Finite Group Databasebeta

← #25065905

Subgroups — #25065905

Order 11008.

612 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143724C212yesmaximal
2C8×#10621898C211yesmaximal, characteristic
3#19133383C212yesmaximal, complemented
4#19133382C214yesmaximal, complemented
5#19133354C211yesmaximal, characteristic, complemented
6#19133352C212yesmaximal, complemented
7#19133342C212yesmaximal, complemented
8C43×#1564C211yesmaximal, characteristic, complemented
9C4×#10621898C2211yescharacteristic
10C8×Dic86—22no—
11C8×Dic86C411yescharacteristic
12C8×Dic86C411yescharacteristic
13#14582978—22no—
14#14582974—24no—
15C8×D172C411yescharacteristic
16C8×D172C411yescharacteristic
17C8×C22⋊D43C412yes—
18C8×C22⋊D43C412yes—
19#14582952C2211yescharacteristic
20#14582951C2214yes—
21#14582950C2212yes—
22#14582923C2212yes—
23#14582921C2214yes—
24C4×C8×D43C2212yes—
25#14582652C2212yes—
26#14582652C2212yes—
27#14582651C2214yes—
28#14582649C2214yes—
29C43×#431C2212yes—
30C2×C4×C8×C43C2211yescharacteristic
31C43×#335C2211yescharacteristic
32C43×#335C2211yescharacteristic
33C43×#334C2212yes—
34C2×#10621898Q811yescharacteristic
35C2×#10621877—22no—
36C2×#10621872—24no—
37C2×C8×D43C2×C412yes—
38C2×C8×D43C2×C412yes—
39C4×Dic86C2×C411yescharacteristic
40C4×Dic86D411yescharacteristic
41C4×D172C2×C411yescharacteristic
42C4×D172D411yescharacteristic
43C4×C22⋊D43C2×C412yes—
44C4×C22⋊D43D412yes—
45#13063284Q811yescharacteristic
46#13063282Q812yes—
47C42×D43C2312yes—
48C4⋊(C43⋊C8)—22no—
49C4⋊(C43⋊C8)C2×C411yescharacteristic
50C4⋊(C43⋊C8)C2×C411yescharacteristic
51C4⋊(C43⋊C8)C2314yes—
52Dic43⋊C8—24no—
53Dic43⋊C8C2×C412yes—
54Dic43⋊C8C2×C412yes—
55C22⋊(C43⋊C8)C2×C412yes—
56(C2×D43)⋊C8—24no—
57(C2×D43)⋊C8C2×C412yes—
58(C2×D43)⋊C8C2×C412yes—
59C4×C43⋊C8C2312yes—
60C8×Dic43—24no—
61C8×Dic43C2×C412yes—
62C8×Dic43C2×C412yes—
63C22×C8×C43C2×C411yescharacteristic
64C22×C8×C43C2×C411yescharacteristic
65C2×C42×C43C2311yescharacteristic
66C4⋊C8×C43C2312yes—
67C4⋊C8×C43C2312yes—
68C22⋊C8×C43—22no—
69C4×C8×C43—22no—
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
84C2×C8×C43—22no—
85C2×C8×C43—22no—
86C2×C8×C43—22no—
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—
106#10621877—82no—
107C2×C43⋊C8—24no—
108C2×C43⋊C8C22×C412yes—
109C2×C43⋊C8C22×C412yes—
110#10621872—84no—
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—21no—
118C2×C4×C43—21no—
119C2×C4×C43—22no—
120C2×C4×C43C2×C4⋊C411yescharacteristic
121C2×C4×C43C2×C4⋊C411yescharacteristic
122C2×C4×C43C2×C4⋊C411yescharacteristic
123C2×C4×C43C23×C411yescharacteristic
124C2×C4×C43C22×D411yescharacteristic
125C2×C4×C43C22×Q811yescharacteristic
126C22⋊D43—24no—
127C2×Dic43C2×C4⋊C412yes—
128C2×Dic43C2×C4⋊C412yes—
129C2×Dic43C2×C4⋊C412yes—
130D172—22no—
131C4×D43—22no—
132C4×D43—22no—
133C4×D43—22no—
134C4×D43—22no—
135C4×D43—24no—
136Dic86#10814yes—
137C8×C43—21no—
138C8×C43—21no—
139C8×C43—21no—
140C8×C43—42no—
141C8×C43—42no—
142C8×C43#13112yes—
143C43⋊C8—22no—
144C43⋊C8—22no—
145C43⋊C8—44no—
146#17837—431nomaximal, Sylow
147C22×C43—21no—
148C22×C43—21no—
149C22×C43—21no—
150C22×C43C22×C4⋊C411yescharacteristic
151C2×D43—22no—
152C2×D43—22no—
153C2×D43—22no—
154C4×C43—21no—
155C4×C43—21no—
156C4×C43—21no—
157C4×C43C2×#10812yes—
158C4×C43C2×#13111yescharacteristic
159C4×C43#56811yescharacteristic
160C4×C43#57611yescharacteristic
161C4×C43#57811yescharacteristic
162Dic43—22no—
163Dic43—22no—
164Dic43C2×#10814yes—
165#2991—432no—
166C8×#41—431no—
167#1574—432no—
168#1574—434no—
169#1567—431no—
170#1567—432no—
171#1564—432no—
172#1564D4311yescharacteristic, complemented
173C2×C43—41no—
174C2×C43#290611yescharacteristic
175C2×C43#291311yescharacteristic
176C2×C43C22×#10811yescharacteristic
177D43—42no—
178C4×#41—431no—
179C8×Q8—431no—
180C8×Q8—431no—
181C8×Q8—862no—
182#436—862no—
183#436—864no—
184C8×D4—432no—
185C8×D4—432no—
186C8×D4—431no—
187C8×D4—431no—
188#431—431no—
189#431—432no—
190#431—434no—
191#431C2×D4312yes—
192#423—432no—
193#423—434no—
194C2×C4×C8—432no—
195C2×C4×C8C2×D4311yescharacteristic
196#335—434no—
197#335—432no—
198#335—432no—
199#335C2×D4311yescharacteristic
200#335C2×D4311yescharacteristic
201#334—434no—
202#334C2×D4312yes—
203C43#1783711yescharacteristic, complemented, Sylow
204C2×#41—431no—
205C2×M16—864no—
206C2×M16—862no—
207C22×C8—432no—
208C22×C8—432no—
209C22×C8C4×D4311yescharacteristic
210C22×C8C4×D4311yescharacteristic
211C4×Q8—431no—
212C4×Q8—431no—
213C4×D4—432no—
214C4×D4—432no—
215C4×D4—431no—
216C4×D4—431no—
217#117—431no—
218#117—432no—
219C2×C42—432no—
220C2×C42C22×D4311yescharacteristic
221C4⋊C8—432no—
222C4⋊C8—432no—
223C4⋊C8—431no—
224C4⋊C8—431no—
225C4⋊C8—434no—
226C4⋊C8—864no—
227C4⋊C8—862no—
228C4⋊C8C22×D4312yes—
229C4⋊C8C22×D4312yes—
230C22⋊C8—22no—
231C22⋊C8—432no—
232C22⋊C8—432no—
233C22⋊C8—432no—
234C22⋊C8—864no—
235C4×C8—22no—
236C4×C8—432no—
237C4×C8—432no—
238C4×C8—432no—
239C4×C8—864no—
240C4×C8C4×D4311yescharacteristic
241C4×C8C4×D4311yescharacteristic
242C4×C8C22×D4311yescharacteristic
243C4×C8C22×D4311yescharacteristic
244#41—864no—
245C2×Q8—431no—
246C2×D4—432no—
247C2×D4—431no—
248C22×C4—432no—
249C22×C4—432no—
250C22×C4—432no—
251C22×C4C2×C4×D4311yescharacteristic
252C22×C4D4×D4311yescharacteristic
253C22×C4Q8×D4311yescharacteristic
254M16—3444no—
255M16—3442no—
256C2×C8—22no—
257C2×C8—22no—
258C2×C8—22no—
259C2×C8—41no—
260C2×C8—432no—
261C2×C8—432no—
262C2×C8—864no—
263C2×C8—864no—
264C2×C8—1722no—
265C2×C8C2×C4×D4311yescharacteristic
266C2×C8C2×C4×D4311yescharacteristic
267C2×C8C2×C4×D4311yescharacteristic
268C2×C8C2×C4×D4311yescharacteristic
269C4⋊C4—432no—
270C4⋊C4—432no—
271C4⋊C4—431no—
272C4⋊C4—431no—
273C22⋊C4—432no—
274C22⋊C4—432no—
275C22⋊C4—432no—
276C42—432no—
277C42—432no—
278C42—432no—
279C42C2×C4×D4311yescharacteristic
280C42D4×D4311yescharacteristic
281C42Q8×D4311yescharacteristic
282C42C23×D4311yescharacteristic
283C23—432no—
284C23C4⋊C4×D4311yescharacteristic
285Q8—434no—
286D4—864no—
287D4—862no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—22no—
292C2×C4—21no—
293C2×C4—432no—
294C2×C4—432no—
295C2×C4—432no—
296C2×C4—864no—
297C2×C4—862no—
298C2×C4—862no—
299C2×C4—862no—
300C2×C4—862no—
301C2×C4C4⋊C4×D4311yescharacteristic
302C2×C4C4⋊C4×D4311yescharacteristic
303C2×C4C4⋊C4×D4311yescharacteristic
304C2×C4C22×C4×D4311yescharacteristic
305C2×C4C2×D4×D4311yescharacteristic
306C2×C4C2×Q8×D4311yescharacteristic
307C8—21no—
308C8—21no—
309C8—21no—
310C8—42no—
311C8—42no—
312C8—862no—
313C8—862no—
314C8—1724no—
315C8#1306333112yes—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—862no—
320C22—862no—
321C22—862no—
322C22C2×C4⋊C4×D4311yescharacteristic
323C4—21no—
324C4—21no—
325C4—21no—
326C4—434no—
327C4—862no—
328C4—862no—
329C4#108×D4312yes—
330C4C2×#1306333111yescharacteristic
331C4#1458366511yescharacteristic
332C4#1458370111yescharacteristic
333C4#1458371311yescharacteristic
334C2—41no—
335C2—1722no—
336C2#1914316011yescharacteristic
337C2#1914319211yescharacteristic
338C2C2×#108×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1564C2
socleC22×C43C22×C4⋊C4
prime radicalC2×#10621898Q8
cosocleC42×C43C24
hypercenter#1564D43
hypocenterC43#17837
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1564

Complements

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

NH ≅ G/Ntype
3. #19133383C2semidirect
4. #19133382C2semidirect
5. #19133354C2semidirect
6. #19133352C2semidirect
7. #19133342C2semidirect
8. C43×#1564C2semidirect
172. #1564D43semidirect
203. C43#17837semidirect

Maximal subgroups

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

subgroupindex
#191437242
C8×#106218982
#191333832
#191333822
#191333542
#191333522
#191333422
C43×#15642
#1783743