Finite Group Databasebeta

← #24994040

Subgroups — #24994040

Order 11008.

840 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 840 conjugacy classes of subgroups — too many to draw. Only its 107 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#19139526C211yesmaximal, characteristic
2#19136948C211yesmaximal, characteristic, complemented
3#19133112C212yesmaximal, complemented
4#19132480C212yesmaximal, complemented
5C43×#1462C211yesmaximal, characteristic, complemented
6C2×#13063308—21no—
7C2×#13063299C2211yescharacteristic
8C2×#13063294—21no—
9C22×C22⋊Dic43—21no—
10#14582835C412yescomplemented
11#14582808C412yescomplemented
12#14582799—22no—
13C22⋊C4×Dic43—24no—
14C4×C22⋊Dic43—21no—
15C4×C22⋊Dic43C2211yescharacteristic
16C4×C22⋊Dic43C2212yes—
17#14582634—24no—
18C22×C22⋊C4×C43C2211yescharacteristic
19C43×#407C2212yes—
20C43×#323—22no—
21C22×D172C2×C411yescharacteristic, complemented
22C22×C22⋊D43—21no—
23C22×C22⋊D43—22no—
24C23×Dic43—22no—
25#13063308—44no—
26#13063299—22no—
27#13063299—22no—
28#13063294—44no—
29C2×C4⋊Dic43C2×C411yescharacteristic, complemented
30C2×Dic43⋊C4—22no—
31C2×C22⋊Dic43—28no—
32C2×C22⋊Dic43—22no—
33C2×C22⋊Dic43—22no—
34C2×C22⋊Dic43—21no—
35C2×C22⋊Dic43—22no—
36C2×(C2×D43)⋊C4—22no—
37C2×(C2×D43)⋊C4—21no—
38C2×C4×Dic43—22no—
39C2×C4×Dic43—21no—
40C2×C4×Dic43—22no—
41C43⋊#95—22no—
42C43⋊#95C2×C412yescomplemented
43C43⋊#95D414yescomplemented
44C25×C43D411yescharacteristic
45C23×C4×C43D411yescharacteristic
46C23×C4×C43C2311yescharacteristic
47C2×M16×C43—22no—
48C2×C22⋊C4×C43—22no—
49C2×C22⋊C4×C43—22no—
50C2×C22⋊C4×C43C2×C412yes—
51C2×C22⋊C4×C43D412yes—
52C22⋊C8×C43—22no—
53C22⋊C8×C43—22no—
54C24×C43—21no—
55C24×C43—24no—
56C24×C43—21no—
57C24×C43—42no—
58C24×C43—81no—
59C24×C43C22⋊C412yes—
60C24×C43C2×D411yescharacteristic
61C23×D43—21no—
62C22×C4×C43—21no—
63C22×C4×C43—21no—
64C22×C4×C43—42no—
65C22×C4×C43—81no—
66C22×C4×C43C22⋊C412yes—
67C22×C4×C43C22×C411yescharacteristic
68C22×C4×C43C2×D411yescharacteristic
69C22×C4×C43C2×D412yes—
70C22×C4×C43#4112yes—
71C2×C22⋊D43—42no—
72C2×C22⋊D43—42no—
73C2×C22⋊D43—44no—
74C2×C22⋊D43—44no—
75C2×C22⋊D43—41no—
76C2×C22⋊D43—41no—
77C2×C22⋊D43—82no—
78C22×Dic43—28no—
79C22×Dic43—22no—
80C22×Dic43—21no—
81C22×Dic43—24no—
82C22×Dic43—82no—
83C22×Dic43—82no—
84C2×D172—22no—
85C2×D172—81no—
86M16×C43—82no—
87C2×C8×C43—42no—
88C22⋊C4×C43—24no—
89C22⋊C4×C43—24no—
90C22⋊Dic43—28no—
91C22⋊Dic43—28no—
92C22⋊Dic43—24no—
93C22⋊Dic43—44no—
94(C2×D43)⋊C4—44no—
95(C2×D43)⋊C4—42no—
96C4⋊Dic43—22no—
97Dic43⋊C4—44no—
98C4×Dic43—82no—
99C4×Dic43—81no—
100C4×Dic43—82no—
101C23×C43—22no—
102C23×C43—22no—
103C23×C43—24no—
104C23×C43—22no—
105C23×C43—22no—
106C23×C43—22no—
107C23×C43—22no—
108C23×C43—41no—
109C23×C43—42no—
110C23×C43—42no—
111C23×C43—42no—
112C23×C43—42no—
113C23×C43—81no—
114C23×C43—81no—
115C23×C43—88no—
116C23×C43#10414yes—
117C23×C43C2×C22⋊C411yescharacteristic
118C23×C43#12011yescharacteristic
119C23×C43#12311yescharacteristic
120C22×D43—41no—
121C22×D43—42no—
122C22×D43—41no—
123C22×D43—41no—
124C22×D43—42no—
125C2×C4×C43—22no—
126C2×C4×C43—42no—
127C2×C4×C43—41no—
128C2×C4×C43—42no—
129C2×C4×C43—41no—
130C2×C4×C43—42no—
131C2×C4×C43—42no—
132C2×C4×C43—81no—
133C2×C4×C43C4×D412yes—
134C2×C4×C43#12112yes—
135C22⋊D43—88no—
136C22⋊D43—82no—
137C22⋊D43—82no—
138C2×Dic43—24no—
139C2×Dic43—28no—
140C2×Dic43—44no—
141C2×Dic43—42no—
142C2×Dic43—42no—
143C2×Dic43—44no—
144C2×Dic43—41no—
145C2×Dic43—41no—
146C2×Dic43—41no—
147C2×Dic43—88no—
148D172—82no—
149C8×C43—82no—
150#9409—431nomaximal, Sylow
151C22×C43—21no—
152C22×C43—21no—
153C22×C43—21no—
154C22×C43—21no—
155C22×C43—21no—
156C22×C43—24no—
157C22×C43—21no—
158C22×C43—21no—
159C22×C43—44no—
160C22×C43—44no—
161C22×C43—44no—
162C22×C43—44no—
163C22×C43—42no—
164C22×C43—42no—
165C22×C43—82no—
166C22×C43—84no—
167C22×C43#38611yescharacteristic
168C22×C43C2×#10412yes—
169C22×C43#45312yes—
170C2×D43—82no—
171C2×D43—82no—
172C2×D43—81no—
173C2×D43—81no—
174C2×D43—81no—
175C4×C43—22no—
176C4×C43—22no—
177C4×C43—42no—
178Dic43—48no—
179Dic43—44no—
180Dic43—81no—
181#2539—431no—
182#2273—431no—
183#1507—432no—
184#1462D4311yescharacteristic, complemented
185#1297—432no—
186C2×C43—22no—
187C2×C43—22no—
188C2×C43—41no—
189C2×C43—44no—
190C2×C43#188711yescharacteristic
191C2×C43#189611yescharacteristic
192C2×C43#191311yescharacteristic
193D43—161no—
194C2×#123—861no—
195C2×#121—431no—
196C2×#120—861no—
197C22×C22⋊C4—861no—
198C22×C22⋊C4C2×D4311yescharacteristic
199#407C2×D4312yes—
200#399—432no—
201#392—432no—
202#390—862no—
203C4×C22⋊C4—431no—
204C4×C22⋊C4—432no—
205C4×C22⋊C4—864no—
206C4×C22⋊C4—861no—
207#327—864no—
208#323—22no—
209C43#940911yescharacteristic, complemented, Sylow
210C25D17211yescharacteristic
211C22×D4—431no—
212C22×D4—862no—
213C22×D4—861no—
214C23×C4—862no—
215C23×C4D17211yescharacteristic
216C23×C4C22×D4311yescharacteristic
217C2×M16—22no—
218#123—1724no—
219#121—862no—
220#121—862no—
221#120—1724no—
222C2×C4⋊C4—431no—
223C2×C4⋊C4—862no—
224C2×C22⋊C4—22no—
225C2×C22⋊C4—22no—
226C2×C22⋊C4—868no—
227C2×C22⋊C4—862no—
228C2×C22⋊C4—862no—
229C2×C22⋊C4—861no—
230C2×C22⋊C4—862no—
231C2×C22⋊C4—862no—
232C2×C22⋊C4—861no—
233C2×C22⋊C4C4×D4312yes—
234C2×C22⋊C4C22⋊D4312yes—
235C2×C42—862no—
236C2×C42—862no—
237C2×C42—861no—
238C22⋊C8—22no—
239C22⋊C8—22no—
240#95—432no—
241#95—434no—
242#95—862no—
243C24—21no—
244C24—24no—
245C24—21no—
246C24—42no—
247C24—81no—
248C24—861no—
249C24(C2×D43)⋊C412yes—
250C24C2×D17211yescharacteristic
251C2×D4—862no—
252C2×D4—3441no—
253C2×D4—3442no—
254C2×D4—1724no—
255C2×D4—1722no—
256C2×D4—1722no—
257C2×D4—1724no—
258C2×D4—1721no—
259C2×D4—1721no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—42no—
263C22×C4—81no—
264C22×C4—868no—
265C22×C4—862no—
266C22×C4—864no—
267C22×C4—861no—
268C22×C4—3442no—
269C22×C4—3442no—
270C22×C4(C2×D43)⋊C412yes—
271C22×C4C2×C4×D4311yescharacteristic
272C22×C4D4×D4312yes—
273C22×C4#1062190012yes—
274C22×C4C2×C22⋊D4311yescharacteristic
275M16—82no—
276C2×C8—42no—
277C4⋊C4—862no—
278C4⋊C4—1724no—
279C22⋊C4—24no—
280C22⋊C4—24no—
281C22⋊C4—868no—
282C22⋊C4—868no—
283C22⋊C4—864no—
284C22⋊C4—1724no—
285C22⋊C4—1724no—
286C22⋊C4—1722no—
287C42—3442no—
288C42—3441no—
289C42—3442no—
290C23—22no—
291C23—22no—
292C23—24no—
293C23—22no—
294C23—22no—
295C23—22no—
296C23—22no—
297C23—41no—
298C23—42no—
299C23—42no—
300C23—42no—
301C23—42no—
302C23—81no—
303C23—81no—
304C23—88no—
305C23—1721no—
306C23—1722no—
307C23—1721no—
308C23—1722no—
309C23—1721no—
310C23#1306325114yes—
311C23C2×(C2×D43)⋊C411yescharacteristic
312C23#1306329511yescharacteristic
313C23#1306330911yescharacteristic
314D4—3442no—
315D4—3442no—
316D4—3442no—
317D4—3448no—
318C2×C4—22no—
319C2×C4—42no—
320C2×C4—41no—
321C2×C4—42no—
322C2×C4—41no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—81no—
326C2×C4—868no—
327C2×C4—864no—
328C2×C4—3448no—
329C2×C4—1721no—
330C2×C4—1721no—
331C2×C4—1721no—
332C2×C4—1724no—
333C2×C4—1722no—
334C2×C4—1724no—
335C2×C4—1722no—
336C2×C4(C22⋊D43)⋊C412yes—
337C2×C4#1306329712yes—
338C8—82no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—24no—
345C22—21no—
346C22—21no—
347C22—44no—
348C22—44no—
349C22—44no—
350C22—44no—
351C22—42no—
352C22—42no—
353C22—82no—
354C22—84no—
355C22—3442no—
356C22—3442no—
357C22—3441no—
358C22—3441no—
359C22—3441no—
360C22#1458277611yescharacteristic
361C22C2×#1306325112yes—
362C22#1458306912yes—
363C4—22no—
364C4—22no—
365C4—42no—
366C4—3441no—
367C4—1728no—
368C4—1724no—
369C2—22no—
370C2—22no—
371C2—41no—
372C2—44no—
373C2—6881no—
374C2#1913499111yescharacteristic
375C2#1913503611yescharacteristic
376C2#1913513511yescharacteristic
subgroupG/H
centerC22#14582776
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1462C2
socleC22×C43#386
prime radical#19139526C2
cosocleC23×C4×C43C23
hypercenter#1462D43
hypocenterC43#9409
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1462

Complements

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

NH ≅ G/Ntype
2. #19136948C2semidirect
3. #19133112C2semidirect
4. #19132480C2semidirect
5. C43×#1462C2semidirect
10. #14582835C4semidirect
11. #14582808C4semidirect
21. C22×D172C2×C4semidirect
29. C2×C4⋊Dic43C2×C4semidirect
42. C43⋊#95C2×C4semidirect
43. C43⋊#95D4semidirect
184. #1462D43semidirect
209. C43#9409semidirect

Maximal subgroups

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

subgroupindex
#191395262
#191369482
#191331122
#191324802
C43×#14622
#940943