Finite Group Databasebeta

← #21450146

Subgroups — #21450146

Order 7808.

546 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519762C211yesmaximal, characteristic
2C2×#14519757C211yesmaximal, characteristic, complemented
3#16839704C211yesmaximal, characteristic, complemented
4#16839689C211yesmaximal, characteristic, complemented
5#16839675C211yesmaximal, characteristic, complemented
6#16839666C211yesmaximal, characteristic, complemented
7#16839654C211yesmaximal, characteristic, complemented
8#16839652C211yesmaximal, characteristic, complemented
9#16839640C211yesmaximal, characteristic
10#16839640C211yesmaximal, characteristic
11#16839627C211yesmaximal, characteristic, complemented
12#16839624C211yesmaximal, characteristic, complemented
13#16839609C211yesmaximal, characteristic, complemented
14#95×D61C211yesmaximal, characteristic, complemented
15C61×#400C211yesmaximal, characteristic, complemented
16C22×Dic122C2211yescharacteristic
17C22×D244C2211yescharacteristic
18C22×C4×D61C2211yescharacteristic
19C22×C4×D61C2211yescharacteristic
20C22×C4×D61C2211yescharacteristic
21#14519762—24no—
22#14519757—24no—
23C2×C4⋊Dic61C2211yescharacteristic
24C2×C4⋊Dic61C2211yescharacteristic
25C2×#11758196C2211yescharacteristic
26C2×#11758198C2211yescharacteristic
27C2×#11758198C2211yescharacteristic
28C2×#11758198C2211yescharacteristic
29C2×#11758198C2211yescharacteristic
30C2×#11758198C2211yescharacteristic
31C2×#11758198C2211yescharacteristic
32C2×#11758198C2211yescharacteristic
33C2×#11758198C2211yescharacteristic
34C2×#11758198C2211yescharacteristic
35C2×C4×Dic61C2211yescharacteristic
36C2×C4×Dic61C2211yescharacteristic
37#14519684C2211yescharacteristic
38#14519684C2211yescharacteristic
39#14519684C2211yescharacteristic
40#14519684C2211yescharacteristic
41#14519684C2211yescharacteristic
42#14519684C2211yescharacteristic
43#14519684C2211yescharacteristic
44#14519684C2211yescharacteristic
45#14519684C2211yescharacteristic
46C2×C4⋊C4×C61C2211yescharacteristic
47C2×C4⋊C4×C61C2211yescharacteristic
48#95×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—22no—
71C2×C4×D61—22no—
72C2×C4×D61—22no—
73C2×C4×D61—22no—
74C2×C4×D61—22no—
75C2×C4×D61—22no—
76C2×C4×D61—22no—
77C2×C4×D61—22no—
78C2×C4×D61—41no—
79C2×C4×D61—41no—
80C2×Dic122—22no—
81C2×Dic122—22no—
82C2×Dic122—41no—
83C4⋊C4×C61—22no—
84C4⋊C4×C61—22no—
85#11758198—22no—
86#11758198—22no—
87#11758198—22no—
88#11758198—22no—
89#11758198—22no—
90#11758198—22no—
91#11758198—41no—
92#11758198—41no—
93#11758198D414yes—
94C4⋊Dic61—22no—
95C4⋊Dic61—22no—
96#11758196—22no—
97C4×Dic61—22no—
98C4×Dic61—41no—
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×D61C2×D412yes—
112C22×D61#4112yes—
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×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61C2×D412yes—
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×Dic61C2×D412yes—
152C2×Dic61#4112yes—
153D244—44no—
154C4×D61—44no—
155C4×D61—44no—
156C4×D61—44no—
157Dic122—44no—
158C22×C61C22×D411yescharacteristic
159C22×C61C2×#4111yescharacteristic
160C22×C61C2×#4111yescharacteristic
161C22×C61C2×#4111yescharacteristic
162C22×C61C2×#4111yescharacteristic
163C22×C61H(5,𝔽2)11yescharacteristic
164C22×C612−1+411yescharacteristic
165C2×D61—22no—
166C2×D61—22no—
167C2×D61—22no—
168C2×D61—22no—
169C2×D61—22no—
170C2×D61—22no—
171C2×D61—41no—
172C2×D61—41no—
173C2×D61—41no—
174C2×D61—41no—
175C2×D61—41no—
176C2×D61—41no—
177C2×D61—41no—
178C2×D61#12414yes—
179C4×C61—22no—
180C4×C61—22no—
181C4×C61—41no—
182C4×C61—41no—
183C4×C61—41no—
184C4×C61—41no—
185C4×C61—41no—
186Dic61—22no—
187Dic61—22no—
188Dic61—41no—
189Dic61—41no—
190Dic61—41no—
191Dic61—41no—
192#2488—611nomaximal, Sylow
193C2×C61C2×#12411yescharacteristic
194C2×C61#52911yescharacteristic
195C2×C61#53911yescharacteristic
196C2×C61#54611yescharacteristic
197C2×C61#54711yescharacteristic
198C2×C61#55111yescharacteristic
199C2×C61#55211yescharacteristic
200D61—24no—
201D61—81no—
202C2×#123—611no—
203C2×C22⋊Q8—611no—
204#400—611no—
205#400D6111yescharacteristic, complemented
206#397—611no—
207#393—611no—
208#391—611no—
209#388—611no—
210#388—611no—
211#386—611no—
212#386—611no—
213#382—611no—
214#381—611no—
215C4×C22⋊C4—611no—
216C2×#95—611no—
217C61#248811yescharacteristic, complemented, Sylow
218C22×Q8—611no—
219C22×D4—611no—
220C23×C4—611no—
221C23×C4—611no—
222C23×C4—611no—
223#123—1224no—
224C22⋊Q8—1224no—
225C2×C4⋊C4—611no—
226C2×C4⋊C4—611no—
227C2×C4⋊C4—611no—
228C2×C4⋊C4C2×D6111yescharacteristic
229C2×C4⋊C4C2×D6111yescharacteristic
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×C42—611no—
240C2×C42—611no—
241#95—611no—
242#95—611no—
243#95—611no—
244#95—611no—
245#95—611no—
246#95—611no—
247#95—611no—
248#95—611no—
249#95—611no—
250#95C2×D6111yescharacteristic
251#95C2×D6111yescharacteristic
252#95C2×D6111yescharacteristic
253#95C2×D6111yescharacteristic
254#95C2×D6111yescharacteristic
255C24—611no—
256C24—611no—
257C2×Q8—1222no—
258C2×Q8—1222no—
259C2×Q8—2441no—
260C2×D4—1222no—
261C2×D4—1222no—
262C2×D4—1222no—
263C22×C4—611no—
264C22×C4—611no—
265C22×C4—611no—
266C22×C4—611no—
267C22×C4—611no—
268C22×C4—611no—
269C22×C4—1222no—
270C22×C4—1222no—
271C22×C4—1222no—
272C22×C4—1222no—
273C22×C4—1222no—
274C22×C4—1222no—
275C22×C4—1222no—
276C22×C4—2441no—
277C22×C4—2441no—
278C22×C4C22×D6111yescharacteristic
279C22×C4C22×D6111yescharacteristic
280C22×C4C22×D6111yescharacteristic
281C22×C4C22×D6111yescharacteristic
282C22×C4C22×D6111yescharacteristic
283C22×C4C22×D6111yescharacteristic
284C22×C4C22×D6111yescharacteristic
285C4⋊C4—22no—
286C4⋊C4—22no—
287C4⋊C4—1222no—
288C4⋊C4—1222no—
289C4⋊C4—1222no—
290C22⋊C4—614no—
291C22⋊C4—1222no—
292C22⋊C4—1222no—
293C22⋊C4—1222no—
294C22⋊C4—1222no—
295C22⋊C4—1222no—
296C22⋊C4—1222no—
297C22⋊C4—2441no—
298C22⋊C4—2441no—
299C42—1222no—
300C42—2441no—
301C23—612no—
302C23—612no—
303C23—612no—
304C23—1221no—
305C23—1221no—
306C23—1221no—
307C23—1221no—
308C23—1221no—
309C23—1221no—
310C23—1221no—
311C23—1221no—
312C23—1221no—
313C23—1221no—
314C23—1221no—
315C23C23×D6111yescharacteristic
316Q8—2444no—
317D4—2444no—
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—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—612no—
338C2×C4—612no—
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×C4—1221no—
350C2×C4—1221no—
351C2×C4—1221no—
352C2×C4—1221no—
353C2×C4—1221no—
354C2×C4—1221no—
355C2×C4—2444no—
356C2×C4—2444no—
357C2×C4—2444no—
358C2×C4D4×D6112yes—
359C2×C4#1175822612yes—
360C22—614no—
361C22—1222no—
362C22—1222no—
363C22—1222no—
364C22—1222no—
365C22—1222no—
366C22—1222no—
367C22—2441no—
368C22—2441no—
369C22—2441no—
370C22—2441no—
371C22—2441no—
372C22—2441no—
373C22—2441no—
374C22C2×D4×D6111yescharacteristic
375C22#41×D6111yescharacteristic
376C22#41×D6111yescharacteristic
377C22#41×D6111yescharacteristic
378C22C2×#1175822611yescharacteristic
379C22#1451982311yescharacteristic
380C22#1451982411yescharacteristic
381C4—22no—
382C4—22no—
383C4—41no—
384C4—41no—
385C4—41no—
386C4—41no—
387C4—41no—
388C4—1222no—
389C4—1222no—
390C4—2441no—
391C4—2441no—
392C4—2441no—
393C4—2441no—
394C2—1224no—
395C2—4881no—
396C2#124×D6111yescharacteristic
397C2#1684029711yescharacteristic
398C2#1684035311yescharacteristic
399C2#1684040311yescharacteristic
400C2#1684041011yescharacteristic
401C2#1684043711yescharacteristic
402C2#1684045011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#400C2
hypercenter#400D61
hypocenterC61#2488
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
2. C2×#14519757C2semidirect
3. #16839704C2semidirect
4. #16839689C2semidirect
5. #16839675C2semidirect
6. #16839666C2semidirect
7. #16839654C2semidirect
8. #16839652C2semidirect
11. #16839627C2semidirect
12. #16839624C2semidirect
13. #16839609C2semidirect
14. #95×D61C2semidirect
15. C61×#400C2semidirect
205. #400D61semidirect
217. C61#2488semidirect