Finite Group Databasebeta

← #24994249

Subgroups — #24994249

Order 11008.

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

normal subgroups only

This group has 516 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#19143233C211yesmaximal, characteristic, complemented
2#19139053C211yesmaximal, characteristic
3#19133123C212yesmaximal
4#19132447C212yesmaximal, complemented
5C43×#1820C211yesmaximal, characteristic, complemented
6C2×#13063299C2211yescharacteristic
7#14582960—24no—
8#14582923—21no—
9#14582863C2212yes—
10C4×#10621877—21no—
11#14582814—21no—
12#14582814—21no—
13#14582800C411yescharacteristic, complemented
14#14582800C411yescharacteristic, complemented
15#14582790—21no—
16#14582790—21no—
17#14582768C411yescharacteristic, complemented
18#14582764C411yescharacteristic, complemented
19C4×C22⋊Dic43C2211yescharacteristic
20#14582632—24no—
21C2×#117×C43C2211yescharacteristic
22C43×#381C2212yes—
23C43×#342—21no—
24C43×#342—21no—
25C22×D172C2×C411yescharacteristic
26C22×C22⋊D43—21no—
27C2×#10621877—22no—
28#13063299—22no—
29#13063299—22no—
30C2×C4⋊Dic43C2×C411yescharacteristic
31C2×Dic43⋊C4—21no—
32C2×Dic43⋊C4—21no—
33C2×C22⋊Dic43—21no—
34C2×(C2×D43)⋊C4—21no—
35C2×(C2×D43)⋊C4—21no—
36C2×(C2×D43)⋊C4—21no—
37C2×(C2×D43)⋊C4—21no—
38C2×(C2×D43)⋊C4—21no—
39C2×C4×Dic43C2×C411yescharacteristic
40C2×C4×Dic43C2×C411yescharacteristic
41C4⋊(C43⋊C8)—24no—
42C22⋊(C43⋊C8)—22no—
43C22⋊(C43⋊C8)D414yes—
44#13063236—22no—
45C4×C43⋊C8—22no—
46C43⋊#95—21no—
47C43⋊#95—21no—
48C43⋊#95—21no—
49C23×C4×C43C2311yescharacteristic
50#117×C43—22no—
51#117×C43—22no—
52C2×C4⋊C4×C43C2×C411yescharacteristic
53C2×C4⋊C4×C43C2×C411yescharacteristic
54C2×C22⋊C4×C43—22no—
55C2×C22⋊C4×C43D411yescharacteristic
56C2×C22⋊C4×C43D411yescharacteristic
57C2×C42×C43D411yescharacteristic
58C2×C42×C43D411yescharacteristic
59#95×C43—22no—
60#95×C43—22no—
61C24×C43C2×D411yescharacteristic
62C23×D43—21no—
63C22×C4×C43—41no—
64C22×C4×C43—41no—
65C22×C4×C43—42no—
66C22×C4×C43C22⋊C411yescharacteristic
67C22×C4×C43C22⋊C411yescharacteristic
68C22×C4×C43C22⋊C411yescharacteristic
69C22×C4×C43C22⋊C411yescharacteristic
70C22×C4×C43C22×C411yescharacteristic
71C22×C4×C43C2×D411yescharacteristic
72C22×C4×C43C2×D412yes—
73C22×C4×C43#4112yes—
74C2×C22⋊D43—42no—
75C2×C22⋊D43—81no—
76C2×C22⋊D43—81no—
77C22×Dic43—21no—
78C22×Dic43—21no—
79C22×Dic43—21no—
80C2×D172—22no—
81C2×D172—41no—
82C2×D172—41no—
83C4⋊C4×C43—22no—
84C4⋊C4×C43—22no—
85C22⋊C4×C43—22no—
86C22⋊C4×C43—22no—
87C22⋊C4×C43—42no—
88C22⋊C4×C43—42no—
89C42×C43—21no—
90C42×C43—21no—
91C42×C43—21no—
92C42×C43—21no—
93C22⋊Dic43—42no—
94(C2×D43)⋊C4—42no—
95(C2×D43)⋊C4—42no—
96(C2×D43)⋊C4—41no—
97(C2×D43)⋊C4—41no—
98(C2×D43)⋊C4—81no—
99(C2×D43)⋊C4—81no—
100C4⋊Dic43—22no—
101Dic43⋊C4—81no—
102Dic43⋊C4—81no—
103C4×Dic43—41no—
104C4×Dic43—41no—
105#10621877—42no—
106#10621877—42no—
107C2×C43⋊C8—24no—
108C23×C43—21no—
109C23×C43—21no—
110C23×C43—41no—
111C23×C43—41no—
112C23×C43C2×C22⋊C411yescharacteristic
113C23×C43#12112yes—
114C22×D43—41no—
115C22×D43—41no—
116C22×D43—41no—
117C22×D43—41no—
118C22×D43—41no—
119C22×D43—41no—
120C22×D43—41no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—42no—
130C2×C4×C43—42no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43—41no—
135C2×C4×C43—82no—
136C2×C4×C43—82no—
137C2×C4×C43—82no—
138C2×C4×C43C4×D412yes—
139C2×C4×C43#12011yescharacteristic
140C2×C4×C43#12311yescharacteristic
141C22⋊D43—84no—
142C2×Dic43—22no—
143C2×Dic43—41no—
144C2×Dic43—41no—
145C2×Dic43—41no—
146C2×Dic43—41no—
147C2×Dic43—41no—
148C2×Dic43—41no—
149C2×Dic43—41no—
150C2×Dic43—41no—
151D172—82no—
152C43⋊C8—44no—
153#9446—431nomaximal, Sylow
154C22×C43—21no—
155C22×C43—21no—
156C22×C43—22no—
157C22×C43—22no—
158C22×C43—22no—
159C22×C43—81no—
160C22×C43—81no—
161C22×C43#38611yescharacteristic
162C22×C43#41011yescharacteristic
163C22×C43#41011yescharacteristic
164C2×D43—81no—
165C2×D43—81no—
166C2×D43—81no—
167C2×D43—81no—
168C2×D43—81no—
169C2×D43—81no—
170C2×D43—81no—
171C4×C43—21no—
172C4×C43—22no—
173C4×C43—21no—
174C4×C43—41no—
175C4×C43—41no—
176C4×C43—41no—
177C4×C43—41no—
178C4×C43—162no—
179Dic43—42no—
180Dic43—81no—
181Dic43—81no—
182#2921—431no—
183#2500—431no—
184#1820D4311yescharacteristic, complemented
185#1510—432no—
186#1284—432no—
187C2×C43—21no—
188C2×C43—21no—
189C2×C43—42no—
190C2×C43#188411yescharacteristic
191C2×C43#189911yescharacteristic
192C2×C43#191011yescharacteristic
193D43—161no—
194C2×#121—431no—
195C2×#117C2×D4311yescharacteristic
196#433—864no—
197#423—861no—
198#407—432no—
199C4×M16—861no—
200#394—861no—
201#394—861no—
202#390—431no—
203#390—431no—
204#388—861no—
205#388—861no—
206#384—431no—
207#382—431no—
208#381C2×D4312yes—
209C4×C22⋊C4—431no—
210#342—21no—
211#342—21no—
212#327—864no—
213C43#944611yescharacteristic, complemented, Sylow
214C22×D4—431no—
215C22×D4—861no—
216C23×C4C22×D4311yescharacteristic
217C2×M16—862no—
218#121—862no—
219#121—862no—
220#117—22no—
221#117—22no—
222C2×C4⋊C4—431no—
223C2×C4⋊C4—861no—
224C2×C4⋊C4—861no—
225C2×C4⋊C4C4×D4311yescharacteristic
226C2×C4⋊C4C4×D4311yescharacteristic
227C2×C22⋊C4—22no—
228C2×C22⋊C4—861no—
229C2×C22⋊C4—861no—
230C2×C22⋊C4—861no—
231C2×C22⋊C4—861no—
232C2×C22⋊C4—861no—
233C2×C22⋊C4—861no—
234C2×C22⋊C4C22⋊D4311yescharacteristic
235C2×C22⋊C4C22⋊D4311yescharacteristic
236C2×C42—431no—
237C2×C42—431no—
238C2×C42D17211yescharacteristic
239C2×C42D17211yescharacteristic
240C4⋊C8—864no—
241C22⋊C8—434no—
242C22⋊C8—862no—
243#97—862no—
244C4×C8—862no—
245#95—22no—
246#95—22no—
247#95—861no—
248#95—861no—
249#95—861no—
250C24—861no—
251C24C2×C22⋊D4311yescharacteristic
252C2×D4—862no—
253C2×D4—3441no—
254C2×D4—3441no—
255C2×D4—1721no—
256C2×D4—1721no—
257C2×D4—1722no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4—42no—
261C22×C4—861no—
262C22×C4—861no—
263C22×C4—861no—
264C22×C4(C2×D43)⋊C411yescharacteristic
265C22×C4(C2×D43)⋊C411yescharacteristic
266C22×C4(C2×D43)⋊C411yescharacteristic
267C22×C4(C2×D43)⋊C411yescharacteristic
268C22×C4C2×C4×D4311yescharacteristic
269C22×C4C2×D17211yescharacteristic
270C22×C4D4×D4312yes—
271C22×C4#1062190012yes—
272M16—1722no—
273M16—1722no—
274C2×C8—864no—
275C4⋊C4—22no—
276C4⋊C4—22no—
277C4⋊C4—862no—
278C4⋊C4—3441no—
279C4⋊C4—3441no—
280C22⋊C4—22no—
281C22⋊C4—22no—
282C22⋊C4—42no—
283C22⋊C4—42no—
284C22⋊C4—3441no—
285C22⋊C4—3441no—
286C22⋊C4—1722no—
287C22⋊C4—1722no—
288C22⋊C4—1722no—
289C22⋊C4—1721no—
290C22⋊C4—1721no—
291C42—21no—
292C42—21no—
293C42—21no—
294C42—21no—
295C42—1721no—
296C42—1721no—
297C23—21no—
298C23—21no—
299C23—41no—
300C23—41no—
301C23—1721no—
302C23—1721no—
303C23—1721no—
304C23—1721no—
305C23—1721no—
306C23—1721no—
307C23—1721no—
308C23C2×(C2×D43)⋊C411yescharacteristic
309C23#1306329712yes—
310D4—3442no—
311D4—3444no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—82no—
327C2×C4—82no—
328C2×C4—82no—
329C2×C4—862no—
330C2×C4—1721no—
331C2×C4—1721no—
332C2×C4—1721no—
333C2×C4—1721no—
334C2×C4—1721no—
335C2×C4—1721no—
336C2×C4—1721no—
337C2×C4—1721no—
338C2×C4(C22⋊D43)⋊C412yes—
339C2×C4#1306329511yescharacteristic
340C2×C4#1306330911yescharacteristic
341C8—1724no—
342C22—21no—
343C22—21no—
344C22—22no—
345C22—22no—
346C22—22no—
347C22—81no—
348C22—81no—
349C22—3441no—
350C22—3441no—
351C22—3441no—
352C22—3441no—
353C22—3441no—
354C22—3441no—
355C22—3441no—
356C22#1458277611yescharacteristic
357C22#1458287211yescharacteristic
358C22#1458287211yescharacteristic
359C4—21no—
360C4—22no—
361C4—21no—
362C4—41no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—162no—
367C4—3441no—
368C4—3441no—
369C4—1722no—
370C2—21no—
371C2—21no—
372C2—42no—
373C2—6881no—
374C2#1913497611yescharacteristic
375C2#1913505111yescharacteristic
376C2#1913512011yescharacteristic
subgroupG/H
centerC22#14582776
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1820C2
socleC22×C43#386
prime radicalC2×#13063299C22
cosocleC23×C4×C43C23
hypercenter#1820D43
hypocenterC43#9446
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1820

Complements

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

NH ≅ G/Ntype
1. #19143233C2semidirect
4. #19132447C2semidirect
5. C43×#1820C2semidirect
13. #14582800C4semidirect
14. #14582800C4semidirect
17. #14582768C4semidirect
18. #14582764C4semidirect
184. #1820D43semidirect
213. C43#9446semidirect

Maximal subgroups

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

subgroupindex
#191432332
#191390532
#191331232
#191324472
C43×#18202
#944643