Finite Group Databasebeta

← #25009778

Subgroups — #25009778

Order 11008.

372 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 59 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#19135756C211yesmaximal, characteristic, complemented
2#19133568C211yesmaximal, characteristic, complemented
3#19133534C211yesmaximal, characteristic
4#19132625C211yesmaximal, characteristic, complemented
5#19132598C211yesmaximal, characteristic
6#19132529C211yesmaximal, characteristic, complemented
7C43×#2832C211yesmaximal, characteristic
8#14583530C2211yescharacteristic
9#14583055—21no—
10#14583050—21no—
11#14582908—21no—
12#14582668C2211yescharacteristic
13#14582659—21no—
14#14582635—21no—
15#14582635—21no—
16#14582625C2211yescharacteristic
17#14582625C2211yescharacteristic
18C43×#400—21no—
19C43×#397—21no—
20C43×#395C2211yescharacteristic
21C43×#394—21no—
22C43×#394C2211yescharacteristic
23C43×#393—21no—
24C43×#393—21no—
25C43×#391C2211yescharacteristic
26C43×#388—21no—
27C2×#10621885—41no—
28C2×#10621883—41no—
29C2×#10621877—21no—
30#13063324—41no—
31#13063316—41no—
32#13063304—21no—
33#13063304—21no—
34#13063284—21no—
35#13063249—41no—
36#13063249—41no—
37#13063249—41no—
38#13063246—41no—
39C22⋊(C43⋊C8)—21no—
40C22⋊(C43⋊C8)—21no—
41C22×Q8×C43D411yescharacteristic
42C22×Q8×C43D411yescharacteristic
43C22×D4×C43D411yescharacteristic
44C2×C4⋊C4×C43—21no—
45C2×C4⋊C4×C43—21no—
46C2×C4⋊C4×C43C2311yescharacteristic
47C2×C22⋊C4×C43—21no—
48C2×C22⋊C4×C43—21no—
49C2×C22⋊C4×C43—21no—
50C2×C22⋊C4×C43—21no—
51C2×C22⋊C4×C43—21no—
52C2×C22⋊C4×C43—21no—
53C2×C42×C43D411yescharacteristic
54#95×C43—21no—
55#95×C43—21no—
56#95×C43—21no—
57#95×C43—21no—
58#95×C43—21no—
59#95×C43—21no—
60#95×C43D411yescharacteristic
61#95×C43D411yescharacteristic
62C24×C43—21no—
63C2×Q8×C43—21no—
64C2×Q8×C43—21no—
65C2×Q8×C43—41no—
66C2×Q8×C43—41no—
67C2×Q8×C43—41no—
68C2×Q8×C43—81no—
69C2×D4×C43—41no—
70C2×D4×C43—81no—
71C22×C4×C43—21no—
72C22×C4×C43—21no—
73C22×C4×C43—21no—
74C22×C4×C43—21no—
75C22×C4×C43—21no—
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43C2×D411yescharacteristic
78C22×C4×C43C2×D411yescharacteristic
79C2×Dic86—21no—
80C2×Dic86—21no—
81C4⋊C4×C43—41no—
82C4⋊C4×C43—81no—
83C4⋊C4×C43—81no—
84C22⋊C4×C43—41no—
85C22⋊C4×C43—41no—
86C22⋊C4×C43—81no—
87C22⋊C4×C43—81no—
88C22⋊C4×C43—81no—
89C22⋊C4×C43—81no—
90C22⋊C4×C43—81no—
91C42×C43—41no—
92C22⋊Dic43—41no—
93#10621885—82no—
94#10621883—82no—
95C4⋊Dic43—21no—
96C4⋊Dic43—21no—
97C4⋊Dic43—21no—
98C4⋊Dic43—21no—
99Dic43⋊C4—41no—
100Dic43⋊C4—41no—
101C4×Dic43—41no—
102#10621877—41no—
103#10621877—41no—
104C2×C43⋊C8—41no—
105C2×C43⋊C8—41no—
106C2×C43⋊C8—41no—
107C23×C43—41no—
108C23×C43—41no—
109C23×C43—41no—
110C23×C43—41no—
111C23×C43—41no—
112C23×C43—41no—
113C23×C43—41no—
114C23×C43#12011yescharacteristic
115Q8×C43—42no—
116Q8×C43—42no—
117Q8×C43—81no—
118Q8×C43—81no—
119D4×C43—42no—
120D4×C43—81no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
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—41no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43—41no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43—41no—
138C2×C4×C43—41no—
139C2×C4×C43—41no—
140C2×C4×C43—41no—
141C2×C4×C43—41no—
142C2×C4×C43#13511yescharacteristic
143C2×C4×C43#13711yescharacteristic
144C2×Dic43—41no—
145C2×Dic43—41no—
146Dic86—81no—
147Dic86—81no—
148C43⋊C8—81no—
149C43⋊C8—81no—
150C43⋊C8—81no—
151#12275—431nomaximal, Sylow
152C22×C43—21no—
153C22×C43—21no—
154C22×C43—81no—
155C22×C43—81no—
156C22×C43—81no—
157C22×C43—81no—
158C22×C43—81no—
159C22×C43—81no—
160C22×C43—81no—
161C22×C43#45211yescharacteristic
162C22×C43#45511yescharacteristic
163C22×C43B(4,𝔽2)11yescharacteristic
164C4×C43—21no—
165C4×C43—21no—
166C4×C43—41no—
167C4×C43—41no—
168C4×C43—81no—
169C4×C43—81no—
170C4×C43—81no—
171C4×C43—81no—
172C4×C43—81no—
173Dic43—81no—
174Dic43—81no—
175#2832D4311yescharacteristic
176#2028—431no—
177#1605—431no—
178#1599—431no—
179#1354—431no—
180#1345—431no—
181#1319—431no—
182C2×C43—21no—
183C2×C43—21no—
184C2×C43—161no—
185C2×C43#160611yescharacteristic
186C2×C43#219911yescharacteristic
187C2×C43#220311yescharacteristic
188#544—431no—
189#451—861no—
190#450—861no—
191#419—861no—
192#400—21no—
193#397—21no—
194#395C2×D4311yescharacteristic
195#394—21no—
196#394C2×D4311yescharacteristic
197#393—21no—
198#393—21no—
199#391C2×D4311yescharacteristic
200#388—21no—
201#343—431no—
202#339—861no—
203#328—861no—
204#328—861no—
205#324—431no—
206#324—431no—
207C43#1227511yescharacteristic, complemented, Sylow
208C22×Q8C22⋊D4311yescharacteristic
209C22×Q8C22⋊D4311yescharacteristic
210C22×D4C22⋊D4311yescharacteristic
211C2×Q16—1721no—
212C2×SD16—1721no—
213C2×M16—861no—
214C4⋊Q8—1721no—
215#125—1721no—
216C22⋊Q8—861no—
217C22⋊Q8—861no—
218#117—861no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4C22×D4311yescharacteristic
222C2×C22⋊C4—21no—
223C2×C22⋊C4—21no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4—21no—
226C2×C22⋊C4—21no—
227C2×C22⋊C4—21no—
228C2×C42C22⋊D4311yescharacteristic
229#103—1721no—
230#103—1721no—
231#103—1721no—
232#102—1721no—
233C22⋊C8—861no—
234C22⋊C8—861no—
235#95—21no—
236#95—21no—
237#95—21no—
238#95—21no—
239#95—21no—
240#95—21no—
241#95C22⋊D4311yescharacteristic
242#95C22⋊D4311yescharacteristic
243C24—21no—
244C2×Q8—21no—
245C2×Q8—21no—
246C2×Q8—41no—
247C2×Q8—41no—
248C2×Q8—41no—
249C2×Q8—81no—
250C2×Q8—861no—
251C2×Q8—861no—
252C2×D4—41no—
253C2×D4—81no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4C2×C22⋊D4311yescharacteristic
260C22×C4C2×C22⋊D4311yescharacteristic
261C22×C4C2×C22⋊D4311yescharacteristic
262Q16—3442no—
263SD16—3442no—
264M16—1721no—
265M16—1721no—
266C2×C8—1721no—
267C2×C8—1721no—
268C2×C8—1721no—
269C4⋊C4—41no—
270C4⋊C4—81no—
271C4⋊C4—81no—
272C4⋊C4—861no—
273C4⋊C4—861no—
274C4⋊C4—861no—
275C4⋊C4—861no—
276C4⋊C4—1721no—
277C4⋊C4—1721no—
278C22⋊C4—41no—
279C22⋊C4—41no—
280C22⋊C4—81no—
281C22⋊C4—81no—
282C22⋊C4—81no—
283C22⋊C4—81no—
284C22⋊C4—81no—
285C22⋊C4—1721no—
286C42—41no—
287C42—1721no—
288C23—41no—
289C23—41no—
290C23—41no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23—41no—
295C23#1306329411yescharacteristic
296Q8—42no—
297Q8—42no—
298Q8—81no—
299Q8—81no—
300Q8—3441no—
301Q8—3441no—
302D4—42no—
303D4—81no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—1721no—
326C2×C4—1721no—
327C2×C4#1306334511yescharacteristic
328C2×C4#1306335511yescharacteristic
329C8—3441no—
330C8—3441no—
331C8—3441no—
332C22—21no—
333C22—21no—
334C22—81no—
335C22—81no—
336C22—81no—
337C22—81no—
338C22—81no—
339C22—81no—
340C22—81no—
341C22#1458306111yescharacteristic
342C22#1458307711yescharacteristic
343C22#1458308611yescharacteristic
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—81no—
349C4—81no—
350C4—81no—
351C4—81no—
352C4—81no—
353C4—3441no—
354C4—3441no—
355C2—21no—
356C2—21no—
357C2—161no—
358C2#1913357511yescharacteristic
359C2#1913659611yescharacteristic
360C2#1913661611yescharacteristic
subgroupG/H
centerC22#14583086
commutator, cosocleC2×C4⋊C4×C43C23
FrattiniC2×C4⋊C4C22×D43
FittingC43×#2832C2
socleC22×C43B(4,𝔽2)
prime radicalC22×D4×C43D4
hypercenter#2832D43
hypocenterC43#12275
LCSG ▷ C2×C4⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2832

Complements

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

NH ≅ G/Ntype
1. #19135756C2semidirect
2. #19133568C2semidirect
4. #19132625C2semidirect
6. #19132529C2semidirect
207. C43#12275semidirect

Maximal subgroups

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

subgroupindex
#191357562
#191335682
#191335342
#191326252
#191325982
#191325292
C43×#28322
#1227543