Finite Group Databasebeta

← #21453897

Subgroups — #21453897

Order 7808.

472 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16839704C211yesmaximal, characteristic, complemented
2#16839701C211yesmaximal, characteristic, complemented
3#16839689C211yesmaximal, characteristic, complemented
4#16839679C211yesmaximal, characteristic, complemented
5#16839678C211yesmaximal, characteristic, complemented
6#16839678C211yesmaximal, characteristic, complemented
7#16839677C211yesmaximal, characteristic, complemented
8#16839675C211yesmaximal, characteristic, complemented
9#16839675C211yesmaximal, characteristic, complemented
10#16839674C211yesmaximal, characteristic, complemented
11#16839671C211yesmaximal, characteristic
12#16839640C211yesmaximal, characteristic, complemented
13#16839638C211yesmaximal, characteristic, complemented
14#16839636C211yesmaximal, characteristic, complemented
15C61×#397C211yesmaximal, characteristic, complemented
16C22×Dic122C2211yescharacteristic
17C22×D244C2211yescharacteristic
18C22×C22⋊D61C2211yescharacteristic
19C22×C22⋊D61C2211yescharacteristic
20C22×C4×D61C2211yescharacteristic
21C2×C4⋊Dic61C2211yescharacteristic
22C2×C4⋊Dic61C2211yescharacteristic
23C2×#11758196C2211yescharacteristic
24C2×C22⋊Dic61C2211yescharacteristic
25C2×C22⋊Dic61C2211yescharacteristic
26C2×#11758198C2211yescharacteristic
27C2×#11758198C2211yescharacteristic
28C2×#11758198C2211yescharacteristic
29C2×#11758198C2211yescharacteristic
30C2×#11758198C2211yescharacteristic
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
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
54C22×C4×C61C2311yescharacteristic
55C22×C4×C61C2311yescharacteristic
56C22×C4×C61C2311yescharacteristic
57C22×C4×C61C2311yescharacteristic
58C22×C4×C61C2311yescharacteristic
59C22×C4×C61C2311yescharacteristic
60C2×C22⋊D61—22no—
61C2×C22⋊D61—41no—
62C2×C22⋊D61—41no—
63C2×C22⋊D61—41no—
64C2×C22⋊D61—41no—
65C2×C22⋊D61—41no—
66C22×Dic61C2311yescharacteristic
67C22×Dic61C2311yescharacteristic
68C22×Dic61C2311yescharacteristic
69C22×Dic61C2311yescharacteristic
70C22×Dic61C2311yescharacteristic
71C22×Dic61C2311yescharacteristic
72C2×D244—22no—
73C2×D244—41no—
74C2×D244—41no—
75C2×C4×D61—41no—
76C2×C4×D61—41no—
77C2×C4×D61—41no—
78C2×Dic122—41no—
79C2×Dic122—41no—
80C2×Dic122—41no—
81C4⋊C4×C61—41no—
82C22⋊C4×C61—41no—
83C22⋊C4×C61—41no—
84C22⋊C4×C61—41no—
85C22⋊Dic61—41no—
86C22⋊Dic61—41no—
87#11758198—22no—
88#11758198—41no—
89#11758198—41no—
90#11758198—41no—
91#11758198—41no—
92#11758198—41no—
93#11758198—41no—
94#11758198—41no—
95#11758198—41no—
96C4⋊Dic61—41no—
97C4⋊Dic61—41no—
98#11758196—41no—
99C23×C61—21no—
100C23×C61—21no—
101C23×C61—21no—
102C23×C61—21no—
103C23×C61—21no—
104C23×C61—21no—
105C23×C61—21no—
106C23×C61C2411yescharacteristic
107C22×D61—21no—
108C22×D61—21no—
109C22×D61—21no—
110C22×D61—21no—
111C22×D61—21no—
112C22×D61—21no—
113C22×D61—21no—
114C22×D61—21no—
115C22×D61—21no—
116C22×D61—21no—
117C22×D61—21no—
118C22×D61—21no—
119C22×D61—21no—
120C22×D61#4112yes—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
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—21no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C22⋊D61—44no—
140C22⋊D61—44no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—21no—
152C2×Dic61—21no—
153C2×Dic61—21no—
154C2×Dic61—21no—
155C2×Dic61—21no—
156C2×Dic61—21no—
157C2×Dic61—21no—
158C2×Dic61—21no—
159D244—44no—
160C4×D61—44no—
161Dic122—44no—
162C22×C61—41no—
163C22×C61—41no—
164C22×C61—41no—
165C22×C61—41no—
166C22×C61—41no—
167C22×C61—41no—
168C22×C61—41no—
169C22×C61C2×#4111yescharacteristic
170C22×C61H(5,𝔽2)11yescharacteristic
171C22×C61H(5,𝔽2)11yescharacteristic
172C22×C61H(5,𝔽2)11yescharacteristic
173C22×C61H(5,𝔽2)11yescharacteristic
174C22×C61H(5,𝔽2)11yescharacteristic
175C22×C612−1+411yescharacteristic
176C2×D61—22no—
177C2×D61—22no—
178C2×D61—22no—
179C2×D61—41no—
180C2×D61—41no—
181C2×D61—41no—
182C2×D61—41no—
183C2×D61—41no—
184C2×D61—41no—
185C2×D61—41no—
186C2×D61—41no—
187C2×D61—41no—
188C2×D61—41no—
189C2×D61—41no—
190C4×C61—41no—
191C4×C61—41no—
192C4×C61—41no—
193C4×C61—41no—
194C4×C61—41no—
195C4×C61—41no—
196Dic61—41no—
197Dic61—41no—
198Dic61—41no—
199Dic61—41no—
200Dic61—41no—
201Dic61—41no—
202#2824—611nomaximal, Sylow
203C2×C61—81no—
204C2×C61#53811yescharacteristic
205C2×C61#53811yescharacteristic
206C2×C61#53911yescharacteristic
207C2×C61#56011yescharacteristic
208C2×C61H(3,𝔽4)11yescharacteristic
209C2×C61#56211yescharacteristic
210C2×C61#56211yescharacteristic
211D61—42no—
212D61—81no—
213#400—611no—
214#400—611no—
215#397—611no—
216#397D6111yescharacteristic, complemented
217#394—611no—
218#394—611no—
219#394—611no—
220#394—611no—
221#393—611no—
222#393—611no—
223#393—611no—
224#392—611no—
225#386—611no—
226#386—611no—
227#385—611no—
228C61#282411yescharacteristic, complemented, Sylow
229C22×Q8—611no—
230C22×D4—611no—
231C22×D4—611no—
232C22×D4—611no—
233C23×C4—611no—
234C2×C4⋊C4—611no—
235C2×C4⋊C4—611no—
236C2×C4⋊C4—611no—
237C2×C4⋊C4C2×D6111yescharacteristic
238C2×C22⋊C4—611no—
239C2×C22⋊C4—611no—
240C2×C22⋊C4—611no—
241C2×C22⋊C4—611no—
242C2×C22⋊C4—611no—
243C2×C22⋊C4—611no—
244C2×C22⋊C4—611no—
245C2×C22⋊C4—611no—
246C2×C22⋊C4—611no—
247C2×C22⋊C4—611no—
248C2×C22⋊C4—611no—
249C2×C22⋊C4C2×D6111yescharacteristic
250C2×C22⋊C4C2×D6111yescharacteristic
251C2×C22⋊C4C2×D6111yescharacteristic
252#95—611no—
253#95—611no—
254#95—611no—
255#95—611no—
256#95—611no—
257#95—611no—
258#95—611no—
259#95—611no—
260#95—611no—
261#95C2×D6111yescharacteristic
262#95C2×D6111yescharacteristic
263#95C2×D6111yescharacteristic
264C24—611no—
265C24—611no—
266C24C22×D6111yescharacteristic
267C2×Q8—2441no—
268C2×Q8—2441no—
269C2×Q8—2441no—
270C2×D4—1222no—
271C2×D4—1222no—
272C2×D4—2441no—
273C2×D4—2441no—
274C2×D4—2441no—
275C2×D4—2441no—
276C2×D4—2441no—
277C2×D4—2441no—
278C2×D4—2441no—
279C22×C4—611no—
280C22×C4—611no—
281C22×C4—611no—
282C22×C4—611no—
283C22×C4—611no—
284C22×C4—611no—
285C22×C4—2441no—
286C22×C4—2441no—
287C22×C4—2441no—
288C22×C4C22×D6111yescharacteristic
289C22×C4C22×D6111yescharacteristic
290C22×C4C22×D6111yescharacteristic
291C22×C4C22×D6111yescharacteristic
292C22×C4C22×D6111yescharacteristic
293C22×C4C22×D6111yescharacteristic
294C4⋊C4—41no—
295C4⋊C4—2441no—
296C4⋊C4—2441no—
297C4⋊C4—2441no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—41no—
301C22⋊C4—1222no—
302C22⋊C4—2441no—
303C22⋊C4—2441no—
304C22⋊C4—2441no—
305C22⋊C4—2441no—
306C22⋊C4—2441no—
307C22⋊C4—2441no—
308C22⋊C4—2441no—
309C22⋊C4—2441no—
310C22⋊C4—2441no—
311C22⋊C4—2441no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—612no—
320C23—1221no—
321C23—1221no—
322C23—1221no—
323C23—1221no—
324C23—1221no—
325C23—1221no—
326C23—1221no—
327C23—1221no—
328C23—1221no—
329C23—1221no—
330C23—1221no—
331C23—1221no—
332C23—1221no—
333C23C23×D6111yescharacteristic
334Q8—2444no—
335D4—2444no—
336D4—2444no—
337D4—2444no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—1221no—
357C2×C4—1221no—
358C2×C4—1221no—
359C2×C4—1221no—
360C2×C4—1221no—
361C2×C4—1221no—
362C2×C4—1221no—
363C2×C4—1221no—
364C2×C4—1221no—
365C2×C4—1221no—
366C2×C4—1221no—
367C2×C4—1221no—
368C2×C4—1221no—
369C2×C4—1221no—
370C2×C4—1221no—
371C2×C4—1221no—
372C2×C4—1221no—
373C2×C4—1221no—
374C2×C4—2444no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—1222no—
383C22—1222no—
384C22—1222no—
385C22—2441no—
386C22—2441no—
387C22—2441no—
388C22—2441no—
389C22—2441no—
390C22—2441no—
391C22—2441no—
392C22—2441no—
393C22—2441no—
394C22—2441no—
395C22—2441no—
396C22#41×D6111yescharacteristic
397C22#1451982211yescharacteristic
398C22#1451982211yescharacteristic
399C22#1451982311yescharacteristic
400C22#1451982311yescharacteristic
401C22#1451982311yescharacteristic
402C22#1451982411yescharacteristic
403C4—41no—
404C4—41no—
405C4—41no—
406C4—41no—
407C4—41no—
408C4—41no—
409C4—2441no—
410C4—2441no—
411C4—2441no—
412C4—2441no—
413C4—2441no—
414C4—2441no—
415C2—81no—
416C2—4881no—
417C2—2442no—
418C2#1684034411yescharacteristic
419C2#1684035111yescharacteristic
420C2#1684035311yescharacteristic
421C2#1684050211yescharacteristic
422C2#1684050411yescharacteristic
423C2#1684050911yescharacteristic
424C2#1684050911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#397C2
hypercenter#397D61
hypocenterC61#2824
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. #16839704C2semidirect
2. #16839701C2semidirect
3. #16839689C2semidirect
4. #16839679C2semidirect
5. #16839678C2semidirect
6. #16839678C2semidirect
7. #16839677C2semidirect
8. #16839675C2semidirect
9. #16839675C2semidirect
10. #16839674C2semidirect
12. #16839640C2semidirect
13. #16839638C2semidirect
14. #16839636C2semidirect
15. C61×#397C2semidirect
216. #397D61semidirect
228. C61#2824semidirect