Finite Group Databasebeta

← #21457879

Subgroups — #21457879

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#16840421C211yesmaximal, characteristic
2#16840124C211yesmaximal, characteristic, complemented
3#16840103C211yesmaximal, characteristic, complemented
4#16840086C211yesmaximal, characteristic, complemented
5#16840054C211yesmaximal, characteristic, complemented
6#16840010C211yesmaximal, characteristic, complemented
7#16840001C211yesmaximal, characteristic, complemented
8#16839984C211yesmaximal, characteristic, complemented
9#16839922C211yesmaximal, characteristic, complemented
10#16839917C211yesmaximal, characteristic, complemented
11#16839867C211yesmaximal, characteristic, complemented
12#16839834C211yesmaximal, characteristic, complemented
13#16839770C211yesmaximal, characteristic, complemented
14#16839756C211yesmaximal, characteristic, complemented
15C61×#556C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C22×Dic122C2211yescharacteristic
18C2×#11758202C2211yescharacteristic
19C2×#11758202C2211yescharacteristic
20C2×#11758201C2211yescharacteristic
21C2×#11758194C2211yescharacteristic
22C22×#92418C2211yescharacteristic
23#14519765C2211yescharacteristic
24#14519763—21no—
25#14519756C2211yescharacteristic
26#14519755—21no—
27#14519751C2211yescharacteristic
28#14519749—21no—
29C4×Dic122C2211yescharacteristic
30#14519737—21no—
31#14519710C2211yescharacteristic
32#14519710C2211yescharacteristic
33#14519708C2211yescharacteristic
34C4⋊#92418C2211yescharacteristic
35#14519701C2211yescharacteristic
36#14519700C2211yescharacteristic
37#14519700C2211yescharacteristic
38#14519700C2211yescharacteristic
39#14519700C2211yescharacteristic
40#14519700C2211yescharacteristic
41#14519700C2211yescharacteristic
42#14519697C2211yescharacteristic
43#14519697C2211yescharacteristic
44#14519697C2211yescharacteristic
45C22⋊#92418C2211yescharacteristic
46C22⋊#92418C2211yescharacteristic
47#14519688C2211yescharacteristic
48C4⋊Q8×C61C2211yescharacteristic
49#126×C61—21no—
50#126×C61—21no—
51#124×C61—21no—
52C22⋊Q8×C61C2211yescharacteristic
53C22⋊Q8×C61C2211yescharacteristic
54C4×Q8×C61—21no—
55C4×Q8×C61C2211yescharacteristic
56C4×D4×C61C2211yescharacteristic
57#117×C61C2211yescharacteristic
58#117×C61C2211yescharacteristic
59C2×Q8×C61—21no—
60C2×Q8×C61C2311yescharacteristic
61C2×D4×C61D411yescharacteristic
62C22×C4×C61C2311yescharacteristic
63C22×C4×C61C2311yescharacteristic
64C2×C22⋊D61—21no—
65C2×C22⋊D61—21no—
66C22×Dic61—21no—
67#11758222—22no—
68#11758222—41no—
69C2×D244C2311yescharacteristic
70C2×C4×D61—21no—
71C2×Dic122—22no—
72C2×Dic122—21no—
73C2×Dic122—41no—
74C2×Dic122C2311yescharacteristic
75C2×Dic122C2311yescharacteristic
76C4⋊C4×C61—21no—
77C4⋊C4×C61—21no—
78C4⋊C4×C61—21no—
79C4⋊C4×C61—21no—
80C4⋊C4×C61D411yescharacteristic
81C4⋊C4×C61C2311yescharacteristic
82C4⋊C4×C61C2311yescharacteristic
83C4⋊C4×C61C2311yescharacteristic
84C22⋊C4×C61—21no—
85C22⋊C4×C61—21no—
86C22⋊C4×C61—21no—
87C22⋊C4×C61—21no—
88C22⋊C4×C61D411yescharacteristic
89C22⋊C4×C61D411yescharacteristic
90C42×C61—21no—
91C42×C61—21no—
92C42×C61—21no—
93C42×C61C2311yescharacteristic
94C22⋊Dic61—21no—
95#11758202—22no—
96#11758202—41no—
97#11758201—41no—
98#11758198—21no—
99#11758198—21no—
100#11758198—21no—
101C4⋊Dic61C2311yescharacteristic
102#11758196—21no—
103#11758196—21no—
104C4×Dic61—21no—
105#11758194—41no—
106C2×#92418—41no—
107C2×#92418C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110C2×#92418C2311yescharacteristic
111C23×C61C2×D411yescharacteristic
112C23×C61C2×D411yescharacteristic
113C22×D61—21no—
114Q8×C61—21no—
115Q8×C61—21no—
116Q8×C61—42no—
117D4×C61—41no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61C2×D411yescharacteristic
127C2×C4×C61C2×D411yescharacteristic
128C2×C4×C61C2×D411yescharacteristic
129C2×C4×C61C2×D411yescharacteristic
130C2×C4×C61C2411yescharacteristic
131C22⋊D61—42no—
132C22⋊D61—42no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—42no—
137D244—21no—
138D244—21no—
139C4×D61—42no—
140Dic122—21no—
141Dic122—21no—
142Dic122—21no—
143Dic122—42no—
144Dic122#4112yes—
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×C61C22×D411yescharacteristic
156C2×D61—41no—
157C2×D61—41no—
158C2×D61—41no—
159C4×C61—21no—
160C4×C61—21no—
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—41no—
171Dic61—41no—
172#3313—611nomaximal, Sylow
173C2×C61—41no—
174C2×C61—41no—
175C2×C61#54611yescharacteristic
176C2×C61#57511yescharacteristic
177C2×C61#57811yescharacteristic
178D61—81no—
179#556D6111yescharacteristic, complemented
180#548—611no—
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×#41—611no—
196C22×Q8—611no—
197C2×Q16—611no—
198C2×Q16—611no—
199C2×SD16—611no—
200C2×M16—611no—
201C22×C8—611no—
202C4⋊Q8C2×D6111yescharacteristic
203#126—21no—
204#126—21no—
205#124—21no—
206#124—611no—
207#124—1221no—
208C22⋊Q8—611no—
209C22⋊Q8—1221no—
210C22⋊Q8C2×D6111yescharacteristic
211C22⋊Q8C2×D6111yescharacteristic
212#121—611no—
213#121—1221no—
214C4×Q8—21no—
215C4×Q8—611no—
216C4×Q8C2×D6111yescharacteristic
217C4×D4—1221no—
218C4×D4C2×D6111yescharacteristic
219#117C2×D6111yescharacteristic
220#117C2×D6111yescharacteristic
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—1222no—
239#41—2441no—
240C2×Q8—21no—
241C2×Q8—611no—
242C2×Q8—611no—
243C2×Q8—1222no—
244C2×Q8—1221no—
245C2×Q8—2441no—
246C2×Q8C22×D6111yescharacteristic
247C2×D4—611no—
248C2×D4—1221no—
249C2×D4—1221no—
250C2×D4C22⋊D6111yescharacteristic
251C22×C4—1221no—
252C22×C4—1221no—
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—21no—
267C4⋊C4—21no—
268C4⋊C4—611no—
269C4⋊C4—1221no—
270C4⋊C4—1221no—
271C4⋊C4C22⋊D6111yescharacteristic
272C4⋊C4C22×D6111yescharacteristic
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—21no—
287C42—21no—
288C42—1221no—
289C42C22×D6111yescharacteristic
290C23—1221no—
291C23C2×C22⋊D6111yescharacteristic
292C23C2×C22⋊D6111yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—42no—
296Q8—612no—
297Q8—1221no—
298Q8—1221no—
299Q8—1221no—
300Q8—2442no—
301D4—41no—
302D4—1221no—
303D4—1221no—
304D4—2442no—
305D4—2442no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—1221no—
315C2×C4—1221no—
316C2×C4—1221no—
317C2×C4—2442no—
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—2441no—
335C22—2441no—
336C22—2441no—
337C22C22×C22⋊D6111yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—1222no—
347C4—2441no—
348C4—2441no—
349C4#41×D6111yescharacteristic
350C4#1451982311yescharacteristic
351C2—41no—
352C2—41no—
353C2—4881no—
354C2#1684040011yescharacteristic
355C2#1684056011yescharacteristic
356C2#1684057711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#556C2
socleC22×C61C22×D4
hypercenter#556D61
hypocenterC61#3313
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #556

Complements

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

NH ≅ G/Ntype
2. #16840124C2semidirect
3. #16840103C2semidirect
4. #16840086C2semidirect
5. #16840054C2semidirect
6. #16840010C2semidirect
7. #16840001C2semidirect
8. #16839984C2semidirect
9. #16839922C2semidirect
10. #16839917C2semidirect
11. #16839867C2semidirect
12. #16839834C2semidirect
13. #16839770C2semidirect
14. #16839756C2semidirect
15. C61×#556C2semidirect
179. #556D61semidirect
194. C61#3313semidirect