Finite Group Databasebeta

← #21457915

Subgroups — #21457915

Order 7808.

382 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#16840452C211yesmaximal, characteristic, complemented
2#16840130C211yesmaximal, characteristic, complemented
3#16840100C211yesmaximal, characteristic, complemented
4#16840095C211yesmaximal, characteristic, complemented
5#16840062C211yesmaximal, characteristic, complemented
6#16840018C211yesmaximal, characteristic, complemented
7#16840001C211yesmaximal, characteristic, complemented
8#16839969C211yesmaximal, characteristic, complemented
9#16839924C211yesmaximal, characteristic, complemented
10#16839924C211yesmaximal, characteristic, complemented
11#16839862C211yesmaximal, characteristic, complemented
12#16839834C211yesmaximal, characteristic, complemented
13#16839763C211yesmaximal, characteristic, complemented
14#16839758C211yesmaximal, characteristic, complemented
15C61×#547C211yesmaximal, characteristic
16C2×#11758202C2211yescharacteristic
17C2×#11758202C2211yescharacteristic
18C2×#11758200C2211yescharacteristic
19C2×#11758194C2211yescharacteristic
20C22×#92418C2211yescharacteristic
21#14519770—21no—
22#14519769C2211yescharacteristic
23#14519767—21no—
24#14519758—21no—
25#14519756C2211yescharacteristic
26#14519756C2211yescharacteristic
27C4×Dic122C2211yescharacteristic
28#14519736C2211yescharacteristic
29#14519733—21no—
30C2×C4⋊Dic61C2211yescharacteristic
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
49C2×#41×C61C2211yescharacteristic
50C4⋊Q8×C61C2211yescharacteristic
51#123×C61—21no—
52#123×C61—21no—
53C22⋊Q8×C61C2211yescharacteristic
54C22⋊Q8×C61C2211yescharacteristic
55#121×C61—21no—
56C4×D4×C61C2211yescharacteristic
57C4×D4×C61C2211yescharacteristic
58C2×C4⋊C4×C61—21no—
59#41×C61—22no—
60#41×C61—22no—
61#41×C61—41no—
62#41×C61—41no—
63C2×Q8×C61C2311yescharacteristic
64C2×Q8×C61C2311yescharacteristic
65C2×D4×C61—21no—
66C2×D4×C61—21no—
67C2×D4×C61D411yescharacteristic
68C2×D4×C61C2311yescharacteristic
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61—21no—
72C22×C4×C61C2311yescharacteristic
73C22×C4×C61C2311yescharacteristic
74C22×Dic61—21no—
75C2×Dic122C2311yescharacteristic
76C4⋊C4×C61—21no—
77C4⋊C4×C61—21no—
78C4⋊C4×C61—21no—
79C4⋊C4×C61—21no—
80C4⋊C4×C61D411yescharacteristic
81C4⋊C4×C61C2311yescharacteristic
82C22⋊C4×C61—21no—
83C22⋊C4×C61—21no—
84C22⋊C4×C61—21no—
85C22⋊C4×C61D411yescharacteristic
86C22⋊C4×C61D411yescharacteristic
87C42×C61C2311yescharacteristic
88C22⋊Dic61—21no—
89C22⋊Dic61—21no—
90C22⋊Dic61—21no—
91#11758202—41no—
92#11758202—41no—
93#11758200—22no—
94C4⋊Dic61—21no—
95C4⋊Dic61C2311yescharacteristic
96C4⋊Dic61C2311yescharacteristic
97C4⋊Dic61C2311yescharacteristic
98#11758196—21no—
99#11758196—21no—
100#11758196—21no—
101#11758196—21no—
102#11758196—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—21no—
118D4×C61—21no—
119D4×C61—41no—
120D4×C61—42no—
121D4×C61—42no—
122D4×C61#4112yes—
123C2×C4×C61—21no—
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—42no—
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—
142C2×Dic61—42no—
143Dic122—21no—
144Dic122—21no—
145#92418—21no—
146#92418—21no—
147#92418—21no—
148#92418—21no—
149C22×C61—21no—
150C22×C61—21no—
151C22×C61—22no—
152C22×C61—21no—
153C22×C61—21no—
154C22×C61—21no—
155C22×C61—21no—
156C22×C61—41no—
157C22×C61—41no—
158C22×C61C22×D411yescharacteristic
159C4×C61—21no—
160C4×C61—21no—
161C4×C61—21no—
162C4×C61—21no—
163C4×C61—41no—
164C4×C61—41no—
165C4×C61—41no—
166C4×C61C2×#4111yescharacteristic
167C4×C61H(5,𝔽2)11yescharacteristic
168Dic61—41no—
169Dic61—41no—
170Dic61—41no—
171Dic61—41no—
172#3315—611nomaximal, Sylow
173C2×C61—41no—
174C2×C61—41no—
175C2×C61—42no—
176C2×C61#54611yescharacteristic
177C2×C61#57511yescharacteristic
178C2×C61#57811yescharacteristic
179#552—611no—
180#547D6111yescharacteristic
181#491—611no—
182#485—611no—
183#484—611no—
184#478—611no—
185#470—611no—
186#467—611no—
187#462—611no—
188#452—611no—
189#452—611no—
190#440—611no—
191#435—611no—
192#417—611no—
193#416—611no—
194C61#331511yescharacteristic, complemented, Sylow
195C2×#41C2×D6111yescharacteristic
196C2×#41C2×D6111yescharacteristic
197C2×Q16—611no—
198C2×Q16—611no—
199C2×SD16—611no—
200C2×M16—611no—
201C22×C8—611no—
202C4⋊Q8C2×D6111yescharacteristic
203#126—1221no—
204#125—611no—
205#125—1221no—
206#123—21no—
207#123—21no—
208#123—1221no—
209C22⋊Q8—611no—
210C22⋊Q8—611no—
211C22⋊Q8C2×D6111yescharacteristic
212C22⋊Q8C2×D6111yescharacteristic
213#121—21no—
214C4×Q8—611no—
215C4×D4C2×D6111yescharacteristic
216C4×D4C2×D6111yescharacteristic
217#117—611no—
218#117—1221no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—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—22no—
240#41—41no—
241#41—41no—
242C2×Q8—611no—
243C2×Q8C22×D6111yescharacteristic
244C2×Q8C22×D6111yescharacteristic
245C2×D4—21no—
246C2×D4—21no—
247C2×D4C22⋊D6111yescharacteristic
248C2×D4C22×D6111yescharacteristic
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—1221no—
253C22×C4C22×D6111yescharacteristic
254C22×C4C22×D6111yescharacteristic
255Q16—2441no—
256Q16—2441no—
257SD16—1222no—
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—21no—
267C4⋊C4—21no—
268C4⋊C4—611no—
269C4⋊C4—611no—
270C4⋊C4—611no—
271C4⋊C4—1221no—
272C4⋊C4—1221no—
273C4⋊C4—1221no—
274C4⋊C4—1221no—
275C4⋊C4—1221no—
276C4⋊C4—1221no—
277C4⋊C4C22⋊D6111yescharacteristic
278C4⋊C4C22×D6111yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—1221no—
283C22⋊C4—1221no—
284C22⋊C4—1221no—
285C22⋊C4C22⋊D6111yescharacteristic
286C22⋊C4C22⋊D6111yescharacteristic
287C42—1221no—
288C42—1221no—
289C42C22×D6111yescharacteristic
290C23—21no—
291C23C2×C22⋊D6111yescharacteristic
292C23C2×C22⋊D6111yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—21no—
297Q8—1221no—
298Q8—1221no—
299D4—21no—
300D4—41no—
301D4—42no—
302D4—42no—
303D4#1175822412yes—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—1221no—
315C2×C4—1221no—
316C2×C4—1221no—
317C2×C4—1221no—
318C2×C4—2442no—
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—22no—
335C22—41no—
336C22—41no—
337C22C22×C22⋊D6111yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—2441no—
346C4—2441no—
347C4—2441no—
348C4—2441no—
349C4C2×#1175822411yescharacteristic
350C4#1451982211yescharacteristic
351C2—41no—
352C2—41no—
353C2—42no—
354C2#1684040611yescharacteristic
355C2#1684056011yescharacteristic
356C2#1684057711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#547C2
socleC22×C61C22×D4
hypercenter#547D61
hypocenterC61#3315
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. #16840452C2semidirect
2. #16840130C2semidirect
3. #16840100C2semidirect
4. #16840095C2semidirect
5. #16840062C2semidirect
6. #16840018C2semidirect
7. #16840001C2semidirect
8. #16839969C2semidirect
9. #16839924C2semidirect
10. #16839924C2semidirect
11. #16839862C2semidirect
12. #16839834C2semidirect
13. #16839763C2semidirect
14. #16839758C2semidirect
194. C61#3315semidirect