Finite Group Databasebeta

← #21452161

Subgroups — #21452161

Order 7808.

568 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519760C211yesmaximal, characteristic
2C2×#14519759C211yesmaximal, characteristic
3C2×#14519756C211yesmaximal, characteristic, complemented
4C2×#14519755C211yesmaximal, characteristic, complemented
5#16839696C211yesmaximal, characteristic, complemented
6#16839695C211yesmaximal, characteristic, complemented
7#16839691C211yesmaximal, characteristic, complemented
8#16839690C211yesmaximal, characteristic, complemented
9#16839683C211yesmaximal, characteristic, complemented
10#16839678C211yesmaximal, characteristic
11#16839654C211yesmaximal, characteristic, complemented
12#16839650C211yesmaximal, characteristic, complemented
13#16839633C211yesmaximal, characteristic, complemented
14#16839631C211yesmaximal, characteristic, complemented
15C61×#385C211yesmaximal, characteristic, complemented
16C22×Dic122C2211yescharacteristic
17C22×C22⋊D61C2211yescharacteristic
18C22×C4×D61C2211yescharacteristic
19#14519760—24no—
20#14519759—24no—
21#14519756—24no—
22#14519755—24no—
23C2×C4⋊Dic61C2211yescharacteristic
24C2×C4⋊Dic61C2211yescharacteristic
25C2×C4⋊Dic61C2211yescharacteristic
26C2×#11758196C2211yescharacteristic
27C2×#11758196C2211yescharacteristic
28C2×#11758196C2211yescharacteristic
29C2×#11758196C2211yescharacteristic
30C2×#11758196C2211yescharacteristic
31C2×#11758196C2211yescharacteristic
32C2×#11758196C2211yescharacteristic
33C2×C22⋊Dic61C2211yescharacteristic
34C2×C22⋊Dic61C2211yescharacteristic
35C2×C22⋊Dic61C2211yescharacteristic
36C2×#11758198C2211yescharacteristic
37C2×#11758198C2211yescharacteristic
38C2×#11758198C2211yescharacteristic
39C2×#11758198C2211yescharacteristic
40C2×#11758198C2211yescharacteristic
41C2×C4×Dic61C2211yescharacteristic
42#14519684C2211yescharacteristic
43#14519684C2211yescharacteristic
44#14519684C2211yescharacteristic
45#14519684C2211yescharacteristic
46#14519684C2211yescharacteristic
47#14519684C2211yescharacteristic
48C23×C4×C61C2211yescharacteristic
49C2×C4⋊C4×C61C2211yescharacteristic
50C2×C4⋊C4×C61C2211yescharacteristic
51C2×C22⋊C4×C61C2211yescharacteristic
52C2×C22⋊C4×C61C2211yescharacteristic
53#95×C61C2211yescharacteristic
54#95×C61C2211yescharacteristic
55C24×C61C2311yescharacteristic
56C23×D61C2311yescharacteristic
57C22×C4×C61—22no—
58C22×C4×C61—22no—
59C22×C4×C61—41no—
60C22×C4×C61C2311yescharacteristic
61C22×C4×C61C2311yescharacteristic
62C22×C4×C61C2311yescharacteristic
63C22×C4×C61C2311yescharacteristic
64C22×C4×C61C2311yescharacteristic
65C22×C4×C61C2311yescharacteristic
66C2×C22⋊D61—22no—
67C2×C22⋊D61—22no—
68C2×C22⋊D61—41no—
69C22×Dic61C2311yescharacteristic
70C22×Dic61C2311yescharacteristic
71C22×Dic61C2311yescharacteristic
72C22×Dic61C2311yescharacteristic
73C22×Dic61C2311yescharacteristic
74C22×Dic61C2311yescharacteristic
75C22×Dic61C2311yescharacteristic
76C2×C4×D61—22no—
77C2×C4×D61—22no—
78C2×C4×D61—41no—
79C2×Dic122—22no—
80C2×Dic122—22no—
81C2×Dic122—41no—
82C4⋊C4×C61—22no—
83C4⋊C4×C61—41no—
84C22⋊C4×C61—22no—
85C22⋊C4×C61—22no—
86C22⋊Dic61—22no—
87C22⋊Dic61—22no—
88C22⋊Dic61D414yes—
89#11758198—22no—
90#11758198—22no—
91#11758198—22no—
92#11758198—22no—
93#11758198D414yes—
94C4⋊Dic61—22no—
95C4⋊Dic61—22no—
96C4⋊Dic61—41no—
97#11758196—22no—
98#11758196—22no—
99#11758196—22no—
100#11758196—22no—
101#11758196—22no—
102#11758196—22no—
103#11758196—22no—
104C4×Dic61—22no—
105C23×C61—21no—
106C23×C61—21no—
107C23×C61—21no—
108C23×C61—21no—
109C23×C61—21no—
110C23×C61—21no—
111C23×C61C2×D412yes—
112C23×C61C2411yescharacteristic
113C22×D61—21no—
114C22×D61—21no—
115C22×D61—21no—
116C22×D61—21no—
117C22×D61—21no—
118C22×D61—21no—
119C22×D61C2×D412yes—
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×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—44no—
137C2×C4×C61C2×D412yes—
138C2×C4×C61#4112yes—
139C22⋊D61—44no—
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—21no—
153C2×Dic61—21no—
154C2×Dic61—21no—
155C2×Dic61—21no—
156C2×Dic61—21no—
157C2×Dic61—21no—
158C2×Dic61C2×D412yes—
159C2×Dic61C2×D412yes—
160C2×Dic61C2×D412yes—
161C4×D61—44no—
162Dic122—44no—
163C22×C61—22no—
164C22×C61—22no—
165C22×C61—22no—
166C22×C61—41no—
167C22×C61—41no—
168C22×C61—41no—
169C22×C61—41no—
170C22×C61C22×D411yescharacteristic
171C22×C61C22×D411yescharacteristic
172C22×C61C2×#4111yescharacteristic
173C22×C61H(5,𝔽2)11yescharacteristic
174C22×C612−1+411yescharacteristic
175C22×C612−1+411yescharacteristic
176C22×C612−1+411yescharacteristic
177C2×D61—22no—
178C2×D61—22no—
179C2×D61—22no—
180C2×D61—41no—
181C2×D61—41no—
182C2×D61—41no—
183C2×D61—41no—
184C4×C61—22no—
185C4×C61—22no—
186C4×C61—41no—
187C4×C61—41no—
188C4×C61—41no—
189C4×C61—41no—
190Dic61—22no—
191Dic61—22no—
192Dic61—22no—
193Dic61—41no—
194Dic61—41no—
195Dic61—41no—
196Dic61—41no—
197#2680—611nomaximal, Sylow
198C2×C61—42no—
199C2×C61#53611yescharacteristic
200C2×C61#53611yescharacteristic
201C2×C61#53911yescharacteristic
202C2×C61D4211yescharacteristic
203C2×C61#54711yescharacteristic
204C2×C61#54711yescharacteristic
205C2×C61#56311yescharacteristic
206D61—42no—
207C2×#123—611no—
208C2×#123—611no—
209C2×C22⋊Q8—611no—
210C2×C22⋊Q8—611no—
211#398—611no—
212#398—611no—
213#397—611no—
214#397—611no—
215#395—611no—
216#394—611no—
217#388—611no—
218#388—611no—
219#385—611no—
220#385D6111yescharacteristic, complemented
221#384—611no—
222C61#268011yescharacteristic, complemented, Sylow
223C22×Q8—611no—
224C22×D4—611no—
225C23×C4—611no—
226C23×C4C2×D6111yescharacteristic
227#123—1224no—
228#123—1224no—
229C22⋊Q8—1224no—
230C22⋊Q8—1224no—
231C2×C4⋊C4—611no—
232C2×C4⋊C4—611no—
233C2×C4⋊C4—611no—
234C2×C4⋊C4—611no—
235C2×C4⋊C4—611no—
236C2×C4⋊C4—611no—
237C2×C4⋊C4—611no—
238C2×C4⋊C4—611no—
239C2×C4⋊C4—611no—
240C2×C4⋊C4—611no—
241C2×C4⋊C4C2×D6111yescharacteristic
242C2×C4⋊C4C2×D6111yescharacteristic
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⋊C4—611no—
250C2×C22⋊C4—611no—
251C2×C22⋊C4C2×D6111yescharacteristic
252C2×C22⋊C4C2×D6111yescharacteristic
253C2×C42—611no—
254#95—611no—
255#95—611no—
256#95—611no—
257#95—611no—
258#95—611no—
259#95—611no—
260#95C2×D6111yescharacteristic
261#95C2×D6111yescharacteristic
262C24—611no—
263C24C22×D6111yescharacteristic
264C2×Q8—1222no—
265C2×Q8—1222no—
266C2×Q8—2441no—
267C2×D4—1222no—
268C2×D4—1222no—
269C2×D4—2441no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—41no—
273C22×C4—611no—
274C22×C4—611no—
275C22×C4—611no—
276C22×C4—611no—
277C22×C4—611no—
278C22×C4—611no—
279C22×C4—611no—
280C22×C4—1222no—
281C22×C4—1222no—
282C22×C4—2441no—
283C22×C4C22×D6111yescharacteristic
284C22×C4C22×D6111yescharacteristic
285C22×C4C22×D6111yescharacteristic
286C22×C4C22×D6111yescharacteristic
287C22×C4C22×D6111yescharacteristic
288C22×C4C22×D6111yescharacteristic
289C4⋊C4—22no—
290C4⋊C4—41no—
291C4⋊C4—1222no—
292C4⋊C4—1222no—
293C4⋊C4—1222no—
294C4⋊C4—1222no—
295C4⋊C4—1222no—
296C4⋊C4—1222no—
297C4⋊C4—1222no—
298C4⋊C4—1222no—
299C4⋊C4—1222no—
300C4⋊C4—2441no—
301C22⋊C4—22no—
302C22⋊C4—22no—
303C22⋊C4—614no—
304C22⋊C4—614no—
305C22⋊C4—1222no—
306C22⋊C4—1222no—
307C22⋊C4—1222no—
308C22⋊C4—1222no—
309C22⋊C4—1222no—
310C22⋊C4—1222no—
311C42—1222no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—612no—
319C23—1221no—
320C23—1221no—
321C23—1221no—
322C23—1221no—
323C23—1221no—
324C23—1221no—
325C23D4×D6112yes—
326C23C23×D6111yescharacteristic
327Q8—2444no—
328D4—2444no—
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—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—44no—
346C2×C4—612no—
347C2×C4—612no—
348C2×C4—612no—
349C2×C4—1221no—
350C2×C4—1221no—
351C2×C4—1221no—
352C2×C4—1221no—
353C2×C4—1221no—
354C2×C4—1221no—
355C2×C4—1221no—
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—2444no—
368C2×C4#1175822212yes—
369C2×C4D4×D6112yes—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—1222no—
378C22—1222no—
379C22—1222no—
380C22—2441no—
381C22—2441no—
382C22—2441no—
383C22—2441no—
384C22C2×D4×D6111yescharacteristic
385C22C2×D4×D6111yescharacteristic
386C22C2×#1175822211yescharacteristic
387C22#1451982211yescharacteristic
388C22#1451982411yescharacteristic
389C22#1451982411yescharacteristic
390C22#1451982511yescharacteristic
391C4—22no—
392C4—22no—
393C4—41no—
394C4—41no—
395C4—41no—
396C4—41no—
397C4—1222no—
398C4—1222no—
399C4—1222no—
400C4—2441no—
401C4—2441no—
402C4—2441no—
403C4—2441no—
404C2—42no—
405C2—2442no—
406C2#1684033411yescharacteristic
407C2#1684033511yescharacteristic
408C2#1684035411yescharacteristic
409C2#1684039411yescharacteristic
410C2#1684041311yescharacteristic
411C2#1684041711yescharacteristic
412C2#1684051311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#385C2
hypercenter#385D61
hypocenterC61#2680
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
3. C2×#14519756C2semidirect
4. C2×#14519755C2semidirect
5. #16839696C2semidirect
6. #16839695C2semidirect
7. #16839691C2semidirect
8. #16839690C2semidirect
9. #16839683C2semidirect
11. #16839654C2semidirect
12. #16839650C2semidirect
13. #16839633C2semidirect
14. #16839631C2semidirect
15. C61×#385C2semidirect
220. #385D61semidirect
222. C61#2680semidirect