Finite Group Databasebeta

← #21456311

Subgroups — #21456311

Order 7808.

532 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
1C2×#14519809C211yesmaximal, characteristic, complemented
2C2×#14519806C211yesmaximal, characteristic, complemented
3C2×#14519798C211yesmaximal, characteristic
4C2×Q16×D61C211yesmaximal, characteristic, complemented
5#16840337C211yesmaximal, characteristic, complemented
6#16840332C211yesmaximal, characteristic, complemented
7#16840156C211yesmaximal, characteristic, complemented
8#16840155C211yesmaximal, characteristic, complemented
9#16840153C211yesmaximal, characteristic, complemented
10#16840144C211yesmaximal, characteristic, complemented
11#16840143C211yesmaximal, characteristic, complemented
12#16840141C211yesmaximal, characteristic, complemented
13#16840140C211yesmaximal, characteristic, complemented
14#16839719C211yesmaximal, characteristic, complemented
15C61×#497C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×#11758224C2211yescharacteristic
18C2×Q8×D61C2211yescharacteristic
19C2×Q8×D61C2211yescharacteristic
20#14519809—24no—
21#14519806—24no—
22#14519798—24no—
23C2×Dic244C2211yescharacteristic
24C2×Dic244C2211yescharacteristic
25C2×#11758202C2211yescharacteristic
26C2×#11758202C2211yescharacteristic
27C2×#11758202C2211yescharacteristic
28C2×#11758202C2211yescharacteristic
29C2×#11758202C2211yescharacteristic
30Q16×D61—24no—
31C2×#11758190C2211yescharacteristic
32C2×#11758190C2211yescharacteristic
33C2×#11758200C2211yescharacteristic
34C2×#11758201C2211yescharacteristic
35C2×#11758199C2211yescharacteristic
36C2×#11758189C2211yescharacteristic
37C2×C8×D61C2211yescharacteristic
38#14519777C2211yescharacteristic
39#14519775C2211yescharacteristic
40#14519775C2211yescharacteristic
41#14519766C2211yescharacteristic
42#14519765C2211yescharacteristic
43#14519764C2211yescharacteristic
44#14519762—22no—
45#14519759—22no—
46#14519755—22no—
47#14519754—22no—
48#14519734C2211yescharacteristic
49#14519687C2211yescharacteristic
50C4×#92418C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52C2×Q16×C61C2211yescharacteristic
53C2×Q16×C61C2211yescharacteristic
54C2×SD16×C61C2211yescharacteristic
55C2×SD16×C61C2211yescharacteristic
56C4⋊Q8×C61C2211yescharacteristic
57#124×C61C2211yescharacteristic
58#97×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60C2×Q8×C61C2311yescharacteristic
61C2×Q8×C61C2311yescharacteristic
62C2×D4×C61C2311yescharacteristic
63C2×C22⋊D61—21no—
64C22×Dic61—21no—
65#11758226—22no—
66#11758226—22no—
67Q8×D61—22no—
68Q8×D61—22no—
69Q8×D61—22no—
70Q8×D61—22no—
71#11758224—22no—
72#11758224—22no—
73C2×D244—21no—
74C2×D244C2311yescharacteristic
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×C4×D61C2311yescharacteristic
79C2×Dic122—21no—
80C2×Dic122—21no—
81C2×Dic122C2311yescharacteristic
82C2×Dic122C2311yescharacteristic
83C2×Dic122C2311yescharacteristic
84Q16×C61—22no—
85Q16×C61—22no—
86SD16×C61—22no—
87SD16×C61—22no—
88C2×C8×C61C2311yescharacteristic
89C2×C8×C61C2311yescharacteristic
90C4⋊C4×C61—22no—
91C22⋊C4×C61—22no—
92C42×C61C2311yescharacteristic
93C22⋊Dic61—22no—
94#11758202—22no—
95#11758202—22no—
96#11758202—22no—
97#11758202—22no—
98#11758202—22no—
99#11758201—22no—
100#11758200—22no—
101#11758199—22no—
102#11758198—22no—
103#11758198—22no—
104#11758198D412yes—
105C4⋊Dic61—22no—
106#11758196—22no—
107#11758196—22no—
108#11758196D412yes—
109C4×Dic61C2311yescharacteristic
110C2×#92418C2311yescharacteristic
111C2×#92418C2311yescharacteristic
112Dic244—22no—
113Dic244—22no—
114#11758190—22no—
115#11758190—22no—
116#11758189D414yes—
117C8×D61D414yes—
118C23×C61—21no—
119C22×D61—21no—
120C22×D61C2×D411yescharacteristic
121Q8×C61—21no—
122Q8×C61—21no—
123Q8×C61—21no—
124Q8×C61—21no—
125Q8×C61—21no—
126Q8×C61—21no—
127D4×C61—21no—
128D4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61C2×D412yes—
133C2×C4×C61C2411yescharacteristic
134C22⋊D61—42no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—42no—
139C2×Dic61C2×D412yes—
140C2×Dic61C2×D411yescharacteristic
141D244—21no—
142D244—21no—
143D244—42no—
144C4×D61—42no—
145C4×D61—42no—
146C4×D61—42no—
147C4×D61C2×D412yes—
148C4×D61C2×D412yes—
149Dic122—21no—
150Dic122—21no—
151Dic122—21no—
152Dic122—21no—
153Dic122—21no—
154Dic122—21no—
155Dic122—42no—
156Dic122—42no—
157C8×C61C2×D412yes—
158C8×C61C2×D412yes—
159#92418C2×D412yes—
160#92418C2×D412yes—
161C22×C61—41no—
162C22×C61—42no—
163C22×C61C22×D411yescharacteristic
164C2×D61—22no—
165C2×D61—41no—
166C2×D61—42no—
167C2×D61#12712yes—
168C4×C61—22no—
169C4×C61—41no—
170C4×C61—41no—
171C4×C61—41no—
172C4×C61C22×D411yescharacteristic
173C4×C61C22×D411yescharacteristic
174Dic61—22no—
175Dic61—41no—
176Dic61—41no—
177Dic61—41no—
178Dic61#12712yes—
179#3156—611nomaximal, Sylow
180C2×C61—81no—
181C2×C61C2×#12711yescharacteristic
182C2×C61#57812yes—
183D61—22no—
184D61—81no—
185C2×#137—611no—
186C2×#137—611no—
187C2×#135—611no—
188C22×Q16—611no—
189#536—611no—
190#536—611no—
191#497—611no—
192#497—611no—
193#497—611no—
194#497D6111yescharacteristic, complemented
195#495—611no—
196#495—611no—
197#494—611no—
198#494—611no—
199#405—611no—
200C61#315611yescharacteristic, complemented, Sylow
201C2×#41—611no—
202C2×#41—611no—
203C22×Q8—611no—
204C22×Q8—611no—
205#137—1224no—
206#137—1224no—
207#135—1224no—
208C2×Q16—611no—
209C2×Q16—611no—
210C2×Q16—611no—
211C2×Q16—611no—
212C2×Q16—611no—
213C2×Q16—611no—
214C2×Q16—611no—
215C2×Q16—1224no—
216C2×Q16C2×D6111yescharacteristic
217C2×Q16C2×D6111yescharacteristic
218C2×SD16—611no—
219C2×SD16—611no—
220C2×SD16—611no—
221C2×SD16—611no—
222C2×SD16C2×D6111yescharacteristic
223C2×SD16C2×D6111yescharacteristic
224C2×D8—611no—
225C2×M16—611no—
226C22×C8—611no—
227C4⋊Q8—611no—
228C4⋊Q8—611no—
229C4⋊Q8—611no—
230C4⋊Q8C2×D6111yescharacteristic
231#124—611no—
232#124—611no—
233#124—611no—
234#124C2×D6111yescharacteristic
235#123—1222no—
236#123—1222no—
237C22⋊Q8—1222no—
238C22⋊Q8—1222no—
239#117—611no—
240#97—611no—
241#97C2×D6111yescharacteristic
242C4×C8—611no—
243C4×C8—611no—
244#41—1222no—
245#41—1222no—
246#41—1222no—
247#41—1222no—
248C2×Q8—611no—
249C2×Q8—611no—
250C2×Q8—611no—
251C2×Q8—1221no—
252C2×Q8—1221no—
253C2×Q8—1222no—
254C2×Q8—1222no—
255C2×Q8—1222no—
256C2×Q8—1222no—
257C2×Q8C22×D6111yescharacteristic
258C2×Q8C22×D6111yescharacteristic
259C2×Q8C22×D6111yescharacteristic
260C2×D4—611no—
261C2×D4—1221no—
262C2×D4—1221no—
263C2×D4C22×D6111yescharacteristic
264C22×C4—611no—
265C22×C4—1221no—
266C22×C4—1221no—
267C22×C4—1221no—
268C22×C4—1221no—
269Q16—22no—
270Q16—22no—
271Q16—1222no—
272Q16—1222no—
273Q16—1222no—
274Q16—1222no—
275Q16—1222no—
276Q16—1222no—
277Q16—1222no—
278SD16—22no—
279SD16—22no—
280SD16—1222no—
281SD16—1222no—
282SD16—1222no—
283SD16—1222no—
284D8—1222no—
285M16—614no—
286C2×C8—611no—
287C2×C8—611no—
288C2×C8—614no—
289C2×C8C22×D6111yescharacteristic
290C2×C8C22×D6111yescharacteristic
291C4⋊C4—22no—
292C4⋊C4—612no—
293C4⋊C4—1222no—
294C4⋊C4—1222no—
295C4⋊C4—1222no—
296C22⋊C4—22no—
297C22⋊C4—612no—
298C22⋊C4—1222no—
299C22⋊C4—1222no—
300C22⋊C4—1222no—
301C42—611no—
302C42C22×D6111yescharacteristic
303C23—21no—
304C23—611no—
305C23—1221no—
306Q8—21no—
307Q8—21no—
308Q8—21no—
309Q8—21no—
310Q8—21no—
311Q8—21no—
312Q8—1221no—
313Q8—1221no—
314Q8—1221no—
315Q8—1221no—
316Q8—1221no—
317Q8—1221no—
318Q8—2442no—
319Q8—2442no—
320D4—21no—
321D4—21no—
322D4—1221no—
323D4—1221no—
324D4—2442no—
325D4—2442no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—611no—
330C2×C4—612no—
331C2×C4—612no—
332C2×C4—612no—
333C2×C4—1221no—
334C2×C4—1221no—
335C2×C4—1221no—
336C2×C4—2442no—
337C2×C4—2442no—
338C2×C4—2442no—
339C2×C4—2442no—
340C2×C4D4×D6112yes—
341C2×C4C23×D6111yescharacteristic
342C8—612no—
343C8—612no—
344C8D4×D6112yes—
345C8D4×D6112yes—
346C22—41no—
347C22—42no—
348C22—612no—
349C22—1222no—
350C22—2441no—
351C22—2442no—
352C22C2×D4×D6111yescharacteristic
353C4—22no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—612no—
358C4—1222no—
359C4—2441no—
360C4—2441no—
361C4—2441no—
362C4C2×D4×D6111yescharacteristic
363C4C2×D4×D6111yescharacteristic
364C2—81no—
365C2—1222no—
366C2—4881no—
367C2#127×D6111yescharacteristic
368C2#1684057812yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#497C2
socleC22×C61C22×D4
hypercenter#497D61
hypocenterC61#3156
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
1. C2×#14519809C2semidirect
2. C2×#14519806C2semidirect
4. C2×Q16×D61C2semidirect
5. #16840337C2semidirect
6. #16840332C2semidirect
7. #16840156C2semidirect
8. #16840155C2semidirect
9. #16840153C2semidirect
10. #16840144C2semidirect
11. #16840143C2semidirect
12. #16840141C2semidirect
13. #16840140C2semidirect
14. #16839719C2semidirect
15. C61×#497C2semidirect
194. #497D61semidirect
200. C61#3156semidirect