Finite Group Databasebeta

← #21455272

Subgroups — #21455272

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×#14519799C211yesmaximal, characteristic, complemented
2C2×#14519797C211yesmaximal, characteristic, complemented
3#16840308C211yesmaximal, characteristic, complemented
4#16840230C211yesmaximal, characteristic, complemented
5#16839987C211yesmaximal, characteristic, complemented
6#16839983C211yesmaximal, characteristic, complemented
7#16839980C211yesmaximal, characteristic, complemented
8#16839976C211yesmaximal, characteristic, complemented
9#16839971C211yesmaximal, characteristic, complemented
10#16839966C211yesmaximal, characteristic, complemented
11#16839961C211yesmaximal, characteristic, complemented
12#16839956C211yesmaximal, characteristic, complemented
13C2×#14519706C211yesmaximal, characteristic, complemented
14#16839756C211yesmaximal, characteristic, complemented
15C61×#416C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C2×#11758222C2211yescharacteristic
18#14519799—24no—
19#14519797—24no—
20C2×Dic244C2211yescharacteristic
21C2×#11758202C2211yescharacteristic
22C2×#11758190C2211yescharacteristic
23C2×#11758190C2211yescharacteristic
24C2×#11758200C2211yescharacteristic
25C2×#11758201C2211yescharacteristic
26C2×D488C2211yescharacteristic
27C2×#11758199C2211yescharacteristic
28C22×#92418C2211yescharacteristic
29#14519775C2211yescharacteristic
30#14519773C2211yescharacteristic
31#14519766C2211yescharacteristic
32#14519764C2211yescharacteristic
33#14519749—21no—
34#14519749—21no—
35#14519742C2211yescharacteristic
36#14519742C2211yescharacteristic
37#14519739C2211yescharacteristic
38#14519739C2211yescharacteristic
39C4×C22⋊D61—21no—
40C4×C22⋊D61—21no—
41#14519737—21no—
42#14519737—21no—
43#14519734—21no—
44C2×C4×Dic61C2211yescharacteristic
45C42×D61—21no—
46#14519706C2211yescharacteristic
47#14519706C2211yescharacteristic
48#14519706C2211yescharacteristic
49#14519706C2211yescharacteristic
50#14519700C2211yescharacteristic
51#14519700C2211yescharacteristic
52#14519697C2211yescharacteristic
53#14519697C2211yescharacteristic
54C2×#41×C61C2211yescharacteristic
55C22×C8×C61C2211yescharacteristic
56#117×C61C2211yescharacteristic
57#103×C61C2211yescharacteristic
58#103×C61C2211yescharacteristic
59#102×C61C2211yescharacteristic
60#102×C61C2211yescharacteristic
61#41×C61—22no—
62#41×C61—22no—
63C2×Q8×C61C2311yescharacteristic
64C2×D4×C61—21no—
65C2×D4×C61C2311yescharacteristic
66C22×C4×C61—21no—
67C22×C4×C61C2311yescharacteristic
68C2×C22⋊D61—21no—
69C2×C22⋊D61—21no—
70C2×C22⋊D61—21no—
71C2×C22⋊D61—21no—
72C22×Dic61D411yescharacteristic
73C22×Dic61D411yescharacteristic
74#11758222—22no—
75#11758222—22no—
76#11758222—22no—
77#11758222D414yescomplemented
78C2×D244C2311yescharacteristic
79C2×D244C2311yescharacteristic
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×Dic122C2311yescharacteristic
85C2×Dic122C2311yescharacteristic
86C2×C8×C61—22no—
87C2×C8×C61C2311yescharacteristic
88C2×C8×C61C2311yescharacteristic
89C4⋊C4×C61C2311yescharacteristic
90C4⋊C4×C61C2311yescharacteristic
91C22⋊C4×C61—21no—
92C42×C61—21no—
93C22⋊Dic61—21no—
94C22⋊Dic61—21no—
95#11758202—22no—
96#11758201—22no—
97#11758200—22no—
98#11758199—22no—
99#11758198—21no—
100#11758198—21no—
101#11758198—21no—
102#11758198—21no—
103#11758196—21no—
104#11758196—21no—
105#11758196—21no—
106#11758196—21no—
107C4×Dic61—21no—
108C4×Dic61—21no—
109C4×Dic61D411yescharacteristic
110C4×Dic61D411yescharacteristic
111C4×Dic61C2311yescharacteristic
112C4×Dic61C2311yescharacteristic
113C2×#92418—22no—
114C2×#92418C2311yescharacteristic
115C2×#92418C2311yescharacteristic
116Dic244—22no—
117D488—22no—
118#11758190—22no—
119#11758190—22no—
120C23×C61—21no—
121C23×C61C2×D411yescharacteristic
122C22×D61—21no—
123C22×D61—21no—
124Q8×C61—21no—
125Q8×C61—21no—
126D4×C61—21no—
127D4×C61—21no—
128D4×C61—42no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—42no—
133C2×C4×C61C2×D411yescharacteristic
134C2×C4×C61C2×D412yes—
135C2×C4×C61#4112yes—
136C2×C4×C61C2411yescharacteristic
137C22⋊D61—24no—
138C22⋊D61—42no—
139C22⋊D61—42no—
140C22⋊D61—42no—
141C2×Dic61—21no—
142C2×Dic61—22no—
143C2×Dic61—21no—
144C2×Dic61—41no—
145C2×Dic61C2×D411yescharacteristic
146C2×Dic61C2×D411yescharacteristic
147C2×Dic61C2×D411yescharacteristic
148C2×Dic61C2×D411yescharacteristic
149D244—21no—
150D244—21no—
151D244—21no—
152D244C2×D412yes—
153C4×D61—24no—
154C4×D61—42no—
155C4×D61—42no—
156C4×D61—42no—
157Dic122—21no—
158Dic122—21no—
159Dic122—21no—
160Dic122C2×D412yes—
161C8×C61—21no—
162C8×C61—21no—
163#92418—21no—
164#92418—21no—
165C22×C61—21no—
166C22×C61—21no—
167C22×C61—41no—
168C22×C61—41no—
169C22×C61—41no—
170C22×C61#12112yes—
171C22×C61C22×D411yescharacteristic
172C2×D61—22no—
173C2×D61—41no—
174C2×D61—41no—
175C2×D61—41no—
176C2×D61—41no—
177C2×D61—41no—
178C4×C61—41no—
179C4×C61—41no—
180C4×C61—41no—
181C4×C61#12112yes—
182C4×C61C22×D411yescharacteristic
183C4×C61C2×#4111yescharacteristic
184Dic61—22no—
185Dic61—21no—
186Dic61—21no—
187Dic61—21no—
188Dic61—41no—
189Dic61#13512yescomplemented
190#3035—611nomaximal, Sylow
191C2×C61—22no—
192C2×C61—81no—
193C2×C61C2×#12111yescharacteristic
194C2×C61C2×#13511yescharacteristic
195C2×C61#57511yescharacteristic
196D61—42no—
197D61—81no—
198C2×#135—611no—
199C2×#135—611no—
200#532—611no—
201C4×#41—611no—
202#464—611no—
203#464—611no—
204#463—611no—
205#463—611no—
206#462—611no—
207#461—611no—
208#460—611no—
209#459—611no—
210C2×C4⋊C8—611no—
211#416—611no—
212#416D6111yescharacteristic, complemented
213C61#303511yescharacteristic, complemented, Sylow
214C2×#41—611no—
215C2×#41—611no—
216C2×#41C2×D6111yescharacteristic
217#135—1224no—
218#135—1224no—
219C2×Q16—611no—
220C2×Q16—611no—
221C2×SD16—611no—
222C2×SD16—611no—
223C2×SD16—611no—
224C2×SD16—611no—
225C2×D8—611no—
226C2×D8—611no—
227C22×C8—611no—
228C22×C8C2×D6111yescharacteristic
229C4⋊Q8—611no—
230#127—611no—
231#124—611no—
232#124—611no—
233#121—1221no—
234#121—1221no—
235C4×Q8—611no—
236C4×Q8—611no—
237C4×D4—611no—
238C4×D4—611no—
239C4×D4—1221no—
240C4×D4—1221no—
241C4×D4—1221no—
242C4×D4—1221no—
243#117—1221no—
244#117C2×D6111yescharacteristic
245C2×C42—611no—
246C2×C42—1221no—
247C4⋊C8—611no—
248C4⋊C8—611no—
249C4⋊C8—611no—
250C4⋊C8—611no—
251#103—611no—
252#103—611no—
253#103C2×D6111yescharacteristic
254#103C2×D6111yescharacteristic
255#102—611no—
256#102—611no—
257#102C2×D6111yescharacteristic
258#102C2×D6111yescharacteristic
259#41—22no—
260#41—22no—
261#41—614no—
262#41—1222no—
263#41—1222no—
264#41—1222no—
265C2×Q8—611no—
266C2×Q8—611no—
267C2×Q8C22×D6111yescharacteristic
268C2×D4—21no—
269C2×D4—611no—
270C2×D4—611no—
271C2×D4—1221no—
272C2×D4—1221no—
273C2×D4—1221no—
274C2×D4—1221no—
275C2×D4C22×D6111yescharacteristic
276C22×C4—21no—
277C22×C4—611no—
278C22×C4—611no—
279C22×C4—1221no—
280C22×C4—1221no—
281C22×C4—1221no—
282C22×C4—1221no—
283C22×C4C22×D6111yescharacteristic
284Q16—1222no—
285Q16—1222no—
286SD16—1222no—
287SD16—1222no—
288SD16—1222no—
289SD16—1222no—
290D8—1222no—
291D8—1222no—
292C2×C8—22no—
293C2×C8—611no—
294C2×C8—611no—
295C2×C8—1222no—
296C2×C8C22×D6111yescharacteristic
297C2×C8C22×D6111yescharacteristic
298C4⋊C4—1221no—
299C4⋊C4—1221no—
300C4⋊C4—1221no—
301C4⋊C4—1221no—
302C4⋊C4C22×D6111yescharacteristic
303C4⋊C4C22×D6111yescharacteristic
304C22⋊C4—21no—
305C22⋊C4—1221no—
306C22⋊C4—1221no—
307C22⋊C4—1221no—
308C22⋊C4—1221no—
309C22⋊C4—1221no—
310C22⋊C4—1221no—
311C42—21no—
312C42—611no—
313C42—611no—
314C42—611no—
315C42—611no—
316C42—1221no—
317C42—1221no—
318C23—21no—
319C23—1221no—
320C23—1221no—
321C23D4×D6111yescharacteristic
322Q8—21no—
323Q8—21no—
324Q8—612no—
325Q8—1221no—
326Q8—1221no—
327Q8—1221no—
328D4—21no—
329D4—21no—
330D4—42no—
331D4—612no—
332D4—1224no—
333D4—1221no—
334D4—1221no—
335D4—1221no—
336D4—2442no—
337D4—2442no—
338D4—2442no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—42no—
343C2×C4—611no—
344C2×C4—611no—
345C2×C4—611no—
346C2×C4—611no—
347C2×C4—1222no—
348C2×C4—1221no—
349C2×C4—1224no—
350C2×C4—1221no—
351C2×C4—2442no—
352C2×C4—2442no—
353C2×C4—2441no—
354C2×C4—2442no—
355C2×C4#1175822212yes—
356C2×C4D4×D6112yes—
357C2×C4D4×D6111yescharacteristic
358C2×C4C23×D6111yescharacteristic
359C8—21no—
360C8—21no—
361C8—1221no—
362C8—1221no—
363C22—21no—
364C22—21no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—1222no—
369C22—2441no—
370C22—2441no—
371C22—2441no—
372C22—2441no—
373C22—2441no—
374C22#1451975012yes—
375C22C2×D4×D6111yescharacteristic
376C4—41no—
377C4—41no—
378C4—41no—
379C4—612no—
380C4—1222no—
381C4—1221no—
382C4—1221no—
383C4—1221no—
384C4—2441no—
385C4#1451975012yes—
386C4C2×D4×D6111yescharacteristic
387C4C2×#1175822211yescharacteristic
388C2—22no—
389C2—81no—
390C2—4881no—
391C2—2442no—
392C2C2×#1451975011yescharacteristic
393C2#135×D6111yescharacteristic
394C2#1684055911yescharacteristic
subgroupG/H
centerC2×C4D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#416C2
socleC22×C61C22×D4
hypercenter#416D61
hypocenterC61#3035
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. C2×#14519799C2semidirect
2. C2×#14519797C2semidirect
3. #16840308C2semidirect
4. #16840230C2semidirect
5. #16839987C2semidirect
6. #16839983C2semidirect
7. #16839980C2semidirect
8. #16839976C2semidirect
9. #16839971C2semidirect
10. #16839966C2semidirect
11. #16839961C2semidirect
12. #16839956C2semidirect
13. C2×#14519706C2semidirect
14. #16839756C2semidirect
15. C61×#416C2semidirect
77. #11758222D4semidirect
189. Dic61#135semidirect
212. #416D61semidirect
213. C61#3035semidirect