Finite Group Databasebeta

← #24999946

Subgroups — #24999946

Order 11008.

620 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 113 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#19140709C211yesmaximal, characteristic
2#19134900C212yesmaximal
3C2×#14582637C212yesmaximal
4#19132859C211yesmaximal, characteristic
5C43×#1280C211yesmaximal, characteristic
6C2×#13063304C2212yes—
7C22×C4⋊Dic43C2211yescharacteristic
8C22×Dic43⋊C4—21no—
9C2×#13063250—22no—
10#14582831—22no—
11#14582820—22no—
12#14582759—21no—
13#14582759—21no—
14C2×C43⋊#95—21no—
15C2×C43⋊#95C2211yescharacteristic
16#14582662—22no—
17#14582637—24no—
18C2×C22⋊C8×C43C2212yes—
19C2×#95×C43C2211yescharacteristic
20C22×Dic86D412yes—
21C23×Dic43—21no—
22C23×Dic43—21no—
23#13063304—22no—
24#13063304—22no—
25#13063304—22no—
26#13063304—22no—
27C2×C4⋊Dic43—22no—
28C2×C4⋊Dic43—21no—
29C2×C4⋊Dic43—21no—
30C2×C4⋊Dic43—21no—
31C2×C4⋊Dic43—21no—
32C2×C4⋊Dic43—42no—
33C2×C4⋊Dic43D412yes—
34C2×Dic43⋊C4—22no—
35C2×Dic43⋊C4—42no—
36C2×Dic43⋊C4—42no—
37C2×Dic43⋊C4—42no—
38C2×C22⋊Dic43—22no—
39#13063250—44no—
40C43⋊#95—22no—
41C43⋊#95—22no—
42C43⋊#95—21no—
43C43⋊#95—42no—
44C43⋊#95D412yes—
45C23×C4×C43D411yescharacteristic
46C23×C4×C43D411yescharacteristic
47C23×C4×C43C2311yescharacteristic
48C22×C8×C43—22no—
49C22⋊C8×C43—22no—
50C22⋊C8×C43—22no—
51#95×C43—22no—
52C24×C43C2×D411yescharacteristic
53C22×C4×C43—21no—
54C22×C4×C43—21no—
55C22×C4×C43—21no—
56C22×C4×C43—21no—
57C22×C4×C43—41no—
58C22×C4×C43—41no—
59C22×C4×C43—41no—
60C22×C4×C43—41no—
61C22×C4×C43—41no—
62C22×C4×C43—41no—
63C22×C4×C43SD1612yes—
64C22×C4×C43Q1612yes—
65C22×C4×C43C2×D412yes—
66C22×C4×C43C2×D411yescharacteristic
67C22×C4×C43#4111yescharacteristic
68C22×C4×C43#4112yes—
69C22×Dic43—22no—
70C22×Dic43—22no—
71C22×Dic43—22no—
72C22×Dic43—22no—
73C22×Dic43—22no—
74C22×Dic43—22no—
75C22×Dic43—41no—
76C22×Dic43—41no—
77C22×Dic43—41no—
78C22×Dic43—41no—
79C22×Dic43—41no—
80C22×Dic43—41no—
81C22×Dic43—41no—
82C22×Dic43—41no—
83C22×Dic43—41no—
84C22×Dic43—41no—
85C2×Dic86—22no—
86C2×Dic86—22no—
87C2×Dic86—42no—
88C2×Dic86—42no—
89C2×C8×C43—42no—
90C2×C8×C43—42no—
91C2×C8×C43—42no—
92C22⋊Dic43—42no—
93C22⋊Dic43—42no—
94C4⋊Dic43—24no—
95C4⋊Dic43—22no—
96C4⋊Dic43—22no—
97C4⋊Dic43—42no—
98C4⋊Dic43—81no—
99C4⋊Dic43—81no—
100C4⋊Dic43—81no—
101C4⋊Dic43—81no—
102Dic43⋊C4—48no—
103Dic43⋊C4—42no—
104Dic43⋊C4—42no—
105C23×C43—21no—
106C23×C43—21no—
107C23×C43—21no—
108C23×C43—21no—
109C23×C43#12011yescharacteristic
110C23×C43#12111yescharacteristic
111C23×C43#12411yescharacteristic
112C23×C43C2×SD1611yescharacteristic
113C23×C43C2×Q1611yescharacteristic
114C23×C43#13711yescharacteristic
115C23×C43#13711yescharacteristic
116C2×C4×C43—22no—
117C2×C4×C43—22no—
118C2×C4×C43—22no—
119C2×C4×C43—22no—
120C2×C4×C43—41no—
121C2×C4×C43—42no—
122C2×C4×C43—41no—
123C2×C4×C43—41no—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43—42no—
128C2×C4×C43—42no—
129C2×C4×C43—81no—
130C2×C4×C43—81no—
131C2×C4×C43#12112yes—
132C2×C4×C43#12312yes—
133C2×Dic43—24no—
134C2×Dic43—42no—
135C2×Dic43—42no—
136C2×Dic43—42no—
137C2×Dic43—42no—
138C2×Dic43—42no—
139C2×Dic43—42no—
140C2×Dic43—42no—
141C2×Dic43—42no—
142C2×Dic43—42no—
143C2×Dic43—42no—
144C2×Dic43—42no—
145C2×Dic43—42no—
146C2×Dic43—42no—
147C2×Dic43—42no—
148C2×Dic43—42no—
149C2×Dic43—81no—
150C2×Dic43—81no—
151C2×Dic43—81no—
152C2×Dic43—81no—
153Dic86—44no—
154Dic86—82no—
155C8×C43—82no—
156#10406—431nomaximal, Sylow
157C22×C43—21no—
158C22×C43—21no—
159C22×C43—21no—
160C22×C43—21no—
161C22×C43—21no—
162C22×C43—21no—
163C22×C43—21no—
164C22×C43—21no—
165C22×C43—21no—
166C22×C43—21no—
167C22×C43—21no—
168C22×C43—21no—
169C22×C43#39411yescharacteristic
170C22×C43#44811yescharacteristic
171C22×C43#45111yescharacteristic
172C22×C43#45311yescharacteristic
173C22×C43#45611yescharacteristic
174C22×C43B(4,𝔽2)11yescharacteristic
175C22×C43#45811yescharacteristic
176C22×C43#46111yescharacteristic
177C22×C43#46211yescharacteristic
178C22×C43#48711yescharacteristic
179C22×C43#49111yescharacteristic
180C4×C43—22no—
181C4×C43—22no—
182C4×C43—42no—
183C4×C43—42no—
184Dic43—44no—
185Dic43—82no—
186Dic43—82no—
187Dic43—82no—
188#2659—431no—
189#1872—432no—
190C2×#328—432no—
191#1444—431no—
192#1280D4311yescharacteristic
193C2×C43—21no—
194C2×C43—21no—
195C2×C43—21no—
196C2×C43—21no—
197C2×C43#159611yescharacteristic
198C2×C43#160511yescharacteristic
199C2×C43#161111yescharacteristic
200C2×C43#161411yescharacteristic
201C2×C43#203911yescharacteristic
202C2×C43#204311yescharacteristic
203C2×C43#204411yescharacteristic
204C2×C22⋊Q8—432no—
205C22×C4⋊C4—431no—
206C22×C4⋊C4—861no—
207C2×#103—862no—
208C2×C22⋊C8C2×D4312yes—
209#398—862no—
210#395—862no—
211#380—861no—
212#380—861no—
213C2×#95—431no—
214C2×#95—861no—
215C2×#95C2×D4311yescharacteristic
216#340—862no—
217#328—864no—
218C43#1040611yescharacteristic, complemented, Sylow
219C22×Q8—432no—
220C23×C4—861no—
221C23×C4—861no—
222C23×C4D17211yescharacteristic
223C23×C4D17211yescharacteristic
224C23×C4C22×D4311yescharacteristic
225C22×C8—22no—
226C22⋊Q8—862no—
227C22⋊Q8—862no—
228C22⋊Q8—862no—
229C22⋊Q8—862no—
230C2×C4⋊C4—432no—
231C2×C4⋊C4—862no—
232C2×C4⋊C4—861no—
233C2×C4⋊C4—861no—
234C2×C4⋊C4—861no—
235C2×C4⋊C4—861no—
236C2×C4⋊C4—862no—
237C2×C4⋊C4—1722no—
238C2×C4⋊C4—1722no—
239C2×C4⋊C4—1722no—
240C2×C4⋊C4—1722no—
241C2×C22⋊C4—862no—
242#103—1724no—
243C22⋊C8—22no—
244C22⋊C8—22no—
245#95—22no—
246#95—432no—
247#95—862no—
248#95—862no—
249#95—861no—
250#95—1722no—
251C24C2×D17211yescharacteristic
252C2×Q8—862no—
253C2×Q8—862no—
254C2×Q8—1722no—
255C2×Q8—1722no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—862no—
267C22×C4—862no—
268C22×C4—862no—
269C22×C4—862no—
270C22×C4—862no—
271C22×C4—862no—
272C22×C4—1721no—
273C22×C4—1721no—
274C22×C4—1721no—
275C22×C4—1721no—
276C22×C4—1721no—
277C22×C4—1721no—
278C22×C4—1721no—
279C22×C4—1721no—
280C22×C4—1721no—
281C22×C4—1721no—
282C22×C4#1062187312yes—
283C22×C4Dic17212yes—
284C22×C4#1062189812yes—
285C22×C4D4×D4312yes—
286C22×C4D4×D4311yescharacteristic
287C22×C4#1062190211yescharacteristic
288C2×C8—42no—
289C2×C8—42no—
290C2×C8—42no—
291C4⋊C4—864no—
292C4⋊C4—862no—
293C4⋊C4—862no—
294C4⋊C4—3441no—
295C4⋊C4—3441no—
296C4⋊C4—3441no—
297C4⋊C4—3441no—
298C4⋊C4—1722no—
299C4⋊C4—1728no—
300C4⋊C4—1722no—
301C4⋊C4—1722no—
302C22⋊C4—1722no—
303C22⋊C4—1722no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23#1306329511yescharacteristic
309C23#1306330011yescharacteristic
310C23#1306331311yescharacteristic
311C23C2×#1062187311yescharacteristic
312C23C2×Dic17211yescharacteristic
313C23#1306335811yescharacteristic
314C23#1306335811yescharacteristic
315Q8—3442no—
316Q8—1724no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—42no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4—864no—
333C2×C4—3441no—
334C2×C4—3441no—
335C2×C4—3441no—
336C2×C4—3441no—
337C2×C4—1722no—
338C2×C4—1722no—
339C2×C4—1722no—
340C2×C4—1722no—
341C2×C4—1722no—
342C2×C4—1722no—
343C2×C4—1722no—
344C2×C4—1722no—
345C2×C4—1722no—
346C2×C4—1722no—
347C2×C4—1722no—
348C2×C4—1722no—
349C2×C4—1722no—
350C2×C4—1722no—
351C2×C4—1722no—
352C2×C4#1306329812yes—
353C2×C4#1306331012yes—
354C8—82no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22#1458281711yescharacteristic
368C22#1458304011yescharacteristic
369C22#1458305711yescharacteristic
370C22#1458306911yescharacteristic
371C22#1458308411yescharacteristic
372C22#1458308711yescharacteristic
373C22#1458309011yescharacteristic
374C22#1458310511yescharacteristic
375C22#1458311011yescharacteristic
376C22#1458325011yescharacteristic
377C22#1458326811yescharacteristic
378C4—22no—
379C4—22no—
380C4—42no—
381C4—42no—
382C4—3442no—
383C4—3442no—
384C4—3442no—
385C4—1724no—
386C2—21no—
387C2—21no—
388C2—21no—
389C2—21no—
390C2#1913352011yescharacteristic
391C2#1913357111yescharacteristic
392C2#1913360511yescharacteristic
393C2#1913362211yescharacteristic
394C2#1913582011yescharacteristic
395C2#1913584211yescharacteristic
396C2#1913584711yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#1280C2
socleC23×C43#120
prime radicalC24×C43C2×D4
hypercenter#1280D43
hypocenterC43#10406
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

Complements

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

NH ≅ G/Ntype
218. C43#10406semidirect

Maximal subgroups

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

subgroupindex
#191407092
#191349002
C2×#145826372
#191328592
C43×#12802
#1040643