Finite Group Databasebeta

← #21458299

Subgroups — #21458299

Order 7808.

356 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840470C211yesmaximal, characteristic, complemented
2#16840459C211yesmaximal, characteristic
3#16840170C211yesmaximal, characteristic, complemented
4#16840100C211yesmaximal, characteristic, complemented
5#16840096C211yesmaximal, characteristic, complemented
6#16840079C211yesmaximal, characteristic, complemented
7#16840073C211yesmaximal, characteristic, complemented
8#16840067C211yesmaximal, characteristic, complemented
9#16840040C211yesmaximal, characteristic, complemented
10#16839988C211yesmaximal, characteristic, complemented
11#16839863C211yesmaximal, characteristic, complemented
12#16839831C211yesmaximal, characteristic, complemented
13#16839804C211yesmaximal, characteristic, complemented
14#107×D61C211yesmaximal, characteristic, complemented
15C61×#468C211yesmaximal, characteristic, complemented
16C2×C8×D61C2211yescharacteristic
17#14519776C2211yescharacteristic
18#14519770—21no—
19#14519768C2211yescharacteristic
20#14519767—21no—
21#14519758—21no—
22#14519757—21no—
23#14519754—21no—
24#14519753C2211yescharacteristic
25#14519748—21no—
26#14519748C2211yescharacteristic
27Q8×Dic61C2211yescharacteristic
28D4×Dic61C2211yescharacteristic
29C4×C22⋊D61C2211yescharacteristic
30#14519737—21no—
31#14519737—21no—
32#14519736C2211yescharacteristic
33C2×C4⋊Dic61C2211yescharacteristic
34C4⋊C4×D61C2211yescharacteristic
35C4⋊C4×D61C2211yescharacteristic
36#14519711C2211yescharacteristic
37#14519711C2211yescharacteristic
38#14519710C2211yescharacteristic
39#14519710C2211yescharacteristic
40#14519710C2211yescharacteristic
41#14519709C2211yescharacteristic
42#14519709C2211yescharacteristic
43#14519708C2211yescharacteristic
44#14519706C2211yescharacteristic
45#14519701C2211yescharacteristic
46#14519701C2211yescharacteristic
47#14519698C2211yescharacteristic
48#14519698C2211yescharacteristic
49C22⋊#92418C2211yescharacteristic
50#14519689C2211yescharacteristic
51#14519687C2211yescharacteristic
52C2×SD16×C61C2211yescharacteristic
53C2×M16×C61C2211yescharacteristic
54C22⋊Q8×C61C2211yescharacteristic
55#121×C61C2211yescharacteristic
56#107×C61C2211yescharacteristic
57#103×C61C2211yescharacteristic
58#102×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60C2×D4×C61—21no—
61C2×D4×C61C2311yescharacteristic
62C22×C4×C61C2311yescharacteristic
63C2×C22⋊D61—21no—
64C2×C22⋊D61D411yescharacteristic
65C22×Dic61—21no—
66C22×Dic61—21no—
67C2×C4×D61—21no—
68C2×C4×D61—21no—
69C2×C4×D61C2311yescharacteristic
70C2×Dic122—21no—
71SD16×C61—22no—
72M16×C61—22no—
73C2×C8×C61C2311yescharacteristic
74C2×C8×C61C2311yescharacteristic
75C4⋊C4×C61—21no—
76C4⋊C4×C61C2311yescharacteristic
77C4⋊C4×C61C2311yescharacteristic
78C22⋊C4×C61—21no—
79C22⋊C4×C61—21no—
80C22⋊Dic61—21no—
81C22⋊Dic61—21no—
82C22⋊Dic61—21no—
83C22⋊Dic61D411yescharacteristic
84#11758198—21no—
85#11758198D411yescharacteristic
86C4⋊Dic61—21no—
87C4⋊Dic61—21no—
88C4⋊Dic61—21no—
89C4⋊Dic61C2311yescharacteristic
90C4⋊Dic61C2311yescharacteristic
91C4⋊Dic61C2311yescharacteristic
92C4⋊Dic61C2311yescharacteristic
93#11758196—21no—
94#11758196—21no—
95#11758196—21no—
96#11758196—21no—
97#11758196—21no—
98#11758196D411yescharacteristic
99C4×Dic61—21no—
100C4×Dic61—21no—
101C4×Dic61C2311yescharacteristic
102C2×#92418C2311yescharacteristic
103C2×#92418C2311yescharacteristic
104C8×D61—22no—
105C23×C61—21no—
106C23×C61C2×D411yescharacteristic
107C22×D61C2×D411yescharacteristic
108Q8×C61—21no—
109Q8×C61—21no—
110D4×C61—21no—
111D4×C61—21no—
112D4×C61—81no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61C2×D411yescharacteristic
119C2×C4×C61C2411yescharacteristic
120C22⋊D61—22no—
121C22⋊D61—42no—
122C2×Dic61—21no—
123C2×Dic61—21no—
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—81no—
127C2×Dic61—81no—
128C2×Dic61C2×D411yescharacteristic
129C2×Dic61C2×D411yescharacteristic
130C2×Dic61C2×D411yescharacteristic
131C4×D61—21no—
132C4×D61—21no—
133C4×D61—81no—
134C4×D61—81no—
135Dic122—81no—
136C8×C61—21no—
137C8×C61#4112yes—
138#92418—21no—
139#92418—21no—
140C22×C61—21no—
141C22×C61—21no—
142C22×C61—21no—
143C22×C61—41no—
144C22×C61—41no—
145C22×C61—41no—
146C22×C61C22×D411yescharacteristic
147C2×D61—21no—
148C2×D61—21no—
149C2×D61#13712yes—
150C4×C61—21no—
151C4×C61—41no—
152C4×C61—41no—
153C4×C61—41no—
154C4×C61C2×#4111yescharacteristic
155C4×C612−1+411yescharacteristic
156Dic61—21no—
157Dic61—21no—
158Dic61—21no—
159Dic61—41no—
160Dic61—41no—
161Dic61—41no—
162Dic61—41no—
163#3346—611nomaximal, Sylow
164C2×C61—41no—
165C2×C61—81no—
166C2×C61#54711yescharacteristic
167C2×C61C2×#13711yescharacteristic
168C2×C61#57611yescharacteristic
169D61—22no—
170#554—611no—
171#553—611no—
172#501—611no—
173#485—611no—
174#484—611no—
175#481—611no—
176#480—611no—
177#479—611no—
178#474—611no—
179#468D6111yescharacteristic, complemented
180#465—611no—
181#440—611no—
182#435—611no—
183#428—611no—
184C2×#107—611no—
185C61#334611yescharacteristic, complemented, Sylow
186C2×SD16C2×D6111yescharacteristic
187C2×M16C2×D6111yescharacteristic
188C22×C8—611no—
189C4⋊Q8—611no—
190#126—1221no—
191#125—611no—
192#125—1221no—
193#123—1221no—
194C22⋊Q8—611no—
195C22⋊Q8—1221no—
196C22⋊Q8—1221no—
197C22⋊Q8C2×D6111yescharacteristic
198#121—611no—
199#121—1221no—
200#121C2×D6111yescharacteristic
201C4×Q8—611no—
202C4×D4—611no—
203C4×D4—611no—
204C4×D4—1221no—
205C4×D4—1221no—
206#117—611no—
207C2×C4⋊C4—611no—
208C2×C4⋊C4—611no—
209C2×C4⋊C4—611no—
210#107—611no—
211#107—611no—
212#107—611no—
213#107—611no—
214#107—611no—
215#107C2×D6111yescharacteristic
216#106—611no—
217#106—611no—
218#106—611no—
219C4⋊C8—611no—
220#103—611no—
221#103—611no—
222#103C2×D6111yescharacteristic
223#102—611no—
224#102—611no—
225#102C2×D6111yescharacteristic
226C22⋊C8—611no—
227C22⋊C8—611no—
228#97—611no—
229C2×Q8—1221no—
230C2×Q8C22×D6111yescharacteristic
231C2×D4—21no—
232C2×D4—611no—
233C2×D4—1221no—
234C2×D4C22×D6111yescharacteristic
235C22×C4—611no—
236C22×C4—1221no—
237C22×C4—1221no—
238C22×C4—1221no—
239C22×C4—1221no—
240C22×C4C22×D6111yescharacteristic
241SD16—22no—
242M16—22no—
243C2×C8—611no—
244C2×C8—611no—
245C2×C8—1222no—
246C2×C8C22×D6111yescharacteristic
247C2×C8C22×D6111yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—611no—
250C4⋊C4—611no—
251C4⋊C4—611no—
252C4⋊C4—611no—
253C4⋊C4—611no—
254C4⋊C4—1221no—
255C4⋊C4—1221no—
256C4⋊C4—1221no—
257C4⋊C4—1221no—
258C4⋊C4—1221no—
259C4⋊C4—1221no—
260C4⋊C4—1221no—
261C4⋊C4—1221no—
262C4⋊C4C22×D6111yescharacteristic
263C4⋊C4C22×D6111yescharacteristic
264C22⋊C4—21no—
265C22⋊C4—21no—
266C22⋊C4—611no—
267C22⋊C4—611no—
268C22⋊C4—1221no—
269C22⋊C4—1221no—
270C22⋊C4—1221no—
271C22⋊C4—1221no—
272C42—611no—
273C42—1221no—
274C42—1221no—
275C23—21no—
276C23—611no—
277C23D4×D6111yescharacteristic
278Q8—21no—
279Q8—21no—
280Q8—4881no—
281D4—21no—
282D4—21no—
283D4—81no—
284D4—1222no—
285D4—2442no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—611no—
292C2×C4—611no—
293C2×C4—611no—
294C2×C4—1221no—
295C2×C4—1221no—
296C2×C4—1221no—
297C2×C4—1221no—
298C2×C4—1221no—
299C2×C4—1221no—
300C2×C4—4881no—
301C2×C4—4881no—
302C2×C4—4881no—
303C2×C4—4881no—
304C2×C4D4×D6111yescharacteristic
305C2×C4C23×D6111yescharacteristic
306C8—21no—
307C8—1221no—
308C8—1221no—
309C8#1175822412yes—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—612no—
317C22—1221no—
318C22—1221no—
319C22C2×D4×D6111yescharacteristic
320C4—21no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—1221no—
325C4—1221no—
326C4—1221no—
327C4—2441no—
328C4—2441no—
329C4—2441no—
330C4—2441no—
331C4C2×#1175822411yescharacteristic
332C4#1451982411yescharacteristic
333C2—41no—
334C2—81no—
335C2—1222no—
336C2#1684041211yescharacteristic
337C2#137×D6111yescharacteristic
338C2#1684056611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#468C2
socleC22×C61C22×D4
hypercenter#468D61
hypocenterC61#3346
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #16840470C2semidirect
3. #16840170C2semidirect
4. #16840100C2semidirect
5. #16840096C2semidirect
6. #16840079C2semidirect
7. #16840073C2semidirect
8. #16840067C2semidirect
9. #16840040C2semidirect
10. #16839988C2semidirect
11. #16839863C2semidirect
12. #16839831C2semidirect
13. #16839804C2semidirect
14. #107×D61C2semidirect
15. C61×#468C2semidirect
179. #468D61semidirect
185. C61#3346semidirect