Finite Group Databasebeta

← #25009031

Subgroups — #25009031

Order 11008.

372 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 57 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#19142661C211yesmaximal, characteristic, complemented
2#19135821C211yesmaximal, characteristic
3#19133598C211yesmaximal, characteristic
4#19132602C211yesmaximal, characteristic, complemented
5#19132601C211yesmaximal, characteristic, complemented
6#19132538C211yesmaximal, characteristic, complemented
7C43×#1610C211yesmaximal, characteristic
8C2×#13063315—21no—
9#14583210—21no—
10C2×#13063252—21no—
11#14582900—21no—
12#14582841—21no—
13#14582840—21no—
14#14582833—21no—
15#14582832—21no—
16#14582832—21no—
17#14582829C2211yescharacteristic
18#14582764C2211yescharacteristic
19#14582668C2211yescharacteristic
20#14582633—21no—
21#14582625C2211yescharacteristic
22C43×#537C2211yescharacteristic
23C43×#480—21no—
24C43×#398C2211yescharacteristic
25C43×#327—21no—
26C43×#324C2211yescharacteristic
27C2×#10621877—21no—
28#13063315—42no—
29#13063315—42no—
30C2×C4⋊Dic43—21no—
31C2×C4⋊Dic43D411yescharacteristic
32C2×C4⋊Dic43D411yescharacteristic
33C2×Dic43⋊C4—21no—
34C2×Dic43⋊C4—21no—
35C2×Dic43⋊C4—21no—
36C2×Dic43⋊C4—21no—
37C2×Dic43⋊C4—21no—
38C2×C4×Dic43D411yescharacteristic
39#13063258—41no—
40#13063252—42no—
41#13063249—41no—
42#13063246—41no—
43#13063246—41no—
44C22⋊(C43⋊C8)—21no—
45C43⋊#95—21no—
46C43⋊#95—21no—
47C43⋊#95—21no—
48C43⋊#95—21no—
49C43⋊#95—21no—
50C43⋊#95—21no—
51C43⋊#95D411yescharacteristic
52C2×#41×C43—21no—
53C22⋊Q8×C43—41no—
54#121×C43—21no—
55#121×C43—21no—
56#121×C43—41no—
57C2×C4⋊C4×C43—21no—
58C2×C4⋊C4×C43D411yescharacteristic
59C2×C4⋊C4×C43C2311yescharacteristic
60#107×C43—41no—
61#102×C43—41no—
62C22⋊C8×C43—21no—
63#95×C43—21no—
64#95×C43D411yescharacteristic
65#41×C43—41no—
66#41×C43—41no—
67#41×C43—41no—
68#41×C43—41no—
69C2×Q8×C43—21no—
70C2×D4×C43—21no—
71C2×D4×C43—21no—
72C2×D4×C43—21no—
73C2×D4×C43—41no—
74C22×C4×C43—21no—
75C22×C4×C43—21no—
76C22×C4×C43—41no—
77C22×C4×C43C2×D411yescharacteristic
78C22×C4×C43C2×D411yescharacteristic
79C22×C4×C43C2×D411yescharacteristic
80C22×Dic43—21no—
81C22×Dic43—21no—
82C22×Dic43—21no—
83C22×Dic43—21no—
84C2×C8×C43—41no—
85C4⋊C4×C43—21no—
86C4⋊C4×C43—21no—
87C4⋊C4×C43—41no—
88C4⋊C4×C43—41no—
89C4⋊C4×C43—41no—
90C4⋊C4×C43—41no—
91C22⋊C4×C43—41no—
92C22⋊C4×C43—41no—
93C4⋊Dic43—42no—
94C4⋊Dic43—41no—
95C4⋊Dic43—41no—
96Dic43⋊C4—42no—
97Dic43⋊C4—42no—
98Dic43⋊C4—42no—
99Dic43⋊C4—41no—
100Dic43⋊C4—41no—
101Dic43⋊C4—81no—
102C4×Dic43—21no—
103C4×Dic43D812yes—
104#10621877—41no—
105#10621877—41no—
106C2×C43⋊C8—41no—
107C2×C43⋊C8—41no—
108C23×C43—41no—
109C23×C43#12011yescharacteristic
110Q8×C43—41no—
111Q8×C43—41no—
112D4×C43—41no—
113D4×C43—41no—
114D4×C43—81no—
115D4×C43—81no—
116D4×C43—81no—
117D4×C43—81no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—41no—
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—41no—
131C2×C4×C43—81no—
132C2×C4×C43—81no—
133C2×C4×C43C2×D811yescharacteristic
134C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
135C2×Dic43—22no—
136C2×Dic43—41no—
137C2×Dic43—41no—
138C2×Dic43—41no—
139C2×Dic43—41no—
140C2×Dic43—42no—
141C2×Dic43—41no—
142C2×Dic43—41no—
143C2×Dic43—41no—
144C2×Dic43—41no—
145C2×Dic43—41no—
146C8×C43—81no—
147C43⋊C8—81no—
148C43⋊C8—81no—
149#12157—431nomaximal, Sylow
150C22×C43—21no—
151C22×C43—21no—
152C22×C43—81no—
153C22×C43—81no—
154C22×C43—81no—
155C22×C43#44711yescharacteristic
156C22×C43#45411yescharacteristic
157C22×C43B(4,𝔽2)11yescharacteristic
158C4×C43—21no—
159C4×C43—21no—
160C4×C43—41no—
161C4×C43—41no—
162C4×C43—81no—
163C4×C43—81no—
164C4×C43—81no—
165Dic43—42no—
166Dic43—81no—
167Dic43—81no—
168Dic43—81no—
169#2822—431no—
170#2040—431no—
171#1610—431no—
172#1610D4311yescharacteristic
173#1346—431no—
174#1346—431no—
175#1324—431no—
176C2×C43—21no—
177C2×C43—21no—
178C2×C43—161no—
179C2×C43#159811yescharacteristic
180C2×C43#220111yescharacteristic
181C2×C43#220311yescharacteristic
182#537C2×D4311yescharacteristic
183C2×#125—861no—
184#480—21no—
185#480—861no—
186C2×#104—861no—
187#417—861no—
188#400—861no—
189#400—861no—
190#398—431no—
191#398—861no—
192#398—861no—
193#398—861no—
194#398C2×D4311yescharacteristic
195#382—431no—
196#343—431no—
197#327—21no—
198#327—861no—
199#324—431no—
200#324C2×D4311yescharacteristic
201C43#1215711yescharacteristic, complemented, Sylow
202C2×#41—21no—
203C2×M16—861no—
204#125—1722no—
205#125—1722no—
206C22⋊Q8—41no—
207#121—21no—
208#121—21no—
209#121—41no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—431no—
212C2×C4⋊C4—431no—
213C2×C4⋊C4—861no—
214C2×C4⋊C4—861no—
215C2×C4⋊C4—861no—
216C2×C4⋊C4—861no—
217C2×C4⋊C4—861no—
218C2×C4⋊C4—861no—
219C2×C4⋊C4C22⋊D4311yescharacteristic
220C2×C4⋊C4C22×D4311yescharacteristic
221C2×C42—431no—
222#107—41no—
223#107—1721no—
224#104—1722no—
225#103—1721no—
226#102—41no—
227#102—1721no—
228#102—1721no—
229C22⋊C8—21no—
230C22⋊C8—861no—
231#95—21no—
232#95—431no—
233#95—861no—
234#95—861no—
235#95—861no—
236#95—861no—
237#95—861no—
238#95—861no—
239#95C22⋊D4311yescharacteristic
240#41—41no—
241#41—41no—
242#41—41no—
243#41—41no—
244C2×Q8—21no—
245C2×D4—21no—
246C2×D4—21no—
247C2×D4—21no—
248C2×D4—41no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—41no—
252C22×C4—861no—
253C22×C4—861no—
254C22×C4—861no—
255C22×C4—861no—
256C22×C4D4×D4311yescharacteristic
257C22×C4D4×D4311yescharacteristic
258C22×C4C2×C22⋊D4311yescharacteristic
259M16—1721no—
260M16—1721no—
261C2×C8—41no—
262C2×C8—1721no—
263C2×C8—1721no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—3441no—
271C4⋊C4—1721no—
272C4⋊C4—1721no—
273C4⋊C4—1722no—
274C4⋊C4—1722no—
275C4⋊C4—1722no—
276C4⋊C4—1722no—
277C4⋊C4—1721no—
278C4⋊C4—1721no—
279C22⋊C4—41no—
280C22⋊C4—41no—
281C42—432no—
282C42—861no—
283C23—41no—
284C23#1306329311yescharacteristic
285Q8—41no—
286Q8—41no—
287D4—41no—
288D4—41no—
289D4—81no—
290D4—81no—
291D4—81no—
292D4—81no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—862no—
309C2×C4—1721no—
310C2×C4—1721no—
311C2×C4—1722no—
312C2×C4—1721no—
313C2×C4—1721no—
314C2×C4—1721no—
315C2×C4—1721no—
316C2×C4—1721no—
317C2×C4—1721no—
318C2×C4—1721no—
319C2×C4D8×D4311yescharacteristic
320C2×C4#1306334911yescharacteristic
321C8—81no—
322C8—3441no—
323C8—3441no—
324C22—21no—
325C22—21no—
326C22—81no—
327C22—81no—
328C22—81no—
329C22#1458303111yescharacteristic
330C22#1458307011yescharacteristic
331C22#1458308511yescharacteristic
332C4—21no—
333C4—21no—
334C4—41no—
335C4—41no—
336C4—81no—
337C4—81no—
338C4—81no—
339C4—3441no—
340C4—3441no—
341C4—3441no—
342C4—1722no—
343C2—21no—
344C2—21no—
345C2—161no—
346C2#1913352811yescharacteristic
347C2#1913660611yescharacteristic
348C2#1913661411yescharacteristic
subgroupG/H
centerC22#14583085
commutator, cosocleC2×C4⋊C4×C43C23
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1610C2
socleC22×C43B(4,𝔽2)
prime radicalC43×#537C22
hypercenter#1610D43
hypocenterC43#12157
LCSG ▷ C2×C4⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1610

Complements

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

NH ≅ G/Ntype
1. #19142661C2semidirect
4. #19132602C2semidirect
5. #19132601C2semidirect
6. #19132538C2semidirect
201. C43#12157semidirect

Maximal subgroups

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

subgroupindex
#191426612
#191358212
#191335982
#191326022
#191326012
#191325382
C43×#16102
#1215743