Finite Group Databasebeta

← #25065815

Subgroups — #25065815

Order 11008.

572 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143712C212yesmaximal
2#19133384C212yesmaximal, complemented
3#19133380C212yesmaximal, complemented
4#19133375C212yesmaximal, complemented
5#19133370C212yesmaximal, complemented
6#19133362C212yesmaximal, complemented
7#19133358C211yesmaximal, characteristic, complemented
8#19133354C211yesmaximal, characteristic, complemented
9C43×#2922C211yesmaximal, characteristic
10#14583030—22no—
11#14582977—22no—
12#14582971—22no—
13#14582971—22no—
14#14582956C2212yes—
15#14582956C2212yes—
16#14582952C2212yes—
17#14582923C2212yes—
18#14582923C2212yes—
19C2×C4⋊(C43⋊C8)C2212yes—
20#14582652C2212yes—
21#14582652C2211yescharacteristic
22#14582652C2211yescharacteristic
23#14582652C2211yescharacteristic
24#14582652C2211yescharacteristic
25#14582652C2212yes—
26#14582652C2212yes—
27#14582650C2212yes—
28#14582650C2212yes—
29#14582650C2212yes—
30C4×#41×C43C2211yescharacteristic
31C43×#433C414yes—
32C43×#431C2212yes—
33C43×#431C2212yes—
34C43×#424C412yes—
35C43×#408C412yes—
36C4×M16×C43C2211yescharacteristic
37C2×C4×C8×C43C2211yescharacteristic
38C2×#10621877—22no—
39C2×#10621877—22no—
40C22×C43⋊C8—22no—
41C4⋊(C43⋊C8)—22no—
42C4⋊(C43⋊C8)—22no—
43C4⋊(C43⋊C8)—22no—
44C4⋊(C43⋊C8)C2312yes—
45C4⋊(C43⋊C8)C2312yes—
46C4⋊(C43⋊C8)C2312yes—
47C4⋊(C43⋊C8)C2312yes—
48C22⋊(C43⋊C8)—22no—
49C22⋊(C43⋊C8)—22no—
50C22⋊(C43⋊C8)—22no—
51#13063236—22no—
52#13063236—22no—
53C4×C43⋊C8—22no—
54C2×#41×C43C2×C411yescharacteristic
55C2×M16×C43C2×C412yes—
56C22×C8×C43C2×C412yes—
57C4×Q8×C43D411yescharacteristic
58C4×Q8×C43Q811yescharacteristic
59C4×D4×C43D411yescharacteristic
60C4×D4×C43D412yes—
61C4×D4×C43Q812yes—
62C4×D4×C43Q811yescharacteristic
63#117×C43C2×C411yescharacteristic
64#117×C43C2×C412yes—
65C2×C42×C43C2312yes—
66C2×C42×C43C2311yescharacteristic
67C4⋊C8×C43C2×C414yes—
68C4⋊C8×C43C2×C414yes—
69C22⋊C8×C43C2×C414yes—
70C22⋊C8×C43C2×C414yes—
71#97×C43C2×C412yes—
72C4×C8×C43C2×C412yes—
73C4×C8×C43C2311yescharacteristic
74C4×C8×C43C2312yes—
75C4×C8×C43C2311yescharacteristic
76#41×C43—42no—
77C2×Q8×C43C4⋊C411yescharacteristic
78C2×D4×C43C4⋊C411yescharacteristic
79C2×D4×C43C4⋊C412yes—
80C22×C4×C43C22×C412yes—
81C22×C4×C43C22×C411yescharacteristic
82C22×C4×C43C2×D412yes—
83C22×C4×C43C2×D411yescharacteristic
84C22×C4×C43C2×Q812yes—
85C22×C4×C43C2×Q811yescharacteristic
86M16×C43—42no—
87C2×C8×C43—42no—
88C2×C8×C43C22×C412yes—
89C2×C8×C43C22×C412yes—
90C2×C8×C43C22×C414yes—
91C4⋊C4×C43C4⋊C411yescharacteristic
92C4⋊C4×C43C4⋊C412yes—
93C4⋊C4×C43C4⋊C411yescharacteristic
94C4⋊C4×C43C4⋊C412yes—
95C22⋊C4×C43C4⋊C412yes—
96C22⋊C4×C43C4⋊C412yes—
97C22⋊C4×C43C4⋊C412yes—
98C42×C43C22×C411yescharacteristic
99C42×C43C22×C412yes—
100C42×C43C2×D412yes—
101C42×C43C2×D411yescharacteristic
102C42×C43C2×Q812yes—
103C42×C43C2×Q811yescharacteristic
104C42×C43C2411yescharacteristic
105#10621877—82no—
106#10621877—82no—
107C2×C43⋊C8—22no—
108C2×C43⋊C8—22no—
109C2×C43⋊C8—22no—
110C2×C43⋊C8—22no—
111C2×C43⋊C8—82no—
112C23×C43C2×C4⋊C412yes—
113C23×C43C2×C4⋊C411yescharacteristic
114Q8×C43—41no—
115D4×C43—41no—
116D4×C43—42no—
117C2×C4×C43—22no—
118C2×C4×C43—24no—
119C2×C4×C43—22no—
120C2×C4×C43—21no—
121C2×C4×C43—22no—
122C2×C4×C43—21no—
123C2×C4×C43—42no—
124C2×C4×C43—41no—
125C2×C4×C43C2×C4⋊C411yescharacteristic
126C2×C4×C43C2×C4⋊C412yes—
127C2×C4×C43C2×C4⋊C411yescharacteristic
128C2×C4×C43C2×C4⋊C412yes—
129C2×C4×C43C2×C4⋊C412yes—
130C2×C4×C43C2×C4⋊C411yescharacteristic
131C2×C4×C43C23×C411yescharacteristic
132C2×C4×C43C22×D411yescharacteristic
133C2×C4×C43C22×Q811yescharacteristic
134C8×C43—22no—
135C8×C43—22no—
136C8×C43—24no—
137C43⋊C8—42no—
138C43⋊C8—42no—
139C43⋊C8—42no—
140C43⋊C8—42no—
141#17825—431nomaximal, Sylow
142C22×C43—21no—
143C22×C43—22no—
144C22×C43—22no—
145C22×C43—21no—
146C22×C43—22no—
147C22×C43—21no—
148C22×C43C22×C4⋊C411yescharacteristic
149C4×C43—21no—
150C4×C43—22no—
151C4×C43—22no—
152C4×C43—21no—
153C4×C43—21no—
154C4×C43—21no—
155C4×C43—22no—
156C4×C43#56812yes—
157C4×C43#57611yescharacteristic
158C4×C43#57811yescharacteristic
159#2989—432no—
160#2922D4311yescharacteristic
161#1574—432no—
162#1573—432no—
163#1572—432no—
164#1571—432no—
165#1569—432no—
166#1568—431no—
167#1567—431no—
168C2×C43—41no—
169C2×C43—42no—
170C2×C43#290511yescharacteristic
171C2×C43#291311yescharacteristic
172C2×C43#291611yescharacteristic
173C4×#41C2×D4311yescharacteristic
174#446—862no—
175#436—862no—
176#435—862no—
177#435—862no—
178#433Dic4314yes—
179#432—432no—
180#432—432no—
181#431—432no—
182#431C2×D4312yes—
183#431C2×D4312yes—
184#424Dic4312yes—
185#423—432no—
186#423—432no—
187C2×C4⋊C8—432no—
188#408Dic4312yes—
189C4×M16C2×D4311yescharacteristic
190C2×C4×C8C2×D4311yescharacteristic
191#335—432no—
192#335—431no—
193#335—431no—
194#335—431no—
195#335—431no—
196#335—432no—
197#335—432no—
198#334—432no—
199#334—432no—
200#334—432no—
201C43#1782511yescharacteristic, complemented, Sylow
202C2×#41C2×Dic4311yescharacteristic
203C2×M16—862no—
204C2×M16—862no—
205C2×M16C2×Dic4312yes—
206C22×C8—862no—
207C22×C8C2×Dic4312yes—
208C4×Q8Dic8611yescharacteristic
209C4×Q8D17211yescharacteristic
210C4×D4Dic8611yescharacteristic
211C4×D4Dic8612yes—
212C4×D4D17211yescharacteristic
213C4×D4D17212yes—
214#117C2×Dic4311yescharacteristic
215#117C2×Dic4312yes—
216C2×C42C22×D4311yescharacteristic
217C2×C42C22×D4312yes—
218C4⋊C8—432no—
219C4⋊C8—432no—
220C4⋊C8—432no—
221C4⋊C8—432no—
222C4⋊C8—862no—
223C4⋊C8—862no—
224C4⋊C8—862no—
225C4⋊C8C2×Dic4314yes—
226C4⋊C8C2×Dic4314yes—
227C22⋊C8—862no—
228C22⋊C8—862no—
229C22⋊C8—862no—
230C22⋊C8C2×Dic4314yes—
231C22⋊C8C2×Dic4314yes—
232#97—862no—
233#97—862no—
234#97C2×Dic4312yes—
235C4×C8—862no—
236C4×C8C2×Dic4312yes—
237C4×C8C22×D4311yescharacteristic
238C4×C8C22×D4312yes—
239C4×C8C22×D4311yescharacteristic
240#41—42no—
241C2×Q8C4⋊Dic4311yescharacteristic
242C2×D4C4⋊Dic4311yescharacteristic
243C2×D4C4⋊Dic4312yes—
244C22×C4C2×Dic8611yescharacteristic
245C22×C4C2×Dic8612yes—
246C22×C4C2×D17212yes—
247C22×C4C2×D17211yescharacteristic
248C22×C4C22×Dic4312yes—
249C22×C4C22×Dic4311yescharacteristic
250M16—42no—
251M16—3442no—
252M16—3442no—
253C2×C8—42no—
254C2×C8—862no—
255C2×C8—862no—
256C2×C8—862no—
257C2×C8—862no—
258C2×C8—3442no—
259C2×C8C22×Dic4312yes—
260C2×C8C22×Dic4312yes—
261C2×C8C22×Dic4314yes—
262C4⋊C4C4⋊Dic4311yescharacteristic
263C4⋊C4C4⋊Dic4312yes—
264C4⋊C4C4⋊Dic4311yescharacteristic
265C4⋊C4C4⋊Dic4312yes—
266C22⋊C4C4⋊Dic4312yes—
267C22⋊C4C4⋊Dic4312yes—
268C22⋊C4C4⋊Dic4312yes—
269C42C2×Dic8611yescharacteristic
270C42C2×Dic8612yes—
271C42C2×D17212yes—
272C42C2×D17211yescharacteristic
273C42C22×Dic4311yescharacteristic
274C42C22×Dic4312yes—
275C42C23×D4311yescharacteristic
276C23C2×C4⋊Dic4312yes—
277C23C2×C4⋊Dic4311yescharacteristic
278Q8—41no—
279D4—41no—
280D4—42no—
281C2×C4—22no—
282C2×C4—24no—
283C2×C4—22no—
284C2×C4—21no—
285C2×C4—22no—
286C2×C4—21no—
287C2×C4—41no—
288C2×C4—42no—
289C2×C4C2×C4⋊Dic4312yes—
290C2×C4C2×C4⋊Dic4311yescharacteristic
291C2×C4C2×C4⋊Dic4311yescharacteristic
292C2×C4C2×C4⋊Dic4312yes—
293C2×C4C2×C4⋊Dic4312yes—
294C2×C4C2×C4⋊Dic4311yescharacteristic
295C2×C4C23×Dic4311yescharacteristic
296C2×C4C22×D17211yescharacteristic
297C2×C4C22×Dic8611yescharacteristic
298C8—22no—
299C8—22no—
300C8—24no—
301C8—1722no—
302C8—1722no—
303C8—1722no—
304C8—1722no—
305C22—22no—
306C22—21no—
307C22—22no—
308C22—21no—
309C22—21no—
310C22—22no—
311C22C22×C4⋊Dic4311yescharacteristic
312C4—22no—
313C4—21no—
314C4—21no—
315C4—22no—
316C4—21no—
317C4—21no—
318C4—22no—
319C4#1458366612yes—
320C4#1458370411yescharacteristic
321C4#1458371611yescharacteristic
322C2—42no—
323C2—41no—
324C2#1914315911yescharacteristic
325C2#1914319511yescharacteristic
326C2#1914320611yescharacteristic
subgroupG/H
centerC2×C4C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#2922C2
socleC22×C43C22×C4⋊C4
prime radicalC2×#41×C43C2×C4
cosocleC42×C43C24
hypercenter#2922D43
hypocenterC43#17825
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #2922

Complements

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

NH ≅ G/Ntype
2. #19133384C2semidirect
3. #19133380C2semidirect
4. #19133375C2semidirect
5. #19133370C2semidirect
6. #19133362C2semidirect
7. #19133358C2semidirect
8. #19133354C2semidirect
201. C43#17825semidirect

Maximal subgroups

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

subgroupindex
#191437122
#191333842
#191333802
#191333752
#191333702
#191333622
#191333582
#191333542
C43×#29222
#1782543