Finite Group Databasebeta

← #21457809

Subgroups — #21457809

Order 7808.

420 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840420C211yesmaximal, characteristic, complemented
2#16840415C211yesmaximal, characteristic, complemented
3#16840096C211yesmaximal, characteristic, complemented
4#16840074C211yesmaximal, characteristic, complemented
5#16840054C211yesmaximal, characteristic, complemented
6#16840011C211yesmaximal, characteristic, complemented
7#16839997C211yesmaximal, characteristic, complemented
8#16839974C211yesmaximal, characteristic, complemented
9#16839908C211yesmaximal, characteristic, complemented
10#16839902C211yesmaximal, characteristic, complemented
11#16839864C211yesmaximal, characteristic, complemented
12#16839835C211yesmaximal, characteristic, complemented
13#16839760C211yesmaximal, characteristic, complemented
14#103×D61C211yesmaximal, characteristic, complemented
15C61×#489C211yesmaximal, characteristic, complemented
16C2×#11758226—21no—
17C2×#11758224C2211yescharacteristic
18C2×Q8×D61C2211yescharacteristic
19C2×#11758190C2211yescharacteristic
20C2×#11758201C2211yescharacteristic
21C2×#11758199C2211yescharacteristic
22C2×#11758189C2211yescharacteristic
23C2×C8×D61C2211yescharacteristic
24#14519763—21no—
25#14519762—21no—
26#14519762—21no—
27#14519754—21no—
28#14519753—21no—
29#14519753C2211yescharacteristic
30#14519752C2211yescharacteristic
31#14519752C2211yescharacteristic
32#14519750—21no—
33#14519748C2211yescharacteristic
34C4×Dic122C2211yescharacteristic
35C4×D244C2211yescharacteristic
36C4×D244C2211yescharacteristic
37#14519737—21no—
38C4⋊C4×D61C2211yescharacteristic
39C4⋊C4×D61C2211yescharacteristic
40#14519711C2211yescharacteristic
41#14519710C2211yescharacteristic
42#14519710C2211yescharacteristic
43C4⋊#92418C2211yescharacteristic
44#14519702C2211yescharacteristic
45#14519701C2211yescharacteristic
46#14519700C2211yescharacteristic
47#14519700C2211yescharacteristic
48#14519699C2211yescharacteristic
49#14519698C2211yescharacteristic
50#14519689C2211yescharacteristic
51#14519689C2211yescharacteristic
52C4⋊Q8×C61C2211yescharacteristic
53#124×C61C2211yescharacteristic
54#103×C61C2211yescharacteristic
55#103×C61C2211yescharacteristic
56#102×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic
58#97×C61C2211yescharacteristic
59C2×Q8×C61—21no—
60C2×Q8×C61C2311yescharacteristic
61C2×D4×C61C2311yescharacteristic
62C2×C22⋊D61—21no—
63C2×C22⋊D61—21no—
64C22×Dic61—21no—
65#11758226—44no—
66Q8×D61—22no—
67Q8×D61—41no—
68#11758224—22no—
69#11758224—41no—
70C2×D244—21no—
71C2×D244—21no—
72C2×D244D411yescharacteristic
73C2×D244C2311yescharacteristic
74C2×C4×D61—21no—
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×C4×D61C2311yescharacteristic
79C2×C4×D61C2311yescharacteristic
80C2×Dic122—21no—
81C2×Dic122C2311yescharacteristic
82C2×C8×C61C2311yescharacteristic
83C2×C8×C61C2311yescharacteristic
84C4⋊C4×C61—21no—
85C4⋊C4×C61C2311yescharacteristic
86C4⋊C4×C61C2311yescharacteristic
87C22⋊C4×C61—21no—
88C22⋊C4×C61—21no—
89C42×C61C2311yescharacteristic
90C22⋊Dic61—21no—
91#11758201—41no—
92#11758199—41no—
93#11758198—21no—
94#11758198—21no—
95#11758198—21no—
96#11758198—21no—
97#11758198D411yescharacteristic
98#11758198D411yescharacteristic
99C4⋊Dic61D411yescharacteristic
100C4⋊Dic61C2311yescharacteristic
101C4⋊Dic61C2311yescharacteristic
102#11758196—21no—
103#11758196—21no—
104#11758196—21no—
105#11758196—21no—
106C4×Dic61—21no—
107C2×#92418C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109#11758190—22no—
110#11758189—41no—
111C8×D61—41no—
112C23×C61—21no—
113C22×D61—21no—
114C22×D61C2×D411yescharacteristic
115C22×D61C2×D411yescharacteristic
116Q8×C61—21no—
117Q8×C61—21no—
118Q8×C61—42no—
119D4×C61—21no—
120D4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61C2×D411yescharacteristic
125C2×C4×C61C2×D411yescharacteristic
126C2×C4×C61C2411yescharacteristic
127C22⋊D61—42no—
128C22⋊D61—42no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—42no—
133C2×Dic61C2×D411yescharacteristic
134C2×Dic61C2×D411yescharacteristic
135D244—22no—
136D244—21no—
137D244—21no—
138D244—42no—
139D244—42no—
140C4×D61—21no—
141C4×D61—21no—
142C4×D61—21no—
143C4×D61—21no—
144C4×D61—42no—
145C4×D61—42no—
146C4×D61—42no—
147C4×D61—42no—
148Dic122—21no—
149Dic122—42no—
150Dic122#4112yescomplemented
151C8×C61—21no—
152C8×C61—21no—
153#92418—21no—
154#92418—21no—
155C22×C61—41no—
156C22×C61—41no—
157C22×C61—41no—
158C22×C61C22×D411yescharacteristic
159C2×D61—21no—
160C2×D61—21no—
161C2×D61—21no—
162C2×D61—21no—
163C2×D61—21no—
164C2×D61—41no—
165C2×D61—41no—
166C2×D61—41no—
167C2×D61AGL(1,ℤ/8)12yes—
168C4×C61—21no—
169C4×C61—21no—
170C4×C61—41no—
171C4×C61—41no—
172C4×C61—41no—
173C4×C61C2×#4111yescharacteristic
174C4×C61H(5,𝔽2)11yescharacteristic
175Dic61—22no—
176Dic61—21no—
177Dic61—21no—
178Dic61—41no—
179Dic61—41no—
180#3308—611nomaximal, Sylow
181C2×C61—81no—
182C2×C61#54611yescharacteristic
183C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
184C2×C61#57811yescharacteristic
185D61—22no—
186D61—41no—
187D61—81no—
188#548—611no—
189#547—611no—
190#489D6111yescharacteristic, complemented
191#484—611no—
192#480—611no—
193#477—611no—
194#468—611no—
195#466—611no—
196#463—611no—
197#449—611no—
198#448—611no—
199#440—611no—
200#435—611no—
201#417—611no—
202C2×#103—611no—
203C61#330811yescharacteristic, complemented, Sylow
204C2×#41—611no—
205C2×#41—1221no—
206C22×Q8—611no—
207C2×SD16—611no—
208C2×SD16—611no—
209C2×D8—611no—
210C2×M16—611no—
211C22×C8—611no—
212C4⋊Q8C2×D6111yescharacteristic
213#124—1221no—
214#124C2×D6111yescharacteristic
215#123—1221no—
216#123—1221no—
217C22⋊Q8—611no—
218C22⋊Q8—1221no—
219C22⋊Q8—1221no—
220#121—611no—
221#121—611no—
222#121—611no—
223#121—1221no—
224C4×Q8—611no—
225C4×D4—611no—
226C4×D4—611no—
227C4×D4—1221no—
228C2×C4⋊C4—611no—
229C2×C4⋊C4—611no—
230#107—611no—
231#107—611no—
232#107—611no—
233C4⋊C8—611no—
234#103—611no—
235#103—611no—
236#103—611no—
237#103—611no—
238#103C2×D6111yescharacteristic
239#103C2×D6111yescharacteristic
240#102—611no—
241#102—611no—
242#102C2×D6111yescharacteristic
243#102C2×D6111yescharacteristic
244C22⋊C8—611no—
245C22⋊C8—611no—
246#97C2×D6111yescharacteristic
247#41—1222no—
248#41—2441no—
249#41—2444no—
250C2×Q8—21no—
251C2×Q8—611no—
252C2×Q8—1221no—
253C2×Q8—1222no—
254C2×Q8—2441no—
255C2×Q8C22×D6111yescharacteristic
256C2×D4—611no—
257C2×D4—611no—
258C2×D4—1221no—
259C2×D4—1221no—
260C2×D4—1221no—
261C2×D4—1221no—
262C2×D4C22×D6111yescharacteristic
263C22×C4—611no—
264C22×C4—611no—
265C22×C4—1221no—
266C22×C4—1221no—
267C22×C4—1221no—
268C22×C4—1221no—
269C22×C4—1221no—
270SD16—1222no—
271SD16—2441no—
272D8—2441no—
273M16—2441no—
274C2×C8—611no—
275C2×C8—611no—
276C2×C8—2441no—
277C2×C8C22×D6111yescharacteristic
278C2×C8C22×D6111yescharacteristic
279C4⋊C4—21no—
280C4⋊C4—611no—
281C4⋊C4—611no—
282C4⋊C4—611no—
283C4⋊C4—1221no—
284C4⋊C4—1221no—
285C4⋊C4—1221no—
286C4⋊C4—1221no—
287C4⋊C4C22×D6111yescharacteristic
288C4⋊C4C22×D6111yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—611no—
292C22⋊C4—611no—
293C22⋊C4—1221no—
294C22⋊C4—1221no—
295C22⋊C4—1221no—
296C22⋊C4—1221no—
297C22⋊C4—1221no—
298C42—1221no—
299C42C22×D6111yescharacteristic
300C23—21no—
301C23—611no—
302C23—611no—
303C23—1221no—
304Q8—21no—
305Q8—21no—
306Q8—42no—
307Q8—612no—
308Q8—1221no—
309Q8—2442no—
310D4—21no—
311D4—21no—
312D4—1222no—
313D4—1221no—
314D4—1221no—
315D4—2442no—
316D4—2442no—
317D4—2442no—
318D4—2442no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—611no—
323C2×C4—611no—
324C2×C4—1221no—
325C2×C4—1221no—
326C2×C4—1221no—
327C2×C4—1221no—
328C2×C4—1221no—
329C2×C4—1221no—
330C2×C4—1221no—
331C2×C4—2442no—
332C2×C4—2442no—
333C2×C4—2442no—
334C2×C4—2442no—
335C2×C4—2442no—
336C2×C4D4×D6111yescharacteristic
337C2×C4D4×D6111yescharacteristic
338C2×C4C23×D6111yescharacteristic
339C8—21no—
340C8—21no—
341C8—1221no—
342C8—1221no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—612no—
347C22—1221no—
348C22—1221no—
349C22—1221no—
350C22—1221no—
351C22—1221no—
352C22—2441no—
353C22—2441no—
354C22—2441no—
355C22C2×D4×D6111yescharacteristic
356C4—21no—
357C4—21no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—1221no—
362C4—1221no—
363C4—1222no—
364C4—2441no—
365C4—2441no—
366C4#41×D6111yescharacteristic
367C4#1451982311yescharacteristic
368C2—81no—
369C2—1222no—
370C2—4881no—
371C2—2441no—
372C2#1684040511yescharacteristic
373C2AGL(1,ℤ/8)×D6111yescharacteristic
374C2#1684057811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#489C2
socleC22×C61C22×D4
hypercenter#489D61
hypocenterC61#3308
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #16840420C2semidirect
2. #16840415C2semidirect
3. #16840096C2semidirect
4. #16840074C2semidirect
5. #16840054C2semidirect
6. #16840011C2semidirect
7. #16839997C2semidirect
8. #16839974C2semidirect
9. #16839908C2semidirect
10. #16839902C2semidirect
11. #16839864C2semidirect
12. #16839835C2semidirect
13. #16839760C2semidirect
14. #103×D61C2semidirect
15. C61×#489C2semidirect
150. Dic122#41semidirect
190. #489D61semidirect
203. C61#3308semidirect