Finite Group Databasebeta

← #21452574

Subgroups — #21452574

Order 7808.

540 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519767C211yesmaximal, characteristic, complemented
2C2×#14519752C211yesmaximal, characteristic
3#16839699C211yesmaximal, characteristic, complemented
4#16839684C211yesmaximal, characteristic, complemented
5#16839680C211yesmaximal, characteristic, complemented
6#16839680C211yesmaximal, characteristic, complemented
7#16839680C211yesmaximal, characteristic, complemented
8#16839680C211yesmaximal, characteristic, complemented
9#16839664C211yesmaximal, characteristic, complemented
10#16839663C211yesmaximal, characteristic, complemented
11#16839654C211yesmaximal, characteristic, complemented
12#16839653C211yesmaximal, characteristic, complemented
13#16839636C211yesmaximal, characteristic, complemented
14#16839636C211yesmaximal, characteristic, complemented
15C61×#387C211yesmaximal, characteristic, complemented
16C22×D244C2211yescharacteristic
17C22×D244C2211yescharacteristic
18C22×D244C2211yescharacteristic
19C22×C4×D61C2211yescharacteristic
20#14519767—24no—
21#14519752—24no—
22C2×C4⋊Dic61C2211yescharacteristic
23C2×C4⋊Dic61C2211yescharacteristic
24C2×C4⋊Dic61C2211yescharacteristic
25C2×#11758196C2211yescharacteristic
26C2×#11758196C2211yescharacteristic
27C2×#11758196C2211yescharacteristic
28C2×#11758196C2211yescharacteristic
29C2×#11758198C2211yescharacteristic
30C2×#11758198C2211yescharacteristic
31C2×#11758198C2211yescharacteristic
32C2×#11758198C2211yescharacteristic
33C2×#11758198C2211yescharacteristic
34C2×#11758198C2211yescharacteristic
35C2×#11758198C2211yescharacteristic
36C2×#11758198C2211yescharacteristic
37C2×#11758198C2211yescharacteristic
38C2×#11758198C2211yescharacteristic
39C2×#11758198C2211yescharacteristic
40C2×#11758198C2211yescharacteristic
41C2×#11758198C2211yescharacteristic
42C2×#11758198C2211yescharacteristic
43C2×C4×Dic61C2211yescharacteristic
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
55C23×D61C2311yescharacteristic
56C22×C4×C61C2311yescharacteristic
57C22×C4×C61C2311yescharacteristic
58C22×C4×C61C2311yescharacteristic
59C22×C4×C61C2311yescharacteristic
60C22×C4×C61C2311yescharacteristic
61C22×C4×C61C2311yescharacteristic
62C22×C4×C61C2311yescharacteristic
63C22×Dic61C2311yescharacteristic
64C22×Dic61C2311yescharacteristic
65C22×Dic61C2311yescharacteristic
66C22×Dic61C2311yescharacteristic
67C22×Dic61C2311yescharacteristic
68C2×D244—22no—
69C2×D244—22no—
70C2×D244—22no—
71C2×D244—22no—
72C2×D244—22no—
73C2×D244—41no—
74C2×D244—41no—
75C2×D244—41no—
76C2×D244—41no—
77C2×C4×D61—22no—
78C2×C4×D61—41no—
79C2×C4×D61—41no—
80C4⋊C4×C61—41no—
81C4⋊C4×C61D414yes—
82C42×C61—41no—
83#11758198—22no—
84#11758198—22no—
85#11758198—22no—
86#11758198—22no—
87#11758198—22no—
88#11758198—22no—
89#11758198—41no—
90#11758198—41no—
91#11758198—41no—
92#11758198—41no—
93#11758198—41no—
94#11758198—41no—
95#11758198—41no—
96#11758198—41no—
97C4⋊Dic61—22no—
98C4⋊Dic61—41no—
99C4⋊Dic61—41no—
100#11758196—22no—
101#11758196—22no—
102#11758196—22no—
103#11758196—22no—
104C4×Dic61—22no—
105C23×C61C2411yescharacteristic
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×D61—21no—
117C22×D61—21no—
118C22×D61—21no—
119C22×D61—21no—
120C22×D61—21no—
121C22×D61—21no—
122C22×D61—21no—
123C22×D61—21no—
124C22×D61—21no—
125C22×D61—21no—
126C22×D61#4112yes—
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—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61C2×D412yes—
146C2×C4×C61C2×D412yes—
147C2×C4×C61C2×D412yes—
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—
159C2×Dic61—21no—
160C2×Dic61—21no—
161C2×Dic61—21no—
162C2×Dic61#4112yes—
163D244—44no—
164D244—44no—
165D244—44no—
166C4×D61—44no—
167C22×C61C22×D411yescharacteristic
168C22×C61C2×#4111yescharacteristic
169C22×C61C2×#4111yescharacteristic
170C22×C61H(5,𝔽2)11yescharacteristic
171C22×C61H(5,𝔽2)11yescharacteristic
172C22×C61H(5,𝔽2)11yescharacteristic
173C22×C612−1+411yescharacteristic
174C2×D61—22no—
175C2×D61—22no—
176C2×D61—22no—
177C2×D61—41no—
178C2×D61—41no—
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—
190C2×D61—41no—
191C2×D61—41no—
192C2×D61—41no—
193C2×D61—41no—
194C2×D61—41no—
195C4×C61—22no—
196C4×C61—22no—
197C4×C61—22no—
198C4×C61—41no—
199C4×C61—41no—
200C4×C61—41no—
201C4×C61—41no—
202Dic61—22no—
203Dic61—41no—
204Dic61—41no—
205Dic61—41no—
206Dic61—41no—
207#2711—611nomaximal, Sylow
208C2×C61#53511yescharacteristic
209C2×C61#53911yescharacteristic
210C2×C61#54011yescharacteristic
211C2×C61#54611yescharacteristic
212C2×C61#54811yescharacteristic
213C2×C61#55311yescharacteristic
214C2×C61#56211yescharacteristic
215D61—42no—
216D61—81no—
217D61—81no—
218C2×#125—611no—
219C2×#121—611no—
220#399—611no—
221#396—611no—
222#394—611no—
223#394—611no—
224#394—611no—
225#394—611no—
226#390—611no—
227#390—611no—
228#388—611no—
229#388—611no—
230#387D6111yescharacteristic, complemented
231#385—611no—
232#385—611no—
233C61#271111yescharacteristic, complemented, Sylow
234C22×D4—611no—
235C22×D4—611no—
236C22×D4—611no—
237C23×C4—611no—
238#125—1224no—
239#121—1224no—
240C2×C4⋊C4—611no—
241C2×C4⋊C4—611no—
242C2×C4⋊C4—611no—
243C2×C4⋊C4—611no—
244C2×C4⋊C4—611no—
245C2×C4⋊C4—611no—
246C2×C4⋊C4—611no—
247C2×C4⋊C4C2×D6111yescharacteristic
248C2×C4⋊C4C2×D6111yescharacteristic
249C2×C22⋊C4—611no—
250C2×C22⋊C4—611no—
251C2×C22⋊C4—611no—
252C2×C22⋊C4—611no—
253C2×C22⋊C4—611no—
254C2×C22⋊C4—611no—
255C2×C22⋊C4—611no—
256C2×C22⋊C4—611no—
257C2×C22⋊C4—611no—
258C2×C22⋊C4—611no—
259C2×C22⋊C4—611no—
260C2×C22⋊C4—611no—
261C2×C22⋊C4—611no—
262C2×C22⋊C4—611no—
263C2×C42—611no—
264C2×C42C2×D6111yescharacteristic
265#95—611no—
266#95—611no—
267#95C2×D6111yescharacteristic
268#95C2×D6111yescharacteristic
269#95C2×D6111yescharacteristic
270#95C2×D6111yescharacteristic
271C24—611no—
272C24—611no—
273C24—611no—
274C2×D4—1222no—
275C2×D4—1222no—
276C2×D4—1222no—
277C2×D4—1222no—
278C2×D4—1222no—
279C2×D4—2441no—
280C2×D4—2441no—
281C2×D4—2441no—
282C2×D4—2441no—
283C22×C4—611no—
284C22×C4—611no—
285C22×C4—611no—
286C22×C4—611no—
287C22×C4—611no—
288C22×C4—1222no—
289C22×C4—2441no—
290C22×C4—2441no—
291C22×C4C22×D6111yescharacteristic
292C22×C4C22×D6111yescharacteristic
293C22×C4C22×D6111yescharacteristic
294C22×C4C22×D6111yescharacteristic
295C22×C4C22×D6111yescharacteristic
296C22×C4C22×D6111yescharacteristic
297C22×C4C22×D6111yescharacteristic
298C4⋊C4—41no—
299C4⋊C4—1222no—
300C4⋊C4—1222no—
301C4⋊C4—1222no—
302C4⋊C4—1222no—
303C4⋊C4—1222no—
304C4⋊C4—2441no—
305C4⋊C4—2441no—
306C4⋊C4D24414yes—
307C22⋊C4—1222no—
308C22⋊C4—1222no—
309C22⋊C4—1222no—
310C22⋊C4—1222no—
311C22⋊C4—1222no—
312C22⋊C4—1222no—
313C22⋊C4—2441no—
314C22⋊C4—2441no—
315C22⋊C4—2441no—
316C22⋊C4—2441no—
317C22⋊C4—2441no—
318C22⋊C4—2441no—
319C22⋊C4—2441no—
320C22⋊C4—2441no—
321C42—41no—
322C42—1222no—
323C23—612no—
324C23—1221no—
325C23—1221no—
326C23—1221no—
327C23—1221no—
328C23—1221no—
329C23—1221no—
330C23—1221no—
331C23—1221no—
332C23—1221no—
333C23—1221no—
334C23—1221no—
335C23—1221no—
336C23—1221no—
337C23—1221no—
338C23—1221no—
339C23—1221no—
340C23—1221no—
341C23—1221no—
342C23—1221no—
343C23—1221no—
344C23C23×D6111yescharacteristic
345D4—2444no—
346D4—2444no—
347D4—2444no—
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—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—612no—
367C2×C4—1221no—
368C2×C4—1221no—
369C2×C4—1221no—
370C2×C4—1221no—
371C2×C4—1221no—
372C2×C4—1221no—
373C2×C4—1221no—
374C2×C4—1221no—
375C2×C4—1221no—
376C2×C4—1221no—
377C2×C4—1221no—
378C2×C4—1221no—
379C2×C4—1221no—
380C2×C4—1221no—
381C2×C4—2444no—
382C2×C4C2×D24412yes—
383C2×C4C2×D24412yes—
384C2×C4C2×D24412yes—
385C22—1222no—
386C22—1222no—
387C22—1222no—
388C22—2441no—
389C22—2441no—
390C22—2441no—
391C22—2441no—
392C22—2441no—
393C22—2441no—
394C22—2441no—
395C22—2441no—
396C22—2441no—
397C22—2441no—
398C22—2441no—
399C22—2441no—
400C22—2441no—
401C22—2441no—
402C22—2441no—
403C22—2441no—
404C22—2441no—
405C22—2441no—
406C22C22×D24411yescharacteristic
407C22#41×D6111yescharacteristic
408C22#41×D6111yescharacteristic
409C22#1451982211yescharacteristic
410C22#1451982311yescharacteristic
411C22#1451982311yescharacteristic
412C22#1451982511yescharacteristic
413C4—22no—
414C4—22no—
415C4—22no—
416C4—41no—
417C4—41no—
418C4—41no—
419C4—41no—
420C4—1222no—
421C4—2441no—
422C4—2441no—
423C4—2441no—
424C4—2441no—
425C2—4881no—
426C2—4881no—
427C2—2442no—
428C2#1684033111yescharacteristic
429C2#1684036011yescharacteristic
430C2#1684036411yescharacteristic
431C2#1684040711yescharacteristic
432C2#1684042411yescharacteristic
433C2#1684046311yescharacteristic
434C2#1684050811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#387C2
hypercenter#387D61
hypocenterC61#2711
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
1. C2×#14519767C2semidirect
3. #16839699C2semidirect
4. #16839684C2semidirect
5. #16839680C2semidirect
6. #16839680C2semidirect
7. #16839680C2semidirect
8. #16839680C2semidirect
9. #16839664C2semidirect
10. #16839663C2semidirect
11. #16839654C2semidirect
12. #16839653C2semidirect
13. #16839636C2semidirect
14. #16839636C2semidirect
15. C61×#387C2semidirect
230. #387D61semidirect
233. C61#2711semidirect