Finite Group Databasebeta

← #21457950

Subgroups — #21457950

Order 7808.

392 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840453C211yesmaximal, characteristic, complemented
2#16840434C211yesmaximal, characteristic
3#16840127C211yesmaximal, characteristic, complemented
4#16840088C211yesmaximal, characteristic, complemented
5#16840082C211yesmaximal, characteristic, complemented
6#16840069C211yesmaximal, characteristic, complemented
7#16840011C211yesmaximal, characteristic, complemented
8#16839994C211yesmaximal, characteristic, complemented
9#16839962C211yesmaximal, characteristic, complemented
10#16839923C211yesmaximal, characteristic, complemented
11#16839923C211yesmaximal, characteristic, complemented
12#16839835C211yesmaximal, characteristic, complemented
13#16839762C211yesmaximal, characteristic, complemented
14#16839757C211yesmaximal, characteristic, complemented
15C61×#441C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×#11758226C2211yescharacteristic
18C2×#11758201C2211yescharacteristic
19C2×#11758201C2211yescharacteristic
20C2×#11758189C2211yescharacteristic
21C2×C8×D61C2211yescharacteristic
22#14519774—21no—
23#14519774C2211yescharacteristic
24#14519771—21no—
25#14519769C2211yescharacteristic
26#14519767—21no—
27#14519762—21no—
28#14519753C2211yescharacteristic
29#14519753C2211yescharacteristic
30#14519752—21no—
31#14519752—21no—
32#14519752C2211yescharacteristic
33#14519752C2211yescharacteristic
34C4×D244—21no—
35C4×D244C2211yescharacteristic
36#14519735C2211yescharacteristic
37#14519734—21no—
38C4⋊C4×D61C2211yescharacteristic
39#14519710C2211yescharacteristic
40#14519708C2211yescharacteristic
41C4⋊#92418C2211yescharacteristic
42#14519701C2211yescharacteristic
43#14519701C2211yescharacteristic
44#14519699C2211yescharacteristic
45#14519699C2211yescharacteristic
46#14519699C2211yescharacteristic
47#14519699C2211yescharacteristic
48#14519697C2211yescharacteristic
49#14519697C2211yescharacteristic
50#14519689C2211yescharacteristic
51#14519689C2211yescharacteristic
52C2×Q16×C61C2211yescharacteristic
53C4×Q8×C61C2211yescharacteristic
54C4×Q8×C61C2211yescharacteristic
55#106×C61C2211yescharacteristic
56#103×C61C2211yescharacteristic
57#103×C61C2211yescharacteristic
58#97×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60C2×Q8×C61C2311yescharacteristic
61#11758226—22no—
62#11758226—22no—
63#11758226—41no—
64#11758226—41no—
65C2×D244—21no—
66C2×D244—21no—
67C2×D244—21no—
68C2×D244—21no—
69C2×D244—21no—
70C2×D244—21no—
71C2×D244D411yescharacteristic
72C2×D244C2311yescharacteristic
73C2×D244C2311yescharacteristic
74C2×C4×D61—21no—
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C2×C4×D61C2311yescharacteristic
78C2×C4×D61C2311yescharacteristic
79Q16×C61—22no—
80C2×C8×C61C2311yescharacteristic
81C2×C8×C61C2311yescharacteristic
82C4⋊C4×C61—21no—
83C4⋊C4×C61—21no—
84C4⋊C4×C61C2311yescharacteristic
85C4⋊C4×C61C2311yescharacteristic
86C42×C61—21no—
87C42×C61—21no—
88C42×C61C2311yescharacteristic
89#11758201—41no—
90#11758201—41no—
91#11758198—21no—
92#11758198—21no—
93#11758198—21no—
94#11758198—21no—
95#11758198—21no—
96#11758198D411yescharacteristic
97#11758198D411yescharacteristic
98C4⋊Dic61D411yescharacteristic
99C4⋊Dic61C2311yescharacteristic
100C4⋊Dic61C2311yescharacteristic
101#11758196—21no—
102#11758196—21no—
103#11758196—21no—
104#11758196—21no—
105#11758196—21no—
106C4×Dic61—21no—
107C2×#92418C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109#11758189—41no—
110C8×D61—41no—
111C22×D61—21no—
112C22×D61—21no—
113C22×D61C2×D411yescharacteristic
114C22×D61C2×D411yescharacteristic
115Q8×C61—21no—
116Q8×C61—21no—
117Q8×C61—21no—
118Q8×C61#4112yes—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61C2×D411yescharacteristic
124C2×C4×C61C2×D411yescharacteristic
125C2×C4×C61C2411yescharacteristic
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61C2×D411yescharacteristic
129C2×Dic61C2×D411yescharacteristic
130D244—21no—
131D244—21no—
132D244—21no—
133D244—21no—
134D244—41no—
135D244—42no—
136D244—42no—
137D244—42no—
138D244—81no—
139D244—81no—
140D244—81no—
141C4×D61—21no—
142C4×D61—21no—
143C4×D61—21no—
144C4×D61—21no—
145C4×D61—42no—
146C4×D61—42no—
147C4×D61—42no—
148C8×C61—21no—
149C8×C61—21no—
150#92418—21no—
151#92418—21no—
152C22×C61C22×D411yescharacteristic
153C2×D61—21no—
154C2×D61—21no—
155C2×D61—21no—
156C2×D61—21no—
157C2×D61—21no—
158C2×D61—21no—
159C2×D61—41no—
160C2×D61—41no—
161C2×D61—41no—
162C2×D61—41no—
163C2×D61—41no—
164C2×D61—41no—
165C4×C61—22no—
166C4×C61—21no—
167C4×C61—21no—
168C4×C61—41no—
169C4×C61—41no—
170C4×C61—41no—
171C4×C61C2×#4111yescharacteristic
172C4×C61H(5,𝔽2)11yescharacteristic
173Dic61—21no—
174Dic61—21no—
175Dic61—41no—
176Dic61—41no—
177#3317—611nomaximal, Sylow
178C2×C61#54611yescharacteristic
179C2×C61#57511yescharacteristic
180C2×C61#57711yescharacteristic
181D61—41no—
182D61—41no—
183D61—81no—
184D61—81no—
185#552—611no—
186#550—611no—
187#490—611no—
188#482—611no—
189#481—611no—
190#479—611no—
191#468—611no—
192#465—611no—
193#460—611no—
194#452—611no—
195#452—611no—
196#441D6111yescharacteristic, complemented
197#435—611no—
198#417—611no—
199#416—611no—
200C61#331711yescharacteristic, complemented, Sylow
201C2×#41—611no—
202C2×#41—611no—
203C2×Q16C2×D6111yescharacteristic
204C2×SD16—611no—
205C2×SD16—611no—
206C2×M16—611no—
207C22×C8—611no—
208#127—611no—
209#127—1221no—
210#126—1221no—
211#125—611no—
212#125—1221no—
213#123—1221no—
214C22⋊Q8—611no—
215C22⋊Q8—611no—
216#121—611no—
217#121—611no—
218#121—1221no—
219#121—1221no—
220C4×Q8C2×D6111yescharacteristic
221C4×Q8C2×D6111yescharacteristic
222C4×D4—611no—
223C4×D4—1221no—
224#117—611no—
225#117—1221no—
226C2×C4⋊C4—611no—
227#107—611no—
228#106—611no—
229#106C2×D6111yescharacteristic
230C4⋊C8—611no—
231#103—611no—
232#103—611no—
233#103C2×D6111yescharacteristic
234#103C2×D6111yescharacteristic
235#102—611no—
236#102—611no—
237#102—611no—
238#102—611no—
239#102—611no—
240#102—611no—
241C22⋊C8—611no—
242C22⋊C8—611no—
243#97C2×D6111yescharacteristic
244#41—1222no—
245#41—1222no—
246#41—2441no—
247#41—2441no—
248C2×Q8C22×D6111yescharacteristic
249C2×Q8C22×D6111yescharacteristic
250C2×D4—611no—
251C2×D4—611no—
252C2×D4—611no—
253C2×D4—1221no—
254C2×D4—1221no—
255C2×D4—1221no—
256C2×D4—1221no—
257C2×D4—1221no—
258C2×D4—1221no—
259C22×C4—611no—
260C22×C4—611no—
261C22×C4—1221no—
262C22×C4—1221no—
263C22×C4—1221no—
264Q16—22no—
265SD16—2441no—
266SD16—2441no—
267M16—2441no—
268C2×C8—611no—
269C2×C8—611no—
270C2×C8—2441no—
271C2×C8C22×D6111yescharacteristic
272C2×C8C22×D6111yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—611no—
276C4⋊C4—611no—
277C4⋊C4—611no—
278C4⋊C4—1221no—
279C4⋊C4—1221no—
280C4⋊C4—1221no—
281C4⋊C4—1221no—
282C4⋊C4—1221no—
283C4⋊C4C22×D6111yescharacteristic
284C4⋊C4C22×D6111yescharacteristic
285C22⋊C4—611no—
286C22⋊C4—611no—
287C22⋊C4—1221no—
288C22⋊C4—1221no—
289C22⋊C4—1221no—
290C22⋊C4—1221no—
291C22⋊C4—1221no—
292C42—21no—
293C42—21no—
294C42—1221no—
295C42C22×D6111yescharacteristic
296C23—611no—
297C23—611no—
298C23—1221no—
299C23—1221no—
300Q8—21no—
301Q8—21no—
302Q8—21no—
303Q8#1175822212yes—
304D4—1221no—
305D4—1221no—
306D4—1221no—
307D4—1221no—
308D4—4881no—
309D4—4881no—
310D4—4881no—
311D4—2441no—
312D4—2442no—
313D4—2442no—
314D4—2442no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—611no—
320C2×C4—611no—
321C2×C4—1221no—
322C2×C4—1221no—
323C2×C4—1221no—
324C2×C4—1221no—
325C2×C4—1221no—
326C2×C4—1221no—
327C2×C4—2442no—
328C2×C4—2442no—
329C2×C4—2442no—
330C2×C4D4×D6111yescharacteristic
331C2×C4D4×D6111yescharacteristic
332C2×C4C23×D6111yescharacteristic
333C8—21no—
334C8—21no—
335C8—1221no—
336C8—1221no—
337C22—1221no—
338C22—1221no—
339C22—1221no—
340C22—1221no—
341C22—1221no—
342C22—1221no—
343C22—2441no—
344C22—2441no—
345C22—2441no—
346C22—2441no—
347C22—2441no—
348C22—2441no—
349C22C2×D4×D6111yescharacteristic
350C4—21no—
351C4—21no—
352C4—22no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—1221no—
357C4—1221no—
358C4—2441no—
359C4—2441no—
360C4C2×#1175822211yescharacteristic
361C4#1451982311yescharacteristic
362C2—4881no—
363C2—4881no—
364C2—2441no—
365C2—2441no—
366C2#1684040811yescharacteristic
367C2#1684056111yescharacteristic
368C2#1684057111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#441C2
socleC22×C61C22×D4
hypercenter#441D61
hypocenterC61#3317
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
1. #16840453C2semidirect
3. #16840127C2semidirect
4. #16840088C2semidirect
5. #16840082C2semidirect
6. #16840069C2semidirect
7. #16840011C2semidirect
8. #16839994C2semidirect
9. #16839962C2semidirect
10. #16839923C2semidirect
11. #16839923C2semidirect
12. #16839835C2semidirect
13. #16839762C2semidirect
14. #16839757C2semidirect
15. C61×#441C2semidirect
196. #441D61semidirect
200. C61#3317semidirect