Finite Group Databasebeta

← #25012901

Subgroups — #25012901

Order 11008.

420 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#427×D43C211yesmaximal, characteristic
2#19136205C211yesmaximal, characteristic
3#19134617C211yesmaximal, characteristic
4#19132702C211yesmaximal, characteristic, complemented
5#19132701C211yesmaximal, characteristic, complemented
6#19132700C211yesmaximal, characteristic, complemented
7C43×#1386C211yesmaximal, characteristic, complemented
8C22×C8×D43C2211yescharacteristic
9#117×D43—21no—
10C2×#13063265C2211yescharacteristic
11#14582937C2211yescharacteristic
12#14582936C411yescharacteristic, complemented
13#14582936C411yescharacteristic, complemented
14#14582935—21no—
15#14582934—21no—
16#107×D43C411yescharacteristic, complemented
17#107×D43C411yescharacteristic, complemented
18C2×#13063257C2211yescharacteristic
19#106×D43—21no—
20#14582756—21no—
21(C2×D43)⋊C16—21no—
22(C2×D43)⋊C16—21no—
23#14582661—21no—
24C2×M32×C43C2211yescharacteristic
25C43×#427C2211yescharacteristic
26C2×#106×C43C2211yescharacteristic
27C22×C4×D43D411yescharacteristic
28C22×C43⋊C8D411yescharacteristic
29C2×C8×D43—21no—
30C2×C8×D43—21no—
31C2×C8×D43—21no—
32C2×C8×D43—21no—
33C2×C8×D43C2×C411yescharacteristic
34C2×C8×D43C2×C411yescharacteristic
35C2×C8×D43D411yescharacteristic
36C2×C8×D43D411yescharacteristic
37#13063284—21no—
38#13063283—21no—
39#13063283—21no—
40#13063282—41no—
41#13063281—41no—
42C2×C4⋊Dic43—21no—
43C4⋊C4×D43—21no—
44C4⋊C4×D43—21no—
45C2×(C2×D43)⋊C4—41no—
46C22⋊C4×D43—41no—
47C42×D43—41no—
48#13063265—21no—
49#13063265—21no—
50C2×C43⋊C16—21no—
51#13063259C2×C411yescharacteristic
52#13063259C2×C411yescharacteristic
53#13063258—21no—
54#13063258—21no—
55#13063257—21no—
56#13063257—21no—
57#13063257—21no—
58#13063256—21no—
59#13063256—21no—
60C43⋊#95—41no—
61C22×C8×C43C2311yescharacteristic
62#117×C43—21no—
63C2×C4⋊C4×C43—21no—
64M32×C43—21no—
65M32×C43—21no—
66C2×C16×C43—21no—
67#107×C43C2×C411yescharacteristic
68#107×C43C2×C411yescharacteristic
69#106×C43—21no—
70#106×C43—21no—
71#106×C43—21no—
72C23×D43D811yescharacteristic
73C22×C4×C43—41no—
74C22×C4×C43C2×D411yescharacteristic
75C22×Dic43—41no—
76C22×Dic43D811yescharacteristic
77C2×C4×D43—21no—
78C2×C4×D43—21no—
79C2×C4×D43—21no—
80C2×C4×D43—21no—
81C2×C4×D43—41no—
82C2×C4×D43—41no—
83C2×C4×D43C22⋊C411yescharacteristic
84C2×C4×D43C22⋊C411yescharacteristic
85C2×C4×D43SD1611yescharacteristic
86C2×C4×D43SD1611yescharacteristic
87C2×C8×C43C22×C411yescharacteristic
88C2×C8×C43C2×D411yescharacteristic
89C2×C8×C43#4111yescharacteristic
90C2×C8×C43#4111yescharacteristic
91C2×C8×C43#4111yescharacteristic
92C2×C8×C43#4111yescharacteristic
93C4⋊C4×C43—21no—
94C4⋊C4×C43—21no—
95C4⋊C4×C43—41no—
96C4⋊C4×C43—41no—
97C22⋊C4×C43—41no—
98C42×C43—41no—
99C22⋊Dic43—41no—
100(C2×D43)⋊C4—41no—
101(C2×D43)⋊C4—41no—
102(C2×D43)⋊C4—82no—
103C4⋊Dic43—21no—
104C4⋊Dic43—21no—
105C4⋊Dic43—41no—
106C4⋊Dic43—41no—
107Dic43⋊C4—41no—
108Dic43⋊C4—41no—
109C4×Dic43—41no—
110C4×Dic43—41no—
111C4×Dic43—41no—
112C2×C43⋊C8—21no—
113C2×C43⋊C8—21no—
114C2×C43⋊C8C22⋊C411yescharacteristic
115C2×C43⋊C8C22⋊C411yescharacteristic
116C8×D43—21no—
117C8×D43—21no—
118C8×D43—21no—
119C8×D43—21no—
120C8×D43—21no—
121C8×D43—21no—
122C8×D43—21no—
123C8×D43—21no—
124C16×C43—41no—
125C43⋊C16—41no—
126C23×C43C2×D811yescharacteristic
127C22×D43—21no—
128C22×D43—21no—
129C22×D43—22no—
130C22×D43—41no—
131C22×D43#10211yescharacteristic
132C22×D43#10211yescharacteristic
133C2×C4×C43—41no—
134C2×C4×C43—41no—
135C2×C4×C43—81no—
136C2×C4×C43—81no—
137C2×C4×C43—81no—
138C2×C4×C43C2×C22⋊C411yescharacteristic
139C2×C4×C43#12311yescharacteristic
140C2×C4×C43#12311yescharacteristic
141C2×C4×C43C2×SD1611yescharacteristic
142C2×C4×C43#13711yescharacteristic
143C2×C4×C43#13711yescharacteristic
144C2×Dic43—21no—
145C2×Dic43—21no—
146C2×Dic43—41no—
147C2×Dic43—41no—
148C2×Dic43—81no—
149C2×Dic43—81no—
150C2×Dic43—81no—
151C2×Dic43#10211yescharacteristic
152C2×Dic43#10211yescharacteristic
153C4×D43—21no—
154C4×D43—21no—
155C4×D43—21no—
156C4×D43—21no—
157C4×D43—21no—
158C4×D43—21no—
159C4×D43—21no—
160C4×D43—21no—
161C4×D43—82no—
162C4×D43—82no—
163C8×C43#11711yescharacteristic
164C8×C43#11711yescharacteristic
165C8×C43#12311yescharacteristic
166C8×C43#12311yescharacteristic
167C43⋊C8—21no—
168C43⋊C8—21no—
169#12870—431nomaximal, Sylow
170C22×C43—21no—
171C22×C43—21no—
172C22×C43C2×#10211yescharacteristic
173C22×C43#48011yescharacteristic
174C22×C43#48011yescharacteristic
175C2×D43—21no—
176C2×D43—21no—
177C2×D43—21no—
178C2×D43—21no—
179C2×D43—21no—
180C2×D43—42no—
181C2×D43—42no—
182C2×D43#36012yes—
183C4×C43—81no—
184C4×C43—81no—
185C4×C43—161no—
186C4×C43#38111yescharacteristic
187C4×C43#41911yescharacteristic
188C4×C43#48311yescharacteristic
189C4×C43#48311yescharacteristic
190Dic43—21no—
191Dic43—21no—
192Dic43—81no—
193Dic43—81no—
194Dic43—161no—
195C2×#427—431no—
196#2112—431no—
197#1807—431no—
198#1386—431no—
199#1386—431no—
200#1386—431no—
201#1386D4311yescharacteristic, complemented
202C2×C43—21no—
203C2×C43—21no—
204C2×C43#182311yescharacteristic
205C2×C43C2×#36011yescharacteristic
206C2×C43#214511yescharacteristic
207D43—22no—
208D43—41no—
209C23×C8—431no—
210C2×#117—861no—
211C2×M32—431no—
212C2×M32C2×D4311yescharacteristic
213#427—431no—
214#427—431no—
215#427—431no—
216#427—861no—
217#427—861no—
218#427C2×D4311yescharacteristic
219C2×#107—431no—
220C2×#107—431no—
221C2×#106—431no—
222C2×#106—861no—
223C2×#106C2×D4311yescharacteristic
224#380—861no—
225C22⋊C16—861no—
226C22⋊C16—861no—
227#340—861no—
228C43#1287011yescharacteristic, complemented, Sylow
229C23×C4—431no—
230C22×C8—431no—
231C22×C8—431no—
232C22×C8—431no—
233C22×C8—431no—
234C22×C8—431no—
235C22×C8—861no—
236C22×C8—861no—
237C22×C8—861no—
238C22×C8—861no—
239C22×C8C22×D4311yescharacteristic
240#117—21no—
241#117—861no—
242#117—861no—
243#117—861no—
244#117—1721no—
245#117—1721no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—861no—
248C2×C4⋊C4—861no—
249C2×C4⋊C4—861no—
250C2×C22⋊C4—1721no—
251C2×C22⋊C4—1721no—
252C2×C42—1721no—
253M32—21no—
254M32—21no—
255M32—861no—
256M32—861no—
257C2×C16—21no—
258C2×C16—861no—
259#107—431no—
260#107—431no—
261#107—861no—
262#107—861no—
263#107C4×D4311yescharacteristic
264#107C4×D4311yescharacteristic
265#106—21no—
266#106—21no—
267#106—21no—
268#106—861no—
269#106—861no—
270#106—861no—
271#106—861no—
272#106—861no—
273#95—1721no—
274C24—431no—
275C22×C4—41no—
276C22×C4—431no—
277C22×C4—431no—
278C22×C4—431no—
279C22×C4—431no—
280C22×C4—431no—
281C22×C4—861no—
282C22×C4—861no—
283C22×C4—861no—
284C22×C4—861no—
285C22×C4—1721no—
286C22×C4—1721no—
287C22×C4—1721no—
288C22×C4D4×D4311yescharacteristic
289C2×C8—431no—
290C2×C8—431no—
291C2×C8—861no—
292C2×C8—861no—
293C2×C8—861no—
294C2×C8—861no—
295C2×C8—861no—
296C2×C8—861no—
297C2×C8—861no—
298C2×C8—861no—
299C2×C8—861no—
300C2×C8—861no—
301C2×C8C2×C4×D4311yescharacteristic
302C2×C8#1062189811yescharacteristic
303C2×C8#1062189811yescharacteristic
304C2×C8D4×D4311yescharacteristic
305C2×C8#1062190011yescharacteristic
306C2×C8#1062190211yescharacteristic
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—861no—
312C4⋊C4—861no—
313C4⋊C4—1721no—
314C4⋊C4—1721no—
315C4⋊C4—1721no—
316C4⋊C4—1721no—
317C22⋊C4—41no—
318C22⋊C4—3442no—
319C22⋊C4—1721no—
320C22⋊C4—1721no—
321C22⋊C4—1721no—
322C42—41no—
323C42—1721no—
324C42—1721no—
325C42—1721no—
326C16—41no—
327C16—1721no—
328C23—431no—
329C23—431no—
330C23—862no—
331C23—861no—
332C23—861no—
333C23—1721no—
334C23D8×D4311yescharacteristic
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—431no—
341C2×C4—431no—
342C2×C4—861no—
343C2×C4—861no—
344C2×C4—861no—
345C2×C4—861no—
346C2×C4—861no—
347C2×C4—861no—
348C2×C4—861no—
349C2×C4—861no—
350C2×C4—861no—
351C2×C4—861no—
352C2×C4—3442no—
353C2×C4—3442no—
354C2×C4—3441no—
355C2×C4—3441no—
356C2×C4—3441no—
357C2×C4—1721no—
358C2×C4—1721no—
359C2×C4C22⋊C4×D4311yescharacteristic
360C2×C4#1306330711yescharacteristic
361C2×C4#1306331011yescharacteristic
362C2×C4SD16×D4311yescharacteristic
363C2×C4#1306335411yescharacteristic
364C2×C4#1306335711yescharacteristic
365C8—861no—
366C8—861no—
367C8#1306328211yescharacteristic
368C8#1306328311yescharacteristic
369C8#1306330711yescharacteristic
370C8#1306331011yescharacteristic
371C22—21no—
372C22—21no—
373C22—432no—
374C22—861no—
375C22—861no—
376C22—861no—
377C22—861no—
378C22—861no—
379C22—1722no—
380C22—1722no—
381C22#102×D4311yescharacteristic
382C22#1458321111yescharacteristic
383C22#1458321411yescharacteristic
384C4—81no—
385C4—81no—
386C4—161no—
387C4—861no—
388C4—861no—
389C4—3441no—
390C4—3441no—
391C4—6881no—
392C4#1458276111yescharacteristic
393C4#1458290611yescharacteristic
394C4#1458322811yescharacteristic
395C4#1458323111yescharacteristic
396C2—21no—
397C2—21no—
398C2—862no—
399C2—1721no—
400C2#1913468011yescharacteristic
401C2#360×D4311yescharacteristic
402C2#1913632911yescharacteristic
subgroupG/H
centerC22#102×D43
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC43×#1386C2
socleC22×C43C2×#102
prime radicalC23×D43D8
cosocleC22×C8×C43C23
hypercenter#1386D43
hypocenterC43#12870
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1386

Complements

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

NH ≅ G/Ntype
4. #19132702C2semidirect
5. #19132701C2semidirect
6. #19132700C2semidirect
7. C43×#1386C2semidirect
12. #14582936C4semidirect
13. #14582936C4semidirect
16. #107×D43C4semidirect
17. #107×D43C4semidirect
201. #1386D43semidirect
228. C43#12870semidirect

Maximal subgroups

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

subgroupindex
#427×D432
#191362052
#191346172
#191327022
#191327012
#191327002
C43×#13862
#1287043