Finite Group Databasebeta

← #21450048

Subgroups — #21450048

Order 7808.

518 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519772C211yesmaximal, characteristic, complemented
2C2×#14519735C211yesmaximal, characteristic, complemented
3#16839699C211yesmaximal, characteristic, complemented
4#16839699C211yesmaximal, characteristic, complemented
5#16839694C211yesmaximal, characteristic, complemented
6#16839679C211yesmaximal, characteristic
7#16839664C211yesmaximal, characteristic
8#16839661C211yesmaximal, characteristic, complemented
9#16839654C211yesmaximal, characteristic, complemented
10#16839654C211yesmaximal, characteristic, complemented
11#16839654C211yesmaximal, characteristic, complemented
12#16839640C211yesmaximal, characteristic
13#16839636C211yesmaximal, characteristic, complemented
14C4×C4⋊Dic61C211yesmaximal, characteristic, complemented
15C61×#387C211yesmaximal, characteristic, complemented
16C22×D244C2211yescharacteristic
17C22×C4×D61C2211yescharacteristic
18#14519772—24no—
19#14519735—24no—
20C2×C4⋊Dic61C2211yescharacteristic
21C2×C4⋊Dic61C2211yescharacteristic
22C2×C4⋊Dic61C2211yescharacteristic
23C2×C4⋊Dic61C2211yescharacteristic
24C2×C4⋊Dic61C2211yescharacteristic
25C2×C4⋊Dic61C2211yescharacteristic
26C2×C4⋊Dic61C2211yescharacteristic
27C2×#11758196C2211yescharacteristic
28C2×#11758198C2211yescharacteristic
29C2×#11758198C2211yescharacteristic
30C2×#11758198C2211yescharacteristic
31C2×#11758198C2211yescharacteristic
32C2×#11758198C2211yescharacteristic
33C2×#11758198C2211yescharacteristic
34C2×#11758198C2211yescharacteristic
35C2×#11758198C2211yescharacteristic
36C2×#11758198C2211yescharacteristic
37C2×#11758198C2211yescharacteristic
38C2×#11758198C2211yescharacteristic
39C2×C4×Dic61C2211yescharacteristic
40C2×C4×Dic61C2211yescharacteristic
41C2×C4×Dic61C2211yescharacteristic
42#14519684C2211yescharacteristic
43#14519684C2211yescharacteristic
44#14519684C2211yescharacteristic
45#14519684C2211yescharacteristic
46C2×C4⋊C4×C61C2211yescharacteristic
47C2×C4⋊C4×C61C2211yescharacteristic
48C2×C42×C61C2211yescharacteristic
49#95×C61C2211yescharacteristic
50#95×C61C2211yescharacteristic
51#95×C61C2211yescharacteristic
52#95×C61C2211yescharacteristic
53C23×D61C2311yescharacteristic
54C23×D61C2311yescharacteristic
55C22×C4×C61C2311yescharacteristic
56C22×C4×C61C2311yescharacteristic
57C22×C4×C61C2311yescharacteristic
58C22×C4×C61C2311yescharacteristic
59C22×C4×C61C2311yescharacteristic
60C22×C4×C61C2311yescharacteristic
61C22×C4×C61C2311yescharacteristic
62C22×Dic61C2311yescharacteristic
63C22×Dic61C2311yescharacteristic
64C22×Dic61C2311yescharacteristic
65C22×Dic61C2311yescharacteristic
66C22×Dic61C2311yescharacteristic
67C22×Dic61C2311yescharacteristic
68C2×D244—22no—
69C2×D244—22no—
70C2×D244—41no—
71C2×C4×D61—22no—
72C2×C4×D61—22no—
73C2×C4×D61—22no—
74C4⋊C4×C61—22no—
75C4⋊C4×C61D414yescomplemented
76C42×C61—22no—
77#11758198—22no—
78#11758198—22no—
79#11758198—22no—
80#11758198—22no—
81#11758198—22no—
82#11758198—22no—
83#11758198—22no—
84#11758198—22no—
85#11758198—22no—
86#11758198—41no—
87#11758198—41no—
88C4⋊Dic61—22no—
89C4⋊Dic61—22no—
90C4⋊Dic61—22no—
91C4⋊Dic61—22no—
92C4⋊Dic61—41no—
93C4⋊Dic61—41no—
94C4⋊Dic61—41no—
95#11758196—22no—
96C4×Dic61—22no—
97C4×Dic61—22no—
98C4×Dic61—22no—
99C23×C61C2411yescharacteristic
100C22×D61—21no—
101C22×D61—21no—
102C22×D61—21no—
103C22×D61—21no—
104C22×D61—21no—
105C22×D61—21no—
106C22×D61—21no—
107C22×D61—21no—
108C22×D61—21no—
109C22×D61—21no—
110C22×D61—21no—
111C22×D61—21no—
112C22×D61—21no—
113C22×D61#4112yes—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
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×C61C2×D412yes—
131C2×C4×C61C2×D412yes—
132C2×C4×C61C2×D412yes—
133C2×C4×C61#4112yes—
134C2×C4×C61#4112yes—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—21no—
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#4112yes—
153D244—44no—
154C4×D61—28no—
155C22×C61C22×D411yescharacteristic
156C22×C61C2×#4111yescharacteristic
157C22×C61C2×#4111yescharacteristic
158C22×C61C2×#4111yescharacteristic
159C22×C61C2×#4111yescharacteristic
160C22×C61H(5,𝔽2)11yescharacteristic
161C22×C612−1+411yescharacteristic
162C2×D61—22no—
163C2×D61—22no—
164C2×D61—22no—
165C2×D61—41no—
166C2×D61—41no—
167C2×D61—41no—
168C2×D61—41no—
169C2×D61—41no—
170C2×D61—41no—
171C2×D61—41no—
172C2×D61—41no—
173C2×D61—41no—
174C2×D61—41no—
175C2×D61—41no—
176C4×C61—22no—
177C4×C61—22no—
178C4×C61—22no—
179C4×C61—22no—
180C4×C61—22no—
181C4×C61—41no—
182C4×C61—41no—
183Dic61—22no—
184Dic61—41no—
185Dic61—41no—
186Dic61—41no—
187Dic61—41no—
188Dic61—41no—
189#2479—611nomaximal, Sylow
190C2×C61#52511yescharacteristic
191C2×C61#52911yescharacteristic
192C2×C61#54211yescharacteristic
193C2×C61#54711yescharacteristic
194C2×C61#55011yescharacteristic
195C2×C61#55111yescharacteristic
196C2×C61#55211yescharacteristic
197D61—42no—
198D61—81no—
199C2×#126—611no—
200C2×#117—611no—
201#399—611no—
202#399—611no—
203#398—611no—
204#394—611no—
205#390—611no—
206#389—611no—
207#388—611no—
208#388—611no—
209#388—611no—
210#387D6111yescharacteristic, complemented
211#386—611no—
212#385—611no—
213C4×C4⋊C4—611no—
214C61#247911yescharacteristic, complemented, Sylow
215C22×D4—611no—
216C23×C4—611no—
217#126—1224no—
218#117—1224no—
219C2×C4⋊C4—611no—
220C2×C4⋊C4—611no—
221C2×C4⋊C4—611no—
222C2×C4⋊C4—611no—
223C2×C4⋊C4—611no—
224C2×C4⋊C4—611no—
225C2×C4⋊C4—611no—
226C2×C4⋊C4—611no—
227C2×C4⋊C4C2×D6111yescharacteristic
228C2×C4⋊C4C2×D6111yescharacteristic
229C2×C22⋊C4—611no—
230C2×C22⋊C4—611no—
231C2×C22⋊C4—611no—
232C2×C22⋊C4—611no—
233C2×C22⋊C4—611no—
234C2×C22⋊C4—611no—
235C2×C22⋊C4—611no—
236C2×C22⋊C4—611no—
237C2×C22⋊C4—611no—
238C2×C22⋊C4—611no—
239C2×C22⋊C4—611no—
240C2×C42—611no—
241C2×C42—611no—
242C2×C42—611no—
243C2×C42C2×D6111yescharacteristic
244#95—611no—
245#95—611no—
246#95—611no—
247#95—611no—
248#95C2×D6111yescharacteristic
249#95C2×D6111yescharacteristic
250#95C2×D6111yescharacteristic
251#95C2×D6111yescharacteristic
252C24—611no—
253C24—611no—
254C2×D4—1222no—
255C2×D4—1222no—
256C2×D4—2441no—
257C22×C4—611no—
258C22×C4—611no—
259C22×C4—611no—
260C22×C4—611no—
261C22×C4—611no—
262C22×C4—611no—
263C22×C4—1222no—
264C22×C4—1222no—
265C22×C4—1222no—
266C22×C4C22×D6111yescharacteristic
267C22×C4C22×D6111yescharacteristic
268C22×C4C22×D6111yescharacteristic
269C22×C4C22×D6111yescharacteristic
270C22×C4C22×D6111yescharacteristic
271C22×C4C22×D6111yescharacteristic
272C22×C4C22×D6111yescharacteristic
273C4⋊C4—22no—
274C4⋊C4—1222no—
275C4⋊C4—1222no—
276C4⋊C4—1222no—
277C4⋊C4—1222no—
278C4⋊C4—1222no—
279C4⋊C4—2441no—
280C4⋊C4—2441no—
281C4⋊C4—2441no—
282C4⋊C4D24414yescomplemented
283C22⋊C4—1222no—
284C22⋊C4—1222no—
285C22⋊C4—1222no—
286C22⋊C4—1222no—
287C22⋊C4—1222no—
288C22⋊C4—1222no—
289C22⋊C4—1222no—
290C22⋊C4—1222no—
291C22⋊C4—1222no—
292C22⋊C4—2441no—
293C22⋊C4—2441no—
294C42—22no—
295C42—1222no—
296C42—1222no—
297C42—1222no—
298C23—612no—
299C23—1221no—
300C23—1221no—
301C23—1221no—
302C23—1221no—
303C23—1221no—
304C23—1221no—
305C23—1221no—
306C23—1221no—
307C23—1221no—
308C23—1221no—
309C23—1221no—
310C23—1221no—
311C23—1221no—
312C23C23×D6111yescharacteristic
313D4—2444no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—612no—
331C2×C4—1228no—
332C2×C4—1221no—
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—1221no—
342C2×C4—1221no—
343C2×C4—1221no—
344C2×C4—1221no—
345C2×C4—1221no—
346C2×C4—1221no—
347C2×C4—1221no—
348C2×C4—1221no—
349C2×C4C2×D24412yes—
350C2×C4C2×D24412yes—
351C2×C4C2×D24412yes—
352C2×C4#1175822412yes—
353C2×C4#1175822612yes—
354C22—1222no—
355C22—1222no—
356C22—1222no—
357C22—2441no—
358C22—2441no—
359C22—2441no—
360C22—2441no—
361C22—2441no—
362C22—2441no—
363C22—2441no—
364C22—2441no—
365C22—2441no—
366C22—2441no—
367C22—2441no—
368C22C22×D24411yescharacteristic
369C22#41×D6111yescharacteristic
370C22#41×D6111yescharacteristic
371C22C2×#1175822411yescharacteristic
372C22C2×#1175822611yescharacteristic
373C22#1451982311yescharacteristic
374C22#1451982411yescharacteristic
375C4—22no—
376C4—22no—
377C4—22no—
378C4—22no—
379C4—22no—
380C4—41no—
381C4—41no—
382C4—1222no—
383C4—2441no—
384C4—2441no—
385C4—2441no—
386C4—2441no—
387C4—2441no—
388C2—4881no—
389C2—2442no—
390C2#1684027411yescharacteristic
391C2#1684029811yescharacteristic
392C2#1684037811yescharacteristic
393C2#1684041611yescharacteristic
394C2#1684043411yescharacteristic
395C2#1684043511yescharacteristic
396C2#1684045011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#387C2
hypercenter#387D61
hypocenterC61#2479
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
1. C2×#14519772C2semidirect
2. C2×#14519735C2semidirect
3. #16839699C2semidirect
4. #16839699C2semidirect
5. #16839694C2semidirect
8. #16839661C2semidirect
9. #16839654C2semidirect
10. #16839654C2semidirect
11. #16839654C2semidirect
13. #16839636C2semidirect
14. C4×C4⋊Dic61C2semidirect
15. C61×#387C2semidirect
75. C4⋊C4×C61D4semidirect
210. #387D61semidirect
214. C61#2479semidirect
282. C4⋊C4D244semidirect