Finite Group Databasebeta

← #21456876

Subgroups — #21456876

Order 7808.

388 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840365C211yesmaximal, characteristic, complemented
2#16840336C211yesmaximal, characteristic, complemented
3#16840148C211yesmaximal, characteristic, complemented
4#16840133C211yesmaximal, characteristic, complemented
5#16840129C211yesmaximal, characteristic, complemented
6#16840118C211yesmaximal, characteristic, complemented
7#16839980C211yesmaximal, characteristic, complemented
8#16839979C211yesmaximal, characteristic, complemented
9#16839966C211yesmaximal, characteristic, complemented
10#16839965C211yesmaximal, characteristic, complemented
11#16839909C211yesmaximal, characteristic, complemented
12#16839905C211yesmaximal, characteristic, complemented
13#16839901C211yesmaximal, characteristic, complemented
14#16839820C211yesmaximal, characteristic, complemented
15C61×#448C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C2×#11758190C2211yescharacteristic
18C2×#11758200C2211yescharacteristic
19C2×#11758201C2211yescharacteristic
20C2×#11758201C2211yescharacteristic
21C2×D488C2211yescharacteristic
22C2×#11758199C2211yescharacteristic
23#14519775C2211yescharacteristic
24#14519775C2211yescharacteristic
25#14519773C2211yescharacteristic
26#14519768C2211yescharacteristic
27#14519766C2211yescharacteristic
28#14519766C2211yescharacteristic
29#14519761—21no—
30#14519760—21no—
31#14519760—21no—
32#14519759—21no—
33#14519753—21no—
34#14519753—21no—
35#14519751C2211yescharacteristic
36#14519749—21no—
37#14519748—21no—
38D4×Dic61C2211yescharacteristic
39#14519739C2211yescharacteristic
40#14519736C2211yescharacteristic
41#14519706C2211yescharacteristic
42#14519706C2211yescharacteristic
43#14519702C2211yescharacteristic
44#14519701C2211yescharacteristic
45#14519701C2211yescharacteristic
46#14519700C2211yescharacteristic
47#14519699C2211yescharacteristic
48#14519697C2211yescharacteristic
49C22⋊#92418C2211yescharacteristic
50#14519687C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52C22×Q8×C61C2211yescharacteristic
53C2×SD16×C61C2211yescharacteristic
54C2×SD16×C61C2211yescharacteristic
55#121×C61C2211yescharacteristic
56#103×C61C2211yescharacteristic
57#103×C61C2211yescharacteristic
58C22⋊C8×C61C2211yescharacteristic
59C2×Q8×C61—21no—
60C2×Q8×C61—41no—
61C2×Q8×C61—41no—
62C2×Q8×C61C2311yescharacteristic
63C2×Q8×C61C2311yescharacteristic
64C2×D4×C61—21no—
65C2×D4×C61C2311yescharacteristic
66C22×C4×C61—21no—
67C22×C4×C61C2311yescharacteristic
68C2×C22⋊D61—21no—
69C2×C22⋊D61—21no—
70C2×C22⋊D61—21no—
71C2×C22⋊D61—21no—
72C22×Dic61—21no—
73#11758222—41no—
74#11758222—41no—
75C2×D244C2311yescharacteristic
76C2×D244C2311yescharacteristic
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×Dic122C2311yescharacteristic
80SD16×C61—41no—
81SD16×C61—41no—
82C2×C8×C61C2311yescharacteristic
83C2×C8×C61C2311yescharacteristic
84C4⋊C4×C61C2311yescharacteristic
85C22⋊C4×C61—21no—
86C22⋊Dic61—21no—
87C22⋊Dic61D411yescharacteristic
88C22⋊Dic61D411yescharacteristic
89#11758201—41no—
90#11758201—41no—
91#11758200—41no—
92#11758199—41no—
93#11758198—21no—
94#11758198—21no—
95#11758198—21no—
96#11758198—21no—
97#11758198—21no—
98#11758198—21no—
99C4⋊Dic61—21no—
100C4⋊Dic61D411yescharacteristic
101C4⋊Dic61D411yescharacteristic
102C4⋊Dic61C2311yescharacteristic
103#11758196—21no—
104#11758196—21no—
105#11758196—21no—
106#11758196—21no—
107#11758196—21no—
108C4×Dic61C2311yescharacteristic
109C4×Dic61C2311yescharacteristic
110C2×#92418C2311yescharacteristic
111C2×#92418C2311yescharacteristic
112D488—41no—
113#11758190—41no—
114C23×C61—21no—
115C23×C61C2×D411yescharacteristic
116C22×D61—21no—
117C22×D61—21no—
118Q8×C61—21no—
119Q8×C61—21no—
120Q8×C61—21no—
121Q8×C61—21no—
122Q8×C61—42no—
123D4×C61—21no—
124D4×C61—21no—
125D4×C61—81no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—42no—
132C2×C4×C61C2×D411yescharacteristic
133C2×C4×C61C2411yescharacteristic
134C22⋊D61—42no—
135C22⋊D61—81no—
136C22⋊D61—81no—
137C22⋊D61—81no—
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—81no—
141C2×Dic61C2×D411yescharacteristic
142C2×Dic61C2×D411yescharacteristic
143C2×Dic61C2×D411yescharacteristic
144C2×Dic61C2×D411yescharacteristic
145D244—21no—
146D244—21no—
147D244—21no—
148D244—21no—
149C4×D61—42no—
150C4×D61—81no—
151Dic122—21no—
152Dic122—21no—
153C8×C61—21no—
154C8×C61—21no—
155#92418—21no—
156#92418—21no—
157C22×C61—21no—
158C22×C61—21no—
159C22×C61—21no—
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—
170C4×C61—21no—
171C4×C61—41no—
172C4×C61—41no—
173C4×C61—41no—
174C4×C61H(5,𝔽2)11yescharacteristic
175C4×C61H(5,𝔽2)11yescharacteristic
176Dic61—21no—
177Dic61—21no—
178Dic61—21no—
179Dic61—21no—
180Dic61—41no—
181Dic61—41no—
182#3221—611nomaximal, Sylow
183C2×C61—41no—
184C2×C61—81no—
185C2×C61#53511yescharacteristic
186C2×C61#57711yescharacteristic
187C2×C61#57711yescharacteristic
188D61—81no—
189D61—81no—
190#540—611no—
191#536—611no—
192#496—611no—
193#492—611no—
194#491—611no—
195#488—611no—
196#463—611no—
197#463—611no—
198#461—611no—
199#461—611no—
200#449—611no—
201#449—611no—
202#448—611no—
203#448D6111yescharacteristic, complemented
204#433—611no—
205C61#322111yescharacteristic, complemented, Sylow
206C2×#41—611no—
207C22×Q8C2×D6111yescharacteristic
208C2×SD16—611no—
209C2×SD16—611no—
210C2×SD16—611no—
211C2×SD16—611no—
212C2×SD16C2×D6111yescharacteristic
213C2×SD16C2×D6111yescharacteristic
214C2×D8—611no—
215C2×D8—611no—
216C4⋊Q8—611no—
217C4⋊Q8—611no—
218#127—611no—
219#125—611no—
220#124—611no—
221#124—611no—
222#123—1221no—
223#123—1221no—
224#123—1221no—
225#123—1221no—
226C22⋊Q8—1221no—
227C22⋊Q8—1221no—
228#121—611no—
229#121—1221no—
230#121—1221no—
231#121C2×D6111yescharacteristic
232C4×D4—611no—
233C4×D4—611no—
234#117—611no—
235C4⋊C8—611no—
236C4⋊C8—611no—
237#103—611no—
238#103—611no—
239#103—611no—
240#103—611no—
241#103C2×D6111yescharacteristic
242#103C2×D6111yescharacteristic
243#102—611no—
244#102—611no—
245C22⋊C8—611no—
246C22⋊C8C2×D6111yescharacteristic
247#97—611no—
248C4×C8—611no—
249#41—2441no—
250#41—2441no—
251C2×Q8—21no—
252C2×Q8—41no—
253C2×Q8—41no—
254C2×Q8—611no—
255C2×Q8C22×D6111yescharacteristic
256C2×Q8C22×D6111yescharacteristic
257C2×D4—21no—
258C2×D4—611no—
259C2×D4—611no—
260C2×D4—1221no—
261C2×D4—1221no—
262C2×D4—1221no—
263C2×D4—1221no—
264C2×D4C22×D6111yescharacteristic
265C22×C4—21no—
266C22×C4—1221no—
267C22×C4—1221no—
268C22×C4—1221no—
269C22×C4C22×D6111yescharacteristic
270SD16—41no—
271SD16—41no—
272SD16—2441no—
273SD16—2441no—
274SD16—2441no—
275SD16—2441no—
276D8—2441no—
277D8—2441no—
278C2×C8—611no—
279C2×C8—611no—
280C2×C8C22×D6111yescharacteristic
281C2×C8C22×D6111yescharacteristic
282C4⋊C4—611no—
283C4⋊C4—611no—
284C4⋊C4—611no—
285C4⋊C4—1221no—
286C4⋊C4—1221no—
287C4⋊C4—1221no—
288C4⋊C4—1221no—
289C4⋊C4—1221no—
290C4⋊C4—1221no—
291C4⋊C4C22×D6111yescharacteristic
292C22⋊C4—21no—
293C22⋊C4—611no—
294C22⋊C4—611no—
295C22⋊C4—1221no—
296C22⋊C4—1221no—
297C22⋊C4—1221no—
298C22⋊C4—1221no—
299C22⋊C4—1221no—
300C22⋊C4—1221no—
301C22⋊C4—1221no—
302C42—611no—
303C42—611no—
304C23—21no—
305C23—1221no—
306C23—1221no—
307C23D4×D6111yescharacteristic
308Q8—21no—
309Q8—21no—
310Q8—21no—
311Q8—21no—
312Q8—42no—
313Q8—1221no—
314Q8—1221no—
315D4—21no—
316D4—21no—
317D4—81no—
318D4—1221no—
319D4—1221no—
320D4—1221no—
321D4—1221no—
322D4—4881no—
323D4—4881no—
324D4—4881no—
325D4—2442no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—42no—
332C2×C4—611no—
333C2×C4—611no—
334C2×C4—611no—
335C2×C4—611no—
336C2×C4—1221no—
337C2×C4—1221no—
338C2×C4—4881no—
339C2×C4—4881no—
340C2×C4—2442no—
341C2×C4D4×D6111yescharacteristic
342C2×C4C23×D6111yescharacteristic
343C8—21no—
344C8—21no—
345C8—1221no—
346C8—1221no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—2441no—
354C22—2441no—
355C22—2441no—
356C22—2441no—
357C22—2441no—
358C22—2441no—
359C22C2×D4×D6111yescharacteristic
360C4—21no—
361C4—41no—
362C4—41no—
363C4—41no—
364C4—1221no—
365C4—1221no—
366C4—1221no—
367C4—1221no—
368C4—2441no—
369C4—2441no—
370C4#1451982211yescharacteristic
371C4#1451982211yescharacteristic
372C2—41no—
373C2—81no—
374C2—4881no—
375C2—4881no—
376C2#1684032711yescharacteristic
377C2#1684056811yescharacteristic
378C2#1684057111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#448C2
socleC22×C61C22×D4
hypercenter#448D61
hypocenterC61#3221
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. #16840365C2semidirect
2. #16840336C2semidirect
3. #16840148C2semidirect
4. #16840133C2semidirect
5. #16840129C2semidirect
6. #16840118C2semidirect
7. #16839980C2semidirect
8. #16839979C2semidirect
9. #16839966C2semidirect
10. #16839965C2semidirect
11. #16839909C2semidirect
12. #16839905C2semidirect
13. #16839901C2semidirect
14. #16839820C2semidirect
15. C61×#448C2semidirect
203. #448D61semidirect
205. C61#3221semidirect