Finite Group Databasebeta

← #25069450

Subgroups — #25069450

Order 11008.

934 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 934 conjugacy classes of subgroups — too many to draw. Only its 167 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#19148405C211yesmaximal, characteristic, complemented
2#19144694C212yesmaximal
3#19133636C214yesmaximal, complemented
4#19133534C214yesmaximal
5#19133106C212yesmaximal, complemented
6#19132939C211yesmaximal, characteristic, complemented
7C43×#2398C211yesmaximal, characteristic
8Q8×Dic86—22no—
9#14583628—22no—
10#14583625—24no—
11#14583530—21no—
12#14583530C2214yes—
13#14583456—22no—
14#14583456C2212yes—
15#14583377—21no—
16#14583234C2214yes—
17#14583179—22no—
18#14583104—22no—
19#14583050C2214yes—
20#14582999—24no—
21#14582956C2212yes—
22#14582635C2218yes—
23#14582625C2214yes—
24C2×C4×Q8×C43C2211yescharacteristic
25C2×C4×D4×C43C2211yescharacteristic
26C43×#400C2212yes—
27C43×#397—21no—
28C43×#394C2212yes—
29C43×#393—21no—
30C4×C22⋊C4×C43—22no—
31C43×#376C2211yescharacteristic
32C2×#10621883—24no—
33#13063325—22no—
34#13063325—22no—
35#13063325D412yes—
36#13063325D412yes—
37#13063324—24no—
38#13063324—28no—
39#13063317—24no—
40#13063317—22no—
41#13063316—24no—
42#13063316—28no—
43#13063304—22no—
44#13063304—24no—
45#13063304C2314yes—
46Q8×Dic43—24no—
47Q8×Dic43—24no—
48C4×Dic86—24no—
49C4×Dic86—24no—
50C4×Dic86—22no—
51C4×Dic86D414yes—
52#13063284—24no—
53#13063284—22no—
54#13063258—24no—
55C4⋊(C43⋊C8)—22no—
56#13063248—24no—
57#13063246—24no—
58C22⋊(C43⋊C8)C2314yes—
59#13063236—22no—
60C22×Q8×C43D411yescharacteristic
61C22×D4×C43C2311yescharacteristic
62C23×C4×C43—21no—
63C4×Q8×C43—22no—
64C4×Q8×C43—22no—
65C4×D4×C43—22no—
66C4×D4×C43—22no—
67C2×C4⋊C4×C43D411yescharacteristic
68C2×C4⋊C4×C43C2311yescharacteristic
69C2×C4⋊C4×C43C2312yes—
70C2×C22⋊C4×C43—21no—
71C2×C22⋊C4×C43—22no—
72C2×C22⋊C4×C43—22no—
73C2×C42×C43—21no—
74C2×C42×C43D412yes—
75C2×C42×C43C2311yescharacteristic
76#95×C43—21no—
77#95×C43—22no—
78#95×C43—22no—
79#95×C43C2312yes—
80C24×C43—21no—
81C2×Q8×C43—22no—
82C2×Q8×C43—24no—
83C2×D4×C43—22no—
84C2×D4×C43—42no—
85C22×C4×C43—21no—
86C22×C4×C43—22no—
87C22×C4×C43—44no—
88C22×C4×C43—41no—
89C22×C4×C43—41no—
90C22×C4×C43C2×D411yescharacteristic
91C22×C4×C43C2×D411yescharacteristic
92C22×C4×C43C2×D412yes—
93C22×C4×C43C2×D412yes—
94C22×C4×C43C2411yescharacteristic
95C2×Dic86—22no—
96C2×Dic86—24no—
97C2×Dic86C2×D414yes—
98C4⋊C4×C43—22no—
99C4⋊C4×C43—24no—
100C4⋊C4×C43—22no—
101C22⋊C4×C43—44no—
102C22⋊C4×C43—42no—
103C22⋊C4×C43—44no—
104C42×C43—22no—
105C42×C43—22no—
106C42×C43—42no—
107C42×C43C2×D412yes—
108C42×C43C2×D412yes—
109C22⋊Dic43—24no—
110#10621883—48no—
111C4⋊Dic43—24no—
112C4⋊Dic43—24no—
113C4⋊Dic43—24no—
114C4⋊Dic43—22no—
115C4⋊Dic43—22no—
116C4⋊Dic43—22no—
117C4⋊Dic43C2×D414yes—
118Dic43⋊C4—28no—
119Dic43⋊C4—24no—
120Dic43⋊C4—24no—
121C4×Dic43—28no—
122C4×Dic43—24no—
123C2×C43⋊C8—24no—
124C23×C43—22no—
125C23×C43—42no—
126C23×C43—41no—
127C23×C43—41no—
128C23×C43—42no—
129C23×C43C22×D411yescharacteristic
130Q8×C43—28no—
131D4×C43—24no—
132D4×C43—42no—
133C2×C4×C43—22no—
134C2×C4×C43—22no—
135C2×C4×C43—22no—
136C2×C4×C43—22no—
137C2×C4×C43—22no—
138C2×C4×C43—41no—
139C2×C4×C43—42no—
140C2×C4×C43—42no—
141C2×C4×C43—42no—
142C2×C4×C43—42no—
143C2×C4×C43—41no—
144C2×C4×C43—42no—
145C2×C4×C43—82no—
146C2×C4×C43—82no—
147C2×C4×C43#12012yes—
148C2×C4×C43#12011yescharacteristic
149C2×C4×C43#12011yescharacteristic
150C2×C4×C43#13714yes—
151C2×C4×C43C22×D412yes—
152C2×Dic43—24no—
153C2×Dic43—24no—
154Dic86—44no—
155Dic86—44no—
156Dic86—84no—
157C43⋊C8—44no—
158#18188—431nomaximal, Sylow
159C22×C43—21no—
160C22×C43—21no—
161C22×C43—44no—
162C22×C43—42no—
163C22×C43—82no—
164C22×C43—81no—
165C22×C43—81no—
166C22×C43C2×#12011yescharacteristic
167C22×C43C2×#13712yes—
168C4×C43—22no—
169C4×C43—24no—
170C4×C43—21no—
171C4×C43—22no—
172C4×C43—42no—
173C4×C43—82no—
174C4×C43—81no—
175C4×C43#45412yes—
176Dic43—44no—
177Dic43—44no—
178#3502—431no—
179#3110—432no—
180#2398D4311yescharacteristic
181#1617—434no—
182#1599—434no—
183#1506—432no—
184#1467—431no—
185C2×C43—22no—
186C2×C43—82no—
187C2×C43#300411yescharacteristic
188C2×C43C2×#45411yescharacteristic
189C2×C43#302511yescharacteristic
190Q82—862no—
191#557—864no—
192#557—862no—
193#544—434no—
194#544—861no—
195#533—432no—
196#533—862no—
197#519—861no—
198C2×C4×Q8C2×D4311yescharacteristic
199C2×C4×D4C2×D4311yescharacteristic
200#484—434no—
201#474—862no—
202#461—862no—
203#450—434no—
204#440—864no—
205#432—432no—
206#400C2×D4312yes—
207#397—21no—
208#394C2×D4312yes—
209#393—21no—
210C4×C22⋊C4—22no—
211#376C2×D4311yescharacteristic
212#328—438no—
213#324—434no—
214C43#1818811yescharacteristic, complemented, Sylow
215C22×Q8C22⋊D4311yescharacteristic
216C22×D4C22×D4311yescharacteristic
217C23×C4—21no—
218C2×SD16—864no—
219C4⋊Q8—432no—
220C4⋊Q8—432no—
221C4⋊Q8—862no—
222C4⋊Q8—862no—
223C4⋊Q8—868no—
224C4⋊Q8—864no—
225#125—864no—
226#125—868no—
227#125—864no—
228#125—862no—
229C22⋊Q8—434no—
230C22⋊Q8—862no—
231C22⋊Q8—864no—
232C4×Q8—22no—
233C4×Q8—22no—
234C4×Q8—434no—
235C4×Q8—864no—
236C4×Q8—864no—
237C4×Q8—864no—
238C4×Q8—864no—
239C4×Q8—862no—
240C4×D4—22no—
241C4×D4—22no—
242#117—862no—
243#117—864no—
244C2×C4⋊C4C22⋊D4311yescharacteristic
245C2×C4⋊C4C22×D4311yescharacteristic
246C2×C4⋊C4C22×D4312yes—
247C2×C22⋊C4—21no—
248C2×C22⋊C4—22no—
249C2×C22⋊C4—22no—
250C2×C42—21no—
251C2×C42C22⋊D4312yes—
252C2×C42C22×D4311yescharacteristic
253#107—864no—
254C4⋊C8—862no—
255#103—864no—
256#102—864no—
257C22⋊C8—434no—
258#97—862no—
259#95—21no—
260#95—22no—
261#95—22no—
262#95C22×D4312yes—
263C24—21no—
264C2×Q8—22no—
265C2×Q8—24no—
266C2×Q8—434no—
267C2×Q8—864no—
268C2×Q8—862no—
269C2×D4—22no—
270C2×D4—42no—
271C22×C4—21no—
272C22×C4—22no—
273C22×C4—44no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4C2×C22⋊D4311yescharacteristic
277C22×C4C2×C22⋊D4311yescharacteristic
278C22×C4C2×C22⋊D4312yes—
279C22×C4C2×C22⋊D4312yes—
280C22×C4C23×D4311yescharacteristic
281SD16—1728no—
282C2×C8—864no—
283C4⋊C4—22no—
284C4⋊C4—24no—
285C4⋊C4—22no—
286C4⋊C4—434no—
287C4⋊C4—864no—
288C4⋊C4—864no—
289C4⋊C4—864no—
290C4⋊C4—868no—
291C4⋊C4—862no—
292C4⋊C4—862no—
293C4⋊C4—864no—
294C4⋊C4—862no—
295C4⋊C4—864no—
296C22⋊C4—44no—
297C22⋊C4—42no—
298C22⋊C4—44no—
299C22⋊C4—864no—
300C42—22no—
301C42—22no—
302C42—42no—
303C42—868no—
304C42—864no—
305C42D4×D4312yes—
306C42D4×D4312yes—
307C23—22no—
308C23—42no—
309C23—41no—
310C23—41no—
311C23—42no—
312C23C22×C22⋊D4311yescharacteristic
313Q8—28no—
314Q8—3444no—
315Q8—1724no—
316Q8—1724no—
317D4—24no—
318D4—42no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—41no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—41no—
330C2×C4—42no—
331C2×C4—82no—
332C2×C4—82no—
333C2×C4—864no—
334C2×C4—864no—
335C2×C4#1306329311yescharacteristic
336C2×C4#1306329312yes—
337C2×C4#1306329311yescharacteristic
338C2×C4#1306335514yes—
339C2×C4C2×D4×D4312yes—
340C8—1724no—
341C22—21no—
342C22—21no—
343C22—44no—
344C22—42no—
345C22—82no—
346C22—81no—
347C22—81no—
348C22C2×#1306329311yescharacteristic
349C22C2×#1306335512yes—
350C4—22no—
351C4—22no—
352C4—24no—
353C4—21no—
354C4—42no—
355C4—82no—
356C4—81no—
357C4—1724no—
358C4—1724no—
359C4#1458307112yes—
360C2—22no—
361C2—82no—
362C2#1914382811yescharacteristic
363C2C2×#1458307111yescharacteristic
364C2#1914398611yescharacteristic
subgroupG/H
centerC22C2×#13063293
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2398C2
socleC22×C43C2×#120
prime radicalC22×D4×C43C23
hypercenter#2398D43
hypocenterC43#18188
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2398

Complements

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

NH ≅ G/Ntype
1. #19148405C2semidirect
3. #19133636C2semidirect
5. #19133106C2semidirect
6. #19132939C2semidirect
214. C43#18188semidirect

Maximal subgroups

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

subgroupindex
#191484052
#191446942
#191336362
#191335342
#191331062
#191329392
C43×#23982
#1818843