Finite Group Databasebeta

← #21454887

Subgroups — #21454887

Order 7808.

394 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840309C211yesmaximal, characteristic
2#16839836C211yesmaximal, characteristic, complemented
3#16839835C211yesmaximal, characteristic, complemented
4#16839834C211yesmaximal, characteristic, complemented
5#16839833C211yesmaximal, characteristic, complemented
6#16839832C211yesmaximal, characteristic, complemented
7#16839831C211yesmaximal, characteristic, complemented
8#16839830C211yesmaximal, characteristic, complemented
9#16839818C211yesmaximal, characteristic, complemented
10#16839817C211yesmaximal, characteristic, complemented
11#16839730C211yesmaximal, characteristic, complemented
12#16839728C211yesmaximal, characteristic, complemented
13#16839727C211yesmaximal, characteristic, complemented
14#16839727C211yesmaximal, characteristic, complemented
15C61×#435C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C2×#11758222C2211yescharacteristic
18C2×#11758194C2211yescharacteristic
19C2×#11758189C2211yescharacteristic
20C2×#11758189C2211yescharacteristic
21C22×#92418C2211yescharacteristic
22C2×C8×D61C2211yescharacteristic
23C2×C8×D61C2211yescharacteristic
24#14519776C411yescharacteristic
25#14519773C411yescharacteristic
26#14519763C411yescharacteristic
27#14519763C411yescharacteristic
28#14519752C411yescharacteristic
29#14519750C411yescharacteristic
30#14519750C411yescharacteristic
31#14519748C411yescharacteristic
32C4×D244C2211yescharacteristic
33C4×C22⋊D61C2211yescharacteristic
34C4×C22⋊D61C2211yescharacteristic
35C42×D61C2211yescharacteristic
36C4⋊#92418C2211yescharacteristic
37#14519706C2211yescharacteristic
38#14519706C2211yescharacteristic
39C22⋊#92418C2211yescharacteristic
40C22⋊#92418C2211yescharacteristic
41#14519689C2211yescharacteristic
42#14519689C2211yescharacteristic
43#14519689C2211yescharacteristic
44#14519689C2211yescharacteristic
45#14519689C2211yescharacteristic
46#14519689C2211yescharacteristic
47#14519689C2211yescharacteristic
48#14519689C2211yescharacteristic
49#14519688C2211yescharacteristic
50#14519687C2211yescharacteristic
51#14519687C2211yescharacteristic
52C2×M16×C61C2211yescharacteristic
53C22×C8×C61C2211yescharacteristic
54C4×D4×C61C2211yescharacteristic
55C4⋊C8×C61C2211yescharacteristic
56C22⋊C8×C61C2211yescharacteristic
57C22⋊C8×C61C2211yescharacteristic
58#97×C61C2211yescharacteristic
59C2×D4×C61C2×C411yescharacteristic
60C22×C4×C61C2311yescharacteristic
61C22×C4×C61C2311yescharacteristic
62C2×C22⋊D61C2×C411yescharacteristic
63C2×C22⋊D61C2×C411yescharacteristic
64C2×C22⋊D61C2×C411yescharacteristic
65C2×C22⋊D61C2×C411yescharacteristic
66C2×C22⋊D61C2×C411yescharacteristic
67C2×C22⋊D61C2×C411yescharacteristic
68#11758222—41no—
69#11758222—41no—
70#11758222—41no—
71#11758222—41no—
72C2×D244C2×C411yescharacteristic
73C2×D244C2×C411yescharacteristic
74C2×D244C2×C411yescharacteristic
75C2×C4×D61C2×C411yescharacteristic
76C2×C4×D61C2×C411yescharacteristic
77C2×C4×D61C2311yescharacteristic
78C2×C4×D61C2311yescharacteristic
79C2×C4×D61C2311yescharacteristic
80C2×Dic122C2×C411yescharacteristic
81C2×Dic122C2×C411yescharacteristic
82M16×C61—41no—
83C2×C8×C61—41no—
84C2×C8×C61C2311yescharacteristic
85C2×C8×C61C2311yescharacteristic
86C2×C8×C61C2311yescharacteristic
87C2×C8×C61C2311yescharacteristic
88C4⋊C4×C61C2×C411yescharacteristic
89C22⋊C4×C61C2×C411yescharacteristic
90C22⋊C4×C61C2×C411yescharacteristic
91C42×C61C2311yescharacteristic
92C22⋊Dic61C2×C411yescharacteristic
93C22⋊Dic61C2×C411yescharacteristic
94#11758198C2×C411yescharacteristic
95#11758198C2×C411yescharacteristic
96#11758198C2×C411yescharacteristic
97#11758198C2×C411yescharacteristic
98C4⋊Dic61C2×C411yescharacteristic
99#11758196C2×C411yescharacteristic
100#11758196C2×C411yescharacteristic
101C4×Dic61C2×C411yescharacteristic
102C4×Dic61C2×C411yescharacteristic
103C4×Dic61C2311yescharacteristic
104#11758194—41no—
105C2×#92418—41no—
106C2×#92418C2311yescharacteristic
107C2×#92418C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110#11758189—41no—
111#11758189—41no—
112C8×D61—41no—
113C8×D61—41no—
114C23×C61C22×C411yescharacteristic
115C23×C61C22×C411yescharacteristic
116C22×D61C22×C411yescharacteristic
117C22×D61C22×C411yescharacteristic
118C22×D61C22×C411yescharacteristic
119D4×C61—41no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61C22×C411yescharacteristic
125C2×C4×C61C22×C411yescharacteristic
126C2×C4×C61C22×C411yescharacteristic
127C2×C4×C61C22×C411yescharacteristic
128C2×C4×C61C2411yescharacteristic
129C22⋊D61—41no—
130C22⋊D61—41no—
131C22⋊D61—41no—
132C22⋊D61—41no—
133C22⋊D61—41no—
134C22⋊D61—41no—
135C2×Dic61C22×C411yescharacteristic
136C2×Dic61C22×C411yescharacteristic
137C2×Dic61C22×C411yescharacteristic
138C2×Dic61C22×C411yescharacteristic
139C2×Dic61C22×C411yescharacteristic
140D244—41no—
141D244—41no—
142D244—41no—
143C4×D61—21no—
144C4×D61—21no—
145C4×D61—21no—
146C4×D61—21no—
147C4×D61—21no—
148C4×D61—21no—
149C4×D61—41no—
150C4×D61—41no—
151Dic122—41no—
152Dic122—41no—
153C8×C61—21no—
154C8×C61—21no—
155C8×C61—21no—
156C8×C61—21no—
157#92418—21no—
158#92418—21no—
159#92418—21no—
160#92418—21no—
161C22×C61—21no—
162C22×C61—21no—
163C22×C61—21no—
164C22×C61—21no—
165C22×C61—21no—
166C22×C61—21no—
167C22×C61C23×C411yescharacteristic
168C2×D61—21no—
169C2×D61—21no—
170C2×D61—21no—
171C2×D61—21no—
172C2×D61—21no—
173C2×D61—21no—
174C2×D61—21no—
175C2×D61—21no—
176C2×D61—21no—
177C4×C61—21no—
178C4×C61—21no—
179C4×C61—21no—
180C4×C61—21no—
181C4×C61H(5,𝔽2)11yescharacteristic
182C4×C61H(5,𝔽2)11yescharacteristic
183Dic61—21no—
184Dic61—21no—
185Dic61—21no—
186Dic61—21no—
187Dic61—21no—
188#2980—611nomaximal, Sylow
189C2×C61—41no—
190C2×C61—41no—
191C2×C61#51811yescharacteristic
192C2×C61#56811yescharacteristic
193C2×C61#56811yescharacteristic
194D61—41no—
195D61—41no—
196D61—41no—
197#532—611no—
198#435—611no—
199#435—611no—
200#435—611no—
201#435—611no—
202#435—611no—
203#435—611no—
204#435—611no—
205#435D6111yescharacteristic, complemented
206#432—611no—
207#432—611no—
208#408—611no—
209#408—611no—
210#408—611no—
211#408—611no—
212C61#298011yescharacteristic, complemented, Sylow
213C2×#41—611no—
214C2×#41—611no—
215C2×M16—611no—
216C2×M16—611no—
217C2×M16—611no—
218C2×M16C2×D6111yescharacteristic
219C22×C8—611no—
220C22×C8—611no—
221C22×C8—611no—
222C22×C8C2×D6111yescharacteristic
223C4⋊Q8—611no—
224#127—611no—
225#124—611no—
226#124—611no—
227#121—611no—
228#121—611no—
229#121—611no—
230#121—611no—
231C4×D4—611no—
232C4×D4—611no—
233C4×D4—611no—
234C4×D4C2×D6111yescharacteristic
235C2×C42—611no—
236C4⋊C8—611no—
237C4⋊C8—611no—
238C4⋊C8—611no—
239C4⋊C8C2×D6111yescharacteristic
240C22⋊C8—611no—
241C22⋊C8—611no—
242C22⋊C8—611no—
243C22⋊C8—611no—
244C22⋊C8—611no—
245C22⋊C8—611no—
246C22⋊C8—611no—
247C22⋊C8—611no—
248C22⋊C8—611no—
249C22⋊C8—611no—
250C22⋊C8C2×D6111yescharacteristic
251C22⋊C8C2×D6111yescharacteristic
252#97—611no—
253#97—611no—
254#97—611no—
255#97C2×D6111yescharacteristic
256#41—2441no—
257#41—2441no—
258#41—2441no—
259#41—2441no—
260C2×Q8—611no—
261C2×Q8—611no—
262C2×D4—611no—
263C2×D4—611no—
264C2×D4—611no—
265C2×D4—611no—
266C2×D4—611no—
267C2×D4—611no—
268C2×D4—611no—
269C2×D4—611no—
270C2×D4—611no—
271C2×D4C4×D6111yescharacteristic
272C22×C4—611no—
273C22×C4—611no—
274C22×C4—611no—
275C22×C4—611no—
276C22×C4—611no—
277C22×C4C22×D6111yescharacteristic
278C22×C4C22×D6111yescharacteristic
279M16—41no—
280M16—2441no—
281M16—2441no—
282M16—2441no—
283C2×C8—41no—
284C2×C8—611no—
285C2×C8—611no—
286C2×C8—611no—
287C2×C8—611no—
288C2×C8—2441no—
289C2×C8—2441no—
290C2×C8—2441no—
291C2×C8C22×D6111yescharacteristic
292C2×C8C22×D6111yescharacteristic
293C2×C8C22×D6111yescharacteristic
294C2×C8C22×D6111yescharacteristic
295C4⋊C4—611no—
296C4⋊C4—611no—
297C4⋊C4—611no—
298C4⋊C4C4×D6111yescharacteristic
299C22⋊C4—611no—
300C22⋊C4—611no—
301C22⋊C4—611no—
302C22⋊C4—611no—
303C22⋊C4—611no—
304C22⋊C4—611no—
305C22⋊C4C4×D6111yescharacteristic
306C22⋊C4C4×D6111yescharacteristic
307C42—611no—
308C42—611no—
309C42—611no—
310C42C22×D6111yescharacteristic
311C23—611no—
312C23—611no—
313C23—611no—
314C23C2×C4×D6111yescharacteristic
315C23C2×C4×D6111yescharacteristic
316Q8—2441no—
317Q8—2441no—
318D4—41no—
319D4—2441no—
320D4—2441no—
321D4—2441no—
322D4—2441no—
323D4—2441no—
324D4—2441no—
325D4—2441no—
326D4—2441no—
327D4—2441no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—611no—
333C2×C4—611no—
334C2×C4—611no—
335C2×C4—611no—
336C2×C4—611no—
337C2×C4—1221no—
338C2×C4—1221no—
339C2×C4—1221no—
340C2×C4—1221no—
341C2×C4—1221no—
342C2×C4—1221no—
343C2×C4—2441no—
344C2×C4—2441no—
345C2×C4C2×C4×D6111yescharacteristic
346C2×C4C2×C4×D6111yescharacteristic
347C2×C4C2×C4×D6111yescharacteristic
348C2×C4C2×C4×D6111yescharacteristic
349C2×C4C23×D6111yescharacteristic
350C8—21no—
351C8—21no—
352C8—21no—
353C8—21no—
354C8—1221no—
355C8—1221no—
356C8—1221no—
357C8—1221no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—1221no—
365C22—1221no—
366C22—1221no—
367C22—1221no—
368C22—1221no—
369C22—1221no—
370C22—1221no—
371C22—1221no—
372C22—1221no—
373C22C22×C4×D6111yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—1221no—
379C4—1221no—
380C4—1221no—
381C4—1221no—
382C4—1221no—
383C4#1451982211yescharacteristic
384C4#1451982311yescharacteristic
385C2—41no—
386C2—41no—
387C2—2441no—
388C2—2441no—
389C2—2441no—
390C2#1684023411yescharacteristic
391C2#1684052711yescharacteristic
392C2#1684052811yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D61
commutator, socleC22×C61C23×C4
FittingC61×#435C2
hypercenter#435D61
hypocenterC61#2980
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ #435

Complements

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

NH ≅ G/Ntype
2. #16839836C2semidirect
3. #16839835C2semidirect
4. #16839834C2semidirect
5. #16839833C2semidirect
6. #16839832C2semidirect
7. #16839831C2semidirect
8. #16839830C2semidirect
9. #16839818C2semidirect
10. #16839817C2semidirect
11. #16839730C2semidirect
12. #16839728C2semidirect
13. #16839727C2semidirect
14. #16839727C2semidirect
15. C61×#435C2semidirect
205. #435D61semidirect
212. C61#2980semidirect