Finite Group Databasebeta

← #25006908

Subgroups — #25006908

Order 11008.

452 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582668C211yesmaximal, characteristic
2C2×#14582625C211yesmaximal, characteristic
3#19132625C212yesmaximal, complemented
4#19132622C212yesmaximal, complemented
5C43×#2627C211yesmaximal, characteristic
6C22×#10621877—21no—
7C2×C22⋊(C43⋊C8)—21no—
8#14582668—21no—
9#14582668C2212yes—
10#14582625—21no—
11#14582625C2212yes—
12C2×C22⋊Q8×C43C411yescharacteristic
13C22×C4⋊C4×C43C2211yescharacteristic
14C43×#400C411yescharacteristic
15C43×#400C2211yescharacteristic
16C43×#398—21no—
17C43×#398—21no—
18C43×#395C411yescharacteristic
19C43×#395C2211yescharacteristic
20C43×#385—21no—
21C43×#381—21no—
22C43×#380C411yescharacteristic
23C2×#10621877—24no—
24C2×#10621877—22no—
25C2×#10621877—41no—
26C2×#10621877—42no—
27C22×C43⋊C8—41no—
28C22×C43⋊C8—41no—
29C22⋊(C43⋊C8)—22no—
30C22⋊(C43⋊C8)—41no—
31C22×Q8×C43C2×C411yescharacteristic
32C23×C4×C43C2×C411yescharacteristic
33C23×C4×C43D411yescharacteristic
34C23×C4×C43D411yescharacteristic
35C22⋊Q8×C43—41no—
36C22⋊Q8×C43—41no—
37C2×C4⋊C4×C43—21no—
38C2×C4⋊C4×C43—21no—
39C2×C4⋊C4×C43—21no—
40C2×C4⋊C4×C43—21no—
41C2×C4⋊C4×C43—41no—
42C2×C4⋊C4×C43—41no—
43C2×C4⋊C4×C43C2×C411yescharacteristic
44C2×C4⋊C4×C43C2×C411yescharacteristic
45C2×C4⋊C4×C43D411yescharacteristic
46C2×C4⋊C4×C43D411yescharacteristic
47C2×C4⋊C4×C43C2311yescharacteristic
48C2×C22⋊C4×C43—21no—
49C2×C22⋊C4×C43—21no—
50#95×C43—21no—
51#95×C43—21no—
52#95×C43—21no—
53#95×C43—21no—
54#95×C43—21no—
55#95×C43—21no—
56#95×C43C2×C411yescharacteristic
57#95×C43C2×C411yescharacteristic
58C24×C43C22⋊C411yescharacteristic
59C2×Q8×C43—41no—
60C2×Q8×C43—81no—
61C22×C4×C43—21no—
62C22×C4×C43—21no—
63C22×C4×C43—21no—
64C22×C4×C43—21no—
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43—22no—
68C22×C4×C43—21no—
69C22×C4×C43—21no—
70C22×C4×C43—21no—
71C22×C4×C43—21no—
72C22×C4×C43—81no—
73C22×C4×C43—81no—
74C22×C4×C43C22⋊C411yescharacteristic
75C22×C4×C43C22⋊C411yescharacteristic
76C22×C4×C43C22⋊C411yescharacteristic
77C22×C4×C43SD1612yes—
78C22×C4×C43Q1612yes—
79C22×C4×C43C22×C411yescharacteristic
80C22×C4×C43C2×D411yescharacteristic
81C22×C4×C43C2×D411yescharacteristic
82C4⋊C4×C43—41no—
83C4⋊C4×C43—41no—
84C4⋊C4×C43—41no—
85C4⋊C4×C43—41no—
86C4⋊C4×C43—41no—
87C4⋊C4×C43—42no—
88C4⋊C4×C43—81no—
89C4⋊C4×C43—81no—
90C4⋊C4×C43—81no—
91C22⋊C4×C43—41no—
92C22⋊C4×C43—41no—
93C22⋊C4×C43—42no—
94#10621877—24no—
95#10621877—44no—
96#10621877—42no—
97C2×C43⋊C8—44no—
98C2×C43⋊C8—42no—
99C2×C43⋊C8—42no—
100C2×C43⋊C8—82no—
101C23×C43—41no—
102C23×C43—41no—
103C23×C43#9911yescharacteristic
104C23×C43#9911yescharacteristic
105C23×C43#10312yes—
106C23×C43#10412yes—
107C23×C43C2×C22⋊C411yescharacteristic
108Q8×C43—82no—
109C2×C4×C43—22no—
110C2×C4×C43—22no—
111C2×C4×C43—22no—
112C2×C4×C43—22no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—42no—
122C2×C4×C43—41no—
123C2×C4×C43—41no—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43—42no—
133C2×C4×C43—41no—
134C2×C4×C43—41no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43—81no—
138C2×C4×C43—81no—
139C2×C4×C43—81no—
140C2×C4×C43#10312yes—
141C2×C4×C43C2×SD1611yescharacteristic
142C2×C4×C43C2×Q1611yescharacteristic
143C43⋊C8—44no—
144C43⋊C8—82no—
145#11722—431nomaximal, Sylow
146C22×C43—21no—
147C22×C43—21no—
148C22×C43—21no—
149C22×C43—21no—
150C22×C43—21no—
151C22×C43—21no—
152C22×C43—42no—
153C22×C43—42no—
154C22×C43#32812yes—
155C22×C43#32812yes—
156C22×C43C2×#9911yescharacteristic
157C22×C43C2×#10311yescharacteristic
158C22×C43C2×#10411yescharacteristic
159C4×C43—21no—
160C4×C43—22no—
161C4×C43—21no—
162C4×C43—41no—
163C4×C43—41no—
164C4×C43—41no—
165C4×C43—41no—
166C4×C43—81no—
167C4×C43—81no—
168C4×C43—81no—
169C4×C43—81no—
170#2627D4311yescharacteristic
171C2×#343—431no—
172C2×#324—431no—
173#1354—432no—
174#1353—432no—
175C2×C43—21no—
176C2×C43—22no—
177C2×C43—22no—
178C2×C43—21no—
179C2×C43C2×#32811yescharacteristic
180C2×C43#212111yescharacteristic
181C2×C43#213311yescharacteristic
182C22×M16—861no—
183C2×C22⋊Q8Dic4311yescharacteristic
184C22×C4⋊C4C2×D4311yescharacteristic
185C2×C22⋊C8—861no—
186#400Dic4311yescharacteristic
187#400C2×D4311yescharacteristic
188#398—21no—
189#398—21no—
190#395Dic4311yescharacteristic
191#395C2×D4311yescharacteristic
192#385—21no—
193#381—21no—
194#380Dic4311yescharacteristic
195#343—432no—
196#343—861no—
197#324—432no—
198#324—861no—
199C43#1172211yescharacteristic, complemented, Sylow
200C22×Q8C2×Dic4311yescharacteristic
201C23×C4C2×Dic4311yescharacteristic
202C23×C4C22⋊D4311yescharacteristic
203C23×C4C22⋊D4311yescharacteristic
204C2×M16—864no—
205C2×M16—862no—
206C2×M16—1721no—
207C2×M16—1722no—
208C22×C8—1721no—
209C22×C8—1721no—
210C22⋊Q8—41no—
211C22⋊Q8—41no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—41no—
217C2×C4⋊C4—41no—
218C2×C4⋊C4C2×Dic4311yescharacteristic
219C2×C4⋊C4C2×Dic4311yescharacteristic
220C2×C4⋊C4C22⋊D4311yescharacteristic
221C2×C4⋊C4C22⋊D4311yescharacteristic
222C2×C4⋊C4C22×D4311yescharacteristic
223C2×C22⋊C4—21no—
224C2×C22⋊C4—21no—
225C22⋊C8—862no—
226C22⋊C8—1721no—
227#95—21no—
228#95—21no—
229#95—21no—
230#95—21no—
231#95—21no—
232#95—21no—
233#95C2×Dic4311yescharacteristic
234#95C2×Dic4311yescharacteristic
235C24C22⋊Dic4311yescharacteristic
236C2×Q8—41no—
237C2×Q8—81no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—22no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—81no—
250C22×C4—81no—
251C22×C4#1062188412yes—
252C22×C4#1062188512yes—
253C22×C4C22⋊Dic4311yescharacteristic
254C22×C4C22⋊Dic4311yescharacteristic
255C22×C4C22⋊Dic4311yescharacteristic
256C22×C4C22×Dic4311yescharacteristic
257C22×C4C2×C22⋊D4311yescharacteristic
258C22×C4C2×C22⋊D4311yescharacteristic
259M16—864no—
260M16—1724no—
261M16—1722no—
262C2×C8—3442no—
263C2×C8—1722no—
264C2×C8—1722no—
265C2×C8—1724no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—42no—
272C4⋊C4—81no—
273C4⋊C4—81no—
274C4⋊C4—81no—
275C22⋊C4—41no—
276C22⋊C4—41no—
277C22⋊C4—42no—
278C23—41no—
279C23—41no—
280C23#1306324011yescharacteristic
281C23#1306324011yescharacteristic
282C23#1306324912yes—
283C23#1306325212yes—
284C23C2×C22⋊Dic4311yescharacteristic
285Q8—82no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—42no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—42no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4#1306324912yes—
318C2×C4C2×#1062188411yescharacteristic
319C2×C4C2×#1062188511yescharacteristic
320C8—3442no—
321C8—1724no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—42no—
329C22—42no—
330C22#1458263612yes—
331C22#1458263612yes—
332C22C2×#1306324011yescharacteristic
333C22C2×#1306324911yescharacteristic
334C22C2×#1306325211yescharacteristic
335C4—21no—
336C4—22no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—81no—
343C4—81no—
344C4—81no—
345C4—81no—
346C2—21no—
347C2—21no—
348C2—22no—
349C2—22no—
350C2C2×#1458263611yescharacteristic
351C2#1913624111yescharacteristic
352C2#1913628411yescharacteristic
subgroupG/H
centerC22C2×#13063240
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#2627C2
socleC22×C43C2×#99
prime radicalC24×C43C22⋊C4
cosocleC2×C4⋊C4×C43C23
hypercenter#2627D43
hypocenterC43#11722
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #2627

Complements

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

NH ≅ G/Ntype
3. #19132625C2semidirect
4. #19132622C2semidirect
199. C43#11722semidirect

Maximal subgroups

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

subgroupindex
C2×#145826682
C2×#145826252
#191326252
#191326222
C43×#26272
#1172243