Finite Group Databasebeta

← #21453907

Subgroups — #21453907

Order 7808.

522 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61⋊#401C211yesmaximal, characteristic, complemented
2#16839691C211yesmaximal, characteristic, complemented
3#16839690C211yesmaximal, characteristic, complemented
4#16839687C211yesmaximal, characteristic, complemented
5#16839685C211yesmaximal, characteristic, complemented
6#16839678C211yesmaximal, characteristic, complemented
7#16839677C211yesmaximal, characteristic, complemented
8#16839676C211yesmaximal, characteristic, complemented
9#16839670C211yesmaximal, characteristic, complemented
10#16839670C211yesmaximal, characteristic, complemented
11#16839670C211yesmaximal, characteristic, complemented
12#16839642C211yesmaximal, characteristic, complemented
13#16839642C211yesmaximal, characteristic, complemented
14#16839639C211yesmaximal, characteristic, complemented
15C61×#392C211yesmaximal, characteristic, complemented
16C22×C22⋊D61C2211yescharacteristic
17C22×C22⋊D61C2211yescharacteristic
18C22×C22⋊D61C2211yescharacteristic
19C23×Dic61C2211yescharacteristic
20C2×C4⋊Dic61C2211yescharacteristic
21C2×#11758196C2211yescharacteristic
22C2×#11758196C2211yescharacteristic
23C2×C22⋊Dic61C2211yescharacteristic
24C2×C22⋊Dic61C2211yescharacteristic
25C2×C22⋊Dic61C2211yescharacteristic
26C2×C22⋊Dic61C2211yescharacteristic
27C2×C22⋊Dic61C2211yescharacteristic
28C2×C22⋊Dic61C2211yescharacteristic
29C2×C22⋊Dic61C2211yescharacteristic
30C2×C22⋊Dic61C2211yescharacteristic
31C2×#11758198C2211yescharacteristic
32C2×#11758198C2211yescharacteristic
33C2×#11758198C2211yescharacteristic
34C2×#11758198C2211yescharacteristic
35#14519684C2211yescharacteristic
36#14519684C2211yescharacteristic
37#14519684C2211yescharacteristic
38#14519684C2211yescharacteristic
39#14519684C2211yescharacteristic
40#14519684C2211yescharacteristic
41#14519684C2211yescharacteristic
42#14519684C2211yescharacteristic
43#14519684C2211yescharacteristic
44C22×D4×C61C2211yescharacteristic
45C22×D4×C61C2211yescharacteristic
46C22×D4×C61C2211yescharacteristic
47C2×C22⋊C4×C61C2211yescharacteristic
48C2×C22⋊C4×C61C2211yescharacteristic
49C2×C22⋊C4×C61C2211yescharacteristic
50#95×C61C2211yescharacteristic
51C24×C61C2311yescharacteristic
52C24×C61C2311yescharacteristic
53C24×C61C2311yescharacteristic
54C23×D61C2311yescharacteristic
55C2×D4×C61—22no—
56C2×D4×C61—22no—
57C2×D4×C61—41no—
58C2×D4×C61—41no—
59C2×D4×C61—41no—
60C2×D4×C61—41no—
61C2×D4×C61—41no—
62C2×D4×C61—41no—
63C2×D4×C61—41no—
64C22×C4×C61C2311yescharacteristic
65C22×C4×C61C2311yescharacteristic
66C22×C4×C61C2311yescharacteristic
67C22×C4×C61C2311yescharacteristic
68C2×C22⋊D61—22no—
69C2×C22⋊D61—41no—
70C2×C22⋊D61—41no—
71C2×C22⋊D61—41no—
72C2×C22⋊D61—41no—
73C2×C22⋊D61—41no—
74C2×C22⋊D61—41no—
75C2×C22⋊D61—41no—
76C2×C22⋊D61—41no—
77C22×Dic61—41no—
78C22×Dic61—41no—
79C22×Dic61—41no—
80C22×Dic61C2311yescharacteristic
81C22×Dic61C2311yescharacteristic
82C22×Dic61C2311yescharacteristic
83C22×Dic61C2311yescharacteristic
84C22×Dic61C2311yescharacteristic
85C22×Dic61C2311yescharacteristic
86C22×Dic61C2311yescharacteristic
87C22⋊C4×C61—41no—
88C22⋊C4×C61—41no—
89C22⋊C4×C61—41no—
90C22⋊Dic61—41no—
91C22⋊Dic61—41no—
92C22⋊Dic61—41no—
93C22⋊Dic61—41no—
94C22⋊Dic61—41no—
95C22⋊Dic61—41no—
96C22⋊Dic61—41no—
97C22⋊Dic61—41no—
98#11758198—41no—
99#11758198—41no—
100#11758198—41no—
101#11758198—41no—
102C4⋊Dic61—41no—
103#11758196—41no—
104#11758196—41no—
105C23×C61—21no—
106C23×C61—21no—
107C23×C61—21no—
108C23×C61—21no—
109C23×C61—21no—
110C23×C61—21no—
111C23×C61—21no—
112C23×C61—21no—
113C23×C61—21no—
114C23×C61—21no—
115C23×C61—21no—
116C23×C61—21no—
117C23×C61—21no—
118C23×C61—21no—
119C23×C61—21no—
120C23×C61—21no—
121C23×C61—21no—
122C23×C61—21no—
123C23×C61—21no—
124C23×C61—21no—
125C23×C61#4112yes—
126C23×C61C2411yescharacteristic
127C22×D61—21no—
128C22×D61—21no—
129C22×D61—21no—
130C22×D61—21no—
131C22×D61—21no—
132C22×D61—21no—
133C22×D61—21no—
134D4×C61—44no—
135D4×C61—44no—
136D4×C61—44no—
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—21no—
147C2×C4×C61—21no—
148C2×C4×C61—21no—
149C22⋊D61—44no—
150C22⋊D61—44no—
151C22⋊D61—44no—
152C2×Dic61—21no—
153C2×Dic61—21no—
154C2×Dic61—21no—
155C2×Dic61—21no—
156C2×Dic61—21no—
157C2×Dic61—21no—
158C2×Dic61—21no—
159C2×Dic61—21no—
160C2×Dic61—21no—
161C2×Dic61—21no—
162C2×Dic61—21no—
163C2×Dic61—21no—
164C2×Dic61—21no—
165C2×Dic61—21no—
166C2×Dic61—21no—
167C2×Dic61—21no—
168C2×Dic61—21no—
169C2×Dic61—21no—
170C2×Dic61—21no—
171C2×Dic61—21no—
172C2×Dic61—21no—
173C2×Dic61—44no—
174C22×C61—22no—
175C22×C61—22no—
176C22×C61—22no—
177C22×C61—41no—
178C22×C61—41no—
179C22×C61—41no—
180C22×C61—41no—
181C22×C61—41no—
182C22×C61—41no—
183C22×C61—41no—
184C22×C61—41no—
185C22×C61—41no—
186C22×C61—41no—
187C22×C61—41no—
188C22×C61—41no—
189C22×C61—41no—
190C22×C61—41no—
191C22×C61—41no—
192C22×C61—41no—
193C22×C61—41no—
194C22×C61—41no—
195C22×C61C2×#4111yescharacteristic
196C22×C61H(5,𝔽2)11yescharacteristic
197C22×C61H(5,𝔽2)11yescharacteristic
198C22×C61H(5,𝔽2)11yescharacteristic
199C22×C61H(5,𝔽2)11yescharacteristic
200C22×C61H(5,𝔽2)11yescharacteristic
201C22×C61H(5,𝔽2)11yescharacteristic
202C2×D61—41no—
203C2×D61—41no—
204C2×D61—41no—
205C2×D61—41no—
206C2×D61—41no—
207C2×D61—41no—
208C2×D61—41no—
209C4×C61—41no—
210C4×C61—41no—
211C4×C61—41no—
212C4×C61—41no—
213Dic61—41no—
214Dic61—41no—
215Dic61—41no—
216Dic61—41no—
217Dic61—41no—
218Dic61—41no—
219Dic61—41no—
220#2825—611nomaximal, Sylow
221C2×C61—42no—
222C2×C61—81no—
223C2×C61—81no—
224C2×C61#53811yescharacteristic
225C2×C61#53811yescharacteristic
226C2×C61#53811yescharacteristic
227C2×C61#56011yescharacteristic
228C2×C61#56011yescharacteristic
229C2×C61#56011yescharacteristic
230C2×C61#56011yescharacteristic
231D61—81no—
232#401—611no—
233#397—611no—
234#397—611no—
235#397—611no—
236#396—611no—
237#394—611no—
238#394—611no—
239#394—611no—
240#392—611no—
241#392—611no—
242#392—611no—
243#392D6111yescharacteristic, complemented
244#386—611no—
245#386—611no—
246#386—611no—
247C61#282511yescharacteristic, complemented, Sylow
248C22×D4—611no—
249C22×D4—611no—
250C22×D4—611no—
251C22×D4C2×D6111yescharacteristic
252C22×D4C2×D6111yescharacteristic
253C22×D4C2×D6111yescharacteristic
254C23×C4—611no—
255C2×C4⋊C4—611no—
256C2×C4⋊C4—611no—
257C2×C4⋊C4—611no—
258C2×C22⋊C4—611no—
259C2×C22⋊C4—611no—
260C2×C22⋊C4—611no—
261C2×C22⋊C4—611no—
262C2×C22⋊C4—611no—
263C2×C22⋊C4—611no—
264C2×C22⋊C4—611no—
265C2×C22⋊C4—611no—
266C2×C22⋊C4—611no—
267C2×C22⋊C4—611no—
268C2×C22⋊C4—611no—
269C2×C22⋊C4—611no—
270C2×C22⋊C4C2×D6111yescharacteristic
271C2×C22⋊C4C2×D6111yescharacteristic
272C2×C22⋊C4C2×D6111yescharacteristic
273#95—611no—
274#95—611no—
275#95—611no—
276#95—611no—
277#95—611no—
278#95—611no—
279#95—611no—
280#95—611no—
281#95—611no—
282#95C2×D6111yescharacteristic
283C24—611no—
284C24C22×D6111yescharacteristic
285C24C22×D6111yescharacteristic
286C24C22×D6111yescharacteristic
287C2×D4—22no—
288C2×D4—22no—
289C2×D4—41no—
290C2×D4—41no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—1222no—
297C2×D4—2441no—
298C2×D4—2441no—
299C2×D4—2441no—
300C2×D4—2441no—
301C2×D4—2441no—
302C2×D4—2441no—
303C2×D4—2441no—
304C2×D4—2441no—
305C22×C4—611no—
306C22×C4—611no—
307C22×C4—611no—
308C22×C4—611no—
309C22×C4—611no—
310C22×C4—611no—
311C22×C4—611no—
312C22×C4—2441no—
313C22×C4—2441no—
314C22×C4—2441no—
315C22×C4C22×D6111yescharacteristic
316C22×C4C22×D6111yescharacteristic
317C22×C4C22×D6111yescharacteristic
318C22×C4C22×D6111yescharacteristic
319C4⋊C4—2441no—
320C4⋊C4—2441no—
321C4⋊C4—2441no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C22⋊C4—2441no—
326C22⋊C4—2441no—
327C22⋊C4—2441no—
328C22⋊C4—2441no—
329C22⋊C4—2441no—
330C22⋊C4—2441no—
331C22⋊C4—2441no—
332C22⋊C4—2441no—
333C22⋊C4—2441no—
334C22⋊C4—2441no—
335C22⋊C4—2441no—
336C22⋊C4—2441no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—21no—
348C23—21no—
349C23—21no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—1221no—
358C23—1221no—
359C23—1221no—
360C23—1221no—
361C23—1221no—
362C23—1221no—
363C23—1221no—
364C23#1175822412yes—
365C23C23×D6111yescharacteristic
366D4—44no—
367D4—44no—
368D4—44no—
369D4—2444no—
370D4—2444no—
371D4—2444no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—1221no—
385C2×C4—1221no—
386C2×C4—1221no—
387C2×C4—1221no—
388C2×C4—1221no—
389C2×C4—1221no—
390C2×C4—1221no—
391C2×C4—1221no—
392C2×C4—1221no—
393C2×C4—1221no—
394C2×C4—1221no—
395C2×C4—1221no—
396C2×C4—1221no—
397C2×C4—1221no—
398C2×C4—1221no—
399C2×C4—1221no—
400C2×C4—1221no—
401C2×C4—1221no—
402C2×C4—1221no—
403C2×C4—1221no—
404C2×C4—1221no—
405C2×C4—2444no—
406C22—22no—
407C22—22no—
408C22—22no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22—41no—
420C22—41no—
421C22—41no—
422C22—41no—
423C22—41no—
424C22—41no—
425C22—41no—
426C22—41no—
427C22—2441no—
428C22—2441no—
429C22—2441no—
430C22—2441no—
431C22—2441no—
432C22—2441no—
433C22—2441no—
434C22C2×#1175822411yescharacteristic
435C22#1451982211yescharacteristic
436C22#1451982211yescharacteristic
437C22#1451982211yescharacteristic
438C22#1451982211yescharacteristic
439C22#1451982211yescharacteristic
440C22#1451982311yescharacteristic
441C4—41no—
442C4—41no—
443C4—41no—
444C4—41no—
445C4—2441no—
446C4—2441no—
447C4—2441no—
448C4—2441no—
449C4—2441no—
450C4—2441no—
451C4—2441no—
452C2—42no—
453C2—81no—
454C2—81no—
455C2—4881no—
456C2#1684034711yescharacteristic
457C2#1684034711yescharacteristic
458C2#1684034911yescharacteristic
459C2#1684049911yescharacteristic
460C2#1684050011yescharacteristic
461C2#1684050011yescharacteristic
462C2#1684050111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#392C2
hypercenter#392D61
hypocenterC61#2825
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C61⋊#401C2semidirect
2. #16839691C2semidirect
3. #16839690C2semidirect
4. #16839687C2semidirect
5. #16839685C2semidirect
6. #16839678C2semidirect
7. #16839677C2semidirect
8. #16839676C2semidirect
9. #16839670C2semidirect
10. #16839670C2semidirect
11. #16839670C2semidirect
12. #16839642C2semidirect
13. #16839642C2semidirect
14. #16839639C2semidirect
15. C61×#392C2semidirect
243. #392D61semidirect
247. C61#2825semidirect