Finite Group Databasebeta

← #25007529

Subgroups — #25007529

Order 11008.

412 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 71 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#19139971C211yesmaximal, characteristic
2#19134674C211yesmaximal, characteristic
3#324×D43C211yesmaximal, characteristic
4#19132625C211yesmaximal, characteristic, complemented
5#19132602C211yesmaximal, characteristic, complemented
6#19132600C211yesmaximal, characteristic, complemented
7C43×#1354C211yesmaximal, characteristic, complemented
8C2×#13063301C411yescharacteristic
9C2×C4⋊C4×D43C2211yescharacteristic
10#14582862—21no—
11C22⋊C8×D43—21no—
12#14582831C411yescharacteristic
13#14582829C2211yescharacteristic
14#14582818C411yescharacteristic
15#14582796—21no—
16#14582795—21no—
17#14582773—21no—
18#14582770—21no—
19#14582746C411yescharacteristic
20#14582668C2211yescharacteristic
21#14582667—21no—
22#14582625C2211yescharacteristic
23#14582624—21no—
24C43×#395C2211yescharacteristic
25C43×#343C2211yescharacteristic
26C43×#324C2211yescharacteristic
27C22×C4×D43C2×C411yescharacteristic
28C22×C4×D43D411yescharacteristic
29C22×C4×D43D411yescharacteristic
30C2×#10621877—21no—
31C2×C8×D43—41no—
32#13063301—41no—
33#13063301—41no—
34C2×C4⋊Dic43—21no—
35C2×C4⋊Dic43C2×C411yescharacteristic
36C2×C4⋊Dic43D411yescharacteristic
37C2×Dic43⋊C4—21no—
38C2×Dic43⋊C4—21no—
39C2×Dic43⋊C4—21no—
40C2×Dic43⋊C4C2×C411yescharacteristic
41C2×Dic43⋊C4D411yescharacteristic
42C4⋊C4×D43—41no—
43C4⋊C4×D43—41no—
44C2×(C2×D43)⋊C4—21no—
45C2×(C2×D43)⋊C4—21no—
46C2×C4×Dic43—21no—
47C22⋊(C43⋊C8)—21no—
48(C2×D43)⋊C8—41no—
49(C2×D43)⋊C8—41no—
50(C2×D43)⋊C8—41no—
51C43⋊#95—21no—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C43⋊#95C2×C411yescharacteristic
55C22×Q8×C43C2×C411yescharacteristic
56C2×M16×C43—21no—
57C2×C4⋊C4×C43—21no—
58C2×C4⋊C4×C43C2311yescharacteristic
59C22⋊C8×C43—21no—
60#95×C43—21no—
61#95×C43C2×C411yescharacteristic
62C23×D43C22⋊C411yescharacteristic
63C2×Q8×C43—41no—
64C2×Q8×C43—81no—
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43C22×C411yescharacteristic
68C22×C4×C43C2×D411yescharacteristic
69C22×C4×C43C2×D411yescharacteristic
70C22×Dic43—21no—
71C22×Dic43—21no—
72C22×Dic43C22⋊C411yescharacteristic
73C22×Dic43C22⋊C411yescharacteristic
74C22×Dic43C22⋊C411yescharacteristic
75C2×C4×D43—21no—
76C2×C4×D43—21no—
77C2×C4×D43—21no—
78C2×C4×D43—21no—
79C2×C4×D43—21no—
80C2×C4×D43—21no—
81C2×C4×D43—21no—
82C2×C4×D43—21no—
83C2×C4×D43—41no—
84C2×C4×D43—81no—
85C2×C4×D43—81no—
86M16×C43—41no—
87M16×C43—41no—
88C2×C8×C43—41no—
89C2×C8×C43—41no—
90C4⋊C4×C43—41no—
91C4⋊C4×C43—81no—
92(C2×D43)⋊C4—24no—
93(C2×D43)⋊C4—41no—
94(C2×D43)⋊C4—41no—
95C4⋊Dic43—41no—
96C4⋊Dic43—42no—
97C4⋊Dic43—41no—
98Dic43⋊C4—41no—
99Dic43⋊C4—41no—
100Dic43⋊C4—42no—
101Dic43⋊C4—41no—
102Dic43⋊C4—41no—
103Dic43⋊C4—81no—
104C4×Dic43—81no—
105#10621877—41no—
106#10621877—41no—
107C2×C43⋊C8—41no—
108C2×C43⋊C8—41no—
109C8×D43—82no—
110C23×C43C2×C22⋊C411yescharacteristic
111C22×D43—21no—
112C22×D43—21no—
113C22×D43—22no—
114C22×D43—41no—
115C22×D43#9911yescharacteristic
116C22×D43#9911yescharacteristic
117Q8×C43—82no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—22no—
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—41no—
128C2×C4×C43—41no—
129C2×C4×C43—41no—
130C2×C4×C43#13511yescharacteristic
131C2×C4×C43#13511yescharacteristic
132C2×Dic43—22no—
133C2×Dic43—21no—
134C2×Dic43—21no—
135C2×Dic43—21no—
136C2×Dic43—21no—
137C2×Dic43—21no—
138C2×Dic43—41no—
139C2×Dic43—41no—
140C2×Dic43—41no—
141C2×Dic43—41no—
142C2×Dic43—41no—
143C2×Dic43—41no—
144C2×Dic43—41no—
145C4×D43—41no—
146C4×D43—41no—
147C4×D43—41no—
148C4×D43—41no—
149C4×D43—42no—
150C4×D43—81no—
151C4×D43—81no—
152C4×D43—81no—
153C8×C43—81no—
154C8×C43—81no—
155C43⋊C8—81no—
156C43⋊C8—81no—
157#11854—431nomaximal, Sylow
158C22×C43—21no—
159C22×C43—21no—
160C22×C43C2×#9911yescharacteristic
161C22×C43#41611yescharacteristic
162C22×C43#42111yescharacteristic
163C2×D43—21no—
164C2×D43—21no—
165C2×D43—21no—
166C2×D43—21no—
167C2×D43—21no—
168C2×D43—42no—
169C2×D43—42no—
170C2×D43#35612yes—
171C4×C43—21no—
172C4×C43—21no—
173C4×C43—42no—
174C4×C43—41no—
175C4×C43—41no—
176C4×C43—81no—
177Dic43—42no—
178Dic43—41no—
179Dic43—41no—
180Dic43—41no—
181Dic43—81no—
182#2583—431no—
183#1821—431no—
184C2×#324—431no—
185#1354—431no—
186#1354D4311yescharacteristic, complemented
187#1346—431no—
188#1346—431no—
189C2×C43—21no—
190C2×C43—21no—
191C2×C43#151611yescharacteristic
192C2×C43#212111yescharacteristic
193C2×C43C2×#35611yescharacteristic
194D43—22no—
195D43—41no—
196C2×C22⋊Q8—431no—
197C22×C4⋊C4—431no—
198#407—861no—
199C2×C22⋊C8—861no—
200#398—431no—
201#398—431no—
202#395—431no—
203#395C2×D4311yescharacteristic
204#389—861no—
205#389—861no—
206#385—861no—
207#385—861no—
208C4×C22⋊C4—431no—
209#343—431no—
210#343—861no—
211#343C2×D4311yescharacteristic
212#324—431no—
213#324—861no—
214#324C2×D4311yescharacteristic
215C43#1185411yescharacteristic, complemented, Sylow
216C22×Q8C4×D4311yescharacteristic
217C23×C4—431no—
218C23×C4—431no—
219C23×C4—431no—
220C2×M16—21no—
221C2×M16—861no—
222C22×C8—1721no—
223C22⋊Q8—1721no—
224C22⋊Q8—1721no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—431no—
227C2×C4⋊C4—431no—
228C2×C4⋊C4—431no—
229C2×C4⋊C4—431no—
230C2×C4⋊C4—861no—
231C2×C4⋊C4—861no—
232C2×C4⋊C4—861no—
233C2×C4⋊C4—861no—
234C2×C4⋊C4—1721no—
235C2×C4⋊C4—1721no—
236C2×C4⋊C4C22×D4311yescharacteristic
237C2×C22⋊C4—861no—
238C2×C22⋊C4—861no—
239C2×C42—861no—
240C22⋊C8—21no—
241C22⋊C8—861no—
242C22⋊C8—1721no—
243C22⋊C8—1721no—
244C22⋊C8—1721no—
245#95—21no—
246#95—431no—
247#95—861no—
248#95—861no—
249#95—861no—
250#95C4×D4311yescharacteristic
251C24—431no—
252C2×Q8—41no—
253C2×Q8—81no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—431no—
257C22×C4—431no—
258C22×C4—431no—
259C22×C4—861no—
260C22×C4—861no—
261C22×C4—861no—
262C22×C4—861no—
263C22×C4—861no—
264C22×C4—861no—
265C22×C4—861no—
266C22×C4—861no—
267C22×C4—861no—
268C22×C4—861no—
269C22×C4—3441no—
270C22×C4—3441no—
271C22×C4—1721no—
272C22×C4C2×C4×D4311yescharacteristic
273C22×C4D4×D4311yescharacteristic
274C22×C4D4×D4311yescharacteristic
275M16—41no—
276M16—41no—
277M16—1721no—
278M16—1721no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—3442no—
282C2×C8—1721no—
283C2×C8—1721no—
284C4⋊C4—41no—
285C4⋊C4—81no—
286C4⋊C4—3441no—
287C4⋊C4—1721no—
288C4⋊C4—1721no—
289C4⋊C4—1721no—
290C4⋊C4—1721no—
291C4⋊C4—1722no—
292C4⋊C4—1722no—
293C4⋊C4—1721no—
294C4⋊C4—1721no—
295C22⋊C4—864no—
296C22⋊C4—1721no—
297C22⋊C4—1721no—
298C42—3441no—
299C23—431no—
300C23—431no—
301C23—862no—
302C23—861no—
303C23—861no—
304C23—1721no—
305C23C22⋊C4×D4311yescharacteristic
306Q8—82no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—22no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—862no—
320C2×C4—861no—
321C2×C4—861no—
322C2×C4—861no—
323C2×C4—861no—
324C2×C4—861no—
325C2×C4—3441no—
326C2×C4—3441no—
327C2×C4—3441no—
328C2×C4—1721no—
329C2×C4—1721no—
330C2×C4—1721no—
331C2×C4—1721no—
332C2×C4—1722no—
333C2×C4—1721no—
334C2×C4—1721no—
335C2×C4—1721no—
336C2×C4—1721no—
337C2×C4—1721no—
338C2×C4—1721no—
339C2×C4—1721no—
340C2×C4#1306334611yescharacteristic
341C2×C4#1306334811yescharacteristic
342C8—81no—
343C8—81no—
344C8—3441no—
345C8—3441no—
346C22—21no—
347C22—21no—
348C22—432no—
349C22—861no—
350C22—861no—
351C22—861no—
352C22—861no—
353C22—861no—
354C22—1722no—
355C22—1722no—
356C22#99×D4311yescharacteristic
357C22#1458289411yescharacteristic
358C22#1458291411yescharacteristic
359C4—21no—
360C4—21no—
361C4—42no—
362C4—41no—
363C4—41no—
364C4—81no—
365C4—3441no—
366C4—1722no—
367C4—1721no—
368C4—1721no—
369C4—1721no—
370C2—21no—
371C2—21no—
372C2—862no—
373C2—1721no—
374C2#1913315011yescharacteristic
375C2#1913623811yescharacteristic
376C2#356×D4311yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1354C2
socleC22×C43C2×#99
prime radicalC23×D43C22⋊C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1354D43
hypocenterC43#11854
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1354

Complements

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

NH ≅ G/Ntype
4. #19132625C2semidirect
5. #19132602C2semidirect
6. #19132600C2semidirect
7. C43×#1354C2semidirect
186. #1354D43semidirect
215. C43#11854semidirect

Maximal subgroups

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

subgroupindex
#191399712
#191346742
#324×D432
#191326252
#191326022
#191326002
C43×#13542
#1185443