Finite Group Databasebeta

← #24989774

Subgroups — #24989774

Order 11008.

432 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143562C211yesmaximal, characteristic
2#19134615C211yesmaximal, characteristic
3C4×#13063256C211yesmaximal, characteristic, complemented
4#19133353C211yesmaximal, characteristic, complemented
5#19132498C211yesmaximal, characteristic, complemented
6#19132496C211yesmaximal, characteristic, complemented
7C43×#1806C211yesmaximal, characteristic
8#14583030C411yescharacteristic, complemented
9#14583030C411yescharacteristic, complemented
10#14582977C411yescharacteristic, complemented
11#14582977C411yescharacteristic, complemented
12#14582971—21no—
13#14582971—21no—
14#14582952—21no—
15#14582952C2211yescharacteristic
16C2×#13063256—21no—
17#14582923C2211yescharacteristic
18C2×#13063252—21no—
19C4×#10621877—21no—
20C2×C4×C43⋊C8C2211yescharacteristic
21C4×C4⋊Dic43C2211yescharacteristic
22#14582661—21no—
23#14582658—21no—
24#14582651—21no—
25#14582651—21no—
26C4×#41×C43C2211yescharacteristic
27C43×#423C2211yescharacteristic
28C2×#104×C43—21no—
29C4×C4⋊C4×C43C2211yescharacteristic
30C43×#339—21no—
31C2×#10621877—21no—
32C2×#10621877—21no—
33C2×#10621877—21no—
34C22×C43⋊C8D411yescharacteristic
35C22×C43⋊C8D411yescharacteristic
36C2×C4⋊Dic43—21no—
37C2×C4×Dic43—21no—
38#13063256—24no—
39C4⋊(C43⋊C8)—21no—
40C4⋊(C43⋊C8)—21no—
41C4⋊(C43⋊C8)—21no—
42C4⋊(C43⋊C8)—21no—
43C4⋊(C43⋊C8)C2×C411yescharacteristic
44C4⋊(C43⋊C8)C2×C411yescharacteristic
45#13063252—42no—
46C22⋊(C43⋊C8)—21no—
47C22⋊(C43⋊C8)—21no—
48C22⋊(C43⋊C8)—21no—
49#13063236—21no—
50#13063236—21no—
51C4×C43⋊C8—21no—
52C4×C43⋊C8C2×C411yescharacteristic
53C4×C43⋊C8C2×C411yescharacteristic
54C4×C43⋊C8D411yescharacteristic
55C4×C43⋊C8D411yescharacteristic
56C43⋊#95—21no—
57C2×#41×C43D411yescharacteristic
58C2×M16×C43—21no—
59C4×Q8×C43C2×C411yescharacteristic
60C4×Q8×C43Q811yescharacteristic
61C4×D4×C43—21no—
62C4×D4×C43—21no—
63C4×D4×C43C2×C411yescharacteristic
64C4×D4×C43Q811yescharacteristic
65#117×C43—21no—
66#117×C43D411yescharacteristic
67C2×C4⋊C4×C43—21no—
68C2×C42×C43—21no—
69C2×C42×C43—21no—
70C2×C42×C43C2311yescharacteristic
71C4⋊C8×C43—21no—
72C4⋊C8×C43—21no—
73#104×C43—42no—
74#95×C43—21no—
75#41×C43—21no—
76#41×C43—21no—
77#41×C43—21no—
78#41×C43—21no—
79C2×Q8×C43C4⋊C411yescharacteristic
80C2×D4×C43—21no—
81C2×D4×C43C4⋊C411yescharacteristic
82C22×C4×C43—21no—
83C22×C4×C43—21no—
84C22×C4×C43—21no—
85C22×C4×C43—41no—
86C22×C4×C43C2×D411yescharacteristic
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43#4111yescharacteristic
89C22×Dic43—41no—
90M16×C43—41no—
91M16×C43—41no—
92C2×C8×C43—41no—
93C4⋊C4×C43—21no—
94C4⋊C4×C43—21no—
95C4⋊C4×C43—22no—
96C4⋊C4×C43—41no—
97C4⋊C4×C43C4⋊C411yescharacteristic
98C4⋊C4×C43C4⋊C411yescharacteristic
99C22⋊C4×C43—21no—
100C22⋊C4×C43—21no—
101C22⋊C4×C43—21no—
102C42×C43—21no—
103C42×C43—21no—
104C42×C43—21no—
105C42×C43—41no—
106C42×C43—41no—
107C42×C43C22×C411yescharacteristic
108C42×C43C2×D411yescharacteristic
109C42×C43C2×Q811yescharacteristic
110C42×C43#4111yescharacteristic
111C4⋊Dic43—22no—
112C4⋊Dic43—41no—
113C4×Dic43—41no—
114C4×Dic43—41no—
115#10621877—42no—
116#10621877—42no—
117#10621877—41no—
118#10621877—41no—
119C2×C43⋊C8—22no—
120C2×C43⋊C8—21no—
121C2×C43⋊C8—21no—
122C2×C43⋊C8—41no—
123C2×C43⋊C8—41no—
124C2×C43⋊C8C22⋊C411yescharacteristic
125C2×C43⋊C8C22⋊C411yescharacteristic
126C2×C43⋊C8C22⋊C411yescharacteristic
127C2×C43⋊C8C22⋊C411yescharacteristic
128C23×C43—21no—
129C23×C43#12111yescharacteristic
130Q8×C43—21no—
131Q8×C43—21no—
132D4×C43—21no—
133D4×C43—21no—
134D4×C43—41no—
135D4×C43—41no—
136C2×C4×C43—21no—
137C2×C4×C43—21no—
138C2×C4×C43—21no—
139C2×C4×C43—21no—
140C2×C4×C43—21no—
141C2×C4×C43—41no—
142C2×C4×C43—42no—
143C2×C4×C43—41no—
144C2×C4×C43—41no—
145C2×C4×C43—41no—
146C2×C4×C43—41no—
147C2×C4×C43—42no—
148C2×C4×C43—81no—
149C2×C4×C43—81no—
150C2×C4×C43C2×C22⋊C411yescharacteristic
151C2×C4×C43C2×C4⋊C411yescharacteristic
152C2×C4×C43#11711yescharacteristic
153C2×C4×C43#12111yescharacteristic
154C2×C4×C43C22⋊Q811yescharacteristic
155C2×C4×C43C22⋊Q811yescharacteristic
156C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C43#13711yescharacteristic
159C2×C4×C43#13711yescharacteristic
160C2×Dic43—42no—
161C2×Dic43—81no—
162C2×Dic43—81no—
163C8×C43—81no—
164C43⋊C8—21no—
165C43⋊C8—21no—
166C43⋊C8—21no—
167C43⋊C8—41no—
168C43⋊C8—41no—
169C43⋊C8—81no—
170C43⋊C8#10412yescomplemented
171#8669—431nomaximal, Sylow
172C22×C43—21no—
173C22×C43—21no—
174C22×C43—41no—
175C22×C43—41no—
176C22×C43—41no—
177C22×C43#38011yescharacteristic
178C22×C43#46811yescharacteristic
179C22×C43#46811yescharacteristic
180C4×C43—21no—
181C4×C43—21no—
182C4×C43—21no—
183C4×C43—41no—
184C4×C43—41no—
185C4×C43—41no—
186C4×C43—82no—
187C4×C43C2×#10411yescharacteristic
188C4×C43#42111yescharacteristic
189C4×C43#42811yescharacteristic
190C4×C43#42811yescharacteristic
191C4×C43#46911yescharacteristic
192C4×C43#47011yescharacteristic
193Dic43—82no—
194#2965—431no—
195#1806—431no—
196#1806D4311yescharacteristic
197C4×#106—431no—
198#1567—431no—
199#1303—431no—
200#1303—431no—
201C2×C43—21no—
202C2×C43—21no—
203C2×C43—81no—
204C2×C43#180611yescharacteristic
205C2×C43#180911yescharacteristic
206C2×C43#181411yescharacteristic
207C4×#41C2×D4311yescharacteristic
208#446—431no—
209#446—431no—
210#436—431no—
211#436—431no—
212#435—861no—
213#435—861no—
214#431—431no—
215#431—861no—
216C2×#106—861no—
217#423—431no—
218#423C2×D4311yescharacteristic
219C2×#104—21no—
220C2×#104—861no—
221C4×M16—861no—
222C2×C4×C8—431no—
223C4×C4⋊C4—431no—
224C4×C4⋊C4C2×D4311yescharacteristic
225#340—861no—
226#339—21no—
227#339—861no—
228#335—861no—
229#335—861no—
230C43#866911yescharacteristic, complemented, Sylow
231C2×#41C22⋊D4311yescharacteristic
232C2×M16—21no—
233C2×M16—861no—
234C2×M16—861no—
235C2×M16—861no—
236C22×C8—431no—
237C22×C8—431no—
238C4×Q8Dic8611yescharacteristic
239C4×Q8C4×D4311yescharacteristic
240C4×D4—21no—
241C4×D4—21no—
242C4×D4Dic8611yescharacteristic
243C4×D4C4×D4311yescharacteristic
244#117—21no—
245#117C22⋊D4311yescharacteristic
246C2×C4⋊C4—21no—
247C2×C4⋊C4—861no—
248C2×C42—21no—
249C2×C42—21no—
250C2×C42—861no—
251C2×C42C22×D4311yescharacteristic
252#106—864no—
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8—431no—
256C4⋊C8—431no—
257C4⋊C8—861no—
258C4⋊C8—861no—
259C4⋊C8—861no—
260C4⋊C8—861no—
261#104—42no—
262#104—1722no—
263C22⋊C8—861no—
264C22⋊C8—861no—
265C22⋊C8—861no—
266#97—861no—
267#97—861no—
268C4×C8—431no—
269C4×C8—431no—
270C4×C8—431no—
271C4×C8—431no—
272C4×C8—861no—
273#95—21no—
274#95—861no—
275#41—21no—
276#41—21no—
277#41—21no—
278#41—21no—
279C2×Q8Dic43⋊C411yescharacteristic
280C2×D4—21no—
281C2×D4Dic43⋊C411yescharacteristic
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—41no—
286C22×C4—1721no—
287C22×C4D4×D4311yescharacteristic
288C22×C4#1062190011yescharacteristic
289C22×C4C2×C22⋊D4311yescharacteristic
290M16—41no—
291M16—41no—
292M16—1722no—
293M16—1722no—
294M16—1721no—
295M16—1721no—
296C2×C8—41no—
297C2×C8—431no—
298C2×C8—431no—
299C2×C8—431no—
300C2×C8—431no—
301C2×C8—862no—
302C2×C8—861no—
303C2×C8—861no—
304C2×C8—1721no—
305C2×C8—1721no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—22no—
309C4⋊C4—41no—
310C4⋊C4—862no—
311C4⋊C4—1721no—
312C4⋊C4Dic43⋊C411yescharacteristic
313C4⋊C4Dic43⋊C411yescharacteristic
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—21no—
317C42—21no—
318C42—21no—
319C42—21no—
320C42—41no—
321C42—41no—
322C42—1721no—
323C42—1721no—
324C42C2×Dic8611yescharacteristic
325C42C2×C4×D4311yescharacteristic
326C42D4×D4311yescharacteristic
327C42#1062190011yescharacteristic
328C23—21no—
329C23#1306329711yescharacteristic
330Q8—21no—
331Q8—21no—
332D4—21no—
333D4—21no—
334D4—41no—
335D4—41no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—42no—
348C2×C4—81no—
349C2×C4—81no—
350C2×C4—3441no—
351C2×C4—3441no—
352C2×C4—1722no—
353C2×C4C22⋊C4×D4311yescharacteristic
354C2×C4C2×Dic43⋊C411yescharacteristic
355C2×C4#1306328111yescharacteristic
356C2×C4#1306329711yescharacteristic
357C2×C4#1306330211yescharacteristic
358C2×C4#1306330211yescharacteristic
359C2×C4#1306335011yescharacteristic
360C2×C4#1306335111yescharacteristic
361C2×C4#1306335511yescharacteristic
362C2×C4#1306335611yescharacteristic
363C8—81no—
364C8—432no—
365C8—861no—
366C8—861no—
367C8—861no—
368C8—3441no—
369C8—1721no—
370C8—1721no—
371C22—21no—
372C22—21no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22#1458275711yescharacteristic
377C22#1458314311yescharacteristic
378C22#1458314711yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—41no—
383C4—41no—
384C4—41no—
385C4—82no—
386C4—3442no—
387C4#104×D4311yescharacteristic
388C4#1458291411yescharacteristic
389C4#1458293911yescharacteristic
390C4#1458294211yescharacteristic
391C4#1458315011yescharacteristic
392C4#1458315511yescharacteristic
393C2—21no—
394C2—21no—
395C2—81no—
396C2#1913461311yescharacteristic
397C2#1913462611yescharacteristic
398C2#1913464711yescharacteristic
subgroupG/H
centerC2×C4#13063297
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1806C2
socleC22×C43#380
prime radicalC2×#41×C43D4
cosocleC2×C42×C43C23
hypercenter#1806D43
hypocenterC43#8669
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1806

Complements

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

NH ≅ G/Ntype
3. C4×#13063256C2semidirect
4. #19133353C2semidirect
5. #19132498C2semidirect
6. #19132496C2semidirect
8. #14583030C4semidirect
9. #14583030C4semidirect
10. #14582977C4semidirect
11. #14582977C4semidirect
170. C43⋊C8#104semidirect
230. C43#8669semidirect

Maximal subgroups

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

subgroupindex
#191435622
#191346152
C4×#130632562
#191333532
#191324982
#191324962
C43×#18062
#866943