Finite Group Databasebeta

← #27206685

Subgroups — #27206685

Order 13184.

510 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15693046C211yesmaximal, characteristic, complemented
2C2×#15693041C211yesmaximal, characteristic, complemented
3#20268437C211yesmaximal, characteristic, complemented
4#20268178C211yesmaximal, characteristic, complemented
5#20268035C211yesmaximal, characteristic, complemented
6#20268025C211yesmaximal, characteristic, complemented
7#20268013C211yesmaximal, characteristic, complemented
8#20267983C211yesmaximal, characteristic, complemented
9#20267953C211yesmaximal, characteristic, complemented
10#20267936C211yesmaximal, characteristic, complemented
11#20267934C211yesmaximal, characteristic, complemented
12#20267924C211yesmaximal, characteristic, complemented
13#20267889C211yesmaximal, characteristic, complemented
14#20267863C211yesmaximal, characteristic, complemented
15#550×C103C211yesmaximal, characteristic, complemented
16C2×#13110105C2211yescharacteristic
17C22×D412C2211yescharacteristic
18#15693046—24no—
19#15693041—24no—
20C2×#13110095C2211yescharacteristic, complemented
21C2×#13110093C2211yescharacteristic, complemented
22C2×#13110093C2211yescharacteristic, complemented
23C2×#13110092C2211yescharacteristic
24C2×#13110092C2211yescharacteristic
25C2×#13110090C2211yescharacteristic
26C2×#13110090C2211yescharacteristic
27C2×#13110090C2211yescharacteristic
28C2×#13110090C2211yescharacteristic
29C2×#13110089C2211yescharacteristic
30C22×C103⋊C8C2211yescharacteristic, complemented
31#15693009C2211yescharacteristic
32#15693006—21no—
33#15693000C2211yescharacteristic
34#15692995C2211yescharacteristic
35#15692994—21no—
36#15692989—21no—
37C4×D412C2211yescharacteristic
38C22⋊C4×D103—21no—
39#15692954C2211yescharacteristic, complemented
40C4⋊(C103⋊C8)C2211yescharacteristic, complemented
41#15692945C2211yescharacteristic, complemented
42#15692944C2211yescharacteristic, complemented
43#15692942C2211yescharacteristic, complemented
44#15692942C2211yescharacteristic, complemented
45#15692941C2211yescharacteristic
46#15692941C2211yescharacteristic
47C22⋊(C103⋊C8)C2211yescharacteristic
48C22⋊(C103⋊C8)C2211yescharacteristic, complemented
49#15692932C2211yescharacteristic, complemented
50C2×#41×C103C2211yescharacteristic
51C2×#41×C103C2211yescharacteristic, complemented
52#127×C103—21no—
53#127×C103C2211yescharacteristic, complemented
54#121×C103—21no—
55#121×C103—21no—
56#121×C103C2211yescharacteristic
57#121×C103C2211yescharacteristic, complemented
58C4×Q8×C103C2211yescharacteristic, complemented
59C4×D4×C103—21no—
60C4×D4×C103C2211yescharacteristic
61C23×D103—21no—
62#13110105—22no—
63#13110105—41no—
64C2×Dic206C2311yescharacteristic
65C2×D412—22no—
66C2×D412—21no—
67C2×D412—41no—
68C2×D412C2311yescharacteristic
69C2×D412C2311yescharacteristic
70C2×C22⋊D103—21no—
71C2×C22⋊D103—21no—
72C2×C4×D103—21no—
73C2×C4×D103—21no—
74#13110095—22no—
75#13110093—22no—
76#13110093—41no—
77#13110092—22no—
78#13110092D414yescomplemented
79#13110090—22no—
80#13110090—22no—
81#13110090—22no—
82#13110090—41no—
83#13110089—22no—
84C2×C103⋊C8—22no—
85C2×C103⋊C8C2311yescharacteristic
86C2×C103⋊C8C2311yescharacteristic
87C2×C103⋊C8C2311yescharacteristic
88C2×C103⋊C8C2311yescharacteristic
89C4⋊Dic103C2311yescharacteristic
90Dic103⋊C4—21no—
91C22⋊Dic103—21no—
92(C2×D103)⋊C4—21no—
93(C2×D103)⋊C4—21no—
94(C2×D103)⋊C4—21no—
95(C2×D103)⋊C4—21no—
96#41×C103—22no—
97#41×C103—22no—
98#41×C103—41no—
99#41×C103—41no—
100C2×Q8×C103C2311yescharacteristic
101C2×D4×C103—21no—
102C2×D4×C103—21no—
103C2×D4×C103—21no—
104C2×D4×C103—21no—
105C2×D4×C103—21no—
106C2×D4×C103—21no—
107C2×D4×C103D411yescharacteristic
108C2×D4×C103C2311yescharacteristic
109C2×D4×C103C2311yescharacteristic
110C22×C4×C103—21no—
111C22×C4×C103—21no—
112C22×C4×C103C2311yescharacteristic
113C22×C4×C103C2311yescharacteristic
114C4⋊C4×C103—21no—
115C4⋊C4×C103D411yescharacteristic
116C4⋊C4×C103C2311yescharacteristic
117C22⋊C4×C103—21no—
118C22⋊C4×C103—21no—
119C22⋊C4×C103D411yescharacteristic
120C22⋊C4×C103D411yescharacteristic
121C42×C103—21no—
122C42×C103C2311yescharacteristic
123C23×C103—21no—
124C23×C103—21no—
125C23×C103C2×D411yescharacteristic
126C23×C103C2×D411yescharacteristic
127C22×D103—21no—
128C22×D103—21no—
129C22×D103—42no—
130C22×D103—42no—
131C22×D103—81no—
132Q8×C103—21no—
133Q8×C103C2×D412yes—
134D4×C103—21no—
135D4×C103—21no—
136D4×C103—21no—
137D4×C103—21no—
138D4×C103—41no—
139D4×C103—42no—
140D4×C103—42no—
141D4×C103—42no—
142D4×C103—81no—
143D4×C103—81no—
144D4×C103—81no—
145C2×C4×C103—21no—
146C2×C4×C103—21no—
147C2×C4×C103—21no—
148C2×C4×C103—21no—
149C2×C4×C103—21no—
150C2×C4×C103—21no—
151C2×C4×C103—42no—
152C2×C4×C103—42no—
153C2×C4×C103C2×D411yescharacteristic
154C2×C4×C103C2×D411yescharacteristic
155C2×C4×C103C2×D411yescharacteristic
156C2×C4×C103C2×D411yescharacteristic
157C2×C4×C103C2411yescharacteristic
158C22⋊D103—42no—
159C22⋊D103—81no—
160C2×Dic103—21no—
161C2×Dic103—21no—
162D412—21no—
163D412—21no—
164D412—21no—
165D412—42no—
166D412C2×D412yes—
167C4×D103—42no—
168C4×D103—81no—
169Dic206—21no—
170Dic206—21no—
171C103⋊C8—21no—
172C103⋊C8—21no—
173C103⋊C8—21no—
174C103⋊C8C2×D412yes—
175C22×C103—21no—
176C22×C103—21no—
177C22×C103—21no—
178C22×C103—21no—
179C22×C103—21no—
180C22×C103—21no—
181C22×C103—41no—
182C22×C103—41no—
183C22×C103—41no—
184C22×C103—41no—
185C22×C103—41no—
186C22×C103—41no—
187C22×C103C22×D411yescharacteristic
188C2×D103—22no—
189C2×D103—41no—
190C2×D103—41no—
191C2×D103—41no—
192C2×D103—41no—
193C2×D103—41no—
194C2×D103—84no—
195C4×C103—21no—
196C4×C103—21no—
197C4×C103—22no—
198C4×C103—21no—
199C4×C103—21no—
200C4×C103—41no—
201C4×C103C22×D411yescharacteristic
202C4×C103H(5,𝔽2)11yescharacteristic
203Dic103—41no—
204Dic103—41no—
205C2×C103—41no—
206C2×C103—41no—
207C2×C103—81no—
208C2×C103—81no—
209C2×C103D4211yescharacteristic
210C2×C103#57511yescharacteristic
211C2×C103#57611yescharacteristic
212D103—42no—
213D103—81no—
214#3268—1031nomaximal, Sylow
215C103#326811yescharacteristic, complemented, Sylow
216C2×AGL(1,ℤ/8)—1031no—
217C2×#135—1031no—
218#550D10311yescharacteristic, complemented
219#546—1031no—
220#496—1031no—
221#468—1031no—
222#466—1031no—
223#464—1031no—
224#459—1031no—
225#452—1031no—
226#449—1031no—
227#449—1031no—
228#447—1031no—
229#440—1031no—
230#435—1031no—
231C2×#41—1031no—
232C2×#41C2×D10311yescharacteristic
233C2×#41C2×D10311yescharacteristic, complemented
234C22×D4—1031no—
235AGL(1,ℤ/8)—2064no—
236#135—2064no—
237C2×Q16—1031no—
238C2×SD16—1031no—
239C2×SD16—1031no—
240C2×SD16—1031no—
241C2×SD16—1031no—
242C2×D8—1031no—
243C2×D8—1031no—
244C2×D8—1031no—
245C2×D8—1031no—
246C2×M16—1031no—
247C22×C8—1031no—
248#127—21no—
249#127C2×D10311yescharacteristic, complemented
250#124—1031no—
251#123—2061no—
252C22⋊Q8—1031no—
253#121—21no—
254#121—21no—
255#121—1031no—
256#121—2061no—
257#121C2×D10311yescharacteristic
258#121C2×D10311yescharacteristic, complemented
259#120—2061no—
260C4×Q8C2×D10311yescharacteristic, complemented
261C4×D4—21no—
262C4×D4—1031no—
263C4×D4C2×D10311yescharacteristic
264C2×C22⋊C4—2061no—
265#107—1031no—
266C4⋊C8—1031no—
267#103—1031no—
268#103—1031no—
269#102—1031no—
270#102—1031no—
271#102—1031no—
272#102—1031no—
273C22⋊C8—1031no—
274C22⋊C8—1031no—
275#97—1031no—
276C24—2061no—
277#41—22no—
278#41—22no—
279#41—41no—
280#41—41no—
281#41—4121no—
282#41—2062no—
283C2×Q8—1031no—
284C2×Q8C22×D10311yescharacteristic
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—1031no—
292C2×D4—1031no—
293C2×D4—4121no—
294C2×D4—2062no—
295C2×D4—2061no—
296C2×D4—2061no—
297C2×D4—2061no—
298C2×D4C22⋊D10311yescharacteristic
299C2×D4C22×D10311yescharacteristic
300C2×D4C22×D10311yescharacteristic
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—2061no—
304C22×C4—2061no—
305C22×C4C22×D10311yescharacteristic
306C22×C4C22×D10311yescharacteristic
307Q16—2062no—
308SD16—1034no—
309SD16—4121no—
310SD16—2062no—
311SD16—2062no—
312D8—4121no—
313D8—2062no—
314D8—2062no—
315D8—2062no—
316M16—2062no—
317C2×C8—1031no—
318C2×C8—1031no—
319C2×C8—1031no—
320C2×C8—1031no—
321C2×C8—2062no—
322C4⋊C4—21no—
323C4⋊C4—1031no—
324C4⋊C4—2061no—
325C4⋊C4C22⋊D10311yescharacteristic
326C4⋊C4C22×D10311yescharacteristic
327C22⋊C4—21no—
328C22⋊C4—21no—
329C22⋊C4—2061no—
330C22⋊C4—2061no—
331C22⋊C4—2061no—
332C22⋊C4—2061no—
333C22⋊C4—2061no—
334C22⋊C4C22⋊D10311yescharacteristic
335C22⋊C4C22⋊D10311yescharacteristic
336C42—21no—
337C42C22×D10311yescharacteristic
338C23—21no—
339C23—21no—
340C23—8241no—
341C23—4122no—
342C23—4122no—
343C23—2061no—
344C23—2061no—
345C23C2×C22⋊D10311yescharacteristic
346C23C2×C22⋊D10311yescharacteristic
347Q8—21no—
348Q8—2061no—
349Q8—2061no—
350Q8D4×D10312yes—
351D4—21no—
352D4—21no—
353D4—21no—
354D4—21no—
355D4—41no—
356D4—42no—
357D4—42no—
358D4—42no—
359D4—81no—
360D4—81no—
361D4—81no—
362D4—8241no—
363D4—1032no—
364D4—4122no—
365D4—4122no—
366D4—2061no—
367D4—2061no—
368D4—2061no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—8241no—
378C2×C4—4122no—
379C2×C4—2061no—
380C2×C4—2061no—
381C2×C4C2×C22⋊D10311yescharacteristic
382C2×C4C2×C22⋊D10311yescharacteristic
383C2×C4C2×C22⋊D10311yescharacteristic
384C2×C4C2×C22⋊D10311yescharacteristic
385C2×C4C23×D10311yescharacteristic
386C8—1032no—
387C8—2061no—
388C8—2061no—
389C8—2061no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—8244no—
403C22—4121no—
404C22—4121no—
405C22—4121no—
406C22—4121no—
407C22—4121no—
408C22—2062no—
409C22C22×C22⋊D10311yescharacteristic
410C4—21no—
411C4—21no—
412C4—21no—
413C4—21no—
414C4—22no—
415C4—41no—
416C4—4121no—
417C4—4121no—
418C4C2×D4×D10311yescharacteristic
419C4#1569306611yescharacteristic
420C2—41no—
421C2—41no—
422C2—81no—
423C2—81no—
424C2—8241no—
425C2—4122no—
426C2D4×C22⋊D10311yescharacteristic
427C2#2026858911yescharacteristic
428C2#2026859411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#550×C103C2
socleC22×C103C22×D4
hypercenter#550D103
hypocenterC103#3268
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C4×D4 ◁ #550

Complements

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

NH ≅ G/Ntype
1. C2×#15693046C2semidirect
2. C2×#15693041C2semidirect
3. #20268437C2semidirect
4. #20268178C2semidirect
5. #20268035C2semidirect
6. #20268025C2semidirect
7. #20268013C2semidirect
8. #20267983C2semidirect
9. #20267953C2semidirect
10. #20267936C2semidirect
11. #20267934C2semidirect
12. #20267924C2semidirect
13. #20267889C2semidirect
14. #20267863C2semidirect
15. #550×C103C2semidirect
20. C2×#13110095C22semidirect
21. C2×#13110093C22semidirect
22. C2×#13110093C22semidirect
30. C22×C103⋊C8C22semidirect
39. #15692954C22semidirect
40. C4⋊(C103⋊C8)C22semidirect
41. #15692945C22semidirect
42. #15692944C22semidirect
43. #15692942C22semidirect
44. #15692942C22semidirect
48. C22⋊(C103⋊C8)C22semidirect
49. #15692932C22semidirect
51. C2×#41×C103C22semidirect
53. #127×C103C22semidirect
57. #121×C103C22semidirect
58. C4×Q8×C103C22semidirect
78. #13110092D4semidirect
215. C103#3268semidirect
218. #550D103semidirect
233. C2×#41C2×D103semidirect
249. #127C2×D103semidirect
258. #121C2×D103semidirect
260. C4×Q8C2×D103semidirect

Maximal subgroups

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

subgroupindex
C2×#156930462
C2×#156930412
#202684372
#202681782
#202680352
#202680252
#202680132
#202679832
#202679532
#202679362
#202679342
#202679242
#202678892
#202678632
#550×C1032
#3268103