Finite Group Databasebeta

← #21453940

Subgroups — #21453940

Order 7808.

508 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16839703C211yesmaximal, characteristic, complemented
2#16839689C211yesmaximal, characteristic, complemented
3#16839680C211yesmaximal, characteristic, complemented
4#16839680C211yesmaximal, characteristic, complemented
5#16839679C211yesmaximal, characteristic, complemented
6#16839678C211yesmaximal, characteristic, complemented
7#16839677C211yesmaximal, characteristic, complemented
8#16839672C211yesmaximal, characteristic, complemented
9#16839671C211yesmaximal, characteristic, complemented
10#16839671C211yesmaximal, characteristic, complemented
11#16839671C211yesmaximal, characteristic, complemented
12#16839662C211yesmaximal, characteristic, complemented
13#16839654C211yesmaximal, characteristic, complemented
14#16839652C211yesmaximal, characteristic, complemented
15C61×#397C211yesmaximal, characteristic, complemented
16C22×D244C2211yescharacteristic
17C22×D244C2211yescharacteristic
18C22×D244C2211yescharacteristic
19C22×C22⋊D61C2211yescharacteristic
20C22×C22⋊D61C2211yescharacteristic
21C22×C22⋊D61C2211yescharacteristic
22C2×C4⋊Dic61C2211yescharacteristic
23C2×#11758196C2211yescharacteristic
24C2×#11758196C2211yescharacteristic
25C2×C22⋊Dic61C2211yescharacteristic
26C2×#11758198C2211yescharacteristic
27C2×#11758198C2211yescharacteristic
28C2×#11758198C2211yescharacteristic
29C2×#11758198C2211yescharacteristic
30C2×#11758198C2211yescharacteristic
31C2×#11758198C2211yescharacteristic
32C2×#11758198C2211yescharacteristic
33C2×#11758198C2211yescharacteristic
34C2×#11758198C2211yescharacteristic
35C2×#11758198C2211yescharacteristic
36C2×#11758198C2211yescharacteristic
37C2×#11758198C2211yescharacteristic
38C2×C4×Dic61C2211yescharacteristic
39#14519684C2211yescharacteristic
40#14519684C2211yescharacteristic
41#14519684C2211yescharacteristic
42#14519684C2211yescharacteristic
43#14519684C2211yescharacteristic
44C2×C4⋊C4×C61C2211yescharacteristic
45C2×C22⋊C4×C61C2211yescharacteristic
46C2×C22⋊C4×C61C2211yescharacteristic
47C2×C22⋊C4×C61C2211yescharacteristic
48#95×C61C2211yescharacteristic
49#95×C61C2211yescharacteristic
50#95×C61C2211yescharacteristic
51C24×C61C2311yescharacteristic
52C23×D61C2311yescharacteristic
53C23×D61C2311yescharacteristic
54C23×D61C2311yescharacteristic
55C22×C4×C61C2311yescharacteristic
56C22×C4×C61C2311yescharacteristic
57C22×C4×C61C2311yescharacteristic
58C22×C4×C61C2311yescharacteristic
59C22×C4×C61C2311yescharacteristic
60C22×C4×C61C2311yescharacteristic
61C2×C22⋊D61—22no—
62C2×C22⋊D61—41no—
63C2×C22⋊D61—41no—
64C2×C22⋊D61—41no—
65C2×C22⋊D61—41no—
66C2×C22⋊D61—41no—
67C2×C22⋊D61—41no—
68C2×C22⋊D61—41no—
69C2×C22⋊D61—41no—
70C22×Dic61C2311yescharacteristic
71C22×Dic61C2311yescharacteristic
72C22×Dic61C2311yescharacteristic
73C22×Dic61C2311yescharacteristic
74C22×Dic61C2311yescharacteristic
75C2×D244—41no—
76C2×D244—41no—
77C2×D244—41no—
78C2×D244—41no—
79C2×D244—41no—
80C2×D244—41no—
81C2×D244—41no—
82C2×D244—41no—
83C2×D244—41no—
84C4⋊C4×C61—41no—
85C22⋊C4×C61—41no—
86C22⋊C4×C61—41no—
87C22⋊C4×C61—41no—
88C22⋊Dic61—41no—
89#11758198—22no—
90#11758198—22no—
91#11758198—41no—
92#11758198—41no—
93#11758198—41no—
94#11758198—41no—
95#11758198—41no—
96#11758198—41no—
97#11758198—41no—
98#11758198—41no—
99#11758198—41no—
100#11758198—41no—
101C4⋊Dic61—41no—
102#11758196—41no—
103#11758196—41no—
104C4×Dic61—41no—
105C23×C61—21no—
106C23×C61—21no—
107C23×C61—21no—
108C23×C61—21no—
109C23×C61—21no—
110C23×C61—21no—
111C23×C61—21no—
112C23×C61C2411yescharacteristic
113C22×D61—21no—
114C22×D61—21no—
115C22×D61—21no—
116C22×D61—21no—
117C22×D61—21no—
118C22×D61—21no—
119C22×D61—21no—
120C22×D61—21no—
121C22×D61—21no—
122C22×D61—21no—
123C22×D61—21no—
124C22×D61—21no—
125C22×D61—21no—
126C22×D61—21no—
127C22×D61—21no—
128C22×D61—21no—
129C22×D61—21no—
130C22×D61—21no—
131C22×D61—21no—
132C22×D61—21no—
133C22×D61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
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—
149C2×C4×C61—21no—
150C2×C4×C61—21no—
151C2×C4×C61—21no—
152C22⋊D61—44no—
153C22⋊D61—44no—
154C22⋊D61—44no—
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#4112yes—
170D244—44no—
171D244—44no—
172D244—44no—
173C22×C61—41no—
174C22×C61—41no—
175C22×C61—41no—
176C22×C61—41no—
177C22×C61—41no—
178C22×C61—41no—
179C22×C61—41no—
180C22×C61C2×#4111yescharacteristic
181C22×C61H(5,𝔽2)11yescharacteristic
182C22×C61H(5,𝔽2)11yescharacteristic
183C22×C61H(5,𝔽2)11yescharacteristic
184C22×C61H(5,𝔽2)11yescharacteristic
185C22×C61H(5,𝔽2)11yescharacteristic
186C22×C61H(5,𝔽2)11yescharacteristic
187C2×D61—41no—
188C2×D61—41no—
189C2×D61—41no—
190C2×D61—41no—
191C2×D61—41no—
192C2×D61—41no—
193C2×D61—41no—
194C2×D61—41no—
195C2×D61—41no—
196C2×D61—41no—
197C2×D61—41no—
198C2×D61—41no—
199C2×D61—41no—
200C2×D61—41no—
201C2×D61—41no—
202C2×D61—41no—
203C2×D61—41no—
204C2×D61—41no—
205C2×D61—41no—
206C2×D61—41no—
207C2×D61—41no—
208C4×C61—41no—
209C4×C61—41no—
210C4×C61—41no—
211C4×C61—41no—
212C4×C61—41no—
213C4×C61—41no—
214Dic61—22no—
215Dic61—41no—
216Dic61—41no—
217Dic61—41no—
218Dic61—41no—
219#2828—611nomaximal, Sylow
220C2×C61—81no—
221C2×C61#53811yescharacteristic
222C2×C61#54011yescharacteristic
223C2×C61#54011yescharacteristic
224C2×C61#56011yescharacteristic
225C2×C61#56011yescharacteristic
226C2×C61#56011yescharacteristic
227C2×C61H(3,𝔽4)11yescharacteristic
228D61—81no—
229D61—81no—
230D61—81no—
231#400—611no—
232#397—611no—
233#397D6111yescharacteristic, complemented
234#394—611no—
235#394—611no—
236#394—611no—
237#394—611no—
238#394—611no—
239#392—611no—
240#392—611no—
241#392—611no—
242#392—611no—
243#390—611no—
244#388—611no—
245#388—611no—
246C61#282811yescharacteristic, complemented, Sylow
247C22×D4—611no—
248C22×D4—611no—
249C22×D4—611no—
250C22×D4—611no—
251C22×D4—611no—
252C22×D4—611no—
253C2×C4⋊C4—611no—
254C2×C4⋊C4—611no—
255C2×C4⋊C4—611no—
256C2×C4⋊C4C2×D6111yescharacteristic
257C2×C22⋊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
273C2×C42—611no—
274#95—611no—
275#95—611no—
276#95—611no—
277#95—611no—
278#95—611no—
279#95C2×D6111yescharacteristic
280#95C2×D6111yescharacteristic
281#95C2×D6111yescharacteristic
282C24—611no—
283C24—611no—
284C24—611no—
285C24C22×D6111yescharacteristic
286C2×D4—1222no—
287C2×D4—2441no—
288C2×D4—2441no—
289C2×D4—2441no—
290C2×D4—2441no—
291C2×D4—2441no—
292C2×D4—2441no—
293C2×D4—2441no—
294C2×D4—2441no—
295C2×D4—2441no—
296C2×D4—2441no—
297C2×D4—2441no—
298C2×D4—2441no—
299C2×D4—2441no—
300C2×D4—2441no—
301C2×D4—2441no—
302C2×D4—2441no—
303C2×D4—2441no—
304C22×C4—611no—
305C22×C4—611no—
306C22×C4—611no—
307C22×C4—611no—
308C22×C4—611no—
309C22×C4C22×D6111yescharacteristic
310C22×C4C22×D6111yescharacteristic
311C22×C4C22×D6111yescharacteristic
312C22×C4C22×D6111yescharacteristic
313C22×C4C22×D6111yescharacteristic
314C22×C4C22×D6111yescharacteristic
315C4⋊C4—41no—
316C4⋊C4—2441no—
317C4⋊C4—2441no—
318C4⋊C4—2441no—
319C22⋊C4—41no—
320C22⋊C4—41no—
321C22⋊C4—41no—
322C22⋊C4—1222no—
323C22⋊C4—1222no—
324C22⋊C4—2441no—
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—
335C42—2441no—
336C23—21no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—1221no—
344C23—1221no—
345C23—1221no—
346C23—1221no—
347C23—1221no—
348C23—1221no—
349C23—1221no—
350C23—1221no—
351C23—1221no—
352C23—1221no—
353C23—1221no—
354C23—1221no—
355C23—1221no—
356C23—1221no—
357C23—1221no—
358C23—1221no—
359C23—1221no—
360C23—1221no—
361C23—1221no—
362C23—1221no—
363C23—1221no—
364C23C23×D6111yescharacteristic
365D4—2444no—
366D4—2444no—
367D4—2444no—
368D4—2444no—
369D4—2444no—
370D4—2444no—
371C2×C4—21no—
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—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—612no—
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—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—2441no—
412C22—2441no—
413C22—2441no—
414C22—2441no—
415C22—2441no—
416C22—2441no—
417C22—2441no—
418C22—2441no—
419C22—2441no—
420C22—2441no—
421C22—2441no—
422C22—2441no—
423C22—2441no—
424C22—2441no—
425C22—2441no—
426C22—2441no—
427C22—2441no—
428C22—2441no—
429C22—2441no—
430C22—2441no—
431C22—2441no—
432C22#41×D6111yescharacteristic
433C22#1451982211yescharacteristic
434C22#1451982211yescharacteristic
435C22#1451982311yescharacteristic
436C22#1451982311yescharacteristic
437C22#1451982311yescharacteristic
438C22#1451982311yescharacteristic
439C4—41no—
440C4—41no—
441C4—41no—
442C4—41no—
443C4—41no—
444C4—41no—
445C4—1222no—
446C4—2441no—
447C4—2441no—
448C4—2441no—
449C4—2441no—
450C2—81no—
451C2—4881no—
452C2—4881no—
453C2—4881no—
454C2#1684035111yescharacteristic
455C2#1684036411yescharacteristic
456C2#1684036411yescharacteristic
457C2#1684050011yescharacteristic
458C2#1684050211yescharacteristic
459C2#1684050311yescharacteristic
460C2#1684050411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#397C2
hypercenter#397D61
hypocenterC61#2828
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. #16839703C2semidirect
2. #16839689C2semidirect
3. #16839680C2semidirect
4. #16839680C2semidirect
5. #16839679C2semidirect
6. #16839678C2semidirect
7. #16839677C2semidirect
8. #16839672C2semidirect
9. #16839671C2semidirect
10. #16839671C2semidirect
11. #16839671C2semidirect
12. #16839662C2semidirect
13. #16839654C2semidirect
14. #16839652C2semidirect
15. C61×#397C2semidirect
233. #397D61semidirect
246. C61#2828semidirect