Finite Group Databasebeta

← #24998154

Subgroups — #24998154

Order 11008.

454 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 89 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#19145736C211yesmaximal, characteristic
2#19145142C211yesmaximal, characteristic
3#19135583C211yesmaximal, characteristic
4#19133190C211yesmaximal, characteristic
5#19133016C211yesmaximal, characteristic
6#19132484C211yesmaximal, characteristic
7C43×#3255C211yesmaximal, characteristic
8C2×#13063325C2211yescharacteristic
9#14583309—22no—
10#14583302—21no—
11#14583295—21no—
12#14583295—21no—
13#14583249—21no—
14#14583227—22no—
15#14583184—22no—
16#14582952C2211yescharacteristic
17#14582942—22no—
18C4×#10621877C2211yescharacteristic
19C4×#10621877C2211yescharacteristic
20#14582667—22no—
21#14582641—22no—
22Q8⋊(C43⋊C8)—22no—
23C43×#533C2211yescharacteristic
24C43×#533C2211yescharacteristic
25C43×#475—21no—
26C43×#475—21no—
27C43×#470—22no—
28C43×#462—21no—
29C43×#462—21no—
30C43×#423C2211yescharacteristic
31C22×Dic86—21no—
32C2×#10621877—21no—
33C2×#10621877—21no—
34#13063325—21no—
35#13063325—21no—
36#13063325—21no—
37#13063325—21no—
38C2×C4⋊Dic43—21no—
39C2×C4⋊Dic43D412yes—
40#13063258—24no—
41#13063256—24no—
42#13063256—24no—
43C4⋊(C43⋊C8)D412yes—
44#13063249—24no—
45C22⋊(C43⋊C8)—21no—
46#13063236—21no—
47#13063236D412yes—
48C4×C43⋊C8—21no—
49C4×C43⋊C8—21no—
50C4×C43⋊C8—21no—
51C2×Q16×C43—22no—
52C2×M16×C43D412yes—
53C4⋊Q8×C43D411yescharacteristic
54C4⋊Q8×C43D411yescharacteristic
55C4⋊Q8×C43D411yescharacteristic
56C4⋊Q8×C43D411yescharacteristic
57#125×C43—21no—
58#125×C43—21no—
59C22⋊Q8×C43—21no—
60C22⋊Q8×C43—21no—
61C22⋊Q8×C43—21no—
62C22⋊Q8×C43—21no—
63C4×Q8×C43—21no—
64C4×Q8×C43—21no—
65C4×Q8×C43—21no—
66C4×Q8×C43—21no—
67#117×C43—21no—
68#117×C43—21no—
69C2×C42×C43C2311yescharacteristic
70#106×C43—22no—
71C4⋊C8×C43—21no—
72C4⋊C8×C43—21no—
73#103×C43—22no—
74#103×C43—22no—
75C2×Q8×C43—21no—
76C2×Q8×C43—21no—
77C2×Q8×C43—21no—
78C2×Q8×C43—21no—
79C22×C4×C43C2×D411yescharacteristic
80C22×C4×C43C2×D411yescharacteristic
81C22×C4×C43#4111yescharacteristic
82C22×Dic43—22no—
83C2×Dic86—41no—
84C2×Dic86—41no—
85C2×Dic86—82no—
86Q16×C43—82no—
87M16×C43—42no—
88C2×C8×C43—22no—
89C4⋊C4×C43—21no—
90C4⋊C4×C43—21no—
91C4⋊C4×C43—21no—
92C4⋊C4×C43—21no—
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—
101C22⋊C4×C43—41no—
102C22⋊C4×C43—41no—
103C42×C43—41no—
104C42×C43—41no—
105C42×C43C2×D411yescharacteristic
106C42×C43C2×D411yescharacteristic
107C42×C43C2×D411yescharacteristic
108C42×C43C2×D411yescharacteristic
109C4⋊Dic43—22no—
110C4⋊Dic43—22no—
111C4⋊Dic43—41no—
112C4⋊Dic43—41no—
113#10621877—24no—
114#10621877—22no—
115#10621877—41no—
116C2×C43⋊C8—22no—
117C2×C43⋊C8—22no—
118C2×C43⋊C8—41no—
119C23×C43#12111yescharacteristic
120Q8×C43—41no—
121Q8×C43—41no—
122Q8×C43—42no—
123Q8×C43—41no—
124Q8×C43—41no—
125Q8×C43—42no—
126C2×C4×C43—21no—
127C2×C4×C43—22no—
128C2×C4×C43—21no—
129C2×C4×C43—22no—
130C2×C4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43#12011yescharacteristic
135C2×C4×C43#12011yescharacteristic
136C2×C4×C43#12011yescharacteristic
137C2×C4×C43#12111yescharacteristic
138C2×C4×C43#12111yescharacteristic
139C2×C4×C43#12711yescharacteristic
140C2×Dic43—42no—
141C2×Dic43—82no—
142Dic86—82no—
143Dic86—82no—
144C8×C43—42no—
145C43⋊C8—24no—
146C43⋊C8—42no—
147C43⋊C8—42no—
148#10119—431nomaximal, Sylow
149C22×C43—21no—
150C22×C43—21no—
151C22×C43—21no—
152C22×C43#39211yescharacteristic
153C4×C43—21no—
154C4×C43—21no—
155C4×C43—21no—
156C4×C43—81no—
157C4×C43—81no—
158C4×C43—81no—
159C4×C43—81no—
160C4×C43#45511yescharacteristic
161C4×C43#45612yes—
162C4×C43#45611yescharacteristic
163C4×C43#47112yes—
164Dic43—82no—
165#3255D4311yescharacteristic
166#3229—431no—
167#3165—431no—
168#1997—431no—
169#1526—431no—
170#1485—431no—
171#1299—431no—
172C2×C43—41no—
173C2×C43#200511yescharacteristic
174C2×C43#200711yescharacteristic
175C2×C43#201911yescharacteristic
176#533C2×D4311yescharacteristic
177#533C2×D4311yescharacteristic
178C2×C4⋊Q8—431no—
179#501—862no—
180#500—861no—
181#498—861no—
182#498—861no—
183#487—861no—
184#483—862no—
185#475—21no—
186#475—21no—
187#475—862no—
188#470—22no—
189#462—21no—
190#462—21no—
191#431—431no—
192#428—862no—
193#423C2×D4311yescharacteristic
194C4×M16—431no—
195C4×M16—431no—
196#343—862no—
197#330—862no—
198Q8⋊C8—862no—
199C43#1011911yescharacteristic, complemented, Sylow
200C22×Q8—861no—
201C2×Q16—22no—
202C2×M16—861no—
203C2×M16—861no—
204C2×M16C22⋊D4312yes—
205C4⋊Q8—861no—
206C4⋊Q8—861no—
207C4⋊Q8—861no—
208C4⋊Q8—861no—
209C4⋊Q8C22⋊D4311yescharacteristic
210C4⋊Q8C22⋊D4311yescharacteristic
211C4⋊Q8C22⋊D4311yescharacteristic
212C4⋊Q8C22⋊D4311yescharacteristic
213#125—21no—
214#125—21no—
215C22⋊Q8—21no—
216C22⋊Q8—21no—
217C22⋊Q8—21no—
218C22⋊Q8—21no—
219C4×Q8—21no—
220C4×Q8—21no—
221C4×Q8—21no—
222C4×Q8—21no—
223#117—21no—
224#117—21no—
225C2×C4⋊C4—432no—
226C2×C4⋊C4—861no—
227C2×C42C22×D4311yescharacteristic
228#107—864no—
229#106—22no—
230#106—864no—
231#106—864no—
232C4⋊C8—21no—
233C4⋊C8—21no—
234C4⋊C8—432no—
235#103—22no—
236#103—22no—
237#103—864no—
238C22⋊C8—861no—
239#97—432no—
240#97—861no—
241C4×C8—861no—
242C4×C8—861no—
243C4×C8—861no—
244C2×Q8—21no—
245C2×Q8—21no—
246C2×Q8—21no—
247C2×Q8—21no—
248C2×Q8—3442no—
249C2×Q8—1721no—
250C2×Q8—1721no—
251C22×C4—862no—
252C22×C4D4×D4311yescharacteristic
253C22×C4#1062190011yescharacteristic
254C22×C4C2×C22⋊D4311yescharacteristic
255Q16—82no—
256M16—42no—
257M16—864no—
258M16—862no—
259M16—1721no—
260C2×C8—22no—
261C2×C8—862no—
262C2×C8—862no—
263C2×C8—1721no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—862no—
277C4⋊C4—862no—
278C4⋊C4—1721no—
279C4⋊C4—1721no—
280C22⋊C4—41no—
281C22⋊C4—41no—
282C42—41no—
283C42—41no—
284C42D4×D4311yescharacteristic
285C42D4×D4311yescharacteristic
286C42C2×C22⋊D4311yescharacteristic
287C42C2×C22⋊D4311yescharacteristic
288C23#1306329611yescharacteristic
289Q8—41no—
290Q8—41no—
291Q8—42no—
292Q8—41no—
293Q8—41no—
294Q8—42no—
295Q8—3442no—
296Q8—3442no—
297C2×C4—21no—
298C2×C4—22no—
299C2×C4—21no—
300C2×C4—22no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—3442no—
306C2×C4—1722no—
307C2×C4#1306329311yescharacteristic
308C2×C4#1306329311yescharacteristic
309C2×C4#1306329411yescharacteristic
310C2×C4#1306329711yescharacteristic
311C2×C4#1306329711yescharacteristic
312C2×C4#1306332111yescharacteristic
313C8—42no—
314C8—864no—
315C8—1722no—
316C8—1722no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22#1458280711yescharacteristic
321C4—21no—
322C4—21no—
323C4—21no—
324C4—81no—
325C4—81no—
326C4—81no—
327C4—81no—
328C4—3442no—
329C4#1458307711yescharacteristic
330C4#1458308012yes—
331C4#1458308211yescharacteristic
332C4#1458316412yes—
333C2—41no—
334C2#1913562811yescharacteristic
335C2#1913564211yescharacteristic
336C2#1913570611yescharacteristic
subgroupG/H
centerC22#14582807
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#3255C2
socleC22×C43#392
prime radicalC23×C43#121
hypercenter#3255D43
hypocenterC43#10119
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3255

Complements

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

NH ≅ G/Ntype
199. C43#10119semidirect

Maximal subgroups

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

subgroupindex
#191457362
#191451422
#191355832
#191331902
#191330162
#191324842
C43×#32552
#1011943