Finite Group Databasebeta

← #24998213

Subgroups — #24998213

Order 11008.

420 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 79 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#19145811C211yesmaximal, characteristic
2#19145801C211yesmaximal, characteristic
3#19145144C211yesmaximal, characteristic
4#19133069C211yesmaximal, characteristic
5#19133015C211yesmaximal, characteristic
6#19132468C211yesmaximal, characteristic
7C43×#1470C211yesmaximal, characteristic
8#14583456C2211yescharacteristic
9#14583456C2211yescharacteristic
10#14583309—21no—
11#14583309—21no—
12#14583309—21no—
13#14583308—21no—
14#14583298—22no—
15#14583269—21no—
16#14583268—21no—
17#14583241—22no—
18#14583234—21no—
19#14583229—21no—
20#14583203—22no—
21#14583195—21no—
22#14583185—21no—
23#14582956C2211yescharacteristic
24#14582939—21no—
25#14582939—21no—
26C4×#10621877C2211yescharacteristic
27#14582631—22no—
28#14582629—22no—
29C2×#125×C43C2211yescharacteristic
30C43×#432C2211yescharacteristic
31C43×#431C2211yescharacteristic
32C43×#324—22no—
33C2×#10621877—21no—
34#13063325D411yescharacteristic
35#13063325D411yescharacteristic
36#13063325D411yescharacteristic
37#13063325D411yescharacteristic
38#13063317—21no—
39#13063317—21no—
40#13063304—21no—
41#13063304—21no—
42#13063304—21no—
43#13063304—21no—
44C4×Dic86—21no—
45C4×Dic86—21no—
46C4×Dic86—21no—
47C4×Dic86—21no—
48#13063284—21no—
49#13063284—21no—
50#13063259—22no—
51#13063258—22no—
52#13063258—22no—
53#13063258—22no—
54#13063257—22no—
55#13063256—22no—
56#13063256—22no—
57#13063256—22no—
58C4⋊(C43⋊C8)D412yes—
59#13063250—22no—
60#13063250—22no—
61#13063248—22no—
62#13063248—22no—
63C22⋊(C43⋊C8)—21no—
64#13063236—21no—
65#13063236—21no—
66C4×C43⋊C8D412yes—
67#125×C43—21no—
68#125×C43—21no—
69#125×C43—21no—
70#125×C43—21no—
71C2×C4⋊C4×C43—21no—
72C2×C4⋊C4×C43—21no—
73C2×C4⋊C4×C43D411yescharacteristic
74C2×C4⋊C4×C43D411yescharacteristic
75C2×C42×C43C2311yescharacteristic
76C4⋊C8×C43—21no—
77C4⋊C8×C43—21no—
78C22⋊C8×C43—21no—
79C22⋊C8×C43D412yes—
80#97×C43—21no—
81C4×C8×C43—21no—
82C22×C4×C43—21no—
83C22×C4×C43—21no—
84C22×C4×C43C2×D411yescharacteristic
85C22×C4×C43C2×D411yescharacteristic
86C22×C4×C43#4111yescharacteristic
87C2×Dic86—21no—
88C2×Dic86—21no—
89C2×Dic86—21no—
90C2×Dic86—21no—
91C2×C8×C43—22no—
92C2×C8×C43—41no—
93C4⋊C4×C43—21no—
94C4⋊C4×C43—21no—
95C4⋊C4×C43—21no—
96C4⋊C4×C43—21no—
97C4⋊C4×C43—41no—
98C4⋊C4×C43—41no—
99C4⋊C4×C43—41no—
100C4⋊C4×C43—41no—
101C42×C43C2×D411yescharacteristic
102C42×C43C2×D411yescharacteristic
103C42×C43C2×D411yescharacteristic
104C42×C43C2×D411yescharacteristic
105C22⋊Dic43—41no—
106C22⋊Dic43—41no—
107C4⋊Dic43—21no—
108C4⋊Dic43—21no—
109C4⋊Dic43—21no—
110C4⋊Dic43—21no—
111C4⋊Dic43—21no—
112C4⋊Dic43—21no—
113C4⋊Dic43—21no—
114C4⋊Dic43—21no—
115Dic43⋊C4—41no—
116Dic43⋊C4—41no—
117Dic43⋊C4—41no—
118Dic43⋊C4—41no—
119C4×Dic43—41no—
120C4×Dic43—41no—
121#10621877—24no—
122C2×C43⋊C8—22no—
123C2×C43⋊C8—22no—
124C23×C43#12111yescharacteristic
125C2×C4×C43—22no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43—42no—
129C2×C4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43—81no—
132C2×C4×C43#12011yescharacteristic
133C2×C4×C43#12011yescharacteristic
134C2×C4×C43#12011yescharacteristic
135C2×C4×C43#12111yescharacteristic
136C2×C4×C43#12111yescharacteristic
137C2×C4×C43#12711yescharacteristic
138C2×Dic43—41no—
139C2×Dic43—41no—
140C2×Dic43—41no—
141C2×Dic43—41no—
142Dic86—42no—
143Dic86—42no—
144Dic86—42no—
145Dic86—42no—
146C8×C43—42no—
147C8×C43—81no—
148C43⋊C8—24no—
149C43⋊C8—42no—
150#10127—431nomaximal, Sylow
151C22×C43—21no—
152C22×C43—21no—
153C22×C43—21no—
154C22×C43#39211yescharacteristic
155C4×C43—21no—
156C4×C43—21no—
157C4×C43—21no—
158C4×C43—21no—
159C4×C43—21no—
160C4×C43—81no—
161C4×C43—81no—
162C4×C43#45612yes—
163Dic43—81no—
164Dic43—81no—
165Dic43—81no—
166Dic43—81no—
167#3237—431no—
168#3236—431no—
169#3166—431no—
170#1497—431no—
171#1485—431no—
172#1470D4311yescharacteristic
173#1291—431no—
174C2×C43—41no—
175C2×C43#200511yescharacteristic
176C2×C43#200911yescharacteristic
177C2×C43#201711yescharacteristic
178#533—431no—
179#533—431no—
180C2×#125C2×D4311yescharacteristic
181#501—861no—
182#501—861no—
183#501—861no—
184#501—861no—
185#499—862no—
186#491—861no—
187#491—861no—
188#485—862no—
189#484—861no—
190#483—861no—
191#479—862no—
192#477—861no—
193#475—861no—
194#432—431no—
195#432C2×D4311yescharacteristic
196#431C2×D4311yescharacteristic
197#428—861no—
198#428—861no—
199C4×M16—431no—
200Q8⋊C8—862no—
201Q8⋊C8—862no—
202#324—22no—
203C43#1012711yescharacteristic, complemented, Sylow
204C2×M16—861no—
205C4⋊Q8—431no—
206C4⋊Q8—431no—
207C4⋊Q8—431no—
208C4⋊Q8—431no—
209#125—21no—
210#125—21no—
211#125—21no—
212#125—21no—
213#125—861no—
214#125—861no—
215C22⋊Q8—861no—
216C22⋊Q8—861no—
217C22⋊Q8—861no—
218C22⋊Q8—861no—
219C4×Q8—861no—
220C4×Q8—861no—
221C4×Q8—861no—
222C4×Q8—861no—
223#117—861no—
224#117—861no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4D17211yescharacteristic
228C2×C4⋊C4D17211yescharacteristic
229C2×C42C22×D4311yescharacteristic
230#107—862no—
231#107—862no—
232#107—862no—
233#107—862no—
234#106—862no—
235#106—862no—
236#106—862no—
237#106—862no—
238C4⋊C8—21no—
239C4⋊C8—21no—
240C4⋊C8—432no—
241#103—862no—
242#103—862no—
243#103—862no—
244#103—862no—
245C22⋊C8—21no—
246C22⋊C8—861no—
247C22⋊C8C22⋊D4312yes—
248#97—21no—
249#97—861no—
250#97—861no—
251C4×C8—21no—
252C4×C8—432no—
253C2×Q8—861no—
254C2×Q8—861no—
255C2×Q8—861no—
256C2×Q8—861no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4C2×D17211yescharacteristic
260C22×C4#1062189811yescharacteristic
261C22×C4C2×C22⋊D4311yescharacteristic
262M16—864no—
263C2×C8—22no—
264C2×C8—41no—
265C2×C8—862no—
266C2×C8—862no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—861no—
276C4⋊C4—861no—
277C4⋊C4—861no—
278C4⋊C4—861no—
279C4⋊C4—861no—
280C4⋊C4—861no—
281C4⋊C4—861no—
282C4⋊C4—861no—
283C4⋊C4—1721no—
284C4⋊C4—1721no—
285C4⋊C4—1721no—
286C4⋊C4—1721no—
287C22⋊C4—1721no—
288C22⋊C4—1721no—
289C42—1721no—
290C42—1721no—
291C42D4×D4311yescharacteristic
292C42D4×D4311yescharacteristic
293C42D4×D4311yescharacteristic
294C42D4×D4311yescharacteristic
295C23#1306329911yescharacteristic
296Q8—1722no—
297Q8—1722no—
298Q8—1722no—
299Q8—1722no—
300C2×C4—22no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—42no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—81no—
307C2×C4—1721no—
308C2×C4—1721no—
309C2×C4—1721no—
310C2×C4—1721no—
311C2×C4#1306329311yescharacteristic
312C2×C4#1306329511yescharacteristic
313C2×C4#1306329511yescharacteristic
314C2×C4#1306329811yescharacteristic
315C2×C4#1306329811yescharacteristic
316C2×C4#1306332111yescharacteristic
317C8—42no—
318C8—81no—
319C8—864no—
320C8—1722no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22#1458280811yescharacteristic
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—81no—
331C4—81no—
332C4—3441no—
333C4—3441no—
334C4—3441no—
335C4—3441no—
336C4#1458308412yes—
337C2—41no—
338C2#1913563311yescharacteristic
339C2#1913565411yescharacteristic
340C2#1913569911yescharacteristic
subgroupG/H
centerC22#14582808
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1470C2
socleC22×C43#392
prime radicalC23×C43#121
hypercenter#1470D43
hypocenterC43#10127
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1470

Complements

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

NH ≅ G/Ntype
203. C43#10127semidirect

Maximal subgroups

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

subgroupindex
#191458112
#191458012
#191451442
#191330692
#191330152
#191324682
C43×#14702
#1012743