Finite Group Databasebeta

← #25006967

Subgroups — #25006967

Order 11008.

434 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 87 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
1#19137878C211yesmaximal, characteristic
2C4×#13063244C211yesmaximal, characteristic, complemented
3#19132623C212yesmaximal, complemented
4#19132599C212yesmaximal
5C43×#1461C211yesmaximal, characteristic, complemented
6C2×C4×D172C411yescharacteristic
7C2×#13063244—21no—
8C4×#10621877—21no—
9#14582838C411yescharacteristic
10#14582838C2211yescharacteristic
11#14582825—21no—
12#14582816C411yescharacteristic
13#14582816C2211yescharacteristic
14#14582810—21no—
15C4×(C2×D43)⋊C4—21no—
16C4×(C2×D43)⋊C4—21no—
17#14582745C411yescharacteristic
18#14582668C2212yes—
19C2×C4×Q8×C43C2211yescharacteristic
20C43×#431—21no—
21C43×#324—21no—
22C43×#324C2212yes—
23C22×D172C2×C411yescharacteristic
24C22×C4×D43—21no—
25C2×#10621877—22no—
26C4×D172—41no—
27C4×D172—41no—
28C2×C4⋊Dic43C2×C411yescharacteristic
29C2×(C2×D43)⋊C4—21no—
30C2×(C2×D43)⋊C4—21no—
31C2×(C2×D43)⋊C4—21no—
32C2×(C2×D43)⋊C4—21no—
33C2×(C2×D43)⋊C4—21no—
34C2×C4×Dic43—21no—
35#13063244—24no—
36#13063236—41no—
37C4×C43⋊C8—41no—
38C43⋊#95—21no—
39C43⋊#95—21no—
40C43⋊#95—21no—
41C43⋊#95—21no—
42C43⋊#95—21no—
43C43⋊#95C2×C411yescharacteristic
44C43⋊#95C2×C411yescharacteristic
45C22×Q8×C43D411yescharacteristic
46C4×Q8×C43—41no—
47C4×Q8×C43—41no—
48C2×C4⋊C4×C43C2×C411yescharacteristic
49C2×C4⋊C4×C43D411yescharacteristic
50C2×C4⋊C4×C43C2311yescharacteristic
51C2×C42×C43C2×C411yescharacteristic
52C2×C42×C43D411yescharacteristic
53C2×C42×C43D411yescharacteristic
54C4⋊C8×C43—41no—
55C22⋊C8×C43—22no—
56C4×C8×C43—41no—
57C23×D43—21no—
58C2×Q8×C43—22no—
59C2×Q8×C43—22no—
60C2×Q8×C43—41no—
61C22×C4×C43C22⋊C411yescharacteristic
62C22×C4×C43C22⋊C411yescharacteristic
63C22×C4×C43C22⋊C411yescharacteristic
64C22×C4×C43C22⋊C411yescharacteristic
65C22×C4×C43C22×C411yescharacteristic
66C22×C4×C43C2×D411yescharacteristic
67C22×C4×C43C2×D411yescharacteristic
68C22×Dic43—21no—
69C22×Dic43—21no—
70C22×Dic43—21no—
71C2×D172—42no—
72C2×D172—41no—
73C2×C4×D43—42no—
74C2×C4×D43—42no—
75C2×C4×D43—41no—
76C2×C4×D43—41no—
77C2×C8×C43—42no—
78C4⋊C4×C43—41no—
79C4⋊C4×C43—41no—
80C4⋊C4×C43—41no—
81C42×C43—21no—
82C42×C43—21no—
83C42×C43—21no—
84C42×C43—21no—
85C42×C43—21no—
86C42×C43—21no—
87(C2×D43)⋊C4—42no—
88(C2×D43)⋊C4—42no—
89(C2×D43)⋊C4—42no—
90(C2×D43)⋊C4—42no—
91(C2×D43)⋊C4—42no—
92C4⋊Dic43—41no—
93C4×Dic43—42no—
94#10621877—24no—
95#10621877—42no—
96C2×C43⋊C8—42no—
97C23×C43C2×C22⋊C411yescharacteristic
98C22×D43—22no—
99C22×D43—41no—
100C22×D43—41no—
101C22×D43—41no—
102C22×D43—41no—
103C22×D43—41no—
104C22×D43—41no—
105Q8×C43—44no—
106C2×C4×C43—21no—
107C2×C4×C43—21no—
108C2×C4×C43—21no—
109C2×C4×C43—21no—
110C2×C4×C43—22no—
111C2×C4×C43—21no—
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—41no—
118C2×C4×C43—41no—
119C2×C4×C43—41no—
120C2×C4×C43#9911yescharacteristic
121C2×C4×C43#9911yescharacteristic
122C2×C4×C43#10412yes—
123C2×C4×C43#13512yes—
124C2×Dic43—41no—
125C2×Dic43—41no—
126C2×Dic43—41no—
127C2×Dic43—41no—
128C2×Dic43—41no—
129C2×Dic43—41no—
130C2×Dic43—41no—
131C2×Dic43—41no—
132C2×Dic43—41no—
133D172—42no—
134D172—42no—
135C4×D43—82no—
136C4×D43—82no—
137C8×C43—82no—
138C43⋊C8—44no—
139#11734—431nomaximal, Sylow
140C22×C43—21no—
141C22×C43—21no—
142C22×C43C2×#9911yescharacteristic
143C22×C43#41611yescharacteristic
144C22×C43C2×#10411yescharacteristic
145C2×D43—42no—
146C2×D43—42no—
147C2×D43—42no—
148C2×D43—81no—
149C2×D43—81no—
150C2×D43—81no—
151C2×D43—81no—
152C4×C43—21no—
153C4×C43—22no—
154C4×C43—22no—
155C4×C43—41no—
156C4×C43—41no—
157C4×C43—41no—
158C4×C43—41no—
159C4×C43#35512yes—
160Dic43—81no—
161Dic43—81no—
162Dic43—81no—
163#2398—431no—
164C4×#101—431no—
165#1461D4311yescharacteristic, complemented
166#1353—432no—
167#1345—432no—
168C2×C43—21no—
169C2×C43—21no—
170C2×C43#150111yescharacteristic
171C2×C43#212011yescharacteristic
172C2×C43C2×#35511yescharacteristic
173D43—82no—
174C2×C4×Q8C2×D4311yescharacteristic
175C2×C4×D4—431no—
176#431—21no—
177C2×#101—861no—
178C4×M16—861no—
179#400—431no—
180#400—431no—
181#397—861no—
182#394—431no—
183#394—431no—
184#393—861no—
185C4×C22⋊C4—861no—
186C4×C22⋊C4—861no—
187#376—431no—
188#343—432no—
189#324—21no—
190#324C2×D4312yes—
191C43#1173411yescharacteristic, complemented, Sylow
192C22×Q8D17211yescharacteristic
193C22×D4—431no—
194C23×C4—861no—
195C2×M16—862no—
196C4×Q8—41no—
197C4×Q8—41no—
198C4×D4—1721no—
199C4×D4—1721no—
200C2×C4⋊C4—431no—
201C2×C4⋊C4C4×D4311yescharacteristic
202C2×C4⋊C4C22⋊D4311yescharacteristic
203C2×C4⋊C4C22×D4311yescharacteristic
204C2×C22⋊C4—861no—
205C2×C22⋊C4—861no—
206C2×C22⋊C4—861no—
207C2×C22⋊C4—861no—
208C2×C22⋊C4—861no—
209C2×C42—861no—
210C2×C42C4×D4311yescharacteristic
211C2×C42D17211yescharacteristic
212C2×C42C22⋊D4311yescharacteristic
213C4⋊C8—41no—
214#101—864no—
215C22⋊C8—22no—
216#97—1721no—
217C4×C8—41no—
218C4×C8—1721no—
219#95—431no—
220#95—431no—
221#95—861no—
222#95—861no—
223#95—861no—
224#95—861no—
225#95—861no—
226C24—861no—
227C2×Q8—22no—
228C2×Q8—22no—
229C2×Q8—41no—
230C2×D4—1721no—
231C2×D4—1722no—
232C22×C4—861no—
233C22×C4—861no—
234C22×C4—861no—
235C22×C4—1722no—
236C22×C4—1722no—
237C22×C4—1721no—
238C22×C4—1721no—
239C22×C4(C2×D43)⋊C411yescharacteristic
240C22×C4(C2×D43)⋊C411yescharacteristic
241C22×C4(C2×D43)⋊C411yescharacteristic
242C22×C4(C2×D43)⋊C411yescharacteristic
243C22×C4C2×C4×D4311yescharacteristic
244C22×C4C2×D17211yescharacteristic
245C22×C4C2×C22⋊D4311yescharacteristic
246M16—864no—
247M16—1722no—
248C2×C8—42no—
249C2×C8—1722no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—1721no—
254C22⋊C4—1722no—
255C22⋊C4—1722no—
256C22⋊C4—1722no—
257C22⋊C4—1722no—
258C22⋊C4—1722no—
259C42—21no—
260C42—21no—
261C42—21no—
262C42—21no—
263C42—21no—
264C42—21no—
265C42—1722no—
266C23—862no—
267C23—1721no—
268C23—1721no—
269C23—1721no—
270C23—1721no—
271C23—1721no—
272C23—1721no—
273C23C2×(C2×D43)⋊C411yescharacteristic
274Q8—44no—
275D4—1722no—
276D4—1722no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—22no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—3442no—
292C2×C4—3442no—
293C2×C4—1721no—
294C2×C4—1721no—
295C2×C4—1721no—
296C2×C4—1721no—
297C2×C4—1721no—
298C2×C4—1721no—
299C2×C4—1721no—
300C2×C4—1721no—
301C2×C4—1721no—
302C2×C4#1306323911yescharacteristic
303C2×C4#1306323911yescharacteristic
304C2×C4#1306325112yes—
305C2×C4#1306334712yes—
306C8—82no—
307C8—1724no—
308C22—21no—
309C22—21no—
310C22—3441no—
311C22—3441no—
312C22—3441no—
313C22—3441no—
314C22—1722no—
315C22—1722no—
316C22—1722no—
317C22C2×#1306323911yescharacteristic
318C22#1458289611yescharacteristic
319C22C2×#1306325111yescharacteristic
320C4—21no—
321C4—22no—
322C4—22no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—3441no—
328C4—3441no—
329C4—3441no—
330C4#1458269512yes—
331C2—21no—
332C2—21no—
333C2—3442no—
334C2#1913308711yescharacteristic
335C2#1913623411yescharacteristic
336C2C2×#1458269511yescharacteristic
subgroupG/H
centerC2×C4#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1461C2
socleC22×C43C2×#99
prime radicalC22×D172C2×C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1461D43
hypocenterC43#11734
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1461

Complements

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

NH ≅ G/Ntype
2. C4×#13063244C2semidirect
3. #19132623C2semidirect
5. C43×#1461C2semidirect
165. #1461D43semidirect
191. C43#11734semidirect

Maximal subgroups

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

subgroupindex
#191378782
C4×#130632442
#191326232
#191325992
C43×#14612
#1173443