Finite Group Databasebeta

← #24997522

Subgroups — #24997522

Order 11008.

470 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 81 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#19145144C211yesmaximal, characteristic
2#19144725C211yesmaximal, characteristic
3#19133222C211yesmaximal, characteristic
4#19133145C211yesmaximal, characteristic
5#19133042C211yesmaximal, characteristic
6#19132459C211yesmaximal, characteristic
7C43×#2634C211yesmaximal, characteristic
8#14583456C2211yescharacteristic
9#14583309—21no—
10#14583309—21no—
11#14583298—22no—
12#14583229—21no—
13#14583184—21no—
14#14583109—21no—
15#14583055—21no—
16#14583004—22no—
17#14582956C2211yescharacteristic
18#14582956C2211yescharacteristic
19#14582939—21no—
20#14582939—21no—
21C4×#10621877C2211yescharacteristic
22#14582641—22no—
23#14582635—22no—
24Q8⋊(C43⋊C8)—22no—
25C2×#125×C43C2211yescharacteristic
26C2×C4×Q8×C43C2211yescharacteristic
27C43×#400—21no—
28C43×#400—21no—
29C43×#398—21no—
30C43×#395—21no—
31C43×#387—22no—
32C43×#383C2211yescharacteristic
33C2×#10621885—22no—
34C2×#10621877—21no—
35#13063325D411yescharacteristic
36#13063325D411yescharacteristic
37#13063317—21no—
38#13063304—21no—
39#13063304—21no—
40C4×Dic86—21no—
41C4×Dic86—21no—
42#13063284—21no—
43#13063258—22no—
44#13063258—22no—
45#13063256—22no—
46#13063256—22no—
47#13063256—22no—
48C4⋊(C43⋊C8)—21no—
49C4⋊(C43⋊C8)—21no—
50#13063249—22no—
51#13063248—22no—
52C22⋊(C43⋊C8)—21no—
53C22⋊(C43⋊C8)—21no—
54#13063236—21no—
55#13063236—21no—
56#13063236D412yes—
57C4×C43⋊C8D412yes—
58C22×Q8×C43D411yescharacteristic
59#125×C43—21no—
60#125×C43—21no—
61#125×C43—21no—
62#125×C43—21no—
63C4×Q8×C43—21no—
64C4×Q8×C43—21no—
65C4×Q8×C43—21no—
66C4×Q8×C43—21no—
67C2×C4⋊C4×C43—22no—
68C2×C4⋊C4×C43—21no—
69C2×C4⋊C4×C43—21no—
70C2×C4⋊C4×C43—21no—
71C2×C4⋊C4×C43D411yescharacteristic
72C2×C4⋊C4×C43D411yescharacteristic
73C2×C4⋊C4×C43D411yescharacteristic
74C2×C42×C43—21no—
75C2×C42×C43C2311yescharacteristic
76#95×C43—22no—
77#95×C43—22no—
78#95×C43—22no—
79#95×C43—21no—
80#95×C43—21no—
81#95×C43D412yes—
82C2×Q8×C43—21no—
83C2×Q8×C43—21no—
84C2×Q8×C43—42no—
85C22×C4×C43—21no—
86C22×C4×C43—22no—
87C22×C4×C43—21no—
88C22×C4×C43—21no—
89C22×C4×C43—21no—
90C22×C4×C43C2×D411yescharacteristic
91C22×C4×C43C2×D411yescharacteristic
92C22×C4×C43C2×D411yescharacteristic
93C2×Dic86—21no—
94C2×Dic86—21no—
95C4⋊C4×C43—21no—
96C4⋊C4×C43—21no—
97C4⋊C4×C43—21no—
98C4⋊C4×C43—21no—
99C4⋊C4×C43—21no—
100C4⋊C4×C43—21no—
101C4⋊C4×C43—44no—
102C4⋊C4×C43—41no—
103C4⋊C4×C43—41no—
104C4⋊C4×C43—41no—
105C4⋊C4×C43—41no—
106C4⋊C4×C43—41no—
107C4⋊C4×C43—41no—
108C42×C43—41no—
109C42×C43—41no—
110C42×C43C2×D411yescharacteristic
111C42×C43C2×D411yescharacteristic
112C42×C43C2×D411yescharacteristic
113C42×C43#4111yescharacteristic
114C22⋊Dic43—41no—
115#10621885—44no—
116C4⋊Dic43—21no—
117C4⋊Dic43—21no—
118C4⋊Dic43—21no—
119C4⋊Dic43—21no—
120Dic43⋊C4—41no—
121Dic43⋊C4—41no—
122C4×Dic43—41no—
123#10621877—24no—
124C2×C43⋊C8—22no—
125C2×C43⋊C8—22no—
126C2×C43⋊C8—41no—
127C23×C43#12011yescharacteristic
128Q8×C43—22no—
129Q8×C43—22no—
130Q8×C43—41no—
131Q8×C43—41no—
132C2×C4×C43—22no—
133C2×C4×C43—22no—
134C2×C4×C43—41no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43—41no—
138C2×C4×C43—42no—
139C2×C4×C43—42no—
140C2×C4×C43—42no—
141C2×C4×C43—42no—
142C2×C4×C43—41no—
143C2×C4×C43—41no—
144C2×C4×C43—41no—
145C2×C4×C43—42no—
146C2×C4×C43—42no—
147C2×C4×C43#12011yescharacteristic
148C2×C4×C43#12011yescharacteristic
149C2×C4×C43#12111yescharacteristic
150C2×C4×C43#12111yescharacteristic
151C2×C4×C43#12111yescharacteristic
152C2×C4×C43#12711yescharacteristic
153C2×Dic43—41no—
154C2×Dic43—41no—
155Dic86—42no—
156Dic86—81no—
157C43⋊C8—24no—
158C43⋊C8—42no—
159C43⋊C8—81no—
160#10025—431nomaximal, Sylow
161C22×C43—21no—
162C22×C43—21no—
163C22×C43#39211yescharacteristic
164C22×C43#45612yes—
165C4×C43—21no—
166C4×C43—21no—
167C4×C43—21no—
168C4×C43—21no—
169C4×C43—21no—
170C4×C43—21no—
171C4×C43—42no—
172C4×C43—82no—
173C4×C43—81no—
174C4×C43—81no—
175C4×C43—81no—
176Dic43—81no—
177Dic43—81no—
178#3166—431no—
179#3113—431no—
180#2634D4311yescharacteristic
181#1534—431no—
182#1515—431no—
183#1491—431no—
184#1288—431no—
185C2×C43—22no—
186C2×C43#200511yescharacteristic
187C2×C43#200911yescharacteristic
188C2×C43#201011yescharacteristic
189#533—431no—
190C2×#125C2×D4311yescharacteristic
191C2×C4×Q8C2×D4311yescharacteristic
192#501—861no—
193#501—861no—
194#499—862no—
195#483—861no—
196#475—861no—
197#462—861no—
198#451—861no—
199#441—862no—
200#432—431no—
201#432—431no—
202#428—861no—
203#428—861no—
204C4×M16—431no—
205#400—21no—
206#400—21no—
207#398—21no—
208#395—21no—
209#387—22no—
210#383C2×D4311yescharacteristic
211#330—862no—
212#328—862no—
213Q8⋊C8—862no—
214C43#1002511yescharacteristic, complemented, Sylow
215C22×Q8C22⋊D4311yescharacteristic
216C2×Q16—862no—
217C2×M16—861no—
218C4⋊Q8—431no—
219C4⋊Q8—431no—
220#125—21no—
221#125—21no—
222#125—21no—
223#125—21no—
224#125—861no—
225C22⋊Q8—861no—
226C22⋊Q8—861no—
227C4×Q8—21no—
228C4×Q8—21no—
229C4×Q8—21no—
230C4×Q8—21no—
231C4×Q8—861no—
232C4×Q8—861no—
233#117—861no—
234C2×C4⋊C4—22no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4C22⋊D4311yescharacteristic
239C2×C4⋊C4C22⋊D4311yescharacteristic
240C2×C4⋊C4C22⋊D4311yescharacteristic
241C2×C42—21no—
242C2×C42C22×D4311yescharacteristic
243#107—862no—
244#107—862no—
245#106—862no—
246#106—862no—
247#106—862no—
248C4⋊C8—861no—
249C4⋊C8—861no—
250#103—862no—
251#103—862no—
252C22⋊C8—861no—
253C22⋊C8—861no—
254#97—432no—
255#97—861no—
256#97—861no—
257C4×C8—432no—
258#95—22no—
259#95—22no—
260#95—22no—
261#95—21no—
262#95—21no—
263#95C22⋊D4312yes—
264C2×Q8—21no—
265C2×Q8—21no—
266C2×Q8—42no—
267C2×Q8—861no—
268C2×Q8—861no—
269C22×C4—21no—
270C22×C4—22no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4C2×C22⋊D4311yescharacteristic
275C22×C4C2×C22⋊D4311yescharacteristic
276C22×C4C2×C22⋊D4311yescharacteristic
277Q16—1724no—
278M16—864no—
279C2×C8—862no—
280C2×C8—862no—
281C2×C8—1721no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—44no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—861no—
296C4⋊C4—861no—
297C4⋊C4—861no—
298C4⋊C4—861no—
299C4⋊C4—1721no—
300C4⋊C4—1721no—
301C22⋊C4—1721no—
302C42—41no—
303C42—41no—
304C42—1721no—
305C42D4×D4311yescharacteristic
306C42D4×D4311yescharacteristic
307C42D4×D4311yescharacteristic
308C42#1062190011yescharacteristic
309C23#1306329411yescharacteristic
310Q8—22no—
311Q8—22no—
312Q8—41no—
313Q8—41no—
314Q8—3441no—
315Q8—1722no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—1721no—
332C2×C4—1721no—
333C2×C4#1306329311yescharacteristic
334C2×C4#1306329311yescharacteristic
335C2×C4#1306329611yescharacteristic
336C2×C4#1306329711yescharacteristic
337C2×C4#1306329711yescharacteristic
338C2×C4#1306332111yescharacteristic
339C8—864no—
340C8—3441no—
341C8—1722no—
342C22—21no—
343C22—21no—
344C22#1458280711yescharacteristic
345C22#1458308212yes—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—42no—
353C4—82no—
354C4—81no—
355C4—81no—
356C4—81no—
357C4—3441no—
358C4—3441no—
359C2—22no—
360C2#1913562911yescharacteristic
361C2#1913565511yescharacteristic
362C2#1913566011yescharacteristic
subgroupG/H
centerC22#14582807
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#2634C2
socleC22×C43#392
prime radicalC23×C43#120
hypercenter#2634D43
hypocenterC43#10025
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2634

Complements

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

NH ≅ G/Ntype
214. C43#10025semidirect

Maximal subgroups

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

subgroupindex
#191451442
#191447252
#191332222
#191331452
#191330422
#191324592
C43×#26342
#1002543