C22×C43—41no—
150C22×C43—41no—
151C22×C43—81no—
152C22×C43—81no—
153C22×C43—81no—
154C22×C43C2×#9911yescharacteristic
155C22×C43#41611yescharacteristic
156C22×C43C2×#10411yescharacteristic
157C4×C43—21no—
158C4×C43—21no—
159C4×C43—22no—
160C4×C43—41no—
161C4×C43—41no—
162C4×C43—41no—
163Dic43—81no—
164Dic43—81no—
165Dic43—81no—
166Dic43—81no—
167#2638—431no—
168C4×#100—431no—
169#1459D4311yescharacteristic
170#1354—432no—
171#1346—432no—
172C2×C43—21no—
173C2×C43—21no—
174C2×C43—42no—
175C2×C43—81no—
176C2×C43#150111yescharacteristic
177C2×C43#212111yescharacteristic
178C2×C43#213511yescharacteristic
179C2×C22⋊Q8—431no—
180C2×C4×D4C2×D4311yescharacteristic
181C2×#100—861no—
182C2×C22⋊C8—21no—
183C4×M16—861no—
184#398—431no—
185#397—431no—
186#397—861no—
187#395—431no—
188#394—861no—
189#393—431no—
190#387—861no—
191#385—861no—
192#381—431no—
193#343—432no—
194#324C2×D4312yes—
195#323—21no—
196C43#1173911yescharacteristic, complemented, Sylow
197C22×Q8—431no—
198C22×D4D17211yescharacteristic
199C23×C4C4×D4311yescharacteristic
200C23×C4C22⋊D4311yescharacteristic
201C2×M16—862no—
202C22×C8—41no—
203C22⋊Q8—1721no—
204C22⋊Q8—1721no—
205C4×D4—41no—
206C4×D4—41no—
207C2×C4⋊C4—431no—
208C2×C4⋊C4—861no—
209C2×C4⋊C4—861no—
210C2×C4⋊C4—861no—
211C2×C4⋊C4C22×D4311yescharacteristic
212C2×C22⋊C4—861no—
213C2×C22⋊C4—861no—
214C2×C22⋊C4—861no—
215C2×C22⋊C4—861no—
216C2×C22⋊C4C4×D4311yescharacteristic
217C2×C22⋊C4C22⋊D4311yescharacteristic
218C2×C42D17211yescharacteristic
219#100—864no—
220C22⋊C8—22no—
221C22⋊C8—41no—
222#97—1721no—
223C4×C8—1721no—
224#95—431no—
225#95—431no—
226#95—861no—
227#95—861no—
228#95—861no—
229#95—861no—
230#95—861no—
231C24(C2×D43)⋊C411yescharacteristic
232C24(C2×D43)⋊C411yescharacteristic
233C2×Q8—3441no—
234C2×Q8—1721no—
235C2×D4—22no—
236C2×D4—22no—
237C2×D4—41no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—81no—
243C22×C4—81no—
244C22×C4—861no—
245C22×C4—861no—
246C22×C4—861no—
247C22×C4—861no—
248C22×C4(C2×D43)⋊C411yescharacteristic
249C22×C4(C2×D43)⋊C411yescharacteristic
250C22×C4C2×C4×D4311yescharacteristic
251C22×C4C2×D17211yescharacteristic
252C22×C4C2×C22⋊D4311yescharacteristic
253M16—864no—
254M16—1722no—
255C2×C8—42no—
256C2×C8—82no—
257C2×C8—1722no—
258C4⋊C4—41no—
259C4⋊C4—3441no—
260C4⋊C4—1721no—
261C4⋊C4—1721no—
262C4⋊C4—1721no—
263C4⋊C4—1722no—
264C22⋊C4—41no—
265C22⋊C4—41no—
266C22⋊C4—3441no—
267C22⋊C4—3441no—
268C22⋊C4—1722no—
269C22⋊C4—1722no—
270C42—21no—
271C42—21no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—41no—
278C23—41no—
279C23—41no—
280C23—41no—
281C23#1306325112yes—
282C23C2×(C2×D43)⋊C411yescharacteristic
283Q8—3442no—
284D4—44no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—41no—
291C2×C4—42no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—81no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—1721no—
299C2×C4—1721no—
300C2×C4—1721no—
301C2×C4—1721no—
302C2×C4—1721no—
303C2×C4—1721no—
304C2×C4—1721no—
305C2×C4—1721no—
306C2×C4—1721no—
307C2×C4—1721no—
308C2×C4—1721no—
309C2×C4—1721no—
310C2×C4#1306323911yescharacteristic
311C2×C4#1306323911yescharacteristic
312C2×C4#1306334712yes—
313C8—82no—
314C8—1724no—
315C22—21no—
316C22—21no—
317C22—22no—
318C22—42no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—81no—
325C22—81no—
326C22—81no—
327C22C2×#1306323911yescharacteristic
328C22#1458289611yescharacteristic
329C22C2×#1306325111yescharacteristic
330C4—22no—
331C4—21no—
332C4—21no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—3441no—
337C4—3441no—
338C4—3441no—
339C4—3441no—
340C2—21no—
341C2—21no—
342C2—42no—
343C2—81no—
344C2#1913308711yescharacteristic
345C2#1913623911yescharacteristic
346C2#1913628911yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1459C2
socleC22×C43C2×#99
prime radicalC22×D4×C43D4
cosocleC2×C4⋊C4×C43C23
hypercenter#1459D43
hypocenterC43#11739
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1459

Complements

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

NH ≅ G/Ntype
3. #19132626C2semidirect
4. #19132602C2semidirect
196. C43#11739semidirect

Maximal subgroups

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

subgroupindex
#191405122
C4×#130632422
#191326262
#191326022
C43×#14592
#1173943