Finite Group Databasebeta

← #21452840

Subgroups — #21452840

Order 7808.

528 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519757C211yesmaximal, characteristic, complemented
2C2×#14519755C211yesmaximal, characteristic, complemented
3#16839697C211yesmaximal, characteristic, complemented
4#16839697C211yesmaximal, characteristic, complemented
5#16839695C211yesmaximal, characteristic, complemented
6#16839686C211yesmaximal, characteristic, complemented
7#16839684C211yesmaximal, characteristic, complemented
8#16839666C211yesmaximal, characteristic, complemented
9#16839663C211yesmaximal, characteristic
10#16839659C211yesmaximal, characteristic, complemented
11#16839640C211yesmaximal, characteristic
12#16839640C211yesmaximal, characteristic
13#16839636C211yesmaximal, characteristic, complemented
14#16839633C211yesmaximal, characteristic, complemented
15C61×#398C211yesmaximal, characteristic, complemented
16C22×Dic122C2211yescharacteristic
17C22×D244C2211yescharacteristic
18C22×C4×D61C2211yescharacteristic
19C22×C4×D61C2211yescharacteristic
20#14519757—24no—
21#14519755—24no—
22C2×C4⋊Dic61C2211yescharacteristic
23C2×C4⋊Dic61C2211yescharacteristic
24C2×#11758196C2211yescharacteristic
25C2×#11758196C2211yescharacteristic
26C2×#11758196C2211yescharacteristic
27C2×#11758196C2211yescharacteristic
28C2×#11758196C2211yescharacteristic
29C2×#11758196C2211yescharacteristic
30C2×#11758198C2211yescharacteristic
31C2×#11758198C2211yescharacteristic
32C2×#11758198C2211yescharacteristic
33C2×#11758198C2211yescharacteristic
34C2×#11758198C2211yescharacteristic
35C2×#11758198C2211yescharacteristic
36C2×#11758198C2211yescharacteristic
37C2×#11758198C2211yescharacteristic
38C2×#11758198C2211yescharacteristic
39C2×#11758198C2211yescharacteristic
40C2×C4×Dic61C2211yescharacteristic
41#14519684C2211yescharacteristic
42#14519684C2211yescharacteristic
43#14519684C2211yescharacteristic
44#14519684C2211yescharacteristic
45#14519684C2211yescharacteristic
46C2×C4⋊C4×C61C2211yescharacteristic
47C2×C4⋊C4×C61C2211yescharacteristic
48C2×C4⋊C4×C61C2211yescharacteristic
49C2×C4⋊C4×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—41no—
69C2×D244—41no—
70C2×D244Q814yescomplemented
71C2×C4×D61—22no—
72C2×C4×D61—22no—
73C2×C4×D61—41no—
74C2×C4×D61—41no—
75C2×C4×D61—41no—
76C2×C4×D61—41no—
77C2×Dic122—41no—
78C2×Dic122—41no—
79C2×Dic122D414yescomplemented
80C4⋊C4×C61—22no—
81C4⋊C4×C61—22no—
82C4⋊C4×C61—41no—
83C4⋊C4×C61—41no—
84#11758198—22no—
85#11758198—22no—
86#11758198—22no—
87#11758198—22no—
88#11758198—22no—
89#11758198—22no—
90#11758198—41no—
91#11758198—41no—
92#11758198—41no—
93#11758198—41no—
94C4⋊Dic61—22no—
95C4⋊Dic61—22no—
96#11758196—22no—
97#11758196—22no—
98#11758196—22no—
99#11758196—41no—
100#11758196—41no—
101#11758196—41no—
102C4×Dic61—41no—
103C23×C61C2411yescharacteristic
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—21no—
114C22×D61—21no—
115C22×D61—21no—
116C22×D61C2×Q812yes—
117C22×D61C2×Q812yes—
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×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61C2×D412yes—
138C2×C4×C61C2×Q812yes—
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—21no—
153C2×Dic61—21no—
154C2×Dic61C2×D412yes—
155C2×Dic61C2×D412yes—
156C2×Dic61#4112yes—
157D244—44no—
158C4×D61—44no—
159C4×D61—44no—
160Dic122—44no—
161C22×C61C22×D411yescharacteristic
162C22×C61C22×Q811yescharacteristic
163C22×C61C2×#4111yescharacteristic
164C22×C61H(5,𝔽2)11yescharacteristic
165C22×C61H(5,𝔽2)11yescharacteristic
166C22×C61H(5,𝔽2)11yescharacteristic
167C22×C612−1+411yescharacteristic
168C2×D61—22no—
169C2×D61—22no—
170C2×D61—22no—
171C2×D61—22no—
172C2×D61—22no—
173C2×D61—22no—
174C2×D61—41no—
175C2×D61—41no—
176C2×D61—41no—
177C2×D61—41no—
178C2×D61—41no—
179C2×D61—41no—
180C2×D61—41no—
181C2×D61—41no—
182C4×C61—22no—
183C4×C61—22no—
184C4×C61—41no—
185C4×C61—41no—
186C4×C61—41no—
187C4×C61—41no—
188C4×C61—41no—
189Dic61—22no—
190Dic61—22no—
191Dic61—22no—
192Dic61—41no—
193Dic61—41no—
194Dic61—41no—
195#2732—611nomaximal, Sylow
196C2×C61#53411yescharacteristic
197C2×C61#53911yescharacteristic
198C2×C61#54311yescharacteristic
199C2×C61D4×Q811yescharacteristic
200C2×C61#55011yescharacteristic
201C2×C61#55411yescharacteristic
202C2×C61#56211yescharacteristic
203D61—42no—
204D61—42no—
205C2×C22⋊Q8—611no—
206C2×C22⋊Q8—611no—
207#399—611no—
208#399—611no—
209#398—611no—
210#398D6111yescharacteristic, complemented
211#396—611no—
212#396—611no—
213#391—611no—
214#390—611no—
215#389—611no—
216#386—611no—
217#386—611no—
218#385—611no—
219#385—611no—
220C61#273211yescharacteristic, complemented, Sylow
221C22×Q8—611no—
222C22×D4—611no—
223C23×C4—611no—
224C23×C4—611no—
225C22⋊Q8—1224no—
226C22⋊Q8—1224no—
227C2×C4⋊C4—611no—
228C2×C4⋊C4—611no—
229C2×C4⋊C4—611no—
230C2×C4⋊C4—611no—
231C2×C4⋊C4—611no—
232C2×C4⋊C4—611no—
233C2×C4⋊C4—611no—
234C2×C4⋊C4—611no—
235C2×C4⋊C4C2×D6111yescharacteristic
236C2×C4⋊C4C2×D6111yescharacteristic
237C2×C4⋊C4C2×D6111yescharacteristic
238C2×C4⋊C4C2×D6111yescharacteristic
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×C42—611no—
250#95—611no—
251#95—611no—
252#95—611no—
253#95—611no—
254#95—611no—
255#95C2×D6111yescharacteristic
256#95C2×D6111yescharacteristic
257#95C2×D6111yescharacteristic
258C24—611no—
259C24—611no—
260C2×Q8—614no—
261C2×Q8—2441no—
262C2×Q8—2441no—
263C2×D4—614no—
264C2×D4—2441no—
265C2×D4—2441no—
266C22×C4—611no—
267C22×C4—611no—
268C22×C4—611no—
269C22×C4—611no—
270C22×C4—611no—
271C22×C4—611no—
272C22×C4—1222no—
273C22×C4—1222no—
274C22×C4—2441no—
275C22×C4—2441no—
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—41no—
288C4⋊C4—41no—
289C4⋊C4—1222no—
290C4⋊C4—1222no—
291C4⋊C4—1222no—
292C4⋊C4—1222no—
293C4⋊C4—1222no—
294C4⋊C4—2441no—
295C4⋊C4—2441no—
296C4⋊C4—2441no—
297C22⋊C4—1222no—
298C22⋊C4—1222no—
299C22⋊C4—1222no—
300C22⋊C4—1222no—
301C22⋊C4—1222no—
302C22⋊C4—1222no—
303C22⋊C4—2441no—
304C22⋊C4—2441no—
305C22⋊C4—2441no—
306C22⋊C4—2441no—
307C42—2441no—
308C23—612no—
309C23—612no—
310C23—1221no—
311C23—1221no—
312C23—1221no—
313C23—1221no—
314C23—1221no—
315C23—1221no—
316C23—1221no—
317C23—1221no—
318C23—1221no—
319C23—1221no—
320C23—1221no—
321C23—1221no—
322C23C23×D6111yescharacteristic
323Q8—2444no—
324D4—2444no—
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—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—612no—
345C2×C4—612no—
346C2×C4—612no—
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—1221no—
356C2×C4—1221no—
357C2×C4—1221no—
358C2×C4—1221no—
359C2×C4—1221no—
360C2×C4—1221no—
361C2×C4—1221no—
362C2×C4—2444no—
363C2×C4—2444no—
364C2×C4D4×D6112yes—
365C2×C4Q8×D6112yes—
366C22—1222no—
367C22—1222no—
368C22—1222no—
369C22—1222no—
370C22—1222no—
371C22—1222no—
372C22—2441no—
373C22—2441no—
374C22—2441no—
375C22—2441no—
376C22—2441no—
377C22—2441no—
378C22—2441no—
379C22—2441no—
380C22C2×D4×D6111yescharacteristic
381C22C2×Q8×D6111yescharacteristic
382C22#41×D6111yescharacteristic
383C22#1451982211yescharacteristic
384C22#1451982311yescharacteristic
385C22#1451982311yescharacteristic
386C22#1451982511yescharacteristic
387C4—22no—
388C4—22no—
389C4—41no—
390C4—41no—
391C4—41no—
392C4—41no—
393C4—41no—
394C4—1222no—
395C4—1222no—
396C4—1222no—
397C4—2441no—
398C4—2441no—
399C4—2441no—
400C2—2442no—
401C2—2442no—
402C2#1684032311yescharacteristic
403C2#1684036011yescharacteristic
404C2#1684038711yescharacteristic
405C2#1684042711yescharacteristic
406C2#1684043011yescharacteristic
407C2#1684046811yescharacteristic
408C2#1684050811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#398C2
hypercenter#398D61
hypocenterC61#2732
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C2×#14519757C2semidirect
2. C2×#14519755C2semidirect
3. #16839697C2semidirect
4. #16839697C2semidirect
5. #16839695C2semidirect
6. #16839686C2semidirect
7. #16839684C2semidirect
8. #16839666C2semidirect
10. #16839659C2semidirect
13. #16839636C2semidirect
14. #16839633C2semidirect
15. C61×#398C2semidirect
70. C2×D244Q8semidirect
79. C2×Dic122D4semidirect
210. #398D61semidirect
220. C61#2732semidirect