Finite Group Databasebeta

← #27206670

Subgroups — #27206670

Order 13184.

500 conjugacy classes of subgroups.

The subgroup lattice has 418 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#20268183C211yesmaximal, characteristic, complemented
5#20268047C211yesmaximal, characteristic, complemented
6#20268022C211yesmaximal, characteristic, complemented
7#20268006C211yesmaximal, characteristic, complemented
8#20267993C211yesmaximal, characteristic, complemented
9#20267953C211yesmaximal, characteristic, complemented
10#20267951C211yesmaximal, characteristic, complemented
11#20267941C211yesmaximal, characteristic, complemented
12#20267936C211yesmaximal, characteristic, complemented
13#20267901C211yesmaximal, characteristic, complemented
14#20267863C211yesmaximal, characteristic, complemented
15#547×C103C211yesmaximal, characteristic, complemented
16C2×#13110105C2211yescharacteristic
17C22×D412C2211yescharacteristic
18#15693046—24no—
19#15693041—24no—
20C2×#13110095C2211yescharacteristic, complemented
21C2×#13110095C2211yescharacteristic, complemented
22C2×#13110093C2211yescharacteristic, complemented
23C2×#13110092C2211yescharacteristic
24C2×#13110092C2211yescharacteristic
25C2×#13110092C2211yescharacteristic
26C2×#13110092C2211yescharacteristic
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#15692952C2211yescharacteristic, complemented
40C4⋊(C103⋊C8)C2211yescharacteristic, complemented
41#15692945C2211yescharacteristic, complemented
42#15692945C2211yescharacteristic, complemented
43#15692944C2211yescharacteristic, 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
52C4⋊Q8×C103C2211yescharacteristic, complemented
53#123×C103—21no—
54#123×C103—21no—
55C22⋊Q8×C103C2211yescharacteristic
56C22⋊Q8×C103C2211yescharacteristic, complemented
57#121×C103—21no—
58C4×D4×C103C2211yescharacteristic
59C4×D4×C103C2211yescharacteristic, complemented
60C2×C4⋊C4×C103—21no—
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#13110095—41no—
76#13110093—22no—
77#13110092—22no—
78#13110092—22no—
79#13110092—22no—
80#13110092—41no—
81#13110090—22no—
82#13110090D414yescomplemented
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×Q8×C103C2311yescharacteristic
102C2×D4×C103—21no—
103C2×D4×C103—21no—
104C2×D4×C103D411yescharacteristic
105C2×D4×C103C2311yescharacteristic
106C22×C4×C103—21no—
107C22×C4×C103—21no—
108C22×C4×C103—21no—
109C22×C4×C103C2311yescharacteristic
110C22×C4×C103C2311yescharacteristic
111C4⋊C4×C103—21no—
112C4⋊C4×C103—21no—
113C4⋊C4×C103—21no—
114C4⋊C4×C103—21no—
115C4⋊C4×C103D411yescharacteristic
116C4⋊C4×C103C2311yescharacteristic
117C22⋊C4×C103—21no—
118C22⋊C4×C103—21no—
119C22⋊C4×C103—21no—
120C22⋊C4×C103D411yescharacteristic
121C22⋊C4×C103D411yescharacteristic
122C42×C103C2311yescharacteristic
123C23×C103—21no—
124C23×C103C2×D411yescharacteristic
125C23×C103C2×D411yescharacteristic
126C22×D103—21no—
127C22×D103—21no—
128C22×D103—42no—
129C22×D103—42no—
130C22×D103—81no—
131Q8×C103—21no—
132Q8×C103—21no—
133Q8×C103—21no—
134Q8×C103—21no—
135D4×C103—21no—
136D4×C103—41no—
137D4×C103—42no—
138D4×C103—42no—
139D4×C103C2×D412yes—
140C2×C4×C103—21no—
141C2×C4×C103—21no—
142C2×C4×C103—21no—
143C2×C4×C103—21no—
144C2×C4×C103—21no—
145C2×C4×C103—21no—
146C2×C4×C103—21no—
147C2×C4×C103—42no—
148C2×C4×C103—42no—
149C2×C4×C103—42no—
150C2×C4×C103C2×D411yescharacteristic
151C2×C4×C103C2×D411yescharacteristic
152C2×C4×C103C2×D411yescharacteristic
153C2×C4×C103C2×D411yescharacteristic
154C2×C4×C103C2411yescharacteristic
155C22⋊D103—42no—
156C22⋊D103—81no—
157C2×Dic103—21no—
158C2×Dic103—21no—
159D412—21no—
160D412—21no—
161D412—21no—
162D412—42no—
163D412C2×D412yes—
164C4×D103—42no—
165C4×D103—81no—
166Dic206—21no—
167Dic206—21no—
168C103⋊C8—21no—
169C103⋊C8—21no—
170C103⋊C8—21no—
171C103⋊C8C2×D412yes—
172C22×C103—21no—
173C22×C103—21no—
174C22×C103—22no—
175C22×C103—21no—
176C22×C103—21no—
177C22×C103—21no—
178C22×C103—21no—
179C22×C103—41no—
180C22×C103—41no—
181C22×C103C22×D411yescharacteristic
182C2×D103—22no—
183C2×D103—41no—
184C2×D103—41no—
185C2×D103—41no—
186C2×D103—41no—
187C2×D103—41no—
188C2×D103—84no—
189C4×C103—21no—
190C4×C103—21no—
191C4×C103—21no—
192C4×C103—21no—
193C4×C103—41no—
194C4×C103—41no—
195C4×C103—41no—
196C4×C103C22×D411yescharacteristic
197C4×C103H(5,𝔽2)11yescharacteristic
198Dic103—41no—
199Dic103—41no—
200C2×C103—41no—
201C2×C103—41no—
202C2×C103—42no—
203C2×C103D4211yescharacteristic
204C2×C103#57511yescharacteristic
205C2×C103#57711yescharacteristic
206D103—42no—
207D103—81no—
208#3267—1031nomaximal, Sylow
209C103#326711yescharacteristic, complemented, Sylow
210C2×AGL(1,ℤ/8)—1031no—
211C2×#135—1031no—
212#547D10311yescharacteristic, complemented
213#546—1031no—
214#497—1031no—
215#470—1031no—
216#465—1031no—
217#463—1031no—
218#461—1031no—
219#452—1031no—
220#452—1031no—
221#450—1031no—
222#449—1031no—
223#442—1031no—
224#435—1031no—
225C2×#41—1031no—
226C2×#41C2×D10311yescharacteristic
227C2×#41C2×D10311yescharacteristic, complemented
228C22×D4—1031no—
229AGL(1,ℤ/8)—2064no—
230#135—2064no—
231C2×Q16—1031no—
232C2×Q16—1031no—
233C2×SD16—1031no—
234C2×SD16—1031no—
235C2×SD16—1031no—
236C2×SD16—1031no—
237C2×SD16—1031no—
238C2×D8—1031no—
239C2×D8—1031no—
240C2×M16—1031no—
241C22×C8—1031no—
242C4⋊Q8C2×D10311yescharacteristic, complemented
243#124—1031no—
244#123—21no—
245#123—21no—
246#123—2061no—
247C22⋊Q8—1031no—
248C22⋊Q8C2×D10311yescharacteristic
249C22⋊Q8C2×D10311yescharacteristic, complemented
250#121—21no—
251#121—1031no—
252#121—2061no—
253#120—2061no—
254C4×D4—1031no—
255C4×D4C2×D10311yescharacteristic
256C4×D4C2×D10311yescharacteristic, complemented
257C2×C4⋊C4—21no—
258C2×C22⋊C4—2061no—
259#106—1031no—
260C4⋊C8—1031no—
261#103—1031no—
262#103—1031no—
263#103—1031no—
264#102—1031no—
265#102—1031no—
266#102—1031no—
267C22⋊C8—1031no—
268C22⋊C8—1031no—
269#97—1031no—
270C24—2061no—
271#41—22no—
272#41—22no—
273#41—41no—
274#41—41no—
275#41—4121no—
276#41—2062no—
277C2×Q8—1031no—
278C2×Q8C22×D10311yescharacteristic
279C2×Q8C22×D10311yescharacteristic
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—1031no—
283C2×D4—1031no—
284C2×D4—4121no—
285C2×D4—2062no—
286C2×D4—2061no—
287C2×D4—2061no—
288C2×D4—2061no—
289C2×D4C22⋊D10311yescharacteristic
290C2×D4C22×D10311yescharacteristic
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—2061no—
295C22×C4—2061no—
296C22×C4C22×D10311yescharacteristic
297C22×C4C22×D10311yescharacteristic
298Q16—4121no—
299Q16—2062no—
300SD16—4121no—
301SD16—2062no—
302SD16—2062no—
303SD16—2062no—
304SD16—2062no—
305D8—1034no—
306D8—2062no—
307M16—2062no—
308C2×C8—1031no—
309C2×C8—1031no—
310C2×C8—1031no—
311C2×C8—1031no—
312C2×C8—2062no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—1031no—
318C4⋊C4—2061no—
319C4⋊C4C22⋊D10311yescharacteristic
320C4⋊C4C22×D10311yescharacteristic
321C22⋊C4—21no—
322C22⋊C4—21no—
323C22⋊C4—21no—
324C22⋊C4—2061no—
325C22⋊C4—2061no—
326C22⋊C4—2061no—
327C22⋊C4—2061no—
328C22⋊C4—2061no—
329C22⋊C4C22⋊D10311yescharacteristic
330C22⋊C4C22⋊D10311yescharacteristic
331C42C22×D10311yescharacteristic
332C23—21no—
333C23—8241no—
334C23—4122no—
335C23—4122no—
336C23—2061no—
337C23—2061no—
338C23C2×C22⋊D10311yescharacteristic
339C23C2×C22⋊D10311yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—21no—
343Q8—21no—
344Q8—2061no—
345Q8—2061no—
346D4—21no—
347D4—41no—
348D4—42no—
349D4—42no—
350D4—8241no—
351D4—1032no—
352D4—4122no—
353D4—4122no—
354D4—2061no—
355D4—2061no—
356D4—2061no—
357D4D4×D10312yes—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—8241no—
369C2×C4—4122no—
370C2×C4—2061no—
371C2×C4—2061no—
372C2×C4C2×C22⋊D10311yescharacteristic
373C2×C4C2×C22⋊D10311yescharacteristic
374C2×C4C2×C22⋊D10311yescharacteristic
375C2×C4C2×C22⋊D10311yescharacteristic
376C2×C4C23×D10311yescharacteristic
377C8—1032no—
378C8—2061no—
379C8—2061no—
380C8—2061no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—22no—
388C22—41no—
389C22—41no—
390C22—8244no—
391C22—4121no—
392C22—4121no—
393C22—4121no—
394C22—4121no—
395C22—4121no—
396C22—2062no—
397C22C22×C22⋊D10311yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—41no—
403C4—41no—
404C4—41no—
405C4—4121no—
406C4—4121no—
407C4C2×D4×D10311yescharacteristic
408C4#1569306611yescharacteristic
409C2—41no—
410C2—41no—
411C2—42no—
412C2—8241no—
413C2—4122no—
414C2D4×C22⋊D10311yescharacteristic
415C2#2026858911yescharacteristic
416C2#2026859911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#547×C103C2
socleC22×C103C22×D4
hypercenter#547D103
hypocenterC103#3267
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. C2×#15693046C2semidirect
2. C2×#15693041C2semidirect
3. #20268437C2semidirect
4. #20268183C2semidirect
5. #20268047C2semidirect
6. #20268022C2semidirect
7. #20268006C2semidirect
8. #20267993C2semidirect
9. #20267953C2semidirect
10. #20267951C2semidirect
11. #20267941C2semidirect
12. #20267936C2semidirect
13. #20267901C2semidirect
14. #20267863C2semidirect
15. #547×C103C2semidirect
20. C2×#13110095C22semidirect
21. C2×#13110095C22semidirect
22. C2×#13110093C22semidirect
30. C22×C103⋊C8C22semidirect
39. #15692952C22semidirect
40. C4⋊(C103⋊C8)C22semidirect
41. #15692945C22semidirect
42. #15692945C22semidirect
43. #15692944C22semidirect
44. #15692942C22semidirect
48. C22⋊(C103⋊C8)C22semidirect
49. #15692932C22semidirect
51. C2×#41×C103C22semidirect
52. C4⋊Q8×C103C22semidirect
56. C22⋊Q8×C103C22semidirect
59. C4×D4×C103C22semidirect
82. #13110090D4semidirect
209. C103#3267semidirect
212. #547D103semidirect
227. C2×#41C2×D103semidirect
242. C4⋊Q8C2×D103semidirect
249. C22⋊Q8C2×D103semidirect
256. C4×D4C2×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
#202681832
#202680472
#202680222
#202680062
#202679932
#202679532
#202679512
#202679412
#202679362
#202679012
#202678632
#547×C1032
#3267103