Finite Group Databasebeta

← #24997519

Subgroups — #24997519

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#19145148C211yesmaximal, characteristic
2#19140471C211yesmaximal, characteristic
3#19133221C211yesmaximal, characteristic
4#19133146C211yesmaximal, characteristic
5#19133042C211yesmaximal, characteristic
6#19132461C211yesmaximal, characteristic
7C43×#3113C211yesmaximal, characteristic
8C2×#13063317C2211yescharacteristic
9#14583305—21no—
10#14583305—21no—
11#14583298—22no—
12#14582956C2211yescharacteristic
13#14582942—21no—
14#14582942—21no—
15C4×#10621877C2211yescharacteristic
16#14582838—21no—
17#14582837—21no—
18#14582829—21no—
19#14582818—21no—
20#14582783—22no—
21#14582767C2211yescharacteristic
22#14582640—22no—
23#14582636—22no—
24Q8⋊(C43⋊C8)—22no—
25C43×#533C2211yescharacteristic
26C2×C4×Q8×C43C2211yescharacteristic
27C43×#483—21no—
28C43×#475—21no—
29C43×#462—21no—
30C43×#451—21no—
31C43×#441—22no—
32C43×#432C2211yescharacteristic
33C2×#10621877—21no—
34#13063317—21no—
35#13063317—21no—
36#13063317—21no—
37#13063317—21no—
38C2×C4⋊Dic43D411yescharacteristic
39C2×C4⋊Dic43D411yescharacteristic
40C2×Dic43⋊C4—22no—
41C2×Dic43⋊C4—21no—
42C2×Dic43⋊C4—21no—
43#13063258—22no—
44#13063258—22no—
45#13063256—22no—
46#13063256—22no—
47C4⋊(C43⋊C8)—21no—
48C22⋊(C43⋊C8)—21no—
49#13063236—21no—
50#13063236—21no—
51C4×C43⋊C8D412yes—
52C43⋊#95—22no—
53C43⋊#95—22no—
54C43⋊#95—22no—
55C43⋊#95—21no—
56C43⋊#95—21no—
57C43⋊#95D412yes—
58C22×Q8×C43D411yescharacteristic
59C2×Q16×C43—22no—
60C4⋊Q8×C43D411yescharacteristic
61C4⋊Q8×C43D411yescharacteristic
62#125×C43—21no—
63C22⋊Q8×C43—21no—
64C22⋊Q8×C43—21no—
65C4×Q8×C43—21no—
66C4×Q8×C43—21no—
67C4×Q8×C43—21no—
68C4×Q8×C43—21no—
69C4×Q8×C43—21no—
70C4×Q8×C43—21no—
71#117×C43—21no—
72C2×C4⋊C4×C43—21no—
73C2×C4⋊C4×C43D411yescharacteristic
74C2×C42×C43—21no—
75C2×C42×C43C2311yescharacteristic
76#106×C43—22no—
77C4⋊C8×C43—21no—
78#103×C43—22no—
79#103×C43—22no—
80C22⋊C8×C43—21no—
81#97×C43D412yes—
82C2×Q8×C43—21no—
83C2×Q8×C43—21no—
84C2×Q8×C43—21no—
85C2×Q8×C43—21no—
86C2×Q8×C43—42no—
87C22×C4×C43—21no—
88C22×C4×C43—21no—
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43C2×D411yescharacteristic
91C22×C4×C43C2×D411yescharacteristic
92C22×Dic43—22no—
93C22×Dic43—21no—
94C22×Dic43—21no—
95Q16×C43—44no—
96C2×C8×C43—22no—
97C4⋊C4×C43—21no—
98C4⋊C4×C43—21no—
99C4⋊C4×C43—21no—
100C4⋊C4×C43—21no—
101C4⋊C4×C43—21no—
102C4⋊C4×C43—21no—
103C4⋊C4×C43—41no—
104C4⋊C4×C43—41no—
105C4⋊C4×C43—41no—
106C4⋊C4×C43—41no—
107C22⋊C4×C43—41no—
108C42×C43—41no—
109C42×C43—41no—
110C42×C43—41no—
111C42×C43C2×D411yescharacteristic
112C42×C43C2×D411yescharacteristic
113C42×C43C2×D411yescharacteristic
114C42×C43#4111yescharacteristic
115C4⋊Dic43—21no—
116C4⋊Dic43—21no—
117C4⋊Dic43—21no—
118C4⋊Dic43—21no—
119Dic43⋊C4—44no—
120Dic43⋊C4—41no—
121Dic43⋊C4—41no—
122Dic43⋊C4—41no—
123Dic43⋊C4—41no—
124#10621877—24no—
125C2×C43⋊C8—22no—
126C2×C43⋊C8—41no—
127C23×C43#12011yescharacteristic
128Q8×C43—22no—
129Q8×C43—22no—
130Q8×C43—41no—
131Q8×C43—41no—
132Q8×C43—42no—
133Q8×C43—81no—
134C2×C4×C43—22no—
135C2×C4×C43—22no—
136C2×C4×C43—41no—
137C2×C4×C43—41no—
138C2×C4×C43—41no—
139C2×C4×C43—41no—
140C2×C4×C43—41no—
141C2×C4×C43—41no—
142C2×C4×C43—41no—
143C2×C4×C43—42no—
144C2×C4×C43#12011yescharacteristic
145C2×C4×C43#12011yescharacteristic
146C2×C4×C43#12111yescharacteristic
147C2×C4×C43#12111yescharacteristic
148C2×C4×C43#12111yescharacteristic
149C2×C4×C43#12711yescharacteristic
150C2×Dic43—42no—
151C2×Dic43—42no—
152C2×Dic43—42no—
153C2×Dic43—42no—
154C2×Dic43—41no—
155C2×Dic43—41no—
156C2×Dic43—42no—
157C8×C43—42no—
158C43⋊C8—24no—
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—81no—
173C4×C43—81no—
174C4×C43—81no—
175Dic43—82no—
176Dic43—81no—
177Dic43—81no—
178#3166—431no—
179#3113D4311yescharacteristic
180#2634—431no—
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#533C2×D4311yescharacteristic
190C2×#125—431no—
191C2×C4×Q8C2×D4311yescharacteristic
192#501—861no—
193#501—861no—
194#499—862no—
195#483—21no—
196#475—21no—
197#462—21no—
198#451—21no—
199#441—22no—
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#383—431no—
211#330—862no—
212#328—862no—
213Q8⋊C8—862no—
214C43#1002511yescharacteristic, complemented, Sylow
215C22×Q8C22⋊D4311yescharacteristic
216C2×Q16—22no—
217C2×M16—861no—
218C4⋊Q8C22⋊D4311yescharacteristic
219C4⋊Q8C22⋊D4311yescharacteristic
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—21no—
230C4×Q8—21no—
231C4×Q8—21no—
232C4×Q8—21no—
233#117—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—431no—
236C2×C4⋊C4—431no—
237C2×C4⋊C4—862no—
238C2×C4⋊C4—861no—
239C2×C4⋊C4—861no—
240C2×C4⋊C4C22⋊D4311yescharacteristic
241C2×C42—21no—
242C2×C42C22×D4311yescharacteristic
243#107—862no—
244#107—862no—
245#106—22no—
246#106—862no—
247#106—862no—
248C4⋊C8—21no—
249C4⋊C8—861no—
250#103—22no—
251#103—22no—
252C22⋊C8—21no—
253C22⋊C8—861no—
254#97—861no—
255#97—861no—
256#97C22⋊D4312yes—
257C4×C8—432no—
258#95—432no—
259#95—862no—
260#95—862no—
261#95—862no—
262#95—861no—
263#95—861no—
264C2×Q8—21no—
265C2×Q8—21no—
266C2×Q8—21no—
267C2×Q8—21no—
268C2×Q8—42no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—862no—
272C22×C4—861no—
273C22×C4—861no—
274C22×C4D4×D4311yescharacteristic
275C22×C4D4×D4311yescharacteristic
276C22×C4C2×C22⋊D4311yescharacteristic
277Q16—44no—
278M16—864no—
279C2×C8—22no—
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—41no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—861no—
293C4⋊C4—861no—
294C4⋊C4—861no—
295C4⋊C4—861no—
296C4⋊C4—1724no—
297C4⋊C4—1721no—
298C4⋊C4—1721no—
299C4⋊C4—1721no—
300C4⋊C4—1721no—
301C22⋊C4—41no—
302C42—41no—
303C42—41no—
304C42—41no—
305C42D4×D4311yescharacteristic
306C42#1062190011yescharacteristic
307C42C2×C22⋊D4311yescharacteristic
308C42C2×C22⋊D4311yescharacteristic
309C23#1306329311yescharacteristic
310Q8—22no—
311Q8—22no—
312Q8—41no—
313Q8—41no—
314Q8—42no—
315Q8—81no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—42no—
326C2×C4—1722no—
327C2×C4—1722no—
328C2×C4—1722no—
329C2×C4—1722no—
330C2×C4—1721no—
331C2×C4—1721no—
332C2×C4—1722no—
333C2×C4#1306329311yescharacteristic
334C2×C4#1306329411yescharacteristic
335C2×C4#1306329611yescharacteristic
336C2×C4#1306329711yescharacteristic
337C2×C4#1306329711yescharacteristic
338C2×C4#1306332111yescharacteristic
339C8—42no—
340C8—864no—
341C8—3441no—
342C22—21no—
343C22—21no—
344C22#1458280711yescharacteristic
345C22#1458308012yes—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—42no—
353C4—81no—
354C4—81no—
355C4—81no—
356C4—3442no—
357C4—3441no—
358C4—3441no—
359C2—22no—
360C2#1913562811yescharacteristic
361C2#1913565311yescharacteristic
362C2#1913566011yescharacteristic
subgroupG/H
centerC22#14582807
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#3113C2
socleC22×C43#392
prime radicalC23×C43#120
hypercenter#3113D43
hypocenterC43#10025
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3113

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
#191404712
#191332212
#191331462
#191330422
#191324612
C43×#31132
#1002543