Finite Group Databasebeta

← #28374823

Subgroups — #28374823

Order 13952.

460 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20295837C211yesmaximal, characteristic, complemented
2#20295834C211yesmaximal, characteristic, complemented
3#20295833C211yesmaximal, characteristic, complemented
4#20295397C211yesmaximal, characteristic, complemented
5#20295291C211yesmaximal, characteristic, complemented
6#20295289C211yesmaximal, characteristic, complemented
7#20295287C211yesmaximal, characteristic, complemented
8#20295286C211yesmaximal, characteristic, complemented
9#20295209C211yesmaximal, characteristic, complemented
10#20295207C211yesmaximal, characteristic, complemented
11#20295194C211yesmaximal, characteristic, complemented
12#20295192C211yesmaximal, characteristic, complemented
13#20295143C211yesmaximal, characteristic, complemented
14#20295141C211yesmaximal, characteristic, complemented
15#577×C109C211yesmaximal, characteristic, complemented
16#16812746C2211yescharacteristic
17#16812745C2211yescharacteristic, complemented
18#16812731—21no—
19#16812730—21no—
20#16812730C2211yescharacteristic, complemented
21#16812729—21no—
22#16812729C2211yescharacteristic, complemented
23#16812729C2211yescharacteristic, complemented
24#16812725—21no—
25#16812725C2211yescharacteristic
26#16812724—21no—
27#16812724C2211yescharacteristic
28#16812724C2211yescharacteristic
29#16812723—21no—
30#16812720—21no—
31#16812719—21no—
32#16812719—21no—
33#16812719C2211yescharacteristic
34C2×#13182018C2211yescharacteristic, complemented
35C2×#13182017—21no—
36C2×#13182017C2211yescharacteristic, complemented
37C2×#13182016—21no—
38C2×#13182016C2211yescharacteristic, complemented
39SD16×D109—21no—
40#16812706C2211yescharacteristic, complemented
41#16812706C2211yescharacteristic, complemented
42#16812705C2211yescharacteristic, complemented
43#16812697C2211yescharacteristic, complemented
44#16812695C2211yescharacteristic
45#16812635C2211yescharacteristic, complemented
46#16812634C2211yescharacteristic, complemented
47#16812626C2211yescharacteristic, complemented
48#16812626C2211yescharacteristic, complemented
49#16812626C2211yescharacteristic, complemented
50#16812625C2211yescharacteristic, complemented
51#16812618C2211yescharacteristic, complemented
52#16812617C2211yescharacteristic, complemented
53#16812616C2211yescharacteristic, complemented
54#16812615C2211yescharacteristic, complemented
55C8×Dic109C2211yescharacteristic, complemented
562−1+4×C109C2211yescharacteristic
57H(5,𝔽2)×C109C2211yescharacteristic, complemented
58#137×C109—21no—
59#137×C109C2211yescharacteristic, complemented
60AGL(1,ℤ/8)×C109—21no—
61AGL(1,ℤ/8)×C109C2211yescharacteristic
62#135×C109—21no—
63#135×C109C2211yescharacteristic
64C2×SD16×C109—21no—
65C2×SD16×C109C2211yescharacteristic, complemented
66#131×C109C2211yescharacteristic, complemented
67#13182030—21no—
68#13182029—21no—
69#13182029—21no—
70#13182029C2311yescharacteristic
71#13182028—21no—
72#13182028—41no—
73C2×Dic218—21no—
74C2×Dic218C2311yescharacteristic
75Q8×D109—21no—
76C2×D436—21no—
77C2×D436C2311yescharacteristic
78C2×C22⋊D109—41no—
79D4×D109—21no—
80D4×D109—41no—
81#13182019—21no—
82#13182019—21no—
83#13182019—21no—
84#13182019D411yescharacteristic, complemented
85#13182018—21no—
86#13182018—21no—
87#13182017—21no—
88#13182017—21no—
89#13182017—21no—
90#13182017—21no—
91#13182017—21no—
92#13182017D411yescharacteristic, complemented
93#13182016—21no—
94#13182016—21no—
95#13182016—21no—
96#13182016—21no—
97#13182016—21no—
98#13182016D411yescharacteristic, complemented
99#13182014—21no—
100#13182014—21no—
101#13182014—21no—
102#13182014D411yescharacteristic, complemented
103#13182013—21no—
104#13182013—21no—
105#13182013C2311yescharacteristic
106#13182013C2311yescharacteristic
107#13182013C2311yescharacteristic
108#13182012—21no—
109C2×#11724784—21no—
110C2×#11724784—21no—
111C2×#11724784C2311yescharacteristic
112C8×D109—21no—
113#13182008—41no—
114C4×Dic109C2311yescharacteristic
115#41×C109—21no—
116#41×C109—21no—
117#41×C109—21no—
118#41×C109—21no—
119#41×C109—41no—
120#41×C109C2311yescharacteristic
121#41×C109C2311yescharacteristic
122#41×C109C2311yescharacteristic
123C2×Q8×C109—21no—
124C2×Q8×C109—21no—
125C2×Q8×C109C2311yescharacteristic
126C2×D4×C109—21no—
127C2×D4×C109—21no—
128C2×D4×C109—41no—
129C2×D4×C109C2311yescharacteristic
130Q16×C109—21no—
131Q16×C109D411yescharacteristic, complemented
132SD16×C109—21no—
133SD16×C109—21no—
134SD16×C109—21no—
135SD16×C109—21no—
136SD16×C109D411yescharacteristic, complemented
137SD16×C109D411yescharacteristic, complemented
138D8×C109—21no—
139D8×C109D411yescharacteristic, complemented
140M16×C109—21no—
141M16×C109C2311yescharacteristic
142C2×C8×C109—21no—
143C2×C8×C109C2311yescharacteristic
144C23×C109—21no—
145C23×C109—41no—
146C22×D109—21no—
147C22×D109—41no—
148Q8×C109—21no—
149Q8×C109—21no—
150Q8×C109—41no—
151Q8×C109C2×D411yescharacteristic
152Q8×C109C2×D411yescharacteristic
153Q8×C109C2×D411yescharacteristic
154D4×C109—21no—
155D4×C109—21no—
156D4×C109—21no—
157D4×C109—21no—
158D4×C109—21no—
159D4×C109—41no—
160D4×C109—41no—
161D4×C109—41no—
162D4×C109C2×D411yescharacteristic
163D4×C109C2×D411yescharacteristic
164D4×C109C2×D411yescharacteristic
165C2×C4×C109—21no—
166C2×C4×C109—21no—
167C2×C4×C109—21no—
168C2×C4×C109—21no—
169C2×C4×C109—41no—
170C2×C4×C109—41no—
171C2×C4×C109—41no—
172C2×C4×C109C2411yescharacteristic
173C22⋊D109—21no—
174C22⋊D109—41no—
175C22⋊D109—41no—
176C22⋊D109—82no—
177C2×Dic109—21no—
178C2×Dic109—21no—
179C2×Dic109—41no—
180D436—21no—
181D436—21no—
182D436—41no—
183D436C2×D411yescharacteristic
184C4×D109—21no—
185C4×D109—41no—
186C4×D109—41no—
187Dic218—21no—
188Dic218—21no—
189Dic218—41no—
190Dic218C2×D411yescharacteristic
191C8×C109—21no—
192C8×C109C2×D411yescharacteristic
193C8×C109C2×D411yescharacteristic
194#11724784—21no—
195#11724784—21no—
196#11724784—21no—
197#11724784C2×D411yescharacteristic
198#11724784C2×D411yescharacteristic
199C22×C109—21no—
200C22×C109—21no—
201C22×C109—21no—
202C22×C109—41no—
203C22×C109—81no—
204C22×C109—161no—
205C22×C109H(5,𝔽2)11yescharacteristic
206C2×D109—21no—
207C2×D109—41no—
208C2×D109—81no—
209C2×D109—161no—
210C4×C109—21no—
211C4×C109—21no—
212C4×C109—21no—
213C4×C109—41no—
214C4×C109C22×D411yescharacteristic
215C4×C109C22×D411yescharacteristic
216Dic109—22no—
217Dic109—21no—
218Dic109—41no—
219C2×C109—21no—
220C2×C109—41no—
221C2×C109—41no—
222C2×C109—41no—
223C2×C109—81no—
224C2×C109D4211yescharacteristic
225D109—41no—
226D109—81no—
227#3291—1091nomaximal, Sylow
228C109#329111yescharacteristic, complemented, Sylow
229#577—1091no—
230#577—1091no—
231#577—1091no—
232#577D10911yescharacteristic, complemented
233#492—1091no—
234#471—1091no—
235#471—1091no—
236#471—1091no—
237#471—1091no—
238#456—1091no—
239#456—1091no—
240#453—1091no—
241#453—1091no—
242#443—1091no—
243#443—1091no—
2442−1+4—1091no—
2452−1+4C2×D10911yescharacteristic
246H(5,𝔽2)—1091no—
247H(5,𝔽2)C2×D10911yescharacteristic, complemented
248#137—21no—
249#137—1091no—
250#137—1091no—
251#137—1091no—
252#137—2181no—
253#137—2181no—
254#137—2181no—
255#137C2×D10911yescharacteristic, complemented
256AGL(1,ℤ/8)—21no—
257AGL(1,ℤ/8)—1091no—
258AGL(1,ℤ/8)—1091no—
259AGL(1,ℤ/8)—1091no—
260AGL(1,ℤ/8)—2181no—
261AGL(1,ℤ/8)—2181no—
262AGL(1,ℤ/8)—2181no—
263AGL(1,ℤ/8)C2×D10911yescharacteristic
264#135—21no—
265#135—1091no—
266#135—2181no—
267#135—2181no—
268#135—2181no—
269#135C2×D10911yescharacteristic
270C2×SD16—21no—
271C2×SD16—1091no—
272C2×SD16—1091no—
273C2×SD16—1091no—
274C2×SD16—2181no—
275C2×SD16—2181no—
276C2×SD16—2181no—
277C2×SD16C2×D10911yescharacteristic, complemented
278#131—1091no—
279#131—1091no—
280#131—1091no—
281#131C2×D10911yescharacteristic, complemented
282C4⋊Q8—1091no—
283#127—1091no—
284#108—1091no—
285#108—1091no—
286#104—1091no—
287#104—1091no—
288#104—1091no—
289#104—1091no—
290#101—1091no—
291#101—1091no—
292#100—1091no—
293#100—1091no—
294C4×C8—1091no—
295#41—21no—
296#41—21no—
297#41—21no—
298#41—21no—
299#41—41no—
300#41—1091no—
301#41—4361no—
302#41—2181no—
303#41—2181no—
304#41—2181no—
305#41—2181no—
306#41C22×D10911yescharacteristic
307#41C22×D10911yescharacteristic
308#41C22×D10911yescharacteristic
309C2×Q8—21no—
310C2×Q8—21no—
311C2×Q8—1091no—
312C2×Q8—2181no—
313C2×Q8—2181no—
314C2×Q8C22×D10911yescharacteristic
315C2×D4—21no—
316C2×D4—21no—
317C2×D4—41no—
318C2×D4—1091no—
319C2×D4—4361no—
320C2×D4—4361no—
321C2×D4—2181no—
322C2×D4—2181no—
323C2×D4C22×D10911yescharacteristic
324Q16—21no—
325Q16—1091no—
326Q16—2181no—
327Q16—2181no—
328Q16—2181no—
329Q16C22⋊D10911yescharacteristic, complemented
330SD16—21no—
331SD16—21no—
332SD16—21no—
333SD16—21no—
334SD16—1091no—
335SD16—1091no—
336SD16—2181no—
337SD16—2181no—
338SD16—2181no—
339SD16—2181no—
340SD16—2181no—
341SD16—2181no—
342SD16—2181no—
343SD16—2181no—
344SD16—2181no—
345SD16—2181no—
346SD16—2181no—
347SD16—2181no—
348SD16C22⋊D10911yescharacteristic, complemented
349SD16C22⋊D10911yescharacteristic, complemented
350D8—21no—
351D8—1091no—
352D8—2181no—
353D8—2181no—
354D8—2181no—
355D8C22⋊D10911yescharacteristic, complemented
356M16—21no—
357M16—1091no—
358M16—1091no—
359M16—1091no—
360M16—2181no—
361M16—2181no—
362M16—2181no—
363M16C22×D10911yescharacteristic
364C2×C8—21no—
365C2×C8—1091no—
366C2×C8—2181no—
367C2×C8—2181no—
368C2×C8—2181no—
369C2×C8C22×D10911yescharacteristic
370C4⋊C4—4361no—
371C42—1091no—
372C23—21no—
373C23—41no—
374C23—4361no—
375C23—2181no—
376Q8—21no—
377Q8—21no—
378Q8—41no—
379Q8—1091no—
380Q8—4361no—
381Q8—2181no—
382Q8—2181no—
383Q8D4×D10911yescharacteristic
384Q8C2×C22⋊D10911yescharacteristic
385Q8C2×C22⋊D10911yescharacteristic
386D4—21no—
387D4—21no—
388D4—21no—
389D4—21no—
390D4—21no—
391D4—41no—
392D4—41no—
393D4—41no—
394D4—8722no—
395D4—1091no—
396D4—4361no—
397D4—4361no—
398D4—4361no—
399D4—2181no—
400D4—2181no—
401D4—2181no—
402D4D4×D10911yescharacteristic
403D4C2×C22⋊D10911yescharacteristic
404D4C2×C22⋊D10911yescharacteristic
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—4361no—
413C2×C4—4361no—
414C2×C4—4361no—
415C2×C4—2181no—
416C2×C4—2181no—
417C2×C4—2181no—
418C2×C4C23×D10911yescharacteristic
419C8—21no—
420C8—1091no—
421C8—1091no—
422C8—2181no—
423C8—2181no—
424C8—2181no—
425C8C2×C22⋊D10911yescharacteristic
426C8C2×C22⋊D10911yescharacteristic
427C22—21no—
428C22—21no—
429C22—21no—
430C22—41no—
431C22—81no—
432C22—161no—
433C22—8721no—
434C22—4361no—
435C22—17441no—
436C22—2181no—
437C22#1681274411yescharacteristic
438C4—21no—
439C4—21no—
440C4—21no—
441C4—41no—
442C4—4361no—
443C4—2182no—
444C4—2181no—
445C4C2×D4×D10911yescharacteristic
446C4C22×C22⋊D10911yescharacteristic
447C2—21no—
448C2—41no—
449C2—41no—
450C2—41no—
451C2—81no—
452C2—8721no—
453C2—4361no—
454C2D4×C22⋊D10911yescharacteristic
subgroupG/H
centerC2D4×C22⋊D109
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
Fitting#577×C109C2
socleC2×C109D42
hypercenter#577D109
hypocenterC109#3291
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2 ◁ C2×C4 ◁ #577

Complements

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

NH ≅ G/Ntype
1. #20295837C2semidirect
2. #20295834C2semidirect
3. #20295833C2semidirect
4. #20295397C2semidirect
5. #20295291C2semidirect
6. #20295289C2semidirect
7. #20295287C2semidirect
8. #20295286C2semidirect
9. #20295209C2semidirect
10. #20295207C2semidirect
11. #20295194C2semidirect
12. #20295192C2semidirect
13. #20295143C2semidirect
14. #20295141C2semidirect
15. #577×C109C2semidirect
17. #16812745C22semidirect
20. #16812730C22semidirect
22. #16812729C22semidirect
23. #16812729C22semidirect
34. C2×#13182018C22semidirect
36. C2×#13182017C22semidirect
38. C2×#13182016C22semidirect
40. #16812706C22semidirect
41. #16812706C22semidirect
42. #16812705C22semidirect
43. #16812697C22semidirect
45. #16812635C22semidirect
46. #16812634C22semidirect
47. #16812626C22semidirect
48. #16812626C22semidirect
49. #16812626C22semidirect
50. #16812625C22semidirect
51. #16812618C22semidirect
52. #16812617C22semidirect
53. #16812616C22semidirect
54. #16812615C22semidirect
55. C8×Dic109C22semidirect
57. H(5,𝔽2)×C109C22semidirect
59. #137×C109C22semidirect
65. C2×SD16×C109C22semidirect
66. #131×C109C22semidirect
84. #13182019D4semidirect
92. #13182017D4semidirect
98. #13182016D4semidirect
102. #13182014D4semidirect
131. Q16×C109D4semidirect
136. SD16×C109D4semidirect
137. SD16×C109D4semidirect
139. D8×C109D4semidirect
228. C109#3291semidirect
232. #577D109semidirect
247. H(5,𝔽2)C2×D109semidirect
255. #137C2×D109semidirect
277. C2×SD16C2×D109semidirect
281. #131C2×D109semidirect
329. Q16C22⋊D109semidirect
348. SD16C22⋊D109semidirect
349. SD16C22⋊D109semidirect
355. D8C22⋊D109semidirect

Maximal subgroups

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

subgroupindex
#202958372
#202958342
#202958332
#202953972
#202952912
#202952892
#202952872
#202952862
#202952092
#202952072
#202951942
#202951922
#202951432
#202951412
#577×C1092
#3291109