Finite Group Databasebeta

← #25100124

Subgroups — #25100124

Order 11008.

906 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582948C212yesmaximal
2C2×#14582923C211yesmaximal, characteristic
3C2×C4×#10621877C211yesmaximal, characteristic
4#19135371C218yesmaximal, complemented
5#19134322C212yesmaximal
6C2×C43×#423C211yesmaximal, characteristic
7C22×#10621877C2212yes—
8C22×#10621877C2211yescharacteristic
9C22×#10621877C2211yescharacteristic
10#14582948—28no—
11C2×#13063261C2218yes—
12#14582923—21no—
13#14582923—21no—
14#14582923C2214yes—
15C2×C4⋊(C43⋊C8)—22no—
16C4×#10621877—22no—
17C4×#10621877C2214yes—
18C2×#13063236—21no—
19C2×C4×C43⋊C8—21no—
20#14582664C2218yes—
21C22×M16×C43C2212yes—
22C22×C42×C43C2211yescharacteristic
23C43×#423C412yes—
24C43×#423C414yes—
25C43×#423C412yes—
26C2×C4⋊C8×C43C2214yes—
27C2×#10621877—21no—
28C2×#10621877—21no—
29C2×#10621877—22no—
30C2×#10621877—22no—
31C2×#10621877—22no—
32C2×#10621877—24no—
33C2×#10621877—24no—
34C2×#10621877D414yes—
35C2×#10621877Q814yes—
36C2×#10621877C2314yes—
37C2×#10621877C2312yes—
38C2×#10621877C2312yes—
39C22×C43⋊C8—21no—
40C22×C43⋊C8—21no—
41C22×C43⋊C8—22no—
42#13063261—216no—
43C4⋊(C43⋊C8)—24no—
44C4⋊(C43⋊C8)—24no—
45#13063236—24no—
46C4×C43⋊C8—24no—
47C23×C4×C43Q812yes—
48C23×C4×C43C2311yescharacteristic
49C2×M16×C43—24no—
50C2×M16×C43—24no—
51C2×M16×C43C2×C414yes—
52C2×M16×C43C2×C414yes—
53C22×C8×C43C2314yes—
54C2×C42×C43C2×C411yescharacteristic
55C2×C42×C43C2×C412yes—
56C2×C42×C43C2×C411yescharacteristic
57C2×C42×C43D411yescharacteristic
58C2×C42×C43D411yescharacteristic
59C2×C42×C43D412yes—
60C2×C42×C43Q811yescharacteristic
61C2×C42×C43Q811yescharacteristic
62C2×C42×C43C2312yes—
63C4⋊C8×C43C2×C418yes—
64C4⋊C8×C43C2×C418yes—
65C24×C43C2×Q811yescharacteristic
66C22×C4×C43—44no—
67C22×C4×C43C4⋊C412yes—
68C22×C4×C43C4⋊C412yes—
69C22×C4×C43C4⋊C412yes—
70C22×C4×C43C4⋊C412yes—
71C22×C4×C43C22×C411yescharacteristic
72C22×C4×C43C22×C411yescharacteristic
73C22×C4×C43C2×D411yescharacteristic
74C22×C4×C43C2×D411yescharacteristic
75C22×C4×C43C2×D412yes—
76C22×C4×C43C2×Q812yes—
77C22×C4×C43C2×Q812yes—
78C22×C4×C43C2×Q812yes—
79C22×C4×C43C2×Q811yescharacteristic
80C22×C4×C43#4112yes—
81C22×C4×C43#4112yes—
82C22×C4×C43C2411yescharacteristic
83M16×C43—28no—
84M16×C43—28no—
85C2×C8×C43—24no—
86C2×C8×C43—24no—
87C2×C8×C43C22×C418yes—
88C42×C43C4⋊C411yescharacteristic
89C42×C43C4⋊C411yescharacteristic
90C42×C43C4⋊C411yescharacteristic
91C42×C43C4⋊C412yes—
92C42×C43C4⋊C412yes—
93C42×C43C4⋊C411yescharacteristic
94C42×C43C22×C412yes—
95C42×C43C22×C412yes—
96C42×C43C2×D412yes—
97C42×C43C2×D412yes—
98#10621877—24no—
99#10621877—24no—
100#10621877—22no—
101#10621877—22no—
102#10621877—24no—
103#10621877—24no—
104#10621877—44no—
105#10621877C2×D414yes—
106#10621877C2×Q814yes—
107C2×C43⋊C8—24no—
108C2×C43⋊C8—24no—
109C2×C43⋊C8—22no—
110C2×C43⋊C8—22no—
111C2×C43⋊C8—24no—
112C2×C43⋊C8—44no—
113C23×C43—42no—
114C23×C43C2×C4⋊C411yescharacteristic
115C23×C43C2×C4⋊C411yescharacteristic
116C23×C43#12512yes—
117C23×C43C4⋊Q812yes—
118C23×C43C22×Q811yescharacteristic
119C2×C4×C43—24no—
120C2×C4×C43—24no—
121C2×C4×C43—24no—
122C2×C4×C43—42no—
123C2×C4×C43—42no—
124C2×C4×C43—42no—
125C2×C4×C43C2×C4⋊C412yes—
126C2×C4×C43C2×C4⋊C412yes—
127C2×C4×C43C2×C4⋊C412yes—
128C2×C4×C43C2×C4⋊C411yescharacteristic
129C2×C4×C43C2×C4⋊C411yescharacteristic
130C2×C4×C43C2×C4⋊C412yes—
131C2×C4×C43C4×D412yes—
132C2×C4×C43C4×D412yes—
133C2×C4×C43C4×Q812yes—
134C2×C4×C43C4×Q812yes—
135C2×C4×C43#12112yes—
136C2×C4×C43#12112yes—
137C2×C4×C43C22⋊Q812yes—
138C2×C4×C43C22⋊Q812yes—
139C2×C4×C43#12512yes—
140C2×C4×C43C4⋊Q812yes—
141C2×C4×C43C23×C411yescharacteristic
142C2×C4×C43C22×D411yescharacteristic
143C2×C4×C43C22×D411yescharacteristic
144C2×C4×C43C22×Q811yescharacteristic
145C2×C4×C43C2×#4111yescharacteristic
146C2×C4×C43C2×#4111yescharacteristic
147C8×C43—28no—
148C43⋊C8—24no—
149C43⋊C8—24no—
150C43⋊C8—44no—
151#21177—431nomaximal, Sylow
152C22×C43—22no—
153C22×C43—22no—
154C22×C43—22no—
155C22×C43—42no—
156C22×C43—42no—
157C22×C43#38912yes—
158C22×C43#38912yes—
159C22×C43C22×C4⋊C411yescharacteristic
160C22×C43C2×#12511yescharacteristic
161C22×C43C2×C4⋊Q811yescharacteristic
162C4×C43—22no—
163C4×C43—22no—
164C4×C43—22no—
165C4×C43#38912yes—
166C4×C43#38912yes—
167C4×C43#43014yescomplemented
168C4×C43C2×C4×D411yescharacteristic
169C4×C43C2×C4×Q811yescharacteristic
170C4×C43C2×#12111yescharacteristic
171C4×C43C2×C22⋊Q811yescharacteristic
172C2×#430—432no—
173C2×#423—431no—
174C2×#423D4311yescharacteristic
175C2×C4×M16—431no—
176#1950—438no—
177#1738—432no—
178C2×C43—21no—
179C2×C43—21no—
180C2×C43—22no—
181C2×C43—22no—
182C2×C43C2×#38911yescharacteristic
183C2×C43C2×#43012yes—
184C22×M16—431no—
185C22×M16—431no—
186C22×M16—432no—
187C22×M16C2×D4312yes—
188C22×C42C2×D4311yescharacteristic
189#430—868no—
190C2×#108—438no—
191#423—434no—
192#423—861no—
193#423—861no—
194#423Dic4312yes—
195#423Dic4314yes—
196#423Dic4312yes—
197C2×C4⋊C8—862no—
198C2×C4⋊C8C2×D4314yes—
199C4×M16—434no—
200C4×M16—862no—
201C2×#97—861no—
202C2×C4×C8—861no—
203#341—438no—
204C43#2117711yescharacteristic, complemented, Sylow
205C23×C4Dic8612yes—
206C23×C4C22×D4311yescharacteristic
207C2×M16—24no—
208C2×M16—24no—
209C2×M16—434no—
210C2×M16—434no—
211C2×M16—432no—
212C2×M16—432no—
213C2×M16—434no—
214C2×M16—861no—
215C2×M16—861no—
216C2×M16—862no—
217C2×M16—862no—
218C2×M16—862no—
219C2×M16—864no—
220C2×M16—864no—
221C2×M16C2×Dic4314yes—
222C2×M16C2×Dic4314yes—
223C22×C8—861no—
224C22×C8—861no—
225C22×C8—862no—
226C22×C8C22×D4314yes—
227C2×C42Dic8611yescharacteristic
228C2×C42Dic8611yescharacteristic
229C2×C42D17211yescharacteristic
230C2×C42D17211yescharacteristic
231C2×C42D17212yes—
232C2×C42C2×Dic4311yescharacteristic
233C2×C42C2×Dic4312yes—
234C2×C42C2×Dic4311yescharacteristic
235C2×C42C22×D4312yes—
236#108—8616no—
237C4⋊C8—864no—
238C4⋊C8—864no—
239C4⋊C8C2×Dic4318yes—
240C4⋊C8C2×Dic4318yes—
241#97—864no—
242C4×C8—864no—
243C24C2×Dic8611yescharacteristic
244C22×C4—44no—
245C22×C4C4⋊Dic4312yes—
246C22×C4C4⋊Dic4312yes—
247C22×C4C4⋊Dic4312yes—
248C22×C4C4⋊Dic4312yes—
249C22×C4C2×Dic8612yes—
250C22×C4C2×Dic8612yes—
251C22×C4C2×Dic8611yescharacteristic
252C22×C4C2×D17211yescharacteristic
253C22×C4C2×D17211yescharacteristic
254C22×C4D4×D4312yes—
255C22×C4#1062190012yes—
256C22×C4Q8×D4312yes—
257C22×C4#1062190212yes—
258C22×C4C22×Dic4311yescharacteristic
259C22×C4C22×Dic4311yescharacteristic
260C22×C4C23×D4311yescharacteristic
261M16—28no—
262M16—28no—
263M16—434no—
264M16—434no—
265M16—864no—
266M16—864no—
267M16—862no—
268M16—862no—
269M16—864no—
270M16—864no—
271M16—1724no—
272C2×C8—24no—
273C2×C8—24no—
274C2×C8—864no—
275C2×C8—864no—
276C2×C8—862no—
277C2×C8—862no—
278C2×C8—864no—
279C2×C8—1724no—
280C2×C8C22×Dic4318yes—
281C42C4⋊Dic4311yescharacteristic
282C42C4⋊Dic4311yescharacteristic
283C42C4⋊Dic4311yescharacteristic
284C42C4⋊Dic4312yes—
285C42C4⋊Dic4312yes—
286C42C4⋊Dic4311yescharacteristic
287C42C2×D17212yes—
288C42C2×D17212yes—
289C42C22×Dic4312yes—
290C42C22×Dic4312yes—
291C23—42no—
292C23C2×C4⋊Dic4311yescharacteristic
293C23C2×C4⋊Dic4311yescharacteristic
294C23#1306331612yes—
295C23#1306332412yes—
296C23C22×Dic8611yescharacteristic
297C2×C4—24no—
298C2×C4—24no—
299C2×C4—24no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4C2×C4⋊Dic4312yes—
304C2×C4C2×C4⋊Dic4312yes—
305C2×C4C2×C4⋊Dic4312yes—
306C2×C4C2×C4⋊Dic4311yescharacteristic
307C2×C4C2×C4⋊Dic4311yescharacteristic
308C2×C4C2×C4⋊Dic4312yes—
309C2×C4D4×Dic4312yes—
310C2×C4D4×Dic4312yes—
311C2×C4Q8×Dic4312yes—
312C2×C4Q8×Dic4312yes—
313C2×C4#1306330012yes—
314C2×C4#1306330012yes—
315C2×C4#1306330512yes—
316C2×C4#1306330512yes—
317C2×C4#1306331612yes—
318C2×C4#1306332412yes—
319C2×C4C23×Dic4311yescharacteristic
320C2×C4C2×D4×D4311yescharacteristic
321C2×C4C22×D17211yescharacteristic
322C2×C4C2×Q8×D4311yescharacteristic
323C2×C4C2×#1062190011yescharacteristic
324C2×C4C2×#1062190211yescharacteristic
325C8—28no—
326C8—864no—
327C8—864no—
328C8—1724no—
329C22—22no—
330C22—22no—
331C22—22no—
332C22—42no—
333C22—42no—
334C22#1458279812yes—
335C22#1458279812yes—
336C22C22×C4⋊Dic4311yescharacteristic
337C22C2×#1306331611yescharacteristic
338C22C2×#1306332411yescharacteristic
339C4—22no—
340C4—22no—
341C4—22no—
342C4#1458279812yes—
343C4#1458279812yes—
344C4#1458294814yescomplemented
345C4C2×D4×Dic4311yescharacteristic
346C4C2×Q8×Dic4311yescharacteristic
347C4C2×#1306330011yescharacteristic
348C4C2×#1306330511yescharacteristic
349C2—22no—
350C2—22no—
351C2—21no—
352C2—21no—
353C2C2×#1458279811yescharacteristic
354C2C2×#1458294812yes—
subgroupG/H
centerC2×C4C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#423C2
socleC22×C43C22×C4⋊C4
prime radicalC24×C43C2×Q8
cosocleC22×C4×C43C24
hypercenterC2×#423D43
hypocenterC43#21177
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ C2×#423

Complements

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

NH ≅ G/Ntype
4. #19135371C2semidirect
167. C4×C43#430semidirect
204. C43#21177semidirect
344. C4#14582948semidirect

Maximal subgroups

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

subgroupindex
C2×#145829482
C2×#145829232
C2×C4×#106218772
#191353712
#191343222
C2×C43×#4232
#2117743