Finite Group Databasebeta

← #21457353

Subgroups — #21457353

Order 7808.

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×#14519798C211yesmaximal, characteristic, complemented
2#16840431C211yesmaximal, characteristic, complemented
3#16840406C211yesmaximal, characteristic, complemented
4#16840150C211yesmaximal, characteristic, complemented
5#16840008C211yesmaximal, characteristic, complemented
6#16839995C211yesmaximal, characteristic, complemented
7#16839982C211yesmaximal, characteristic, complemented
8#16839955C211yesmaximal, characteristic, complemented
9#16839924C211yesmaximal, characteristic, complemented
10#16839906C211yesmaximal, characteristic, complemented
11#16839904C211yesmaximal, characteristic, complemented
12#16839896C211yesmaximal, characteristic, complemented
13#16839863C211yesmaximal, characteristic, complemented
14#16839831C211yesmaximal, characteristic, complemented
15C2×AGL(1,ℤ/8)×C61C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic, complemented
17C2×#11758224C2211yescharacteristic
18#14519798—24no—
19C2×#11758202C2211yescharacteristic, complemented
20C2×#11758190C2211yescharacteristic, complemented
21C2×#11758200C2211yescharacteristic, complemented
22C2×#11758199C2211yescharacteristic
23C2×#11758199C2211yescharacteristic
24C2×C8×D61C2211yescharacteristic, complemented
25#14519773—21no—
26#14519773C2211yescharacteristic, complemented
27#14519764C2211yescharacteristic
28#14519758—21no—
29#14519756C2211yescharacteristic
30#14519751—21no—
31#14519751C2211yescharacteristic
32#14519749—21no—
33#14519748—21no—
34#14519748C2211yescharacteristic
35#14519748C2211yescharacteristic, complemented
36#14519746—21no—
37Q8×Dic61C2211yescharacteristic, complemented
38D4×Dic61C2211yescharacteristic
39C4×C22⋊D61—21no—
40C4×C22⋊D61C2211yescharacteristic
41C2×C22⋊Dic61—21no—
42#14519711C2211yescharacteristic, complemented
43#14519706C2211yescharacteristic, complemented
44#14519702C2211yescharacteristic, complemented
45#14519701C2211yescharacteristic, complemented
46#14519699C2211yescharacteristic, complemented
47#14519698C2211yescharacteristic
48#14519698C2211yescharacteristic
49#14519698C2211yescharacteristic, complemented
50C22⋊#92418C2211yescharacteristic
51#14519689C2211yescharacteristic, complemented
52#14519687C2211yescharacteristic, complemented
53C2×#41×C61C2211yescharacteristic
54C22×D4×C61C2211yescharacteristic
55AGL(1,ℤ/8)×C61—24no—
56C2×SD16×C61C2211yescharacteristic
57C2×SD16×C61C2211yescharacteristic
58C2×D8×C61C2211yescharacteristic
59C2×D8×C61C2211yescharacteristic
60C2×M16×C61C2211yescharacteristic
61C24×C61—21no—
62#41×C61—22no—
63#41×C61—41no—
64C2×Q8×C61C2311yescharacteristic
65C2×D4×C61—22no—
66C2×D4×C61—21no—
67C2×D4×C61—21no—
68C2×D4×C61—41no—
69C2×D4×C61C2311yescharacteristic
70C2×D4×C61C2311yescharacteristic
71C2×D4×C61C2311yescharacteristic
72C22×C4×C61—21no—
73C22×C4×C61C2311yescharacteristic
74C2×C22⋊D61—21no—
75C2×C22⋊D61—21no—
76C2×C22⋊D61—21no—
77C2×C22⋊D61—21no—
78C2×C22⋊D61—21no—
79C2×C22⋊D61—21no—
80C2×C22⋊D61D411yescharacteristic
81C22×Dic61—21no—
82C22×Dic61—21no—
83#11758226—22no—
84#11758226—41no—
85#11758224—22no—
86#11758224—41no—
87C2×D244—21no—
88C2×D244C2311yescharacteristic
89C2×C4×D61—21no—
90C2×C4×D61C2311yescharacteristic
91C2×Dic122C2311yescharacteristic
92SD16×C61—22no—
93SD16×C61D414yescomplemented
94D8×C61—22no—
95D8×C61—22no—
96M16×C61—22no—
97C2×C8×C61C2311yescharacteristic
98C2×C8×C61C2311yescharacteristic
99C22⋊Dic61—21no—
100C22⋊Dic61—21no—
101C22⋊Dic61—21no—
102C22⋊Dic61—21no—
103C22⋊Dic61—21no—
104C22⋊Dic61—21no—
105C22⋊Dic61D411yescharacteristic
106#11758202—22no—
107#11758200—41no—
108#11758199—22no—
109#11758199—41no—
110#11758198—21no—
111#11758198D411yescharacteristic
112C4⋊Dic61—21no—
113C4⋊Dic61C2311yescharacteristic
114C4⋊Dic61C2311yescharacteristic
115#11758196—21no—
116#11758196D411yescharacteristic
117C4×Dic61—21no—
118C4×Dic61C2311yescharacteristic
119C2×#92418C2311yescharacteristic
120C2×#92418C2311yescharacteristic
121#11758190—22no—
122C8×D61—22no—
123C23×C61—21no—
124C23×C61—21no—
125C23×C61—21no—
126C23×C61—42no—
127C23×C61—42no—
128C23×C61—81no—
129C23×C61C2×D411yescharacteristic
130C22×D61—21no—
131C22×D61C2×D411yescharacteristic
132Q8×C61—21no—
133Q8×C61C2×D412yes—
134D4×C61—21no—
135D4×C61—21no—
136D4×C61—21no—
137D4×C61—21no—
138D4×C61—21no—
139D4×C61—42no—
140D4×C61—42no—
141D4×C61C2×D412yes—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61—42no—
146C2×C4×C61C2×D411yescharacteristic
147C2×C4×C61C2411yescharacteristic
148C22⋊D61—41no—
149C22⋊D61—42no—
150C22⋊D61—42no—
151C22⋊D61—81no—
152C22⋊D61—81no—
153C22⋊D61—81no—
154C22⋊D61—81no—
155C2×Dic61—21no—
156C2×Dic61—21no—
157C2×Dic61—21no—
158C2×Dic61—42no—
159C2×Dic61—81no—
160C2×Dic61C2×D411yescharacteristic
161C2×Dic61C2×D411yescharacteristic
162C2×Dic61C2×D411yescharacteristic
163D244—21no—
164D244—21no—
165D244—42no—
166C4×D61—21no—
167C4×D61—21no—
168C4×D61—42no—
169Dic122—21no—
170Dic122—21no—
171C8×C61—21no—
172C8×C61C2×D412yes—
173#92418—21no—
174#92418—21no—
175C22×C61—22no—
176C22×C61—21no—
177C22×C61—21no—
178C22×C61—21no—
179C22×C61—41no—
180C22×C61—41no—
181C22×C61—41no—
182C22×C61—41no—
183C22×C61—41no—
184C22×C61—41no—
185C22×C61—41no—
186C22×C61—41no—
187C22×C61—84no—
188C22×C61C22×D411yescharacteristic
189C2×D61—21no—
190C2×D61—21no—
191C2×D61—21no—
192C2×D61—41no—
193C2×D61—41no—
194C2×D61—41no—
195C4×C61—22no—
196C4×C61—21no—
197C4×C61C22×D411yescharacteristic
198C4×C61H(5,𝔽2)11yescharacteristic
199Dic61—21no—
200Dic61—21no—
201Dic61—21no—
202Dic61—41no—
203Dic61—41no—
204Dic61—41no—
205#3268—611nomaximal, Sylow
206C2×C61—41no—
207C2×C61—42no—
208C2×C61—81no—
209C2×C61—81no—
210C2×C61D4211yescharacteristic
211C2×C61#57511yescharacteristic
212C2×C61#57611yescharacteristic
213D61—41no—
214D61—81no—
215C2×AGL(1,ℤ/8)D6111yescharacteristic, complemented
216C2×#135—611no—
217#550—611no—
218#546—611no—
219#496—611no—
220#468—611no—
221#466—611no—
222#464—611no—
223#459—611no—
224#452—611no—
225#449—611no—
226#449—611no—
227#447—611no—
228#440—611no—
229#435—611no—
230C61#326811yescharacteristic, complemented, Sylow
231C2×#41—611no—
232C2×#41—611no—
233C2×#41C2×D6111yescharacteristic
234C22×D4C2×D6111yescharacteristic
235AGL(1,ℤ/8)—24no—
236#135—1224no—
237C2×Q16—611no—
238C2×SD16—611no—
239C2×SD16—611no—
240C2×SD16C2×D6111yescharacteristic
241C2×SD16C2×D6111yescharacteristic
242C2×D8—611no—
243C2×D8—611no—
244C2×D8C2×D6111yescharacteristic
245C2×D8C2×D6111yescharacteristic
246C2×M16C2×D6111yescharacteristic
247C22×C8—611no—
248#127—611no—
249#127—1221no—
250#124—611no—
251#123—1221no—
252C22⋊Q8—611no—
253#121—611no—
254#121—611no—
255#121—611no—
256#121—1221no—
257#121—1221no—
258#121—1221no—
259#120—1221no—
260C4×Q8—611no—
261C4×D4—611no—
262C4×D4—611no—
263C4×D4—1221no—
264C2×C22⋊C4—1221no—
265#107—611no—
266C4⋊C8—611no—
267#103—611no—
268#103—611no—
269#102—611no—
270#102—611no—
271#102—611no—
272#102—611no—
273C22⋊C8—611no—
274C22⋊C8—611no—
275#97—611no—
276C24—21no—
277#41—22no—
278#41—41no—
279#41—1222no—
280#41—1222no—
281#41—2441no—
282#41—2441no—
283C2×Q8—611no—
284C2×Q8C22×D6111yescharacteristic
285C2×D4—22no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—41no—
289C2×D4—611no—
290C2×D4—611no—
291C2×D4—1221no—
292C2×D4—1221no—
293C2×D4—1221no—
294C2×D4—1221no—
295C2×D4—1221no—
296C2×D4—1221no—
297C2×D4—1221no—
298C2×D4C22×D6111yescharacteristic
299C2×D4C22×D6111yescharacteristic
300C2×D4C22×D6111yescharacteristic
301C22×C4—21no—
302C22×C4—611no—
303C22×C4—1221no—
304C22×C4—1221no—
305C22×C4—1221no—
306C22×C4C22×D6111yescharacteristic
307Q16—1222no—
308SD16—22no—
309SD16—1222no—
310SD16—2441no—
311SD16C22⋊D6114yescomplemented
312D8—22no—
313D8—22no—
314D8—1222no—
315D8—2441no—
316M16—22no—
317C2×C8—611no—
318C2×C8—611no—
319C2×C8—1222no—
320C2×C8C22×D6111yescharacteristic
321C2×C8C22×D6111yescharacteristic
322C4⋊C4—611no—
323C4⋊C4—611no—
324C4⋊C4—611no—
325C4⋊C4—1221no—
326C4⋊C4—1221no—
327C22⋊C4—611no—
328C22⋊C4—611no—
329C22⋊C4—1221no—
330C22⋊C4—1221no—
331C22⋊C4—1221no—
332C22⋊C4—1221no—
333C22⋊C4—1221no—
334C22⋊C4—1221no—
335C22⋊C4—1221no—
336C42—611no—
337C42—1221no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—42no—
342C23—42no—
343C23—81no—
344C23—611no—
345C23—1221no—
346C23D4×D6111yescharacteristic
347Q8—21no—
348Q8—1221no—
349Q8—1221no—
350Q8C2×C22⋊D6112yes—
351D4—21no—
352D4—21no—
353D4—21no—
354D4—21no—
355D4—21no—
356D4—42no—
357D4—42no—
358D4—1221no—
359D4—1221no—
360D4—4881no—
361D4—4881no—
362D4—4881no—
363D4—4881no—
364D4—2442no—
365D4—2441no—
366D4—2442no—
367D4—2442no—
368D4C2×C22⋊D6112yes—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—42no—
373C2×C4—611no—
374C2×C4—611no—
375C2×C4—611no—
376C2×C4—1221no—
377C2×C4—1221no—
378C2×C4—1221no—
379C2×C4—1221no—
380C2×C4—1221no—
381C2×C4—4881no—
382C2×C4—2442no—
383C2×C4—2442no—
384C2×C4D4×D6111yescharacteristic
385C2×C4C23×D6111yescharacteristic
386C8—21no—
387C8—1221no—
388C8—1221no—
389C8C2×C22⋊D6112yes—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—22no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—84no—
403C22—1221no—
404C22—1221no—
405C22—1221no—
406C22—2441no—
407C22—2441no—
408C22—2441no—
409C22C2×D4×D6111yescharacteristic
410C4—21no—
411C4—22no—
412C4—1221no—
413C4—1221no—
414C4—1221no—
415C4—2441no—
416C4—2441no—
417C4—2441no—
418C4C22×C22⋊D6111yescharacteristic
419C4#1451982211yescharacteristic
420C2—41no—
421C2—42no—
422C2—81no—
423C2—81no—
424C2—4881no—
425C2—2441no—
426C2D4×C22⋊D6111yescharacteristic
427C2#1684055811yescharacteristic
428C2#1684056611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×AGL(1,ℤ/8)×C61C2
socleC22×C61C22×D4
hypercenterC2×AGL(1,ℤ/8)D61
hypocenterC61#3268
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×#14519798C2semidirect
2. #16840431C2semidirect
3. #16840406C2semidirect
4. #16840150C2semidirect
5. #16840008C2semidirect
6. #16839995C2semidirect
7. #16839982C2semidirect
8. #16839955C2semidirect
9. #16839924C2semidirect
10. #16839906C2semidirect
11. #16839904C2semidirect
12. #16839896C2semidirect
13. #16839863C2semidirect
14. #16839831C2semidirect
15. C2×AGL(1,ℤ/8)×C61C2semidirect
16. C2×#11758226C22semidirect
19. C2×#11758202C22semidirect
20. C2×#11758190C22semidirect
21. C2×#11758200C22semidirect
24. C2×C8×D61C22semidirect
26. #14519773C22semidirect
35. #14519748C22semidirect
37. Q8×Dic61C22semidirect
42. #14519711C22semidirect
43. #14519706C22semidirect
44. #14519702C22semidirect
45. #14519701C22semidirect
46. #14519699C22semidirect
49. #14519698C22semidirect
51. #14519689C22semidirect
52. #14519687C22semidirect
93. SD16×C61D4semidirect
215. C2×AGL(1,ℤ/8)D61semidirect
230. C61#3268semidirect
311. SD16C22⋊D61semidirect