Finite Group Databasebeta

← #21457885

Subgroups — #21457885

Order 7808.

380 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#16840482C211yesmaximal, characteristic, complemented
2#16840121C211yesmaximal, characteristic, complemented
3#16840100C211yesmaximal, characteristic, complemented
4#16840083C211yesmaximal, characteristic, complemented
5#16840057C211yesmaximal, characteristic, complemented
6#16840006C211yesmaximal, characteristic, complemented
7#16840001C211yesmaximal, characteristic, complemented
8#16839981C211yesmaximal, characteristic, complemented
9#16839924C211yesmaximal, characteristic, complemented
10#16839918C211yesmaximal, characteristic, complemented
11#16839867C211yesmaximal, characteristic, complemented
12#16839834C211yesmaximal, characteristic, complemented
13#16839771C211yesmaximal, characteristic, complemented
14#16839758C211yesmaximal, characteristic, complemented
15C61×#548C211yesmaximal, characteristic
16C2×#11758202C2211yescharacteristic
17C2×#11758202C2211yescharacteristic
18C2×#11758200C2211yescharacteristic
19C2×#11758194C2211yescharacteristic
20C22×#92418C2211yescharacteristic
21#14519777C2211yescharacteristic
22#14519770—21no—
23#14519770—21no—
24#14519764—21no—
25#14519756C2211yescharacteristic
26#14519756C2211yescharacteristic
27C4×Dic122C2211yescharacteristic
28#14519742—21no—
29#14519736C2211yescharacteristic
30#14519736C2211yescharacteristic
31#14519710C2211yescharacteristic
32#14519710C2211yescharacteristic
33#14519708C2211yescharacteristic
34C4⋊#92418C2211yescharacteristic
35#14519701C2211yescharacteristic
36#14519701C2211yescharacteristic
37#14519701C2211yescharacteristic
38#14519701C2211yescharacteristic
39#14519701C2211yescharacteristic
40#14519701C2211yescharacteristic
41#14519700C2211yescharacteristic
42#14519698C2211yescharacteristic
43#14519698C2211yescharacteristic
44#14519698C2211yescharacteristic
45C22⋊#92418C2211yescharacteristic
46C22⋊#92418C2211yescharacteristic
47#14519688C2211yescharacteristic
48C2×#41×C61C2211yescharacteristic
49C22×Q8×C61C2211yescharacteristic
50#124×C61—21no—
51#124×C61C2211yescharacteristic
52C22⋊Q8×C61—21no—
53C22⋊Q8×C61C2211yescharacteristic
54#121×C61—21no—
55#121×C61C2211yescharacteristic
56C4×Q8×C61C2211yescharacteristic
57C4×D4×C61—21no—
58C4×D4×C61C2211yescharacteristic
59#41×C61—22no—
60#41×C61—41no—
61C2×Q8×C61—21no—
62C2×Q8×C61—22no—
63C2×Q8×C61—41no—
64C2×Q8×C61C2311yescharacteristic
65C2×Q8×C61C2311yescharacteristic
66C2×D4×C61—21no—
67C2×D4×C61—21no—
68C2×D4×C61D411yescharacteristic
69C2×D4×C61C2311yescharacteristic
70C22×C4×C61—21no—
71C22×C4×C61—21no—
72C22×C4×C61C2311yescharacteristic
73C22×C4×C61C2311yescharacteristic
74C2×Dic122—21no—
75C2×Dic122C2311yescharacteristic
76C4⋊C4×C61—21no—
77C4⋊C4×C61—21no—
78C4⋊C4×C61D411yescharacteristic
79C4⋊C4×C61C2311yescharacteristic
80C22⋊C4×C61—21no—
81C22⋊C4×C61—21no—
82C22⋊C4×C61—21no—
83C22⋊C4×C61—21no—
84C22⋊C4×C61D411yescharacteristic
85C22⋊C4×C61D411yescharacteristic
86C42×C61—21no—
87C42×C61C2311yescharacteristic
88C22⋊Dic61—21no—
89C22⋊Dic61—21no—
90C22⋊Dic61—21no—
91C22⋊Dic61—21no—
92#11758202—22no—
93#11758202—41no—
94#11758200—41no—
95C4⋊Dic61—21no—
96C4⋊Dic61C2311yescharacteristic
97C4⋊Dic61C2311yescharacteristic
98C4⋊Dic61C2311yescharacteristic
99#11758196—21no—
100#11758196—21no—
101#11758196—21no—
102C4×Dic61—21no—
103C4×Dic61—21no—
104C4×Dic61—21no—
105#11758194—41no—
106C2×#92418—41no—
107C2×#92418C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110C2×#92418C2311yescharacteristic
111C23×C61—21no—
112C23×C61C2×D411yescharacteristic
113C23×C61C2×D411yescharacteristic
114Q8×C61—21no—
115Q8×C61—21no—
116Q8×C61—21no—
117Q8×C61—42no—
118Q8×C61#4112yes—
119D4×C61—21no—
120D4×C61—21no—
121D4×C61—41no—
122D4×C61—42no—
123D4×C61—42no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—42no—
132C2×C4×C61—42no—
133C2×C4×C61C2×D411yescharacteristic
134C2×C4×C61C2×D411yescharacteristic
135C2×C4×C61C2×D411yescharacteristic
136C2×C4×C61C2×D411yescharacteristic
137C2×C4×C61C2411yescharacteristic
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142Dic122—21no—
143Dic122—21no—
144Dic122—42no—
145#92418—21no—
146#92418—21no—
147#92418—21no—
148#92418—21no—
149C22×C61—21no—
150C22×C61—21no—
151C22×C61—21no—
152C22×C61—21no—
153C22×C61—21no—
154C22×C61—21no—
155C22×C61—41no—
156C22×C61—41no—
157C22×C61—41no—
158C22×C61C22×D411yescharacteristic
159C4×C61—21no—
160C4×C61—21no—
161C4×C61—22no—
162C4×C61—21no—
163C4×C61—21no—
164C4×C61—41no—
165C4×C61—41no—
166C4×C61C2×#4111yescharacteristic
167C4×C61H(5,𝔽2)11yescharacteristic
168Dic61—41no—
169Dic61—41no—
170Dic61—41no—
171Dic61—41no—
172#3313—611nomaximal, Sylow
173C2×C61—41no—
174C2×C61—41no—
175C2×C61—81no—
176C2×C61#54611yescharacteristic
177C2×C61#57511yescharacteristic
178C2×C61#57811yescharacteristic
179#556—611no—
180#548D6111yescharacteristic
181#489—611no—
182#485—611no—
183#482—611no—
184#477—611no—
185#468—611no—
186#467—611no—
187#464—611no—
188#452—611no—
189#451—611no—
190#441—611no—
191#435—611no—
192#419—611no—
193#416—611no—
194C61#331311yescharacteristic, complemented, Sylow
195C2×#41C2×D6111yescharacteristic
196C22×Q8C2×D6111yescharacteristic
197C2×Q16—611no—
198C2×Q16—611no—
199C2×SD16—611no—
200C2×M16—611no—
201C22×C8—611no—
202C4⋊Q8—611no—
203#126—1221no—
204#126—1221no—
205#124—21no—
206#124—1221no—
207#124C2×D6111yescharacteristic
208C22⋊Q8—21no—
209C22⋊Q8—611no—
210C22⋊Q8—611no—
211C22⋊Q8C2×D6111yescharacteristic
212#121—21no—
213#121C2×D6111yescharacteristic
214C4×Q8—611no—
215C4×Q8—1221no—
216C4×Q8C2×D6111yescharacteristic
217C4×D4—21no—
218C4×D4C2×D6111yescharacteristic
219#117—611no—
220#117—611no—
221#107—611no—
222#107—611no—
223#106—611no—
224C4⋊C8—611no—
225#103—611no—
226#103—611no—
227#103—611no—
228#103—611no—
229#103—611no—
230#103—611no—
231#103—611no—
232#102—611no—
233#102—611no—
234#102—611no—
235C22⋊C8—611no—
236C22⋊C8—611no—
237#97—611no—
238#41—22no—
239#41—41no—
240C2×Q8—21no—
241C2×Q8—22no—
242C2×Q8—41no—
243C2×Q8—611no—
244C2×Q8—1221no—
245C2×Q8C22×D6111yescharacteristic
246C2×Q8C22×D6111yescharacteristic
247C2×D4—21no—
248C2×D4—21no—
249C2×D4C22⋊D6111yescharacteristic
250C2×D4C22×D6111yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4C22×D6111yescharacteristic
254C22×C4C22×D6111yescharacteristic
255Q16—1222no—
256Q16—2441no—
257SD16—2441no—
258M16—2441no—
259C2×C8—611no—
260C2×C8—611no—
261C2×C8—611no—
262C2×C8—611no—
263C2×C8—2441no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—611no—
267C4⋊C4—611no—
268C4⋊C4—611no—
269C4⋊C4—1221no—
270C4⋊C4—1221no—
271C4⋊C4—1221no—
272C4⋊C4—1221no—
273C4⋊C4C22⋊D6111yescharacteristic
274C4⋊C4C22×D6111yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—1221no—
280C22⋊C4—1221no—
281C22⋊C4—1221no—
282C22⋊C4—1221no—
283C22⋊C4C22⋊D6111yescharacteristic
284C22⋊C4C22⋊D6111yescharacteristic
285C42—21no—
286C42—1221no—
287C42—1221no—
288C42—1221no—
289C42C22×D6111yescharacteristic
290C23—21no—
291C23C2×C22⋊D6111yescharacteristic
292C23C2×C22⋊D6111yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—42no—
297Q8—1221no—
298Q8—1221no—
299Q8—2442no—
300Q8#1175822412yes—
301D4—21no—
302D4—21no—
303D4—41no—
304D4—42no—
305D4—42no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—1221no—
316C2×C4—1221no—
317C2×C4—1221no—
318C2×C4—1221no—
319C2×C4C2×C22⋊D6111yescharacteristic
320C2×C4C2×C22⋊D6111yescharacteristic
321C2×C4C2×C22⋊D6111yescharacteristic
322C2×C4C2×C22⋊D6111yescharacteristic
323C2×C4C23×D6111yescharacteristic
324C8—1221no—
325C8—1221no—
326C8—1221no—
327C8—1221no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22C22×C22⋊D6111yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—22no—
343C4—41no—
344C4—41no—
345C4—2441no—
346C4—2441no—
347C4—2441no—
348C4—2441no—
349C4C2×#1175822411yescharacteristic
350C4#1451982211yescharacteristic
351C2—41no—
352C2—41no—
353C2—81no—
354C2#1684040611yescharacteristic
355C2#1684056011yescharacteristic
356C2#1684057711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#548C2
socleC22×C61C22×D4
hypercenter#548D61
hypocenterC61#3313
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. #16840482C2semidirect
2. #16840121C2semidirect
3. #16840100C2semidirect
4. #16840083C2semidirect
5. #16840057C2semidirect
6. #16840006C2semidirect
7. #16840001C2semidirect
8. #16839981C2semidirect
9. #16839924C2semidirect
10. #16839918C2semidirect
11. #16839867C2semidirect
12. #16839834C2semidirect
13. #16839771C2semidirect
14. #16839758C2semidirect
194. C61#3313semidirect