Finite Group Databasebeta

← #21458856

Subgroups — #21458856

Order 7808.

418 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840494C211yesmaximal, characteristic, complemented
2#16840433C211yesmaximal, characteristic, complemented
3#16840152C211yesmaximal, characteristic, complemented
4#16840148C211yesmaximal, characteristic, complemented
5#16840137C211yesmaximal, characteristic, complemented
6#16839980C211yesmaximal, characteristic, complemented
7#16839960C211yesmaximal, characteristic, complemented
8#16839958C211yesmaximal, characteristic, complemented
9#16839956C211yesmaximal, characteristic, complemented
10#16839955C211yesmaximal, characteristic, complemented
11#16839891C211yesmaximal, characteristic, complemented
12#16839872C211yesmaximal, characteristic, complemented
13#16839871C211yesmaximal, characteristic, complemented
14#16839847C211yesmaximal, characteristic, complemented
15C61×#463C211yesmaximal, characteristic, complemented
16C2×#11758222—21no—
17C2×#11758201C2211yescharacteristic
18C2×#11758201C2211yescharacteristic
19C2×D488C2211yescharacteristic
20C2×D488C2211yescharacteristic
21C2×#11758199C2211yescharacteristic
22C2×#11758199C2211yescharacteristic
23C2×#11758199C2211yescharacteristic
24#14519774C2211yescharacteristic
25#14519773C2211yescharacteristic
26#14519773C2211yescharacteristic
27#14519773C2211yescharacteristic
28#14519766C2211yescharacteristic
29#14519763—21no—
30#14519761—21no—
31#14519759—21no—
32#14519751—21no—
33#14519750—21no—
34#14519750—21no—
35Q8×Dic61C2211yescharacteristic
36C4×Dic122C2211yescharacteristic
37C4×D244C2211yescharacteristic
38D4×Dic61C2211yescharacteristic
39#14519739C2211yescharacteristic
40#14519739C2211yescharacteristic
41#14519737—21no—
42#14519708C2211yescharacteristic
43#14519706C2211yescharacteristic
44#14519706C2211yescharacteristic
45#14519699C2211yescharacteristic
46#14519699C2211yescharacteristic
47#14519698C2211yescharacteristic
48#14519697C2211yescharacteristic
49#14519688C2211yescharacteristic
50#14519687C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52C2×SD16×C61C2211yescharacteristic
53C2×D8×C61C2211yescharacteristic
54#124×C61C2211yescharacteristic
55C4×D4×C61C2211yescharacteristic
56C4⋊C8×C61C2211yescharacteristic
57#103×C61C2211yescharacteristic
58#102×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60C2×D4×C61C2311yescharacteristic
61C2×D4×C61C2311yescharacteristic
62C22×C4×C61—21no—
63C2×C22⋊D61—21no—
64C2×C22⋊D61—21no—
65C2×C22⋊D61—21no—
66C2×C22⋊D61—21no—
67C2×C22⋊D61—21no—
68C2×C22⋊D61—21no—
69C22×Dic61—21no—
70#11758222—44no—
71C2×D244—21no—
72C2×D244—21no—
73C2×D244C2311yescharacteristic
74C2×D244C2311yescharacteristic
75C2×D244C2311yescharacteristic
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×Dic122D411yescharacteristic
80SD16×C61—41no—
81D8×C61—41no—
82C2×C8×C61C2311yescharacteristic
83C2×C8×C61C2311yescharacteristic
84C4⋊C4×C61C2311yescharacteristic
85C22⋊C4×C61—21no—
86C22⋊C4×C61—21no—
87C22⋊C4×C61—21no—
88C42×C61C2311yescharacteristic
89C22⋊Dic61—21no—
90#11758201—22no—
91#11758201—41no—
92#11758199—22no—
93#11758199—22no—
94#11758199—41no—
95#11758198—21no—
96#11758198—21no—
97#11758198—21no—
98#11758198—21no—
99#11758198—21no—
100C4⋊Dic61—21no—
101C4⋊Dic61D411yescharacteristic
102C4⋊Dic61C2311yescharacteristic
103#11758196D411yescharacteristic
104#11758196D411yescharacteristic
105C4×Dic61—21no—
106C4×Dic61C2311yescharacteristic
107C4×Dic61C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110D488—41no—
111D488—41no—
112C23×C61—21no—
113C23×C61—21no—
114C22×D61—21no—
115C22×D61—21no—
116C22×D61—21no—
117Q8×C61—21no—
118Q8×C61—21no—
119D4×C61—21no—
120D4×C61—21no—
121D4×C61—21no—
122D4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—42no—
126C2×C4×C61C2×D411yescharacteristic
127C2×C4×C61C2×D411yescharacteristic
128C2×C4×C61C2411yescharacteristic
129C22⋊D61—42no—
130C22⋊D61—42no—
131C22⋊D61—42no—
132C22⋊D61—81no—
133C22⋊D61—81no—
134C22⋊D61—81no—
135C2×Dic61—21no—
136C2×Dic61—81no—
137C2×Dic61C2×D411yescharacteristic
138C2×Dic61C2×D411yescharacteristic
139C2×Dic61C2×D411yescharacteristic
140C2×Dic61C2×D411yescharacteristic
141D244—21no—
142D244—21no—
143D244—21no—
144D244—21no—
145D244—21no—
146D244—21no—
147D244—42no—
148D244—81no—
149C4×D61—42no—
150C4×D61—42no—
151C4×D61—81no—
152Dic122—22no—
153C8×C61—21no—
154C8×C61—21no—
155#92418—21no—
156#92418#4112yescomplemented
157C22×C61—41no—
158C22×C61—41no—
159C22×C61—41no—
160C22×C61—41no—
161C22×C61—41no—
162C22×C61—41no—
163C22×C61C22×D411yescharacteristic
164C2×D61—41no—
165C2×D61—41no—
166C2×D61—41no—
167C2×D61—41no—
168C2×D61—41no—
169C2×D61—41no—
170C2×D61—41no—
171C2×D61—41no—
172C2×D61—41no—
173C4×C61—21no—
174C4×C61—21no—
175C4×C61—41no—
176C4×C61—41no—
177C4×C61C2×#4111yescharacteristic
178C4×C61H(5,𝔽2)11yescharacteristic
179Dic61—21no—
180Dic61—21no—
181Dic61—21no—
182Dic61—41no—
183Dic61AGL(1,ℤ/8)12yes—
184#3399—611nomaximal, Sylow
185C2×C61—81no—
186C2×C61—81no—
187C2×C61#55011yescharacteristic
188C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
189C2×C61#57611yescharacteristic
190D61—81no—
191D61—81no—
192D61—81no—
193#559—611no—
194#550—611no—
195#496—611no—
196#496—611no—
197#493—611no—
198#463—611no—
199#463D6111yescharacteristic, complemented
200#460—611no—
201#459—611no—
202#459—611no—
203#459—611no—
204#446—611no—
205#442—611no—
206#442—611no—
207C4×SD16—611no—
208C61#339911yescharacteristic, complemented, Sylow
209C2×#41—1221no—
210C2×SD16—611no—
211C2×SD16—611no—
212C2×SD16C2×D6111yescharacteristic
213C2×D8—611no—
214C2×D8—611no—
215C2×D8—611no—
216C2×D8—611no—
217C2×D8—611no—
218C2×D8C2×D6111yescharacteristic
219#127—611no—
220#127—611no—
221#127—611no—
222#127—611no—
223#124—611no—
224#124—1221no—
225#124C2×D6111yescharacteristic
226#123—1221no—
227#123—1221no—
228#121—1221no—
229#121—1221no—
230#121—1221no—
231C4×Q8—611no—
232C4×Q8—611no—
233C4×D4—611no—
234C4×D4—611no—
235C4×D4—611no—
236C4×D4—611no—
237C4×D4—1221no—
238C4×D4C2×D6111yescharacteristic
239#106—611no—
240C4⋊C8—611no—
241C4⋊C8—611no—
242C4⋊C8C2×D6111yescharacteristic
243#103C2×D6111yescharacteristic
244#102—611no—
245#102—611no—
246#102—611no—
247#102—611no—
248#102C2×D6111yescharacteristic
249#97—611no—
250#97—611no—
251C4×C8—611no—
252#41—2444no—
253C2×Q8—611no—
254C2×Q8C22×D6111yescharacteristic
255C2×D4—611no—
256C2×D4—611no—
257C2×D4—611no—
258C2×D4—1221no—
259C2×D4—1221no—
260C2×D4—1221no—
261C2×D4—1221no—
262C2×D4—1221no—
263C2×D4—1221no—
264C2×D4—1221no—
265C2×D4—1221no—
266C2×D4C22×D6111yescharacteristic
267C2×D4C22×D6111yescharacteristic
268C22×C4—21no—
269C22×C4—1221no—
270C22×C4—1221no—
271C22×C4—1221no—
272C22×C4—1221no—
273SD16—41no—
274SD16—1222no—
275SD16—2441no—
276D8—41no—
277D8—1222no—
278D8—1222no—
279D8—2441no—
280D8—2441no—
281D8—2441no—
282C2×C8—611no—
283C2×C8—611no—
284C2×C8C22×D6111yescharacteristic
285C2×C8C22×D6111yescharacteristic
286C4⋊C4—611no—
287C4⋊C4—611no—
288C4⋊C4—611no—
289C4⋊C4—611no—
290C4⋊C4—1221no—
291C4⋊C4C22×D6111yescharacteristic
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—21no—
295C22⋊C4—1221no—
296C22⋊C4—1221no—
297C22⋊C4—1221no—
298C22⋊C4—1221no—
299C22⋊C4—1221no—
300C22⋊C4—1221no—
301C42—611no—
302C42—611no—
303C42—1221no—
304C42C22×D6111yescharacteristic
305C23—21no—
306C23—21no—
307C23—1221no—
308C23—1221no—
309C23—1221no—
310Q8—21no—
311Q8—21no—
312Q8—1222no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—1221no—
318D4—1221no—
319D4—1221no—
320D4—1221no—
321D4—1221no—
322D4—1221no—
323D4—4881no—
324D4—4881no—
325D4—4881no—
326D4—4881no—
327D4—2442no—
328D4—2442no—
329D4—2442no—
330D4—2442no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—42no—
334C2×C4—611no—
335C2×C4—611no—
336C2×C4—611no—
337C2×C4—611no—
338C2×C4—1221no—
339C2×C4—4881no—
340C2×C4—4881no—
341C2×C4—2442no—
342C2×C4—2442no—
343C2×C4D4×D6111yescharacteristic
344C2×C4D4×D6111yescharacteristic
345C2×C4C23×D6111yescharacteristic
346C8—21no—
347C8—21no—
348C8—612no—
349C8—1221no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—2441no—
357C22—2441no—
358C22—2441no—
359C22—2441no—
360C22—2441no—
361C22—2441no—
362C22—2441no—
363C22—2441no—
364C22—2441no—
365C22C2×D4×D6111yescharacteristic
366C4—21no—
367C4—21no—
368C4—41no—
369C4—41no—
370C4—612no—
371C4—1221no—
372C4—1221no—
373C4—1221no—
374C4—2441no—
375C4#41×D6111yescharacteristic
376C4#1451982211yescharacteristic
377C2—81no—
378C2—81no—
379C2—4881no—
380C2—4881no—
381C2—4881no—
382C2#1684043011yescharacteristic
383C2AGL(1,ℤ/8)×D6111yescharacteristic
384C2#1684056411yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#463C2
socleC22×C61C22×D4
hypercenter#463D61
hypocenterC61#3399
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #16840494C2semidirect
2. #16840433C2semidirect
3. #16840152C2semidirect
4. #16840148C2semidirect
5. #16840137C2semidirect
6. #16839980C2semidirect
7. #16839960C2semidirect
8. #16839958C2semidirect
9. #16839956C2semidirect
10. #16839955C2semidirect
11. #16839891C2semidirect
12. #16839872C2semidirect
13. #16839871C2semidirect
14. #16839847C2semidirect
15. C61×#463C2semidirect
156. #92418#41semidirect
199. #463D61semidirect
208. C61#3399semidirect