Finite Group Databasebeta

← #21456934

Subgroups — #21456934

Order 7808.

376 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840385C211yesmaximal, characteristic, complemented
2#16840336C211yesmaximal, characteristic, complemented
3#16840155C211yesmaximal, characteristic, complemented
4#16840147C211yesmaximal, characteristic, complemented
5#16840123C211yesmaximal, characteristic, complemented
6#16840111C211yesmaximal, characteristic, complemented
7#16839986C211yesmaximal, characteristic, complemented
8#16839980C211yesmaximal, characteristic, complemented
9#16839970C211yesmaximal, characteristic, complemented
10#16839966C211yesmaximal, characteristic, complemented
11#16839922C211yesmaximal, characteristic, complemented
12#16839909C211yesmaximal, characteristic
13#16839901C211yesmaximal, characteristic, complemented
14#16839820C211yesmaximal, characteristic, complemented
15C61×#451C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C2×#11758202C2211yescharacteristic
18C2×#11758190C2211yescharacteristic
19C2×#11758201C2211yescharacteristic
20C2×#11758201C2211yescharacteristic
21C2×#11758201C2211yescharacteristic
22C2×D488C2211yescharacteristic
23#14519776C2211yescharacteristic
24#14519775C2211yescharacteristic
25#14519775C2211yescharacteristic
26#14519772—21no—
27#14519766C2211yescharacteristic
28#14519766C2211yescharacteristic
29#14519766C2211yescharacteristic
30#14519763—21no—
31#14519760—21no—
32#14519760—21no—
33#14519759—21no—
34#14519757—21no—
35#14519753—21no—
36#14519753—21no—
37#14519751C2211yescharacteristic
38Q8×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×Q16×C61C2211yescharacteristic
54C2×Q16×C61C2211yescharacteristic
55C22⋊Q8×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×Q8×C61C2311yescharacteristic
65C22×C4×C61—21no—
66C22×C4×C61C2311yescharacteristic
67C2×C22⋊D61—21no—
68C2×C22⋊D61—21no—
69#11758222—41no—
70#11758222—41no—
71C2×D244C2311yescharacteristic
72C2×D244C2311yescharacteristic
73C2×C4×D61—21no—
74C2×C4×D61—21no—
75C2×Dic122—21no—
76C2×Dic122C2311yescharacteristic
77Q16×C61—41no—
78Q16×C61—41no—
79C2×C8×C61C2311yescharacteristic
80C2×C8×C61C2311yescharacteristic
81C4⋊C4×C61—21no—
82C4⋊C4×C61C2311yescharacteristic
83C22⋊C4×C61—21no—
84C22⋊Dic61D411yescharacteristic
85C22⋊Dic61D411yescharacteristic
86#11758202—41no—
87#11758201—41no—
88#11758201—41no—
89#11758201—41no—
90#11758198—21no—
91#11758198—21no—
92#11758198—21no—
93#11758198—21no—
94#11758198—21no—
95#11758198—21no—
96#11758198—21no—
97#11758198—21no—
98C4⋊Dic61—21no—
99C4⋊Dic61D411yescharacteristic
100C4⋊Dic61D411yescharacteristic
101C4⋊Dic61C2311yescharacteristic
102#11758196—21no—
103#11758196—21no—
104#11758196—21no—
105#11758196—21no—
106#11758196—21no—
107C4×Dic61—21no—
108C4×Dic61C2311yescharacteristic
109C4×Dic61C2311yescharacteristic
110C2×#92418C2311yescharacteristic
111C2×#92418C2311yescharacteristic
112D488—41no—
113#11758190—41no—
114C23×C61C2×D411yescharacteristic
115C22×D61—21no—
116C22×D61—21no—
117Q8×C61—21no—
118Q8×C61—21no—
119Q8×C61—21no—
120Q8×C61—21no—
121Q8×C61—21no—
122Q8×C61—21no—
123Q8×C61—42no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—42no—
131C2×C4×C61C2×D411yescharacteristic
132C2×C4×C61C2411yescharacteristic
133C22⋊D61—42no—
134C22⋊D61—81no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61C2×D411yescharacteristic
138C2×Dic61C2×D411yescharacteristic
139C2×Dic61C2×D411yescharacteristic
140C2×Dic61C2×D411yescharacteristic
141D244—21no—
142D244—21no—
143D244—21no—
144D244—21no—
145C4×D61—42no—
146C4×D61—81no—
147Dic122—21no—
148Dic122—21no—
149Dic122—81no—
150C8×C61—21no—
151C8×C61—21no—
152#92418—21no—
153#92418—21no—
154C22×C61—21no—
155C22×C61—21no—
156C22×C61—21no—
157C22×C61C22×D411yescharacteristic
158C2×D61—41no—
159C2×D61—41no—
160C2×D61—41no—
161C2×D61—41no—
162C2×D61—41no—
163C2×D61—41no—
164C4×C61—21no—
165C4×C61—41no—
166C4×C61—41no—
167C4×C61—41no—
168C4×C61—41no—
169C4×C61H(5,𝔽2)11yescharacteristic
170C4×C61H(5,𝔽2)11yescharacteristic
171Dic61—21no—
172Dic61—21no—
173Dic61—21no—
174Dic61—21no—
175Dic61—41no—
176Dic61—41no—
177#3225—611nomaximal, Sylow
178C2×C61—41no—
179C2×C61#53511yescharacteristic
180C2×C61#57711yescharacteristic
181C2×C61#57811yescharacteristic
182D61—81no—
183D61—81no—
184#542—611no—
185#536—611no—
186#497—611no—
187#495—611no—
188#489—611no—
189#487—611no—
190#464—611no—
191#463—611no—
192#462—611no—
193#461—611no—
194#452—611no—
195#451D6111yescharacteristic, complemented
196#449—611no—
197#448—611no—
198#433—611no—
199C61#322511yescharacteristic, complemented, Sylow
200C2×#41—611no—
201C22×Q8C2×D6111yescharacteristic
202C2×Q16—611no—
203C2×Q16C2×D6111yescharacteristic
204C2×Q16C2×D6111yescharacteristic
205C2×SD16—611no—
206C2×SD16—611no—
207C2×SD16—611no—
208C2×SD16—611no—
209C2×D8—611no—
210C4⋊Q8—611no—
211C4⋊Q8—611no—
212C4⋊Q8—611no—
213#126—1221no—
214#124—611no—
215#124—611no—
216#124—611no—
217#124—1221no—
218#123—1221no—
219#123—1221no—
220#123—1221no—
221C22⋊Q8—1221no—
222C22⋊Q8—1221no—
223C22⋊Q8—1221no—
224C22⋊Q8C2×D6111yescharacteristic
225#121—611no—
226C4×Q8—611no—
227C4×D4—611no—
228#117—611no—
229C4⋊C8—611no—
230C4⋊C8—611no—
231#103—611no—
232#103—611no—
233#103—611no—
234#103—611no—
235#103C2×D6111yescharacteristic
236#103C2×D6111yescharacteristic
237#102—611no—
238#102—611no—
239C22⋊C8—611no—
240C22⋊C8C2×D6111yescharacteristic
241#97—611no—
242C4×C8—611no—
243#41—2441no—
244#41—2441no—
245C2×Q8—21no—
246C2×Q8—41no—
247C2×Q8—41no—
248C2×Q8—611no—
249C2×Q8—1221no—
250C2×Q8C22×D6111yescharacteristic
251C2×Q8C22×D6111yescharacteristic
252C2×Q8C22×D6111yescharacteristic
253C2×D4—611no—
254C2×D4—611no—
255C2×D4—1221no—
256C2×D4—1221no—
257C22×C4—21no—
258C22×C4—1221no—
259C22×C4—1221no—
260C22×C4C22×D6111yescharacteristic
261Q16—41no—
262Q16—41no—
263Q16—2441no—
264SD16—2441no—
265SD16—2441no—
266SD16—2441no—
267SD16—2441no—
268D8—2441no—
269C2×C8—611no—
270C2×C8—611no—
271C2×C8C22×D6111yescharacteristic
272C2×C8C22×D6111yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—611no—
275C4⋊C4—611no—
276C4⋊C4—611no—
277C4⋊C4—1221no—
278C4⋊C4—1221no—
279C4⋊C4—1221no—
280C4⋊C4—1221no—
281C4⋊C4—1221no—
282C4⋊C4—1221no—
283C4⋊C4C22×D6111yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—611no—
286C22⋊C4—611no—
287C22⋊C4—1221no—
288C22⋊C4—1221no—
289C22⋊C4—1221no—
290C22⋊C4—1221no—
291C22⋊C4—1221no—
292C22⋊C4—1221no—
293C22⋊C4—1221no—
294C22⋊C4—1221no—
295C42—611no—
296C42—611no—
297C42—1221no—
298C23—1221no—
299C23—1221no—
300C23D4×D6111yescharacteristic
301Q8—21no—
302Q8—21no—
303Q8—21no—
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—42no—
308Q8—1221no—
309Q8—1221no—
310Q8—4881no—
311D4—1221no—
312D4—1221no—
313D4—1221no—
314D4—1221no—
315D4—4881no—
316D4—2442no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—42no—
324C2×C4—611no—
325C2×C4—611no—
326C2×C4—611no—
327C2×C4—611no—
328C2×C4—1221no—
329C2×C4—1221no—
330C2×C4—4881no—
331C2×C4—2442no—
332C2×C4D4×D6111yescharacteristic
333C2×C4C23×D6111yescharacteristic
334C8—21no—
335C8—21no—
336C8—1221no—
337C8—1221no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—2441no—
342C22—2441no—
343C22—2441no—
344C22—2441no—
345C22—2441no—
346C22—2441no—
347C22C2×D4×D6111yescharacteristic
348C4—21no—
349C4—41no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—1221no—
354C4—1221no—
355C4—1221no—
356C4—1221no—
357C4—2441no—
358C4—2441no—
359C4#1451982211yescharacteristic
360C4#1451982211yescharacteristic
361C2—41no—
362C2—4881no—
363C2—4881no—
364C2#1684032711yescharacteristic
365C2#1684057111yescharacteristic
366C2#1684057511yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#451C2
socleC22×C61C22×D4
hypercenter#451D61
hypocenterC61#3225
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
1. #16840385C2semidirect
2. #16840336C2semidirect
3. #16840155C2semidirect
4. #16840147C2semidirect
5. #16840123C2semidirect
6. #16840111C2semidirect
7. #16839986C2semidirect
8. #16839980C2semidirect
9. #16839970C2semidirect
10. #16839966C2semidirect
11. #16839922C2semidirect
13. #16839901C2semidirect
14. #16839820C2semidirect
15. C61×#451C2semidirect
195. #451D61semidirect
199. C61#3225semidirect