Finite Group Databasebeta

← #25079355

Subgroups — #25079355

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#19145182C211yesmaximal, characteristic, complemented
2#19144663C212yesmaximal
3#19143558C211yesmaximal, characteristic
4#19134152C212yesmaximal, complemented
5#19134144C212yesmaximal, complemented
6#19134110C211yesmaximal, characteristic, complemented
7#19134090C211yesmaximal, characteristic, complemented
8#19134084C211yesmaximal, characteristic, complemented
9#19133340C211yesmaximal, characteristic, complemented
10#19133258C212yesmaximal, complemented
11C43×#1693C211yesmaximal, characteristic, complemented
12#14583454C2212yes—
13C4×#10621900C2211yescharacteristic
14#14583279C2211yescharacteristic
15#14583251C2212yes—
16#14583238—22no—
17#14583185C2212yes—
18#14583179C2212yes—
19#14583141—21no—
20#14583141—21no—
21#14583106C2212yes—
22#14583058—22no—
23#14583029C2211yescharacteristic
24#14583026C2211yescharacteristic
25#14582993—21no—
26#14582993—21no—
27#14582991—22no—
28SD16×Dic43—22no—
29#14582977C2211yescharacteristic
30#14582973—21no—
31#14582968—21no—
32#14582951C2211yescharacteristic
33#14582951C2212yes—
34#14582949—21no—
35M16×Dic43—21no—
36C4×C8×D43C2211yescharacteristic
37#14582651C2212yes—
38#14582650C2211yescharacteristic
39#14582646C2212yes—
40#14582645C2212yes—
41#14582644C2212yes—
42C43×#500C2211yescharacteristic
43C43×#461C2212yes—
44C43×#436C2211yescharacteristic
45C43×#334C2211yescharacteristic
46C43×#332C2212yes—
47C2×#10621900D411yescharacteristic
48C2×Dic172—21no—
49C2×Dic172—21no—
50C2×#10621885—22no—
51C2×#10621877—21no—
52C2×C8×D43D411yescharacteristic
53C2×C8×D43D411yescharacteristic
54#13063325C2312yes—
55#13063316—22no—
56#13063305—22no—
57#13063301—22no—
58Q8×Dic43—22no—
59C4×Dic86C2311yescharacteristic
60#13063290—22no—
61#13063290D411yescharacteristic
62D4×Dic43D411yescharacteristic
63C4×C22⋊D43—21no—
64(C22⋊D43)⋊C4—21no—
65#13063283—22no—
66#13063283D411yescharacteristic
67#13063281—21no—
68C2×C4×Dic43—21no—
69C42×D43C2311yescharacteristic
70#13063258—22no—
71#13063257—22no—
72C4⋊(C43⋊C8)C2312yes—
73C4⋊(C43⋊C8)C2311yescharacteristic
74Dic43⋊C8—21no—
75Dic43⋊C8—21no—
76#13063250—22no—
77#13063249—22no—
78#13063248—22no—
79#13063248—22no—
80#13063246—22no—
81C22⋊(C43⋊C8)—21no—
82(C2×D43)⋊C8—22no—
83(C2×D43)⋊C8—21no—
84#13063235—21no—
85#13063235—21no—
86C4×C43⋊C8C2311yescharacteristic
87C8×Dic43—21no—
88C8×Dic43—22no—
89C8×Dic43D411yescharacteristic
90C8×Dic43D411yescharacteristic
91C2×SD16×C43—22no—
92C2×M16×C43—21no—
93C4⋊Q8×C43C2312yes—
94C4×D4×C43C2311yescharacteristic
95#107×C43—21no—
96#107×C43—21no—
97C4⋊C8×C43C2311yescharacteristic
98C4⋊C8×C43C2312yes—
99#103×C43—22no—
100C22⋊C8×C43—21no—
101C4×C8×C43C2311yescharacteristic
102C2×Q8×C43—22no—
103C2×D4×C43C2×D411yescharacteristic
104C22×C4×C43—21no—
105C2×C22⋊D43—21no—
106C22×Dic43—21no—
107C22×Dic43—21no—
108#10621900—42no—
109C2×C4×D43C2×D411yescharacteristic
110C2×C4×D43C2×D411yescharacteristic
111C2×C4×D43#4111yescharacteristic
112C2×Dic86—22no—
113C2×Dic86C2×D411yescharacteristic
114SD16×C43—44no—
115M16×C43—42no—
116C2×C8×C43—21no—
117C2×C8×C43—22no—
118C2×C8×C43C2×D411yescharacteristic
119C2×C8×C43C2×D411yescharacteristic
120C4⋊C4×C43—22no—
121C4⋊C4×C43—22no—
122C4⋊C4×C43C2×D411yescharacteristic
123C22⋊C4×C43—21no—
124C42×C43C2411yescharacteristic
125C22⋊Dic43—21no—
126#10621885—44no—
127(C2×D43)⋊C4—21no—
128(C2×D43)⋊C4—42no—
129C4⋊Dic43—22no—
130C4⋊Dic43—22no—
131C4⋊Dic43—42no—
132C4⋊Dic43C2×D411yescharacteristic
133Dic43⋊C4—21no—
134Dic43⋊C4—21no—
135Dic43⋊C4—42no—
136C4×Dic43—21no—
137C4×Dic43—21no—
138C4×Dic43—21no—
139C4×Dic43—42no—
140C4×Dic43C2×D411yescharacteristic
141C4×Dic43C2×D411yescharacteristic
142C4×Dic43#4111yescharacteristic
143#10621877—42no—
144C2×C43⋊C8—21no—
145C2×C43⋊C8—22no—
146C2×C43⋊C8C2×D411yescharacteristic
147C2×C43⋊C8C2×D411yescharacteristic
148Dic172—42no—
149Dic172—42no—
150C8×D43—22no—
151C8×D43—41no—
152C23×C43—21no—
153C22×D43#12111yescharacteristic
154Q8×C43—42no—
155Q8×C43—42no—
156D4×C43—22no—
157C2×C4×C43—21no—
158C2×C4×C43—41no—
159C2×C4×C43—41no—
160C2×C4×C43—42no—
161C2×C4×C43C22×D411yescharacteristic
162C2×C4×C43C22×D411yescharacteristic
163C2×C4×C43C2×#4111yescharacteristic
164C22⋊D43—42no—
165C2×Dic43—21no—
166C2×Dic43—21no—
167C2×Dic43—42no—
168C2×Dic43—42no—
169C2×Dic43—42no—
170C2×Dic43#12111yescharacteristic
171C2×Dic43#12111yescharacteristic
172C2×Dic43#12111yescharacteristic
173C4×D43—21no—
174C4×D43—21no—
175C4×D43—22no—
176C4×D43—22no—
177Dic86—22no—
178Dic86—42no—
179Dic86—42no—
180C8×C43—21no—
181C8×C43—41no—
182C8×C43—42no—
183C8×C43#13512yes—
184C43⋊C8—21no—
185C43⋊C8—21no—
186C43⋊C8—41no—
187C43⋊C8—42no—
188#19161—431nomaximal, Sylow
189C22×C43—41no—
190C22×C43—41no—
191C22×C43—41no—
192C22×C43C2×#12111yescharacteristic
193C2×D43—21no—
194C2×D43—21no—
195C2×D43—21no—
196C4×C43—21no—
197C4×C43—41no—
198C4×C43—82no—
199C4×C43C2×#13511yescharacteristic
200C4×C43#57512yes—
201C4×C43#57511yescharacteristic
202Dic43—21no—
203Dic43—21no—
204Dic43—41no—
205Dic43—41no—
206Dic43—82no—
207Dic43#47312yes—
208#3170—431no—
209#3107—432no—
210#2965—431no—
211#1700—432no—
212#1699—432no—
213#1694—431no—
214#1693D4311yescharacteristic, complemented
215#1690—431no—
216#1689—431no—
217#1564—431no—
218#1544—432no—
219C2×C43—81no—
220C2×C43#303511yescharacteristic
221C2×C43#305411yescharacteristic
222C2×C43C2×#47311yescharacteristic
223D43—41no—
224#533—432no—
225C4×#41—431no—
226#500C2×D4311yescharacteristic
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#461C2×D4312yes—
236#452—862no—
237#446—431no—
238#446—431no—
239C4×Q16—861no—
240C4×Q16—861no—
241C4×Q16—862no—
242C4×SD16—862no—
243#436—431no—
244#436C2×D4311yescharacteristic
245#435—861no—
246#435—861no—
247#431—431no—
248#431—432no—
249#431—861no—
250C4×M16—861no—
251C2×C4×C8—431no—
252#335—432no—
253#334—431no—
254#334C2×D4311yescharacteristic
255#332—432no—
256#332—432no—
257#332—432no—
258#332C2×D4312yes—
259C43#1916111yescharacteristic, complemented, Sylow
260C2×#41—431no—
261C2×Q16—862no—
262C2×Q16—861no—
263C2×Q16—861no—
264C2×SD16—22no—
265C2×M16—21no—
266C2×M16—861no—
267C22×C8—431no—
268C22×C8—431no—
269C4⋊Q8—432no—
270C4⋊Q8C22×D4312yes—
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—861no—
280C4×D4—861no—
281C4×D4C22×D4311yescharacteristic
282#117—431no—
283#117—861no—
284#117—862no—
285C2×C42—431no—
286C2×C42—861no—
287#107—21no—
288#107—21no—
289#107—862no—
290#106—862no—
291C4⋊C8—431no—
292C4⋊C8—432no—
293C4⋊C8—861no—
294C4⋊C8—861no—
295C4⋊C8C22×D4311yescharacteristic
296C4⋊C8C22×D4312yes—
297#103—22no—
298#103—862no—
299#103—862no—
300#103—862no—
301#103—862no—
302#102—862no—
303C22⋊C8—21no—
304C22⋊C8—861no—
305C22⋊C8—862no—
306C22⋊C8—861no—
307#97—861no—
308#97—861no—
309C4×C8—431no—
310C4×C8—431no—
311C4×C8—431no—
312C4×C8—861no—
313C4×C8—862no—
314C4×C8C22×D4311yescharacteristic
315#41—1722no—
316C2×Q8—22no—
317C2×Q8—431no—
318C2×Q8—862no—
319C2×D4—861no—
320C2×D4D4×D4311yescharacteristic
321C22×C4—21no—
322C22×C4—431no—
323C22×C4—431no—
324C22×C4—431no—
325C22×C4—861no—
326C22×C4—861no—
327Q16—1722no—
328Q16—1724no—
329Q16—1722no—
330SD16—44no—
331M16—42no—
332M16—1722no—
333C2×C8—21no—
334C2×C8—22no—
335C2×C8—431no—
336C2×C8—431no—
337C2×C8—862no—
338C2×C8—861no—
339C2×C8—862no—
340C2×C8—1721no—
341C2×C8D4×D4311yescharacteristic
342C2×C8D4×D4311yescharacteristic
343C4⋊C4—22no—
344C4⋊C4—22no—
345C4⋊C4—431no—
346C4⋊C4—861no—
347C4⋊C4—861no—
348C4⋊C4—862no—
349C4⋊C4—862no—
350C4⋊C4—1722no—
351C4⋊C4—1722no—
352C4⋊C4D4×D4311yescharacteristic
353C22⋊C4—21no—
354C22⋊C4—861no—
355C22⋊C4—861no—
356C22⋊C4—1722no—
357C42—431no—
358C42—431no—
359C42—431no—
360C42—861no—
361C42—861no—
362C42—861no—
363C42—1722no—
364C42C23×D4311yescharacteristic
365C23—21no—
366C23—431no—
367Q8—42no—
368Q8—42no—
369Q8—862no—
370Q8—1722no—
371Q8—1722no—
372D4—22no—
373D4—1722no—
374C2×C4—21no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—42no—
378C2×C4—431no—
379C2×C4—431no—
380C2×C4—431no—
381C2×C4—862no—
382C2×C4—861no—
383C2×C4—862no—
384C2×C4—861no—
385C2×C4—861no—
386C2×C4—861no—
387C2×C4—1722no—
388C2×C4—1722no—
389C2×C4—1722no—
390C2×C4C2×D4×D4311yescharacteristic
391C2×C4C2×D4×D4311yescharacteristic
392C2×C4#41×D4311yescharacteristic
393C8—21no—
394C8—41no—
395C8—42no—
396C8—861no—
397C8—861no—
398C8—1722no—
399C8—1721no—
400C8#1306334612yes—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—861no—
405C22—861no—
406C22—861no—
407C22#121×D4311yescharacteristic
408C4—21no—
409C4—41no—
410C4—82no—
411C4—432no—
412C4—861no—
413C4—861no—
414C4—3442no—
415C4—1721no—
416C4—1721no—
417C4C2×#1306334611yescharacteristic
418C4#1458369512yes—
419C4#1458369811yescharacteristic
420C2—81no—
421C2—1721no—
422C2#1914405111yescharacteristic
423C2#1914420211yescharacteristic
424C2#473×D4311yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1693C2
socleC22×C43C2×#121
prime radicalC2×#10621900D4
hypercenter#1693D43
hypocenterC43#19161
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1693

Complements

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

NH ≅ G/Ntype
1. #19145182C2semidirect
4. #19134152C2semidirect
5. #19134144C2semidirect
6. #19134110C2semidirect
7. #19134090C2semidirect
8. #19134084C2semidirect
9. #19133340C2semidirect
10. #19133258C2semidirect
11. C43×#1693C2semidirect
214. #1693D43semidirect
259. C43#19161semidirect

Maximal subgroups

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

subgroupindex
#191451822
#191446632
#191435582
#191341522
#191341442
#191341102
#191340902
#191340842
#191333402
#191332582
C43×#16932
#1916143