Finite Group Databasebeta

← #21455326

Subgroups — #21455326

Order 7808.

494 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519804C211yesmaximal, characteristic
2C2×SD16×D61C211yesmaximal, characteristic, complemented
3#16840337C211yesmaximal, characteristic, complemented
4#16840234C211yesmaximal, characteristic, complemented
5#16839980C211yesmaximal, characteristic, complemented
6#16839979C211yesmaximal, characteristic, complemented
7#16839978C211yesmaximal, characteristic, complemented
8#16839977C211yesmaximal, characteristic, complemented
9#16839966C211yesmaximal, characteristic, complemented
10#16839965C211yesmaximal, characteristic, complemented
11#16839964C211yesmaximal, characteristic, complemented
12#16839787C211yesmaximal, characteristic, complemented
13#16839769C211yesmaximal, characteristic, complemented
14#16839757C211yesmaximal, characteristic, complemented
15C61×#461C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×Q8×D61C2211yescharacteristic
18C2×D4×D61C2211yescharacteristic
19#14519804—24no—
20C2×#11758190C2211yescharacteristic
21C2×#11758200C2211yescharacteristic
22C2×#11758201C2211yescharacteristic
23C2×#11758201C2211yescharacteristic
24SD16×D61—24no—
25C2×D488C2211yescharacteristic
26C2×#11758199C2211yescharacteristic
27C2×#11758189C2211yescharacteristic
28C2×C8×D61C2211yescharacteristic
29#14519775C2211yescharacteristic, complemented
30#14519766C2211yescharacteristic, complemented
31#14519765C2211yescharacteristic, complemented
32#14519762—21no—
33#14519762—21no—
34#14519755—21no—
35#14519755—21no—
36C4×D244C2211yescharacteristic
37D4×Dic61C2211yescharacteristic
38#14519739C2211yescharacteristic
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#14519701C2211yescharacteristic, complemented
50#14519701C2211yescharacteristic, complemented
51#14519700C2211yescharacteristic, complemented
52#14519699C2211yescharacteristic, complemented
53#14519697C2211yescharacteristic, complemented
54C2×SD16×C61C2211yescharacteristic
55C2×SD16×C61C2211yescharacteristic
56C4⋊Q8×C61C2211yescharacteristic, complemented
57C4×D4×C61C2211yescharacteristic
58C4⋊C8×C61C2211yescharacteristic, complemented
59#103×C61C2211yescharacteristic, complemented
60#103×C61C2211yescharacteristic, complemented
61C23×D61—21no—
62C2×Q8×C61C2311yescharacteristic
63C2×Q8×C61C2311yescharacteristic
64C2×D4×C61C2311yescharacteristic
65C22×C4×C61—21no—
66C2×C22⋊D61—21no—
67C22×Dic61—21no—
68#11758226—22no—
69#11758226—22no—
70Q8×D61—22no—
71Q8×D61—22no—
72D4×D61—22no—
73D4×D61D414yes—
74C2×D244—21no—
75C2×D244C2311yescharacteristic
76C2×D244C2311yescharacteristic
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×C4×D61—21no—
80C2×C4×D61—21no—
81C2×C4×D61C2311yescharacteristic
82C2×Dic122—21no—
83C2×Dic122C2311yescharacteristic
84SD16×C61—22no—
85SD16×C61—22no—
86C2×C8×C61C2311yescharacteristic
87C2×C8×C61C2311yescharacteristic
88C4⋊C4×C61—21no—
89C4⋊C4×C61—21no—
90C4⋊C4×C61C2311yescharacteristic
91C22⋊C4×C61—21no—
92C42×C61C2311yescharacteristic
93C22⋊Dic61—21no—
94#11758201—22no—
95#11758201—22no—
96#11758200—22no—
97#11758199—22no—
98#11758198—21no—
99#11758198—21no—
100#11758198—21no—
101#11758198—21no—
102#11758198—21no—
103#11758198—21no—
104#11758198—21no—
105#11758198D411yescharacteristic
106#11758198D411yescharacteristic
107C4⋊Dic61C2311yescharacteristic
108#11758196—21no—
109#11758196—21no—
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—
121C22×D61—21no—
122C22×D61—24no—
123C22×D61—21no—
124C22×D61—81no—
125C22×D61—81no—
126C22×D61C2×D411yescharacteristic
127Q8×C61—21no—
128Q8×C61—21no—
129Q8×C61—21no—
130Q8×C61—21no—
131D4×C61—21no—
132D4×C61C2×D412yes—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—81no—
137C2×C4×C61C2×D411yescharacteristic
138C2×C4×C61C2×D411yescharacteristic
139C2×C4×C61C2411yescharacteristic
140C22⋊D61—24no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—81no—
144C2×Dic61C2×D411yescharacteristic
145C2×Dic61C2×D411yescharacteristic
146C2×Dic61C2×D411yescharacteristic
147D244—21no—
148D244—21no—
149D244—21no—
150D244—42no—
151D244C2×D412yes—
152C4×D61—42no—
153C4×D61—42no—
154C4×D61—81no—
155C4×D61—81no—
156C4×D61C2×D412yes—
157C4×D61#4112yes—
158Dic122—21no—
159Dic122—21no—
160Dic122—42no—
161C8×C61—21no—
162C8×C61—21no—
163#92418—21no—
164#92418—21no—
165C22×C61—22no—
166C22×C61—41no—
167C22×C61—41no—
168C22×C61C22×D411yescharacteristic
169C2×D61—21no—
170C2×D61—21no—
171C2×D61—22no—
172C2×D61—41no—
173C2×D61—41no—
174C2×D61—41no—
175C2×D61—41no—
176C2×D61—41no—
177C2×D61—84no—
178C2×D61#12112yes—
179C4×C61—21no—
180C4×C61—21no—
181C4×C61—41no—
182C4×C61—41no—
183C4×C61—41no—
184C4×C61C22×D411yescharacteristic
185C4×C61C2×#4111yescharacteristic
186Dic61—21no—
187Dic61—21no—
188Dic61—41no—
189Dic61—41no—
190Dic61#12112yes—
191#3042—611nomaximal, Sylow
192C2×C61—42no—
193C2×C61C2×#12111yescharacteristic
194C2×C61#57711yescharacteristic
195C2×C61#57711yescharacteristic
196D61—22no—
197D61—42no—
198D61—81no—
199C2×AGL(1,ℤ/8)—611no—
200C22×SD16—611no—
201#536—611no—
202#518—611no—
203#463—611no—
204#463—611no—
205#463—611no—
206#463—611no—
207#461—611no—
208#461—611no—
209#461—611no—
210#461D6111yescharacteristic, complemented
211#424—611no—
212#419—611no—
213#416—611no—
214C61#304211yescharacteristic, complemented, Sylow
215C2×#41—611no—
216C22×Q8—611no—
217C22×D4—611no—
218AGL(1,ℤ/8)—1224no—
219C2×SD16—611no—
220C2×SD16—611no—
221C2×SD16—611no—
222C2×SD16—611no—
223C2×SD16—1224no—
224C2×SD16C2×D6111yescharacteristic
225C2×SD16C2×D6111yescharacteristic
226C2×D8—611no—
227C2×D8—611no—
228C2×M16—611no—
229C22×C8—611no—
230C4⋊Q8—611no—
231C4⋊Q8C2×D6111yescharacteristic, complemented
232#124—611no—
233#124—611no—
234#123—1221no—
235#123—1221no—
236C22⋊Q8—1221no—
237C22⋊Q8—1221no—
238C4×D4—611no—
239C4×D4—611no—
240C4×D4—611no—
241C4×D4—1221no—
242C4×D4—1221no—
243C4×D4C2×D6111yescharacteristic
244#117—611no—
245#117—611no—
246C2×C22⋊C4—1221no—
247C2×C22⋊C4—1221no—
248C4⋊C8—611no—
249C4⋊C8—611no—
250C4⋊C8—611no—
251C4⋊C8C2×D6111yescharacteristic, complemented
252#103—611no—
253#103—611no—
254#103—611no—
255#103—611no—
256#103C2×D6111yescharacteristic, complemented
257#103C2×D6111yescharacteristic, complemented
258#102—611no—
259#102—611no—
260C24—1221no—
261#41—1222no—
262#41—1222no—
263C2×Q8—611no—
264C2×Q8—1221no—
265C2×Q8—1222no—
266C2×Q8—1222no—
267C2×Q8C22×D6111yescharacteristic
268C2×Q8C22×D6111yescharacteristic
269C2×D4—614no—
270C2×D4—611no—
271C2×D4—611no—
272C2×D4—1221no—
273C2×D4—1222no—
274C2×D4—1221no—
275C2×D4C22×D6111yescharacteristic
276C22×C4—21no—
277C22×C4—611no—
278C22×C4—1221no—
279C22×C4—1221no—
280C22×C4—1221no—
281C22×C4—1221no—
282C22×C4—1221no—
283SD16—22no—
284SD16—22no—
285SD16—1222no—
286SD16—1222no—
287SD16—1222no—
288SD16—1222no—
289D8—1222no—
290D8—1222no—
291M16—1222no—
292C2×C8—611no—
293C2×C8—611no—
294C2×C8—1222no—
295C2×C8C22×D6111yescharacteristic
296C2×C8C22×D6111yescharacteristic
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—611no—
300C4⋊C4—611no—
301C4⋊C4—611no—
302C4⋊C4—1221no—
303C4⋊C4—1221no—
304C4⋊C4C22×D6111yescharacteristic
305C22⋊C4—21no—
306C22⋊C4—611no—
307C22⋊C4—611no—
308C22⋊C4—1221no—
309C22⋊C4—1221no—
310C22⋊C4—1221no—
311C22⋊C4—1221no—
312C22⋊C4—1221no—
313C22⋊C4—1221no—
314C22⋊C4—1221no—
315C22⋊C4—1221no—
316C42—611no—
317C42—1221no—
318C42C22×D6111yescharacteristic
319C23—21no—
320C23—611no—
321C23—1224no—
322C23—1221no—
323C23—1221no—
324C23—4881no—
325C23—4881no—
326Q8—21no—
327Q8—21no—
328Q8—21no—
329Q8—21no—
330Q8—1221no—
331Q8—1221no—
332Q8—2442no—
333D4—21no—
334D4—612no—
335D4—1224no—
336D4—1221no—
337D4—1221no—
338D4—1221no—
339D4—2442no—
340D4D4×D6112yes—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—81no—
345C2×C4—611no—
346C2×C4—612no—
347C2×C4—612no—
348C2×C4—611no—
349C2×C4—611no—
350C2×C4—1221no—
351C2×C4—1221no—
352C2×C4—4881no—
353C2×C4—4881no—
354C2×C4—4881no—
355C2×C4—2442no—
356C2×C4—2442no—
357C2×C4D4×D6111yescharacteristic
358C2×C4D4×D6111yescharacteristic
359C2×C4C23×D6111yescharacteristic
360C8—21no—
361C8—21no—
362C8—1221no—
363C8—1221no—
364C22—22no—
365C22—41no—
366C22—41no—
367C22—612no—
368C22—1221no—
369C22—1221no—
370C22—1222no—
371C22—4884no—
372C22—2441no—
373C22—2441no—
374C22—2441no—
375C22—2441no—
376C22—2441no—
377C22C2×D4×D6111yescharacteristic
378C4—21no—
379C4—21no—
380C4—41no—
381C4—41no—
382C4—41no—
383C4—612no—
384C4—1221no—
385C4—1221no—
386C4—2441no—
387C4—2441no—
388C4C2×D4×D6111yescharacteristic
389C4#41×D6111yescharacteristic
390C2—42no—
391C2—1222no—
392C2—4881no—
393C2—2442no—
394C2#121×D6111yescharacteristic
395C2#1684056811yescharacteristic
396C2#1684057111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#461C2
socleC22×C61C22×D4
hypercenter#461D61
hypocenterC61#3042
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
2. C2×SD16×D61C2semidirect
3. #16840337C2semidirect
4. #16840234C2semidirect
5. #16839980C2semidirect
6. #16839979C2semidirect
7. #16839978C2semidirect
8. #16839977C2semidirect
9. #16839966C2semidirect
10. #16839965C2semidirect
11. #16839964C2semidirect
12. #16839787C2semidirect
13. #16839769C2semidirect
14. #16839757C2semidirect
15. C61×#461C2semidirect
29. #14519775C22semidirect
30. #14519766C22semidirect
31. #14519765C22semidirect
45. C4⋊#92418C22semidirect
46. #14519706C22semidirect
47. #14519706C22semidirect
48. #14519702C22semidirect
49. #14519701C22semidirect
50. #14519701C22semidirect
51. #14519700C22semidirect
52. #14519699C22semidirect
53. #14519697C22semidirect
56. C4⋊Q8×C61C22semidirect
58. C4⋊C8×C61C22semidirect
59. #103×C61C22semidirect
60. #103×C61C22semidirect
210. #461D61semidirect
214. C61#3042semidirect
231. C4⋊Q8C2×D61semidirect
251. C4⋊C8C2×D61semidirect
256. #103C2×D61semidirect
257. #103C2×D61semidirect