Finite Group Databasebeta

← #27206669

Subgroups — #27206669

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×#15693045C211yesmaximal, characteristic, complemented
2#20268440C211yesmaximal, characteristic, complemented
3#20268429C211yesmaximal, characteristic, complemented
4#20268184C211yesmaximal, characteristic, complemented
5#20268046C211yesmaximal, characteristic, complemented
6#20268020C211yesmaximal, characteristic, complemented
7#20268008C211yesmaximal, characteristic, complemented
8#20267994C211yesmaximal, characteristic, complemented
9#20267953C211yesmaximal, characteristic, complemented
10#20267950C211yesmaximal, characteristic, complemented
11#20267940C211yesmaximal, characteristic, complemented
12#20267936C211yesmaximal, characteristic, complemented
13#20267903C211yesmaximal, characteristic, complemented
14#20267862C211yesmaximal, characteristic, complemented
15C2×#135×C103C211yesmaximal, characteristic, complemented
16C2×#13110104C2211yescharacteristic
17C2×D4×D103C2211yescharacteristic
18#15693045—24no—
19C2×#13110095C2211yescharacteristic, complemented
20C2×#13110094C2211yescharacteristic
21C2×#13110093C2211yescharacteristic
22C2×#13110092C2211yescharacteristic
23C2×#13110090C2211yescharacteristic
24C2×#13110088C2211yescharacteristic
25#15693019C2211yescharacteristic, complemented
26#15693010C2211yescharacteristic
27#15693004—21no—
28#15693004—21no—
29#15693002—21no—
30#15693000C2211yescharacteristic, complemented
31#15692997C2211yescharacteristic
32#15692997C2211yescharacteristic
33#15692995C2211yescharacteristic
34#15692993—21no—
35#15692993—21no—
36#15692989—21no—
37D4×Dic103C2211yescharacteristic
38D4×Dic103C2211yescharacteristic, complemented
39C4×C22⋊D103C2211yescharacteristic
40C2×Dic103⋊C4—21no—
41C2×(C2×D103)⋊C4—21no—
42#15692953C2211yescharacteristic, complemented
43Dic103⋊C8C2211yescharacteristic, complemented
44#15692946C2211yescharacteristic, complemented
45#15692945C2211yescharacteristic, complemented
46#15692945C2211yescharacteristic, complemented
47#15692943C2211yescharacteristic
48#15692942C2211yescharacteristic
49#15692942C2211yescharacteristic, complemented
50C22⋊(C103⋊C8)C2211yescharacteristic, complemented
51(C2×D103)⋊C8C2211yescharacteristic
52#15692931C2211yescharacteristic, complemented
53C2×#41×C103C2211yescharacteristic
54C2×#41×C103C2211yescharacteristic, complemented
55#135×C103—24no—
56C2×Q16×C103C2211yescharacteristic, complemented
57C2×SD16×C103C2211yescharacteristic
58C2×SD16×C103C2211yescharacteristic, complemented
59C2×D8×C103C2211yescharacteristic
60C22×C8×C103C2211yescharacteristic, complemented
61C23×D103—21no—
62#13110104—22no—
63#13110104—41no—
64C2×Dic206C2311yescharacteristic
65C2×D412C2311yescharacteristic
66C2×C22⋊D103—21no—
67C2×C22⋊D103—21no—
68C2×C22⋊D103—21no—
69C2×C22⋊D103D411yescharacteristic
70D4×D103—22no—
71D4×D103—41no—
72C22×Dic103—21no—
73C22×Dic103—21no—
74C22×Dic103—21no—
75C2×C4×D103C2311yescharacteristic
76#13110095—41no—
77#13110094—22no—
78#13110093—22no—
79#13110092—41no—
80#13110090—22no—
81#13110088—22no—
82C2×C103⋊C8C2311yescharacteristic
83C2×C103⋊C8C2311yescharacteristic
84C4⋊Dic103C2311yescharacteristic
85C4⋊Dic103C2311yescharacteristic
86Dic103⋊C4—21no—
87Dic103⋊C4—21no—
88Dic103⋊C4—21no—
89Dic103⋊C4—21no—
90Dic103⋊C4—21no—
91Dic103⋊C4D411yescharacteristic
92C22⋊Dic103—21no—
93C22⋊Dic103—21no—
94C22⋊Dic103—21no—
95C22⋊Dic103D411yescharacteristic
96(C2×D103)⋊C4—21no—
97(C2×D103)⋊C4—21no—
98(C2×D103)⋊C4—21no—
99(C2×D103)⋊C4—21no—
100(C2×D103)⋊C4—21no—
101(C2×D103)⋊C4D411yescharacteristic
102C4×Dic103C2311yescharacteristic
103#41×C103—22no—
104#41×C103—22no—
105#41×C103—41no—
106#41×C103—41no—
107C2×Q8×C103C2311yescharacteristic
108C2×Q8×C103C2311yescharacteristic
109C2×D4×C103—21no—
110C2×D4×C103—21no—
111C2×D4×C103C2311yescharacteristic
112C2×D4×C103C2311yescharacteristic
113C22×C4×C103—21no—
114C22×C4×C103—21no—
115C22×C4×C103C2311yescharacteristic
116Q16×C103—22no—
117SD16×C103—22no—
118SD16×C103—22no—
119D8×C103D414yescomplemented
120C2×C8×C103—22no—
121C2×C8×C103C2311yescharacteristic
122C2×C8×C103C2311yescharacteristic
123C23×C103—21no—
124C23×C103—21no—
125C23×C103C2×D411yescharacteristic
126C22×D103—21no—
127C22×D103—42no—
128C22×D103—42no—
129C22×D103—81no—
130C22×D103C2×D411yescharacteristic
131Q8×C103—21no—
132Q8×C103—21no—
133Q8×C103—21no—
134Q8×C103—21no—
135D4×C103—21no—
136D4×C103—21no—
137D4×C103—42no—
138D4×C103—42no—
139D4×C103C2×D412yes—
140D4×C103C2×D412yes—
141C2×C4×C103—21no—
142C2×C4×C103—21no—
143C2×C4×C103—21no—
144C2×C4×C103—21no—
145C2×C4×C103—42no—
146C2×C4×C103—42no—
147C2×C4×C103C2×D411yescharacteristic
148C2×C4×C103C2411yescharacteristic
149C22⋊D103—41no—
150C22⋊D103—42no—
151C22⋊D103—42no—
152C22⋊D103—81no—
153C2×Dic103—21no—
154C2×Dic103—21no—
155C2×Dic103—21no—
156C2×Dic103—42no—
157C2×Dic103—42no—
158C2×Dic103—81no—
159C2×Dic103C2×D411yescharacteristic
160C2×Dic103C2×D411yescharacteristic
161C2×Dic103C2×D411yescharacteristic
162D412—21no—
163D412—21no—
164C4×D103—21no—
165C4×D103—21no—
166Dic206—21no—
167Dic206—21no—
168C8×C103—21no—
169C8×C103C2×D412yes—
170C103⋊C8—21no—
171C103⋊C8—21no—
172C22×C103—22no—
173C22×C103—22no—
174C22×C103—21no—
175C22×C103—21no—
176C22×C103—21no—
177C22×C103—41no—
178C22×C103—41no—
179C22×C103—41no—
180C22×C103—41no—
181C22×C103C22×D411yescharacteristic
182C2×D103—21no—
183C2×D103—21no—
184C2×D103—21no—
185C2×D103—41no—
186C2×D103—41no—
187C2×D103—41no—
188C2×D103—84no—
189C4×C103—21no—
190C4×C103—41no—
191C4×C103—41no—
192C4×C103C22×D411yescharacteristic
193C4×C103H(5,𝔽2)11yescharacteristic
194Dic103—21no—
195Dic103—21no—
196Dic103—21no—
197Dic103—41no—
198Dic103—41no—
199Dic103—41no—
200C2×C103—42no—
201C2×C103—41no—
202C2×C103—42no—
203C2×C103D4211yescharacteristic
204C2×C103#57511yescharacteristic
205C2×C103#57711yescharacteristic
206D103—41no—
207D103—81no—
208#3267—1031nomaximal, Sylow
209C103#326711yescharacteristic, complemented, Sylow
210C2×AGL(1,ℤ/8)—1031no—
211C2×#135D10311yescharacteristic, complemented
212#547—1031no—
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—24no—
231C2×Q16—1031no—
232C2×Q16C2×D10311yescharacteristic, complemented
233C2×SD16—1031no—
234C2×SD16—1031no—
235C2×SD16—1031no—
236C2×SD16C2×D10311yescharacteristic
237C2×SD16C2×D10311yescharacteristic, complemented
238C2×D8—1031no—
239C2×D8C2×D10311yescharacteristic
240C2×M16—1031no—
241C22×C8C2×D10311yescharacteristic, complemented
242C4⋊Q8—1031no—
243#124—1031no—
244#123—2061no—
245#123—2061no—
246#123—2061no—
247C22⋊Q8—1031no—
248C22⋊Q8—1031no—
249C22⋊Q8—1031no—
250#121—1031no—
251#121—2061no—
252#121—2061no—
253#120—2061no—
254C4×D4—1031no—
255C4×D4—1031no—
256C4×D4—1031no—
257C2×C4⋊C4—2061no—
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—2061no—
286C2×D4—2061no—
287C2×D4—2061no—
288C2×D4—2062no—
289C2×D4C22×D10311yescharacteristic
290C2×D4C22×D10311yescharacteristic
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—1031no—
294C22×C4—2061no—
295C22×C4—2061no—
296C22×C4—2061no—
297C22×C4C22×D10311yescharacteristic
298Q16—22no—
299Q16—4121no—
300SD16—22no—
301SD16—22no—
302SD16—4121no—
303SD16—2062no—
304SD16—2062no—
305D8—2062no—
306D8C22⋊D10314yescomplemented
307M16—2062no—
308C2×C8—22no—
309C2×C8—1031no—
310C2×C8—1031no—
311C2×C8C22×D10311yescharacteristic
312C2×C8C22×D10311yescharacteristic
313C4⋊C4—1031no—
314C4⋊C4—1031no—
315C4⋊C4—1031no—
316C4⋊C4—2061no—
317C4⋊C4—2061no—
318C4⋊C4—2061no—
319C4⋊C4—2061no—
320C4⋊C4—2061no—
321C22⋊C4—1031no—
322C22⋊C4—1031no—
323C22⋊C4—2061no—
324C22⋊C4—2061no—
325C22⋊C4—2061no—
326C22⋊C4—2061no—
327C22⋊C4—2061no—
328C22⋊C4—2061no—
329C22⋊C4—2061no—
330C22⋊C4—2061no—
331C42—1031no—
332C23—21no—
333C23—21no—
334C23—8241no—
335C23—1031no—
336C23—4122no—
337C23—4122no—
338C23—2061no—
339C23D4×D10311yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—21no—
343Q8—21no—
344Q8—2061no—
345Q8—2061no—
346D4—21no—
347D4—21no—
348D4—42no—
349D4—42no—
350D4—8241no—
351D4—4122no—
352D4—4122no—
353D4—4121no—
354D4—2061no—
355D4—2061no—
356D4C2×C22⋊D10312yes—
357D4C2×C22⋊D10312yes—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—8241no—
365C2×C4—1031no—
366C2×C4—1031no—
367C2×C4—1031no—
368C2×C4—4122no—
369C2×C4—4122no—
370C2×C4—2061no—
371C2×C4—2061no—
372C2×C4—2061no—
373C2×C4—2061no—
374C2×C4—2061no—
375C2×C4D4×D10311yescharacteristic
376C2×C4C23×D10311yescharacteristic
377C8—21no—
378C8—2061no—
379C8—2061no—
380C8C2×C22⋊D10312yes—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—22no—
385C22—22no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—8244no—
391C22—4121no—
392C22—4121no—
393C22—4121no—
394C22—2061no—
395C22—2061no—
396C22—2061no—
397C22C2×D4×D10311yescharacteristic
398C4—21no—
399C4—41no—
400C4—41no—
401C4—4121no—
402C4—4121no—
403C4—4121no—
404C4—2061no—
405C4—2061no—
406C4—2061no—
407C4C22×C22⋊D10311yescharacteristic
408C4#1569306611yescharacteristic
409C2—41no—
410C2—42no—
411C2—42no—
412C2—8241no—
413C2—4121no—
414C2D4×C22⋊D10311yescharacteristic
415C2#2026858811yescharacteristic
416C2#2026859811yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
FittingC2×#135×C103C2
socleC22×C103C22×D4
hypercenterC2×#135D103
hypocenterC103#3267
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#15693045C2semidirect
2. #20268440C2semidirect
3. #20268429C2semidirect
4. #20268184C2semidirect
5. #20268046C2semidirect
6. #20268020C2semidirect
7. #20268008C2semidirect
8. #20267994C2semidirect
9. #20267953C2semidirect
10. #20267950C2semidirect
11. #20267940C2semidirect
12. #20267936C2semidirect
13. #20267903C2semidirect
14. #20267862C2semidirect
15. C2×#135×C103C2semidirect
19. C2×#13110095C22semidirect
25. #15693019C22semidirect
30. #15693000C22semidirect
38. D4×Dic103C22semidirect
42. #15692953C22semidirect
43. Dic103⋊C8C22semidirect
44. #15692946C22semidirect
45. #15692945C22semidirect
46. #15692945C22semidirect
49. #15692942C22semidirect
50. C22⋊(C103⋊C8)C22semidirect
52. #15692931C22semidirect
54. C2×#41×C103C22semidirect
56. C2×Q16×C103C22semidirect
58. C2×SD16×C103C22semidirect
60. C22×C8×C103C22semidirect
119. D8×C103D4semidirect
209. C103#3267semidirect
211. C2×#135D103semidirect
227. C2×#41C2×D103semidirect
232. C2×Q16C2×D103semidirect
237. C2×SD16C2×D103semidirect
241. C22×C8C2×D103semidirect
306. D8C22⋊D103semidirect

Maximal subgroups

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

subgroupindex
C2×#156930452
#202684402
#202684292
#202681842
#202680462
#202680202
#202680082
#202679942
#202679532
#202679502
#202679402
#202679362
#202679032
#202678622
C2×#135×C1032
#3267103