Finite Group Databasebeta

← #25015266

Subgroups — #25015266

Order 11008.

556 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 103 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#19139548C211yesmaximal, characteristic
2C4×#13063240C211yesmaximal, characteristic
3#19132719C214yesmaximal
4C43×#1799C211yesmaximal, characteristic
5C2×#13063325C411yescharacteristic, complemented
6C2×#13063304—21no—
7C2×#13063304—21no—
8C2×#13063240C2212yes—
9#14582835—21no—
10#14582835—21no—
11#14582802C2212yes—
12#14582768C412yescomplemented
13C4×C4⋊Dic43C411yescharacteristic, complemented
14C4×C22⋊Dic43—21no—
15#14582666—21no—
16C2×C4×D4×C43C2211yescharacteristic
17C2×#99×C43C2212yes—
18C43×#380—21no—
19C43×#342—21no—
20C22×Dic86—21no—
21#13063325—41no—
22#13063325—41no—
23#13063304—44no—
24#13063304—44no—
25C2×C4⋊Dic43—21no—
26C2×C4⋊Dic43—21no—
27C2×C4⋊Dic43C2×C412yes—
28C2×Dic43⋊C4—22no—
29C2×Dic43⋊C4—22no—
30C2×C22⋊Dic43—22no—
31C2×C22⋊Dic43—22no—
32C2×C22⋊Dic43—22no—
33C2×C4×Dic43—41no—
34C2×C4×Dic43C2×C412yes—
35#13063240—22no—
36#13063240Q814yescomplemented
37C43⋊#95—21no—
38C43⋊#95—41no—
39C22×D4×C43C2311yescharacteristic
40C23×C4×C43D411yescharacteristic
41C23×C4×C43D411yescharacteristic
42C4×D4×C43—41no—
43C4×D4×C43—41no—
44C2×C4⋊C4×C43—41no—
45C2×C4⋊C4×C43C2×C411yescharacteristic
46C2×C22⋊C4×C43—22no—
47C2×C22⋊C4×C43D411yescharacteristic
48C2×C22⋊C4×C43D411yescharacteristic
49C2×C42×C43C2×C411yescharacteristic
50#99×C43—24no—
51#95×C43—41no—
52C24×C43C2×D411yescharacteristic
53C24×C43C2×D411yescharacteristic
54C2×D4×C43—41no—
55C2×D4×C43—41no—
56C2×D4×C43C2×Q812yes—
57C2×D4×C43#4112yes—
58C22×C4×C43—21no—
59C22×C4×C43—21no—
60C22×C4×C43—21no—
61C22×C4×C43—21no—
62C22×C4×C43—42no—
63C22×C4×C43—42no—
64C22×C4×C43—42no—
65C22×C4×C43C22⋊C411yescharacteristic
66C22×C4×C43C22⋊C411yescharacteristic
67C22×C4×C43C22⋊C411yescharacteristic
68C22×C4×C43C22⋊C411yescharacteristic
69C22×C4×C43C22×C411yescharacteristic
70C22×Dic43—22no—
71C22×Dic43—22no—
72C22×Dic43—42no—
73C2×Dic86—42no—
74C2×Dic86—42no—
75C2×Dic86—41no—
76C2×Dic86—41no—
77C4⋊C4×C43—41no—
78C4⋊C4×C43—82no—
79C22⋊C4×C43—41no—
80C22⋊C4×C43—41no—
81C22⋊C4×C43—42no—
82C22⋊C4×C43—42no—
83C42×C43—21no—
84C42×C43—21no—
85C22⋊Dic43—24no—
86C22⋊Dic43—42no—
87C22⋊Dic43—44no—
88C22⋊Dic43—44no—
89C4⋊Dic43—24no—
90C4⋊Dic43—42no—
91C4⋊Dic43—42no—
92Dic43⋊C4—44no—
93Dic43⋊C4—44no—
94C4×Dic43—42no—
95C4×Dic43—82no—
96C23×C43—21no—
97C23×C43—21no—
98C23×C43—21no—
99C23×C43—21no—
100C23×C43—41no—
101C23×C43—41no—
102C23×C43—41no—
103C23×C43—41no—
104C23×C43C2×C22⋊C411yescharacteristic
105C23×C43C22⋊Q812yes—
106C23×C43#12411yescharacteristic
107C23×C43C4⋊Q811yescharacteristic
108D4×C43—42no—
109D4×C43—42no—
110C2×C4×C43—21no—
111C2×C4×C43—21no—
112C2×C4×C43—22no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—42no—
117C2×C4×C43—42no—
118C2×C4×C43—41no—
119C2×C4×C43—41no—
120C2×C4×C43—41no—
121C2×C4×C43—81no—
122C2×C4×C43—81no—
123C2×C4×C43—82no—
124C2×C4×C43—82no—
125C2×C4×C43—82no—
126C2×C4×C43#9911yescharacteristic
127C2×C4×C43#9911yescharacteristic
128C2×C4×C43C4×Q812yes—
129C2×Dic43—24no—
130C2×Dic43—42no—
131C2×Dic43—42no—
132C2×Dic43—42no—
133C2×Dic43—42no—
134C2×Dic43—44no—
135C2×Dic43—42no—
136C2×Dic43—82no—
137C2×Dic43—82no—
138Dic86—82no—
139Dic86—82no—
140#13298—431nomaximal, Sylow
141C22×C43—21no—
142C22×C43—21no—
143C22×C43—22no—
144C22×C43—21no—
145C22×C43—21no—
146C22×C43—42no—
147C22×C43—41no—
148C22×C43—41no—
149C22×C43—41no—
150C22×C43—41no—
151C22×C43—41no—
152C22×C43—41no—
153C22×C43—81no—
154C22×C43—81no—
155C22×C43#39111yescharacteristic
156C22×C43C2×#9911yescharacteristic
157C22×C43#41011yescharacteristic
158C4×C43—21no—
159C4×C43—22no—
160C4×C43—41no—
161C4×C43—41no—
162C4×C43—41no—
163C4×C43—162no—
164C4×C43#35312yes—
165Dic43—44no—
166Dic43—84no—
167Dic43—82no—
168#2542—431no—
169#1799D4311yescharacteristic
170C4×#99—431no—
171#1393—434no—
172C2×C43—21no—
173C2×C43—21no—
174C2×C43—42no—
175C2×C43—41no—
176C2×C43—41no—
177C2×C43#199611yescharacteristic
178C2×C43C2×#35311yescharacteristic
179C2×C43#212911yescharacteristic
180C2×C4⋊Q8—431no—
181C2×C22⋊Q8—861no—
182C2×C22⋊Q8—861no—
183C2×C4×D4C2×D4311yescharacteristic
184C2×#99—432no—
185C2×#99C2×D4312yes—
186#399—861no—
187#399—861no—
188#390—432no—
189#384—432no—
190#380—21no—
191C4×C4⋊C4—431no—
192C4×C22⋊C4—861no—
193#342—21no—
194#342—861no—
195C43#1329811yescharacteristic, complemented, Sylow
196C22×Q8—861no—
197C22×D4C22×D4311yescharacteristic
198C23×C4D17211yescharacteristic
199C23×C4C22⋊D4311yescharacteristic
200C4⋊Q8—1721no—
201C4⋊Q8—1721no—
202C22⋊Q8—1724no—
203C22⋊Q8—1724no—
204C4×D4—41no—
205C4×D4—41no—
206C2×C4⋊C4—41no—
207C2×C4⋊C4—432no—
208C2×C4⋊C4—861no—
209C2×C4⋊C4—862no—
210C2×C4⋊C4—862no—
211C2×C4⋊C4—861no—
212C2×C4⋊C4C4×D4311yescharacteristic
213C2×C22⋊C4—22no—
214C2×C22⋊C4—862no—
215C2×C22⋊C4—862no—
216C2×C22⋊C4—862no—
217C2×C22⋊C4D17211yescharacteristic
218C2×C22⋊C4C22⋊D4311yescharacteristic
219C2×C42—432no—
220C2×C42—1721no—
221C2×C42C4×D4311yescharacteristic
222#99—24no—
223#99—434no—
224#99—862no—
225#95—41no—
226#95—861no—
227#95—1721no—
228C24C2×D17211yescharacteristic
229C24C2×C22⋊D4311yescharacteristic
230C2×Q8—1722no—
231C2×Q8—1722no—
232C2×Q8—1721no—
233C2×Q8—1721no—
234C2×D4—41no—
235C2×D4—41no—
236C2×D4#1062190012yes—
237C2×D4Q8×D4312yes—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—42no—
243C22×C4—42no—
244C22×C4—42no—
245C22×C4—862no—
246C22×C4—862no—
247C22×C4—1722no—
248C22×C4(C2×D43)⋊C411yescharacteristic
249C22×C4(C2×D43)⋊C411yescharacteristic
250C22×C4(C2×D43)⋊C411yescharacteristic
251C22×C4(C2×D43)⋊C411yescharacteristic
252C22×C4C2×C4×D4311yescharacteristic
253C4⋊C4—41no—
254C4⋊C4—82no—
255C4⋊C4—864no—
256C4⋊C4—1722no—
257C4⋊C4—1722no—
258C4⋊C4—1724no—
259C4⋊C4—1724no—
260C22⋊C4—41no—
261C22⋊C4—41no—
262C22⋊C4—42no—
263C22⋊C4—42no—
264C22⋊C4—864no—
265C22⋊C4—1724no—
266C22⋊C4—1724no—
267C22⋊C4—1722no—
268C42—21no—
269C42—21no—
270C42—3442no—
271C42—1722no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—41no—
277C23—41no—
278C23—41no—
279C23—41no—
280C23C2×(C2×D43)⋊C411yescharacteristic
281C23#1306330512yes—
282C23#1306331211yescharacteristic
283C23#1306332311yescharacteristic
284Q8—3442no—
285Q8—3442no—
286D4—42no—
287D4—42no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—22no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—82no—
302C2×C4—82no—
303C2×C4—82no—
304C2×C4—864no—
305C2×C4—3442no—
306C2×C4—3442no—
307C2×C4—1724no—
308C2×C4—1722no—
309C2×C4—1722no—
310C2×C4—1722no—
311C2×C4—1722no—
312C2×C4—1722no—
313C2×C4#1306323911yescharacteristic
314C2×C4#1306323911yescharacteristic
315C2×C4#1306329012yes—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—22no—
320C22—21no—
321C22—42no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—81no—
329C22—81no—
330C22#1458280411yescharacteristic
331C22C2×#1306323911yescharacteristic
332C22#1458287211yescharacteristic
333C4—22no—
334C4—21no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—162no—
339C4—3444no—
340C4—3442no—
341C4—1724no—
342C4#1458269112yes—
343C2—21no—
344C2—21no—
345C2—41no—
346C2—42no—
347C2—41no—
348C2#1913557911yescharacteristic
349C2C2×#1458269111yescharacteristic
350C2#1913626911yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC22×D4C22×D43
FittingC43×#1799C2
socleC22×C43C2×#99
prime radical, cosocleC22×D4×C43C23
hypercenter#1799D43
hypocenterC43#13298
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1799

Complements

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

NH ≅ G/Ntype
5. C2×#13063325C4semidirect
12. #14582768C4semidirect
13. C4×C4⋊Dic43C4semidirect
36. #13063240Q8semidirect
195. C43#13298semidirect

Maximal subgroups

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

subgroupindex
#191395482
C4×#130632402
#191327192
C43×#17992
#1329843