Finite Group Databasebeta

← #25006181

Subgroups — #25006181

Order 11008.

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

normal subgroups only

This group has 414 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#19139069C211yesmaximal, characteristic
2#19132925C211yesmaximal, characteristic
3#19132540C212yesmaximal, complemented
4#19132528C212yesmaximal, complemented
5C2×C43×#324C211yesmaximal, characteristic
6C2×#13063304C411yescharacteristic
7#14582863—21no—
8#14582830—21no—
9#14582830—21no—
10#14582804C411yescharacteristic
11#14582804C2211yescharacteristic
12#14582772—21no—
13#14582772—21no—
14#14582768C411yescharacteristic
15#14582768C2211yescharacteristic
16C4×C22⋊Dic43C411yescharacteristic
17#14582625—21no—
18#14582625C2212yes—
19C22×C4⋊C4×C43C2211yescharacteristic
20C2×C22⋊C8×C43—21no—
21C43×#324—21no—
22C43×#324C2212yes—
23C22×Dic86C2×C411yescharacteristic
24C2×#10621877—41no—
25#13063304—41no—
26#13063304—41no—
27C2×C4⋊Dic43C2×C411yescharacteristic
28C2×Dic43⋊C4—21no—
29C2×Dic43⋊C4—21no—
30C2×Dic43⋊C4—21no—
31C2×Dic43⋊C4—21no—
32C2×Dic43⋊C4—21no—
33C2×C22⋊Dic43—21no—
34C2×C22⋊Dic43—21no—
35C2×C4×Dic43C2×C411yescharacteristic
36C2×C4×Dic43C2×C411yescharacteristic
37C22⋊(C43⋊C8)—22no—
38C22⋊(C43⋊C8)—41no—
39C43⋊#95—21no—
40C43⋊#95—21no—
41C43⋊#95—21no—
42C43⋊#95—21no—
43C43⋊#95—21no—
44C23×C4×C43C2×C411yescharacteristic
45C23×C4×C43D411yescharacteristic
46C23×C4×C43D411yescharacteristic
47C22×C8×C43—41no—
48C2×C4⋊C4×C43—41no—
49C2×C4⋊C4×C43—41no—
50C2×C4⋊C4×C43C2×C411yescharacteristic
51C2×C4⋊C4×C43D411yescharacteristic
52C2×C4⋊C4×C43D411yescharacteristic
53C2×C4⋊C4×C43C2311yescharacteristic
54C22⋊C8×C43—22no—
55C22⋊C8×C43—41no—
56C24×C43C22⋊C411yescharacteristic
57C22×C4×C43—22no—
58C22×C4×C43—21no—
59C22×C4×C43—21no—
60C22×C4×C43—21no—
61C22×C4×C43—21no—
62C22×C4×C43—21no—
63C22×C4×C43—21no—
64C22×C4×C43—41no—
65C22×C4×C43—81no—
66C22×C4×C43—81no—
67C22×C4×C43C22⋊C411yescharacteristic
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—22no—
78C2×Dic86—41no—
79C2×Dic86—41no—
80C2×C8×C43—42no—
81C2×C8×C43—82no—
82C4⋊C4×C43—41no—
83C4⋊C4×C43—41no—
84C4⋊C4×C43—41no—
85C4⋊C4×C43—41no—
86C22⋊Dic43—24no—
87C22⋊Dic43—41no—
88C22⋊Dic43—41no—
89C4⋊Dic43—41no—
90Dic43⋊C4—42no—
91Dic43⋊C4—81no—
92Dic43⋊C4—81no—
93Dic43⋊C4—81no—
94Dic43⋊C4—81no—
95C4×Dic43—22no—
96C4×Dic43—41no—
97#10621877—82no—
98C2×C43⋊C8—42no—
99C23×C43—22no—
100C23×C43—21no—
101C23×C43—21no—
102C23×C43—41no—
103C23×C43#9911yescharacteristic
104C23×C43#9911yescharacteristic
105C23×C43C2×C22⋊C411yescharacteristic
106C2×C4×C43—21no—
107C2×C4×C43—21no—
108C2×C4×C43—21no—
109C2×C4×C43—21no—
110C2×C4×C43—21no—
111C2×C4×C43—21no—
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—42no—
116C2×C4×C43—42no—
117C2×C4×C43—42no—
118C2×C4×C43—42no—
119C2×C4×C43—41no—
120C2×C4×C43—41no—
121C2×C4×C43—41no—
122C2×C4×C43—41no—
123C2×C4×C43—81no—
124C2×C4×C43—81no—
125C2×C4×C43#13112yes—
126C2×Dic43—22no—
127C2×Dic43—22no—
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—82no—
141#11555—431nomaximal, Sylow
142C22×C43—21no—
143C22×C43—21no—
144C22×C43—21no—
145C22×C43—21no—
146C22×C43—21no—
147C22×C43—21no—
148C22×C43—21no—
149C22×C43—42no—
150C22×C43—42no—
151C22×C43#35612yes—
152C22×C43#40811yescharacteristic
153C22×C43C2×#9911yescharacteristic
154C22×C43#41311yescharacteristic
155C4×C43—22no—
156C4×C43—41no—
157C4×C43—41no—
158C4×C43—41no—
159C4×C43—41no—
160C4×C43—41no—
161Dic43—42no—
162Dic43—42no—
163Dic43—81no—
164Dic43—81no—
165#2502—431no—
166#1463—431no—
167C2×#324D4311yescharacteristic
168#1325—432no—
169#1319—432no—
170C2×C43—21no—
171C2×C43—21no—
172C2×C43—22no—
173C2×C43—41no—
174C2×C43#146811yescharacteristic
175C2×C43#212711yescharacteristic
176C2×C43C2×#35611yescharacteristic
177C2×C22⋊Q8—431no—
178C22×C4⋊C4C2×D4311yescharacteristic
179#407—861no—
180C2×C22⋊C8—21no—
181#398—861no—
182#398—861no—
183#391—431no—
184#391—431no—
185#385—861no—
186#385—861no—
187#384—431no—
188#384—431no—
189C4×C22⋊C4—431no—
190#324—21no—
191#324—432no—
192#324—861no—
193#324C2×D4312yes—
194C43#1155511yescharacteristic, complemented, Sylow
195C22×Q8—431no—
196C23×C4C4×D4311yescharacteristic
197C23×C4D17211yescharacteristic
198C23×C4C22⋊D4311yescharacteristic
199C2×M16—1721no—
200C22×C8—41no—
201C22⋊Q8—1721no—
202C22⋊Q8—1721no—
203C2×C4⋊C4—41no—
204C2×C4⋊C4—41no—
205C2×C4⋊C4—431no—
206C2×C4⋊C4—861no—
207C2×C4⋊C4—861no—
208C2×C4⋊C4—861no—
209C2×C4⋊C4—861no—
210C2×C4⋊C4—861no—
211C2×C4⋊C4C4×D4311yescharacteristic
212C2×C4⋊C4D17211yescharacteristic
213C2×C4⋊C4C22⋊D4311yescharacteristic
214C2×C4⋊C4C22×D4311yescharacteristic
215C2×C22⋊C4—861no—
216C2×C22⋊C4—861no—
217C2×C42—431no—
218C2×C42—431no—
219C22⋊C8—22no—
220C22⋊C8—41no—
221C22⋊C8—862no—
222C22⋊C8—1721no—
223#95—861no—
224#95—861no—
225#95—861no—
226#95—861no—
227#95—861no—
228C24(C2×D43)⋊C411yescharacteristic
229C2×Q8—862no—
230C2×Q8—1721no—
231C2×Q8—1721no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—22no—
239C22×C4—41no—
240C22×C4—81no—
241C22×C4—81no—
242C22×C4—861no—
243C22×C4—861no—
244C22×C4—861no—
245C22×C4—861no—
246C22×C4(C2×D43)⋊C411yescharacteristic
247C22×C4(C2×D43)⋊C411yescharacteristic
248C22×C4(C2×D43)⋊C411yescharacteristic
249C22×C4C2×C4×D4311yescharacteristic
250C22×C4C2×D17211yescharacteristic
251C22×C4C2×C22⋊D4311yescharacteristic
252M16—3442no—
253C2×C8—42no—
254C2×C8—82no—
255C2×C8—1722no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—3441no—
261C4⋊C4—3441no—
262C4⋊C4—3441no—
263C4⋊C4—3441no—
264C4⋊C4—1721no—
265C4⋊C4—1722no—
266C22⋊C4—864no—
267C22⋊C4—1721no—
268C22⋊C4—1721no—
269C42—862no—
270C42—1721no—
271C23—21no—
272C23—21no—
273C23—22no—
274C23—41no—
275C23#1306323911yescharacteristic
276C23#1306323911yescharacteristic
277C23C2×(C2×D43)⋊C411yescharacteristic
278Q8—3442no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—862no—
299C2×C4—862no—
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#1306333112yes—
311C8—82no—
312C8—3442no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—42no—
321C22—42no—
322C22#1458269712yes—
323C22#1458286511yescharacteristic
324C22C2×#1306323911yescharacteristic
325C22#1458288111yescharacteristic
326C4—22no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—3441no—
333C4—3441no—
334C4—1722no—
335C4—1722no—
336C2—21no—
337C2—21no—
338C2—22no—
339C2—41no—
340C2#1913294111yescharacteristic
341C2#1913626211yescharacteristic
342C2C2×#1458269711yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC2×C43×#324C2
socleC22×C43C2×#99
prime radicalC24×C43C22⋊C4
cosocleC2×C4⋊C4×C43C23
hypercenterC2×#324D43
hypocenterC43#11555
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
3. #19132540C2semidirect
4. #19132528C2semidirect
194. C43#11555semidirect

Maximal subgroups

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

subgroupindex
#191390692
#191329252
#191325402
#191325282
C2×C43×#3242
#1155543