Finite Group Databasebeta

← #24992640

Subgroups — #24992640

Order 11008.

684 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 684 conjugacy classes of subgroups — too many to draw. Only its 131 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#19140400C211yesmaximal, characteristic
2#19133166C212yesmaximal, complemented
3C2×#14582623C211yesmaximal, characteristic
4#19132462C212yesmaximal, complemented
5C43×#2315C211yesmaximal, characteristic
6C2×#13063304C2211yescharacteristic
7C2×C22⋊(C43⋊C8)C2212yes—
8#14582835C412yescomplemented
9#14582822—22no—
10#14582811C412yescomplemented
11#14582772—21no—
12#14582759C2211yescharacteristic
13#14582755—21no—
14#14582635—24no—
15#14582623—22no—
16C22×C22⋊C4×C43—21no—
17C22×C22⋊C4×C43C2211yescharacteristic
18C43×#385—24no—
19C43×#380—21no—
20C43×#380C2212yes—
21C22×Dic86C2×C411yescharacteristic, complemented
22C22×C43⋊C8—22no—
23#13063304—22no—
24#13063304—22no—
25C2×C4⋊Dic43—21no—
26C2×C4⋊Dic43C2×C411yescharacteristic, complemented
27C2×Dic43⋊C4—21no—
28C2×Dic43⋊C4—22no—
29C2×C22⋊Dic43—21no—
30C2×C22⋊Dic43—21no—
31C2×C22⋊Dic43—22no—
32C2×C22⋊Dic43—22no—
33C22⋊(C43⋊C8)—22no—
34C22⋊(C43⋊C8)—22no—
35C43⋊#95—22no—
36C43⋊#95C2×C412yescomplemented
37C25×C43D411yescharacteristic
38C23×C4×C43—22no—
39C23×C4×C43D411yescharacteristic
40C23×C4×C43C2311yescharacteristic
41C2×C4⋊C4×C43—22no—
42C2×C4⋊C4×C43—22no—
43C2×C22⋊C4×C43—22no—
44C2×C22⋊C4×C43—22no—
45C2×C22⋊C4×C43—22no—
46C2×C22⋊C4×C43—22no—
47C2×C22⋊C4×C43—42no—
48C2×C22⋊C4×C43—42no—
49C2×C22⋊C4×C43C2×C412yes—
50C2×C22⋊C4×C43D412yes—
51#95×C43—22no—
52#95×C43D414yes—
53C24×C43—21no—
54C24×C43—21no—
55C24×C43—21no—
56C24×C43—21no—
57C24×C43—81no—
58C24×C43—81no—
59C24×C43C22⋊C412yes—
60C24×C43SD1612yes—
61C24×C43Q1612yes—
62C24×C43C2×D411yescharacteristic
63C22×C4×C43—21no—
64C22×C4×C43—24no—
65C22×C4×C43—21no—
66C22×C4×C43—44no—
67C22×C4×C43—81no—
68C22×C4×C43—81no—
69C22×C4×C43—82no—
70C22×C4×C43—82no—
71C22×C4×C43C22⋊C412yes—
72C22×C4×C43C22×C411yescharacteristic
73C22×C4×C43C2×D411yescharacteristic
74C22×C4×C43C2×D412yes—
75C22×C4×C43#4112yes—
76C22×Dic43—21no—
77C22×Dic43—22no—
78C22×Dic43—21no—
79C2×Dic86—22no—
80C2×Dic86—81no—
81C4⋊C4×C43—82no—
82C4⋊C4×C43—82no—
83C22⋊C4×C43—24no—
84C22⋊C4×C43—24no—
85C22⋊C4×C43—44no—
86C22⋊C4×C43—42no—
87C22⋊C4×C43—42no—
88C22⋊Dic43—41no—
89C22⋊Dic43—41no—
90C22⋊Dic43—41no—
91C22⋊Dic43—41no—
92C22⋊Dic43—82no—
93C22⋊Dic43—82no—
94C4⋊Dic43—22no—
95C4⋊Dic43—81no—
96Dic43⋊C4—42no—
97Dic43⋊C4—82no—
98C2×C43⋊C8—42no—
99C2×C43⋊C8—82no—
100C23×C43—22no—
101C23×C43—22no—
102C23×C43—22no—
103C23×C43—22no—
104C23×C43—22no—
105C23×C43—22no—
106C23×C43—41no—
107C23×C43—41no—
108C23×C43—42no—
109C23×C43—42no—
110C23×C43—42no—
111C23×C43—42no—
112C23×C43—81no—
113C23×C43—81no—
114C23×C43—82no—
115C23×C43—82no—
116C23×C43—82no—
117C23×C43—82no—
118C23×C43#10314yes—
119C23×C43C2×C22⋊C411yescharacteristic
120C23×C43#12011yescharacteristic
121C23×C43#12311yescharacteristic
122C23×C43C2×SD1611yescharacteristic
123C23×C43C2×Q1611yescharacteristic
124C23×C43AGL(1,ℤ/8)11yescharacteristic
125C23×C43#13711yescharacteristic
126C2×C4×C43—22no—
127C2×C4×C43—42no—
128C2×C4×C43—41no—
129C2×C4×C43—42no—
130C2×C4×C43—41no—
131C2×C4×C43—42no—
132C2×C4×C43—42no—
133C2×C4×C43—44no—
134C2×C4×C43—44no—
135C2×C4×C43—44no—
136C2×C4×C43—81no—
137C2×C4×C43—88no—
138C2×C4×C43C4×D412yes—
139C2×C4×C43#12112yes—
140C2×Dic43—42no—
141C2×Dic43—42no—
142C2×Dic43—42no—
143C2×Dic43—42no—
144C2×Dic43—41no—
145C2×Dic43—41no—
146C2×Dic43—42no—
147Dic86—82no—
148C43⋊C8—82no—
149#9199—431nomaximal, Sylow
150C22×C43—21no—
151C22×C43—21no—
152C22×C43—21no—
153C22×C43—21no—
154C22×C43—21no—
155C22×C43—21no—
156C22×C43—24no—
157C22×C43—41no—
158C22×C43—41no—
159C22×C43—41no—
160C22×C43—41no—
161C22×C43—44no—
162C22×C43—44no—
163C22×C43—44no—
164C22×C43—42no—
165C22×C43—42no—
166C22×C43—82no—
167C22×C43—82no—
168C22×C43—82no—
169C22×C43#38611yescharacteristic
170C22×C43C2×#10311yescharacteristic
171C22×C43#41711yescharacteristic
172C22×C43#45011yescharacteristic
173C22×C43#45111yescharacteristic
174C22×C43#48311yescharacteristic
175C22×C43#48411yescharacteristic
176C4×C43—22no—
177C4×C43—22no—
178C4×C43—42no—
179C4×C43—84no—
180Dic43—82no—
181Dic43—81no—
182Dic43—81no—
183#2626—431no—
184#2315D4311yescharacteristic
185#1520—432no—
186C2×#323—431no—
187#1289—432no—
188C2×C43—21no—
189C2×C43—21no—
190C2×C43—21no—
191C2×C43—21no—
192C2×C43—21no—
193C2×C43—21no—
194C2×C43—44no—
195C2×C43#187211yescharacteristic
196C2×C43#191111yescharacteristic
197C2×C43#191311yescharacteristic
198C2×C22⋊Q8—431no—
199C22×C22⋊C4—21no—
200C22×C22⋊C4C2×D4311yescharacteristic
201C2×C22⋊C8—432no—
202#399—432no—
203#396—862no—
204#393—432no—
205#385—24no—
206#385—861no—
207#380—21no—
208#380—431no—
209#380C2×D4312yes—
210#379—861no—
211#328—864no—
212#323—862no—
213C43#919911yescharacteristic, complemented, Sylow
214C25C22⋊D4311yescharacteristic
215C22×Q8—431no—
216C23×C4—22no—
217C23×C4C22⋊D4311yescharacteristic
218C23×C4C22×D4311yescharacteristic
219C22×C8—862no—
220C22⋊Q8—862no—
221C22⋊Q8—862no—
222C2×C4⋊C4—22no—
223C2×C4⋊C4—22no—
224C2×C4⋊C4—431no—
225C2×C4⋊C4—862no—
226C2×C4⋊C4—861no—
227C2×C4⋊C4—861no—
228C2×C22⋊C4—22no—
229C2×C22⋊C4—22no—
230C2×C22⋊C4—22no—
231C2×C22⋊C4—22no—
232C2×C22⋊C4—42no—
233C2×C22⋊C4—42no—
234C2×C22⋊C4—862no—
235C2×C22⋊C4—862no—
236C2×C22⋊C4—861no—
237C2×C22⋊C4—861no—
238C2×C22⋊C4C4×D4312yes—
239C2×C22⋊C4D17212yes—
240C22⋊C8—862no—
241C22⋊C8—862no—
242#95—22no—
243#95—432no—
244#95—862no—
245#95C22⋊D4314yes—
246C24—21no—
247C24—21no—
248C24—21no—
249C24—21no—
250C24—81no—
251C24—81no—
252C24(C2×D43)⋊C412yes—
253C24#1062188312yes—
254C24#1062188512yes—
255C24C2×C22⋊D4311yescharacteristic
256C2×Q8—862no—
257C2×Q8—3441no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—24no—
261C22×C4—44no—
262C22×C4—81no—
263C22×C4—81no—
264C22×C4—82no—
265C22×C4—82no—
266C22×C4—862no—
267C22×C4—861no—
268C22×C4—861no—
269C22×C4(C2×D43)⋊C412yes—
270C22×C4C2×C4×D4311yescharacteristic
271C22×C4C2×D17211yescharacteristic
272C22×C4#1062189812yes—
273C22×C4C2×C22⋊D4312yes—
274C2×C8—3442no—
275C2×C8—1722no—
276C4⋊C4—82no—
277C4⋊C4—82no—
278C4⋊C4—862no—
279C4⋊C4—3442no—
280C4⋊C4—3441no—
281C4⋊C4—1722no—
282C22⋊C4—24no—
283C22⋊C4—24no—
284C22⋊C4—44no—
285C22⋊C4—42no—
286C22⋊C4—42no—
287C22⋊C4—3442no—
288C22⋊C4—3442no—
289C22⋊C4—1721no—
290C22⋊C4—1721no—
291C22⋊C4—1721no—
292C22⋊C4—1721no—
293C23—22no—
294C23—22no—
295C23—22no—
296C23—22no—
297C23—22no—
298C23—22no—
299C23—41no—
300C23—41no—
301C23—42no—
302C23—42no—
303C23—42no—
304C23—42no—
305C23—81no—
306C23—81no—
307C23—82no—
308C23—82no—
309C23—82no—
310C23—82no—
311C23#1306324814yes—
312C23C2×(C2×D43)⋊C411yescharacteristic
313C23#1306329411yescharacteristic
314C23#1306330811yescharacteristic
315C23C2×#1062188311yescharacteristic
316C23C2×#1062188511yescharacteristic
317C23#1306335111yescharacteristic
318C23#1306335611yescharacteristic
319Q8—3442no—
320C2×C4—22no—
321C2×C4—42no—
322C2×C4—41no—
323C2×C4—42no—
324C2×C4—41no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—44no—
328C2×C4—44no—
329C2×C4—44no—
330C2×C4—81no—
331C2×C4—88no—
332C2×C4—1722no—
333C2×C4—1722no—
334C2×C4—1722no—
335C2×C4—1722no—
336C2×C4—1722no—
337C2×C4—1721no—
338C2×C4—1721no—
339C2×C4C4×C22⋊D4312yes—
340C2×C4#1306329912yes—
341C8—3442no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—24no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—44no—
354C22—44no—
355C22—44no—
356C22—42no—
357C22—42no—
358C22—82no—
359C22—82no—
360C22—82no—
361C22#1458277811yescharacteristic
362C22C2×#1306324811yescharacteristic
363C22#1458289811yescharacteristic
364C22#1458305011yescharacteristic
365C22#1458305511yescharacteristic
366C22#1458322911yescharacteristic
367C22#1458323411yescharacteristic
368C4—22no—
369C4—22no—
370C4—42no—
371C4—84no—
372C4—3442no—
373C4—3441no—
374C4—3441no—
375C2—21no—
376C2—21no—
377C2—21no—
378C2—21no—
379C2—21no—
380C2—21no—
381C2—44no—
382C2#1913490211yescharacteristic
383C2#1913512711yescharacteristic
384C2#1913513711yescharacteristic
subgroupG/H
centerC22#14582778
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#2315C2
socleC22×C43#386
prime radicalC25×C43D4
cosocleC23×C4×C43C23
hypercenter#2315D43
hypocenterC43#9199
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2315

Complements

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

NH ≅ G/Ntype
2. #19133166C2semidirect
4. #19132462C2semidirect
8. #14582835C4semidirect
10. #14582811C4semidirect
21. C22×Dic86C2×C4semidirect
26. C2×C4⋊Dic43C2×C4semidirect
36. C43⋊#95C2×C4semidirect
213. C43#9199semidirect

Maximal subgroups

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

subgroupindex
#191404002
#191331662
C2×#145826232
#191324622
C43×#23152
#919943