Finite Group Databasebeta

← #21458880

Subgroups — #21458880

Order 7808.

368 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840498C211yesmaximal, characteristic, complemented
2#16840481C211yesmaximal, characteristic, complemented
3#16840153C211yesmaximal, characteristic, complemented
4#16840145C211yesmaximal, characteristic, complemented
5#16839982C211yesmaximal, characteristic, complemented
6#16839981C211yesmaximal, characteristic, complemented
7#16839975C211yesmaximal, characteristic, complemented
8#16839975C211yesmaximal, characteristic, complemented
9#16839965C211yesmaximal, characteristic, complemented
10#16839959C211yesmaximal, characteristic, complemented
11#16839890C211yesmaximal, characteristic, complemented
12#16839874C211yesmaximal, characteristic, complemented
13#16839870C211yesmaximal, characteristic, complemented
14SD16×Dic61C211yesmaximal, characteristic, complemented
15C61×#496C211yesmaximal, characteristic
16C2×Dic244C2211yescharacteristic
17C2×#11758202C2211yescharacteristic
18C2×#11758200C2211yescharacteristic
19C2×#11758200C2211yescharacteristic
20C2×#11758200C2211yescharacteristic
21#14519775C2211yescharacteristic
22#14519770—21no—
23#14519770—21no—
24#14519764—21no—
25#14519764C2211yescharacteristic
26#14519764C2211yescharacteristic
27#14519764C2211yescharacteristic
28#14519758—21no—
29#14519758—21no—
30#14519754—21no—
31Q8×Dic61C2211yescharacteristic
32C4×Dic122C2211yescharacteristic
33C4×Dic122C2211yescharacteristic
34C4×Dic122C2211yescharacteristic
35D4×Dic61—21no—
36D4×Dic61C2211yescharacteristic
37D4×Dic61C2211yescharacteristic
38D4×Dic61C2211yescharacteristic
39#14519733—21no—
40#14519709C2211yescharacteristic
41C4⋊#92418C2211yescharacteristic
42#14519706C2211yescharacteristic
43#14519706C2211yescharacteristic
44#14519702C2211yescharacteristic
45#14519702C2211yescharacteristic
46#14519701C2211yescharacteristic
47#14519698C2211yescharacteristic
48#14519698C2211yescharacteristic
49#14519698C2211yescharacteristic
50#14519687C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52C2×SD16×C61C2211yescharacteristic
53C2×SD16×C61C2211yescharacteristic
54C2×D8×C61C2211yescharacteristic
55C2×D8×C61C2211yescharacteristic
56#127×C61C2211yescharacteristic
57#124×C61C2211yescharacteristic
58#97×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60C2×D4×C61—21no—
61C2×D4×C61—21no—
62C2×D4×C61C2311yescharacteristic
63C2×D4×C61C2311yescharacteristic
64C2×D4×C61C2311yescharacteristic
65C22×Dic61—21no—
66C22×Dic61—21no—
67C22×Dic61—21no—
68C2×Dic122D411yescharacteristic
69C2×Dic122C2311yescharacteristic
70C2×Dic122C2311yescharacteristic
71SD16×C61—22no—
72SD16×C61—41no—
73D8×C61—22no—
74D8×C61—41no—
75C2×C8×C61C2311yescharacteristic
76C2×C8×C61C2311yescharacteristic
77C22⋊C4×C61—21no—
78C22⋊C4×C61—21no—
79C42×C61C2311yescharacteristic
80C22⋊Dic61—21no—
81C22⋊Dic61—21no—
82C22⋊Dic61—21no—
83C22⋊Dic61—21no—
84C22⋊Dic61—21no—
85C22⋊Dic61—21no—
86C22⋊Dic61—21no—
87C22⋊Dic61—21no—
88C22⋊Dic61—21no—
89#11758202—41no—
90#11758200—41no—
91#11758200—41no—
92#11758200—41no—
93C4⋊Dic61—21no—
94C4⋊Dic61D411yescharacteristic
95C4⋊Dic61C2311yescharacteristic
96C4⋊Dic61C2311yescharacteristic
97#11758196—21no—
98#11758196—21no—
99#11758196—21no—
100#11758196—21no—
101#11758196D411yescharacteristic
102#11758196D411yescharacteristic
103C4×Dic61—21no—
104C4×Dic61—21no—
105C4×Dic61—21no—
106C4×Dic61C2311yescharacteristic
107C4×Dic61C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110Dic244—22no—
111C23×C61—21no—
112C23×C61—21no—
113C23×C61—21no—
114Q8×C61—21no—
115Q8×C61—21no—
116D4×C61—21no—
117D4×C61—21no—
118D4×C61—21no—
119D4×C61—21no—
120D4×C61—21no—
121D4×C61—21no—
122D4×C61—42no—
123D4×C61—81no—
124C2×C4×C61—21no—
125C2×C4×C61C2×D411yescharacteristic
126C2×C4×C61C2×D411yescharacteristic
127C2×C4×C61C2411yescharacteristic
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—42no—
133C2×Dic61—81no—
134C2×Dic61—81no—
135C2×Dic61C2×D411yescharacteristic
136C2×Dic61C2×D411yescharacteristic
137C2×Dic61C2×D411yescharacteristic
138C2×Dic61C2×D411yescharacteristic
139Dic122—21no—
140Dic122—21no—
141Dic122—21no—
142Dic122—21no—
143Dic122—41no—
144C8×C61—21no—
145C8×C61#4112yes—
146#92418—21no—
147#92418—21no—
148C22×C61—41no—
149C22×C61—41no—
150C22×C61—41no—
151C22×C61—41no—
152C22×C61—41no—
153C22×C61—41no—
154C22×C61—41no—
155C22×C61—41no—
156C22×C61—41no—
157C22×C61C22×D411yescharacteristic
158C4×C61—21no—
159C4×C61—21no—
160C4×C61—41no—
161C4×C61C2×#4111yescharacteristic
162C4×C61H(5,𝔽2)11yescharacteristic
163Dic61—21no—
164Dic61—21no—
165Dic61—21no—
166Dic61—21no—
167Dic61—41no—
168Dic61—41no—
169Dic61—41no—
170Dic61—41no—
171#3401—611nomaximal, Sylow
172C2×C61—81no—
173C2×C61—81no—
174C2×C61—81no—
175C2×C61#55011yescharacteristic
176C2×C61#57511yescharacteristic
177C2×C61#57711yescharacteristic
178#559—611no—
179#556—611no—
180#497—611no—
181#496D6111yescharacteristic
182#495—611no—
183#464—611no—
184#464—611no—
185#463—611no—
186#463—611no—
187#461—611no—
188#460—611no—
189#446—611no—
190#442—611no—
191#441—611no—
192C4×SD16—611no—
193C61#340111yescharacteristic, complemented, Sylow
194C2×Q16—611no—
195C2×Q16—611no—
196C2×SD16—611no—
197C2×SD16—611no—
198C2×SD16—611no—
199C2×SD16C2×D6111yescharacteristic
200C2×SD16C2×D6111yescharacteristic
201C2×D8C2×D6111yescharacteristic
202C2×D8C2×D6111yescharacteristic
203C4⋊Q8—611no—
204#127C2×D6111yescharacteristic
205#126—1221no—
206#126—1221no—
207#124—611no—
208#124—611no—
209#124—611no—
210#124—1221no—
211#124C2×D6111yescharacteristic
212#123—1221no—
213#123—1221no—
214C22⋊Q8—1221no—
215C4×Q8—611no—
216C4×Q8—611no—
217C4×Q8—611no—
218C4×Q8—611no—
219C4×D4—611no—
220C4×D4—611no—
221C4×D4—611no—
222C4×D4—1221no—
223#117—1221no—
224#106—611no—
225C4⋊C8—611no—
226C4⋊C8—611no—
227C4⋊C8—611no—
228#103—611no—
229#103—611no—
230#103—611no—
231#102—611no—
232#102—611no—
233#102—611no—
234#97—611no—
235#97C2×D6111yescharacteristic
236C4×C8—611no—
237C2×Q8—611no—
238C2×Q8—611no—
239C2×Q8—611no—
240C2×Q8C22×D6111yescharacteristic
241C2×D4—21no—
242C2×D4—21no—
243C2×D4C22×D6111yescharacteristic
244C2×D4C22×D6111yescharacteristic
245C2×D4C22×D6111yescharacteristic
246C22×C4—1221no—
247C22×C4—1221no—
248C22×C4—1221no—
249Q16—1222no—
250Q16—2441no—
251SD16—22no—
252SD16—41no—
253SD16—2441no—
254SD16—2441no—
255SD16—2441no—
256D8—22no—
257D8—41no—
258C2×C8—611no—
259C2×C8—611no—
260C2×C8C22×D6111yescharacteristic
261C2×C8C22×D6111yescharacteristic
262C4⋊C4—611no—
263C4⋊C4—611no—
264C4⋊C4—611no—
265C4⋊C4—611no—
266C4⋊C4—611no—
267C4⋊C4—1221no—
268C4⋊C4—1221no—
269C4⋊C4—1221no—
270C4⋊C4—1221no—
271C4⋊C4—1221no—
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—1221no—
275C22⋊C4—1221no—
276C22⋊C4—1221no—
277C22⋊C4—1221no—
278C22⋊C4—1221no—
279C22⋊C4—1221no—
280C22⋊C4—1221no—
281C22⋊C4—1221no—
282C22⋊C4—1221no—
283C42—611no—
284C42—611no—
285C42—1221no—
286C42—1221no—
287C42—1221no—
288C42C22×D6111yescharacteristic
289C23—21no—
290C23—21no—
291C23—21no—
292Q8—21no—
293Q8—21no—
294Q8—1221no—
295Q8—1221no—
296Q8—1221no—
297Q8—1221no—
298Q8—2441no—
299D4—21no—
300D4—21no—
301D4—21no—
302D4—21no—
303D4—21no—
304D4—21no—
305D4—42no—
306D4—81no—
307C2×C4—21no—
308C2×C4—611no—
309C2×C4—611no—
310C2×C4—611no—
311C2×C4—611no—
312C2×C4—1221no—
313C2×C4—1221no—
314C2×C4—1221no—
315C2×C4—1221no—
316C2×C4—4881no—
317C2×C4—4881no—
318C2×C4—2442no—
319C2×C4D4×D6111yescharacteristic
320C2×C4D4×D6111yescharacteristic
321C2×C4C23×D6111yescharacteristic
322C8—21no—
323C8—1221no—
324C8—1221no—
325C8#1175822412yes—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22C2×D4×D6111yescharacteristic
336C4—21no—
337C4—21no—
338C4—41no—
339C4—1221no—
340C4—1221no—
341C4—1221no—
342C4—1221no—
343C4—2441no—
344C4—2441no—
345C4—2441no—
346C4—2441no—
347C4C2×#1175822411yescharacteristic
348C4#1451982211yescharacteristic
349C2—81no—
350C2—81no—
351C2—81no—
352C2#1684043211yescharacteristic
353C2#1684055811yescharacteristic
354C2#1684057211yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#496C2
socleC22×C61C22×D4
hypercenter#496D61
hypocenterC61#3401
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #16840498C2semidirect
2. #16840481C2semidirect
3. #16840153C2semidirect
4. #16840145C2semidirect
5. #16839982C2semidirect
6. #16839981C2semidirect
7. #16839975C2semidirect
8. #16839975C2semidirect
9. #16839965C2semidirect
10. #16839959C2semidirect
11. #16839890C2semidirect
12. #16839874C2semidirect
13. #16839870C2semidirect
14. SD16×Dic61C2semidirect
193. C61#3401semidirect