Finite Group Databasebeta

← #24991831

Subgroups — #24991831

Order 11008.

500 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145154C211yesmaximal, characteristic
2#19143338C211yesmaximal, characteristic
3#19135538C211yesmaximal, characteristic, complemented
4#19133089C211yesmaximal, characteristic
5#19132997C211yesmaximal, characteristic, complemented
6#19132432C211yesmaximal, characteristic, complemented
7C43×#1279C211yesmaximal, characteristic, complemented
8C2×#13063331—21no—
9#14583456C2211yescharacteristic
10#14583449C2211yescharacteristic
11#14583297C411yescharacteristic, complemented
12#14583272C411yescharacteristic, complemented
13#14583250C411yescharacteristic, complemented
14#14583246C411yescharacteristic, complemented
15#14583128—22no—
16C4×#10621873—22no—
17#14582976—21no—
18#14582969—22no—
19#14582964—21no—
20#14582952C2211yescharacteristic
21#14582865—21no—
22C4×#10621877C2211yescharacteristic
23#14582659—21no—
24#14582659—21no—
25#14582632—22no—
26#14582629—21no—
27#14582629—21no—
28C2×C4⋊C8×C43C2211yescharacteristic
29C2×C4×C8×C43C2211yescharacteristic
30C4×C4⋊C4×C43C2211yescharacteristic
31C2×#10621898—21no—
32C2×#10621873—22no—
33#13063331—42no—
34#13063331—42no—
35C2×#10621877D411yescharacteristic
36C2×#10621877D411yescharacteristic
37C2×#10621872—22no—
38C2×C8×D43—22no—
39#13063325C2×C411yescharacteristic
40#13063325C2×C411yescharacteristic
41#13063325C2×C411yescharacteristic
42#13063322C2×C411yescharacteristic
43#13063317—21no—
44#13063313—21no—
45#13063304—21no—
46#13063304—21no—
47#13063299—21no—
48#13063299D412yes—
49C4×Dic86—21no—
50C4×Dic86—21no—
51C4×D172—21no—
52C4×D172D412yes—
53#13063284—21no—
54#13063257—22no—
55C4⋊(C43⋊C8)—21no—
56#13063250—22no—
57#13063247—22no—
58C22⋊(C43⋊C8)—21no—
59(C2×D43)⋊C8—22no—
60(C2×D43)⋊C8—22no—
61#13063236—21no—
62C4×C43⋊C8—21no—
63C4×C43⋊C8—21no—
64C22×C8×C43—21no—
65C22×C8×C43—21no—
66C2×C4⋊C4×C43—21no—
67C2×C42×C43—21no—
68C2×C42×C43C2311yescharacteristic
69C4⋊C8×C43—21no—
70C4⋊C8×C43D411yescharacteristic
71C4⋊C8×C43D411yescharacteristic
72C4×C8×C43—21no—
73C4×C8×C43C2×C411yescharacteristic
74C4×C8×C43C2×C411yescharacteristic
75#95×C43—21no—
76C22×C4×C43—41no—
77C22×C4×C43C2×D411yescharacteristic
78C22×C4×C43C2×D411yescharacteristic
79C22×C4×C43#4111yescharacteristic
80C2×C22⋊D43—22no—
81#10621898—41no—
82#10621898—41no—
83#10621898—41no—
84#10621898—41no—
85C2×D172—21no—
86C2×D172—21no—
87C2×D172C22⋊C412yes—
88C2×C4×D43—22no—
89C2×Dic86—21no—
90C2×Dic86—21no—
91C2×Dic86—21no—
92C2×C8×C43—21no—
93C2×C8×C43—21no—
94C2×C8×C43—21no—
95C2×C8×C43—21no—
96C2×C8×C43—42no—
97C2×C8×C43—41no—
98C2×C8×C43—41no—
99C4⋊C4×C43—22no—
100C4⋊C4×C43—41no—
101C42×C43—41no—
102C42×C43—41no—
103C42×C43C22×C411yescharacteristic
104C42×C43C2×D411yescharacteristic
105C42×C43C2×D411yescharacteristic
106C42×C43#4111yescharacteristic
107C22⋊Dic43—41no—
108(C2×D43)⋊C4—22no—
109(C2×D43)⋊C4—22no—
110C4⋊Dic43—21no—
111C4⋊Dic43—21no—
112C4⋊Dic43—21no—
113C4⋊Dic43—21no—
114C4⋊Dic43—21no—
115C4⋊Dic43C22⋊C412yes—
116Dic43⋊C4—41no—
117Dic43⋊C4—41no—
118C4×Dic43—41no—
119#10621877—21no—
120#10621877—21no—
121#10621877—21no—
122#10621877SD1612yescomplemented
123C2×C43⋊C8—21no—
124C2×C43⋊C8—21no—
125C2×C43⋊C8—41no—
126#10621873—44no—
127#10621872—44no—
128C8×D43—44no—
129C23×C43#12111yescharacteristic
130C22×D43—22no—
131C2×C4×C43—21no—
132C2×C4×C43—21no—
133C2×C4×C43—41no—
134C2×C4×C43—42no—
135C2×C4×C43—81no—
136C2×C4×C43—81no—
137C2×C4×C43C2×C22⋊C411yescharacteristic
138C2×C4×C43C4×D411yescharacteristic
139C2×C4×C43C4×D411yescharacteristic
140C2×C4×C43#12011yescharacteristic
141C2×C4×C43#12111yescharacteristic
142C2×C4×C43#12311yescharacteristic
143C2×C4×C43C2×SD1611yescharacteristic
144C2×C4×C43#13511yescharacteristic
145C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C43#13711yescharacteristic
147C22⋊D43—42no—
148C22⋊D43—42no—
149C2×Dic43—22no—
150C2×Dic43—41no—
151C2×Dic43—41no—
152D172—42no—
153D172—41no—
154D172—41no—
155D172—41no—
156D172—41no—
157C4×D43—42no—
158C4×D43—42no—
159Dic86—41no—
160Dic86—41no—
161Dic86—42no—
162Dic86—41no—
163Dic86—41no—
164C8×C43—22no—
165C8×C43—41no—
166C8×C43—41no—
167C8×C43—41no—
168C43⋊C8—22no—
169C43⋊C8—41no—
170C43⋊C8—81no—
171#9055—431nomaximal, Sylow
172C22×C43—21no—
173C22×C43—21no—
174C22×C43#38611yescharacteristic
175C22×C43#46111yescharacteristic
176C22×C43#46311yescharacteristic
177C2×D43—42no—
178C2×D43—42no—
179C2×D43—42no—
180C4×C43—21no—
181C4×C43—21no—
182C4×C43—21no—
183C4×C43—82no—
184C4×C43C4×SD1611yescharacteristic
185C4×C43#44011yescharacteristic
186C4×C43#44311yescharacteristic
187C4×C43#44411yescharacteristic
188C4×C43#45011yescharacteristic
189C4×C43#45211yescharacteristic
190Dic43—42no—
191Dic43—81no—
192Dic43—81no—
193#3167—431no—
194#2935—431no—
195#1986—431no—
196#1502—431no—
197#1481—431no—
198#1279D4311yescharacteristic, complemented
199#1278—431no—
200C2×C43—21no—
201C2×C43—21no—
202C2×C43#187611yescharacteristic
203C2×C43#187711yescharacteristic
204C2×C43#188411yescharacteristic
205D43—82no—
206C2×#131—861no—
207#533—431no—
208#532—431no—
209#498—431no—
210#492—431no—
211#487—431no—
212#486—431no—
213#465—862no—
214C4×SD16—862no—
215#436—861no—
216#435—862no—
217C8×D4—861no—
218#431—431no—
219C2×C4⋊C8C2×D4311yescharacteristic
220#408—861no—
221C4×M16—431no—
222C2×C4×C8C2×D4311yescharacteristic
223C4×C4⋊C4C2×D4311yescharacteristic
224#339—861no—
225#339—861no—
226#327—862no—
227Q8⋊C8—861no—
228Q8⋊C8—861no—
229C43#905511yescharacteristic, complemented, Sylow
230C2×#41—861no—
231C2×SD16—862no—
232#131—1722no—
233#131—1722no—
234C2×M16—431no—
235C2×M16—431no—
236C2×M16—862no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—862no—
240C4⋊Q8—431no—
241C4⋊Q8—431no—
242C4⋊Q8—431no—
243#127—431no—
244#125—861no—
245#124—861no—
246C22⋊Q8—861no—
247C22⋊Q8—861no—
248#121—432no—
249#121—861no—
250C4×Q8—861no—
251C4×Q8—861no—
252C4×D4—432no—
253C4×D4—861no—
254#117—861no—
255C2×C4⋊C4—21no—
256C2×C42—21no—
257C2×C42C22×D4311yescharacteristic
258#106—862no—
259C4⋊C8—21no—
260C4⋊C8—861no—
261C4⋊C8D17211yescharacteristic
262C4⋊C8D17211yescharacteristic
263#103—862no—
264#102—862no—
265C22⋊C8—862no—
266C22⋊C8—862no—
267C22⋊C8—861no—
268#97—861no—
269C4×C8—21no—
270C4×C8—861no—
271C4×C8—861no—
272C4×C8C4×D4311yescharacteristic
273C4×C8C4×D4311yescharacteristic
274#95—21no—
275#41—1721no—
276#41—1721no—
277#41—1721no—
278#41—1721no—
279C2×Q8—861no—
280C2×Q8—861no—
281C2×Q8—861no—
282C2×D4—432no—
283C2×D4—862no—
284C2×D4—861no—
285C2×D4—861no—
286C22×C4—41no—
287C22×C4—862no—
288C22×C4#1062189811yescharacteristic
289C22×C4D4×D4311yescharacteristic
290C22×C4D4×D4311yescharacteristic
291SD16—1724no—
292M16—432no—
293M16—861no—
294M16—861no—
295M16—861no—
296M16—1724no—
297C2×C8—21no—
298C2×C8—21no—
299C2×C8—21no—
300C2×C8—21no—
301C2×C8—42no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—861no—
305C2×C8—861no—
306C2×C8—1724no—
307C2×C8—1721no—
308C4⋊C4—22no—
309C4⋊C4—41no—
310C4⋊C4—432no—
311C4⋊C4—861no—
312C4⋊C4—861no—
313C4⋊C4—861no—
314C4⋊C4—861no—
315C4⋊C4—861no—
316C4⋊C4—1721no—
317C4⋊C4—1721no—
318C22⋊C4—862no—
319C22⋊C4—862no—
320C22⋊C4—1721no—
321C42—41no—
322C42—41no—
323C42—1721no—
324C42C2×C4×D4311yescharacteristic
325C42C2×D17211yescharacteristic
326C42D4×D4311yescharacteristic
327C42#1062190211yescharacteristic
328C23—862no—
329C23#1306329811yescharacteristic
330Q8—1722no—
331Q8—1721no—
332Q8—1721no—
333Q8—1721no—
334Q8—1721no—
335D4—1722no—
336D4—1722no—
337D4—1722no—
338D4—1721no—
339D4—1721no—
340D4—1721no—
341D4—1721no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—41no—
345C2×C4—42no—
346C2×C4—81no—
347C2×C4—81no—
348C2×C4—862no—
349C2×C4—1721no—
350C2×C4—1721no—
351C2×C4—1722no—
352C2×C4—1722no—
353C2×C4C22⋊C4×D4311yescharacteristic
354C2×C4#1306328711yescharacteristic
355C2×C4C4×D17211yescharacteristic
356C2×C4#1306329511yescharacteristic
357C2×C4#1306330011yescharacteristic
358C2×C4#1306331011yescharacteristic
359C2×C4SD16×D4311yescharacteristic
360C2×C4#1306334611yescharacteristic
361C2×C4#1306334911yescharacteristic
362C2×C4#1306335711yescharacteristic
363C8—22no—
364C8—41no—
365C8—41no—
366C8—41no—
367C8—862no—
368C8—3441no—
369C8—1721no—
370C22—21no—
371C22—21no—
372C22—1722no—
373C22—1722no—
374C22—1722no—
375C22#1458277711yescharacteristic
376C22#1458310311yescharacteristic
377C22#1458311311yescharacteristic
378C4—21no—
379C4—21no—
380C4—21no—
381C4—82no—
382C4—3441no—
383C4—3441no—
384C4—1722no—
385C4#1458298611yescharacteristic
386C4#1458299811yescharacteristic
387C4#1458301711yescharacteristic
388C4#1458302211yescharacteristic
389C4#1458305111yescharacteristic
390C4#1458306411yescharacteristic
391C2—21no—
392C2—21no—
393C2—3442no—
394C2#1913492111yescharacteristic
395C2#1913493011yescharacteristic
396C2#1913497711yescharacteristic
subgroupG/H
centerC2×C4#13063295
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1279C2
socleC22×C43#386
prime radical#14583449C22
cosocleC2×C42×C43C23
hypercenter#1279D43
hypocenterC43#9055
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
3. #19135538C2semidirect
5. #19132997C2semidirect
6. #19132432C2semidirect
7. C43×#1279C2semidirect
11. #14583297C4semidirect
12. #14583272C4semidirect
13. #14583250C4semidirect
14. #14583246C4semidirect
122. #10621877SD16semidirect
198. #1279D43semidirect
229. C43#9055semidirect

Maximal subgroups

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

subgroupindex
#191451542
#191433382
#191355382
#191330892
#191329972
#191324322
C43×#12792
#905543