Finite Group Databasebeta

← #21456499

Subgroups — #21456499

Order 7808.

374 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840381C211yesmaximal, characteristic, complemented
2#16840366C211yesmaximal, characteristic, complemented
3#16840171C211yesmaximal, characteristic, complemented
4#16840116C211yesmaximal, characteristic, complemented
5#16840108C211yesmaximal, characteristic, complemented
6#16840012C211yesmaximal, characteristic, complemented
7#16840005C211yesmaximal, characteristic, complemented
8#16839995C211yesmaximal, characteristic, complemented
9#16839988C211yesmaximal, characteristic, complemented
10#16839874C211yesmaximal, characteristic, complemented
11#16839863C211yesmaximal, characteristic, complemented
12SD16×Dic61C211yesmaximal, characteristic, complemented
13D8×Dic61C211yesmaximal, characteristic, complemented
14#16839719C211yesmaximal, characteristic, complemented
15C61×#496C211yesmaximal, characteristic, complemented
16C2×#11758189C2211yescharacteristic
17C2×C8×D61C2211yescharacteristic
18#14519777C2211yescharacteristic
19#14519770—21no—
20#14519769C2211yescharacteristic
21#14519763—21no—
22#14519761—21no—
23#14519758—21no—
24#14519758—21no—
25#14519754—21no—
26#14519753C2211yescharacteristic
27#14519749—21no—
28#14519749—21no—
29#14519748C2211yescharacteristic
30#14519748C2211yescharacteristic
31#14519748C2211yescharacteristic
32Q8×Dic61C2211yescharacteristic
33D4×Dic61C2211yescharacteristic
34D4×Dic61C2211yescharacteristic
35D4×Dic61C2211yescharacteristic
36#14519734C2211yescharacteristic
37#14519711C2211yescharacteristic
38#14519711C2211yescharacteristic
39#14519709C2211yescharacteristic
40#14519709C2211yescharacteristic
41#14519701C2211yescharacteristic
42#14519701C2211yescharacteristic
43#14519698C2211yescharacteristic
44#14519698C2211yescharacteristic
45#14519698C2211yescharacteristic
46#14519698C2211yescharacteristic
47#14519698C2211yescharacteristic
48#14519698C2211yescharacteristic
49#14519687C2211yescharacteristic
50C4×#92418C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52C2×SD16×C61C2211yescharacteristic
53C2×SD16×C61C2211yescharacteristic
54C2×D8×C61C2211yescharacteristic
55C2×D8×C61C2211yescharacteristic
56#127×C61C2211yescharacteristic
57#124×C61C2211yescharacteristic
58#97×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60C2×D4×C61—21no—
61C2×D4×C61—21no—
62C2×D4×C61C2311yescharacteristic
63C2×D4×C61C2311yescharacteristic
64C2×D4×C61C2311yescharacteristic
65C2×C22⋊D61—21no—
66C2×C22⋊D61—21no—
67C2×C22⋊D61—21no—
68C22×Dic61—21no—
69C22×Dic61—21no—
70C22×Dic61—21no—
71C2×C4×D61C2311yescharacteristic
72C2×Dic122—21no—
73SD16×C61—22no—
74SD16×C61—22no—
75D8×C61—22no—
76D8×C61—22no—
77C2×C8×C61C2311yescharacteristic
78C2×C8×C61C2311yescharacteristic
79C22⋊C4×C61—21no—
80C22⋊C4×C61—21no—
81C42×C61C2311yescharacteristic
82C22⋊Dic61—21no—
83C22⋊Dic61—21no—
84C22⋊Dic61—21no—
85C22⋊Dic61—21no—
86C22⋊Dic61—21no—
87C22⋊Dic61—21no—
88#11758198—21no—
89#11758198D411yescharacteristic
90#11758198D411yescharacteristic
91C4⋊Dic61—21no—
92C4⋊Dic61—21no—
93C4⋊Dic61C2311yescharacteristic
94C4⋊Dic61C2311yescharacteristic
95C4⋊Dic61C2311yescharacteristic
96C4⋊Dic61C2311yescharacteristic
97#11758196—21no—
98#11758196—21no—
99#11758196—21no—
100#11758196D411yescharacteristic
101#11758196D411yescharacteristic
102C4×Dic61—21no—
103C4×Dic61C2311yescharacteristic
104C2×#92418C2311yescharacteristic
105C2×#92418C2311yescharacteristic
106#11758189—22no—
107C8×D61—22no—
108C23×C61—21no—
109C23×C61—21no—
110C23×C61—21no—
111C22×D61C2×D411yescharacteristic
112Q8×C61—21no—
113Q8×C61—21no—
114D4×C61—21no—
115D4×C61—21no—
116D4×C61—21no—
117D4×C61—21no—
118D4×C61—21no—
119D4×C61—21no—
120D4×C61—81no—
121D4×C61—81no—
122C2×C4×C61—21no—
123C2×C4×C61C2×D411yescharacteristic
124C2×C4×C61C2×D411yescharacteristic
125C2×C4×C61C2411yescharacteristic
126C22⋊D61—81no—
127C22⋊D61—81no—
128C22⋊D61—81no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—81no—
134C2×Dic61—81no—
135C2×Dic61—81no—
136C2×Dic61C2×D411yescharacteristic
137C2×Dic61C2×D411yescharacteristic
138C2×Dic61C2×D411yescharacteristic
139C4×D61—21no—
140C4×D61—21no—
141Dic122—81no—
142C8×C61#4112yes—
143C8×C61#4112yes—
144#92418—21no—
145#92418—21no—
146C22×C61—41no—
147C22×C61—41no—
148C22×C61—41no—
149C22×C61—41no—
150C22×C61—41no—
151C22×C61—41no—
152C22×C61—41no—
153C22×C61—41no—
154C22×C61—41no—
155C22×C61C22×D411yescharacteristic
156C2×D61—21no—
157C2×D61—21no—
158C2×D61—21no—
159C4×C61—21no—
160C4×C61—21no—
161C4×C61—41no—
162C4×C61C2×#4111yescharacteristic
163C4×C61C2×#4111yescharacteristic
164Dic61—21no—
165Dic61—21no—
166Dic61—21no—
167Dic61—41no—
168Dic61—41no—
169Dic61—41no—
170Dic61—41no—
171#3179—611nomaximal, Sylow
172C2×C61—81no—
173C2×C61—81no—
174C2×C61—81no—
175C2×C61#53211yescharacteristic
176C2×C61#57611yescharacteristic
177C2×C61#57711yescharacteristic
178D61—41no—
179#542—611no—
180#540—611no—
181#501—611no—
182#496D6111yescharacteristic, complemented
183#488—611no—
184#486—611no—
185#469—611no—
186#468—611no—
187#466—611no—
188#465—611no—
189#442—611no—
190#440—611no—
191C4×SD16—611no—
192C4×D8—611no—
193#405—611no—
194C61#317911yescharacteristic, complemented, Sylow
195C2×SD16C2×D6111yescharacteristic
196C2×SD16C2×D6111yescharacteristic
197C2×D8C2×D6111yescharacteristic
198C2×D8C2×D6111yescharacteristic
199C2×M16—611no—
200C22×C8—611no—
201C4⋊Q8—611no—
202#127C2×D6111yescharacteristic
203#126—1221no—
204#125—611no—
205#124—1221no—
206#124C2×D6111yescharacteristic
207#123—1221no—
208#123—1221no—
209#123—1221no—
210C22⋊Q8—611no—
211C22⋊Q8—1221no—
212#121—611no—
213#121—611no—
214#121—611no—
215#121—1221no—
216#121—1221no—
217C4×Q8—611no—
218C4×D4—611no—
219C4×D4—611no—
220C4×D4—611no—
221#117—611no—
222#107—611no—
223#107—611no—
224#106—611no—
225#106—611no—
226#103—611no—
227#103—611no—
228#102—611no—
229#102—611no—
230#102—611no—
231#102—611no—
232#102—611no—
233#102—611no—
234#97—611no—
235#97C2×D6111yescharacteristic
236C4×C8—611no—
237C4×C8—611no—
238C2×Q8—1221no—
239C2×Q8C22×D6111yescharacteristic
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—1221no—
243C2×D4—1221no—
244C2×D4—1221no—
245C2×D4C22×D6111yescharacteristic
246C2×D4C22×D6111yescharacteristic
247C2×D4C22×D6111yescharacteristic
248C22×C4—611no—
249C22×C4—1221no—
250C22×C4—1221no—
251C22×C4—1221no—
252SD16—22no—
253SD16—22no—
254D8—22no—
255D8—22no—
256M16—1222no—
257C2×C8—611no—
258C2×C8—611no—
259C2×C8—1222no—
260C2×C8C22×D6111yescharacteristic
261C2×C8C22×D6111yescharacteristic
262C4⋊C4—611no—
263C4⋊C4—611no—
264C4⋊C4—611no—
265C4⋊C4—611no—
266C4⋊C4—611no—
267C4⋊C4—611no—
268C4⋊C4—1221no—
269C4⋊C4—1221no—
270C4⋊C4—1221no—
271C4⋊C4—1221no—
272C4⋊C4—1221no—
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—611no—
276C22⋊C4—611no—
277C22⋊C4—1221no—
278C22⋊C4—1221no—
279C22⋊C4—1221no—
280C22⋊C4—1221no—
281C22⋊C4—1221no—
282C22⋊C4—1221no—
283C22⋊C4—1221no—
284C42—611no—
285C42—1221no—
286C42C22×D6111yescharacteristic
287C23—21no—
288C23—21no—
289C23—21no—
290C23—611no—
291Q8—21no—
292Q8—21no—
293Q8—4881no—
294D4—21no—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—21no—
299D4—21no—
300D4—81no—
301D4—81no—
302D4—4881no—
303D4—4881no—
304D4—4881no—
305C2×C4—21no—
306C2×C4—611no—
307C2×C4—611no—
308C2×C4—611no—
309C2×C4—1221no—
310C2×C4—1221no—
311C2×C4—1221no—
312C2×C4—1221no—
313C2×C4—1221no—
314C2×C4—1221no—
315C2×C4—4881no—
316C2×C4—4881no—
317C2×C4—4881no—
318C2×C4D4×D6111yescharacteristic
319C2×C4D4×D6111yescharacteristic
320C2×C4C23×D6111yescharacteristic
321C8—1221no—
322C8—1221no—
323C8#1175822412yes—
324C8#1175822412yes—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—1221no—
335C22—1221no—
336C22—1221no—
337C22C2×D4×D6111yescharacteristic
338C4—21no—
339C4—21no—
340C4—41no—
341C4—1221no—
342C4—1221no—
343C4—1221no—
344C4—2441no—
345C4—2441no—
346C4—2441no—
347C4—2441no—
348C4C2×#1175822411yescharacteristic
349C4C2×#1175822411yescharacteristic
350C2—81no—
351C2—81no—
352C2—81no—
353C2—2441no—
354C2#1684031011yescharacteristic
355C2#1684056611yescharacteristic
356C2#1684057211yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#496C2
socleC22×C61C22×D4
hypercenter#496D61
hypocenterC61#3179
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #16840381C2semidirect
2. #16840366C2semidirect
3. #16840171C2semidirect
4. #16840116C2semidirect
5. #16840108C2semidirect
6. #16840012C2semidirect
7. #16840005C2semidirect
8. #16839995C2semidirect
9. #16839988C2semidirect
10. #16839874C2semidirect
11. #16839863C2semidirect
12. SD16×Dic61C2semidirect
13. D8×Dic61C2semidirect
14. #16839719C2semidirect
15. C61×#496C2semidirect
182. #496D61semidirect
194. C61#3179semidirect