Finite Group Databasebeta

← #21455433

Subgroups — #21455433

Order 7808.

548 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519804C211yesmaximal, characteristic, complemented
2C2×M16×D61C211yesmaximal, characteristic, complemented
3#16840275C211yesmaximal, characteristic, complemented
4#121×D61C211yesmaximal, characteristic, complemented
5#16840015C211yesmaximal, characteristic, complemented
6#16840013C211yesmaximal, characteristic, complemented
7#16840010C211yesmaximal, characteristic, complemented
8#16839999C211yesmaximal, characteristic, complemented
9#16839997C211yesmaximal, characteristic, complemented
10#16839994C211yesmaximal, characteristic, complemented
11#16839988C211yesmaximal, characteristic, complemented
12#16839803C211yesmaximal, characteristic, complemented
13#16839765C211yesmaximal, characteristic, complemented
14#16839762C211yesmaximal, characteristic, complemented
15C61×#468C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×D4×D61—21no—
18C2×D4×D61C2211yescharacteristic
19C22×C4×D61C2211yescharacteristic
20#14519804—24no—
21C2×#11758201C2211yescharacteristic, complemented
22C2×D488C2211yescharacteristic, complemented
23C2×#11758199C2211yescharacteristic, complemented
24C2×#11758194C2211yescharacteristic, complemented
25C2×#11758189C2211yescharacteristic
26C2×#11758189C2211yescharacteristic
27M16×D61—24no—
28C2×C8×D61C2211yescharacteristic, complemented
29C2×C8×D61C2211yescharacteristic, complemented
30#14519762—21no—
31#14519753C2211yescharacteristic, complemented
32#14519752C2211yescharacteristic
33#14519752C2211yescharacteristic, complemented
34#14519751C2211yescharacteristic
35#14519751C2211yescharacteristic, complemented
36#14519750—21no—
37#14519749—21no—
38#14519748C2211yescharacteristic
39#14519747—21no—
40#14519739—21no—
41#14519737—21no—
42#14519735C2211yescharacteristic
43C4⋊C4×D61C2211yescharacteristic
44C22⋊C4×D61—21no—
45#14519710C2211yescharacteristic, complemented
46#14519709C2211yescharacteristic, complemented
47#14519708C2211yescharacteristic, complemented
48#14519701C2211yescharacteristic, complemented
49#14519699C2211yescharacteristic, complemented
50#14519699C2211yescharacteristic, complemented
51#14519698C2211yescharacteristic, complemented
52#14519697C2211yescharacteristic, complemented
53#14519697C2211yescharacteristic, complemented
54C2×SD16×C61C2211yescharacteristic, complemented
55C2×M16×C61C2211yescharacteristic, complemented
56C22⋊Q8×C61C2211yescharacteristic, complemented
57#121×C61C2211yescharacteristic
58#107×C61C2211yescharacteristic, complemented
59#103×C61C2211yescharacteristic, complemented
60#102×C61C2211yescharacteristic, complemented
61C23×D61—21no—
62C23×D61D411yescharacteristic
63C2×Q8×C61C2311yescharacteristic
64C2×D4×C61—21no—
65C2×D4×C61C2311yescharacteristic
66C22×C4×C61C2311yescharacteristic
67C2×C22⋊D61—21no—
68C2×C22⋊D61—21no—
69C2×C22⋊D61—21no—
70C2×C22⋊D61—21no—
71C22×Dic61D411yescharacteristic
72#11758226—22no—
73#11758226—22no—
74D4×D61—22no—
75D4×D61—22no—
76D4×D61—44no—
77C2×D244—21no—
78C2×D244—21no—
79C2×D244—21no—
80C2×D244C2311yescharacteristic
81C2×D244C2311yescharacteristic
82C2×C4×D61—22no—
83C2×C4×D61—22no—
84C2×C4×D61—21no—
85C2×C4×D61—21no—
86C2×C4×D61D411yescharacteristic
87C2×C4×D61D411yescharacteristic
88C2×C4×D61C2311yescharacteristic
89C2×C4×D61C2311yescharacteristic
90SD16×C61—22no—
91M16×C61—22no—
92C2×C8×C61C2311yescharacteristic
93C2×C8×C61C2311yescharacteristic
94C4⋊C4×C61—21no—
95C4⋊C4×C61C2311yescharacteristic
96C4⋊C4×C61C2311yescharacteristic
97C22⋊C4×C61—21no—
98C22⋊C4×C61—21no—
99C22⋊Dic61—21no—
100#11758201—22no—
101#11758199—22no—
102#11758198—21no—
103#11758198—21no—
104#11758198—21no—
105#11758198—21no—
106#11758198—21no—
107#11758198—21no—
108C4⋊Dic61C2311yescharacteristic
109C4⋊Dic61C2311yescharacteristic
110#11758196—21no—
111#11758196—21no—
112C4×Dic61—21no—
113#11758194—22no—
114C2×#92418C2311yescharacteristic
115C2×#92418C2311yescharacteristic
116D488—22no—
117#11758189—22no—
118#11758189D414yescomplemented
119C8×D61—22no—
120C8×D61—22no—
121C23×C61—21no—
122C23×C61C2×D411yescharacteristic
123C22×D61—22no—
124C22×D61—22no—
125C22×D61—21no—
126C22×D61—21no—
127C22×D61—41no—
128C22×D61—42no—
129C22×D61—42no—
130C22×D61—42no—
131C22×D61C2×D411yescharacteristic
132C22×D61C2×D411yescharacteristic
133Q8×C61—21no—
134Q8×C61—21no—
135D4×C61—21no—
136D4×C61—21no—
137D4×C61—42no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61C2×D411yescharacteristic
144C2×C4×C61C2411yescharacteristic
145C22⋊D61—42no—
146C22⋊D61—42no—
147C22⋊D61—42no—
148C22⋊D61—42no—
149C2×Dic61—22no—
150C2×Dic61—21no—
151C2×Dic61—21no—
152C2×Dic61C2×D411yescharacteristic
153C2×Dic61C2×D411yescharacteristic
154D244—21no—
155D244—21no—
156D244—21no—
157D244—21no—
158D244—42no—
159D244—42no—
160D244—42no—
161C4×D61—22no—
162C4×D61—21no—
163C4×D61—21no—
164C4×D61—22no—
165C4×D61—42no—
166C4×D61—42no—
167C4×D61C2×D412yes—
168C4×D61#4112yes—
169C8×C61—21no—
170C8×C61C2×D412yescomplemented
171#92418—21no—
172#92418C2×D412yescomplemented
173C22×C61—21no—
174C22×C61—21no—
175C22×C61—21no—
176C22×C61—41no—
177C22×C61—41no—
178C22×C61—41no—
179C22×C61C22×D411yescharacteristic
180C2×D61—21no—
181C2×D61—21no—
182C2×D61—21no—
183C2×D61—21no—
184C2×D61—44no—
185C2×D61—41no—
186C2×D61—41no—
187C2×D61—41no—
188C2×D61—41no—
189C2×D61—41no—
190C2×D61—41no—
191C2×D61—84no—
192C2×D61#12112yes—
193C2×D61AGL(1,ℤ/8)12yescomplemented
194C4×C61—21no—
195C4×C61—41no—
196C4×C61—41no—
197C4×C61—41no—
198C4×C61C22×D411yescharacteristic
199C4×C61C2×#4111yescharacteristic
200Dic61—21no—
201Dic61—41no—
202Dic61—41no—
203Dic61#12112yes—
204#3055—611nomaximal, Sylow
205C2×C61—41no—
206C2×C61—81no—
207C2×C61C2×#12111yescharacteristic
208C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
209C2×C61#57511yescharacteristic
210D61—22no—
211D61—22no—
212D61—81no—
213D61—81no—
214C2×AGL(1,ℤ/8)—611no—
215C22×M16—611no—
216#525—611no—
217C2×#121—611no—
218#469—611no—
219#469—611no—
220#468—611no—
221#468D6111yescharacteristic, complemented
222#466—611no—
223#466—611no—
224#465—611no—
225#465—611no—
226#428—611no—
227#418—611no—
228#417—611no—
229C61#305511yescharacteristic, complemented, Sylow
230C2×#41—611no—
231C22×D4—611no—
232C22×D4—1221no—
233C23×C4—611no—
234AGL(1,ℤ/8)—1224no—
235C2×SD16—611no—
236C2×SD16C2×D6111yescharacteristic, complemented
237C2×D8—611no—
238C2×D8—611no—
239C2×M16—611no—
240C2×M16—611no—
241C2×M16—611no—
242C2×M16—1224no—
243C2×M16C2×D6111yescharacteristic, complemented
244C22×C8—611no—
245C22×C8—611no—
246#123—1221no—
247C22⋊Q8—611no—
248C22⋊Q8C2×D6111yescharacteristic, complemented
249#121—611no—
250#121—611no—
251#121—611no—
252#121—611no—
253#121—611no—
254#121—1221no—
255#121—1221no—
256#121C2×D6111yescharacteristic
257#120—1221no—
258C4×D4—1221no—
259C4×D4—1221no—
260#117—611no—
261C2×C4⋊C4—611no—
262C2×C22⋊C4—1221no—
263#107—611no—
264#107C2×D6111yescharacteristic, complemented
265#106—611no—
266#106—611no—
267#103—611no—
268#103C2×D6111yescharacteristic, complemented
269#102—611no—
270#102—611no—
271#102—611no—
272#102—611no—
273#102—611no—
274#102C2×D6111yescharacteristic, complemented
275C24—611no—
276C24—1221no—
277#41—1222no—
278#41—1222no—
279C2×Q8C22×D6111yescharacteristic
280C2×D4—21no—
281C2×D4—611no—
282C2×D4—611no—
283C2×D4—1221no—
284C2×D4—1221no—
285C2×D4—1221no—
286C2×D4—1222no—
287C2×D4—1222no—
288C2×D4—1221no—
289C2×D4—1221no—
290C2×D4—1221no—
291C2×D4—1221no—
292C2×D4—2444no—
293C2×D4C22×D6111yescharacteristic
294C22×C4—611no—
295C22×C4—611no—
296C22×C4—611no—
297C22×C4—611no—
298C22×C4—611no—
299C22×C4—1222no—
300C22×C4—1222no—
301C22×C4—1221no—
302C22×C4—1221no—
303C22×C4C22×D6111yescharacteristic
304SD16—22no—
305SD16—1222no—
306D8—1222no—
307D8—1222no—
308M16—22no—
309M16—614no—
310M16—1222no—
311M16—1222no—
312C2×C8—611no—
313C2×C8—611no—
314C2×C8—1222no—
315C2×C8—1222no—
316C2×C8C22×D6111yescharacteristic
317C2×C8C22×D6111yescharacteristic
318C4⋊C4—21no—
319C4⋊C4—611no—
320C4⋊C4—611no—
321C4⋊C4—1221no—
322C4⋊C4—1221no—
323C4⋊C4C22×D6111yescharacteristic
324C4⋊C4C22×D6111yescharacteristic
325C22⋊C4—21no—
326C22⋊C4—21no—
327C22⋊C4—1221no—
328C22⋊C4—1221no—
329C22⋊C4—1221no—
330C22⋊C4—1221no—
331C22⋊C4—1221no—
332C22⋊C4—1221no—
333C22⋊C4—1221no—
334C42—1221no—
335C23—21no—
336C23—611no—
337C23—611no—
338C23—1222no—
339C23—1222no—
340C23—1221no—
341C23—1221no—
342C23—2441no—
343C23—2442no—
344C23—2442no—
345C23—2442no—
346C23D4×D6111yescharacteristic
347Q8—21no—
348Q8—21no—
349D4—21no—
350D4—21no—
351D4—42no—
352D4—1221no—
353D4—1221no—
354D4—1221no—
355D4—1221no—
356D4—2442no—
357D4—2442no—
358D4—2442no—
359D4—2442no—
360D4—2442no—
361D4—2442no—
362D4—2442no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—611no—
369C2×C4—612no—
370C2×C4—612no—
371C2×C4—611no—
372C2×C4—1222no—
373C2×C4—1222no—
374C2×C4—1222no—
375C2×C4—1221no—
376C2×C4—1221no—
377C2×C4—1221no—
378C2×C4—1221no—
379C2×C4—2442no—
380C2×C4—2442no—
381C2×C4D4×D6111yescharacteristic
382C2×C4C23×D6111yescharacteristic
383C8—21no—
384C8—612no—
385C8—1221no—
386C8D4×D6112yescomplemented
387C22—21no—
388C22—21no—
389C22—21no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—612no—
394C22—612no—
395C22—1221no—
396C22—1221no—
397C22—1221no—
398C22—1221no—
399C22—4884no—
400C22—2444no—
401C22—2441no—
402C22—2441no—
403C22—2441no—
404C22—2441no—
405C22—2441no—
406C22—2441no—
407C22C2×D4×D6111yescharacteristic
408C4—21no—
409C4—41no—
410C4—41no—
411C4—41no—
412C4—612no—
413C4—1221no—
414C4—2441no—
415C4—2441no—
416C4C2×D4×D6111yescharacteristic
417C4#41×D6111yescharacteristic
418C2—41no—
419C2—81no—
420C2—1222no—
421C2—1222no—
422C2—4881no—
423C2—4881no—
424C2#121×D6111yescharacteristic
425C2AGL(1,ℤ/8)×D6111yescharacteristic
426C2#1684056111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#468C2
socleC22×C61C22×D4
hypercenter#468D61
hypocenterC61#3055
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. C2×#14519804C2semidirect
2. C2×M16×D61C2semidirect
3. #16840275C2semidirect
4. #121×D61C2semidirect
5. #16840015C2semidirect
6. #16840013C2semidirect
7. #16840010C2semidirect
8. #16839999C2semidirect
9. #16839997C2semidirect
10. #16839994C2semidirect
11. #16839988C2semidirect
12. #16839803C2semidirect
13. #16839765C2semidirect
14. #16839762C2semidirect
15. C61×#468C2semidirect
21. C2×#11758201C22semidirect
22. C2×D488C22semidirect
23. C2×#11758199C22semidirect
24. C2×#11758194C22semidirect
28. C2×C8×D61C22semidirect
29. C2×C8×D61C22semidirect
31. #14519753C22semidirect
33. #14519752C22semidirect
35. #14519751C22semidirect
45. #14519710C22semidirect
46. #14519709C22semidirect
47. #14519708C22semidirect
48. #14519701C22semidirect
49. #14519699C22semidirect
50. #14519699C22semidirect
51. #14519698C22semidirect
52. #14519697C22semidirect
53. #14519697C22semidirect
54. C2×SD16×C61C22semidirect
55. C2×M16×C61C22semidirect
56. C22⋊Q8×C61C22semidirect
58. #107×C61C22semidirect
59. #103×C61C22semidirect
60. #102×C61C22semidirect
118. #11758189D4semidirect
170. C8×C61C2×D4semidirect
172. #92418C2×D4semidirect
193. C2×D61AGL(1,ℤ/8)semidirect
221. #468D61semidirect
229. C61#3055semidirect
236. C2×SD16C2×D61semidirect
243. C2×M16C2×D61semidirect
248. C22⋊Q8C2×D61semidirect
264. #107C2×D61semidirect
268. #103C2×D61semidirect
274. #102C2×D61semidirect
386. C8D4×D61semidirect