Finite Group Databasebeta

← #25007762

Subgroups — #25007762

Order 11008.

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

normal subgroups only

This group has 388 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#19139799C211yesmaximal, characteristic
2#19134590C211yesmaximal, characteristic
3#19132917C211yesmaximal, characteristic
4#19132626C211yesmaximal, characteristic
5#19132625C211yesmaximal, characteristic
6#19132624C211yesmaximal, characteristic
7C43×#1354C211yesmaximal, characteristic
8C2×#13063323C411yescharacteristic
9C2×#13063290C2211yescharacteristic
10#14582949—21no—
11#14582922—21no—
12C2×#13063243—21no—
13#14582820C411yescharacteristic
14#14582819C2211yescharacteristic
15#14582818C411yescharacteristic
16#14582803—21no—
17#14582796—21no—
18#14582794—21no—
19#14582768—21no—
20#14582750C411yescharacteristic
21#14582668C2211yescharacteristic
22#14582625C2211yescharacteristic
23#14582624—21no—
24C43×#395C2211yescharacteristic
25C43×#343C2211yescharacteristic
26C43×#324C2211yescharacteristic
27C22×Dic86C2×C411yescharacteristic
28C22×Dic86D411yescharacteristic
29C2×#10621877—21no—
30#13063323—41no—
31#13063323—41no—
32#13063290—41no—
33#13063290—41no—
34C2×C4⋊Dic43—21no—
35C2×Dic43⋊C4—21no—
36C2×Dic43⋊C4—21no—
37C2×Dic43⋊C4—21no—
38C2×Dic43⋊C4—21no—
39C2×Dic43⋊C4—21no—
40C2×Dic43⋊C4C2×C411yescharacteristic
41C2×Dic43⋊C4D411yescharacteristic
42C2×C4×Dic43—21no—
43C2×C4×Dic43C2×C411yescharacteristic
44C2×C4×Dic43D411yescharacteristic
45C2×C4×Dic43D411yescharacteristic
46Dic43⋊C8—41no—
47Dic43⋊C8—41no—
48Dic43⋊C8—41no—
49#13063243—42no—
50C22⋊(C43⋊C8)—21no—
51C8×Dic43—41no—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C43⋊#95—21no—
55C43⋊#95C2×C411yescharacteristic
56C22×Q8×C43C2×C411yescharacteristic
57C2×M16×C43—21no—
58C2×C4⋊C4×C43—21no—
59C2×C4⋊C4×C43C2311yescharacteristic
60C22⋊C8×C43—21no—
61#95×C43—21no—
62#95×C43C2×C411yescharacteristic
63C2×Q8×C43—41no—
64C2×Q8×C43—81no—
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43C22×C411yescharacteristic
68C22×C4×C43C2×D411yescharacteristic
69C22×C4×C43C2×D411yescharacteristic
70C22×Dic43—21no—
71C22×Dic43—21no—
72C22×Dic43C22⋊C411yescharacteristic
73C22×Dic43C22⋊C411yescharacteristic
74C22×Dic43C22⋊C411yescharacteristic
75C22×Dic43C22⋊C411yescharacteristic
76C2×Dic86—41no—
77C2×Dic86—41no—
78C2×Dic86—41no—
79C2×Dic86—81no—
80C2×Dic86SD1612yes—
81C2×Dic86Q1612yes—
82M16×C43—41no—
83M16×C43—41no—
84C2×C8×C43—41no—
85C2×C8×C43—41no—
86C4⋊C4×C43—41no—
87C4⋊C4×C43—81no—
88C4⋊Dic43—81no—
89Dic43⋊C4—24no—
90Dic43⋊C4—41no—
91Dic43⋊C4—41no—
92Dic43⋊C4—42no—
93Dic43⋊C4—41no—
94Dic43⋊C4—41no—
95Dic43⋊C4—81no—
96Dic43⋊C4—81no—
97C4×Dic43—21no—
98C4×Dic43—21no—
99C4×Dic43—21no—
100C4×Dic43—21no—
101C4×Dic43—21no—
102C4×Dic43—21no—
103C4×Dic43—42no—
104#10621877—41no—
105#10621877—41no—
106C2×C43⋊C8—41no—
107C2×C43⋊C8—41no—
108C23×C43C2×C22⋊C411yescharacteristic
109Q8×C43—82no—
110C2×C4×C43—21no—
111C2×C4×C43—21no—
112C2×C4×C43—22no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—41no—
116C2×C4×C43—41no—
117C2×C4×C43—41no—
118C2×C4×C43—41no—
119C2×C4×C43—41no—
120C2×C4×C43—41no—
121C2×C4×C43—41no—
122C2×C4×C43C2×SD1611yescharacteristic
123C2×C4×C43C2×Q1611yescharacteristic
124C2×Dic43—21no—
125C2×Dic43—21no—
126C2×Dic43—21no—
127C2×Dic43—21no—
128C2×Dic43—22no—
129C2×Dic43—22no—
130C2×Dic43—21no—
131C2×Dic43—41no—
132C2×Dic43—41no—
133C2×Dic43—41no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137C2×Dic43#9911yescharacteristic
138C2×Dic43#9911yescharacteristic
139C2×Dic43#10312yes—
140C2×Dic43#10312yes—
141Dic86—42no—
142Dic86—42no—
143Dic86—82no—
144C8×C43—81no—
145C8×C43—81no—
146C43⋊C8—81no—
147C43⋊C8—81no—
148#11908—431nomaximal, Sylow
149C22×C43—21no—
150C22×C43—21no—
151C22×C43C2×#9911yescharacteristic
152C22×C43C2×#10311yescharacteristic
153C22×C43#42111yescharacteristic
154C4×C43—21no—
155C4×C43—21no—
156C4×C43—42no—
157C4×C43—41no—
158C4×C43—41no—
159C4×C43—81no—
160Dic43—21no—
161Dic43—22no—
162Dic43—22no—
163Dic43—42no—
164Dic43—41no—
165Dic43—81no—
166Dic43#35612yes—
167#2567—431no—
168#1801—431no—
169#1461—431no—
170#1354—431no—
171#1354—431no—
172#1354—431no—
173#1354D4311yescharacteristic
174C2×C43—21no—
175C2×C43—21no—
176C2×C43#152011yescharacteristic
177C2×C43#212211yescharacteristic
178C2×C43C2×#35611yescharacteristic
179C2×C4⋊Q8—431no—
180C2×C4×Q8—431no—
181#431—861no—
182#423—861no—
183C2×#101—861no—
184#395—431no—
185#395—431no—
186#395—431no—
187#395C2×D4311yescharacteristic
188#391—861no—
189#389—861no—
190#389—861no—
191#384—861no—
192C4×C4⋊C4—431no—
193#343—431no—
194#343C2×D4311yescharacteristic
195#324—431no—
196#324—861no—
197#324C2×D4311yescharacteristic
198C43#1190811yescharacteristic, complemented, Sylow
199C22×Q8—431no—
200C22×Q8—431no—
201C22×Q8C4×D4311yescharacteristic
202C2×M16—21no—
203C2×M16—861no—
204C4⋊Q8—1721no—
205C4⋊Q8—1721no—
206C4×Q8—1721no—
207C4×Q8—1721no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—431no—
210C2×C4⋊C4—431no—
211C2×C4⋊C4—861no—
212C2×C4⋊C4—861no—
213C2×C4⋊C4—861no—
214C2×C4⋊C4—861no—
215C2×C4⋊C4—861no—
216C2×C4⋊C4—861no—
217C2×C4⋊C4C22×D4311yescharacteristic
218C2×C42—431no—
219C2×C42—431no—
220C2×C42—431no—
221C2×C42—861no—
222C4⋊C8—1721no—
223C4⋊C8—1721no—
224C4⋊C8—1721no—
225#101—1722no—
226C22⋊C8—21no—
227C22⋊C8—861no—
228C4×C8—1721no—
229#95—21no—
230#95—431no—
231#95—861no—
232#95—861no—
233#95—861no—
234#95C4×D4311yescharacteristic
235C2×Q8—41no—
236C2×Q8—81no—
237C2×Q8—432no—
238C2×Q8—432no—
239C2×Q8—3441no—
240C2×Q8—1721no—
241C2×Q8—1721no—
242C2×Q8—1721no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—431no—
246C22×C4—431no—
247C22×C4—431no—
248C22×C4—431no—
249C22×C4—861no—
250C22×C4—861no—
251C22×C4C2×C4×D4311yescharacteristic
252C22×C4D4×D4311yescharacteristic
253C22×C4D4×D4311yescharacteristic
254M16—41no—
255M16—41no—
256M16—1721no—
257M16—1721no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8—1721no—
261C2×C8—1721no—
262C4⋊C4—41no—
263C4⋊C4—81no—
264C4⋊C4—864no—
265C4⋊C4—3441no—
266C4⋊C4—3441no—
267C4⋊C4—3441no—
268C4⋊C4—1721no—
269C4⋊C4—1721no—
270C4⋊C4—1721no—
271C4⋊C4—1721no—
272C4⋊C4—1722no—
273C42—861no—
274C42—861no—
275C42—861no—
276C42—861no—
277C42—861no—
278C42—861no—
279C42—1722no—
280C23C22⋊C4×D4311yescharacteristic
281Q8—82no—
282Q8—3442no—
283Q8—1722no—
284Q8—1722no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—22no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—431no—
298C2×C4—431no—
299C2×C4—432no—
300C2×C4—432no—
301C2×C4—862no—
302C2×C4—861no—
303C2×C4—861no—
304C2×C4—861no—
305C2×C4—861no—
306C2×C4—862no—
307C2×C4—861no—
308C2×C4—1721no—
309C2×C4—1721no—
310C2×C4—1721no—
311C2×C4—1721no—
312C2×C4—1721no—
313C2×C4—1721no—
314C2×C4SD16×D4311yescharacteristic
315C2×C4Q16×D4311yescharacteristic
316C8—81no—
317C8—81no—
318C8—3441no—
319C8—3441no—
320C22—21no—
321C22—21no—
322C22#99×D4311yescharacteristic
323C22#103×D4311yescharacteristic
324C22#1458291411yescharacteristic
325C4—21no—
326C4—21no—
327C4—42no—
328C4—41no—
329C4—41no—
330C4—81no—
331C4—432no—
332C4—861no—
333C4—862no—
334C4—862no—
335C4—3441no—
336C4—1722no—
337C4—1721no—
338C2—21no—
339C2—21no—
340C2#1913316511yescharacteristic
341C2#1913624311yescharacteristic
342C2#356×D4311yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1354C2
socleC22×C43C2×#99
prime radicalC23×C43C2×C22⋊C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1354D43
hypocenterC43#11908
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1354

Complements

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

NH ≅ G/Ntype
198. C43#11908semidirect

Maximal subgroups

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

subgroupindex
#191397992
#191345902
#191329172
#191326262
#191326252
#191326242
C43×#13542
#1190843