Finite Group Databasebeta

← #21457357

Subgroups — #21457357

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×#14519803C211yesmaximal, characteristic, complemented
2C2×#14519796C211yesmaximal, characteristic, complemented
3#16840430C211yesmaximal, characteristic, complemented
4#16840406C211yesmaximal, characteristic, complemented
5#16840150C211yesmaximal, characteristic, complemented
6#16840006C211yesmaximal, characteristic, complemented
7#16839997C211yesmaximal, characteristic, complemented
8#16839983C211yesmaximal, characteristic, complemented
9#16839955C211yesmaximal, characteristic, complemented
10#16839926C211yesmaximal, characteristic, complemented
11#16839908C211yesmaximal, characteristic, complemented
12#16839904C211yesmaximal, characteristic, complemented
13#16839859C211yesmaximal, characteristic, complemented
14#16839836C211yesmaximal, characteristic, complemented
15C61×#447C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C2×#11758224C2211yescharacteristic
18C2×#11758224C2211yescharacteristic, complemented
19#14519803—24no—
20#14519796—24no—
21C2×Dic244C2211yescharacteristic, complemented
22C2×#11758190C2211yescharacteristic, complemented
23C2×#11758200C2211yescharacteristic
24C2×#11758200C2211yescharacteristic
25C2×#11758200C2211yescharacteristic, complemented
26C2×#11758199C2211yescharacteristic
27C2×#11758199C2211yescharacteristic
28C2×#11758194C2211yescharacteristic
29C2×C8×D61C2211yescharacteristic, complemented
30#14519773—21no—
31#14519773C2211yescharacteristic, complemented
32#14519764C2211yescharacteristic
33#14519758—21no—
34#14519756C2211yescharacteristic
35#14519752C2211yescharacteristic, complemented
36#14519750—21no—
37#14519749—21no—
38#14519749—21no—
39#14519748C2211yescharacteristic
40#14519746—21no—
41#14519742C2211yescharacteristic, complemented
42D4×Dic61C2211yescharacteristic
43C4×C22⋊D61C2211yescharacteristic
44#14519737—21no—
45C2×C22⋊Dic61—21no—
46#14519710C2211yescharacteristic, complemented
47#14519706C2211yescharacteristic, complemented
48#14519702C2211yescharacteristic, complemented
49#14519700C2211yescharacteristic, complemented
50#14519699C2211yescharacteristic, complemented
51#14519698C2211yescharacteristic, complemented
52#14519689C2211yescharacteristic, complemented
53#14519687C2211yescharacteristic, complemented
54C22×D4×C61C2211yescharacteristic
55C2×D8×C61C2211yescharacteristic
56C2×D8×C61C2211yescharacteristic
57#121×C61C2211yescharacteristic
58#102×C61C2211yescharacteristic
59#102×C61C2211yescharacteristic
60C22⋊C8×C61C2211yescharacteristic
61C24×C61—21no—
62C2×D4×C61—22no—
63C2×D4×C61—21no—
64C2×D4×C61—21no—
65C2×D4×C61—41no—
66C2×D4×C61C2311yescharacteristic
67C2×D4×C61C2311yescharacteristic
68C2×D4×C61C2311yescharacteristic
69C22×C4×C61C2311yescharacteristic
70C2×C22⋊D61—21no—
71C2×C22⋊D61—21no—
72C2×C22⋊D61—21no—
73C2×C22⋊D61—21no—
74C2×C22⋊D61—21no—
75C2×C22⋊D61—21no—
76C2×C22⋊D61D411yescharacteristic
77C22×Dic61—21no—
78C22×Dic61—21no—
79C22×Dic61—21no—
80#11758224—22no—
81#11758224—22no—
82#11758224—41no—
83#11758224—41no—
84#11758222—22no—
85#11758222—41no—
86C2×D244—21no—
87C2×D244C2311yescharacteristic
88C2×C4×D61—21no—
89C2×C4×D61C2311yescharacteristic
90C2×Dic122C2311yescharacteristic
91C2×Dic122C2311yescharacteristic
92D8×C61—22no—
93D8×C61—41no—
94C2×C8×C61C2311yescharacteristic
95C2×C8×C61C2311yescharacteristic
96C4⋊C4×C61C2311yescharacteristic
97C22⋊C4×C61—21no—
98C22⋊Dic61—21no—
99C22⋊Dic61—21no—
100C22⋊Dic61—21no—
101C22⋊Dic61—21no—
102C22⋊Dic61—21no—
103C22⋊Dic61D411yescharacteristic
104#11758200—22no—
105#11758200—22no—
106#11758200D414yescomplemented
107#11758199—22no—
108#11758199—22no—
109#11758198—21no—
110#11758198D411yescharacteristic
111C4⋊Dic61C2311yescharacteristic
112#11758196—21no—
113#11758196—21no—
114#11758196D411yescharacteristic
115C4×Dic61—21no—
116C4×Dic61C2311yescharacteristic
117#11758194—22no—
118C2×#92418C2311yescharacteristic
119C2×#92418C2311yescharacteristic
120Dic244—22no—
121#11758190—41no—
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
132D4×C61—21no—
133D4×C61—21no—
134D4×C61—21no—
135D4×C61—21no—
136D4×C61—21no—
137D4×C61—42no—
138D4×C61—81no—
139D4×C61C2×D412yes—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61C2×D411yescharacteristic
144C2×C4×C61C2411yescharacteristic
145C22⋊D61—41no—
146C22⋊D61—42no—
147C22⋊D61—42no—
148C22⋊D61—42no—
149C22⋊D61—42no—
150C22⋊D61—81no—
151C22⋊D61—81no—
152C2×Dic61—21no—
153C2×Dic61—21no—
154C2×Dic61—21no—
155C2×Dic61—42no—
156C2×Dic61—42no—
157C2×Dic61—81no—
158C2×Dic61C2×D411yescharacteristic
159C2×Dic61C2×D411yescharacteristic
160C2×Dic61C2×D411yescharacteristic
161D244—21no—
162D244—21no—
163D244—81no—
164C4×D61—21no—
165C4×D61—21no—
166C4×D61—42no—
167Dic122—21no—
168Dic122—21no—
169Dic122—21no—
170Dic122C2×D412yes—
171C8×C61—21no—
172C8×C61—21no—
173#92418—21no—
174#92418C2×D412yes—
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—21no—
196C4×C61—41no—
197C4×C61C22×D411yescharacteristic
198C4×C61H(5,𝔽2)11yescharacteristic
199Dic61—22no—
200Dic61—21no—
201Dic61—21no—
202Dic61—21no—
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)—611no—
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#447D6111yescharacteristic, complemented
228#440—611no—
229#435—611no—
230C61#326811yescharacteristic, complemented, Sylow
231C2×#41—611no—
232C2×#41—611no—
233C2×#41—611no—
234C22×D4C2×D6111yescharacteristic
235AGL(1,ℤ/8)—1224no—
236#135—1224no—
237C2×Q16—611no—
238C2×SD16—611no—
239C2×SD16—611no—
240C2×SD16—611no—
241C2×SD16—611no—
242C2×D8—611no—
243C2×D8—611no—
244C2×D8C2×D6111yescharacteristic
245C2×D8C2×D6111yescharacteristic
246C2×M16—611no—
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—1221no—
256#121—1221no—
257#121—1221no—
258#121C2×D6111yescharacteristic
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#102C2×D6111yescharacteristic
272#102C2×D6111yescharacteristic
273C22⋊C8—611no—
274C22⋊C8C2×D6111yescharacteristic
275#97—611no—
276C24—21no—
277#41—1222no—
278#41—1222no—
279#41—1222no—
280#41—2441no—
281#41—2441no—
282#41—2441no—
283C2×Q8—611no—
284C2×Q8—611no—
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—611no—
302C22×C4—1221no—
303C22×C4—1221no—
304C22×C4—1221no—
305C22×C4—1221no—
306C22×C4C22×D6111yescharacteristic
307Q16—1222no—
308SD16—614no—
309SD16—1222no—
310SD16—1222no—
311SD16—2441no—
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—1221no—
325C4⋊C4—1221no—
326C4⋊C4C22×D6111yescharacteristic
327C22⋊C4—21no—
328C22⋊C4—611no—
329C22⋊C4—611no—
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—612no—
348Q8—1221no—
349Q8—1221no—
350Q8—1221no—
351D4—21no—
352D4—21no—
353D4—21no—
354D4—21no—
355D4—21no—
356D4—42no—
357D4—81no—
358D4—1221no—
359D4—1221no—
360D4—4881no—
361D4—4881no—
362D4—4881no—
363D4—2441no—
364D4—2442no—
365D4—2442no—
366D4—2442no—
367D4—2442no—
368D4D4×D6112yes—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—611no—
373C2×C4—611no—
374C2×C4—611no—
375C2×C4—1221no—
376C2×C4—1221no—
377C2×C4—1221no—
378C2×C4—1221no—
379C2×C4—1221no—
380C2×C4—4881no—
381C2×C4—2442no—
382C2×C4—2442no—
383C2×C4—2442no—
384C2×C4D4×D6111yescharacteristic
385C2×C4C23×D6111yescharacteristic
386C8—21no—
387C8—21no—
388C8—612no—
389C8—1221no—
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—41no—
412C4—1221no—
413C4—1221no—
414C4—1221no—
415C4—1222no—
416C4—2441no—
417C4—2441no—
418C4C2×D4×D6111yescharacteristic
419C4#1451982211yescharacteristic
420C2—41no—
421C2—42no—
422C2—81no—
423C2—81no—
424C2—4881no—
425C2—2441no—
426C2#1684039411yescharacteristic
427C2#1684055811yescharacteristic
428C2#1684056311yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#447C2
socleC22×C61C22×D4
hypercenter#447D61
hypocenterC61#3268
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. C2×#14519803C2semidirect
2. C2×#14519796C2semidirect
3. #16840430C2semidirect
4. #16840406C2semidirect
5. #16840150C2semidirect
6. #16840006C2semidirect
7. #16839997C2semidirect
8. #16839983C2semidirect
9. #16839955C2semidirect
10. #16839926C2semidirect
11. #16839908C2semidirect
12. #16839904C2semidirect
13. #16839859C2semidirect
14. #16839836C2semidirect
15. C61×#447C2semidirect
18. C2×#11758224C22semidirect
21. C2×Dic244C22semidirect
22. C2×#11758190C22semidirect
25. C2×#11758200C22semidirect
29. C2×C8×D61C22semidirect
31. #14519773C22semidirect
35. #14519752C22semidirect
41. #14519742C22semidirect
46. #14519710C22semidirect
47. #14519706C22semidirect
48. #14519702C22semidirect
49. #14519700C22semidirect
50. #14519699C22semidirect
51. #14519698C22semidirect
52. #14519689C22semidirect
53. #14519687C22semidirect
106. #11758200D4semidirect
227. #447D61semidirect
230. C61#3268semidirect