Finite Group Databasebeta

← #21455317

Subgroups — #21455317

Order 7808.

526 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519801C211yesmaximal, characteristic, complemented
2C2×D8×D61C211yesmaximal, characteristic, complemented
3#16840325C211yesmaximal, characteristic, complemented
4#16840234C211yesmaximal, characteristic, complemented
5#16839978C211yesmaximal, characteristic, complemented
6#16839977C211yesmaximal, characteristic, complemented
7#16839976C211yesmaximal, characteristic, complemented
8#16839975C211yesmaximal, characteristic, complemented
9#16839956C211yesmaximal, characteristic, complemented
10#16839955C211yesmaximal, characteristic, complemented
11#16839954C211yesmaximal, characteristic, complemented
12#16839787C211yesmaximal, characteristic, complemented
13#16839765C211yesmaximal, characteristic, complemented
14#16839755C211yesmaximal, characteristic, complemented
15C61×#459C211yesmaximal, characteristic, complemented
16C2×#11758224C2211yescharacteristic
17C2×D4×D61C2211yescharacteristic
18C2×D4×D61C2211yescharacteristic
19#14519801—24no—
20C2×#11758190C2211yescharacteristic, complemented
21C2×#11758200C2211yescharacteristic, complemented
22C2×D488C2211yescharacteristic
23C2×#11758199C2211yescharacteristic
24C2×#11758199C2211yescharacteristic
25C2×#11758199C2211yescharacteristic, complemented
26D8×D61—24no—
27C2×#11758189C2211yescharacteristic
28C2×C8×D61C2211yescharacteristic
29#14519773C2211yescharacteristic, complemented
30#14519765C2211yescharacteristic, complemented
31#14519764C2211yescharacteristic, complemented
32#14519749—21no—
33#14519749—21no—
34#14519745—21no—
35#14519745—21no—
36C4×D244C2211yescharacteristic, complemented
37D4×Dic61C2211yescharacteristic, complemented
38#14519739C2211yescharacteristic, complemented
39C4×C22⋊D61—21no—
40#14519737—21no—
41#14519735C2211yescharacteristic
42#14519734C2211yescharacteristic
43C2×#11758198—21no—
44C22⋊C4×D61—21no—
45C4⋊#92418C2211yescharacteristic, complemented
46#14519706C2211yescharacteristic, complemented
47#14519706C2211yescharacteristic, complemented
48#14519702C2211yescharacteristic, complemented
49#14519700C2211yescharacteristic, complemented
50#14519699C2211yescharacteristic, complemented
51#14519698C2211yescharacteristic, complemented
52#14519698C2211yescharacteristic, complemented
53#14519697C2211yescharacteristic, complemented
54C2×D8×C61C2211yescharacteristic
55C2×D8×C61C2211yescharacteristic, complemented
56#127×C61C2211yescharacteristic, complemented
57C4×D4×C61C2211yescharacteristic, complemented
58C4⋊C8×C61C2211yescharacteristic, complemented
59#102×C61C2211yescharacteristic, complemented
60#102×C61C2211yescharacteristic, complemented
61C23×D61—21no—
62C23×D61—21no—
63C2×D4×C61—21no—
64C2×D4×C61—21no—
65C2×D4×C61C2311yescharacteristic
66C2×D4×C61C2311yescharacteristic
67C2×D4×C61C2311yescharacteristic
68C22×C4×C61—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#11758224—22no—
77#11758224—22no—
78D4×D61—22no—
79D4×D61—22no—
80D4×D61—22no—
81D4×D61D414yescomplemented
82C2×D244C2311yescharacteristic
83C2×D244C2311yescharacteristic
84C2×C4×D61—21no—
85C2×C4×D61—21no—
86C2×C4×D61C2311yescharacteristic
87C2×Dic122C2311yescharacteristic
88D8×C61—22no—
89D8×C61—22no—
90C2×C8×C61C2311yescharacteristic
91C2×C8×C61C2311yescharacteristic
92C4⋊C4×C61C2311yescharacteristic
93C22⋊C4×C61—21no—
94C42×C61C2311yescharacteristic
95C22⋊Dic61—21no—
96C22⋊Dic61—21no—
97C22⋊Dic61—21no—
98#11758200—22no—
99#11758199—22no—
100#11758199—22no—
101#11758199—22no—
102#11758198—21no—
103#11758198—21no—
104#11758198—21no—
105#11758198—21no—
106#11758198—21no—
107#11758198D411yescharacteristic
108#11758198D411yescharacteristic
109C4⋊Dic61C2311yescharacteristic
110#11758196D411yescharacteristic
111#11758196D411yescharacteristic
112C4×Dic61—21no—
113C4×Dic61C2311yescharacteristic
114C2×#92418C2311yescharacteristic
115C2×#92418C2311yescharacteristic
116D488—22no—
117#11758190—22no—
118#11758189—22no—
119C8×D61—22no—
120C23×C61—21no—
121C23×C61—21no—
122C23×C61—21no—
123C22×D61—21no—
124C22×D61—24no—
125C22×D61—21no—
126C22×D61—42no—
127C22×D61—81no—
128C22×D61—81no—
129C22×D61—81no—
130C22×D61—81no—
131C22×D61C2×D411yescharacteristic
132D4×C61—21no—
133D4×C61—21no—
134D4×C61—21no—
135D4×C61—21no—
136D4×C61—21no—
137D4×C61—81no—
138D4×C61—81no—
139D4×C61C2×D412yes—
140C2×C4×C61—21no—
141C2×C4×C61—81no—
142C2×C4×C61C2×D411yescharacteristic
143C2×C4×C61C2×D411yescharacteristic
144C2×C4×C61C2411yescharacteristic
145C22⋊D61—24no—
146C22⋊D61—42no—
147C22⋊D61—42no—
148C22⋊D61—81no—
149C22⋊D61—81no—
150C2×Dic61—21no—
151C2×Dic61—21no—
152C2×Dic61—42no—
153C2×Dic61—81no—
154C2×Dic61C2×D411yescharacteristic
155C2×Dic61C2×D411yescharacteristic
156C2×Dic61C2×D411yescharacteristic
157D244—21no—
158D244—21no—
159D244—21no—
160D244C2×D412yes—
161C4×D61—81no—
162C4×D61—81no—
163C4×D61C2×D412yes—
164C4×D61#4112yes—
165Dic122—21no—
166Dic122—21no—
167C8×C61—21no—
168C8×C61—21no—
169#92418—21no—
170#92418—21no—
171C22×C61—22no—
172C22×C61—41no—
173C22×C61—41no—
174C22×C61—41no—
175C22×C61—41no—
176C22×C61—41no—
177C22×C61—41no—
178C22×C61—41no—
179C22×C61—41no—
180C22×C61C22×D411yescharacteristic
181C2×D61—21no—
182C2×D61—21no—
183C2×D61—22no—
184C2×D61—41no—
185C2×D61—41no—
186C2×D61—41no—
187C2×D61—41no—
188C2×D61—41no—
189C2×D61—84no—
190C2×D61—84no—
191C2×D61#12112yes—
192C4×C61—21no—
193C4×C61—21no—
194C4×C61—41no—
195C4×C61C22×D411yescharacteristic
196C4×C61C2×#4111yescharacteristic
197Dic61—21no—
198Dic61—21no—
199Dic61—41no—
200Dic61—41no—
201Dic61#12112yes—
202#3041—611nomaximal, Sylow
203C2×C61—42no—
204C2×C61—81no—
205C2×C61—81no—
206C2×C61C2×#12111yescharacteristic
207C2×C61#57611yescharacteristic
208C2×C61#57611yescharacteristic
209D61—22no—
210D61—42no—
211D61—81no—
212C2×AGL(1,ℤ/8)—611no—
213C22×D8—611no—
214#535—611no—
215#518—611no—
216#463—611no—
217#463—611no—
218#463—611no—
219#463—611no—
220#459—611no—
221#459—611no—
222#459—611no—
223#459D6111yescharacteristic, complemented
224#424—611no—
225#418—611no—
226#416—611no—
227C61#304111yescharacteristic, complemented, Sylow
228C2×#41—611no—
229C22×D4—611no—
230C22×D4—611no—
231AGL(1,ℤ/8)—1224no—
232C2×SD16—611no—
233C2×SD16—611no—
234C2×D8—611no—
235C2×D8—611no—
236C2×D8—611no—
237C2×D8—611no—
238C2×D8—1224no—
239C2×D8C2×D6111yescharacteristic
240C2×D8C2×D6111yescharacteristic, complemented
241C2×M16—611no—
242C22×C8—611no—
243#127—611no—
244#127C2×D6111yescharacteristic, complemented
245#124—611no—
246#124—611no—
247#121—1221no—
248#121—1221no—
249#120—1221no—
250#120—1221no—
251C4×D4—611no—
252C4×D4—611no—
253C4×D4—611no—
254C4×D4—1221no—
255C4×D4—1221no—
256C4×D4C2×D6111yescharacteristic, complemented
257#117—611no—
258#117—611no—
259C2×C22⋊C4—1221no—
260C2×C22⋊C4—1221no—
261C4⋊C8—611no—
262C4⋊C8—611no—
263C4⋊C8—611no—
264C4⋊C8C2×D6111yescharacteristic, complemented
265#103—611no—
266#103—611no—
267#102—611no—
268#102—611no—
269#102—611no—
270#102—611no—
271#102C2×D6111yescharacteristic, complemented
272#102C2×D6111yescharacteristic, complemented
273C24—1221no—
274C24—1221no—
275#41—1222no—
276#41—1222no—
277C2×Q8—611no—
278C2×D4—21no—
279C2×D4—21no—
280C2×D4—614no—
281C2×D4—611no—
282C2×D4—611no—
283C2×D4—1222no—
284C2×D4—1222no—
285C2×D4—1222no—
286C2×D4—1221no—
287C2×D4—1221no—
288C2×D4—1221no—
289C2×D4—1221no—
290C2×D4—1221no—
291C2×D4C22×D6111yescharacteristic
292C2×D4C22×D6111yescharacteristic
293C2×D4C22×D6111yescharacteristic
294C22×C4—21no—
295C22×C4—611no—
296C22×C4—1221no—
297C22×C4—1221no—
298C22×C4—1221no—
299C22×C4—1221no—
300SD16—1222no—
301SD16—1222no—
302D8—22no—
303D8—22no—
304D8—1222no—
305D8—1222no—
306D8—1222no—
307D8—1222no—
308M16—1222no—
309C2×C8—611no—
310C2×C8—611no—
311C2×C8—1222no—
312C2×C8C22×D6111yescharacteristic
313C2×C8C22×D6111yescharacteristic
314C4⋊C4—611no—
315C4⋊C4—611no—
316C4⋊C4—611no—
317C4⋊C4C22×D6111yescharacteristic
318C22⋊C4—21no—
319C22⋊C4—611no—
320C22⋊C4—611no—
321C22⋊C4—1221no—
322C22⋊C4—1221no—
323C22⋊C4—1221no—
324C22⋊C4—1221no—
325C22⋊C4—1221no—
326C22⋊C4—1221no—
327C22⋊C4—1221no—
328C22⋊C4—1221no—
329C42—611no—
330C42—1221no—
331C42C22×D6111yescharacteristic
332C23—21no—
333C23—21no—
334C23—21no—
335C23—611no—
336C23—1224no—
337C23—1221no—
338C23—1221no—
339C23—4881no—
340C23—4881no—
341C23—4881no—
342C23—4881no—
343C23—2442no—
344Q8—1221no—
345Q8—1221no—
346D4—21no—
347D4—21no—
348D4—21no—
349D4—21no—
350D4—21no—
351D4—81no—
352D4—81no—
353D4—612no—
354D4—1224no—
355D4—1221no—
356D4—1221no—
357D4—1221no—
358D4—4881no—
359D4—4881no—
360D4—2442no—
361D4—2442no—
362D4D4×D6112yes—
363C2×C4—21no—
364C2×C4—81no—
365C2×C4—611no—
366C2×C4—612no—
367C2×C4—612no—
368C2×C4—611no—
369C2×C4—611no—
370C2×C4—1221no—
371C2×C4—1221no—
372C2×C4—4881no—
373C2×C4—4881no—
374C2×C4—4881no—
375C2×C4—2442no—
376C2×C4D4×D6111yescharacteristic
377C2×C4D4×D6111yescharacteristic
378C2×C4C23×D6111yescharacteristic
379C8—21no—
380C8—21no—
381C8—1221no—
382C8—1221no—
383C22—22no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—612no—
393C22—1221no—
394C22—1221no—
395C22—1222no—
396C22—4884no—
397C22—4884no—
398C22—2441no—
399C22—2441no—
400C22—2441no—
401C22—2441no—
402C22—2441no—
403C22C2×D4×D6111yescharacteristic
404C4—21no—
405C4—21no—
406C4—41no—
407C4—612no—
408C4—1221no—
409C4—1221no—
410C4—2441no—
411C4—2441no—
412C4C2×D4×D6111yescharacteristic
413C4#41×D6111yescharacteristic
414C2—42no—
415C2—81no—
416C2—81no—
417C2—1222no—
418C2—4881no—
419C2—2442no—
420C2#121×D6111yescharacteristic
421C2#1684056311yescharacteristic
422C2#1684056611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#459C2
socleC22×C61C22×D4
hypercenter#459D61
hypocenterC61#3041
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. C2×#14519801C2semidirect
2. C2×D8×D61C2semidirect
3. #16840325C2semidirect
4. #16840234C2semidirect
5. #16839978C2semidirect
6. #16839977C2semidirect
7. #16839976C2semidirect
8. #16839975C2semidirect
9. #16839956C2semidirect
10. #16839955C2semidirect
11. #16839954C2semidirect
12. #16839787C2semidirect
13. #16839765C2semidirect
14. #16839755C2semidirect
15. C61×#459C2semidirect
20. C2×#11758190C22semidirect
21. C2×#11758200C22semidirect
25. C2×#11758199C22semidirect
29. #14519773C22semidirect
30. #14519765C22semidirect
31. #14519764C22semidirect
36. C4×D244C22semidirect
37. D4×Dic61C22semidirect
38. #14519739C22semidirect
45. C4⋊#92418C22semidirect
46. #14519706C22semidirect
47. #14519706C22semidirect
48. #14519702C22semidirect
49. #14519700C22semidirect
50. #14519699C22semidirect
51. #14519698C22semidirect
52. #14519698C22semidirect
53. #14519697C22semidirect
55. C2×D8×C61C22semidirect
56. #127×C61C22semidirect
57. C4×D4×C61C22semidirect
58. C4⋊C8×C61C22semidirect
59. #102×C61C22semidirect
60. #102×C61C22semidirect
81. D4×D61D4semidirect
223. #459D61semidirect
227. C61#3041semidirect
240. C2×D8C2×D61semidirect
244. #127C2×D61semidirect
256. C4×D4C2×D61semidirect
264. C4⋊C8C2×D61semidirect
271. #102C2×D61semidirect
272. #102C2×D61semidirect