Finite Group Databasebeta

← #25006784

Subgroups — #25006784

Order 11008.

468 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 83 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#19140360C211yesmaximal, characteristic
2#19134326C211yesmaximal, characteristic
3#19132906C211yesmaximal, characteristic
4#19132596C211yesmaximal, characteristic
5#19132595C211yesmaximal, characteristic
6#19132594C211yesmaximal, characteristic
7C43×#1344C211yesmaximal, characteristic
8C2×#13063324C411yescharacteristic, complemented
9C2×#13063302—21no—
10C2×#13063281—21no—
11C2×#13063281C2211yescharacteristic
12#14582949—21no—
13#14582833—21no—
14#14582831C411yescharacteristic, complemented
15#14582830C411yescharacteristic, complemented
16#14582827—21no—
17#14582824C2211yescharacteristic
18#14582803—21no—
19#14582763C411yescharacteristic, complemented
20#14582666C2211yescharacteristic
21#14582665—21no—
22#14582624—21no—
23#14582623C2211yescharacteristic
24C43×#397C2211yescharacteristic
25C43×#342C2211yescharacteristic
26C43×#323C2211yescharacteristic
27C22×Dic86—21no—
28C23×Dic43D411yescharacteristic
29#13063324—41no—
30#13063324—41no—
31#13063302—42no—
32#13063302—42no—
33#13063281—24no—
34#13063281—41no—
35#13063281—41no—
36#13063281—42no—
37C2×C4⋊Dic43—21no—
38C2×C4⋊Dic43C2×C411yescharacteristic
39C2×Dic43⋊C4—21no—
40C2×Dic43⋊C4—21no—
41C2×Dic43⋊C4—21no—
42C2×Dic43⋊C4—41no—
43C2×Dic43⋊C4C2×C411yescharacteristic
44C2×Dic43⋊C4D411yescharacteristic
45C2×C22⋊Dic43—21no—
46C2×C22⋊Dic43—21no—
47C2×C22⋊Dic43D411yescharacteristic
48C2×C4×Dic43—41no—
49C2×C4×Dic43C2×C411yescharacteristic
50C2×C4×Dic43D411yescharacteristic
51Dic43⋊C8—41no—
52C22⋊(C43⋊C8)—21no—
53C8×Dic43—41no—
54C43⋊#95—21no—
55C43⋊#95—21no—
56C43⋊#95—21no—
57C43⋊#95—21no—
58C43⋊#95C2×C411yescharacteristic
59C2×C4⋊C4×C43C2×C411yescharacteristic
60C2×C22⋊C4×C43—21no—
61C2×C22⋊C4×C43—21no—
62C2×C22⋊C4×C43C2311yescharacteristic
63C22⋊C8×C43—21no—
64#95×C43—21no—
65#95×C43C2×C411yescharacteristic
66C24×C43C2×D411yescharacteristic
67C22×C4×C43—21no—
68C22×C4×C43—21no—
69C22×C4×C43—41no—
70C22×C4×C43C22×C411yescharacteristic
71C22×C4×C43C2×D411yescharacteristic
72C22×Dic43—21no—
73C22×Dic43—21no—
74C22×Dic43—22no—
75C22×Dic43—21no—
76C22×Dic43—21no—
77C22×Dic43—41no—
78C22×Dic43C22⋊C411yescharacteristic
79C22×Dic43C22⋊C411yescharacteristic
80C22×Dic43C22⋊C411yescharacteristic
81C22×Dic43C22⋊C411yescharacteristic
82C22×Dic43D812yes—
83C22×Dic43SD1612yes—
84C2×Dic86—41no—
85C2×Dic86—41no—
86C2×Dic86—42no—
87C2×Dic86—42no—
88C2×C8×C43—41no—
89C4⋊C4×C43—41no—
90C22⋊C4×C43—22no—
91C22⋊C4×C43—41no—
92C22⋊C4×C43—41no—
93C22⋊C4×C43—41no—
94C22⋊C4×C43—41no—
95C22⋊Dic43—22no—
96C22⋊Dic43—41no—
97C22⋊Dic43—41no—
98C22⋊Dic43—41no—
99C22⋊Dic43—41no—
100C4⋊Dic43—42no—
101C4⋊Dic43—41no—
102Dic43⋊C4—41no—
103Dic43⋊C4—41no—
104Dic43⋊C4—42no—
105Dic43⋊C4—44no—
106Dic43⋊C4—42no—
107Dic43⋊C4—42no—
108C4×Dic43—21no—
109C4×Dic43—21no—
110C4×Dic43—21no—
111C4×Dic43—21no—
112C4×Dic43—44no—
113C2×C43⋊C8—41no—
114C23×C43—21no—
115C23×C43—21no—
116C23×C43—41no—
117C23×C43—41no—
118C23×C43C2×C22⋊C411yescharacteristic
119C23×C43C2×D811yescharacteristic
120C23×C43C2×SD1611yescharacteristic
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—41no—
124C2×C4×C43—41no—
125C2×C4×C43—42no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43—81no—
133C2×C4×C43—81no—
134C2×Dic43—21no—
135C2×Dic43—21no—
136C2×Dic43—22no—
137C2×Dic43—22no—
138C2×Dic43—22no—
139C2×Dic43—22no—
140C2×Dic43—21no—
141C2×Dic43—21no—
142C2×Dic43—41no—
143C2×Dic43—41no—
144C2×Dic43—42no—
145C2×Dic43—41no—
146C2×Dic43—41no—
147C2×Dic43—41no—
148C2×Dic43—41no—
149C2×Dic43—41no—
150C2×Dic43—41no—
151C2×Dic43—81no—
152C2×Dic43—81no—
153C2×Dic43#9911yescharacteristic
154C2×Dic43#9911yescharacteristic
155C2×Dic43#10212yes—
156C2×Dic43#10212yes—
157C2×Dic43#10412yes—
158Dic86—82no—
159Dic86—82no—
160C8×C43—81no—
161C43⋊C8—81no—
162#11694—431nomaximal, Sylow
163C22×C43—21no—
164C22×C43—21no—
165C22×C43—21no—
166C22×C43—21no—
167C22×C43—41no—
168C22×C43—41no—
169C22×C43—41no—
170C22×C43—41no—
171C22×C43—81no—
172C22×C43C2×#9911yescharacteristic
173C22×C43C2×#10211yescharacteristic
174C22×C43C2×#10411yescharacteristic
175C4×C43—41no—
176C4×C43—41no—
177C4×C43—81no—
178C4×C43—82no—
179C4×C43—81no—
180Dic43—22no—
181Dic43—41no—
182Dic43—41no—
183Dic43—81no—
184Dic43—82no—
185Dic43—81no—
186Dic43#32712yes—
187Dic43#32712yes—
188#2621—431no—
189#1740—431no—
190#1458—431no—
191#1344—431no—
192#1344—431no—
193#1344—431no—
194#1344D4311yescharacteristic
195C2×C43—21no—
196C2×C43—21no—
197C2×C43—41no—
198C2×C43—41no—
199C2×C43C2×#32711yescharacteristic
200C2×C43#212311yescharacteristic
201C2×C43#212911yescharacteristic
202C2×C4⋊Q8—431no—
203C2×C22⋊Q8—861no—
204C2×#117—431no—
205C2×#117—861no—
206#431—861no—
207#398—431no—
208#398—431no—
209#398—861no—
210#397—431no—
211#397—861no—
212#397C2×D4311yescharacteristic
213#391—861no—
214#382—431no—
215#342—431no—
216#342—861no—
217#342C2×D4311yescharacteristic
218#324—861no—
219#323—431no—
220#323C2×D4311yescharacteristic
221C43#1169411yescharacteristic, complemented, Sylow
222C22×Q8—861no—
223C23×C4—431no—
224C4⋊Q8—1721no—
225C4⋊Q8—1721no—
226C22⋊Q8—1722no—
227C22⋊Q8—1722no—
228#117—864no—
229#117—1721no—
230#117—1721no—
231#117—1722no—
232C2×C4⋊C4—431no—
233C2×C4⋊C4—431no—
234C2×C4⋊C4—431no—
235C2×C4⋊C4—861no—
236C2×C4⋊C4—861no—
237C2×C4⋊C4—861no—
238C2×C4⋊C4—861no—
239C2×C4⋊C4—1721no—
240C2×C4⋊C4C4×D4311yescharacteristic
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—431no—
244C2×C22⋊C4—861no—
245C2×C22⋊C4—861no—
246C2×C22⋊C4C22×D4311yescharacteristic
247C2×C42—431no—
248C2×C42—431no—
249C2×C42—1721no—
250C4⋊C8—1721no—
251C22⋊C8—21no—
252C22⋊C8—861no—
253C4×C8—1721no—
254#95—21no—
255#95—431no—
256#95—861no—
257#95—861no—
258#95—861no—
259#95—861no—
260#95C4×D4311yescharacteristic
261C24D4×D4311yescharacteristic
262C2×Q8—1722no—
263C2×Q8—1721no—
264C2×Q8—1721no—
265C2×Q8—1722no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—41no—
269C22×C4—431no—
270C22×C4—431no—
271C22×C4—432no—
272C22×C4—432no—
273C22×C4—431no—
274C22×C4—431no—
275C22×C4—861no—
276C22×C4—861no—
277C22×C4—862no—
278C22×C4—861no—
279C22×C4—861no—
280C22×C4—1721no—
281C22×C4C2×C4×D4311yescharacteristic
282C22×C4D4×D4311yescharacteristic
283C2×C8—41no—
284C2×C8—1721no—
285C4⋊C4—41no—
286C4⋊C4—1721no—
287C4⋊C4—1721no—
288C4⋊C4—1721no—
289C4⋊C4—1722no—
290C4⋊C4—1722no—
291C4⋊C4—1722no—
292C4⋊C4—1722no—
293C4⋊C4—1724no—
294C22⋊C4—22no—
295C22⋊C4—41no—
296C22⋊C4—41no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—862no—
300C22⋊C4—1721no—
301C22⋊C4—1721no—
302C22⋊C4—1721no—
303C22⋊C4—1721no—
304C42—861no—
305C42—861no—
306C42—861no—
307C42—861no—
308C42—1724no—
309C23—21no—
310C23—21no—
311C23—41no—
312C23—41no—
313C23C22⋊C4×D4311yescharacteristic
314C23D8×D4311yescharacteristic
315C23SD16×D4311yescharacteristic
316Q8—3442no—
317Q8—3442no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4—431no—
332C2×C4—431no—
333C2×C4—432no—
334C2×C4—432no—
335C2×C4—432no—
336C2×C4—862no—
337C2×C4—862no—
338C2×C4—862no—
339C2×C4—862no—
340C2×C4—861no—
341C2×C4—861no—
342C2×C4—861no—
343C2×C4—861no—
344C2×C4—3441no—
345C2×C4—3441no—
346C2×C4—1722no—
347C2×C4—1721no—
348C2×C4—1721no—
349C2×C4—1721no—
350C2×C4—1721no—
351C2×C4—1721no—
352C2×C4—1721no—
353C2×C4—1721no—
354C2×C4—1721no—
355C8—81no—
356C8—3441no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—81no—
366C22#99×D4311yescharacteristic
367C22#102×D4311yescharacteristic
368C22#104×D4311yescharacteristic
369C4—41no—
370C4—41no—
371C4—81no—
372C4—82no—
373C4—81no—
374C4—432no—
375C4—432no—
376C4—862no—
377C4—3441no—
378C4—3442no—
379C4—3441no—
380C4—1721no—
381C4—1721no—
382C2—21no—
383C2—21no—
384C2—41no—
385C2—41no—
386C2#327×D4311yescharacteristic
387C2#1913624711yescharacteristic
388C2#1913626811yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C22⋊C4C22×D43
FittingC43×#1344C2
socleC22×C43C2×#99
prime radicalC24×C43C2×D4
cosocleC2×C22⋊C4×C43C23
hypercenter#1344D43
hypocenterC43#11694
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1344

Complements

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

NH ≅ G/Ntype
8. C2×#13063324C4semidirect
14. #14582831C4semidirect
15. #14582830C4semidirect
19. #14582763C4semidirect
221. C43#11694semidirect

Maximal subgroups

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

subgroupindex
#191403602
#191343262
#191329062
#191325962
#191325952
#191325942
C43×#13442
#1169443