Finite Group Databasebeta

← #25007640

Subgroups — #25007640

Order 11008.

440 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 95 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#19139500C211yesmaximal, characteristic
2#19134591C211yesmaximal, characteristic, complemented
3#19132602C212yesmaximal, complemented
4#19132599C212yesmaximal
5C43×#1461C211yesmaximal, characteristic, complemented
6C2×#13063301—21no—
7C2×C4×D172C411yescharacteristic
8#14582923—21no—
9C2×#13063244—21no—
10#14582829C411yescharacteristic
11#14582829C2211yescharacteristic
12#14582816C411yescharacteristic
13#14582816C2211yescharacteristic
14#14582790—21no—
15#14582790—21no—
16#14582765C411yescharacteristic
17#14582756—21no—
18#14582668C2212yes—
19C2×C4×Q8×C43C2211yescharacteristic
20C43×#431—21no—
21C43×#324—21no—
22C43×#324C2212yes—
23C22×D172C2×C411yescharacteristic
24C22×C4×D43—21no—
25C2×#10621877—22no—
26#13063301—42no—
27#13063301—42no—
28C4×D172—41no—
29C4×D172—41no—
30C2×C4⋊Dic43—21no—
31C2×C4⋊Dic43C2×C411yescharacteristic
32C2×Dic43⋊C4—21no—
33C2×Dic43⋊C4—21no—
34C2×(C2×D43)⋊C4—21no—
35C2×(C2×D43)⋊C4—21no—
36C2×(C2×D43)⋊C4—21no—
37C2×(C2×D43)⋊C4—21no—
38C2×(C2×D43)⋊C4—21no—
39C4⋊(C43⋊C8)—41no—
40C4⋊(C43⋊C8)—41no—
41#13063244—42no—
42C43⋊#95—21no—
43C43⋊#95—21no—
44C43⋊#95—21no—
45C43⋊#95C2×C411yescharacteristic
46C43⋊#95C2×C411yescharacteristic
47C22×Q8×C43D411yescharacteristic
48C4×Q8×C43—41no—
49C4×Q8×C43—41no—
50C2×C4⋊C4×C43C2×C411yescharacteristic
51C2×C4⋊C4×C43D411yescharacteristic
52C2×C4⋊C4×C43C2311yescharacteristic
53C2×C42×C43C2×C411yescharacteristic
54C2×C42×C43D411yescharacteristic
55C2×C42×C43D411yescharacteristic
56C4⋊C8×C43—41no—
57C22⋊C8×C43—22no—
58C4×C8×C43—41no—
59C23×D43—21no—
60C2×Q8×C43—41no—
61C2×Q8×C43—41no—
62C2×Q8×C43D812yes—
63C2×Q8×C43SD1612yes—
64C22×C4×C43C22⋊C411yescharacteristic
65C22×C4×C43C22⋊C411yescharacteristic
66C22×C4×C43C22⋊C411yescharacteristic
67C22×C4×C43C22⋊C411yescharacteristic
68C22×C4×C43C22×C411yescharacteristic
69C22×C4×C43C2×D411yescharacteristic
70C22×C4×C43C2×D411yescharacteristic
71C22×Dic43—21no—
72C22×Dic43—21no—
73C22×Dic43—21no—
74C2×D172—42no—
75C2×D172—41no—
76C2×C4×D43—42no—
77C2×C4×D43—42no—
78C2×C4×D43—42no—
79C2×C8×C43—42no—
80C4⋊C4×C43—41no—
81C4⋊C4×C43—41no—
82C4⋊C4×C43—41no—
83C42×C43—21no—
84C42×C43—21no—
85C42×C43—21no—
86C42×C43—21no—
87C42×C43—21no—
88C42×C43—21no—
89(C2×D43)⋊C4—42no—
90(C2×D43)⋊C4—42no—
91(C2×D43)⋊C4—41no—
92(C2×D43)⋊C4—41no—
93(C2×D43)⋊C4—42no—
94(C2×D43)⋊C4—41no—
95(C2×D43)⋊C4—41no—
96C4⋊Dic43—42no—
97C4⋊Dic43—41no—
98Dic43⋊C4—42no—
99Dic43⋊C4—41no—
100Dic43⋊C4—41no—
101#10621877—42no—
102#10621877—42no—
103C2×C43⋊C8—42no—
104C23×C43C2×C22⋊C411yescharacteristic
105C22×D43—22no—
106C22×D43—41no—
107C22×D43—41no—
108C22×D43—41no—
109C22×D43—41no—
110C22×D43—41no—
111C22×D43—41no—
112Q8×C43—42no—
113Q8×C43—42no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—41no—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43#9911yescharacteristic
128C2×C4×C43#9911yescharacteristic
129C2×C4×C43#10212yes—
130C2×C4×C43#10212yes—
131C2×C4×C43C2×D811yescharacteristic
132C2×C4×C43C2×SD1611yescharacteristic
133C2×Dic43—41no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137C2×Dic43—41no—
138C2×Dic43—41no—
139C2×Dic43—41no—
140C2×Dic43—41no—
141C2×Dic43—41no—
142D172—42no—
143D172—42no—
144C4×D43—84no—
145C8×C43—82no—
146C43⋊C8—82no—
147#11879—431nomaximal, Sylow
148C22×C43—21no—
149C22×C43—21no—
150C22×C43C2×#9911yescharacteristic
151C22×C43C2×#10211yescharacteristic
152C22×C43#42111yescharacteristic
153C2×D43—42no—
154C2×D43—42no—
155C2×D43—42no—
156C2×D43—81no—
157C2×D43—81no—
158C2×D43—81no—
159C2×D43—81no—
160C4×C43—21no—
161C4×C43—21no—
162C4×C43—21no—
163C4×C43—22no—
164C4×C43—22no—
165C4×C43—21no—
166C4×C43—41no—
167C4×C43—41no—
168C4×C43—41no—
169Dic43—81no—
170Dic43—81no—
171Dic43—81no—
172#2536—431no—
173#1801—431no—
174#1461D4311yescharacteristic, complemented
175#1346—432no—
176#1345—432no—
177C2×C43—21no—
178C2×C43—21no—
179C2×C43#151911yescharacteristic
180C2×C43#212011yescharacteristic
181C2×C43#213311yescharacteristic
182D43—82no—
183C2×C22⋊Q8—861no—
184C2×C4×Q8C2×D4311yescharacteristic
185C2×C4×D4—431no—
186#431—21no—
187#423—861no—
188C2×#101—861no—
189#398—431no—
190#398—431no—
191#394—431no—
192#394—431no—
193#388—861no—
194#388—861no—
195#382—431no—
196#380—861no—
197#343—432no—
198#324—21no—
199#324C2×D4312yes—
200C43#1187911yescharacteristic, complemented, Sylow
201C22×Q8D17211yescharacteristic
202C22×D4—431no—
203C23×C4—861no—
204C2×M16—862no—
205C22⋊Q8—1722no—
206C22⋊Q8—1722no—
207C4×Q8—41no—
208C4×Q8—41no—
209C4×D4—1721no—
210C4×D4—1721no—
211C2×C4⋊C4—431no—
212C2×C4⋊C4—861no—
213C2×C4⋊C4—861no—
214C2×C4⋊C4—861no—
215C2×C4⋊C4C4×D4311yescharacteristic
216C2×C4⋊C4C22⋊D4311yescharacteristic
217C2×C4⋊C4C22×D4311yescharacteristic
218C2×C22⋊C4—861no—
219C2×C22⋊C4—861no—
220C2×C22⋊C4—861no—
221C2×C22⋊C4—861no—
222C2×C22⋊C4—861no—
223C2×C42C4×D4311yescharacteristic
224C2×C42D17211yescharacteristic
225C2×C42C22⋊D4311yescharacteristic
226C4⋊C8—41no—
227C4⋊C8—1721no—
228C4⋊C8—1721no—
229#101—1722no—
230C22⋊C8—22no—
231C4×C8—41no—
232#95—431no—
233#95—431no—
234#95—861no—
235#95—861no—
236#95—861no—
237C24—861no—
238C2×Q8—41no—
239C2×Q8—41no—
240C2×Q8#1062187312yes—
241C2×Q8D34412yes—
242C2×D4—1721no—
243C2×D4—1722no—
244C22×C4—861no—
245C22×C4—861no—
246C22×C4—861no—
247C22×C4—1722no—
248C22×C4—1722no—
249C22×C4—1722no—
250C22×C4(C2×D43)⋊C411yescharacteristic
251C22×C4(C2×D43)⋊C411yescharacteristic
252C22×C4(C2×D43)⋊C411yescharacteristic
253C22×C4(C2×D43)⋊C411yescharacteristic
254C22×C4C2×C4×D4311yescharacteristic
255C22×C4C2×D17211yescharacteristic
256C22×C4C2×C22⋊D4311yescharacteristic
257M16—1722no—
258M16—1722no—
259C2×C8—42no—
260C2×C8—1722no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—1721no—
265C4⋊C4—1722no—
266C4⋊C4—1722no—
267C4⋊C4—1721no—
268C4⋊C4—1721no—
269C22⋊C4—1722no—
270C22⋊C4—1722no—
271C22⋊C4—1721no—
272C22⋊C4—1721no—
273C22⋊C4—1722no—
274C22⋊C4—1721no—
275C22⋊C4—1721no—
276C42—21no—
277C42—21no—
278C42—21no—
279C42—21no—
280C42—21no—
281C42—21no—
282C23—862no—
283C23—1721no—
284C23—1721no—
285C23—1721no—
286C23—1721no—
287C23—1721no—
288C23—1721no—
289C23C2×(C2×D43)⋊C411yescharacteristic
290Q8—42no—
291Q8—42no—
292D4—1722no—
293D4—1722no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—3444no—
308C2×C4—1721no—
309C2×C4—1721no—
310C2×C4—1721no—
311C2×C4—1721no—
312C2×C4—1721no—
313C2×C4—1721no—
314C2×C4—1721no—
315C2×C4—1721no—
316C2×C4—1721no—
317C2×C4#1306323911yescharacteristic
318C2×C4#1306323911yescharacteristic
319C2×C4#1306324712yes—
320C2×C4#1306324712yes—
321C2×C4C2×D34411yescharacteristic
322C2×C4C2×#1062187311yescharacteristic
323C8—82no—
324C8—3442no—
325C22—21no—
326C22—21no—
327C22—3441no—
328C22—3441no—
329C22—3441no—
330C22—3441no—
331C22—1722no—
332C22—1722no—
333C22—1722no—
334C22C2×#1306323911yescharacteristic
335C22C2×#1306324711yescharacteristic
336C22#1458291511yescharacteristic
337C4—21no—
338C4—21no—
339C4—21no—
340C4—22no—
341C4—22no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—3441no—
347C4—3441no—
348C4—3441no—
349C2—21no—
350C2—21no—
351C2—3442no—
352C2#1913316411yescharacteristic
353C2#1913623411yescharacteristic
354C2#1913628211yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1461C2
socleC22×C43C2×#99
prime radicalC22×D172C2×C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1461D43
hypocenterC43#11879
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1461

Complements

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

NH ≅ G/Ntype
2. #19134591C2semidirect
3. #19132602C2semidirect
5. C43×#1461C2semidirect
174. #1461D43semidirect
200. C43#11879semidirect

Maximal subgroups

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

subgroupindex
#191395002
#191345912
#191326022
#191325992
C43×#14612
#1187943