Finite Group Databasebeta

← #24995702

Subgroups — #24995702

Order 11008.

486 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142972C211yesmaximal, characteristic
2#19134746C211yesmaximal, characteristic
3#19134450C211yesmaximal, characteristic
4C2×#14582646C211yesmaximal, characteristic
5C2×#14582645C211yesmaximal, characteristic
6C2×#14582644C211yesmaximal, characteristic
7C2×C43×#332C211yesmaximal, characteristic
8C2×#13063325C2211yescharacteristic
9C2×C4⋊(C43⋊C8)C2211yescharacteristic
10C2×C4⋊(C43⋊C8)C2211yescharacteristic
11C2×Dic43⋊C8—22no—
12C2×#13063235—21no—
13#14582806—22no—
14#14582804—21no—
15#14582804—21no—
16#14582764C414yes—
17C42×Dic43C2211yescharacteristic
18#14582653—21no—
19#14582646—22no—
20#14582645—22no—
21#14582644—22no—
22C2×C4⋊Q8×C43C2211yescharacteristic
23C2×C4⋊C8×C43C2211yescharacteristic
24C2×C4⋊C8×C43C2211yescharacteristic
25C43×#332—22no—
26C22×Dic86—21no—
27C22×C43⋊C8—21no—
28C22×C43⋊C8—21no—
29#13063325—21no—
30#13063325—21no—
31#13063325—21no—
32#13063325—21no—
33C2×C4⋊Dic43—21no—
34C2×C4⋊Dic43C2×C412yes—
35C2×C4×Dic43C2×C412yes—
36C2×C4×Dic43D411yescharacteristic
37C2×C4×Dic43D411yescharacteristic
38C2×C4×Dic43D412yes—
39C4⋊(C43⋊C8)—21no—
40C4⋊(C43⋊C8)—21no—
41C4⋊(C43⋊C8)—21no—
42C4⋊(C43⋊C8)D412yes—
43Dic43⋊C8—44no—
44#13063235—42no—
45C43⋊#95—24no—
46C43⋊#95—24no—
47C22×Q8×C43—21no—
48C22×C8×C43—21no—
49C22×C8×C43—21no—
50C4⋊Q8×C43—21no—
51C4⋊Q8×C43—21no—
52C4⋊Q8×C43—21no—
53C4⋊Q8×C43—21no—
54C2×C4⋊C4×C43—21no—
55C2×C4⋊C4×C43C2×C412yes—
56C2×C42×C43C2311yescharacteristic
57C4⋊C8×C43—21no—
58C4⋊C8×C43—21no—
59C4⋊C8×C43—21no—
60C4⋊C8×C43D412yes—
61C2×Q8×C43—41no—
62C2×Q8×C43—41no—
63C2×Q8×C43—42no—
64C2×Q8×C43—42no—
65C22×C4×C43—22no—
66C22×C4×C43C22×C411yescharacteristic
67C22×C4×C43C2×D411yescharacteristic
68C22×C4×C43C2×D411yescharacteristic
69C22×Dic43—22no—
70C22×Dic43C22⋊C412yes—
71C22×Dic43C22⋊C412yes—
72C2×Dic86—41no—
73C2×Dic86—41no—
74C2×Dic86—41no—
75C2×Dic86—41no—
76C2×Dic86—41no—
77C2×Dic86—41no—
78C2×C8×C43—22no—
79C2×C8×C43—41no—
80C2×C8×C43—41no—
81C2×C8×C43—41no—
82C2×C8×C43—42no—
83C4⋊C4×C43—22no—
84C4⋊C4×C43—22no—
85C4⋊C4×C43—41no—
86C4⋊C4×C43—41no—
87C42×C43C2×D411yescharacteristic
88C42×C43C2×D411yescharacteristic
89C42×C43#4111yescharacteristic
90C42×C43#4111yescharacteristic
91C4⋊Dic43—22no—
92C4⋊Dic43—22no—
93C4⋊Dic43—41no—
94C4⋊Dic43—41no—
95C4×Dic43—21no—
96C4×Dic43—21no—
97C4×Dic43—21no—
98C4×Dic43—22no—
99C4×Dic43—22no—
100C4×Dic43—21no—
101C4×Dic43—24no—
102C2×C43⋊C8—22no—
103C2×C43⋊C8—41no—
104C2×C43⋊C8—41no—
105C2×C43⋊C8—41no—
106C2×C43⋊C8—42no—
107C23×C43C2×C22⋊C411yescharacteristic
108Q8×C43—82no—
109Q8×C43—81no—
110Q8×C43—81no—
111C2×C4×C43—22no—
112C2×C4×C43—42no—
113C2×C4×C43—44no—
114C2×C4×C43C4×D411yescharacteristic
115C2×C4×C43C4×D411yescharacteristic
116C2×C4×C43#12111yescharacteristic
117C2×C4×C43#12111yescharacteristic
118C2×C4×C43#12411yescharacteristic
119C2×C4×C43#12711yescharacteristic
120C2×C4×C43#13511yescharacteristic
121C2×C4×C43#13511yescharacteristic
122C2×C4×C43AGL(1,ℤ/8)12yes—
123C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
124C2×C4×C43#13712yes—
125C2×C4×C43#13711yescharacteristic
126C2×Dic43—22no—
127C2×Dic43—22no—
128C2×Dic43—22no—
129C2×Dic43—22no—
130C2×Dic43—22no—
131C2×Dic43—42no—
132C2×Dic43—42no—
133C2×Dic43—42no—
134C2×Dic43#10114yes—
135Dic86—81no—
136Dic86—81no—
137Dic86—81no—
138Dic86—81no—
139C8×C43—42no—
140C8×C43—81no—
141C43⋊C8—42no—
142C43⋊C8—81no—
143#9708—431nomaximal, Sylow
144C22×C43#39011yescharacteristic
145C22×C43C2×#10112yes—
146C22×C43#41611yescharacteristic
147C22×C43#41712yes—
148C22×C43#41711yescharacteristic
149C4×C43—21no—
150C4×C43—21no—
151C4×C43—82no—
152C4×C43#46311yescharacteristic
153C4×C43#46311yescharacteristic
154C4×C43#46411yescharacteristic
155C4×C43#46411yescharacteristic
156C4×C43#48912yes—
157C4×C43#49611yescharacteristic
158C4×C43#49711yescharacteristic
159Dic43—24no—
160Dic43—42no—
161Dic43—82no—
162#2862—431no—
163#1842—431no—
164#1767—431no—
165C2×#332—431no—
166C2×#332—431no—
167C2×#332—431no—
168C2×#332D4311yescharacteristic
169C2×C43#155212yes—
170C2×C43#156112yes—
171C2×C43#195911yescharacteristic
172C2×C43#196611yescharacteristic
173C2×C43#198311yescharacteristic
174C2×C4⋊Q8—431no—
175C2×C4⋊Q8C2×D4311yescharacteristic
176C2×C4⋊C8—431no—
177C2×C4⋊C8—431no—
178C2×C4⋊C8—862no—
179C2×C4⋊C8C2×D4311yescharacteristic
180C2×C4⋊C8C2×D4311yescharacteristic
181C2×#97—861no—
182#391—861no—
183#391—861no—
184#391—862no—
185#382—434no—
186C43—431no—
187#336—861no—
188#332—22no—
189#332—862no—
190#332—862no—
191#332—862no—
192C43#970811yescharacteristic, complemented, Sylow
193C22×Q8—21no—
194C22×Q8—861no—
195C22×C8—21no—
196C22×C8—21no—
197C22×C8—861no—
198C22×C8—861no—
199C4⋊Q8—21no—
200C4⋊Q8—21no—
201C4⋊Q8—21no—
202C4⋊Q8—21no—
203C4⋊Q8—861no—
204C4⋊Q8—861no—
205C4⋊Q8—861no—
206C4⋊Q8—861no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—432no—
209C2×C4⋊C4—861no—
210C2×C4⋊C4C4×D4312yes—
211C2×C42—432no—
212C2×C42—431no—
213C2×C42—431no—
214C2×C42—432no—
215C2×C42C22×D4311yescharacteristic
216C4⋊C8—21no—
217C4⋊C8—21no—
218C4⋊C8—21no—
219C4⋊C8—432no—
220C4⋊C8—861no—
221C4⋊C8—861no—
222C4⋊C8—861no—
223C4⋊C8—1724no—
224C4⋊C8C22⋊D4312yes—
225#97—1722no—
226#95—864no—
227#95—864no—
228C2×Q8—41no—
229C2×Q8—41no—
230C2×Q8—42no—
231C2×Q8—42no—
232C2×Q8—1721no—
233C2×Q8—1721no—
234C2×Q8—1721no—
235C2×Q8—1721no—
236C2×Q8—1721no—
237C2×Q8—1721no—
238C22×C4—22no—
239C22×C4—432no—
240C22×C4—432no—
241C22×C4—862no—
242C22×C4C2×C4×D4311yescharacteristic
243C22×C4D4×D4311yescharacteristic
244C22×C4D4×D4311yescharacteristic
245C2×C8—22no—
246C2×C8—41no—
247C2×C8—41no—
248C2×C8—41no—
249C2×C8—42no—
250C2×C8—862no—
251C2×C8—1721no—
252C2×C8—1722no—
253C2×C8—1721no—
254C2×C8—1721no—
255C4⋊C4—22no—
256C4⋊C4—22no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—862no—
260C4⋊C4—862no—
261C4⋊C4—1721no—
262C4⋊C4—1721no—
263C42—864no—
264C42—861no—
265C42—861no—
266C42—862no—
267C42—861no—
268C42—862no—
269C42—861no—
270C42#1062189811yescharacteristic
271C42D4×D4311yescharacteristic
272C42#1062190011yescharacteristic
273C42C2×C22⋊D4311yescharacteristic
274C23C22⋊C4×D4311yescharacteristic
275Q8—82no—
276Q8—81no—
277Q8—81no—
278Q8—3441no—
279Q8—3441no—
280Q8—3441no—
281Q8—3441no—
282C2×C4—22no—
283C2×C4—42no—
284C2×C4—44no—
285C2×C4—434no—
286C2×C4—862no—
287C2×C4—862no—
288C2×C4—862no—
289C2×C4—862no—
290C2×C4—862no—
291C2×C4—1722no—
292C2×C4—1722no—
293C2×C4—1722no—
294C2×C4(C22⋊D43)⋊C411yescharacteristic
295C2×C4C4×C22⋊D4311yescharacteristic
296C2×C4#1306329711yescharacteristic
297C2×C4#1306329811yescharacteristic
298C2×C4#1306331111yescharacteristic
299C2×C4#1306332111yescharacteristic
300C2×C4#1306334611yescharacteristic
301C2×C4#1306334811yescharacteristic
302C2×C4#1306334912yes—
303C2×C4#1306335211yescharacteristic
304C2×C4#1306335412yes—
305C2×C4#1306335711yescharacteristic
306C8—42no—
307C8—81no—
308C8—3441no—
309C8—1722no—
310C22#1458279911yescharacteristic
311C22#101×D4312yes—
312C22#1458289411yescharacteristic
313C22#1458289712yes—
314C22#1458289911yescharacteristic
315C4—21no—
316C4—21no—
317C4—82no—
318C4—864no—
319C4—3442no—
320C4—1722no—
321C4#1458311611yescharacteristic
322C4#1458311711yescharacteristic
323C4#1458312311yescharacteristic
324C4#1458312411yescharacteristic
325C4#1458325712yes—
326C4#1458328711yescharacteristic
327C4#1458329011yescharacteristic
328C2#1913329412yes—
329C2#1913333112yes—
330C2#1913541011yescharacteristic
331C2#1913543711yescharacteristic
332C2#1913552411yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC2×C43×#332C2
socle, prime radicalC23×C43C2×C22⋊C4
cosocleC2×C42×C43C23
hypercenterC2×#332D43
hypocenterC43#9708
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
192. C43#9708semidirect

Maximal subgroups

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

subgroupindex
#191429722
#191347462
#191344502
C2×#145826462
C2×#145826452
C2×#145826442
C2×C43×#3322
#970843