Finite Group Databasebeta

← #21455503

Subgroups — #21455503

Order 7808.

472 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519806C211yesmaximal, characteristic, complemented
2C2×#14519783C211yesmaximal, characteristic, complemented
3#16840341C211yesmaximal, characteristic
4#16840335C211yesmaximal, characteristic, complemented
5#16840021C211yesmaximal, characteristic, complemented
6#16840018C211yesmaximal, characteristic, complemented
7#16840006C211yesmaximal, characteristic, complemented
8#16840005C211yesmaximal, characteristic, complemented
9#16840003C211yesmaximal, characteristic, complemented
10#16840002C211yesmaximal, characteristic, complemented
11#16839990C211yesmaximal, characteristic, complemented
12#16839801C211yesmaximal, characteristic, complemented
13#16839755C211yesmaximal, characteristic, complemented
14#103×D61C211yesmaximal, characteristic, complemented
15C61×#465C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C2×#11758224C2211yescharacteristic
18C2×Q8×D61C2211yescharacteristic
19#14519806—24no—
20C2×Dic244C2211yescharacteristic
21C2×#11758202C2211yescharacteristic
22C2×#11758200C2211yescharacteristic
23#14519783—24no—
24C2×#11758194C2211yescharacteristic
25C2×#11758189C2211yescharacteristic
26C2×#11758189C2211yescharacteristic
27C2×C8×D61C2211yescharacteristic
28C2×C8×D61C2211yescharacteristic
29#14519776—21no—
30#14519763—21no—
31#14519762—21no—
32#14519759—21no—
33#14519757C2211yescharacteristic
34#14519757C2211yescharacteristic
35#14519756C2211yescharacteristic
36#14519756C2211yescharacteristic
37#14519754—21no—
38#14519753C2211yescharacteristic
39#14519750—21no—
40#14519749—21no—
41#14519748—21no—
42#14519748C2211yescharacteristic
43#14519735C2211yescharacteristic
44C4⋊C4×D61C2211yescharacteristic
45#14519711C2211yescharacteristic
46#14519710C2211yescharacteristic
47#14519708C2211yescharacteristic
48#14519702C2211yescharacteristic
49#14519702C2211yescharacteristic
50#14519701C2211yescharacteristic
51#14519700C2211yescharacteristic
52#14519700C2211yescharacteristic
53#14519698C2211yescharacteristic
54C2×SD16×C61C2211yescharacteristic
55C22×C8×C61C2211yescharacteristic
56C22⋊Q8×C61C2211yescharacteristic
57#121×C61C2211yescharacteristic
58#106×C61C2211yescharacteristic
59#103×C61C2211yescharacteristic
60#102×C61C2211yescharacteristic
61C2×Q8×C61C2311yescharacteristic
62C2×D4×C61—21no—
63C2×D4×C61C2311yescharacteristic
64C22×C4×C61C2311yescharacteristic
65C2×C22⋊D61—21no—
66C2×C22⋊D61—21no—
67C2×C22⋊D61D411yescharacteristic
68C2×C22⋊D61D411yescharacteristic
69C22×Dic61—21no—
70Q8×D61—22no—
71Q8×D61—22no—
72#11758224—22no—
73#11758224—22no—
74#11758222—22no—
75#11758222—22no—
76C2×D244D411yescharacteristic
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×C4×D61C2311yescharacteristic
80C2×C4×D61C2311yescharacteristic
81C2×Dic122—21no—
82C2×Dic122D411yescharacteristic
83C2×Dic122C2311yescharacteristic
84C2×Dic122C2311yescharacteristic
85SD16×C61—22no—
86C2×C8×C61—22no—
87C2×C8×C61C2311yescharacteristic
88C2×C8×C61C2311yescharacteristic
89C4⋊C4×C61—21no—
90C4⋊C4×C61C2311yescharacteristic
91C4⋊C4×C61C2311yescharacteristic
92C22⋊C4×C61—21no—
93C22⋊C4×C61—21no—
94C22⋊Dic61—21no—
95C22⋊Dic61—21no—
96C22⋊Dic61—21no—
97#11758202—22no—
98#11758200—22no—
99#11758198—21no—
100#11758198—21no—
101#11758198—21no—
102#11758198—21no—
103C4⋊Dic61—21no—
104C4⋊Dic61—21no—
105C4⋊Dic61C2311yescharacteristic
106C4⋊Dic61C2311yescharacteristic
107#11758196—21no—
108#11758196—21no—
109#11758196—21no—
110#11758196—21no—
111C4×Dic61—21no—
112#11758194—22no—
113C2×#92418C2311yescharacteristic
114C2×#92418C2311yescharacteristic
115Dic244—22no—
116#11758189—22no—
117#11758189D414yescomplemented
118C8×D61—22no—
119C8×D61—22no—
120C23×C61—21no—
121C23×C61C2×D411yescharacteristic
122C22×D61C2×D411yescharacteristic
123C22×D61C2×D411yescharacteristic
124Q8×C61—21no—
125Q8×C61—21no—
126D4×C61—21no—
127D4×C61—21no—
128D4×C61—81no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61C2×D411yescharacteristic
135C2×C4×C61C2411yescharacteristic
136C22⋊D61—22no—
137C22⋊D61—22no—
138C22⋊D61—42no—
139C22⋊D61—81no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—42no—
145C2×Dic61C2×D411yescharacteristic
146C2×Dic61C2×D411yescharacteristic
147D244—22no—
148C4×D61—21no—
149C4×D61—21no—
150C4×D61—42no—
151C4×D61—81no—
152C4×D61C2×D412yes—
153C4×D61#4112yes—
154Dic122—22no—
155Dic122—21no—
156Dic122—21no—
157Dic122—21no—
158Dic122—21no—
159Dic122—42no—
160C8×C61—21no—
161C8×C61C2×D412yes—
162#92418—21no—
163#92418C2×D412yes—
164C22×C61—21no—
165C22×C61—21no—
166C22×C61—21no—
167C22×C61—41no—
168C22×C61—41no—
169C22×C61—41no—
170C22×C61C22×D411yescharacteristic
171C2×D61—21no—
172C2×D61—21no—
173C2×D61—21no—
174C2×D61—21no—
175C2×D61—21no—
176C2×D61#12112yes—
177C4×C61—21no—
178C4×C61—41no—
179C4×C61—41no—
180C4×C61—41no—
181C4×C61C22×D411yescharacteristic
182C4×C61C2×#4111yescharacteristic
183Dic61—21no—
184Dic61—41no—
185Dic61—41no—
186Dic61—41no—
187Dic61—41no—
188Dic61#12112yes—
189#3063—611nomaximal, Sylow
190C2×C61—41no—
191C2×C61—81no—
192C2×C61C2×#12111yescharacteristic
193C2×C61#57711yescharacteristic
194C2×C61#57811yescharacteristic
195D61—22no—
196D61—41no—
197C2×#137—611no—
198C2×#131—611no—
199#537—611no—
200#536—611no—
201#470—611no—
202#470—611no—
203#468—611no—
204#468—611no—
205#467—611no—
206#467—611no—
207#465—611no—
208#465D6111yescharacteristic, complemented
209#428—611no—
210#416—611no—
211C2×#103—611no—
212C61#306311yescharacteristic, complemented, Sylow
213C2×#41—611no—
214C2×#41—611no—
215C22×Q8—611no—
216#137—1224no—
217C2×Q16—611no—
218C2×Q16—611no—
219C2×SD16—611no—
220C2×SD16C2×D6111yescharacteristic
221#131—1224no—
222C2×M16—611no—
223C2×M16—611no—
224C2×M16—611no—
225C22×C8—611no—
226C22×C8—611no—
227C22×C8C2×D6111yescharacteristic
228C4⋊Q8—1221no—
229#124—1221no—
230#123—1221no—
231#123—1221no—
232C22⋊Q8—611no—
233C22⋊Q8—611no—
234C22⋊Q8—611no—
235C22⋊Q8—611no—
236C22⋊Q8—611no—
237C22⋊Q8—1221no—
238C22⋊Q8C2×D6111yescharacteristic
239#121—611no—
240#121—1221no—
241#121—1221no—
242#121—1221no—
243#121C2×D6111yescharacteristic
244#117—611no—
245C2×C4⋊C4—611no—
246#107—611no—
247#107—611no—
248#106—611no—
249#106C2×D6111yescharacteristic
250#103—611no—
251#103—611no—
252#103—611no—
253#103—611no—
254#103—611no—
255#103C2×D6111yescharacteristic
256#102—611no—
257#102C2×D6111yescharacteristic
258#41—1222no—
259#41—1222no—
260#41—1222no—
261#41—1222no—
262C2×Q8—611no—
263C2×Q8—611no—
264C2×Q8—611no—
265C2×Q8—1221no—
266C2×Q8—1222no—
267C2×Q8—1222no—
268C2×Q8C22×D6111yescharacteristic
269C2×D4—21no—
270C2×D4—611no—
271C2×D4—611no—
272C2×D4—611no—
273C2×D4—1221no—
274C2×D4—1221no—
275C2×D4C22×D6111yescharacteristic
276C22×C4—611no—
277C22×C4—611no—
278C22×C4—1221no—
279C22×C4—1221no—
280C22×C4—1221no—
281C22×C4C22×D6111yescharacteristic
282Q16—1222no—
283Q16—1222no—
284SD16—22no—
285SD16—1222no—
286M16—614no—
287M16—1222no—
288M16—1222no—
289C2×C8—22no—
290C2×C8—611no—
291C2×C8—611no—
292C2×C8—1222no—
293C2×C8—1222no—
294C2×C8C22×D6111yescharacteristic
295C2×C8C22×D6111yescharacteristic
296C4⋊C4—21no—
297C4⋊C4—611no—
298C4⋊C4—611no—
299C4⋊C4—1221no—
300C4⋊C4—1221no—
301C4⋊C4—1221no—
302C4⋊C4—1221no—
303C4⋊C4—1221no—
304C4⋊C4—1221no—
305C4⋊C4C22×D6111yescharacteristic
306C4⋊C4C22×D6111yescharacteristic
307C22⋊C4—21no—
308C22⋊C4—21no—
309C22⋊C4—1221no—
310C22⋊C4—1221no—
311C22⋊C4—1221no—
312C22⋊C4—1221no—
313C22⋊C4—1221no—
314C22⋊C4—1221no—
315C22⋊C4—1221no—
316C42—1221no—
317C23—21no—
318C23—611no—
319C23—611no—
320C23D4×D6111yescharacteristic
321Q8—21no—
322Q8—21no—
323Q8—1222no—
324Q8—1221no—
325Q8—1221no—
326Q8—1221no—
327Q8—1221no—
328Q8—2442no—
329D4—21no—
330D4—21no—
331D4—81no—
332D4—1222no—
333D4—1222no—
334D4—1222no—
335D4—4881no—
336D4—2442no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—611no—
343C2×C4—612no—
344C2×C4—612no—
345C2×C4—611no—
346C2×C4—1221no—
347C2×C4—1221no—
348C2×C4—1221no—
349C2×C4—1221no—
350C2×C4—1221no—
351C2×C4—1221no—
352C2×C4—4881no—
353C2×C4—2442no—
354C2×C4—2442no—
355C2×C4D4×D6111yescharacteristic
356C2×C4C23×D6111yescharacteristic
357C8—21no—
358C8—612no—
359C8—1221no—
360C8D4×D6112yes—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—612no—
368C22—1221no—
369C22—1221no—
370C22—1221no—
371C22—1221no—
372C22—1221no—
373C22C2×D4×D6111yescharacteristic
374C4—21no—
375C4—41no—
376C4—41no—
377C4—41no—
378C4—612no—
379C4—1221no—
380C4—2441no—
381C4—2441no—
382C4—2441no—
383C4—2441no—
384C4C2×D4×D6111yescharacteristic
385C4#41×D6111yescharacteristic
386C2—41no—
387C2—81no—
388C2—1222no—
389C2—2441no—
390C2#121×D6111yescharacteristic
391C2#1684056811yescharacteristic
392C2#1684057611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#465C2
socleC22×C61C22×D4
hypercenter#465D61
hypocenterC61#3063
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. C2×#14519806C2semidirect
2. C2×#14519783C2semidirect
4. #16840335C2semidirect
5. #16840021C2semidirect
6. #16840018C2semidirect
7. #16840006C2semidirect
8. #16840005C2semidirect
9. #16840003C2semidirect
10. #16840002C2semidirect
11. #16839990C2semidirect
12. #16839801C2semidirect
13. #16839755C2semidirect
14. #103×D61C2semidirect
15. C61×#465C2semidirect
117. #11758189D4semidirect
208. #465D61semidirect
212. C61#3063semidirect