Finite Group Databasebeta

← #25254179

Subgroups — #25254179

Order 11008.

464 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19146965C211yesmaximal, characteristic
2#19146962C211yesmaximal, characteristic
3#19136871C211yesmaximal, characteristic, complemented
4#19136806C211yesmaximal, characteristic, complemented
5#19136801C211yesmaximal, characteristic, complemented
6#19136799C211yesmaximal, characteristic, complemented
7#19136796C211yesmaximal, characteristic, complemented
8#19136760C211yesmaximal, characteristic, complemented
9#19136702C211yesmaximal, characteristic, complemented
10#19136702C211yesmaximal, characteristic, complemented
11C4×#13063271C211yesmaximal, characteristic, complemented
12#19136426C211yesmaximal, characteristic
13#19136382C211yesmaximal, characteristic, complemented
14#19136380C211yesmaximal, characteristic, complemented
15C43×#2229C211yesmaximal, characteristic, complemented
16#14583590—21no—
17#14583587—21no—
18C2×#13063271C2211yescharacteristic
19C2×#13063264C2211yescharacteristic
20C2×#13063264C2211yescharacteristic
21#14583301C2211yescharacteristic
22#14583243—21no—
23#14583238—21no—
24#14583231—21no—
25#14583228—21no—
26#14583206—21no—
27#14583203—21no—
28#14583141C2211yescharacteristic
29#14583141C2211yescharacteristic
30#14583137C2211yescharacteristic
31#14583137C2211yescharacteristic
32C4×Dic172C2211yescharacteristic
33C8×D172C2211yescharacteristic
34#14582936C2211yescharacteristic
35#14582936C2211yescharacteristic
36#107×D43C2211yescharacteristic
37#107×D43C2211yescharacteristic
38#14582727C2211yescharacteristic
39#14582726C2211yescharacteristic
40#14582726C2211yescharacteristic
41#14582725C2211yescharacteristic
42#14582724C2211yescharacteristic
43#14582724C2211yescharacteristic
44#14582724C2211yescharacteristic
45#14582704C2211yescharacteristic
46#14582704C2211yescharacteristic
47#14582703C2211yescharacteristic
48#14582702C2211yescharacteristic
49(C2×D43)⋊C16C2211yescharacteristic
50(C2×D43)⋊C16C2211yescharacteristic
51C4×C43⋊C16C2211yescharacteristic
52C43×#499C2211yescharacteristic
53C4×Q16×C43C2211yescharacteristic
54C43×#367C2211yescharacteristic
55C43×#366C2211yescharacteristic
56C43×C4⋊C16C2211yescharacteristic
57C43×#358C2211yescharacteristic
58C43×#358C2211yescharacteristic
59C2×Dic172C2311yescharacteristic
60C2×C8×D43C2311yescharacteristic
61C2×C8×D43C2311yescharacteristic
62#13063320—41no—
63#13063319—41no—
64#13063317—21no—
65#13063316—41no—
66#13063315—41no—
67#13063310—41no—
68#13063310—41no—
69#13063305—21no—
70#13063305—21no—
71#13063301—21no—
72#13063301—21no—
73C4×Dic86—21no—
74C4×D172D411yescharacteristic
75#13063283—21no—
76#13063283—21no—
77#13063283—41no—
78#13063282—41no—
79C4⋊C4×D43—21no—
80C4⋊C4×D43—21no—
81#13063271—22no—
82#13063264—22no—
83#13063264—22no—
84C2×C43⋊C16C2311yescharacteristic
85C2×C43⋊C16C2311yescharacteristic
86#13063259C2311yescharacteristic
87#13063259C2311yescharacteristic
88#13063259C2311yescharacteristic
89#13063258—21no—
90#13063258—21no—
91#13063257—21no—
92#13063256—21no—
93#13063256—21no—
94C4⋊(C43⋊C8)D411yescharacteristic
95#13063250—21no—
96#13063249—21no—
97#13063249—21no—
98#13063248—21no—
99#13063248—21no—
100(C2×D43)⋊C8D411yescharacteristic
101(C2×D43)⋊C8D411yescharacteristic
102C2×Q16×C43C2311yescharacteristic
103#125×C43—21no—
104C4×Q8×C43—21no—
105C2×C16×C43C2311yescharacteristic
106C2×C16×C43C2311yescharacteristic
107#107×C43C2311yescharacteristic
108#107×C43C2311yescharacteristic
109#107×C43C2311yescharacteristic
110#106×C43—21no—
111#103×C43—21no—
112C4×C8×C43C2311yescharacteristic
113C2×Q8×C43—21no—
114C2×D172D811yescharacteristic
115C2×C4×D43—41no—
116C2×C4×D43—41no—
117C2×C4×D43C2×D411yescharacteristic
118C2×C4×D43C2×D411yescharacteristic
119C2×Dic86—21no—
120Q16×C43—21no—
121Q16×C43—21no—
122C2×C8×C43C2×D411yescharacteristic
123C2×C8×C43C2411yescharacteristic
124C4⋊C4×C43—21no—
125C4⋊C4×C43—21no—
126C4⋊C4×C43—21no—
127C4⋊C4×C43—41no—
128C4⋊C4×C43—41no—
129C4⋊C4×C43—41no—
130C42×C43—41no—
131C42×C43C2×D411yescharacteristic
132(C2×D43)⋊C4—41no—
133(C2×D43)⋊C4—41no—
134(C2×D43)⋊C4—41no—
135(C2×D43)⋊C4—41no—
136(C2×D43)⋊C4—41no—
137(C2×D43)⋊C4—41no—
138(C2×D43)⋊C4D811yescharacteristic
139(C2×D43)⋊C4D811yescharacteristic
140C4⋊Dic43—21no—
141C4⋊Dic43—21no—
142C4⋊Dic43—21no—
143C4⋊Dic43—41no—
144C4⋊Dic43—41no—
145C4⋊Dic43D811yescharacteristic
146Dic43⋊C4—41no—
147Dic43⋊C4—41no—
148Dic43⋊C4—41no—
149Dic43⋊C4—41no—
150Dic43⋊C4—41no—
151Dic43⋊C4—41no—
152Dic43⋊C4—41no—
153C4×Dic43—41no—
154C4×Dic43—41no—
155C4×Dic43—41no—
156C2×C43⋊C8C2×D411yescharacteristic
157C2×C43⋊C8C2×D411yescharacteristic
158Dic172—21no—
159Dic172—21no—
160C8×D43—21no—
161C8×D43—21no—
162C8×D43—21no—
163C8×D43—21no—
164C16×C43—21no—
165C16×C43—21no—
166C43⋊C16—21no—
167C43⋊C16#4112yes—
168C22×D43C2×D811yescharacteristic
169C22×D43C2×D811yescharacteristic
170Q8×C43—41no—
171Q8×C43—41no—
172C2×C4×C43—41no—
173C2×C4×C43—41no—
174C2×C4×C43—41no—
175C2×C4×C43—41no—
176C2×C4×C43C2×D811yescharacteristic
177C2×C4×C43C2×D811yescharacteristic
178C2×C4×C43C22×D411yescharacteristic
179C2×Dic43—41no—
180C2×Dic43—41no—
181C2×Dic43—41no—
182C2×Dic43—41no—
183C2×Dic43C2×D811yescharacteristic
184C2×Dic43C2×D811yescharacteristic
185D172—41no—
186C4×D43—21no—
187C4×D43—21no—
188C4×D43—21no—
189C4×D43—21no—
190C4×D43—82no—
191C4×D43—82no—
192Dic86—41no—
193Dic86—41no—
194C8×C43—21no—
195C8×C43C2×#4111yescharacteristic
196C8×C432−1+411yescharacteristic
197C43⋊C8—21no—
198C43⋊C8—21no—
199#33919—431nomaximal, Sylow
200C22×C43C22×D811yescharacteristic
201C2×D43—21no—
202C2×D43—21no—
203C2×D43—21no—
204C2×D43—21no—
205C2×D43—21no—
206C2×D43—21no—
207C4×C43—21no—
208C4×C43—21no—
209C4×C43—81no—
210C4×C43—81no—
211C4×C43—81no—
212C4×C43—81no—
213C4×C43#54711yescharacteristic
214C4×C43#57811yescharacteristic
215Dic43—21no—
216Dic43—21no—
217Dic43—81no—
218Dic43—81no—
219Dic43—81no—
220Dic43—81no—
221#3336—431no—
222#3336—431no—
223#2253—431no—
224#2237—431no—
225#2237—431no—
226#2236—431no—
227#2236—431no—
228#2229—431no—
229#2229D4311yescharacteristic, complemented
230#2219—431no—
231#2219—431no—
232C4×Q32—431no—
233#2169—431no—
234#2159—431no—
235#2159—431no—
236C2×C43#333411yescharacteristic
237C2×C43#341411yescharacteristic
238C2×C43#341711yescharacteristic
239D43—41no—
240D43—41no—
241#552—861no—
242#552—861no—
243C2×Q32—431no—
244C2×M32—431no—
245C2×M32—431no—
246#499—431no—
247#499C2×D4311yescharacteristic
248#485—861no—
249#485—861no—
250#483—861no—
251#483—861no—
252#479—861no—
253#479—861no—
254#467—431no—
255#467—431no—
256#467—431no—
257#467—431no—
258C4×Q16—431no—
259C4×Q16C2×D4311yescharacteristic
260C8×D4—431no—
261#427—431no—
262#427—431no—
263C2×#107—431no—
264C2×#107—431no—
265#367—431no—
266#367—431no—
267#367—431no—
268#367C2×D4311yescharacteristic
269#366—431no—
270#366—431no—
271#366—431no—
272#366—431no—
273#366C2×D4311yescharacteristic
274C4⋊C16C2×D4311yescharacteristic
275#358—431no—
276#358—431no—
277#358—431no—
278#358—431no—
279#358C2×D4311yescharacteristic
280#358C2×D4311yescharacteristic
281C22⋊C16—431no—
282C22⋊C16—431no—
283C4×C16—431no—
284C43#3391911yescharacteristic, complemented, Sylow
285C2×Q16—431no—
286C2×Q16C22×D4311yescharacteristic
287C22×C8—431no—
288C22×C8—431no—
289#126—1721no—
290#126—1721no—
291#125—21no—
292#125—861no—
293#125—1721no—
294#125—1721no—
295#123—1721no—
296#123—1721no—
297C22⋊Q8—861no—
298C22⋊Q8—861no—
299C22⋊Q8—861no—
300C22⋊Q8—861no—
301C4×Q8—21no—
302C4×Q8—861no—
303C4×D4—431no—
304#117—861no—
305#117—861no—
306#117—1721no—
307#117—1721no—
308C2×C4⋊C4—861no—
309C2×C4⋊C4—861no—
310Q32—862no—
311M32—862no—
312M32—862no—
313C2×C16—431no—
314C2×C16—431no—
315C2×C16C22×D4311yescharacteristic
316C2×C16C22×D4311yescharacteristic
317#107—431no—
318#107—431no—
319#107—431no—
320#107—861no—
321#107—861no—
322#107C22×D4311yescharacteristic
323#107C22×D4311yescharacteristic
324#107C22×D4311yescharacteristic
325#106—21no—
326#106—861no—
327#106—861no—
328#106—861no—
329C4⋊C8—431no—
330#103—21no—
331#103—861no—
332#103—861no—
333#103—861no—
334#103—861no—
335#103—861no—
336C22⋊C8—431no—
337C22⋊C8—431no—
338C4×C8C22×D4311yescharacteristic
339C2×Q8—21no—
340C2×Q8—861no—
341C2×D4—431no—
342C22×C4—431no—
343C22×C4—431no—
344C22×C4—1721no—
345C22×C4—1721no—
346Q16—21no—
347Q16—21no—
348Q16—861no—
349Q16—861no—
350C2×C8—431no—
351C2×C8—431no—
352C2×C8—861no—
353C2×C8—861no—
354C2×C8—861no—
355C2×C8—861no—
356C2×C8D4×D4311yescharacteristic
357C2×C8C23×D4311yescharacteristic
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—41no—
362C4⋊C4—41no—
363C4⋊C4—41no—
364C4⋊C4—431no—
365C4⋊C4—861no—
366C4⋊C4—861no—
367C4⋊C4—861no—
368C4⋊C4—1721no—
369C4⋊C4—1721no—
370C4⋊C4—1721no—
371C4⋊C4—1721no—
372C4⋊C4—1721no—
373C4⋊C4—1721no—
374C4⋊C4—1721no—
375C4⋊C4—1721no—
376C4⋊C4—1721no—
377C22⋊C4—431no—
378C22⋊C4—431no—
379C22⋊C4—1721no—
380C22⋊C4—1721no—
381C22⋊C4—1721no—
382C22⋊C4—1721no—
383C22⋊C4—1721no—
384C22⋊C4—1721no—
385C42—41no—
386C42—1721no—
387C42—1721no—
388C42—1721no—
389C42D4×D4311yescharacteristic
390C16—21no—
391C16—21no—
392C16—432no—
393C16—861no—
394C23—431no—
395C23—431no—
396Q8—41no—
397Q8—41no—
398Q8—1721no—
399Q8—1721no—
400D4—1721no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—431no—
406C2×C4—431no—
407C2×C4—861no—
408C2×C4—861no—
409C2×C4—861no—
410C2×C4—861no—
411C2×C4—3442no—
412C2×C4—3442no—
413C2×C4—1721no—
414C2×C4—1721no—
415C2×C4—1721no—
416C2×C4—1721no—
417C2×C4D8×D4311yescharacteristic
418C2×C4D8×D4311yescharacteristic
419C2×C4C2×D4×D4311yescharacteristic
420C8—21no—
421C8—861no—
422C8—861no—
423C8#41×D4311yescharacteristic
424C8#1306337311yescharacteristic
425C22—861no—
426C22—861no—
427C22—861no—
428C22—861no—
429C22—861no—
430C22—861no—
431C22C2×D8×D4311yescharacteristic
432C4—21no—
433C4—21no—
434C4—81no—
435C4—81no—
436C4—81no—
437C4—81no—
438C4—861no—
439C4—861no—
440C4—3441no—
441C4—3441no—
442C4—3441no—
443C4—3441no—
444C4#1458355111yescharacteristic
445C4#1458371511yescharacteristic
446C2—1721no—
447C2—1721no—
448C2#1914694111yescharacteristic
449C2#1914772811yescharacteristic
450C2#1914774711yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2229C2
socleC22×C43C22×D8
prime radicalC2×D172D8
hypercenter#2229D43
hypocenterC43#33919
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2229

Complements

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

NH ≅ G/Ntype
3. #19136871C2semidirect
4. #19136806C2semidirect
5. #19136801C2semidirect
6. #19136799C2semidirect
7. #19136796C2semidirect
8. #19136760C2semidirect
9. #19136702C2semidirect
10. #19136702C2semidirect
11. C4×#13063271C2semidirect
13. #19136382C2semidirect
14. #19136380C2semidirect
15. C43×#2229C2semidirect
229. #2229D43semidirect
284. C43#33919semidirect

Maximal subgroups

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

subgroupindex
#191469652
#191469622
#191368712
#191368062
#191368012
#191367992
#191367962
#191367602
#191367022
C4×#130632712
#191364262
#191363822
#191363802
C43×#22292
#3391943