Finite Group Databasebeta

← #24997521

Subgroups — #24997521

Order 11008.

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

normal subgroups only

This group has 470 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#19145148C211yesmaximal, characteristic
2#19144721C211yesmaximal, characteristic
3#19140474C211yesmaximal, characteristic
4#19133221C211yesmaximal, characteristic
5#19133041C211yesmaximal, characteristic
6#19132459C211yesmaximal, characteristic
7C43×#1515C211yesmaximal, characteristic
8C2×#13063317C2211yescharacteristic
9C2×C4×Dic86C2211yescharacteristic
10#14583305—21no—
11#14583305—21no—
12#14583298—22no—
13#14583227—21no—
14#14583181—21no—
15#14583106—21no—
16#14583054—21no—
17#14583004—22no—
18#14582956C2211yescharacteristic
19#14582942—21no—
20#14582942—21no—
21C4×#10621877C2211yescharacteristic
22#14582839—21no—
23#14582839—21no—
24#14582831—21no—
25#14582820—21no—
26#14582784—22no—
27#14582640—22no—
28#14582629—22no—
29C43×#533C2211yescharacteristic
30C43×#432C2211yescharacteristic
31C43×#383C2211yescharacteristic
32C43×#328—22no—
33C22×Dic86D411yescharacteristic
34C2×#10621885—22no—
35C2×#10621877—21no—
36#13063317—21no—
37#13063317—21no—
38#13063317—21no—
39#13063317—21no—
40C4×Dic86—21no—
41C4×Dic86—21no—
42C4×Dic86—21no—
43C4×Dic86—21no—
44C2×C4⋊Dic43—22no—
45C2×C4⋊Dic43D411yescharacteristic
46C2×C4⋊Dic43D411yescharacteristic
47C2×C4⋊Dic43D411yescharacteristic
48C2×Dic43⋊C4—21no—
49C2×Dic43⋊C4—21no—
50C2×Dic43⋊C4—21no—
51C2×C4×Dic43—21no—
52#13063258—22no—
53#13063258—22no—
54#13063256—22no—
55#13063256—22no—
56#13063256—22no—
57C4⋊(C43⋊C8)—21no—
58#13063249—22no—
59#13063248—22no—
60C22⋊(C43⋊C8)—21no—
61#13063236—21no—
62#13063236D412yes—
63C4×C43⋊C8D412yes—
64C43⋊#95—22no—
65C43⋊#95—22no—
66C43⋊#95—22no—
67C4⋊Q8×C43D411yescharacteristic
68C4⋊Q8×C43D411yescharacteristic
69#125×C43—21no—
70C22⋊Q8×C43—21no—
71C22⋊Q8×C43—21no—
72C4×Q8×C43—21no—
73C4×Q8×C43—21no—
74#117×C43—21no—
75C2×C42×C43C2311yescharacteristic
76C4⋊C8×C43—21no—
77C22⋊C8×C43—21no—
78#97×C43—21no—
79#95×C43—21no—
80#95×C43—21no—
81#95×C43D412yes—
82C2×Q8×C43—21no—
83C2×Q8×C43—21no—
84C22×C4×C43—22no—
85C22×C4×C43C2×D411yescharacteristic
86C22×C4×C43C2×D411yescharacteristic
87C22×C4×C43C2×D411yescharacteristic
88C22×Dic43—21no—
89C22×Dic43—21no—
90C22×Dic43—21no—
91C22×Dic43—21no—
92C2×Dic86—21no—
93C2×Dic86—21no—
94C2×Dic86—42no—
95C2×C8×C43—41no—
96C4⋊C4×C43—21no—
97C4⋊C4×C43—21no—
98C4⋊C4×C43—21no—
99C4⋊C4×C43—21no—
100C4⋊C4×C43—41no—
101C4⋊C4×C43—41no—
102C22⋊C4×C43—41no—
103C42×C43—41no—
104C42×C43C2×D411yescharacteristic
105C42×C43C2×D411yescharacteristic
106C42×C43C2×D411yescharacteristic
107C42×C43#4111yescharacteristic
108#10621885—44no—
109C4⋊Dic43—21no—
110C4⋊Dic43—21no—
111C4⋊Dic43—21no—
112C4⋊Dic43—21no—
113C4⋊Dic43—21no—
114C4⋊Dic43—21no—
115C4⋊Dic43—44no—
116Dic43⋊C4—41no—
117Dic43⋊C4—41no—
118Dic43⋊C4—41no—
119Dic43⋊C4—41no—
120Dic43⋊C4—41no—
121Dic43⋊C4—41no—
122C4×Dic43—41no—
123C4×Dic43—41no—
124#10621877—24no—
125C2×C43⋊C8—22no—
126C2×C43⋊C8—22no—
127C23×C43#12011yescharacteristic
128Q8×C43—42no—
129Q8×C43—81no—
130C2×C4×C43—22no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—42no—
134C2×C4×C43—42no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43—42no—
138C2×C4×C43#12011yescharacteristic
139C2×C4×C43#12011yescharacteristic
140C2×C4×C43#12111yescharacteristic
141C2×C4×C43#12111yescharacteristic
142C2×C4×C43#12111yescharacteristic
143C2×C4×C43#12711yescharacteristic
144C2×Dic43—22no—
145C2×Dic43—41no—
146C2×Dic43—41no—
147C2×Dic43—42no—
148C2×Dic43—42no—
149C2×Dic43—41no—
150C2×Dic43—41no—
151C2×Dic43—41no—
152C2×Dic43—42no—
153Dic86—22no—
154Dic86—22no—
155Dic86—41no—
156Dic86—41no—
157C8×C43—81no—
158C43⋊C8—24no—
159C43⋊C8—42no—
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—82no—
172C4×C43—81no—
173C4×C43—81no—
174Dic43—42no—
175Dic43—81no—
176Dic43—81no—
177Dic43—81no—
178#3166—431no—
179#3113—431no—
180#2634—431no—
181#1534—431no—
182#1515D4311yescharacteristic
183#1491—431no—
184#1288—431no—
185C2×C43—22no—
186C2×C43#200511yescharacteristic
187C2×C43#200911yescharacteristic
188C2×C43#201011yescharacteristic
189#533C2×D4311yescharacteristic
190C2×#125—431no—
191C2×C4×Q8—431no—
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#432C2×D4311yescharacteristic
202#428—861no—
203#428—861no—
204C4×M16—431no—
205#400—861no—
206#400—861no—
207#398—861no—
208#395—861no—
209#387—862no—
210#383C2×D4311yescharacteristic
211#330—862no—
212#328—22no—
213Q8⋊C8—862no—
214C43#1002511yescharacteristic, complemented, Sylow
215C22×Q8—431no—
216C2×Q16—862no—
217C2×M16—861no—
218C4⋊Q8D17211yescharacteristic
219C4⋊Q8D17211yescharacteristic
220#125—21no—
221#125—861no—
222#125—861no—
223#125—861no—
224#125—861no—
225C22⋊Q8—21no—
226C22⋊Q8—21no—
227C4×Q8—21no—
228C4×Q8—21no—
229C4×Q8—861no—
230C4×Q8—861no—
231C4×Q8—861no—
232C4×Q8—861no—
233#117—21no—
234C2×C4⋊C4—431no—
235C2×C4⋊C4—431no—
236C2×C4⋊C4—431no—
237C2×C4⋊C4—862no—
238C2×C4⋊C4—861no—
239C2×C4⋊C4—861no—
240C2×C4⋊C4—861no—
241C2×C42—861no—
242C2×C42C22×D4311yescharacteristic
243#107—862no—
244#107—862no—
245#106—862no—
246#106—862no—
247#106—862no—
248C4⋊C8—21no—
249C4⋊C8—861no—
250#103—862no—
251#103—862no—
252C22⋊C8—21no—
253C22⋊C8—861no—
254#97—21no—
255#97—432no—
256#97—861no—
257C4×C8—432no—
258#95—21no—
259#95—21no—
260#95—862no—
261#95—862no—
262#95—862no—
263#95C22⋊D4312yes—
264C2×Q8—21no—
265C2×Q8—21no—
266C2×Q8—861no—
267C2×Q8—861no—
268C2×Q8—1722no—
269C22×C4—22no—
270C22×C4—861no—
271C22×C4—861no—
272C22×C4—861no—
273C22×C4—861no—
274C22×C4D4×D4311yescharacteristic
275C22×C4D4×D4311yescharacteristic
276C22×C4C2×C22⋊D4311yescharacteristic
277Q16—1724no—
278M16—864no—
279C2×C8—41no—
280C2×C8—862no—
281C2×C8—862no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—861no—
289C4⋊C4—861no—
290C4⋊C4—861no—
291C4⋊C4—861no—
292C4⋊C4—861no—
293C4⋊C4—861no—
294C4⋊C4—1724no—
295C4⋊C4—1721no—
296C4⋊C4—1721no—
297C4⋊C4—1721no—
298C4⋊C4—1721no—
299C4⋊C4—1721no—
300C4⋊C4—1721no—
301C22⋊C4—41no—
302C42—41no—
303C42—1721no—
304C42—1721no—
305C42C2×D17211yescharacteristic
306C42#1062189811yescharacteristic
307C42D4×D4311yescharacteristic
308C42D4×D4311yescharacteristic
309C23#1306329311yescharacteristic
310Q8—42no—
311Q8—81no—
312Q8—862no—
313Q8—862no—
314Q8—1721no—
315Q8—1721no—
316C2×C4—22no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—42no—
324C2×C4—862no—
325C2×C4—1722no—
326C2×C4—1722no—
327C2×C4—1721no—
328C2×C4—1721no—
329C2×C4—1721no—
330C2×C4—1722no—
331C2×C4—1721no—
332C2×C4—1721no—
333C2×C4#1306329511yescharacteristic
334C2×C4#1306329511yescharacteristic
335C2×C4#1306329811yescharacteristic
336C2×C4#1306329811yescharacteristic
337C2×C4#1306329911yescharacteristic
338C2×C4#1306332111yescharacteristic
339C8—81no—
340C8—864no—
341C8—1722no—
342C22—21no—
343C22—21no—
344C22#1458280811yescharacteristic
345C22#1458308012yes—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—82no—
353C4—81no—
354C4—81no—
355C4—3441no—
356C4—3441no—
357C4—3441no—
358C4—1722no—
359C2—22no—
360C2#1913563211yescharacteristic
361C2#1913565411yescharacteristic
362C2#1913566111yescharacteristic
subgroupG/H
centerC22#14582808
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1515C2
socleC22×C43#392
prime radicalC23×C43#120
hypercenter#1515D43
hypocenterC43#10025
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1515

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
#191451482
#191447212
#191404742
#191332212
#191330412
#191324592
C43×#15152
#1002543