Finite Group Databasebeta

← #25065830

Subgroups — #25065830

Order 11008.

610 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
1C8×#10621898C211yesmaximal, characteristic
2#19143263C212yesmaximal
3#19133372C214yesmaximal, complemented
4#19133371C212yesmaximal, complemented
5#19133355C212yesmaximal, complemented
6#19133340C212yesmaximal, complemented
7C2×#14582650C211yesmaximal, characteristic, complemented
8C43×#1566C211yesmaximal, characteristic, complemented
9C4×#10621898C2211yescharacteristic
10C8×Dic86C411yescharacteristic
11C8×Dic86C411yescharacteristic
12C8×D172C411yescharacteristic
13C8×D172C411yescharacteristic
14C8×C22⋊D43C412yes—
15C8×C22⋊D43C412yes—
16#14582959—24no—
17#14582955C2214yes—
18#14582952C2211yescharacteristic
19#14582951C2214yes—
20#14582950C2212yes—
21C2×C4⋊(C43⋊C8)C2212yes—
22#14582867—22no—
23#14582857—22no—
24C4×C8×D43C2212yes—
25#14582651C2214yes—
26#14582651C2214yes—
27#14582650C2211yescharacteristic
28#14582650C2211yescharacteristic
29#14582650C2212yes—
30C43×#423C2212yes—
31C2×C4×C8×C43C2211yescharacteristic
32C43×#334C2212yes—
33C43×#334C2212yes—
34C2×#10621898D411yescharacteristic
35C22×C43⋊C8—22no—
36C2×C8×D43C2×C412yes—
37C2×C8×D43C2×C412yes—
38C4×Dic86C2×C411yescharacteristic
39C4×Dic86Q811yescharacteristic
40C4×D172C2×C411yescharacteristic
41C4×D172Q811yescharacteristic
42C4×C22⋊D43C2×C412yes—
43C4×C22⋊D43Q812yes—
44#13063284D411yescharacteristic
45#13063282D412yes—
46C42×D43C2312yes—
47C4⋊(C43⋊C8)—22no—
48C4⋊(C43⋊C8)C2×C411yescharacteristic
49C4⋊(C43⋊C8)C2×C411yescharacteristic
50C4⋊(C43⋊C8)C2312yes—
51C4⋊(C43⋊C8)C2312yes—
52Dic43⋊C8C2×C412yes—
53Dic43⋊C8C2×C412yes—
54C22⋊(C43⋊C8)C2×C412yes—
55(C2×D43)⋊C8—24no—
56(C2×D43)⋊C8—24no—
57(C2×D43)⋊C8C2×C412yes—
58(C2×D43)⋊C8C2×C412yes—
59#13063235—24no—
60C4×C43⋊C8C2312yes—
61C8×Dic43—24no—
62C8×Dic43C2×C412yes—
63C8×Dic43C2×C412yes—
64C2×M16×C43—22no—
65C22×C8×C43C2×C411yescharacteristic
66C22×C8×C43C2×C411yescharacteristic
67C2×C42×C43C2311yescharacteristic
68C4⋊C8×C43—22no—
69C4⋊C8×C43C2314yes—
70C4×C8×C43C2×C411yescharacteristic
71C4×C8×C43C2×C411yescharacteristic
72C4×C8×C43C2311yescharacteristic
73C4×C8×C43C2311yescharacteristic
74C22×C4×C43C22×C411yescharacteristic
75C22×C4×C43C2×D411yescharacteristic
76C22×C4×C43C2×Q811yescharacteristic
77C2×C22⋊D43C4⋊C412yes—
78#10621898—24no—
79C2×D172C4⋊C411yescharacteristic
80C2×C4×D43C22×C412yes—
81C2×C4×D43C2×D412yes—
82C2×C4×D43C2×Q812yes—
83C2×Dic86C4⋊C411yescharacteristic
84M16×C43—44no—
85C2×C8×C43—22no—
86C2×C8×C43—24no—
87C2×C8×C43—41no—
88C2×C8×C43C22×C411yescharacteristic
89C2×C8×C43C22×C411yescharacteristic
90C2×C8×C43C22×C411yescharacteristic
91C2×C8×C43C22×C411yescharacteristic
92C42×C43C22×C411yescharacteristic
93C42×C43C2×D411yescharacteristic
94C42×C43C2×Q811yescharacteristic
95C42×C43C2411yescharacteristic
96C22⋊Dic43C4⋊C412yes—
97(C2×D43)⋊C4C4⋊C412yes—
98(C2×D43)⋊C4C4⋊C412yes—
99C4⋊Dic43C4⋊C411yescharacteristic
100C4⋊Dic43C4⋊C411yescharacteristic
101Dic43⋊C4C4⋊C412yes—
102Dic43⋊C4C4⋊C412yes—
103C4×Dic43C22×C412yes—
104C4×Dic43C2×D412yes—
105C4×Dic43C2×Q812yes—
106C2×C43⋊C8—22no—
107C2×C43⋊C8—22no—
108C2×C43⋊C8—44no—
109C2×C43⋊C8C22×C412yes—
110C2×C43⋊C8C22×C412yes—
111C8×D43—24no—
112C8×D43—42no—
113C23×C43C2×C4⋊C411yescharacteristic
114C22×D43C2×C4⋊C412yes—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—41no—
118C2×C4×C43C2×C4⋊C411yescharacteristic
119C2×C4×C43C2×C4⋊C411yescharacteristic
120C2×C4×C43C2×C4⋊C411yescharacteristic
121C2×C4×C43#13514yes—
122C2×C4×C43C23×C411yescharacteristic
123C2×C4×C43C22×D411yescharacteristic
124C2×C4×C43C22×Q811yescharacteristic
125C22⋊D43—24no—
126C2×Dic43C2×C4⋊C412yes—
127C2×Dic43C2×C4⋊C412yes—
128C2×Dic43C2×C4⋊C412yes—
129D172—22no—
130C4×D43—22no—
131C4×D43—22no—
132C4×D43—24no—
133C4×D43—42no—
134Dic86—22no—
135C8×C43—21no—
136C8×C43—21no—
137C8×C43—21no—
138C8×C43—44no—
139C8×C43#13112yes—
140C43⋊C8—22no—
141C43⋊C8—22no—
142C43⋊C8—42no—
143C43⋊C8—42no—
144#17827—431nomaximal, Sylow
145C22×C43—21no—
146C22×C43—21no—
147C22×C43#42712yes—
148C22×C43C22×C4⋊C411yescharacteristic
149C2×D43—22no—
150C2×D43—22no—
151C2×D43—22no—
152C4×C43—21no—
153C4×C43—21no—
154C4×C43—21no—
155C4×C43#42712yes—
156C4×C43C2×#13111yescharacteristic
157C4×C43#56811yescharacteristic
158C4×C43C2×#13512yes—
159Dic43—22no—
160Dic43—22no—
161Dic43—22no—
162C8×#41—431no—
163#2925—432no—
164#1572—434no—
165#1571—432no—
166#1568—432no—
167#1566D4311yescharacteristic, complemented
168#1564—432no—
169C2×#334—431no—
170C2×C43—22no—
171C2×C43#290611yescharacteristic
172C2×C43C2×#42711yescharacteristic
173C2×C43#291611yescharacteristic
174D43—42no—
175C4×#41—431no—
176C8×Q8—431no—
177C8×Q8—431no—
178C8×D4—432no—
179C8×D4—432no—
180C8×D4—431no—
181C8×D4—431no—
182#433—864no—
183#432—434no—
184#431—431no—
185#431—432no—
186#431—434no—
187#423C2×D4312yes—
188C2×C4⋊C8—432no—
189#408—862no—
190#405—862no—
191C2×C4×C8—432no—
192C2×C4×C8C2×D4311yescharacteristic
193#335—434no—
194#335—434no—
195#334—431no—
196#334—431no—
197#334—432no—
198#334C2×D4312yes—
199#334C2×D4312yes—
200C43#1782711yescharacteristic, complemented, Sylow
201C2×#41—431no—
202C2×M16—22no—
203C22×C8—432no—
204C22×C8—432no—
205C22×C8—862no—
206C22×C8C4×D4311yescharacteristic
207C22×C8C4×D4311yescharacteristic
208C4×Q8—431no—
209C4×Q8—431no—
210C4×D4—432no—
211C4×D4—432no—
212C4×D4—431no—
213C4×D4—431no—
214#117—431no—
215#117—432no—
216C2×C42—432no—
217C2×C42C22×D4311yescharacteristic
218C4⋊C8—22no—
219C4⋊C8—432no—
220C4⋊C8—432no—
221C4⋊C8—431no—
222C4⋊C8—431no—
223C4⋊C8—432no—
224C4⋊C8—432no—
225C4⋊C8—862no—
226C4⋊C8C22×D4314yes—
227C22⋊C8—432no—
228C22⋊C8—432no—
229C22⋊C8—432no—
230C22⋊C8—864no—
231C22⋊C8—864no—
232#97—864no—
233C4×C8—432no—
234C4×C8—432no—
235C4×C8—432no—
236C4×C8—864no—
237C4×C8C4×D4311yescharacteristic
238C4×C8C4×D4311yescharacteristic
239C4×C8C22×D4311yescharacteristic
240C4×C8C22×D4311yescharacteristic
241#41—864no—
242C2×Q8—431no—
243C2×D4—432no—
244C2×D4—431no—
245C22×C4—432no—
246C22×C4—432no—
247C22×C4—432no—
248C22×C4C2×C4×D4311yescharacteristic
249C22×C4D4×D4311yescharacteristic
250C22×C4Q8×D4311yescharacteristic
251M16—44no—
252C2×C8—22no—
253C2×C8—24no—
254C2×C8—41no—
255C2×C8—432no—
256C2×C8—432no—
257C2×C8—864no—
258C2×C8—862no—
259C2×C8—862no—
260C2×C8—1722no—
261C2×C8—1724no—
262C2×C8C2×C4×D4311yescharacteristic
263C2×C8C2×C4×D4311yescharacteristic
264C2×C8C2×C4×D4311yescharacteristic
265C2×C8C2×C4×D4311yescharacteristic
266C4⋊C4—432no—
267C4⋊C4—432no—
268C4⋊C4—431no—
269C4⋊C4—431no—
270C22⋊C4—432no—
271C22⋊C4—432no—
272C22⋊C4—432no—
273C42—432no—
274C42—432no—
275C42—432no—
276C42C2×C4×D4311yescharacteristic
277C42D4×D4311yescharacteristic
278C42Q8×D4311yescharacteristic
279C42C23×D4311yescharacteristic
280C23—432no—
281C23C4⋊C4×D4311yescharacteristic
282Q8—862no—
283D4—864no—
284D4—862no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—41no—
288C2×C4—432no—
289C2×C4—432no—
290C2×C4—432no—
291C2×C4—862no—
292C2×C4—862no—
293C2×C4—864no—
294C2×C4—1722no—
295C2×C4C4⋊C4×D4311yescharacteristic
296C2×C4C4⋊C4×D4311yescharacteristic
297C2×C4C4⋊C4×D4311yescharacteristic
298C2×C4#1306334614yes—
299C2×C4C22×C4×D4311yescharacteristic
300C2×C4C2×D4×D4311yescharacteristic
301C2×C4C2×Q8×D4311yescharacteristic
302C8—21no—
303C8—21no—
304C8—21no—
305C8—44no—
306C8—862no—
307C8—862no—
308C8—1722no—
309C8—1722no—
310C8#1306333312yes—
311C22—21no—
312C22—21no—
313C22—862no—
314C22—862no—
315C22—862no—
316C22#1458293412yes—
317C22C2×C4⋊C4×D4311yescharacteristic
318C4—21no—
319C4—21no—
320C4—21no—
321C4—862no—
322C4—862no—
323C4—862no—
324C4#1458293412yes—
325C4C2×#1306333311yescharacteristic
326C4#1458366511yescharacteristic
327C4C2×#1306334612yes—
328C2—22no—
329C2—1722no—
330C2#1914316411yescharacteristic
331C2C2×#1458293411yescharacteristic
332C2#1914320311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1566C2
socleC22×C43C22×C4⋊C4
prime radicalC2×#10621898D4
cosocleC42×C43C24
hypercenter#1566D43
hypocenterC43#17827
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1566

Complements

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

NH ≅ G/Ntype
3. #19133372C2semidirect
4. #19133371C2semidirect
5. #19133355C2semidirect
6. #19133340C2semidirect
7. C2×#14582650C2semidirect
8. C43×#1566C2semidirect
167. #1566D43semidirect
200. C43#17827semidirect

Maximal subgroups

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

subgroupindex
C8×#106218982
#191432632
#191333722
#191333712
#191333552
#191333402
C2×#145826502
C43×#15662
#1782743