Finite Group Databasebeta

← #24994239

Subgroups — #24994239

Order 11008.

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

normal subgroups only

This group has 474 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#19143233C211yesmaximal, characteristic
2#19139044C211yesmaximal, characteristic
3#19133127C212yesmaximal
4#19132447C212yesmaximal
5C43×#1820C211yesmaximal, characteristic
6C2×#13063304C2211yescharacteristic
7#14582960—24no—
8#14582923—21no—
9#14582863C2212yes—
10C4×#10621877—21no—
11#14582827—21no—
12#14582827—21no—
13#14582804C411yescharacteristic, complemented
14#14582804C411yescharacteristic, complemented
15#14582783—21no—
16#14582783—21no—
17#14582768C411yescharacteristic, complemented
18#14582764C411yescharacteristic, complemented
19C4×C22⋊Dic43C2211yescharacteristic
20#14582635—24no—
21C2×#117×C43C2211yescharacteristic
22C43×#381C2212yes—
23C43×#342—21no—
24C43×#342—21no—
25C22×Dic86C2×C411yescharacteristic
26C2×#10621877—22no—
27#13063304—22no—
28#13063304—22no—
29C2×C4⋊Dic43C2×C411yescharacteristic
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
37C4⋊(C43⋊C8)—24no—
38C22⋊(C43⋊C8)—22no—
39C22⋊(C43⋊C8)D414yes—
40#13063236—22no—
41C4×C43⋊C8—22no—
42C43⋊#95—21no—
43C43⋊#95—21no—
44C43⋊#95—21no—
45C43⋊#95—21no—
46C43⋊#95—21no—
47C43⋊#95—21no—
48C43⋊#95—21no—
49C23×C4×C43C2311yescharacteristic
50#117×C43—22no—
51#117×C43—22no—
52C2×C4⋊C4×C43C2×C411yescharacteristic
53C2×C4⋊C4×C43C2×C411yescharacteristic
54C2×C22⋊C4×C43—22no—
55C2×C22⋊C4×C43D411yescharacteristic
56C2×C22⋊C4×C43D411yescharacteristic
57C2×C42×C43D411yescharacteristic
58C2×C42×C43D411yescharacteristic
59#95×C43—22no—
60#95×C43—22no—
61C24×C43C2×D411yescharacteristic
62C22×C4×C43—41no—
63C22×C4×C43—41no—
64C22×C4×C43—42no—
65C22×C4×C43C22⋊C411yescharacteristic
66C22×C4×C43C22⋊C411yescharacteristic
67C22×C4×C43C22⋊C411yescharacteristic
68C22×C4×C43C22⋊C411yescharacteristic
69C22×C4×C43C22×C411yescharacteristic
70C22×C4×C43C2×D411yescharacteristic
71C22×C4×C43C2×D412yes—
72C22×C4×C43#4112yes—
73C22×Dic43—21no—
74C22×Dic43—21no—
75C22×Dic43—21no—
76C22×Dic43—21no—
77C2×Dic86—22no—
78C2×Dic86—41no—
79C2×Dic86—41no—
80C4⋊C4×C43—22no—
81C4⋊C4×C43—22no—
82C22⋊C4×C43—22no—
83C22⋊C4×C43—22no—
84C22⋊C4×C43—42no—
85C22⋊C4×C43—42no—
86C42×C43—21no—
87C42×C43—21no—
88C42×C43—21no—
89C42×C43—21no—
90C22⋊Dic43—42no—
91C22⋊Dic43—42no—
92C4⋊Dic43—22no—
93Dic43⋊C4—42no—
94Dic43⋊C4—42no—
95Dic43⋊C4—41no—
96Dic43⋊C4—41no—
97C4×Dic43—41no—
98C4×Dic43—41no—
99#10621877—42no—
100#10621877—42no—
101C2×C43⋊C8—24no—
102C23×C43—21no—
103C23×C43—21no—
104C23×C43—41no—
105C23×C43—41no—
106C23×C43C2×C22⋊C411yescharacteristic
107C23×C43#12112yes—
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—21no—
116C2×C4×C43—42no—
117C2×C4×C43—42no—
118C2×C4×C43—41no—
119C2×C4×C43—41no—
120C2×C4×C43—41no—
121C2×C4×C43—41no—
122C2×C4×C43—82no—
123C2×C4×C43—82no—
124C2×C4×C43—82no—
125C2×C4×C43C4×D412yes—
126C2×C4×C43#12011yescharacteristic
127C2×C4×C43#12311yescharacteristic
128C2×Dic43—22no—
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—
138C2×Dic43—41no—
139C2×Dic43—41no—
140Dic86—82no—
141C43⋊C8—44no—
142#9444—431nomaximal, Sylow
143C22×C43—21no—
144C22×C43—21no—
145C22×C43—22no—
146C22×C43—22no—
147C22×C43—22no—
148C22×C43—81no—
149C22×C43—81no—
150C22×C43#38611yescharacteristic
151C22×C43#41011yescharacteristic
152C22×C43#41011yescharacteristic
153C4×C43—21no—
154C4×C43—22no—
155C4×C43—21no—
156C4×C43—41no—
157C4×C43—41no—
158C4×C43—41no—
159C4×C43—41no—
160C4×C43—162no—
161Dic43—42no—
162Dic43—81no—
163Dic43—81no—
164Dic43—81no—
165#2921—431no—
166#2499—431no—
167#1820D4311yescharacteristic
168#1511—432no—
169#1284—432no—
170C2×C43—21no—
171C2×C43—21no—
172C2×C43—42no—
173C2×C43#188411yescharacteristic
174C2×C43#189911yescharacteristic
175C2×C43#190911yescharacteristic
176C2×C22⋊Q8—431no—
177C2×#117C2×D4311yescharacteristic
178#433—864no—
179#423—861no—
180#407—432no—
181C4×M16—861no—
182#397—861no—
183#397—861no—
184#391—431no—
185#391—431no—
186#387—861no—
187#387—861no—
188#384—431no—
189#382—431no—
190#381C2×D4312yes—
191C4×C22⋊C4—431no—
192#342—21no—
193#342—21no—
194#328—864no—
195C43#944411yescharacteristic, complemented, Sylow
196C22×Q8—431no—
197C23×C4C22×D4311yescharacteristic
198C2×M16—862no—
199C22⋊Q8—862no—
200C22⋊Q8—862no—
201#117—22no—
202#117—22no—
203C2×C4⋊C4—431no—
204C2×C4⋊C4—861no—
205C2×C4⋊C4—861no—
206C2×C4⋊C4—861no—
207C2×C4⋊C4C4×D4311yescharacteristic
208C2×C4⋊C4C4×D4311yescharacteristic
209C2×C22⋊C4—22no—
210C2×C22⋊C4—861no—
211C2×C22⋊C4—861no—
212C2×C22⋊C4C22⋊D4311yescharacteristic
213C2×C22⋊C4C22⋊D4311yescharacteristic
214C2×C42—431no—
215C2×C42—431no—
216C2×C42D17211yescharacteristic
217C2×C42D17211yescharacteristic
218C4⋊C8—864no—
219C22⋊C8—434no—
220C22⋊C8—862no—
221#97—862no—
222C4×C8—862no—
223#95—22no—
224#95—22no—
225#95—861no—
226#95—861no—
227#95—861no—
228#95—861no—
229#95—861no—
230#95—861no—
231#95—861no—
232C24C2×C22⋊D4311yescharacteristic
233C2×Q8—862no—
234C2×Q8—1721no—
235C2×Q8—1721no—
236C22×C4—41no—
237C22×C4—41no—
238C22×C4—42no—
239C22×C4—861no—
240C22×C4—861no—
241C22×C4—861no—
242C22×C4—861no—
243C22×C4(C2×D43)⋊C411yescharacteristic
244C22×C4(C2×D43)⋊C411yescharacteristic
245C22×C4(C2×D43)⋊C411yescharacteristic
246C22×C4(C2×D43)⋊C411yescharacteristic
247C22×C4C2×C4×D4311yescharacteristic
248C22×C4C2×D17211yescharacteristic
249C22×C4D4×D4312yes—
250C22×C4#1062190012yes—
251M16—1722no—
252M16—1722no—
253C2×C8—864no—
254C4⋊C4—22no—
255C4⋊C4—22no—
256C4⋊C4—862no—
257C4⋊C4—1722no—
258C4⋊C4—1722no—
259C4⋊C4—1721no—
260C4⋊C4—1721no—
261C22⋊C4—22no—
262C22⋊C4—22no—
263C22⋊C4—42no—
264C22⋊C4—42no—
265C22⋊C4—1722no—
266C22⋊C4—1722no—
267C42—21no—
268C42—21no—
269C42—21no—
270C42—21no—
271C42—1721no—
272C42—1721no—
273C23—21no—
274C23—21no—
275C23—41no—
276C23—41no—
277C23C2×(C2×D43)⋊C411yescharacteristic
278C23#1306329712yes—
279Q8—3442no—
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—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—82no—
295C2×C4—82no—
296C2×C4—82no—
297C2×C4—862no—
298C2×C4—1721no—
299C2×C4—1721no—
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(C22⋊D43)⋊C412yes—
310C2×C4#1306329511yescharacteristic
311C2×C4#1306330911yescharacteristic
312C8—1724no—
313C22—21no—
314C22—21no—
315C22—22no—
316C22—22no—
317C22—22no—
318C22—81no—
319C22—81no—
320C22#1458277611yescharacteristic
321C22#1458287211yescharacteristic
322C22#1458287211yescharacteristic
323C4—21no—
324C4—22no—
325C4—21no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—162no—
331C4—3441no—
332C4—3441no—
333C4—3441no—
334C4—1722no—
335C2—21no—
336C2—21no—
337C2—42no—
338C2#1913497611yescharacteristic
339C2#1913505111yescharacteristic
340C2#1913511511yescharacteristic
subgroupG/H
centerC22#14582776
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1820C2
socleC22×C43#386
prime radicalC24×C43C2×D4
cosocleC23×C4×C43C23
hypercenter#1820D43
hypocenterC43#9444
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1820

Complements

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

NH ≅ G/Ntype
13. #14582804C4semidirect
14. #14582804C4semidirect
17. #14582768C4semidirect
18. #14582764C4semidirect
195. C43#9444semidirect

Maximal subgroups

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

subgroupindex
#191432332
#191390442
#191331272
#191324472
C43×#18202
#944443