Finite Group Databasebeta

← #24995176

Subgroups — #24995176

Order 11008.

404 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19134746C211yesmaximal, characteristic
2C4⋊C8×Dic43C211yesmaximal, characteristic
3C4×Dic43⋊C8C211yesmaximal, characteristic
4C2×#14582649C211yesmaximal, characteristic
5#19132430C211yesmaximal, characteristic
6#19132429C211yesmaximal, characteristic
7C2×C43×#334C211yesmaximal, characteristic
8C2×C4⋊(C43⋊C8)C2211yescharacteristic
9C2×C4⋊(C43⋊C8)C2211yescharacteristic
10C2×Dic43⋊C8—21no—
11C2×Dic43⋊C8—21no—
12C2×Dic43⋊C8C411yescharacteristic
13C2×Dic43⋊C8C411yescharacteristic
14C2×C4×C43⋊C8C2211yescharacteristic
15C2×C8×Dic43—21no—
16C42×Dic43C2211yescharacteristic
17#14582653—21no—
18#14582653C411yescharacteristic
19#14582653C411yescharacteristic
20#14582649—22no—
21C2×C4⋊C8×C43C2211yescharacteristic
22C2×C4⋊C8×C43C2211yescharacteristic
23C2×C4×C8×C43C2211yescharacteristic
24C43×#334—22no—
25C22×C43⋊C8—21no—
26C22×C43⋊C8—21no—
27C22×C43⋊C8C2×C411yescharacteristic
28C22×C43⋊C8C2×C411yescharacteristic
29C2×C4×Dic43C2×C411yescharacteristic
30C2×C4×Dic43C2×C411yescharacteristic
31C2×C4×Dic43D411yescharacteristic
32C2×C4×Dic43D411yescharacteristic
33C2×C4×Dic43Q811yescharacteristic
34C2×C4×Dic43Q811yescharacteristic
35C4⋊(C43⋊C8)—21no—
36C4⋊(C43⋊C8)—21no—
37C4⋊(C43⋊C8)—21no—
38C4⋊(C43⋊C8)Q812yes—
39Dic43⋊C8—22no—
40Dic43⋊C8—42no—
41Dic43⋊C8—42no—
42Dic43⋊C8C814yescomplemented
43C4×C43⋊C8—21no—
44C4×C43⋊C8—21no—
45C8×Dic43—42no—
46C22×C8×C43—21no—
47C22×C8×C43—21no—
48C22×C8×C43C2×C411yescharacteristic
49C22×C8×C43C2×C411yescharacteristic
50C2×C42×C43C2311yescharacteristic
51C4⋊C8×C43—21no—
52C4⋊C8×C43—21no—
53C4⋊C8×C43—21no—
54C4⋊C8×C43D412yes—
55C4×C8×C43—21no—
56C4×C8×C43—21no—
57C22×C4×C43C22×C411yescharacteristic
58C22×C4×C43C2×D411yescharacteristic
59C22×C4×C43C2×Q811yescharacteristic
60C22×Dic43C4⋊C411yescharacteristic
61C22×Dic43C4⋊C411yescharacteristic
62C22×Dic43C4⋊C411yescharacteristic
63C22×Dic43C4⋊C411yescharacteristic
64C2×C8×C43—21no—
65C2×C8×C43—21no—
66C2×C8×C43—21no—
67C2×C8×C43—22no—
68C2×C8×C43—21no—
69C2×C8×C43—21no—
70C2×C8×C43—41no—
71C2×C8×C43—41no—
72C2×C8×C43—41no—
73C2×C8×C43—41no—
74C2×C8×C43—41no—
75C2×C8×C43C2×C812yes—
76C42×C43C2×D411yescharacteristic
77C42×C43C2×Q811yescharacteristic
78C42×C43#4111yescharacteristic
79C42×C43#4111yescharacteristic
80C4×Dic43—21no—
81C4×Dic43—21no—
82C4×Dic43—21no—
83C4×Dic43—21no—
84C4×Dic43—22no—
85C4×Dic43—41no—
86C4×Dic43C2×C812yes—
87C4×Dic43M1612yes—
88C4×Dic43SD1612yes—
89C4×Dic43SD1612yes—
90C2×C43⋊C8—21no—
91C2×C43⋊C8—21no—
92C2×C43⋊C8—21no—
93C2×C43⋊C8—22no—
94C2×C43⋊C8—21no—
95C2×C43⋊C8—21no—
96C2×C43⋊C8—41no—
97C2×C43⋊C8—41no—
98C2×C43⋊C8—41no—
99C2×C43⋊C8—41no—
100C2×C43⋊C8—41no—
101C2×C43⋊C8C2×C812yes—
102C23×C43C2×C4⋊C411yescharacteristic
103C2×C4×C43—21no—
104C2×C4×C43—21no—
105C2×C4×C43C4×D411yescharacteristic
106C2×C4×C43C4×Q811yescharacteristic
107C2×C4×C43#12111yescharacteristic
108C2×C4×C43C22⋊Q811yescharacteristic
109C2×C4×C43#12511yescharacteristic
110C2×C4×C43C4⋊Q811yescharacteristic
111C2×C4×C43C22×C811yescharacteristic
112C2×C4×C43C2×M1611yescharacteristic
113C2×C4×C43#13111yescharacteristic
114C2×C4×C43#13111yescharacteristic
115C2×C4×C43C2×SD1611yescharacteristic
116C2×C4×C43C2×SD1611yescharacteristic
117C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
118C2×C4×C43#13711yescharacteristic
119C2×Dic43—21no—
120C2×Dic43—21no—
121C2×Dic43—21no—
122C2×Dic43—21no—
123C2×Dic43—21no—
124C2×Dic43—21no—
125C2×Dic43—21no—
126C2×Dic43C4⋊C812yes—
127C2×Dic43C4⋊C812yes—
128C2×Dic43#10612yes—
129C2×Dic43#10612yes—
130C2×Dic43#10812yes—
131C8×C43—22no—
132C8×C43—41no—
133C8×C43—42no—
134C8×C43—81no—
135C43⋊C8—22no—
136C43⋊C8—41no—
137C43⋊C8—42no—
138C43⋊C8—81no—
139#9602—431nomaximal, Sylow
140C22×C43#38911yescharacteristic
141C22×C43C2×C4⋊C811yescharacteristic
142C22×C43#42411yescharacteristic
143C22×C43C2×#10611yescharacteristic
144C22×C43#42811yescharacteristic
145C22×C43C2×#10811yescharacteristic
146C22×C43#43011yescharacteristic
147C4×C43—21no—
148C4×C43—21no—
149C4×C43C8×D411yescharacteristic
150C4×C43#43611yescharacteristic
151C4×C43C8×Q811yescharacteristic
152C4×C43#44611yescharacteristic
153C4×C43#46011yescharacteristic
154C4×C43#46111yescharacteristic
155C4×C43#47511yescharacteristic
156C4×C43#47611yescharacteristic
157Dic43—22no—
158Dic43—22no—
159Dic43—41no—
160Dic43#33414yescomplemented
161#1842—431no—
162C4×C4⋊C8—431no—
163C4×C4⋊C8—431no—
164C2×#334—431no—
165C2×#334D4311yescharacteristic
166#1277—431no—
167#1277—431no—
168C2×C43C2×#33411yescharacteristic
169C2×C43#156511yescharacteristic
170C2×C43#157011yescharacteristic
171C2×C43#157411yescharacteristic
172C2×C43#193911yescharacteristic
173C2×C43#194811yescharacteristic
174C2×C43#195011yescharacteristic
175C2×C4⋊C8—431no—
176C2×C4⋊C8—431no—
177C2×C4⋊C8—431no—
178C2×C4⋊C8—431no—
179C2×C4⋊C8—861no—
180C2×C4⋊C8—861no—
181C2×C4⋊C8C2×D4311yescharacteristic
182C2×C4⋊C8C2×D4311yescharacteristic
183C2×C4×C8—431no—
184C2×C4×C8—861no—
185C2×C4×C8C2×D4311yescharacteristic
186C43—431no—
187#336—431no—
188#336—431no—
189#336—861no—
190#334—22no—
191#334—862no—
192C43#960211yescharacteristic, complemented, Sylow
193C22×C8—21no—
194C22×C8—21no—
195C22×C8—431no—
196C22×C8—431no—
197C22×C8—861no—
198C22×C8—861no—
199C22×C8C4×D4311yescharacteristic
200C22×C8C4×D4311yescharacteristic
201C2×C42—431no—
202C2×C42—431no—
203C2×C42—431no—
204C2×C42—431no—
205C2×C42—431no—
206C2×C42—431no—
207C2×C42C22×D4311yescharacteristic
208C4⋊C8—21no—
209C4⋊C8—21no—
210C4⋊C8—21no—
211C4⋊C8—434no—
212C4⋊C8—432no—
213C4⋊C8—862no—
214C4⋊C8—861no—
215C4⋊C8—861no—
216C4⋊C8—861no—
217C4⋊C8—1722no—
218C4⋊C8—1722no—
219C4⋊C8C22⋊D4312yes—
220C4×C8—21no—
221C4×C8—21no—
222C4×C8—861no—
223C4×C8—861no—
224C4×C8—1722no—
225C22×C4—431no—
226C22×C4—431no—
227C22×C4—431no—
228C22×C4—431no—
229C22×C4C2×C4×D4311yescharacteristic
230C22×C4D4×D4311yescharacteristic
231C22×C4Q8×D4311yescharacteristic
232C2×C8—21no—
233C2×C8—21no—
234C2×C8—21no—
235C2×C8—22no—
236C2×C8—21no—
237C2×C8—21no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—432no—
244C2×C8—861no—
245C2×C8—861no—
246C2×C8—861no—
247C2×C8—862no—
248C2×C8—861no—
249C2×C8—861no—
250C2×C8—1721no—
251C2×C8—1721no—
252C2×C8—1721no—
253C2×C8—1721no—
254C2×C8—1721no—
255C2×C8C8×D4312yes—
256C42—432no—
257C42—432no—
258C42—432no—
259C42—432no—
260C42—862no—
261C42—861no—
262C42—861no—
263C42—861no—
264C42—861no—
265C42—1721no—
266C42#1062189811yescharacteristic
267C42#1062190011yescharacteristic
268C42Q8×D4311yescharacteristic
269C42C2×C22⋊D4311yescharacteristic
270C23C4⋊C4×D4311yescharacteristic
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—432no—
274C2×C4—432no—
275C2×C4—432no—
276C2×C4—432no—
277C2×C4—432no—
278C2×C4—861no—
279C2×C4—861no—
280C2×C4—861no—
281C2×C4—861no—
282C2×C4—861no—
283C2×C4—861no—
284C2×C4—861no—
285C2×C4C4×C22⋊D4311yescharacteristic
286C2×C4#1306329011yescharacteristic
287C2×C4#1306329711yescharacteristic
288C2×C4#1306330311yescharacteristic
289C2×C4#1306331511yescharacteristic
290C2×C4#1306332311yescharacteristic
291C2×C4C2×C8×D4311yescharacteristic
292C2×C4M16×D4311yescharacteristic
293C2×C4#1306333111yescharacteristic
294C2×C4#1306333311yescharacteristic
295C2×C4SD16×D4311yescharacteristic
296C2×C4SD16×D4311yescharacteristic
297C2×C4#1306335211yescharacteristic
298C2×C4#1306335411yescharacteristic
299C8—22no—
300C8—42no—
301C8—41no—
302C8—81no—
303C8—862no—
304C8—3441no—
305C8—1722no—
306C8—1721no—
307C22#1458279411yescharacteristic
308C22C4⋊C8×D4311yescharacteristic
309C22#1458292411yescharacteristic
310C22#106×D4311yescharacteristic
311C22#1458293811yescharacteristic
312C22#108×D4311yescharacteristic
313C22#1458294611yescharacteristic
314C4—21no—
315C4—21no—
316C4—434no—
317C4—862no—
318C4—862no—
319C4—1721no—
320C4C8×C22⋊D4311yescharacteristic
321C4#1458297511yescharacteristic
322C4#1458302311yescharacteristic
323C4#1458302811yescharacteristic
324C4#1458309711yescharacteristic
325C4#1458310211yescharacteristic
326C4#1458318311yescharacteristic
327C4#1458318811yescharacteristic
328C2#334×D4311yescharacteristic
329C2#1913334411yescharacteristic
330C2#1913336411yescharacteristic
331C2#1913338211yescharacteristic
332C2#1913531011yescharacteristic
333C2#1913535511yescharacteristic
334C2#1913536711yescharacteristic
subgroupG/H
centerC22×C4D4×D43
commutatorC2×C4×C43C22×C8
FrattiniC2×C42C22×D43
FittingC2×C43×#334C2
socle, prime radicalC23×C43C2×C4⋊C4
cosocleC2×C42×C43C23
hypercenterC2×#334D43
hypocenterC43#9602
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×#334

Complements

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

NH ≅ G/Ntype
42. Dic43⋊C8C8semidirect
160. Dic43#334semidirect
192. C43#9602semidirect

Maximal subgroups

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

subgroupindex
#191347462
C4⋊C8×Dic432
C4×Dic43⋊C82
C2×#145826492
#191324302
#191324292
C2×C43×#3342
#960243