Finite Group Databasebeta

← #21455271

Subgroups — #21455271

Order 7808.

496 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519798C211yesmaximal, characteristic, complemented
2C2×#14519796C211yesmaximal, characteristic, complemented
3#16840311C211yesmaximal, characteristic, complemented
4C4×#11758224C211yesmaximal, characteristic, complemented
5#16839985C211yesmaximal, characteristic, complemented
6#16839981C211yesmaximal, characteristic, complemented
7#16839977C211yesmaximal, characteristic, complemented
8#16839971C211yesmaximal, characteristic, complemented
9#16839965C211yesmaximal, characteristic, complemented
10#16839961C211yesmaximal, characteristic, complemented
11#16839955C211yesmaximal, characteristic, complemented
12C4⋊C8×D61C211yesmaximal, characteristic, complemented
13#16839757C211yesmaximal, characteristic, complemented
14#16839755C211yesmaximal, characteristic, complemented
15C61×#463C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×#11758224C2211yescharacteristic
18C2×#11758224C2211yescharacteristic
19#14519798—24no—
20#14519796—24no—
21C2×Dic244C2211yescharacteristic
22C2×#11758202C2211yescharacteristic
23C2×#11758190C2211yescharacteristic
24C2×#11758200C2211yescharacteristic
25C2×#11758200C2211yescharacteristic
26C2×#11758199C2211yescharacteristic
27C2×C8×D61C2211yescharacteristic
28C2×C8×D61C2211yescharacteristic
29#14519775C2211yescharacteristic
30#14519773C2211yescharacteristic
31#14519765C2211yescharacteristic
32#14519750—21no—
33#14519750—21no—
34C4×Dic122C2211yescharacteristic
35#14519742C2211yescharacteristic
36D4×Dic61C2211yescharacteristic
37C4×C22⋊D61—21no—
38#14519737—21no—
39#14519737—21no—
40#14519737—21no—
41#14519735C2211yescharacteristic
42#14519733—21no—
43C2×C4×Dic61—21no—
44C42×D61C2211yescharacteristic
45C4⋊#92418C2211yescharacteristic
46#14519706C2211yescharacteristic
47#14519706C2211yescharacteristic
48#14519702C2211yescharacteristic
49#14519701C2211yescharacteristic
50#14519700C2211yescharacteristic
51#14519699C2211yescharacteristic
52#14519698C2211yescharacteristic
53#14519697C2211yescharacteristic
54C2×SD16×C61C2211yescharacteristic
55C2×D8×C61C2211yescharacteristic
56#124×C61C2211yescharacteristic
57C4×D4×C61C2211yescharacteristic
58C4⋊C8×C61C2211yescharacteristic
59#103×C61C2211yescharacteristic
60#102×C61C2211yescharacteristic
61C2×Q8×C61C2311yescharacteristic
62C2×D4×C61C2311yescharacteristic
63C2×D4×C61C2311yescharacteristic
64C22×C4×C61—21no—
65C2×C22⋊D61—21no—
66C2×C22⋊D61—21no—
67C2×C22⋊D61—21no—
68C2×C22⋊D61—21no—
69C22×Dic61—21no—
70C22×Dic61—21no—
71C22×Dic61—21no—
72#11758226—22no—
73#11758226—22no—
74#11758224—22no—
75#11758224—22no—
76#11758224—22no—
77#11758224D414yescomplemented
78C2×D244—21no—
79C2×D244C2311yescharacteristic
80C2×C4×D61—21no—
81C2×C4×D61D411yescharacteristic
82C2×C4×D61D411yescharacteristic
83C2×C4×D61C2311yescharacteristic
84C2×Dic122C2311yescharacteristic
85C2×Dic122C2311yescharacteristic
86SD16×C61—22no—
87D8×C61—22no—
88C2×C8×C61C2311yescharacteristic
89C2×C8×C61C2311yescharacteristic
90C4⋊C4×C61C2311yescharacteristic
91C22⋊C4×C61—21no—
92C22⋊C4×C61—21no—
93C22⋊C4×C61—21no—
94C42×C61C2311yescharacteristic
95C22⋊Dic61—21no—
96#11758202—22no—
97#11758200—22no—
98#11758200—22no—
99#11758199—22no—
100#11758198—21no—
101#11758198—21no—
102#11758198—21no—
103C4⋊Dic61C2311yescharacteristic
104#11758196—21no—
105#11758196—21no—
106#11758196—21no—
107#11758196—21no—
108C4×Dic61—21no—
109C4×Dic61—21no—
110C4×Dic61—21no—
111C4×Dic61D411yescharacteristic
112C4×Dic61D411yescharacteristic
113C4×Dic61C2311yescharacteristic
114C2×#92418C2311yescharacteristic
115C2×#92418C2311yescharacteristic
116Dic244—22no—
117#11758190—22no—
118C8×D61—22no—
119C8×D61—22no—
120C23×C61—21no—
121C23×C61—21no—
122C22×D61—21no—
123C22×D61C2×D411yescharacteristic
124Q8×C61—21no—
125Q8×C61—21no—
126D4×C61—21no—
127D4×C61—21no—
128D4×C61—21no—
129D4×C61C2×D412yes—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—42no—
133C2×C4×C61C2×D411yescharacteristic
134C2×C4×C61C2×D411yescharacteristic
135C2×C4×C61C2411yescharacteristic
136C22⋊D61—24no—
137C22⋊D61—42no—
138C22⋊D61—42no—
139C22⋊D61—42no—
140C2×Dic61—21no—
141C2×Dic61—24no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—42no—
145C2×Dic61—42no—
146C2×Dic61C2×D411yescharacteristic
147C2×Dic61C2×D411yescharacteristic
148C2×Dic61C2×D411yescharacteristic
149D244—21no—
150D244—21no—
151D244—42no—
152C4×D61—22no—
153C4×D61—41no—
154C4×D61—42no—
155C4×D61C2×D412yes—
156C4×D61#4112yes—
157Dic122—21no—
158Dic122—21no—
159Dic122—21no—
160Dic122C2×D412yes—
161C8×C61—21no—
162C8×C61—21no—
163#92418—21no—
164#92418—21no—
165C22×C61—22no—
166C22×C61—41no—
167C22×C61—41no—
168C22×C61—41no—
169C22×C61—41no—
170C22×C61—41no—
171C22×C61C22×D411yescharacteristic
172C2×D61—21no—
173C2×D61—21no—
174C2×D61—41no—
175C2×D61—41no—
176C2×D61—41no—
177C2×D61#12112yes—
178C4×C61—21no—
179C4×C61—21no—
180C4×C61—41no—
181C4×C61—41no—
182C4×C61C22×D411yescharacteristic
183C4×C61C2×#4111yescharacteristic
184Dic61—22no—
185Dic61—21no—
186Dic61—41no—
187Dic61—41no—
188Dic61#12112yes—
189Dic61#13512yescomplemented
190#3035—611nomaximal, Sylow
191C2×C61—42no—
192C2×C61—81no—
193C2×C61C2×#12111yescharacteristic
194C2×C61C2×#13511yescharacteristic
195C2×C61#57511yescharacteristic
196D61—22no—
197D61—81no—
198C2×#135—611no—
199C2×#135—611no—
200#532—611no—
201C4×#41—611no—
202#464—611no—
203#464—611no—
204#463—611no—
205#463D6111yescharacteristic, complemented
206#462—611no—
207#461—611no—
208#460—611no—
209#459—611no—
210C2×C4⋊C8—611no—
211#416—611no—
212#416—611no—
213C61#303511yescharacteristic, complemented, Sylow
214C2×#41—611no—
215C2×#41—611no—
216C2×#41—611no—
217#135—1224no—
218#135—1224no—
219C2×Q16—611no—
220C2×Q16—611no—
221C2×SD16—611no—
222C2×SD16—611no—
223C2×SD16—611no—
224C2×SD16C2×D6111yescharacteristic
225C2×D8—611no—
226C2×D8C2×D6111yescharacteristic
227C22×C8—611no—
228C22×C8—611no—
229C4⋊Q8—611no—
230#127—611no—
231#124—611no—
232#124C2×D6111yescharacteristic
233#121—1221no—
234#121—1221no—
235C4×Q8—611no—
236C4×Q8—611no—
237C4×D4—611no—
238C4×D4—1221no—
239C4×D4—1221no—
240C4×D4—1221no—
241C4×D4—1221no—
242C4×D4C2×D6111yescharacteristic
243#117—611no—
244#117—1221no—
245C2×C42—611no—
246C2×C42—1221no—
247C4⋊C8—611no—
248C4⋊C8—611no—
249C4⋊C8—611no—
250C4⋊C8C2×D6111yescharacteristic
251#103—611no—
252#103—611no—
253#103—611no—
254#103C2×D6111yescharacteristic
255#102—611no—
256#102—611no—
257#102—611no—
258#102C2×D6111yescharacteristic
259#41—614no—
260#41—1222no—
261#41—1222no—
262#41—1222no—
263#41—1222no—
264#41—1222no—
265C2×Q8—611no—
266C2×Q8—611no—
267C2×Q8C22×D6111yescharacteristic
268C2×D4—611no—
269C2×D4—1221no—
270C2×D4—1221no—
271C2×D4—1221no—
272C2×D4—1221no—
273C2×D4—1221no—
274C2×D4C22×D6111yescharacteristic
275C2×D4C22×D6111yescharacteristic
276C22×C4—21no—
277C22×C4—611no—
278C22×C4—611no—
279C22×C4—611no—
280C22×C4—1221no—
281C22×C4—1221no—
282C22×C4—1221no—
283C22×C4—1221no—
284Q16—1222no—
285Q16—1222no—
286SD16—22no—
287SD16—1222no—
288SD16—1222no—
289SD16—1222no—
290D8—22no—
291D8—1222no—
292C2×C8—611no—
293C2×C8—611no—
294C2×C8—1222no—
295C2×C8—1222no—
296C2×C8C22×D6111yescharacteristic
297C2×C8C22×D6111yescharacteristic
298C4⋊C4—611no—
299C4⋊C4—1221no—
300C4⋊C4—1221no—
301C4⋊C4—1221no—
302C4⋊C4—1221no—
303C4⋊C4C22×D6111yescharacteristic
304C22⋊C4—21no—
305C22⋊C4—21no—
306C22⋊C4—21no—
307C22⋊C4—1221no—
308C22⋊C4—1221no—
309C22⋊C4—1221no—
310C22⋊C4—1221no—
311C42—611no—
312C42—611no—
313C42—611no—
314C42—1221no—
315C42—1221no—
316C42—1221no—
317C42C22×D6111yescharacteristic
318C23—21no—
319C23—21no—
320C23—611no—
321C23—1221no—
322Q8—21no—
323Q8—21no—
324Q8—612no—
325Q8—1221no—
326Q8—1221no—
327Q8—1221no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—1224no—
332D4—1221no—
333D4—1221no—
334D4—2442no—
335D4—2442no—
336D4—2442no—
337D4—2442no—
338D4D4×D6112yes—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—42no—
342C2×C4—611no—
343C2×C4—611no—
344C2×C4—612no—
345C2×C4—612no—
346C2×C4—611no—
347C2×C4—1222no—
348C2×C4—1224no—
349C2×C4—1221no—
350C2×C4—1221no—
351C2×C4—1221no—
352C2×C4—2441no—
353C2×C4—2442no—
354C2×C4—2442no—
355C2×C4—2442no—
356C2×C4D4×D6111yescharacteristic
357C2×C4D4×D6111yescharacteristic
358C2×C4C23×D6111yescharacteristic
359C8—21no—
360C8—21no—
361C8—1221no—
362C8—1221no—
363C22—22no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—612no—
370C22—1221no—
371C22—1221no—
372C22—2441no—
373C22—2441no—
374C22—2441no—
375C22C2×D4×D6111yescharacteristic
376C4—21no—
377C4—21no—
378C4—41no—
379C4—41no—
380C4—612no—
381C4—612no—
382C4—1222no—
383C4—1221no—
384C4—2441no—
385C4—2441no—
386C4C2×D4×D6111yescharacteristic
387C4#41×D6111yescharacteristic
388C2—42no—
389C2—81no—
390C2—1222no—
391C2—4881no—
392C2#121×D6111yescharacteristic
393C2#135×D6111yescharacteristic
394C2#1684055811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#463C2
socleC22×C61C22×D4
hypercenter#463D61
hypocenterC61#3035
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×#14519798C2semidirect
2. C2×#14519796C2semidirect
3. #16840311C2semidirect
4. C4×#11758224C2semidirect
5. #16839985C2semidirect
6. #16839981C2semidirect
7. #16839977C2semidirect
8. #16839971C2semidirect
9. #16839965C2semidirect
10. #16839961C2semidirect
11. #16839955C2semidirect
12. C4⋊C8×D61C2semidirect
13. #16839757C2semidirect
14. #16839755C2semidirect
15. C61×#463C2semidirect
77. #11758224D4semidirect
189. Dic61#135semidirect
205. #463D61semidirect
213. C61#3035semidirect