Finite Group Databasebeta

← #25012595

Subgroups — #25012595

Order 11008.

500 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 95 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#19137138C211yesmaximal, characteristic
2C2×#14582695C212yesmaximal
3#19134589C212yesmaximal, complemented
4#19132722C211yesmaximal, characteristic, complemented
5C43×#1394C211yesmaximal, characteristic, complemented
6C2×#13063314C2211yescharacteristic
7C2×Q8×Dic43C2211yescharacteristic
8C2×#13063287C411yescharacteristic
9#14582922—22no—
10C2×#13063244C2212yes—
11#14582801C411yescharacteristic
12#14582791—22no—
13#14582764C411yescharacteristic
14#14582746—22no—
15C42×Dic43C411yescharacteristic
16#14582695—24no—
17#14582667—22no—
18C2×#101×C43C2212yes—
19C43×#391C2211yescharacteristic
20C22×D172C2×C411yescharacteristic
21C22×C4×D43—21no—
22C2×#10621877—22no—
23#13063314—22no—
24#13063314D412yes—
25#13063314Q812yes—
26Q8×Dic43—41no—
27Q8×Dic43—41no—
28#13063287—41no—
29#13063287—41no—
30C2×C4⋊Dic43C2×C411yescharacteristic
31C2×C4⋊Dic43D412yes—
32C2×(C2×D43)⋊C4—22no—
33C2×(C2×D43)⋊C4—21no—
34C2×(C2×D43)⋊C4—22no—
35C2×C4×Dic43—21no—
36C2×C4×Dic43—21no—
37C2×C4×Dic43C2×C411yescharacteristic
38C2×C4×Dic43C2×C411yescharacteristic
39C2×C4×Dic43D412yes—
40Dic43⋊C8—42no—
41Dic43⋊C8—42no—
42#13063244—22no—
43#13063244—22no—
44C43⋊#95—22no—
45C22×Q8×C43C2311yescharacteristic
46C2×M16×C43—22no—
47C2×C4⋊C4×C43C2×C411yescharacteristic
48C2×C42×C43C2×C411yescharacteristic
49#101×C43—22no—
50#101×C43—22no—
51#95×C43—22no—
52C23×D43—21no—
53C2×Q8×C43—41no—
54C2×Q8×C43—41no—
55C2×Q8×C43C2×D411yescharacteristic
56C2×Q8×C43C2×Q811yescharacteristic
57C2×Q8×C43#4112yes—
58C22×C4×C43—21no—
59C22×C4×C43—21no—
60C22×C4×C43C22×C411yescharacteristic
61C22×C4×C43C2×D412yes—
62C22×Dic43—21no—
63C22×Dic43C22⋊C411yescharacteristic
64C22×Dic43C22⋊C412yes—
65C22×Dic43C22⋊C411yescharacteristic
66C2×D172—21no—
67C2×D172—41no—
68C2×D172—41no—
69C2×D172C4⋊C412yes—
70C2×C4×D43—44no—
71C2×C4×D43—41no—
72C2×C4×D43—41no—
73M16×C43—42no—
74M16×C43—42no—
75C2×C8×C43—42no—
76C4⋊C4×C43—41no—
77C42×C43—41no—
78(C2×D43)⋊C4—24no—
79(C2×D43)⋊C4—24no—
80(C2×D43)⋊C4—42no—
81(C2×D43)⋊C4—44no—
82C4⋊Dic43—41no—
83C4⋊Dic43—42no—
84C4×Dic43—21no—
85C4×Dic43—22no—
86C4×Dic43—22no—
87C4×Dic43—21no—
88C4×Dic43—21no—
89C4×Dic43—42no—
90C4×Dic43—42no—
91C4×Dic43C4⋊C412yes—
92#10621877—42no—
93#10621877—42no—
94C2×C43⋊C8—42no—
95C23×C43C2×C22⋊C411yescharacteristic
96C22×D43—22no—
97C22×D43—42no—
98C22×D43—42no—
99C22×D43—41no—
100C22×D43—41no—
101Q8×C43—41no—
102Q8×C43—41no—
103Q8×C43—42no—
104C2×C4×C43—22no—
105C2×C4×C43—21no—
106C2×C4×C43—22no—
107C2×C4×C43—21no—
108C2×C4×C43—22no—
109C2×C4×C43—41no—
110C2×C4×C43—41no—
111C2×C4×C43—42no—
112C2×C4×C43—41no—
113C2×C4×C43C2×C4⋊C411yescharacteristic
114C2×C4×C43#11711yescharacteristic
115C2×C4×C43#12112yes—
116C2×C4×C43C22⋊Q812yes—
117C2×Dic43—22no—
118C2×Dic43—22no—
119C2×Dic43—21no—
120C2×Dic43—22no—
121C2×Dic43—41no—
122C2×Dic43—41no—
123C2×Dic43—41no—
124C2×Dic43—42no—
125C2×Dic43#9911yescharacteristic
126C2×Dic43#9911yescharacteristic
127D172—42no—
128D172—42no—
129C4×D43—82no—
130C4×D43—82no—
131C8×C43—82no—
132C43⋊C8—82no—
133#12801—431nomaximal, Sylow
134C22×C43—21no—
135C22×C43—21no—
136C22×C43#38011yescharacteristic
137C22×C43C2×#9911yescharacteristic
138C22×C43#41011yescharacteristic
139C2×D43—44no—
140C2×D43—42no—
141C2×D43—82no—
142C2×D43—81no—
143C2×D43—81no—
144C4×C43—22no—
145C4×C43—21no—
146C4×C43—21no—
147C4×C43—22no—
148C4×C43—42no—
149C4×C43—81no—
150Dic43—21no—
151Dic43—42no—
152Dic43—41no—
153Dic43—42no—
154Dic43#35512yescomplemented
155C4×#124—431no—
156C2×#355—432no—
157#1801—432no—
158#1394—431no—
159#1394D4311yescharacteristic, complemented
160C2×C43—21no—
161C2×C43—21no—
162C2×C43#179911yescharacteristic
163C2×C43C2×#35511yescharacteristic
164C2×C43#213211yescharacteristic
165D43—82no—
166C2×#124—431no—
167C2×C4×Q8—431no—
168C2×C4×D4—431no—
169#423—862no—
170C2×#101—432no—
171C2×#101C2×D4312yes—
172#391C2×D4311yescharacteristic
173#390—431no—
174#388—862no—
175#382—431no—
176C4×C22⋊C4—862no—
177C43—431no—
178#355—864no—
179#343—862no—
180C43#1280111yescharacteristic, complemented, Sylow
181C22×Q8C22×D4311yescharacteristic
182C22×D4—431no—
183C23×C4—861no—
184C2×M16—22no—
185C2×M16—862no—
186#124—432no—
187#124—432no—
188#124—862no—
189C4×Q8—1721no—
190C4×Q8—1721no—
191C4×D4—1721no—
192C4×D4—1721no—
193C2×C4⋊C4—431no—
194C2×C4⋊C4—432no—
195C2×C4⋊C4C4×D4311yescharacteristic
196C2×C22⋊C4—862no—
197C2×C22⋊C4—861no—
198C2×C22⋊C4—862no—
199C2×C42—431no—
200C2×C42—431no—
201C2×C42—432no—
202C2×C42—861no—
203C2×C42—861no—
204C2×C42C4×D4311yescharacteristic
205C4⋊C8—1722no—
206C4⋊C8—1722no—
207#101—22no—
208#101—22no—
209#101—862no—
210#101—862no—
211#95—22no—
212#95—862no—
213C24—861no—
214C2×Q8—41no—
215C2×Q8—41no—
216C2×Q8#1062189812yes—
217C2×Q8D4×D4311yescharacteristic
218C2×Q8Q8×D4311yescharacteristic
219C2×D4—432no—
220C2×D4—861no—
221C2×D4—1721no—
222C2×D4—1721no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—431no—
226C22×C4—432no—
227C22×C4—431no—
228C22×C4—861no—
229C22×C4—1721no—
230C22×C4—1721no—
231C22×C4—1724no—
232C22×C4C2×C4×D4311yescharacteristic
233C22×C4D4×D4312yes—
234M16—42no—
235M16—42no—
236M16—1722no—
237M16—1722no—
238C2×C8—42no—
239C2×C8—1722no—
240C4⋊C4—41no—
241C4⋊C4—1721no—
242C4⋊C4—1722no—
243C22⋊C4—864no—
244C22⋊C4—864no—
245C22⋊C4—1724no—
246C22⋊C4—1722no—
247C42—41no—
248C42—432no—
249C42—862no—
250C42—862no—
251C42—861no—
252C42—861no—
253C42—861no—
254C42—1722no—
255C42—1722no—
256C23—862no—
257C23—1722no—
258C23—1722no—
259C23—1721no—
260C23—1721no—
261C23C22⋊C4×D4311yescharacteristic
262Q8—42no—
263Q8—41no—
264Q8—41no—
265D4—1722no—
266D4—1722no—
267C2×C4—21no—
268C2×C4—22no—
269C2×C4—21no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—42no—
275C2×C4—41no—
276C2×C4—431no—
277C2×C4—431no—
278C2×C4—862no—
279C2×C4—861no—
280C2×C4—862no—
281C2×C4—862no—
282C2×C4—3442no—
283C2×C4—3442no—
284C2×C4—1721no—
285C2×C4—1721no—
286C2×C4—1721no—
287C2×C4—1722no—
288C2×C4C4⋊C4×D4311yescharacteristic
289C2×C4#1306328211yescharacteristic
290C2×C4#1306329812yes—
291C2×C4#1306330312yes—
292C8—82no—
293C8—3442no—
294C22—21no—
295C22—21no—
296C22—3442no—
297C22—3441no—
298C22—3441no—
299C22—1724no—
300C22—1722no—
301C22#1458275811yescharacteristic
302C22#99×D4311yescharacteristic
303C22#1458287111yescharacteristic
304C4—22no—
305C4—21no—
306C4—21no—
307C4—22no—
308C4—42no—
309C4—81no—
310C4—432no—
311C4—861no—
312C4—1722no—
313C4—1721no—
314C4—1722no—
315C2—21no—
316C2—21no—
317C2—3442no—
318C2#1913458211yescharacteristic
319C2#355×D4311yescharacteristic
320C2#1913627911yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC22×Q8C22×D43
FittingC43×#1394C2
socleC22×C43C2×#99
prime radicalC22×D172C2×C4
cosocleC22×Q8×C43C23
hypercenter#1394D43
hypocenterC43#12801
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #1394

Complements

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

NH ≅ G/Ntype
3. #19134589C2semidirect
4. #19132722C2semidirect
5. C43×#1394C2semidirect
154. Dic43#355semidirect
159. #1394D43semidirect
180. C43#12801semidirect

Maximal subgroups

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

subgroupindex
#191371382
C2×#145826952
#191345892
#191327222
C43×#13942
#1280143