Finite Group Databasebeta

← #21456697

Subgroups — #21456697

Order 7808.

390 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840341C211yesmaximal, characteristic
2#16840336C211yesmaximal, characteristic, complemented
3#16840104C211yesmaximal, characteristic, complemented
4#16840096C211yesmaximal, characteristic, complemented
5#16840091C211yesmaximal, characteristic, complemented
6#16840083C211yesmaximal, characteristic, complemented
7#16840019C211yesmaximal, characteristic, complemented
8#16840005C211yesmaximal, characteristic, complemented
9#16840002C211yesmaximal, characteristic, complemented
10#16839988C211yesmaximal, characteristic, complemented
11#16839921C211yesmaximal, characteristic, complemented
12#16839921C211yesmaximal, characteristic, complemented
13#16839918C211yesmaximal, characteristic, complemented
14#16839727C211yesmaximal, characteristic, complemented
15C61×#448C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C2×#11758224C2211yescharacteristic
18C2×#11758202C2211yescharacteristic
19C2×#11758202C2211yescharacteristic
20C2×#11758189C2211yescharacteristic
21C2×C8×D61C2211yescharacteristic
22#14519775—21no—
23#14519766—21no—
24#14519760—21no—
25#14519760—21no—
26#14519757C2211yescharacteristic
27#14519756C2211yescharacteristic
28#14519754—21no—
29#14519753C2211yescharacteristic
30#14519753C2211yescharacteristic
31#14519753C2211yescharacteristic
32#14519753C2211yescharacteristic
33#14519750—21no—
34#14519749—21no—
35#14519748—21no—
36#14519748C2211yescharacteristic
37#14519736C2211yescharacteristic
38C4⋊C4×D61C2211yescharacteristic
39#14519711C2211yescharacteristic
40#14519710C2211yescharacteristic
41#14519709C2211yescharacteristic
42#14519708C2211yescharacteristic
43#14519702C2211yescharacteristic
44#14519702C2211yescharacteristic
45#14519701C2211yescharacteristic
46#14519701C2211yescharacteristic
47#14519698C2211yescharacteristic
48#14519698C2211yescharacteristic
49C22⋊#92418C2211yescharacteristic
50#14519689C2211yescharacteristic
51#14519689C2211yescharacteristic
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⋊D61D411yescharacteristic
71C2×C22⋊D61D411yescharacteristic
72C22×Dic61—21no—
73#11758224—41no—
74#11758224—41no—
75#11758222—41no—
76#11758222—41no—
77C2×D244D411yescharacteristic
78C2×C4×D61—21no—
79C2×C4×D61C2311yescharacteristic
80C2×C4×D61C2311yescharacteristic
81C2×Dic122D411yescharacteristic
82C2×Dic122C2311yescharacteristic
83SD16×C61—41no—
84SD16×C61—41no—
85C2×C8×C61C2311yescharacteristic
86C2×C8×C61C2311yescharacteristic
87C4⋊C4×C61C2311yescharacteristic
88C22⋊C4×C61—21no—
89C22⋊Dic61—21no—
90C22⋊Dic61—21no—
91C22⋊Dic61—21no—
92#11758202—41no—
93#11758202—41no—
94#11758198—21no—
95#11758198—21no—
96#11758198—21no—
97#11758198—21no—
98#11758198—21no—
99C4⋊Dic61—21no—
100C4⋊Dic61C2311yescharacteristic
101C4⋊Dic61C2311yescharacteristic
102C4⋊Dic61C2311yescharacteristic
103#11758196—21no—
104#11758196—21no—
105#11758196—21no—
106#11758196—21no—
107#11758196—21no—
108#11758196—21no—
109C4×Dic61—21no—
110C2×#92418C2311yescharacteristic
111C2×#92418C2311yescharacteristic
112#11758189—41no—
113C8×D61—41no—
114C23×C61—21no—
115C23×C61C2×D411yescharacteristic
116C22×D61C2×D411yescharacteristic
117C22×D61C2×D411yescharacteristic
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—41no—
135C22⋊D61—41no—
136C22⋊D61—42no—
137C22⋊D61—81no—
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—42no—
143C2×Dic61C2×D411yescharacteristic
144C2×Dic61C2×D411yescharacteristic
145D244—41no—
146C4×D61—21no—
147C4×D61—21no—
148C4×D61—21no—
149C4×D61—21no—
150C4×D61—81no—
151Dic122—21no—
152Dic122—21no—
153Dic122—41no—
154C8×C61—21no—
155C8×C61—21no—
156#92418—21no—
157#92418—21no—
158C22×C61—21no—
159C22×C61—21no—
160C22×C61—21no—
161C22×C61—41no—
162C22×C61—41no—
163C22×C61—41no—
164C22×C61C22×D411yescharacteristic
165C2×D61—21no—
166C2×D61—21no—
167C2×D61—21no—
168C2×D61—21no—
169C2×D61—21no—
170C2×D61—21no—
171C4×C61—21no—
172C4×C61—41no—
173C4×C61—41no—
174C4×C61—41no—
175C4×C61H(5,𝔽2)11yescharacteristic
176C4×C61H(5,𝔽2)11yescharacteristic
177Dic61—21no—
178Dic61—21no—
179Dic61—41no—
180Dic61—41no—
181Dic61—41no—
182Dic61—41no—
183#3201—611nomaximal, Sylow
184C2×C61—41no—
185C2×C61—81no—
186C2×C61#53411yescharacteristic
187C2×C61#57711yescharacteristic
188C2×C61#57811yescharacteristic
189D61—41no—
190D61—41no—
191#537—611no—
192#536—611no—
193#485—611no—
194#484—611no—
195#483—611no—
196#482—611no—
197#470—611no—
198#468—611no—
199#467—611no—
200#465—611no—
201#452—611no—
202#452—611no—
203#451—611no—
204#448D6111yescharacteristic, complemented
205#408—611no—
206C61#320111yescharacteristic, complemented, Sylow
207C2×#41—611no—
208C2×#41—611no—
209C22×Q8C2×D6111yescharacteristic
210C2×Q16—611no—
211C2×Q16—611no—
212C2×SD16C2×D6111yescharacteristic
213C2×SD16C2×D6111yescharacteristic
214C2×M16—611no—
215C22×C8—611no—
216C4⋊Q8—1221no—
217#124—1221no—
218#123—1221no—
219#123—1221no—
220C22⋊Q8—611no—
221C22⋊Q8—611no—
222C22⋊Q8—611no—
223C22⋊Q8—611no—
224C22⋊Q8—611no—
225C22⋊Q8—611no—
226C22⋊Q8—1221no—
227#121—611no—
228#121—1221no—
229#121—1221no—
230#121—1221no—
231#121C2×D6111yescharacteristic
232#117—611no—
233C2×C4⋊C4—611no—
234#107—611no—
235#107—611no—
236#106—611no—
237#106—611no—
238#103—611no—
239#103—611no—
240#103—611no—
241#103—611no—
242#103C2×D6111yescharacteristic
243#103C2×D6111yescharacteristic
244#102—611no—
245#102—611no—
246C22⋊C8—611no—
247C22⋊C8—611no—
248C22⋊C8—611no—
249C22⋊C8C2×D6111yescharacteristic
250#41—2441no—
251#41—2441no—
252#41—2441no—
253#41—2441no—
254C2×Q8—21no—
255C2×Q8—41no—
256C2×Q8—41no—
257C2×Q8—611no—
258C2×Q8—611no—
259C2×Q8C22×D6111yescharacteristic
260C2×Q8C22×D6111yescharacteristic
261C2×D4—21no—
262C2×D4—611no—
263C2×D4—611no—
264C2×D4—611no—
265C2×D4—1221no—
266C2×D4—1221no—
267C2×D4C22×D6111yescharacteristic
268C22×C4—21no—
269C22×C4—611no—
270C22×C4—611no—
271C22×C4—1221no—
272C22×C4—1221no—
273C22×C4C22×D6111yescharacteristic
274Q16—2441no—
275Q16—2441no—
276SD16—41no—
277SD16—41no—
278M16—2441no—
279C2×C8—611no—
280C2×C8—611no—
281C2×C8—2441no—
282C2×C8C22×D6111yescharacteristic
283C2×C8C22×D6111yescharacteristic
284C4⋊C4—611no—
285C4⋊C4—611no—
286C4⋊C4—611no—
287C4⋊C4—1221no—
288C4⋊C4—1221no—
289C4⋊C4—1221no—
290C4⋊C4—1221no—
291C4⋊C4—1221no—
292C4⋊C4—1221no—
293C4⋊C4—1221no—
294C4⋊C4C22×D6111yescharacteristic
295C22⋊C4—21no—
296C22⋊C4—1221no—
297C22⋊C4—1221no—
298C22⋊C4—1221no—
299C22⋊C4—1221no—
300C22⋊C4—1221no—
301C22⋊C4—1221no—
302C22⋊C4—1221no—
303C22⋊C4—1221no—
304C42—1221no—
305C23—21no—
306C23—611no—
307C23—611no—
308C23D4×D6111yescharacteristic
309Q8—21no—
310Q8—21no—
311Q8—21no—
312Q8—21no—
313Q8—42no—
314Q8—1221no—
315Q8—1221no—
316Q8—2441no—
317D4—21no—
318D4—21no—
319D4—81no—
320D4—4881no—
321D4—2441no—
322D4—2441no—
323D4—2441no—
324D4—2442no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—42no—
331C2×C4—611no—
332C2×C4—611no—
333C2×C4—1221no—
334C2×C4—1221no—
335C2×C4—1221no—
336C2×C4—1221no—
337C2×C4—1221no—
338C2×C4—1221no—
339C2×C4—1221no—
340C2×C4—1221no—
341C2×C4—4881no—
342C2×C4—2442no—
343C2×C4D4×D6111yescharacteristic
344C2×C4C23×D6111yescharacteristic
345C8—21no—
346C8—21no—
347C8—1221no—
348C8—1221no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—1221no—
356C22—1221no—
357C22—1221no—
358C22—1221no—
359C22—1221no—
360C22—1221no—
361C22C2×D4×D6111yescharacteristic
362C4—21no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—1221no—
367C4—1221no—
368C4—2441no—
369C4—2441no—
370C4—2441no—
371C4—2441no—
372C4#1451982211yescharacteristic
373C4#1451982211yescharacteristic
374C2—41no—
375C2—81no—
376C2—2441no—
377C2—2441no—
378C2#1684032211yescharacteristic
379C2#1684056811yescharacteristic
380C2#1684057811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#448C2
socleC22×C61C22×D4
hypercenter#448D61
hypocenterC61#3201
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
2. #16840336C2semidirect
3. #16840104C2semidirect
4. #16840096C2semidirect
5. #16840091C2semidirect
6. #16840083C2semidirect
7. #16840019C2semidirect
8. #16840005C2semidirect
9. #16840002C2semidirect
10. #16839988C2semidirect
11. #16839921C2semidirect
12. #16839921C2semidirect
13. #16839918C2semidirect
14. #16839727C2semidirect
15. C61×#448C2semidirect
204. #448D61semidirect
206. C61#3201semidirect