Finite Group Databasebeta

← #21456712

Subgroups — #21456712

Order 7808.

378 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840336C211yesmaximal, characteristic
2#16840335C211yesmaximal, characteristic
3#16840104C211yesmaximal, characteristic, complemented
4#16840102C211yesmaximal, characteristic, complemented
5#16840101C211yesmaximal, characteristic, complemented
6#16840100C211yesmaximal, characteristic, complemented
7#16840019C211yesmaximal, characteristic, complemented
8#16840017C211yesmaximal, characteristic, complemented
9#16840002C211yesmaximal, characteristic, complemented
10#16840000C211yesmaximal, characteristic, complemented
11#16839918C211yesmaximal, characteristic, complemented
12#16839916C211yesmaximal, characteristic, complemented
13#16839916C211yesmaximal, characteristic, complemented
14#16839727C211yesmaximal, characteristic
15C61×#451C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C2×Q8×D61C2211yescharacteristic
18C2×#11758202C2211yescharacteristic
19C2×#11758202C2211yescharacteristic
20C2×#11758189C2211yescharacteristic
21C2×C8×D61C2211yescharacteristic
22#14519776—21no—
23#14519775—21no—
24#14519766—21no—
25#14519763—21no—
26#14519762—21no—
27#14519760—21no—
28#14519760—21no—
29#14519759—21no—
30#14519757C2211yescharacteristic
31#14519756C2211yescharacteristic
32#14519753C2211yescharacteristic
33#14519753C2211yescharacteristic
34#14519753C2211yescharacteristic
35#14519753C2211yescharacteristic
36#14519753C2211yescharacteristic
37#14519736C2211yescharacteristic
38#14519735C2211yescharacteristic
39#14519711C2211yescharacteristic
40#14519710C2211yescharacteristic
41#14519709C2211yescharacteristic
42#14519708C2211yescharacteristic
43#14519702C2211yescharacteristic
44#14519702C2211yescharacteristic
45#14519701C2211yescharacteristic
46#14519701C2211yescharacteristic
47#14519701C2211yescharacteristic
48#14519701C2211yescharacteristic
49C22⋊#92418C2211yescharacteristic
50#14519689C2211yescharacteristic
51#14519689C2211yescharacteristic
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⋊D61D411yescharacteristic
68C2×C22⋊D61D411yescharacteristic
69Q8×D61—41no—
70Q8×D61—41no—
71#11758222—41no—
72#11758222—41no—
73C2×D244D411yescharacteristic
74C2×C4×D61—21no—
75C2×C4×D61C2311yescharacteristic
76C2×C4×D61C2311yescharacteristic
77C2×Dic122—21no—
78C2×Dic122D411yescharacteristic
79C2×Dic122C2311yescharacteristic
80Q16×C61—41no—
81Q16×C61—41no—
82C2×C8×C61C2311yescharacteristic
83C2×C8×C61C2311yescharacteristic
84C4⋊C4×C61—21no—
85C4⋊C4×C61C2311yescharacteristic
86C22⋊C4×C61—21no—
87C22⋊Dic61—21no—
88C22⋊Dic61—21no—
89#11758202—41no—
90#11758202—41no—
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⋊Dic61C2311yescharacteristic
100C4⋊Dic61C2311yescharacteristic
101C4⋊Dic61C2311yescharacteristic
102#11758196—21no—
103#11758196—21no—
104#11758196—21no—
105#11758196—21no—
106#11758196—21no—
107#11758196—21no—
108C4×Dic61—21no—
109C4×Dic61—21no—
110C2×#92418C2311yescharacteristic
111C2×#92418C2311yescharacteristic
112#11758189—41no—
113C8×D61—41no—
114C23×C61C2×D411yescharacteristic
115C22×D61C2×D411yescharacteristic
116C22×D61C2×D411yescharacteristic
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—41no—
134C22⋊D61—41no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61C2×D411yescharacteristic
140C2×Dic61C2×D411yescharacteristic
141D244—41no—
142C4×D61—21no—
143C4×D61—21no—
144C4×D61—21no—
145C4×D61—21no—
146C4×D61—42no—
147Dic122—21no—
148Dic122—21no—
149Dic122—41no—
150Dic122—42no—
151C8×C61—21no—
152C8×C61—21no—
153#92418—21no—
154#92418—21no—
155C22×C61—21no—
156C22×C61—21no—
157C22×C61—21no—
158C22×C61C22×D411yescharacteristic
159C2×D61—21no—
160C2×D61—21no—
161C2×D61—21no—
162C2×D61—21no—
163C2×D61—21no—
164C2×D61—21no—
165C4×C61—21no—
166C4×C61—41no—
167C4×C61—41no—
168C4×C61—41no—
169C4×C61—41no—
170C4×C61H(5,𝔽2)11yescharacteristic
171C4×C61H(5,𝔽2)11yescharacteristic
172Dic61—21no—
173Dic61—21no—
174Dic61—41no—
175Dic61—41no—
176Dic61—41no—
177Dic61—41no—
178#3202—611nomaximal, Sylow
179C2×C61—41no—
180C2×C61#53411yescharacteristic
181C2×C61#57811yescharacteristic
182C2×C61#57811yescharacteristic
183D61—41no—
184D61—41no—
185#536—611no—
186#536—611no—
187#485—611no—
188#485—611no—
189#485—611no—
190#485—611no—
191#470—611no—
192#470—611no—
193#467—611no—
194#467—611no—
195#451—611no—
196#451—611no—
197#451—611no—
198#451D6111yescharacteristic, complemented
199#408—611no—
200C61#320211yescharacteristic, complemented, Sylow
201C2×#41—611no—
202C22×Q8—611no—
203C22×Q8C2×D6111yescharacteristic
204C2×Q16—611no—
205C2×Q16—611no—
206C2×Q16C2×D6111yescharacteristic
207C2×Q16C2×D6111yescharacteristic
208C2×M16—611no—
209C22×C8—611no—
210C4⋊Q8—1221no—
211C4⋊Q8—1221no—
212#124—1221no—
213#124—1221no—
214#123—1221no—
215#123—1221no—
216#123—1221no—
217#123—1221no—
218C22⋊Q8—611no—
219C22⋊Q8—611no—
220C22⋊Q8—611no—
221C22⋊Q8—611no—
222C22⋊Q8—611no—
223C22⋊Q8—611no—
224C22⋊Q8—611no—
225C22⋊Q8C2×D6111yescharacteristic
226#117—611no—
227#117—611no—
228#107—611no—
229#107—611no—
230#106—611no—
231#106—611no—
232#103—611no—
233#103—611no—
234#103—611no—
235#103—611no—
236#103—611no—
237#103—611no—
238#103C2×D6111yescharacteristic
239#103C2×D6111yescharacteristic
240C22⋊C8—611no—
241C22⋊C8—611no—
242C22⋊C8—611no—
243C22⋊C8C2×D6111yescharacteristic
244#41—2441no—
245#41—2441no—
246C2×Q8—21no—
247C2×Q8—41no—
248C2×Q8—41no—
249C2×Q8—611no—
250C2×Q8—611no—
251C2×Q8—1221no—
252C2×Q8—2441no—
253C2×Q8—2441no—
254C2×Q8C22×D6111yescharacteristic
255C2×Q8C22×D6111yescharacteristic
256C2×Q8C22×D6111yescharacteristic
257C2×D4—611no—
258C2×D4—611no—
259C2×D4—611no—
260C22×C4—21no—
261C22×C4—611no—
262C22×C4—611no—
263C22×C4—1221no—
264C22×C4C22×D6111yescharacteristic
265Q16—41no—
266Q16—41no—
267Q16—2441no—
268Q16—2441no—
269M16—2441no—
270C2×C8—611no—
271C2×C8—611no—
272C2×C8—2441no—
273C2×C8C22×D6111yescharacteristic
274C2×C8C22×D6111yescharacteristic
275C4⋊C4—21no—
276C4⋊C4—611no—
277C4⋊C4—611no—
278C4⋊C4—611no—
279C4⋊C4—1221no—
280C4⋊C4—1221no—
281C4⋊C4—1221no—
282C4⋊C4—1221no—
283C4⋊C4—1221no—
284C4⋊C4—1221no—
285C4⋊C4—1221no—
286C4⋊C4C22×D6111yescharacteristic
287C22⋊C4—21no—
288C22⋊C4—1221no—
289C22⋊C4—1221no—
290C22⋊C4—1221no—
291C22⋊C4—1221no—
292C22⋊C4—1221no—
293C22⋊C4—1221no—
294C22⋊C4—1221no—
295C22⋊C4—1221no—
296C22⋊C4—1221no—
297C42—1221no—
298C42—1221no—
299C23—611no—
300C23—611no—
301C23D4×D6111yescharacteristic
302Q8—21no—
303Q8—21no—
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—21no—
308Q8—42no—
309Q8—1221no—
310Q8—1221no—
311Q8—2441no—
312Q8—2442no—
313D4—2441no—
314D4—2441no—
315D4—2441no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—611no—
324C2×C4—611no—
325C2×C4—1221no—
326C2×C4—1221no—
327C2×C4—1221no—
328C2×C4—1221no—
329C2×C4—1221no—
330C2×C4—1221no—
331C2×C4—1221no—
332C2×C4—1221no—
333C2×C4—2442no—
334C2×C4D4×D6111yescharacteristic
335C2×C4C23×D6111yescharacteristic
336C8—21no—
337C8—21no—
338C8—1221no—
339C8—1221no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—1221no—
344C22—1221no—
345C22—1221no—
346C22—1221no—
347C22—1221no—
348C22—1221no—
349C22C2×D4×D6111yescharacteristic
350C4—21no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—1221no—
356C4—1221no—
357C4—2441no—
358C4—2441no—
359C4—2441no—
360C4—2441no—
361C4#1451982211yescharacteristic
362C4#1451982211yescharacteristic
363C2—41no—
364C2—2441no—
365C2—2441no—
366C2#1684032211yescharacteristic
367C2#1684057511yescharacteristic
368C2#1684057811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#451C2
socleC22×C61C22×D4
hypercenter#451D61
hypocenterC61#3202
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
3. #16840104C2semidirect
4. #16840102C2semidirect
5. #16840101C2semidirect
6. #16840100C2semidirect
7. #16840019C2semidirect
8. #16840017C2semidirect
9. #16840002C2semidirect
10. #16840000C2semidirect
11. #16839918C2semidirect
12. #16839916C2semidirect
13. #16839916C2semidirect
15. C61×#451C2semidirect
198. #451D61semidirect
200. C61#3202semidirect