Finite Group Databasebeta

← #24996724

Subgroups — #24996724

Order 11008.

430 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142956C211yesmaximal, characteristic
2#19134711C211yesmaximal, characteristic
3C4⋊C8×Dic43C211yesmaximal, characteristic
4#19132479C211yesmaximal, characteristic
5#19132479C211yesmaximal, characteristic
6#19132478C211yesmaximal, characteristic
7C43×#1296C211yesmaximal, characteristic
8C2×#13063316—21no—
9C2×C4⋊(C43⋊C8)C2211yescharacteristic
10C2×C4⋊(C43⋊C8)C2211yescharacteristic
11C2×C8×Dic43—21no—
12#14582798—21no—
13#14582798C412yes—
14#14582795—21no—
15#14582795C412yes—
16#14582769C2211yescharacteristic
17#14582764—21no—
18C42×Dic43C2211yescharacteristic
19#14582653—21no—
20#14582653—21no—
21#14582653—21no—
22C2×C4⋊C8×C43C2211yescharacteristic
23C2×C4⋊C8×C43C2211yescharacteristic
24C43×#384C2211yescharacteristic
25C22×C43⋊C8—21no—
26C22×C43⋊C8—21no—
27#13063316—42no—
28#13063316—42no—
29C2×C4⋊Dic43—21no—
30C2×C4⋊Dic43—21no—
31C2×C4⋊Dic43—22no—
32C2×C4⋊Dic43C2×C412yes—
33C2×Dic43⋊C4—22no—
34C2×C4×Dic43C2×C411yescharacteristic
35C2×C4×Dic43C2×C411yescharacteristic
36C2×C4×Dic43D411yescharacteristic
37C2×C4×Dic43D411yescharacteristic
38C2×C4×Dic43D411yescharacteristic
39C2×C4×Dic43D411yescharacteristic
40C4⋊(C43⋊C8)—21no—
41C4⋊(C43⋊C8)—21no—
42C4⋊(C43⋊C8)—21no—
43C4⋊(C43⋊C8)Q812yes—
44C8×Dic43—42no—
45C43⋊#95—22no—
46C43⋊#95—22no—
47C22×C8×C43—21no—
48C22×C8×C43—21no—
49C2×C4⋊C4×C43—21no—
50C2×C4⋊C4×C43—21no—
51C2×C4⋊C4×C43C2×C412yes—
52C2×C42×C43C2311yescharacteristic
53C4⋊C8×C43—21no—
54C4⋊C8×C43—21no—
55C4⋊C8×C43—21no—
56C4⋊C8×C43Q812yes—
57C22×C4×C43—22no—
58C22×C4×C43C22×C411yescharacteristic
59C22×C4×C43C2×D411yescharacteristic
60C22×C4×C43C2×D411yescharacteristic
61C22×Dic43—22no—
62C22×Dic43C22⋊C411yescharacteristic
63C22×Dic43C22⋊C411yescharacteristic
64C22×Dic43C22⋊C411yescharacteristic
65C22×Dic43C22⋊C411yescharacteristic
66C2×C8×C43—22no—
67C2×C8×C43—41no—
68C2×C8×C43—41no—
69C2×C8×C43—41no—
70C2×C8×C43—41no—
71C2×C8×C43—41no—
72C4⋊C4×C43—42no—
73C4⋊C4×C43—41no—
74C4⋊C4×C43—41no—
75C4⋊C4×C43—41no—
76C4⋊C4×C43—41no—
77C42×C43C2×Q811yescharacteristic
78C42×C43C2×Q811yescharacteristic
79C42×C43#4111yescharacteristic
80C42×C43#4111yescharacteristic
81C4⋊Dic43—41no—
82C4⋊Dic43—41no—
83C4⋊Dic43—41no—
84C4⋊Dic43—41no—
85C4⋊Dic43—44no—
86C4⋊Dic43—42no—
87Dic43⋊C4—44no—
88C4×Dic43—21no—
89C4×Dic43—21no—
90C4×Dic43—21no—
91C4×Dic43—21no—
92C4×Dic43—21no—
93C4×Dic43—21no—
94C4×Dic43—41no—
95C4×Dic43—41no—
96C4×Dic43D812yes—
97C4×Dic43SD1612yes—
98C2×C43⋊C8—22no—
99C2×C43⋊C8—41no—
100C2×C43⋊C8—41no—
101C2×C43⋊C8—41no—
102C2×C43⋊C8—41no—
103C2×C43⋊C8—41no—
104C23×C43C2×C22⋊C411yescharacteristic
105C2×C4×C43—21no—
106C2×C4×C43—21no—
107C2×C4×C43—42no—
108C2×C4×C43—42no—
109C2×C4×C43—42no—
110C2×C4×C43C4×Q811yescharacteristic
111C2×C4×C43C4×Q811yescharacteristic
112C2×C4×C43C22⋊Q811yescharacteristic
113C2×C4×C43C22⋊Q811yescharacteristic
114C2×C4×C43#12411yescharacteristic
115C2×C4×C43C4⋊Q811yescharacteristic
116C2×C4×C43C2×D811yescharacteristic
117C2×C4×C43C2×SD1611yescharacteristic
118C2×C4×C43#13511yescharacteristic
119C2×C4×C43#13511yescharacteristic
120C2×C4×C43#13511yescharacteristic
121C2×C4×C43#13511yescharacteristic
122C2×C4×C43#13711yescharacteristic
123C2×C4×C43#13711yescharacteristic
124C2×Dic43—21no—
125C2×Dic43—21no—
126C2×Dic43—21no—
127C2×Dic43—21no—
128C2×Dic43—21no—
129C2×Dic43—21no—
130C2×Dic43—21no—
131C2×Dic43—21no—
132C2×Dic43—21no—
133C2×Dic43—21no—
134C2×Dic43—42no—
135C2×Dic43—42no—
136C2×Dic43—42no—
137C2×Dic43#10212yes—
138C2×Dic43#10212yes—
139C8×C43—42no—
140C8×C43—81no—
141C43⋊C8—42no—
142C43⋊C8—81no—
143#9899—431nomaximal, Sylow
144C22×C43#39111yescharacteristic
145C22×C43#41311yescharacteristic
146C22×C43#41311yescharacteristic
147C22×C43C2×#10211yescharacteristic
148C22×C43#41611yescharacteristic
149C22×C43#41611yescharacteristic
150C22×C43#41911yescharacteristic
151C4×C43—21no—
152C4×C43—21no—
153C4×C43—82no—
154C4×C43#47411yescharacteristic
155C4×C43#47411yescharacteristic
156C4×C43#47511yescharacteristic
157C4×C43#47511yescharacteristic
158C4×C43#48811yescharacteristic
159C4×C43#48811yescharacteristic
160C4×C43#49911yescharacteristic
161C4×C43#49911yescharacteristic
162Dic43—22no—
163Dic43—22no—
164Dic43—41no—
165Dic43—41no—
166Dic43—82no—
167#2859—431no—
168#1831—431no—
169C4×C4⋊C8—431no—
170#1296—431no—
171#1296—431no—
172#1296—431no—
173#1296D4311yescharacteristic
174C2×C43#154011yescharacteristic
175C2×C43#154011yescharacteristic
176C2×C43#155411yescharacteristic
177C2×C43#155411yescharacteristic
178C2×C43#198811yescharacteristic
179C2×C43#199111yescharacteristic
180C2×C43#199811yescharacteristic
181C2×#125—861no—
182C2×C4⋊C8—431no—
183C2×C4⋊C8—431no—
184C2×C4⋊C8C2×D4311yescharacteristic
185C2×C4⋊C8C2×D4311yescharacteristic
186C2×C4×C8—861no—
187#389—432no—
188#389—432no—
189#389—861no—
190#389—861no—
191#384—431no—
192#384C2×D4311yescharacteristic
193#382—861no—
194C43—431no—
195#336—861no—
196#336—861no—
197#336—861no—
198C43#989911yescharacteristic, complemented, Sylow
199C22×C8—21no—
200C22×C8—21no—
201C22×C8—861no—
202C22×C8—861no—
203#125—1722no—
204#125—1722no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—432no—
208C2×C4⋊C4—862no—
209C2×C4⋊C4—862no—
210C2×C4⋊C4—861no—
211C2×C4⋊C4—861no—
212C2×C4⋊C4C4×D4312yes—
213C2×C42—431no—
214C2×C42—431no—
215C2×C42—431no—
216C2×C42—431no—
217C2×C42—431no—
218C2×C42—431no—
219C2×C42C22×D4311yescharacteristic
220C4⋊C8—21no—
221C4⋊C8—21no—
222C4⋊C8—21no—
223C4⋊C8—432no—
224C4⋊C8—861no—
225C4⋊C8—861no—
226C4⋊C8—861no—
227C4⋊C8Dic8612yes—
228C4×C8—1722no—
229#95—862no—
230#95—862no—
231C22×C4—22no—
232C22×C4—431no—
233C22×C4—431no—
234C22×C4—431no—
235C22×C4—431no—
236C22×C4—862no—
237C22×C4C2×C4×D4311yescharacteristic
238C22×C4D4×D4311yescharacteristic
239C22×C4D4×D4311yescharacteristic
240C2×C8—22no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—862no—
247C2×C8—1721no—
248C2×C8—1721no—
249C2×C8—1721no—
250C2×C8—1721no—
251C2×C8—1721no—
252C4⋊C4—42no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—1722no—
258C4⋊C4—1724no—
259C4⋊C4—1724no—
260C4⋊C4—1721no—
261C4⋊C4—1721no—
262C4⋊C4—1721no—
263C4⋊C4—1721no—
264C42—432no—
265C42—432no—
266C42—861no—
267C42—861no—
268C42—861no—
269C42—861no—
270C42—861no—
271C42—861no—
272C42—1721no—
273C42—1721no—
274C42C2×Dic8611yescharacteristic
275C42#1062189811yescharacteristic
276C42#1062190011yescharacteristic
277C42Q8×D4311yescharacteristic
278C23C22⋊C4×D4311yescharacteristic
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—432no—
285C2×C4—432no—
286C2×C4—861no—
287C2×C4—861no—
288C2×C4—861no—
289C2×C4—861no—
290C2×C4—861no—
291C2×C4—861no—
292C2×C4—861no—
293C2×C4—861no—
294C2×C4—861no—
295C2×C4—861no—
296C2×C4—1722no—
297C2×C4—1722no—
298C2×C4—1722no—
299C2×C4#1306329011yescharacteristic
300C2×C4C4×Dic8611yescharacteristic
301C2×C4#1306330211yescharacteristic
302C2×C4#1306330311yescharacteristic
303C2×C4#1306331111yescharacteristic
304C2×C4#1306332411yescharacteristic
305C2×C4D8×D4311yescharacteristic
306C2×C4SD16×D4311yescharacteristic
307C2×C4#1306334411yescharacteristic
308C2×C4#1306334611yescharacteristic
309C2×C4#1306334611yescharacteristic
310C2×C4#1306334811yescharacteristic
311C2×C4#1306335411yescharacteristic
312C2×C4#1306335711yescharacteristic
313C8—42no—
314C8—81no—
315C8—3441no—
316C8—1722no—
317C22#1458280311yescharacteristic
318C22#1458288011yescharacteristic
319C22#1458288211yescharacteristic
320C22#102×D4311yescharacteristic
321C22#1458289211yescharacteristic
322C22#1458289411yescharacteristic
323C22#1458290611yescharacteristic
324C4—21no—
325C4—21no—
326C4—82no—
327C4—862no—
328C4—862no—
329C4—3442no—
330C4—1721no—
331C4—1721no—
332C4#1458317711yescharacteristic
333C4#1458317811yescharacteristic
334C4#1458318211yescharacteristic
335C4#1458318311yescharacteristic
336C4#1458325211yescharacteristic
337C4#1458325511yescharacteristic
338C4#1458329911yescharacteristic
339C4#1458330011yescharacteristic
340C2#1913324111yescharacteristic
341C2#1913324311yescharacteristic
342C2#1913330211yescharacteristic
343C2#1913330411yescharacteristic
344C2#1913554511yescharacteristic
345C2#1913555811yescharacteristic
346C2#1913558611yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1296C2
socle, prime radicalC23×C43C2×C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1296D43
hypocenterC43#9899
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
198. C43#9899semidirect

Maximal subgroups

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

subgroupindex
#191429562
#191347112
C4⋊C8×Dic432
#191324792
#191324782
C43×#12962
#989943