Finite Group Databasebeta

← #21458142

Subgroups — #21458142

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#16840431C211yesmaximal, characteristic, complemented
2#16840413C211yesmaximal, characteristic, complemented
3#16840107C211yesmaximal, characteristic, complemented
4#16840080C211yesmaximal, characteristic, complemented
5#16840079C211yesmaximal, characteristic, complemented
6#16840045C211yesmaximal, characteristic, complemented
7#16840015C211yesmaximal, characteristic, complemented
8#16840014C211yesmaximal, characteristic, complemented
9#16839956C211yesmaximal, characteristic, complemented
10#16839910C211yesmaximal, characteristic, complemented
11#16839907C211yesmaximal, characteristic, complemented
12#16839847C211yesmaximal, characteristic, complemented
13#16839838C211yesmaximal, characteristic, complemented
14#16839762C211yesmaximal, characteristic, complemented
15C61×#417C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×#11758222—21no—
18C2×#11758201C2211yescharacteristic
19C2×D488C2211yescharacteristic
20C2×#11758199C2211yescharacteristic
21C2×#11758189C2211yescharacteristic
22#14519776C2211yescharacteristic
23#14519773—21no—
24#14519773C2211yescharacteristic
25#14519762—21no—
26#14519760—21no—
27#14519755—21no—
28#14519752C2211yescharacteristic
29#14519751—21no—
30#14519751C2211yescharacteristic
31#14519751C2211yescharacteristic
32#14519748—21no—
33#14519748C2211yescharacteristic
34Q8×Dic61C2211yescharacteristic
35#14519739C2211yescharacteristic
36C4×C22⋊D61—21no—
37C4×C22⋊D61C2211yescharacteristic
38C4⋊C4×D61C2211yescharacteristic
39#14519709C2211yescharacteristic
40#14519708C2211yescharacteristic
41#14519708C2211yescharacteristic
42#14519706C2211yescharacteristic
43#14519701C2211yescharacteristic
44#14519699C2211yescharacteristic
45#14519699C2211yescharacteristic
46#14519698C2211yescharacteristic
47#14519697C2211yescharacteristic
48#14519697C2211yescharacteristic
49C22⋊#92418C2211yescharacteristic
50#14519689C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52C2×#41×C61C2211yescharacteristic
53C2×M16×C61C2211yescharacteristic
54C2×C4⋊C4×C61C2211yescharacteristic
55#103×C61C2211yescharacteristic
56#103×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic
58#102×C61C2211yescharacteristic
59#41×C61—22no—
60#41×C61—41no—
61C2×Q8×C61C2311yescharacteristic
62C2×D4×C61—21no—
63C2×D4×C61C2311yescharacteristic
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61C2311yescharacteristic
67C2×C22⋊D61—21no—
68C2×C22⋊D61—21no—
69C2×C22⋊D61—21no—
70C2×C22⋊D61—21no—
71C2×C22⋊D61—21no—
72C2×C22⋊D61D411yescharacteristic
73#11758226—22no—
74#11758226—41no—
75#11758222—44no—
76C2×D244—21no—
77C2×D244—21no—
78C2×D244C2311yescharacteristic
79C2×D244C2311yescharacteristic
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×C4×D61—21no—
83C2×C4×D61C2311yescharacteristic
84C2×Dic122—21no—
85M16×C61—41no—
86C2×C8×C61C2311yescharacteristic
87C2×C8×C61C2311yescharacteristic
88C4⋊C4×C61—21no—
89C4⋊C4×C61C2311yescharacteristic
90C4⋊C4×C61C2311yescharacteristic
91C22⋊Dic61—21no—
92C22⋊Dic61D411yescharacteristic
93#11758201—22no—
94#11758199—41no—
95#11758198—21no—
96#11758198—21no—
97#11758198—21no—
98#11758198—21no—
99#11758198D411yescharacteristic
100C4⋊Dic61—21no—
101C4⋊Dic61C2311yescharacteristic
102C4⋊Dic61C2311yescharacteristic
103#11758196—21no—
104#11758196—21no—
105#11758196D411yescharacteristic
106C4×Dic61—21no—
107C4×Dic61C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110D488—41no—
111#11758189—41no—
112C23×C61—21no—
113C23×C61C2×D411yescharacteristic
114C22×D61—21no—
115C22×D61—21no—
116C22×D61C2×D411yescharacteristic
117Q8×C61—21no—
118Q8×C61#4112yescomplemented
119D4×C61—21no—
120D4×C61—21no—
121D4×C61—42no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—42no—
128C2×C4×C61—42no—
129C2×C4×C61C2×D411yescharacteristic
130C2×C4×C61C2411yescharacteristic
131C22⋊D61—22no—
132C22⋊D61—42no—
133C22⋊D61—42no—
134C22⋊D61—81no—
135C22⋊D61—81no—
136C22⋊D61—81no—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61C2×D411yescharacteristic
140C2×Dic61C2×D411yescharacteristic
141C2×Dic61C2×D411yescharacteristic
142D244—21no—
143D244—21no—
144D244—21no—
145D244—21no—
146D244—42no—
147D244—42no—
148C4×D61—21no—
149C4×D61—21no—
150C4×D61—42no—
151C4×D61—42no—
152C4×D61—42no—
153Dic122—42no—
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×C61C22×D411yescharacteristic
165C2×D61—21no—
166C2×D61—21no—
167C2×D61—21no—
168C2×D61—41no—
169C2×D61—41no—
170C2×D61—41no—
171C2×D61—41no—
172C2×D61—41no—
173C2×D61—41no—
174C4×C61—22no—
175C4×C61—21no—
176C4×C61—41no—
177C4×C61—41no—
178C4×C61C2×#4111yescharacteristic
179C4×C61H(5,𝔽2)11yescharacteristic
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#54611yescharacteristic
189C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
190C2×C61#57711yescharacteristic
191D61—41no—
192D61—81no—
193D61—81no—
194#550—611no—
195#547—611no—
196#486—611no—
197#481—611no—
198#481—611no—
199#475—611no—
200#469—611no—
201#469—611no—
202#459—611no—
203#449—611no—
204#449—611no—
205C4×SD16—611no—
206#436—611no—
207#417—611no—
208#417D6111yescharacteristic, complemented
209C61#333211yescharacteristic, complemented, Sylow
210C2×#41—611no—
211C2×#41—1221no—
212C2×#41C2×D6111yescharacteristic
213C2×SD16—611no—
214C2×D8—611no—
215C2×D8—611no—
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—611no—
227#121—611no—
228#121—1221no—
229#121—1221no—
230C4×Q8—611no—
231C4×D4—611no—
232C4×D4—611no—
233C4×D4—1221no—
234C2×C4⋊C4—611no—
235C2×C4⋊C4C2×D6111yescharacteristic
236#106—611no—
237#106—611no—
238#106—611no—
239C4⋊C8—611no—
240#103—611no—
241#103C2×D6111yescharacteristic
242#103C2×D6111yescharacteristic
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—22no—
254#41—41no—
255#41—1222no—
256#41—2444no—
257#41—2441no—
258C2×Q8—1221no—
259C2×Q8C22×D6111yescharacteristic
260C2×D4—21no—
261C2×D4—611no—
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×D4—1221no—
271C2×D4C22×D6111yescharacteristic
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—611no—
275C22×C4—1221no—
276C22×C4—1221no—
277C22×C4—1221no—
278C22×C4C22×D6111yescharacteristic
279SD16—1222no—
280D8—2441no—
281D8—2441no—
282M16—41no—
283M16—2441no—
284C2×C8—611no—
285C2×C8—611no—
286C2×C8C22×D6111yescharacteristic
287C2×C8C22×D6111yescharacteristic
288C4⋊C4—21no—
289C4⋊C4—611no—
290C4⋊C4—611no—
291C4⋊C4—611no—
292C4⋊C4—1221no—
293C4⋊C4—1221no—
294C4⋊C4—1221no—
295C4⋊C4C22×D6111yescharacteristic
296C4⋊C4C22×D6111yescharacteristic
297C22⋊C4—611no—
298C22⋊C4—611no—
299C22⋊C4—1221no—
300C22⋊C4—1221no—
301C22⋊C4—1221no—
302C22⋊C4—1221no—
303C22⋊C4—1221no—
304C42—611no—
305C42—1221no—
306C23—21no—
307C23—611no—
308C23—1221no—
309C23—1221no—
310C23D4×D6111yescharacteristic
311Q8—21no—
312Q8—2442no—
313Q8#1175822212yescomplemented
314D4—21no—
315D4—21no—
316D4—42no—
317D4—1222no—
318D4—1221no—
319D4—1221no—
320D4—1221no—
321D4—1221no—
322D4—4881no—
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—21no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—611no—
337C2×C4—611no—
338C2×C4—611no—
339C2×C4—1221no—
340C2×C4—1221no—
341C2×C4—1221no—
342C2×C4—1221no—
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—1221no—
359C22—1221no—
360C22—1221no—
361C22—2441no—
362C22—2441no—
363C22—2441no—
364C22—2441no—
365C22—2441no—
366C22—2441no—
367C22C2×D4×D6111yescharacteristic
368C4—21no—
369C4—22no—
370C4—41no—
371C4—41no—
372C4—612no—
373C4—1221no—
374C4—1221no—
375C4—2441no—
376C4—2441no—
377C4C2×#1175822211yescharacteristic
378C4#1451982211yescharacteristic
379C2—41no—
380C2—81no—
381C2—4881no—
382C2—4881no—
383C2—2441no—
384C2#1684040211yescharacteristic
385C2AGL(1,ℤ/8)×D6111yescharacteristic
386C2#1684057111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#417C2
socleC22×C61C22×D4
hypercenter#417D61
hypocenterC61#3332
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. #16840431C2semidirect
2. #16840413C2semidirect
3. #16840107C2semidirect
4. #16840080C2semidirect
5. #16840079C2semidirect
6. #16840045C2semidirect
7. #16840015C2semidirect
8. #16840014C2semidirect
9. #16839956C2semidirect
10. #16839910C2semidirect
11. #16839907C2semidirect
12. #16839847C2semidirect
13. #16839838C2semidirect
14. #16839762C2semidirect
15. C61×#417C2semidirect
118. Q8×C61#41semidirect
208. #417D61semidirect
209. C61#3332semidirect
313. Q8#11758222semidirect