Finite Group Databasebeta

← #21457358

Subgroups — #21457358

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×#14519801C211yesmaximal, characteristic, complemented
2C2×#14519798C211yesmaximal, characteristic, complemented
3#16840432C211yesmaximal, characteristic, complemented
4#16840405C211yesmaximal, characteristic, complemented
5#16840005C211yesmaximal, characteristic, complemented
6#16839995C211yesmaximal, characteristic, complemented
7#16839981C211yesmaximal, characteristic, complemented
8#16839954C211yesmaximal, characteristic, complemented
9#16839921C211yesmaximal, characteristic, complemented
10#16839906C211yesmaximal, characteristic, complemented
11#16839904C211yesmaximal, characteristic, complemented
12#16839894C211yesmaximal, characteristic, complemented
13#16839864C211yesmaximal, characteristic, complemented
14#16839835C211yesmaximal, characteristic, complemented
15C61×#496C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×#11758224C2211yescharacteristic
18C2×#11758224C2211yescharacteristic, complemented
19C2×D4×D61C2211yescharacteristic
20#14519801—24no—
21#14519798—24no—
22C2×#11758202C2211yescharacteristic, complemented
23C2×#11758190C2211yescharacteristic
24C2×#11758200C2211yescharacteristic
25C2×#11758199C2211yescharacteristic
26C2×#11758199C2211yescharacteristic
27C2×#11758189C2211yescharacteristic
28C2×C8×D61C2211yescharacteristic, complemented
29#14519773—21no—
30#14519759—21no—
31#14519753C2211yescharacteristic
32#14519750—21no—
33#14519749—21no—
34#14519749—21no—
35#14519748C2211yescharacteristic
36#14519748C2211yescharacteristic
37#14519748C2211yescharacteristic, complemented
38#14519747—21no—
39C4×Dic122C2211yescharacteristic, complemented
40C4×D244C2211yescharacteristic
41C4×D244C2211yescharacteristic
42D4×Dic61—21no—
43C22⋊C4×D61—21no—
44#14519711C2211yescharacteristic, complemented
45C4⋊#92418C2211yescharacteristic, complemented
46#14519702C2211yescharacteristic, complemented
47#14519701C2211yescharacteristic, complemented
48#14519699C2211yescharacteristic
49#14519698C2211yescharacteristic
50#14519698C2211yescharacteristic, complemented
51#14519698C2211yescharacteristic, complemented
52#14519689C2211yescharacteristic
53#14519689C2211yescharacteristic, complemented
54C2×SD16×C61C2211yescharacteristic, complemented
55C2×SD16×C61C2211yescharacteristic, complemented
56C2×D8×C61C2211yescharacteristic
57C2×D8×C61C2211yescharacteristic
58#127×C61C2211yescharacteristic, complemented
59#124×C61C2211yescharacteristic
60#97×C61C2211yescharacteristic, complemented
61C23×D61—21no—
62C2×Q8×C61C2311yescharacteristic
63C2×D4×C61—21no—
64C2×D4×C61—21no—
65C2×D4×C61C2311yescharacteristic
66C2×D4×C61C2311yescharacteristic
67C2×D4×C61C2311yescharacteristic
68C2×C22⋊D61—21no—
69C2×C22⋊D61—21no—
70C2×C22⋊D61—21no—
71C2×C22⋊D61—21no—
72C2×C22⋊D61—21no—
73C2×C22⋊D61—21no—
74C22×Dic61—21no—
75C22×Dic61—21no—
76#11758226—22no—
77#11758226—41no—
78#11758224—22no—
79#11758224—22no—
80#11758224—41no—
81#11758224—41no—
82D4×D61—22no—
83D4×D61—41no—
84C2×D244—21no—
85C2×D244D411yescharacteristic
86C2×D244C2311yescharacteristic
87C2×C4×D61—21no—
88C2×C4×D61—21no—
89C2×C4×D61C2311yescharacteristic
90C2×C4×D61C2311yescharacteristic
91C2×Dic122C2311yescharacteristic
92SD16×C61—22no—
93SD16×C61—41no—
94D8×C61—22no—
95D8×C61—41no—
96C2×C8×C61C2311yescharacteristic
97C2×C8×C61C2311yescharacteristic
98C22⋊C4×C61—21no—
99C22⋊C4×C61—21no—
100C42×C61C2311yescharacteristic
101C22⋊Dic61—21no—
102C22⋊Dic61—21no—
103C22⋊Dic61—21no—
104#11758202—22no—
105#11758200—22no—
106#11758199—22no—
107#11758199—22no—
108#11758198—21no—
109#11758198—21no—
110#11758198D411yescharacteristic
111#11758198D411yescharacteristic
112C4⋊Dic61D411yescharacteristic
113C4⋊Dic61C2311yescharacteristic
114C4⋊Dic61C2311yescharacteristic
115#11758196—21no—
116#11758196—21no—
117C4×Dic61—21no—
118C2×#92418C2311yescharacteristic
119C2×#92418C2311yescharacteristic
120#11758190D414yescomplemented
121#11758189—22no—
122C8×D61—22no—
123C23×C61—21no—
124C23×C61—21no—
125C23×C61—21no—
126C22×D61—21no—
127C22×D61—42no—
128C22×D61—42no—
129C22×D61—81no—
130C22×D61C2×D411yescharacteristic
131C22×D61C2×D411yescharacteristic
132Q8×C61—21no—
133Q8×C61—21no—
134D4×C61—21no—
135D4×C61—21no—
136D4×C61—21no—
137D4×C61—21no—
138D4×C61—21no—
139D4×C61—21no—
140D4×C61—42no—
141D4×C61—81no—
142C2×C4×C61—21no—
143C2×C4×C61C2×D411yescharacteristic
144C2×C4×C61C2×D411yescharacteristic
145C2×C4×C61C2411yescharacteristic
146C22⋊D61—42no—
147C22⋊D61—42no—
148C22⋊D61—42no—
149C22⋊D61—81no—
150C22⋊D61—81no—
151C22⋊D61—81no—
152C2×Dic61—21no—
153C2×Dic61—21no—
154C2×Dic61—21no—
155C2×Dic61—42no—
156C2×Dic61—42no—
157C2×Dic61C2×D411yescharacteristic
158C2×Dic61C2×D411yescharacteristic
159D244—21no—
160D244—41no—
161D244—42no—
162D244C2×D412yes—
163C4×D61—21no—
164C4×D61—21no—
165C4×D61—21no—
166C4×D61—21no—
167C4×D61—42no—
168C4×D61—81no—
169Dic122—21no—
170Dic122C2×D412yes—
171C8×C61—21no—
172C8×C61C2×D412yes—
173#92418—21no—
174#92418—21no—
175C22×C61—41no—
176C22×C61—41no—
177C22×C61—41no—
178C22×C61—41no—
179C22×C61—41no—
180C22×C61—41no—
181C22×C61—41no—
182C22×C61—41no—
183C22×C61—41no—
184C22×C61C22×D411yescharacteristic
185C2×D61—21no—
186C2×D61—21no—
187C2×D61—22no—
188C2×D61—21no—
189C2×D61—21no—
190C2×D61—21no—
191C2×D61—21no—
192C2×D61—41no—
193C2×D61—41no—
194C2×D61—84no—
195C4×C61—21no—
196C4×C61—21no—
197C4×C61—41no—
198C4×C61C22×D411yescharacteristic
199C4×C61H(5,𝔽2)11yescharacteristic
200Dic61—22no—
201Dic61—21no—
202Dic61—21no—
203Dic61—41no—
204Dic61—41no—
205#3268—611nomaximal, Sylow
206C2×C61—81no—
207C2×C61—81no—
208C2×C61—81no—
209C2×C61D4211yescharacteristic
210C2×C61#57511yescharacteristic
211C2×C61#57611yescharacteristic
212D61—41no—
213D61—41no—
214D61—42no—
215C2×AGL(1,ℤ/8)—611no—
216C2×#135—611no—
217#550—611no—
218#546—611no—
219#496D6111yescharacteristic, complemented
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×#41—611no—
234C22×D4—611no—
235AGL(1,ℤ/8)—1224no—
236#135—1224no—
237C2×Q16—611no—
238C2×SD16—611no—
239C2×SD16—611no—
240C2×SD16C2×D6111yescharacteristic, complemented
241C2×SD16C2×D6111yescharacteristic, complemented
242C2×D8—611no—
243C2×D8—611no—
244C2×D8C2×D6111yescharacteristic
245C2×D8C2×D6111yescharacteristic
246C2×M16—611no—
247C22×C8—611no—
248#127—1221no—
249#127C2×D6111yescharacteristic, complemented
250#124C2×D6111yescharacteristic
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#97C2×D6111yescharacteristic, complemented
276C24—1221no—
277#41—1222no—
278#41—1222no—
279#41—1222no—
280#41—2441no—
281#41—2441no—
282#41—2441no—
283C2×Q8—611no—
284C2×Q8C22×D6111yescharacteristic
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—611no—
288C2×D4—611no—
289C2×D4—1221no—
290C2×D4—1221no—
291C2×D4—1222no—
292C2×D4—1221no—
293C2×D4—1221no—
294C2×D4—1221no—
295C2×D4—1221no—
296C2×D4—1221no—
297C2×D4—2441no—
298C2×D4C22×D6111yescharacteristic
299C2×D4C22×D6111yescharacteristic
300C2×D4C22×D6111yescharacteristic
301C22×C4—611no—
302C22×C4—611no—
303C22×C4—1221no—
304C22×C4—1221no—
305C22×C4—1221no—
306C22×C4—1221no—
307Q16—1222no—
308SD16—22no—
309SD16—41no—
310SD16—614no—
311SD16—1222no—
312D8—22no—
313D8—41no—
314D8—1222no—
315D8—1222no—
316M16—1222no—
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—21no—
328C22⋊C4—21no—
329C22⋊C4—611no—
330C22⋊C4—611no—
331C22⋊C4—1221no—
332C22⋊C4—1221no—
333C22⋊C4—1221no—
334C22⋊C4—1221no—
335C22⋊C4—1221no—
336C42—1221no—
337C42C22×D6111yescharacteristic
338C23—21no—
339C23—21no—
340C23—21no—
341C23—611no—
342C23—611no—
343C23—1221no—
344C23—4881no—
345C23—2442no—
346C23—2442no—
347Q8—21no—
348Q8—21no—
349Q8—612no—
350Q8—1221no—
351D4—21no—
352D4—21no—
353D4—21no—
354D4—21no—
355D4—21no—
356D4—21no—
357D4—42no—
358D4—81no—
359D4—612no—
360D4—1221no—
361D4—4881no—
362D4—4881no—
363D4—4881no—
364D4—2441no—
365D4—2442no—
366D4—2442no—
367D4—2442no—
368D4—2442no—
369C2×C4—21no—
370C2×C4—611no—
371C2×C4—611no—
372C2×C4—1221no—
373C2×C4—1221no—
374C2×C4—1221no—
375C2×C4—1221no—
376C2×C4—1221no—
377C2×C4—1221no—
378C2×C4—1221no—
379C2×C4—4881no—
380C2×C4—2442no—
381C2×C4—2442no—
382C2×C4—2442no—
383C2×C4D4×D6111yescharacteristic
384C2×C4D4×D6111yescharacteristic
385C2×C4C23×D6111yescharacteristic
386C8—21no—
387C8—1221no—
388C8—1221no—
389C8D4×D6112yes—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—1221no—
400C22—1221no—
401C22—1221no—
402C22—1221no—
403C22—1221no—
404C22—1221no—
405C22—1222no—
406C22—4884no—
407C22—2441no—
408C22—2441no—
409C22C2×D4×D6111yescharacteristic
410C4—21no—
411C4—21no—
412C4—41no—
413C4—1221no—
414C4—1221no—
415C4—1222no—
416C4—2441no—
417C4—2441no—
418C4C2×D4×D6111yescharacteristic
419C4#1451982211yescharacteristic
420C2—81no—
421C2—81no—
422C2—81no—
423C2—2441no—
424C2—2441no—
425C2—2442no—
426C2#1684039711yescharacteristic
427C2#1684055811yescharacteristic
428C2#1684056611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#496C2
socleC22×C61C22×D4
hypercenter#496D61
hypocenterC61#3268
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. C2×#14519801C2semidirect
2. C2×#14519798C2semidirect
3. #16840432C2semidirect
4. #16840405C2semidirect
5. #16840005C2semidirect
6. #16839995C2semidirect
7. #16839981C2semidirect
8. #16839954C2semidirect
9. #16839921C2semidirect
10. #16839906C2semidirect
11. #16839904C2semidirect
12. #16839894C2semidirect
13. #16839864C2semidirect
14. #16839835C2semidirect
15. C61×#496C2semidirect
18. C2×#11758224C22semidirect
22. C2×#11758202C22semidirect
28. C2×C8×D61C22semidirect
37. #14519748C22semidirect
39. C4×Dic122C22semidirect
44. #14519711C22semidirect
45. C4⋊#92418C22semidirect
46. #14519702C22semidirect
47. #14519701C22semidirect
50. #14519698C22semidirect
51. #14519698C22semidirect
53. #14519689C22semidirect
54. C2×SD16×C61C22semidirect
55. C2×SD16×C61C22semidirect
58. #127×C61C22semidirect
60. #97×C61C22semidirect
120. #11758190D4semidirect
219. #496D61semidirect
230. C61#3268semidirect
240. C2×SD16C2×D61semidirect
241. C2×SD16C2×D61semidirect
249. #127C2×D61semidirect
275. #97C2×D61semidirect