Finite Group Databasebeta

← #24993303

Subgroups — #24993303

Order 11008.

470 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145739C211yesmaximal, characteristic
2#19135576C211yesmaximal, characteristic
3#19133267C211yesmaximal, characteristic
4#19133158C211yesmaximal, characteristic
5#19132453C211yesmaximal, characteristic
6#19132424C211yesmaximal, characteristic
7C43×#2327C211yesmaximal, characteristic
8#14583456C2211yescharacteristic
9#14583295C412yescomplemented
10#14583251C412yescomplemented
11#14583229—22no—
12#14583181—22no—
13#14582952C2211yescharacteristic
14#14582952C2211yescharacteristic
15#14582923C2211yescharacteristic
16#14582659—21no—
17#14582659—21no—
18#14582645—22no—
19#14582635—22no—
20C2×C4⋊Q8×C43C2211yescharacteristic
21C2×C4×Q8×C43—21no—
22C43×#391—21no—
23C43×#387—22no—
24C43×#387—22no—
25C43×#382C2211yescharacteristic
26C43×#376C2211yescharacteristic
27C2×#10621877—21no—
28#13063325C2×C411yescharacteristic
29#13063325C2×C411yescharacteristic
30#13063317—21no—
31#13063304—21no—
32#13063304—21no—
33C4×Dic86—21no—
34C4×Dic86—21no—
35#13063284—21no—
36#13063256—24no—
37C4⋊(C43⋊C8)—21no—
38C4⋊(C43⋊C8)—21no—
39C4⋊(C43⋊C8)—21no—
40C4⋊(C43⋊C8)—21no—
41#13063248—24no—
42C22⋊(C43⋊C8)—21no—
43C22⋊(C43⋊C8)—21no—
44C4×C43⋊C8—21no—
45C4×C43⋊C8C2×C412yes—
46C22×Q8×C43—21no—
47C4⋊Q8×C43—21no—
48C4⋊Q8×C43—21no—
49C4⋊Q8×C43C2×C412yes—
50C4⋊Q8×C43D412yes—
51C4×Q8×C43—42no—
52C4×Q8×C43—42no—
53C2×C4⋊C4×C43—21no—
54C2×C4⋊C4×C43—22no—
55C2×C4⋊C4×C43—21no—
56C2×C4⋊C4×C43D412yes—
57C2×C42×C43—22no—
58C2×C42×C43D411yescharacteristic
59C2×C42×C43D411yescharacteristic
60C2×C42×C43C2311yescharacteristic
61#95×C43—24no—
62#95×C43—21no—
63#95×C43—21no—
64#95×C43—21no—
65#95×C43D412yes—
66C2×Q8×C43—22no—
67C2×Q8×C43—22no—
68C2×Q8×C43—41no—
69C2×Q8×C43—41no—
70C2×Q8×C43—41no—
71C2×Q8×C43—41no—
72C22×C4×C43—21no—
73C22×C4×C43—22no—
74C22×C4×C43—21no—
75C22×C4×C43—22no—
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43C2×D411yescharacteristic
78C22×C4×C43C2×D411yescharacteristic
79C2×Dic86—21no—
80C2×Dic86—21no—
81C4⋊C4×C43—22no—
82C4⋊C4×C43—22no—
83C4⋊C4×C43—22no—
84C4⋊C4×C43—44no—
85C4⋊C4×C43—41no—
86C4⋊C4×C43—41no—
87C4⋊C4×C43C22⋊C414yes—
88C42×C43—21no—
89C42×C43—21no—
90C42×C43—21no—
91C42×C43—44no—
92C42×C43SD1612yes—
93C42×C43C22×C411yescharacteristic
94C42×C43C2×D411yescharacteristic
95C42×C43#4111yescharacteristic
96C42×C43#4111yescharacteristic
97C22⋊Dic43—41no—
98C4⋊Dic43—21no—
99C4⋊Dic43—21no—
100C4⋊Dic43—21no—
101C4⋊Dic43—21no—
102Dic43⋊C4—41no—
103Dic43⋊C4—41no—
104C4×Dic43—41no—
105#10621877—41no—
106#10621877—41no—
107C2×C43⋊C8—22no—
108C2×C43⋊C8—41no—
109C2×C43⋊C8—41no—
110C23×C43#12011yescharacteristic
111Q8×C43—42no—
112Q8×C43—42no—
113Q8×C43—42no—
114Q8×C43—42no—
115C2×C4×C43—24no—
116C2×C4×C43—22no—
117C2×C4×C43—41no—
118C2×C4×C43—41no—
119C2×C4×C43—41no—
120C2×C4×C43—41no—
121C2×C4×C43—42no—
122C2×C4×C43—42no—
123C2×C4×C43—41no—
124C2×C4×C43—42no—
125C2×C4×C43—41no—
126C2×C4×C43—42no—
127C2×C4×C43—42no—
128C2×C4×C43—41no—
129C2×C4×C43C2×C22⋊C411yescharacteristic
130C2×C4×C43C4×D411yescharacteristic
131C2×C4×C43C4×D411yescharacteristic
132C2×C4×C43#12111yescharacteristic
133C2×C4×C43#12111yescharacteristic
134C2×C4×C43#12311yescharacteristic
135C2×C4×C43C2×SD1611yescharacteristic
136C2×C4×C43#13511yescharacteristic
137C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C43#13711yescharacteristic
139C2×Dic43—41no—
140C2×Dic43—41no—
141Dic86—42no—
142Dic86—81no—
143C43⋊C8—42no—
144C43⋊C8—81no—
145C43⋊C8—81no—
146#9296—431nomaximal, Sylow
147C22×C43—21no—
148C22×C43—21no—
149C22×C43#38611yescharacteristic
150C22×C43#45011yescharacteristic
151C22×C43#45211yescharacteristic
152C4×C43—21no—
153C4×C43—21no—
154C4×C43—21no—
155C4×C43—21no—
156C4×C43—42no—
157C4×C43—44no—
158C4×C43—82no—
159C4×C43—81no—
160C4×C43C4×SD1611yescharacteristic
161C4×C43#44011yescharacteristic
162C4×C43#46111yescharacteristic
163C4×C43#46311yescharacteristic
164Dic43—81no—
165Dic43—81no—
166#3229—431no—
167#2327D4311yescharacteristic
168#1995—431no—
169#1546—431no—
170#1518—431no—
171#1286—431no—
172#1274—431no—
173C2×C43—21no—
174C2×C43—21no—
175C2×C43#187711yescharacteristic
176C2×C43#190511yescharacteristic
177C2×C43#191211yescharacteristic
178#533—431no—
179C2×C4⋊Q8C2×D4311yescharacteristic
180C2×C4×Q8—21no—
181#498—432no—
182#487—432no—
183#483—862no—
184#475—862no—
185#431—431no—
186#431—431no—
187#423—431no—
188#391—21no—
189#387—22no—
190#387—22no—
191#382C2×D4311yescharacteristic
192#376C2×D4311yescharacteristic
193#339—861no—
194#339—861no—
195#332—862no—
196#328—862no—
197C43#929611yescharacteristic, complemented, Sylow
198C22×Q8—21no—
199C2×M16—861no—
200C4⋊Q8—21no—
201C4⋊Q8—21no—
202C4⋊Q8—431no—
203C4⋊Q8—431no—
204C4⋊Q8C4×D4312yes—
205C4⋊Q8D17212yes—
206#125—861no—
207C22⋊Q8—861no—
208C22⋊Q8—861no—
209C4×Q8—42no—
210C4×Q8—42no—
211C4×Q8—861no—
212C4×Q8—861no—
213#117—861no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—22no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4C22⋊D4312yes—
218C2×C42—22no—
219C2×C42C22⋊D4311yescharacteristic
220C2×C42C22⋊D4311yescharacteristic
221C2×C42C22×D4311yescharacteristic
222#106—864no—
223C4⋊C8—861no—
224C4⋊C8—861no—
225C4⋊C8—861no—
226C4⋊C8—861no—
227#103—864no—
228C22⋊C8—861no—
229C22⋊C8—861no—
230C4×C8—432no—
231C4×C8—861no—
232#95—24no—
233#95—21no—
234#95—21no—
235#95—21no—
236#95C22⋊D4312yes—
237C2×Q8—22no—
238C2×Q8—22no—
239C2×Q8—41no—
240C2×Q8—41no—
241C2×Q8—41no—
242C2×Q8—41no—
243C2×Q8—861no—
244C2×Q8—861no—
245C22×C4—21no—
246C22×C4—22no—
247C22×C4—21no—
248C22×C4—22no—
249C22×C4C2×C22⋊D4311yescharacteristic
250C22×C4C2×C22⋊D4311yescharacteristic
251C22×C4C2×C22⋊D4311yescharacteristic
252M16—1721no—
253M16—1721no—
254C2×C8—862no—
255C2×C8—1721no—
256C2×C8—1721no—
257C4⋊C4—22no—
258C4⋊C4—22no—
259C4⋊C4—22no—
260C4⋊C4—44no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—861no—
264C4⋊C4—861no—
265C4⋊C4—861no—
266C4⋊C4—861no—
267C4⋊C4—1721no—
268C4⋊C4—1721no—
269C4⋊C4(C2×D43)⋊C414yes—
270C22⋊C4—1721no—
271C42—21no—
272C42—21no—
273C42—21no—
274C42—44no—
275C42—1721no—
276C42#1062188312yes—
277C42C2×C4×D4311yescharacteristic
278C42C2×D17211yescharacteristic
279C42#1062189811yescharacteristic
280C42#1062189811yescharacteristic
281C23#1306329411yescharacteristic
282Q8—42no—
283Q8—42no—
284Q8—42no—
285Q8—42no—
286Q8—3441no—
287Q8—1722no—
288C2×C4—22no—
289C2×C4—24no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—41no—
297C2×C4—42no—
298C2×C4—41no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—41no—
302C2×C4—1721no—
303C2×C4—1721no—
304C2×C4C2×(C2×D43)⋊C411yescharacteristic
305C2×C4C4×C22⋊D4311yescharacteristic
306C2×C4C4×C22⋊D4311yescharacteristic
307C2×C4#1306329911yescharacteristic
308C2×C4#1306329911yescharacteristic
309C2×C4#1306330811yescharacteristic
310C2×C4C2×#1062188311yescharacteristic
311C2×C4#1306334511yescharacteristic
312C2×C4#1306335111yescharacteristic
313C2×C4#1306335511yescharacteristic
314C8—3441no—
315C8—3441no—
316C8—1722no—
317C22—21no—
318C22—21no—
319C22#1458277811yescharacteristic
320C22#1458305011yescharacteristic
321C22#1458306111yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—42no—
327C4—44no—
328C4—82no—
329C4—81no—
330C4—3441no—
331C4—3441no—
332C4C4×#1062188311yescharacteristic
333C4#1458299911yescharacteristic
334C4#1458310411yescharacteristic
335C4#1458311411yescharacteristic
336C2—21no—
337C2—21no—
338C2#1913492911yescharacteristic
339C2#1913508911yescharacteristic
340C2#1913513211yescharacteristic
subgroupG/H
centerC22#14582778
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2327C2
socleC22×C43#386
prime radicalC23×C43#120
cosocleC2×C42×C43C23
hypercenter#2327D43
hypocenterC43#9296
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2327

Complements

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

NH ≅ G/Ntype
9. #14583295C4semidirect
10. #14583251C4semidirect
197. C43#9296semidirect

Maximal subgroups

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

subgroupindex
#191457392
#191355762
#191332672
#191331582
#191324532
#191324242
C43×#23272
#929643