Finite Group Databasebeta

← #25079356

Subgroups — #25079356

Order 11008.

598 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145181C211yesmaximal, characteristic, complemented
2#19144667C212yesmaximal
3#19143561C211yesmaximal, characteristic
4#19134150C212yesmaximal, complemented
5#19134143C212yesmaximal, complemented
6#19134114C211yesmaximal, characteristic, complemented
7#19134109C211yesmaximal, characteristic, complemented
8#19134090C211yesmaximal, characteristic, complemented
9#19134085C211yesmaximal, characteristic, complemented
10#19133259C212yesmaximal, complemented
11C43×#1564C211yesmaximal, characteristic, complemented
12#14583456C2212yes—
13C4×#10621898C2211yescharacteristic
14#14583304C2211yescharacteristic
15#14583279C2211yescharacteristic
16#14583250C2212yes—
17#14583241—22no—
18#14583185C2212yes—
19#14583180C2212yes—
20#14583140—21no—
21#14583140—21no—
22#14583110C2212yes—
23#14583105C2212yes—
24#14583063—22no—
25#14583029C2211yescharacteristic
26#14583029C2211yescharacteristic
27C4×Dic172—22no—
28C4×Dic172—21no—
29C4×Dic172—21no—
30C4×#10621873—22no—
31#14582978C2211yescharacteristic
32#14582978C2211yescharacteristic
33#14582970—21no—
34#14582970—21no—
35#14582952C2211yescharacteristic
36#14582950—21no—
37C4×#10621872—21no—
38#14582646C2212yes—
39#14582646C2212yes—
40#14582644C2212yes—
41#14582644C2212yes—
42C43×#431C2212yes—
43C2×C4×C8×C43C2211yescharacteristic
44C43×#335C2212yes—
45C43×#334C2211yescharacteristic
46C43×#334C2211yescharacteristic
47C2×#10621898D411yescharacteristic
48C2×Dic172—22no—
49C2×Dic172—21no—
50C2×Dic172—21no—
51C2×#10621873—22no—
52C2×#10621872—21no—
53C2×#10621872—21no—
54#13063325C2312yes—
55#13063325C2312yes—
56#13063317—22no—
57#13063304—22no—
58#13063304—22no—
59C4×Dic86—22no—
60C4×Dic86—22no—
61C4×Dic86D411yescharacteristic
62C4×Dic86C2311yescharacteristic
63C4×D172D411yescharacteristic
64C4×D172C2311yescharacteristic
65C4×C22⋊D43—21no—
66C4×C22⋊D43—21no—
67#13063284—22no—
68#13063284D411yescharacteristic
69#13063282—21no—
70C42×D43—21no—
71#13063259—21no—
72#13063259—21no—
73#13063259—22no—
74#13063257—22no—
75C4⋊(C43⋊C8)C2311yescharacteristic
76C4⋊(C43⋊C8)C2311yescharacteristic
77Dic43⋊C8—21no—
78Dic43⋊C8—21no—
79#13063250—22no—
80#13063250—22no—
81#13063250—22no—
82#13063250—22no—
83#13063250—22no—
84#13063247—22no—
85C22⋊(C43⋊C8)—21no—
86(C2×D43)⋊C8—21no—
87(C2×D43)⋊C8—21no—
88#13063235—21no—
89#13063235—21no—
90C4×C43⋊C8—21no—
91C22×C8×C43D411yescharacteristic
92C22×C8×C43D411yescharacteristic
93C2×C42×C43C2311yescharacteristic
94C4⋊C8×C43C2312yes—
95C4⋊C8×C43C2312yes—
96C22⋊C8×C43—22no—
97C4×C8×C43—22no—
98C4×C8×C43D411yescharacteristic
99C4×C8×C43D411yescharacteristic
100C4×C8×C43C2311yescharacteristic
101C4×C8×C43C2311yescharacteristic
102C22×C4×C43C2×D411yescharacteristic
103C22×C4×C43C2×D411yescharacteristic
104C22×C4×C43#4111yescharacteristic
105C2×C22⋊D43—21no—
106#10621898—42no—
107C2×D172C2×D411yescharacteristic
108C2×C4×D43—21no—
109C2×C4×D43—21no—
110C2×C4×D43—21no—
111C2×Dic86—22no—
112C2×Dic86—22no—
113C2×Dic86C2×D411yescharacteristic
114C2×C8×C43—22no—
115C2×C8×C43—22no—
116C2×C8×C43—22no—
117C2×C8×C43—41no—
118C2×C8×C43C2×D411yescharacteristic
119C2×C8×C43C2×D411yescharacteristic
120C2×C8×C43C2×D411yescharacteristic
121C2×C8×C43C2×D411yescharacteristic
122C42×C43C2×D411yescharacteristic
123C42×C43C2×D411yescharacteristic
124C42×C43#4111yescharacteristic
125C42×C43C2411yescharacteristic
126C22⋊Dic43—21no—
127C22⋊Dic43—42no—
128(C2×D43)⋊C4—21no—
129(C2×D43)⋊C4—21no—
130C4⋊Dic43—22no—
131C4⋊Dic43—22no—
132C4⋊Dic43—22no—
133C4⋊Dic43—22no—
134C4⋊Dic43C2×D411yescharacteristic
135C4⋊Dic43C2×D411yescharacteristic
136Dic43⋊C4—21no—
137Dic43⋊C4—21no—
138Dic43⋊C4—42no—
139Dic43⋊C4—42no—
140C4×Dic43—21no—
141C4×Dic43—21no—
142C4×Dic43—21no—
143C4×Dic43—42no—
144C2×C43⋊C8—21no—
145C2×C43⋊C8—21no—
146Dic172—42no—
147Dic172—44no—
148Dic172—42no—
149#10621873—44no—
150#10621872—42no—
151#10621872—42no—
152C23×C43#12111yescharacteristic
153C22×D43—21no—
154C2×C4×C43—21no—
155C2×C4×C43—21no—
156C2×C4×C43—22no—
157C2×C4×C43—22no—
158C2×C4×C43#12111yescharacteristic
159C2×C4×C43#12111yescharacteristic
160C2×C4×C43#12111yescharacteristic
161C2×C4×C43C22×D411yescharacteristic
162C2×C4×C43C22×D411yescharacteristic
163C2×C4×C43C2×#4111yescharacteristic
164C22⋊D43—42no—
165C2×Dic43—21no—
166C2×Dic43—21no—
167C2×Dic43—21no—
168C2×Dic43—42no—
169C2×Dic43—42no—
170D172—22no—
171C4×D43—42no—
172C4×D43—41no—
173C4×D43—41no—
174C4×D43—42no—
175Dic86—22no—
176Dic86—42no—
177Dic86—42no—
178Dic86—42no—
179Dic86—42no—
180C8×C43—21no—
181C8×C43—21no—
182C8×C43—21no—
183C8×C43—42no—
184C8×C43—42no—
185C8×C43#13512yes—
186C43⋊C8—41no—
187C43⋊C8—41no—
188#19161—431nomaximal, Sylow
189C22×C43—21no—
190C22×C43—21no—
191C22×C43—21no—
192C22×C43C2×#12111yescharacteristic
193C2×D43—41no—
194C2×D43—41no—
195C2×D43—41no—
196C4×C43—21no—
197C4×C43—21no—
198C4×C43—21no—
199C4×C43#47312yes—
200C4×C43C2×#13511yescharacteristic
201C4×C43#57512yes—
202C4×C43#57511yescharacteristic
203Dic43—41no—
204Dic43—41no—
205Dic43—41no—
206Dic43—82no—
207Dic43—82no—
208#3170—431no—
209#3107—432no—
210#2965—431no—
211#1700—432no—
212#1699—432no—
213#1694—431no—
214#1693—431no—
215#1690—431no—
216#1689—431no—
217#1564D4311yescharacteristic, complemented
218#1544—432no—
219C2×C43—41no—
220C2×C43#303511yescharacteristic
221C2×C43#305411yescharacteristic
222C2×C43C2×#47311yescharacteristic
223D43—81no—
224#533—432no—
225C4×#41—431no—
226#500—431no—
227#494—431no—
228#487—432no—
229#485—862no—
230#475—432no—
231#474—432no—
232#467—861no—
233#467—861no—
234#462—432no—
235#461—432no—
236#452—862no—
237#446—431no—
238#446—431no—
239C4×Q16—862no—
240C4×Q16—861no—
241C4×Q16—861no—
242C4×SD16—862no—
243#436—431no—
244#436—431no—
245#435—861no—
246#435—861no—
247#431—431no—
248#431—861no—
249#431C2×D4312yes—
250C4×M16—861no—
251C2×C4×C8C2×D4311yescharacteristic
252#335C2×D4312yes—
253#334C2×D4311yescharacteristic
254#334C2×D4311yescharacteristic
255#332—432no—
256#332—432no—
257#332—432no—
258#332—432no—
259C43#1916111yescharacteristic, complemented, Sylow
260C2×#41—431no—
261C2×Q16—862no—
262C2×Q16—861no—
263C2×Q16—861no—
264C2×SD16—862no—
265C2×M16—861no—
266C2×M16—861no—
267C22×C8D17211yescharacteristic
268C22×C8D17211yescharacteristic
269C4⋊Q8—432no—
270C4⋊Q8—432no—
271#125—862no—
272C22⋊Q8—862no—
273C22⋊Q8—862no—
274C4×Q8—431no—
275C4×Q8—431no—
276C4×Q8—862no—
277C4×Q8—862no—
278C4×D4—431no—
279C4×D4—431no—
280C4×D4—861no—
281C4×D4—861no—
282#117—431no—
283#117—861no—
284#117—862no—
285C2×C42—861no—
286C2×C42C22×D4311yescharacteristic
287#107—862no—
288#107—861no—
289#107—861no—
290#106—862no—
291C4⋊C8—431no—
292C4⋊C8—431no—
293C4⋊C8—861no—
294C4⋊C8—861no—
295C4⋊C8C22×D4312yes—
296C4⋊C8C22×D4312yes—
297#103—862no—
298#103—862no—
299#103—862no—
300#103—862no—
301#103—862no—
302#102—862no—
303C22⋊C8—22no—
304C22⋊C8—861no—
305C22⋊C8—861no—
306C22⋊C8—861no—
307#97—861no—
308#97—861no—
309C4×C8—22no—
310C4×C8—861no—
311C4×C8D17211yescharacteristic
312C4×C8D17211yescharacteristic
313C4×C8C22×D4311yescharacteristic
314C4×C8C22×D4311yescharacteristic
315#41—1722no—
316C2×Q8—431no—
317C2×Q8—862no—
318C2×Q8—862no—
319C2×D4—431no—
320C2×D4—861no—
321C22×C4—861no—
322C22×C4—861no—
323C22×C4—861no—
324C22×C4C2×D17211yescharacteristic
325C22×C4D4×D4311yescharacteristic
326C22×C4#1062190211yescharacteristic
327Q16—1722no—
328Q16—1724no—
329Q16—1722no—
330SD16—1724no—
331M16—1722no—
332M16—1722no—
333C2×C8—22no—
334C2×C8—22no—
335C2×C8—22no—
336C2×C8—41no—
337C2×C8—861no—
338C2×C8—861no—
339C2×C8C2×D17211yescharacteristic
340C2×C8C2×D17211yescharacteristic
341C2×C8C2×D17211yescharacteristic
342C2×C8C2×D17211yescharacteristic
343C4⋊C4—431no—
344C4⋊C4—431no—
345C4⋊C4—861no—
346C4⋊C4—861no—
347C4⋊C4—862no—
348C4⋊C4—862no—
349C4⋊C4—862no—
350C4⋊C4—862no—
351C4⋊C4—1722no—
352C4⋊C4—1722no—
353C22⋊C4—861no—
354C22⋊C4—861no—
355C22⋊C4—861no—
356C22⋊C4—1722no—
357C42—861no—
358C42—861no—
359C42—861no—
360C42—1722no—
361C42C2×D17211yescharacteristic
362C42D4×D4311yescharacteristic
363C42#1062190211yescharacteristic
364C42C23×D4311yescharacteristic
365C23—861no—
366C23#1306330011yescharacteristic
367Q8—862no—
368Q8—1722no—
369Q8—1722no—
370Q8—1722no—
371Q8—1722no—
372D4—862no—
373D4—1722no—
374C2×C4—21no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—21no—
378C2×C4—861no—
379C2×C4—861no—
380C2×C4—861no—
381C2×C4—1722no—
382C2×C4—1722no—
383C2×C4—1722no—
384C2×C4—1721no—
385C2×C4—1722no—
386C2×C4—1721no—
387C2×C4#1306330011yescharacteristic
388C2×C4#1306330011yescharacteristic
389C2×C4#1306330011yescharacteristic
390C2×C4C2×D4×D4311yescharacteristic
391C2×C4C22×D17211yescharacteristic
392C2×C4C2×#1062190211yescharacteristic
393C8—21no—
394C8—21no—
395C8—21no—
396C8—42no—
397C8—42no—
398C8—1721no—
399C8—1721no—
400C8#1306334712yes—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—1721no—
405C22—1721no—
406C22—1721no—
407C22C2×#1306330011yescharacteristic
408C4—21no—
409C4—21no—
410C4—21no—
411C4—3442no—
412C4—3442no—
413C4—1721no—
414C4—1721no—
415C4—1721no—
416C4#1458317512yes—
417C4C2×#1306334711yescharacteristic
418C4#1458369612yes—
419C4#1458369911yescharacteristic
420C2—41no—
421C2—3441no—
422C2#1914405211yescharacteristic
423C2#1914420511yescharacteristic
424C2C2×#1458317511yescharacteristic
subgroupG/H
centerC2×C4#13063300
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1564C2
socleC22×C43C2×#121
prime radicalC2×#10621898D4
hypercenter#1564D43
hypocenterC43#19161
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1564

Complements

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

NH ≅ G/Ntype
1. #19145181C2semidirect
4. #19134150C2semidirect
5. #19134143C2semidirect
6. #19134114C2semidirect
7. #19134109C2semidirect
8. #19134090C2semidirect
9. #19134085C2semidirect
10. #19133259C2semidirect
11. C43×#1564C2semidirect
217. #1564D43semidirect
259. C43#19161semidirect

Maximal subgroups

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

subgroupindex
#191451812
#191446672
#191435612
#191341502
#191341432
#191341142
#191341092
#191340902
#191340852
#191332592
C43×#15642
#1916143