Finite Group Databasebeta

← #21458862

Subgroups — #21458862

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#16840495C211yesmaximal, characteristic, complemented
2#16840433C211yesmaximal, characteristic, complemented
3#16840151C211yesmaximal, characteristic, complemented
4#16840150C211yesmaximal, characteristic, complemented
5#16840137C211yesmaximal, characteristic, complemented
6#16839977C211yesmaximal, characteristic, complemented
7#16839976C211yesmaximal, characteristic, complemented
8#16839961C211yesmaximal, characteristic, complemented
9#16839957C211yesmaximal, characteristic, complemented
10#16839956C211yesmaximal, characteristic, complemented
11#16839956C211yesmaximal, characteristic, complemented
12#16839890C211yesmaximal, characteristic, complemented
13#16839873C211yesmaximal, characteristic, complemented
14#16839849C211yesmaximal, characteristic, complemented
15C61×#442C211yesmaximal, characteristic, complemented
16C2×#11758222—21no—
17C2×#11758190C2211yescharacteristic
18C2×#11758190C2211yescharacteristic
19C2×#11758200C2211yescharacteristic
20C2×D488C2211yescharacteristic
21C2×D488C2211yescharacteristic
22C2×#11758199C2211yescharacteristic
23C2×#11758199C2211yescharacteristic
24C2×#11758199C2211yescharacteristic
25#14519774C2211yescharacteristic
26#14519773C2211yescharacteristic
27#14519773C2211yescharacteristic
28#14519773C2211yescharacteristic
29#14519765C2211yescharacteristic
30#14519764C2211yescharacteristic
31#14519763—21no—
32#14519760—21no—
33#14519759—21no—
34#14519751—21no—
35#14519750—21no—
36#14519750—21no—
37C4×Dic122C2211yescharacteristic
38#14519742C2211yescharacteristic
39#14519739C2211yescharacteristic
40#14519739C2211yescharacteristic
41#14519739C2211yescharacteristic
42C4×C22⋊D61—21no—
43C4⋊#92418C2211yescharacteristic
44#14519706C2211yescharacteristic
45#14519706C2211yescharacteristic
46#14519700C2211yescharacteristic
47#14519697C2211yescharacteristic
48#14519697C2211yescharacteristic
49#14519697C2211yescharacteristic
50#14519687C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52C2×D8×C61C2211yescharacteristic
53C4×D4×C61C2211yescharacteristic
54C4×D4×C61C2211yescharacteristic
55#106×C61C2211yescharacteristic
56#102×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic
58#97×C61C2211yescharacteristic
59C2×D4×C61C2311yescharacteristic
60C2×D4×C61C2311yescharacteristic
61C22×C4×C61—21no—
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—
69#11758222—44no—
70C2×D244—21no—
71C2×D244—21no—
72C2×D244C2311yescharacteristic
73C2×D244C2311yescharacteristic
74C2×D244C2311yescharacteristic
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×Dic122D411yescharacteristic
79C2×Dic122C2311yescharacteristic
80D8×C61—22no—
81C2×C8×C61C2311yescharacteristic
82C2×C8×C61C2311yescharacteristic
83C4⋊C4×C61C2311yescharacteristic
84C4⋊C4×C61C2311yescharacteristic
85C22⋊C4×C61—21no—
86C22⋊C4×C61—21no—
87C42×C61C2311yescharacteristic
88C22⋊Dic61—21no—
89C22⋊Dic61—21no—
90#11758200—41no—
91#11758199—41no—
92#11758199—41no—
93#11758199—41no—
94#11758198—21no—
95#11758198—21no—
96#11758198—21no—
97#11758198—21no—
98#11758198—21no—
99C4⋊Dic61D411yescharacteristic
100#11758196—21no—
101#11758196D411yescharacteristic
102#11758196D411yescharacteristic
103C4×Dic61—21no—
104C4×Dic61C2311yescharacteristic
105C4×Dic61C2311yescharacteristic
106C2×#92418C2311yescharacteristic
107C2×#92418C2311yescharacteristic
108D488—22no—
109D488—41no—
110#11758190—22no—
111#11758190—41no—
112C23×C61—21no—
113C23×C61—21no—
114C22×D61—21no—
115C22×D61—21no—
116C22×D61—21no—
117D4×C61—21no—
118D4×C61—21no—
119D4×C61—21no—
120D4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—42no—
124C2×C4×C61—81no—
125C2×C4×C61C2×D411yescharacteristic
126C2×C4×C61C2×D411yescharacteristic
127C2×C4×C61C2411yescharacteristic
128C22⋊D61—42no—
129C22⋊D61—42no—
130C22⋊D61—42no—
131C22⋊D61—81no—
132C22⋊D61—81no—
133C22⋊D61—81no—
134C2×Dic61—21no—
135C2×Dic61C2×D411yescharacteristic
136C2×Dic61C2×D411yescharacteristic
137C2×Dic61C2×D411yescharacteristic
138C2×Dic61C2×D411yescharacteristic
139D244—21no—
140D244—21no—
141D244—21no—
142D244—21no—
143D244—21no—
144D244—21no—
145D244—42no—
146D244—81no—
147C4×D61—42no—
148C4×D61—42no—
149C4×D61—81no—
150Dic122—22no—
151Dic122—21no—
152Dic122—21no—
153C8×C61—21no—
154C8×C61#4112yescomplemented
155#92418—21no—
156#92418—21no—
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#463—611no—
200#460—611no—
201#459—611no—
202#459—611no—
203#459—611no—
204#446—611no—
205#442—611no—
206#442D6111yescharacteristic, complemented
207C4×SD16—611no—
208C61#339911yescharacteristic, complemented, Sylow
209C2×#41—1221no—
210C2×SD16—611no—
211C2×SD16—611no—
212C2×SD16—611no—
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—611no—
225#124—1221no—
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—1221no—
237C4×D4C2×D6111yescharacteristic
238C4×D4C2×D6111yescharacteristic
239#106C2×D6111yescharacteristic
240C4⋊C8—611no—
241C4⋊C8—611no—
242C4⋊C8—611no—
243#103—611no—
244#102—611no—
245#102—611no—
246#102—611no—
247#102C2×D6111yescharacteristic
248#102C2×D6111yescharacteristic
249#97—611no—
250#97C2×D6111yescharacteristic
251C4×C8—611no—
252#41—2444no—
253C2×Q8—611no—
254C2×Q8—611no—
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—21no—
270C22×C4—1221no—
271C22×C4—1221no—
272C22×C4—1221no—
273SD16—1222no—
274SD16—2441no—
275SD16—2441no—
276D8—22no—
277D8—1222no—
278D8—2441no—
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—1221no—
290C4⋊C4C22×D6111yescharacteristic
291C4⋊C4C22×D6111yescharacteristic
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—1221no—
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—1222no—
311Q8—1221no—
312Q8—1221no—
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—81no—
335C2×C4—611no—
336C2×C4—611no—
337C2×C4—611no—
338C2×C4—611no—
339C2×C4—1221no—
340C2×C4—4881no—
341C2×C4—2442no—
342C2×C4—2442no—
343C2×C4D4×D6111yescharacteristic
344C2×C4D4×D6111yescharacteristic
345C2×C4C23×D6111yescharacteristic
346C8—21no—
347C8—1221no—
348C8—1221no—
349C8#1175822212yescomplemented
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—
375C4C2×#1175822211yescharacteristic
376C4#1451982311yescharacteristic
377C2—81no—
378C2—81no—
379C2—4881no—
380C2—4881no—
381C2—4881no—
382C2#1684043311yescharacteristic
383C2AGL(1,ℤ/8)×D6111yescharacteristic
384C2#1684056611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#442C2
socleC22×C61C22×D4
hypercenter#442D61
hypocenterC61#3399
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #16840495C2semidirect
2. #16840433C2semidirect
3. #16840151C2semidirect
4. #16840150C2semidirect
5. #16840137C2semidirect
6. #16839977C2semidirect
7. #16839976C2semidirect
8. #16839961C2semidirect
9. #16839957C2semidirect
10. #16839956C2semidirect
11. #16839956C2semidirect
12. #16839890C2semidirect
13. #16839873C2semidirect
14. #16839849C2semidirect
15. C61×#442C2semidirect
154. C8×C61#41semidirect
206. #442D61semidirect
208. C61#3399semidirect
349. C8#11758222semidirect