Finite Group Databasebeta

← #21458141

Subgroups — #21458141

Order 7808.

430 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840430C211yesmaximal, characteristic, complemented
2#16840412C211yesmaximal, characteristic, complemented
3#16840107C211yesmaximal, characteristic, complemented
4#16840082C211yesmaximal, characteristic, complemented
5#16840078C211yesmaximal, characteristic, complemented
6#16840046C211yesmaximal, characteristic, complemented
7#16840014C211yesmaximal, characteristic, complemented
8#16839955C211yesmaximal, characteristic, complemented
9#16839905C211yesmaximal, characteristic, complemented
10#16839904C211yesmaximal, characteristic, complemented
11#16839853C211yesmaximal, characteristic, complemented
12#16839838C211yesmaximal, characteristic, complemented
13#16839764C211yesmaximal, characteristic, complemented
14#16839760C211yesmaximal, characteristic, complemented
15C61×#469C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C2×#11758224—21no—
18C2×#11758224C2211yescharacteristic
19C2×#11758200C2211yescharacteristic
20C2×#11758199C2211yescharacteristic
21C2×#11758189C2211yescharacteristic
22#14519776C2211yescharacteristic
23#14519773—21no—
24#14519773C2211yescharacteristic
25#14519759—21no—
26#14519758—21no—
27#14519754—21no—
28#14519752C2211yescharacteristic
29#14519750—21no—
30#14519749—21no—
31#14519748C2211yescharacteristic
32#14519742C2211yescharacteristic
33D4×Dic61C2211yescharacteristic
34C4×C22⋊D61C2211yescharacteristic
35#14519737—21no—
36C2×C4⋊Dic61C2211yescharacteristic
37C4⋊C4×D61C2211yescharacteristic
38#14519708C2211yescharacteristic
39#14519708C2211yescharacteristic
40#14519706C2211yescharacteristic
41#14519702C2211yescharacteristic
42#14519702C2211yescharacteristic
43#14519700C2211yescharacteristic
44#14519699C2211yescharacteristic
45#14519699C2211yescharacteristic
46#14519698C2211yescharacteristic
47#14519698C2211yescharacteristic
48#14519697C2211yescharacteristic
49C22⋊#92418C2211yescharacteristic
50#14519689C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52C2×D8×C61C2211yescharacteristic
53C2×M16×C61C2211yescharacteristic
54#121×C61C2211yescharacteristic
55#121×C61C2211yescharacteristic
56#106×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic
58#102×C61C2211yescharacteristic
59C2×D4×C61—21no—
60C2×D4×C61—21no—
61C2×D4×C61C2311yescharacteristic
62C2×D4×C61C2311yescharacteristic
63C22×C4×C61C2311yescharacteristic
64C2×C22⋊D61—21no—
65C2×C22⋊D61—21no—
66C2×C22⋊D61—21no—
67C2×C22⋊D61—21no—
68C2×C22⋊D61—21no—
69C2×C22⋊D61D411yescharacteristic
70C22×Dic61—21no—
71C22×Dic61—21no—
72C22×Dic61—21no—
73#11758224—22no—
74#11758224—41no—
75#11758224—44no—
76#11758222—22no—
77#11758222—41no—
78C2×D244—21no—
79C2×D244C2311yescharacteristic
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×C4×D61C2311yescharacteristic
83C2×Dic122—21no—
84C2×Dic122C2311yescharacteristic
85D8×C61—41no—
86M16×C61—41no—
87C2×C8×C61C2311yescharacteristic
88C2×C8×C61C2311yescharacteristic
89C4⋊C4×C61C2311yescharacteristic
90C4⋊C4×C61C2311yescharacteristic
91C22⋊C4×C61—21no—
92C22⋊C4×C61—21no—
93C22⋊Dic61—21no—
94C22⋊Dic61—21no—
95C22⋊Dic61D411yescharacteristic
96#11758200—22no—
97#11758199—41no—
98#11758198—21no—
99#11758198D411yescharacteristic
100C4⋊Dic61—21no—
101C4⋊Dic61C2311yescharacteristic
102C4⋊Dic61C2311yescharacteristic
103#11758196—21no—
104#11758196—21no—
105#11758196—21no—
106#11758196D411yescharacteristic
107C4×Dic61—21no—
108C4×Dic61C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110C2×#92418C2311yescharacteristic
111#11758189—41no—
112C23×C61—21no—
113C23×C61—21no—
114C23×C61C2×D411yescharacteristic
115C22×D61—21no—
116C22×D61C2×D411yescharacteristic
117D4×C61—21no—
118D4×C61—21no—
119D4×C61—21no—
120D4×C61—21no—
121D4×C61—42no—
122D4×C61—81no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61C2×D411yescharacteristic
128C2×C4×C61C2411yescharacteristic
129C22⋊D61—22no—
130C22⋊D61—42no—
131C22⋊D61—42no—
132C22⋊D61—42no—
133C22⋊D61—42no—
134C22⋊D61—81no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—42no—
139C2×Dic61—42no—
140C2×Dic61—42no—
141C2×Dic61C2×D411yescharacteristic
142C2×Dic61C2×D411yescharacteristic
143C2×Dic61C2×D411yescharacteristic
144D244—21no—
145D244—21no—
146D244—81no—
147C4×D61—21no—
148C4×D61—21no—
149C4×D61—42no—
150C4×D61—42no—
151Dic122—21no—
152Dic122—42no—
153Dic122#4112yescomplemented
154C8×C61—21no—
155C8×C61—21no—
156#92418—21no—
157#92418—21no—
158C22×C61—21no—
159C22×C61—21no—
160C22×C61—21no—
161C22×C61—41no—
162C22×C61—41no—
163C22×C61—41no—
164C22×C61—41no—
165C22×C61—41no—
166C22×C61—41no—
167C22×C61C22×D411yescharacteristic
168C2×D61—21no—
169C2×D61—21no—
170C2×D61—21no—
171C2×D61—41no—
172C2×D61—41no—
173C2×D61—41no—
174C4×C61—21no—
175C4×C61—41no—
176C4×C61—41no—
177C4×C61C2×#4111yescharacteristic
178C4×C61H(5,𝔽2)11yescharacteristic
179Dic61—22no—
180Dic61—21no—
181Dic61—21no—
182Dic61—41no—
183Dic61—41no—
184Dic61AGL(1,ℤ/8)12yes—
185#3332—611nomaximal, Sylow
186C2×C61—41no—
187C2×C61—81no—
188C2×C61—81no—
189C2×C61#54611yescharacteristic
190C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
191C2×C61#57711yescharacteristic
192D61—41no—
193D61—81no—
194#550—611no—
195#547—611no—
196#486—611no—
197#481—611no—
198#481—611no—
199#475—611no—
200#469—611no—
201#469D6111yescharacteristic, complemented
202#459—611no—
203#449—611no—
204#449—611no—
205C4×SD16—611no—
206#436—611no—
207#417—611no—
208#417—611no—
209C61#333211yescharacteristic, complemented, Sylow
210C2×#41—611no—
211C2×#41—611no—
212C2×#41—1221no—
213C2×SD16—611no—
214C2×D8—611no—
215C2×D8C2×D6111yescharacteristic
216C2×M16—611no—
217C2×M16C2×D6111yescharacteristic
218C4⋊Q8—611no—
219#127—611no—
220#127—1221no—
221#123—1221no—
222#123—1221no—
223C22⋊Q8—1221no—
224#121—611no—
225#121—611no—
226#121—1221no—
227#121—1221no—
228#121C2×D6111yescharacteristic
229#121C2×D6111yescharacteristic
230C4×Q8—611no—
231C4×D4—611no—
232C4×D4—611no—
233C4×D4—1221no—
234C2×C4⋊C4—611no—
235C2×C4⋊C4—611no—
236#106—611no—
237#106—611no—
238#106C2×D6111yescharacteristic
239C4⋊C8—611no—
240#103—611no—
241#103—611no—
242#103—611no—
243#102—611no—
244#102—611no—
245#102—611no—
246#102—611no—
247#102—611no—
248#102C2×D6111yescharacteristic
249#102C2×D6111yescharacteristic
250C22⋊C8—611no—
251C22⋊C8—611no—
252C4×C8—611no—
253#41—1222no—
254#41—1222no—
255#41—2441no—
256#41—2441no—
257#41—2444no—
258C2×Q8—611no—
259C2×Q8—1221no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—611no—
263C2×D4—611no—
264C2×D4—1221no—
265C2×D4—1221no—
266C2×D4—1221no—
267C2×D4—1221no—
268C2×D4—1221no—
269C2×D4—1221no—
270C2×D4C22×D6111yescharacteristic
271C2×D4C22×D6111yescharacteristic
272C22×C4—611no—
273C22×C4—1221no—
274C22×C4—1221no—
275C22×C4—1221no—
276C22×C4—1221no—
277C22×C4—1221no—
278C22×C4C22×D6111yescharacteristic
279SD16—1222no—
280D8—41no—
281D8—2441no—
282M16—41no—
283M16—2441no—
284C2×C8—611no—
285C2×C8—611no—
286C2×C8C22×D6111yescharacteristic
287C2×C8C22×D6111yescharacteristic
288C4⋊C4—611no—
289C4⋊C4—611no—
290C4⋊C4—611no—
291C4⋊C4—1221no—
292C4⋊C4—1221no—
293C4⋊C4—1221no—
294C4⋊C4—1221no—
295C4⋊C4C22×D6111yescharacteristic
296C4⋊C4C22×D6111yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—611no—
300C22⋊C4—611no—
301C22⋊C4—1221no—
302C22⋊C4—1221no—
303C22⋊C4—1221no—
304C42—611no—
305C42—1221no—
306C23—21no—
307C23—21no—
308C23—611no—
309C23—1221no—
310C23D4×D6111yescharacteristic
311Q8—612no—
312Q8—1221no—
313Q8—2442no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—21no—
318D4—42no—
319D4—81no—
320D4—1222no—
321D4—1221no—
322D4—1221no—
323D4—4881no—
324D4—4881no—
325D4—2442no—
326D4—2442no—
327D4—2442no—
328D4—2442no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—611no—
334C2×C4—611no—
335C2×C4—611no—
336C2×C4—1221no—
337C2×C4—1221no—
338C2×C4—1221no—
339C2×C4—1221no—
340C2×C4—1221no—
341C2×C4—2442no—
342C2×C4—2442no—
343C2×C4—2442no—
344C2×C4—2442no—
345C2×C4—2442no—
346C2×C4D4×D6111yescharacteristic
347C2×C4C23×D6111yescharacteristic
348C8—21no—
349C8—21no—
350C8—1221no—
351C8—1221no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—1221no—
362C22—1221no—
363C22—1221no—
364C22—2441no—
365C22—2441no—
366C22—2441no—
367C22C2×D4×D6111yescharacteristic
368C4—21no—
369C4—41no—
370C4—41no—
371C4—612no—
372C4—1221no—
373C4—1221no—
374C4—1222no—
375C4—2441no—
376C4—2441no—
377C4#41×D6111yescharacteristic
378C4#1451982211yescharacteristic
379C2—41no—
380C2—81no—
381C2—81no—
382C2—4881no—
383C2—2441no—
384C2#1684040111yescharacteristic
385C2AGL(1,ℤ/8)×D6111yescharacteristic
386C2#1684057211yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#469C2
socleC22×C61C22×D4
hypercenter#469D61
hypocenterC61#3332
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #16840430C2semidirect
2. #16840412C2semidirect
3. #16840107C2semidirect
4. #16840082C2semidirect
5. #16840078C2semidirect
6. #16840046C2semidirect
7. #16840014C2semidirect
8. #16839955C2semidirect
9. #16839905C2semidirect
10. #16839904C2semidirect
11. #16839853C2semidirect
12. #16839838C2semidirect
13. #16839764C2semidirect
14. #16839760C2semidirect
15. C61×#469C2semidirect
153. Dic122#41semidirect
201. #469D61semidirect
209. C61#3332semidirect