Finite Group Databasebeta

← #24991910

Subgroups — #24991910

Order 11008.

404 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 97 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#19145105C211yesmaximal, characteristic
2#19143696C211yesmaximal, characteristic
3#19133189C211yesmaximal, characteristic
4#19133016C211yesmaximal, characteristic
5#19132433C211yesmaximal, characteristic
6#19132431C211yesmaximal, characteristic
7C43×#1485C211yesmaximal, characteristic
8#14583456C2211yescharacteristic
9#14583302C411yescharacteristic
10#14583302C411yescharacteristic
11#14583298—22no—
12#14583295C411yescharacteristic
13#14583295C411yescharacteristic
14#14583029—21no—
15#14583026—21no—
16C8×Dic86—21no—
17#14583023—21no—
18#14582957—22no—
19#14582952C2211yescharacteristic
20#14582935—22no—
21C4×#10621877C2211yescharacteristic
22C2×C4×C43⋊C8C2211yescharacteristic
23#14582640—22no—
24Q8⋊(C43⋊C8)—21no—
25Q8⋊(C43⋊C8)—21no—
26C43×#533C2211yescharacteristic
27C43×#431C2211yescharacteristic
28C4×M16×C43C2211yescharacteristic
29C43×Q8⋊C8—21no—
30C43×Q8⋊C8—21no—
31C2×#10621877—21no—
32C22×C43⋊C8—21no—
33#13063325C2×C411yescharacteristic
34#13063325C2×C411yescharacteristic
35#13063317D412yes—
36#13063304—21no—
37#13063304—21no—
38C4×Dic86—21no—
39C4×Dic86—21no—
40#13063284D412yes—
41#13063258—22no—
42#13063258—22no—
43#13063256—22no—
44#13063256—22no—
45C4⋊(C43⋊C8)D411yescharacteristic
46C4⋊(C43⋊C8)D411yescharacteristic
47Dic43⋊C8—22no—
48Dic43⋊C8—22no—
49C22⋊(C43⋊C8)—21no—
50#13063236—21no—
51#13063235—22no—
52C4×C43⋊C8—21no—
53C4×C43⋊C8—21no—
54C4×C43⋊C8—21no—
55C4×C43⋊C8C2×C411yescharacteristic
56C4×C43⋊C8C2×C411yescharacteristic
57C8×Dic43—22no—
58C2×M16×C43—21no—
59C4⋊Q8×C43C2×C411yescharacteristic
60C4⋊Q8×C43C2×C411yescharacteristic
61#125×C43—21no—
62C22⋊Q8×C43—21no—
63C22⋊Q8×C43—21no—
64C4×Q8×C43—21no—
65C4×Q8×C43—21no—
66#117×C43—21no—
67C2×C42×C43C2311yescharacteristic
68C4⋊C8×C43D411yescharacteristic
69C4⋊C8×C43D411yescharacteristic
70C22⋊C8×C43—21no—
71#97×C43—21no—
72C4×C8×C43—21no—
73C4×C8×C43—21no—
74C2×Q8×C43—21no—
75C2×Q8×C43—21no—
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43#4111yescharacteristic
78C22×C4×C43#4111yescharacteristic
79C2×Dic86—21no—
80C2×Dic86—21no—
81M16×C43—22no—
82M16×C43—41no—
83C2×C8×C43—21no—
84C2×C8×C43—21no—
85C2×C8×C43—41no—
86C4⋊C4×C43—21no—
87C4⋊C4×C43—21no—
88C4⋊C4×C43—21no—
89C4⋊C4×C43—21no—
90C4⋊C4×C43—41no—
91C4⋊C4×C43—41no—
92C22⋊C4×C43—41no—
93C42×C43—41no—
94C42×C43C22×C411yescharacteristic
95C42×C43C2×D411yescharacteristic
96C42×C43C2×D411yescharacteristic
97C42×C43C2×D411yescharacteristic
98C22⋊Dic43—22no—
99C4⋊Dic43—21no—
100C4⋊Dic43—21no—
101C4⋊Dic43C22⋊C412yes—
102C4⋊Dic43C22⋊C412yes—
103Dic43⋊C4—22no—
104Dic43⋊C4—22no—
105C4×Dic43—22no—
106#10621877—22no—
107#10621877—41no—
108C2×C43⋊C8—22no—
109C2×C43⋊C8—22no—
110C2×C43⋊C8—21no—
111C2×C43⋊C8—21no—
112C2×C43⋊C8—21no—
113C2×C43⋊C8—21no—
114C2×C43⋊C8—41no—
115C23×C43#12311yescharacteristic
116Q8×C43—41no—
117Q8×C43—41no—
118Q8×C43—41no—
119Q8×C43—41no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43C2×C22⋊C411yescharacteristic
129C2×C4×C43C4×D411yescharacteristic
130C2×C4×C43C4×D411yescharacteristic
131C2×C4×C43#12011yescharacteristic
132C2×C4×C43#12111yescharacteristic
133C2×C4×C43#12111yescharacteristic
134C2×Dic43—22no—
135C2×Dic43—22no—
136Dic86—41no—
137Dic86—41no—
138Dic86—41no—
139Dic86—41no—
140C8×C43—42no—
141C8×C43—41no—
142C8×C43—41no—
143C43⋊C8—22no—
144C43⋊C8—22no—
145C43⋊C8—42no—
146C43⋊C8—41no—
147C43⋊C8—41no—
148#9068—431nomaximal, Sylow
149C22×C43—21no—
150C22×C43—21no—
151C22×C43—21no—
152C22×C43#38611yescharacteristic
153C4×C43—21no—
154C4×C43—21no—
155C4×C43—21no—
156C4×C43—81no—
157C4×C43—81no—
158C4×C43#44311yescharacteristic
159C4×C43#44311yescharacteristic
160C4×C43#44411yescharacteristic
161C4×C43#44411yescharacteristic
162C4×C43#45611yescharacteristic
163C4×C43#45611yescharacteristic
164Dic43—42no—
165Dic43—42no—
166#3160—431no—
167#2986—431no—
168#1526—431no—
169#1485—431no—
170#1485D4311yescharacteristic
171#1278—431no—
172#1278—431no—
173C2×C43—41no—
174C2×C43#187611yescharacteristic
175C2×C43#187611yescharacteristic
176C2×C43#188611yescharacteristic
177#533—431no—
178#533C2×D4311yescharacteristic
179#500—431no—
180#500—431no—
181#499—862no—
182#498—431no—
183#498—431no—
184#446—861no—
185#446—861no—
186C8×Q8—861no—
187C8×Q8—861no—
188#433—862no—
189#431—431no—
190#431C2×D4311yescharacteristic
191#427—862no—
192C4×M16—431no—
193C4×M16C2×D4311yescharacteristic
194C2×C4×C8—431no—
195#330—862no—
196Q8⋊C8—21no—
197Q8⋊C8—21no—
198Q8⋊C8—861no—
199Q8⋊C8—861no—
200C43#906811yescharacteristic, complemented, Sylow
201C2×M16—21no—
202C2×M16—861no—
203C22×C8—861no—
204C4⋊Q8—431no—
205C4⋊Q8—431no—
206C4⋊Q8C4×D4311yescharacteristic
207C4⋊Q8C4×D4311yescharacteristic
208#125—21no—
209#125—432no—
210C22⋊Q8—21no—
211C22⋊Q8—21no—
212C22⋊Q8—861no—
213C22⋊Q8—861no—
214C4×Q8—21no—
215C4×Q8—21no—
216C4×Q8—861no—
217C4×Q8—861no—
218#117—21no—
219#117—432no—
220C2×C42C22×D4311yescharacteristic
221#107—862no—
222#107—862no—
223#106—862no—
224#106—862no—
225C4⋊C8—431no—
226C4⋊C8—431no—
227C4⋊C8—862no—
228C4⋊C8—862no—
229C4⋊C8C22⋊D4311yescharacteristic
230C4⋊C8C22⋊D4311yescharacteristic
231C22⋊C8—21no—
232C22⋊C8—861no—
233#97—21no—
234#97—862no—
235#97—861no—
236C4×C8—21no—
237C4×C8—21no—
238C4×C8—431no—
239C4×C8—431no—
240C4×C8—862no—
241C4×C8—861no—
242C4×C8—861no—
243C4×C8—861no—
244C2×Q8—21no—
245C2×Q8—21no—
246C2×Q8—861no—
247C2×Q8—861no—
248C22×C4#1062189811yescharacteristic
249C22×C4D4×D4311yescharacteristic
250C22×C4#1062190011yescharacteristic
251M16—22no—
252M16—41no—
253M16—862no—
254M16—1721no—
255C2×C8—21no—
256C2×C8—21no—
257C2×C8—41no—
258C2×C8—862no—
259C2×C8—862no—
260C2×C8—861no—
261C2×C8—861no—
262C2×C8—861no—
263C2×C8—861no—
264C2×C8—1721no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—432no—
272C4⋊C4—432no—
273C4⋊C4—861no—
274C4⋊C4—861no—
275C4⋊C4—862no—
276C4⋊C4—862no—
277C22⋊C4—41no—
278C22⋊C4—862no—
279C42—41no—
280C42—862no—
281C42C2×C4×D4311yescharacteristic
282C42D4×D4311yescharacteristic
283C42D4×D4311yescharacteristic
284C42C2×C22⋊D4311yescharacteristic
285C23#1306330711yescharacteristic
286Q8—41no—
287Q8—41no—
288Q8—41no—
289Q8—41no—
290Q8—1721no—
291Q8—1721no—
292Q8—1721no—
293Q8—1721no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—862no—
303C2×C4—862no—
304C2×C4C22⋊C4×D4311yescharacteristic
305C2×C4(C22⋊D43)⋊C411yescharacteristic
306C2×C4C4×C22⋊D4311yescharacteristic
307C2×C4#1306329311yescharacteristic
308C2×C4#1306329611yescharacteristic
309C2×C4#1306329811yescharacteristic
310C8—42no—
311C8—41no—
312C8—41no—
313C8—862no—
314C8—862no—
315C8—1722no—
316C8—1721no—
317C8—1721no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22#1458277511yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—81no—
326C4—81no—
327C4—1722no—
328C4—1722no—
329C4#1458301311yescharacteristic
330C4#1458301411yescharacteristic
331C4#1458301811yescharacteristic
332C4#1458301911yescharacteristic
333C4#1458308011yescharacteristic
334C4#1458308011yescharacteristic
335C2—41no—
336C2#1913491911yescharacteristic
337C2#1913492511yescharacteristic
338C2#1913498511yescharacteristic
subgroupG/H
centerC2×C4#13063293
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1485C2
socleC22×C43#386
prime radicalC23×C43#123
cosocleC2×C42×C43C23
hypercenter#1485D43
hypocenterC43#9068
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1485

Complements

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

NH ≅ G/Ntype
200. C43#9068semidirect

Maximal subgroups

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

subgroupindex
#191451052
#191436962
#191331892
#191330162
#191324332
#191324312
C43×#14852
#906843