Finite Group Databasebeta

← #24990132

Subgroups — #24990132

Order 11008.

438 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 87 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#19137212C211yesmaximal, characteristic
2#19132924C211yesmaximal, characteristic
3#19132924C211yesmaximal, characteristic
4#19132502C211yesmaximal, characteristic
5#19132501C211yesmaximal, characteristic
6#19132500C211yesmaximal, characteristic
7C43×#1305C211yesmaximal, characteristic
8C2×#13063281C411yescharacteristic
9C2×#13063281C411yescharacteristic
10C22×Dic43⋊C4C2211yescharacteristic
11#14582863C2211yescharacteristic
12#14582863C2211yescharacteristic
13#14582796—21no—
14#14582796—21no—
15#14582794—21no—
16#14582794—21no—
17#14582759C2211yescharacteristic
18#14582757C411yescharacteristic
19#14582757C411yescharacteristic
20#14582624—21no—
21#14582624—21no—
22#14582624—21no—
23#14582624—21no—
24C43×#407C2211yescharacteristic
25C43×#407C2211yescharacteristic
26C43×#380C2211yescharacteristic
27C23×Dic43C2×C411yescharacteristic
28C23×Dic43C2×C411yescharacteristic
29C2×#10621877—21no—
30C2×#10621877—21no—
31#13063281—42no—
32#13063281—42no—
33C2×C4⋊Dic43—21no—
34C2×Dic43⋊C4—21no—
35C2×Dic43⋊C4—21no—
36C2×Dic43⋊C4—21no—
37C2×Dic43⋊C4—21no—
38C2×Dic43⋊C4—21no—
39C2×Dic43⋊C4—21no—
40C2×Dic43⋊C4—21no—
41C2×Dic43⋊C4—21no—
42C2×Dic43⋊C4D411yescharacteristic
43C2×Dic43⋊C4D411yescharacteristic
44C2×Dic43⋊C4D411yescharacteristic
45C2×Dic43⋊C4D411yescharacteristic
46C2×C22⋊Dic43C2×C411yescharacteristic
47C2×C22⋊Dic43C2×C411yescharacteristic
48C2×C4×Dic43—21no—
49C2×C4×Dic43—21no—
50C22⋊(C43⋊C8)—21no—
51C22⋊(C43⋊C8)—21no—
52C22⋊(C43⋊C8)—21no—
53C22⋊(C43⋊C8)—21no—
54C43⋊#95—21no—
55C43⋊#95—21no—
56C43⋊#95—21no—
57C23×C4×C43C2311yescharacteristic
58C2×M16×C43—21no—
59C2×M16×C43—21no—
60C2×C4⋊C4×C43—21no—
61C2×C22⋊C4×C43C2×C411yescharacteristic
62C2×C22⋊C4×C43C2×C411yescharacteristic
63C22⋊C8×C43—21no—
64C22⋊C8×C43—21no—
65C22⋊C8×C43—21no—
66C22⋊C8×C43—21no—
67#95×C43—21no—
68C24×C43C22×C411yescharacteristic
69C22×C4×C43—21no—
70C22×C4×C43—21no—
71C22×C4×C43—81no—
72C22×C4×C43C2×D411yescharacteristic
73C22×C4×C43C2×D411yescharacteristic
74C22×C4×C43#4111yescharacteristic
75C22×C4×C43#4111yescharacteristic
76C22×C4×C43#4111yescharacteristic
77C22×C4×C43#4111yescharacteristic
78C22×Dic43—22no—
79C22×Dic43—22no—
80C22×Dic43—21no—
81C22×Dic43—21no—
82C22×Dic43—21no—
83C22×Dic43—21no—
84C22×Dic43—21no—
85C22×Dic43—21no—
86C22×Dic43—81no—
87C22×Dic43C22⋊C411yescharacteristic
88C22×Dic43C22⋊C411yescharacteristic
89C22×Dic43C22⋊C411yescharacteristic
90C22×Dic43C22⋊C411yescharacteristic
91M16×C43—81no—
92M16×C43—81no—
93C2×C8×C43—41no—
94C2×C8×C43—41no—
95C4⋊C4×C43—81no—
96C22⋊C4×C43—41no—
97C22⋊C4×C43—41no—
98C22⋊Dic43—41no—
99C22⋊Dic43—41no—
100C4⋊Dic43—81no—
101Dic43⋊C4—21no—
102Dic43⋊C4—21no—
103Dic43⋊C4—21no—
104Dic43⋊C4—21no—
105Dic43⋊C4—21no—
106Dic43⋊C4—21no—
107Dic43⋊C4—21no—
108Dic43⋊C4—21no—
109Dic43⋊C4—42no—
110Dic43⋊C4—42no—
111Dic43⋊C4—81no—
112Dic43⋊C4—81no—
113C4×Dic43—42no—
114C4×Dic43—42no—
115#10621877—81no—
116#10621877—81no—
117C2×C43⋊C8—41no—
118C2×C43⋊C8—41no—
119C23×C43—21no—
120C23×C43—21no—
121C23×C43—41no—
122C23×C43—41no—
123C23×C43C2×C22⋊C411yescharacteristic
124C23×C43#11711yescharacteristic
125C23×C43#11711yescharacteristic
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43—41no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43—41no—
138C2×C4×C43#12311yescharacteristic
139C2×C4×C43#12311yescharacteristic
140C2×C4×C43#12311yescharacteristic
141C2×C4×C43#12311yescharacteristic
142C2×Dic43—24no—
143C2×Dic43—24no—
144C2×Dic43—21no—
145C2×Dic43—21no—
146C2×Dic43—21no—
147C2×Dic43—21no—
148C2×Dic43—21no—
149C2×Dic43—21no—
150C2×Dic43—41no—
151C2×Dic43—41no—
152C2×Dic43—41no—
153C2×Dic43—41no—
154C2×Dic43—41no—
155C2×Dic43—41no—
156C2×Dic43—41no—
157C2×Dic43—41no—
158C2×Dic43—81no—
159C2×Dic43—81no—
160C2×Dic43#10012yes—
161C2×Dic43#10112yes—
162C8×C43—81no—
163C8×C43—81no—
164C43⋊C8—81no—
165C43⋊C8—81no—
166#8757—431nomaximal, Sylow
167C22×C43—21no—
168C22×C43—21no—
169C22×C43—21no—
170C22×C43—21no—
171C22×C43—21no—
172C22×C43—21no—
173C22×C43—21no—
174C22×C43—21no—
175C22×C43—42no—
176C22×C43—42no—
177C22×C43#38111yescharacteristic
178C22×C43C2×#10011yescharacteristic
179C22×C43C2×#10111yescharacteristic
180C4×C43—21no—
181C4×C43—21no—
182C4×C43—21no—
183C4×C43—21no—
184C4×C43—81no—
185C4×C43—81no—
186Dic43—22no—
187Dic43—22no—
188Dic43—41no—
189Dic43—41no—
190Dic43—81no—
191Dic43—81no—
192#2316—431no—
193#1463—431no—
194#1463—431no—
195#1305—431no—
196#1305—431no—
197#1305—431no—
198#1305D4311yescharacteristic
199C2×C43—21no—
200C2×C43—21no—
201C2×C43—41no—
202C2×C43—41no—
203C2×C43#182111yescharacteristic
204C2×C43#182811yescharacteristic
205C2×C43#183011yescharacteristic
206C2×#117—431no—
207C2×#117—431no—
208C22×C4⋊C4—431no—
209#407—431no—
210#407—431no—
211#407C2×D4311yescharacteristic
212#407C2×D4311yescharacteristic
213#389—861no—
214#389—861no—
215#389—861no—
216#389—861no—
217#380—431no—
218#380—431no—
219#380—431no—
220#380C2×D4311yescharacteristic
221#324—861no—
222#324—861no—
223#324—861no—
224#324—861no—
225C43#875711yescharacteristic, complemented, Sylow
226C23×C4—431no—
227C23×C4—431no—
228C23×C4C22×D4311yescharacteristic
229C2×M16—21no—
230C2×M16—21no—
231C2×M16—861no—
232C2×M16—861no—
233#117—1722no—
234#117—1722no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—431no—
237C2×C4⋊C4—431no—
238C2×C4⋊C4—431no—
239C2×C4⋊C4—431no—
240C2×C4⋊C4—861no—
241C2×C4⋊C4—861no—
242C2×C4⋊C4—861no—
243C2×C4⋊C4—861no—
244C2×C4⋊C4—861no—
245C2×C4⋊C4—861no—
246C2×C4⋊C4—861no—
247C2×C4⋊C4—861no—
248C2×C4⋊C4—861no—
249C2×C22⋊C4—431no—
250C2×C22⋊C4—431no—
251C2×C22⋊C4C4×D4311yescharacteristic
252C2×C22⋊C4C4×D4311yescharacteristic
253C2×C42—861no—
254C2×C42—861no—
255C22⋊C8—21no—
256C22⋊C8—21no—
257C22⋊C8—21no—
258C22⋊C8—21no—
259C22⋊C8—861no—
260C22⋊C8—861no—
261C22⋊C8—861no—
262C22⋊C8—861no—
263#95—21no—
264#95—861no—
265#95—861no—
266#95—861no—
267C24C2×C4×D4311yescharacteristic
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—81no—
271C22×C4—431no—
272C22×C4—431no—
273C22×C4—431no—
274C22×C4—431no—
275C22×C4—862no—
276C22×C4—862no—
277C22×C4—861no—
278C22×C4—861no—
279C22×C4—861no—
280C22×C4—861no—
281C22×C4—861no—
282C22×C4—861no—
283C22×C4—3441no—
284C22×C4#1062189811yescharacteristic
285C22×C4#1062189811yescharacteristic
286C22×C4D4×D4311yescharacteristic
287C22×C4D4×D4311yescharacteristic
288C22×C4#1062190011yescharacteristic
289C22×C4#1062190211yescharacteristic
290M16—81no—
291M16—81no—
292M16—3441no—
293M16—3441no—
294C2×C8—41no—
295C2×C8—41no—
296C2×C8—1721no—
297C2×C8—1721no—
298C4⋊C4—81no—
299C4⋊C4—861no—
300C4⋊C4—861no—
301C4⋊C4—861no—
302C4⋊C4—861no—
303C4⋊C4—861no—
304C4⋊C4—861no—
305C4⋊C4—861no—
306C4⋊C4—861no—
307C4⋊C4—3441no—
308C4⋊C4—3441no—
309C4⋊C4—3441no—
310C4⋊C4—1722no—
311C4⋊C4—1722no—
312C22⋊C4—41no—
313C22⋊C4—41no—
314C22⋊C4—1721no—
315C22⋊C4—1721no—
316C42—1722no—
317C42—1722no—
318C23—21no—
319C23—21no—
320C23—41no—
321C23—41no—
322C23C22⋊C4×D4311yescharacteristic
323C23#1306328211yescharacteristic
324C23#1306328311yescharacteristic
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—432no—
338C2×C4—432no—
339C2×C4—864no—
340C2×C4—864no—
341C2×C4—861no—
342C2×C4—861no—
343C2×C4—861no—
344C2×C4—861no—
345C2×C4—861no—
346C2×C4—861no—
347C2×C4—3441no—
348C2×C4—3441no—
349C2×C4—1721no—
350C2×C4—1721no—
351C2×C4—1721no—
352C2×C4—1721no—
353C2×C4—1721no—
354C2×C4—1721no—
355C2×C4—1721no—
356C2×C4—1721no—
357C2×C4#1306330711yescharacteristic
358C2×C4#1306330711yescharacteristic
359C2×C4#1306331011yescharacteristic
360C2×C4#1306331011yescharacteristic
361C8—81no—
362C8—81no—
363C8—3441no—
364C8—3441no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—42no—
374C22—42no—
375C22#1458276111yescharacteristic
376C22#100×D4311yescharacteristic
377C22#101×D4311yescharacteristic
378C4—21no—
379C4—21no—
380C4—21no—
381C4—21no—
382C4—81no—
383C4—81no—
384C4—862no—
385C4—862no—
386C4—3441no—
387C4—3441no—
388C4—1721no—
389C4—1721no—
390C2—21no—
391C2—21no—
392C2—41no—
393C2—41no—
394C2#1913467411yescharacteristic
395C2#1913470211yescharacteristic
396C2#1913470811yescharacteristic
subgroupG/H
centerC22#14582761
commutator, prime radicalC24×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1305C2
socleC22×C43#381
cosocleC23×C4×C43C23
hypercenter#1305D43
hypocenterC43#8757
LCSG ▷ C24×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1305

Complements

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

NH ≅ G/Ntype
225. C43#8757semidirect

Maximal subgroups

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

subgroupindex
#191372122
#191329242
#191325022
#191325012
#191325002
C43×#13052
#875743