Finite Group Databasebeta

← #21457989

Subgroups — #21457989

Order 7808.

388 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840465C211yesmaximal, characteristic
2#16840427C211yesmaximal, characteristic, complemented
3#16840102C211yesmaximal, characteristic, complemented
4#16840096C211yesmaximal, characteristic, complemented
5#16840066C211yesmaximal, characteristic, complemented
6#16840011C211yesmaximal, characteristic, complemented
7#16839994C211yesmaximal, characteristic, complemented
8#16839964C211yesmaximal, characteristic, complemented
9#16839902C211yesmaximal, characteristic, complemented
10#16839902C211yesmaximal, characteristic, complemented
11#16839864C211yesmaximal, characteristic, complemented
12#16839835C211yesmaximal, characteristic, complemented
13#16839769C211yesmaximal, characteristic, complemented
14#103×D61C211yesmaximal, characteristic, complemented
15C61×#491C211yesmaximal, characteristic, complemented
16C2×Q8×D61C2211yescharacteristic
17C2×Q8×D61C2211yescharacteristic
18C2×#11758190C2211yescharacteristic
19C2×#11758201C2211yescharacteristic
20C2×#11758201C2211yescharacteristic
21C2×#11758189C2211yescharacteristic
22C2×C8×D61C2211yescharacteristic
23#14519776—21no—
24#14519772—21no—
25#14519762—21no—
26#14519755—21no—
27#14519755—21no—
28#14519753C2211yescharacteristic
29#14519753C2211yescharacteristic
30#14519752—21no—
31#14519752C2211yescharacteristic
32#14519752C2211yescharacteristic
33C4×Dic122C2211yescharacteristic
34C4×D244C2211yescharacteristic
35C4×D244C2211yescharacteristic
36#14519739—21no—
37#14519739—21no—
38#14519735C2211yescharacteristic
39C4⋊C4×D61C2211yescharacteristic
40#14519711C2211yescharacteristic
41#14519710C2211yescharacteristic
42#14519708C2211yescharacteristic
43C4⋊#92418C2211yescharacteristic
44#14519702C2211yescharacteristic
45#14519701C2211yescharacteristic
46#14519701C2211yescharacteristic
47#14519700C2211yescharacteristic
48#14519700C2211yescharacteristic
49#14519699C2211yescharacteristic
50#14519689C2211yescharacteristic
51#14519689C2211yescharacteristic
52C4⋊Q8×C61C2211yescharacteristic
53#125×C61C2211yescharacteristic
54#103×C61C2211yescharacteristic
55#103×C61C2211yescharacteristic
56#103×C61C2211yescharacteristic
57#103×C61C2211yescharacteristic
58#97×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60C2×Q8×C61C2311yescharacteristic
61Q8×D61—22no—
62Q8×D61—22no—
63Q8×D61—41no—
64Q8×D61—41no—
65C2×D244—21no—
66C2×D244—21no—
67C2×D244D411yescharacteristic
68C2×D244C2311yescharacteristic
69C2×C4×D61—21no—
70C2×C4×D61—21no—
71C2×C4×D61—21no—
72C2×C4×D61—21no—
73C2×C4×D61C2311yescharacteristic
74C2×C4×D61C2311yescharacteristic
75C2×Dic122—21no—
76C2×Dic122—21no—
77C2×Dic122C2311yescharacteristic
78C2×C8×C61C2311yescharacteristic
79C2×C8×C61C2311yescharacteristic
80C4⋊C4×C61—21no—
81C4⋊C4×C61—21no—
82C4⋊C4×C61—21no—
83C4⋊C4×C61—21no—
84C4⋊C4×C61C2311yescharacteristic
85C4⋊C4×C61C2311yescharacteristic
86C42×C61C2311yescharacteristic
87#11758201—41no—
88#11758201—41no—
89#11758198—21no—
90#11758198—21no—
91#11758198—21no—
92#11758198—21no—
93#11758198—21no—
94#11758198—21no—
95#11758198D411yescharacteristic
96#11758198D411yescharacteristic
97C4⋊Dic61D411yescharacteristic
98C4⋊Dic61C2311yescharacteristic
99C4⋊Dic61C2311yescharacteristic
100#11758196—21no—
101#11758196—21no—
102#11758196—21no—
103#11758196—21no—
104C4×Dic61—21no—
105C4×Dic61—21no—
106C2×#92418C2311yescharacteristic
107C2×#92418C2311yescharacteristic
108#11758190—22no—
109#11758189—41no—
110C8×D61—41no—
111C22×D61—21no—
112C22×D61C2×D411yescharacteristic
113C22×D61C2×D411yescharacteristic
114Q8×C61—21no—
115Q8×C61—21no—
116Q8×C61—21no—
117Q8×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61C2×D411yescharacteristic
123C2×C4×C61C2×D411yescharacteristic
124C2×C4×C61C2411yescharacteristic
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61C2×D411yescharacteristic
129C2×Dic61C2×D411yescharacteristic
130D244—22no—
131D244—21no—
132D244—21no—
133D244—42no—
134D244—81no—
135C4×D61—21no—
136C4×D61—21no—
137C4×D61—21no—
138C4×D61—21no—
139C4×D61—42no—
140C4×D61—42no—
141C4×D61—81no—
142C4×D61—81no—
143Dic122—21no—
144Dic122—42no—
145Dic122—42no—
146Dic122#4112yes—
147C8×C61—21no—
148C8×C61—21no—
149#92418—21no—
150#92418—21no—
151C22×C61C22×D411yescharacteristic
152C2×D61—21no—
153C2×D61—21no—
154C2×D61—21no—
155C2×D61—21no—
156C2×D61—21no—
157C2×D61—41no—
158C2×D61—41no—
159C2×D61—41no—
160C2×D61#13712yes—
161C4×C61—21no—
162C4×C61—21no—
163C4×C61—41no—
164C4×C61—41no—
165C4×C61—41no—
166C4×C61—41no—
167C4×C61C2×#4111yescharacteristic
168C4×C61H(5,𝔽2)11yescharacteristic
169Dic61—22no—
170Dic61—21no—
171Dic61—21no—
172Dic61—41no—
173Dic61—41no—
174#3320—611nomaximal, Sylow
175C2×C61#54611yescharacteristic
176C2×C61C2×#13711yescharacteristic
177C2×C61#57711yescharacteristic
178D61—22no—
179D61—41no—
180D61—81no—
181#553—611no—
182D4×Q8—611no—
183#491D6111yescharacteristic, complemented
184#485—611no—
185#484—611no—
186#479—611no—
187#468—611no—
188#465—611no—
189#461—611no—
190#448—611no—
191#448—611no—
192#440—611no—
193#435—611no—
194#419—611no—
195C2×#103—611no—
196C61#332011yescharacteristic, complemented, Sylow
197C22×Q8—611no—
198C22×Q8—611no—
199C2×SD16—611no—
200C2×SD16—611no—
201C2×SD16—611no—
202C2×M16—611no—
203C22×C8—611no—
204C4⋊Q8—1221no—
205C4⋊Q8C2×D6111yescharacteristic
206#126—1221no—
207#125C2×D6111yescharacteristic
208#123—1221no—
209C22⋊Q8—611no—
210C22⋊Q8—611no—
211C22⋊Q8—1221no—
212C22⋊Q8—1221no—
213#121—611no—
214#121—611no—
215#121—1221no—
216C4×Q8—611no—
217C4×D4—611no—
218C4×D4—611no—
219C4×D4—1221no—
220C4×D4—1221no—
221#117—611no—
222C2×C4⋊C4—611no—
223#107—611no—
224#107—611no—
225#106—611no—
226C4⋊C8—611no—
227#103—611no—
228#103—611no—
229#103—611no—
230#103—611no—
231#103—611no—
232#103C2×D6111yescharacteristic
233#103C2×D6111yescharacteristic
234#103C2×D6111yescharacteristic
235#103C2×D6111yescharacteristic
236#102—611no—
237C22⋊C8—611no—
238C22⋊C8—611no—
239#97C2×D6111yescharacteristic
240C2×Q8—611no—
241C2×Q8—1221no—
242C2×Q8—1221no—
243C2×Q8—1222no—
244C2×Q8—1222no—
245C2×Q8—2441no—
246C2×Q8—2441no—
247C2×Q8C22×D6111yescharacteristic
248C2×Q8C22×D6111yescharacteristic
249C2×D4—611no—
250C2×D4—611no—
251C2×D4—1221no—
252C2×D4—1221no—
253C22×C4—611no—
254C22×C4—611no—
255C22×C4—1221no—
256C22×C4—1221no—
257C22×C4—1221no—
258C22×C4—1221no—
259SD16—1222no—
260SD16—2441no—
261SD16—2441no—
262M16—2441no—
263C2×C8—611no—
264C2×C8—611no—
265C2×C8—2441no—
266C2×C8C22×D6111yescharacteristic
267C2×C8C22×D6111yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—611no—
273C4⋊C4—611no—
274C4⋊C4—611no—
275C4⋊C4—1221no—
276C4⋊C4—1221no—
277C4⋊C4—1221no—
278C4⋊C4—1221no—
279C4⋊C4C22×D6111yescharacteristic
280C4⋊C4C22×D6111yescharacteristic
281C22⋊C4—611no—
282C22⋊C4—611no—
283C22⋊C4—1221no—
284C22⋊C4—1221no—
285C22⋊C4—1221no—
286C22⋊C4—1221no—
287C22⋊C4—1221no—
288C22⋊C4—1221no—
289C42—1221no—
290C42—1221no—
291C42C22×D6111yescharacteristic
292C23—611no—
293C23—611no—
294C23—1221no—
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—21no—
299Q8—612no—
300Q8—1221no—
301Q8—2442no—
302Q8—2442no—
303D4—1222no—
304D4—1221no—
305D4—1221no—
306D4—4881no—
307D4—2442no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—611no—
313C2×C4—611no—
314C2×C4—1221no—
315C2×C4—1221no—
316C2×C4—1221no—
317C2×C4—1221no—
318C2×C4—1221no—
319C2×C4—1221no—
320C2×C4—1221no—
321C2×C4—4881no—
322C2×C4—4881no—
323C2×C4—2442no—
324C2×C4—2442no—
325C2×C4D4×D6111yescharacteristic
326C2×C4D4×D6111yescharacteristic
327C2×C4C23×D6111yescharacteristic
328C8—21no—
329C8—21no—
330C8—1221no—
331C8—1221no—
332C22—612no—
333C22—1221no—
334C22—1221no—
335C22—1221no—
336C22—1221no—
337C22—1221no—
338C22—2441no—
339C22—2441no—
340C22—2441no—
341C22C2×D4×D6111yescharacteristic
342C4—21no—
343C4—21no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—1221no—
349C4—1221no—
350C4—1222no—
351C4—2441no—
352C4—2441no—
353C4#41×D6111yescharacteristic
354C4#1451982311yescharacteristic
355C2—1222no—
356C2—4881no—
357C2—2441no—
358C2#1684040511yescharacteristic
359C2#137×D6111yescharacteristic
360C2#1684057111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#491C2
socleC22×C61C22×D4
hypercenter#491D61
hypocenterC61#3320
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
2. #16840427C2semidirect
3. #16840102C2semidirect
4. #16840096C2semidirect
5. #16840066C2semidirect
6. #16840011C2semidirect
7. #16839994C2semidirect
8. #16839964C2semidirect
9. #16839902C2semidirect
10. #16839902C2semidirect
11. #16839864C2semidirect
12. #16839835C2semidirect
13. #16839769C2semidirect
14. #103×D61C2semidirect
15. C61×#491C2semidirect
183. #491D61semidirect
196. C61#3320semidirect