Finite Group Databasebeta

← #21454892

Subgroups — #21454892

Order 7808.

402 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#16840308C211yesmaximal, characteristic
2#16839838C211yesmaximal, characteristic, complemented
3#16839837C211yesmaximal, characteristic, complemented
4#16839836C211yesmaximal, characteristic, complemented
5#16839833C211yesmaximal, characteristic, complemented
6#16839831C211yesmaximal, characteristic, complemented
7#16839830C211yesmaximal, characteristic, complemented
8C8×C22⋊D61C211yesmaximal, characteristic, complemented
9#16839825C211yesmaximal, characteristic, complemented
10#16839816C211yesmaximal, characteristic, complemented
11#16839812C211yesmaximal, characteristic, complemented
12#16839729C211yesmaximal, characteristic, complemented
13#16839727C211yesmaximal, characteristic, complemented
14#16839727C211yesmaximal, characteristic, complemented
15C61×#408C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C2×#11758194C2211yescharacteristic
18C2×#11758189C2211yescharacteristic
19C2×#11758189C2211yescharacteristic
20C22×#92418C2211yescharacteristic
21C2×C8×D61C2211yescharacteristic
22C2×C8×D61C2211yescharacteristic
23#14519775C411yescharacteristic
24#14519773C411yescharacteristic
25#14519766C411yescharacteristic
26#14519764C411yescharacteristic
27#14519749C411yescharacteristic
28#14519749C411yescharacteristic
29#14519749C411yescharacteristic
30#14519749C411yescharacteristic
31C4×C22⋊D61C2211yescharacteristic
32C4×C22⋊D61C2211yescharacteristic
33C4×C22⋊D61C2211yescharacteristic
34C4×C22⋊D61C2211yescharacteristic
35C2×C4×Dic61C2211yescharacteristic
36#14519706C2211yescharacteristic
37#14519706C2211yescharacteristic
38#14519706C2211yescharacteristic
39#14519706C2211yescharacteristic
40C22⋊#92418C2211yescharacteristic
41C22⋊#92418C2211yescharacteristic
42C22⋊#92418C2211yescharacteristic
43C22⋊#92418C2211yescharacteristic
44#14519689C2211yescharacteristic
45#14519689C2211yescharacteristic
46#14519689C2211yescharacteristic
47#14519689C2211yescharacteristic
48#14519687C2211yescharacteristic
49#14519687C2211yescharacteristic
50C8×Dic61C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52C2×#41×C61C2211yescharacteristic
53C2×M16×C61C2211yescharacteristic
54C22×C8×C61C2211yescharacteristic
55C22⋊C8×C61C2211yescharacteristic
56C22⋊C8×C61C2211yescharacteristic
57C22⋊C8×C61C2211yescharacteristic
58C22⋊C8×C61C2211yescharacteristic
59#41×C61—41no—
60#41×C61—41no—
61C2×Q8×C61C2×C411yescharacteristic
62C2×D4×C61C2×C411yescharacteristic
63C2×D4×C61C2×C411yescharacteristic
64C2×D4×C61C2×C411yescharacteristic
65C22×C4×C61C2311yescharacteristic
66C22×C4×C61C2311yescharacteristic
67C22×C4×C61C2311yescharacteristic
68C2×C22⋊D61C2×C411yescharacteristic
69C2×C22⋊D61C2×C411yescharacteristic
70C2×C22⋊D61C2×C411yescharacteristic
71C2×C22⋊D61C2×C411yescharacteristic
72C2×C22⋊D61C2×C411yescharacteristic
73C2×C22⋊D61C2×C411yescharacteristic
74C22×Dic61C2×C411yescharacteristic
75C22×Dic61C2×C411yescharacteristic
76#11758222—41no—
77#11758222—41no—
78C2×D244C2×C411yescharacteristic
79C2×C4×D61C2311yescharacteristic
80C2×C4×D61C2311yescharacteristic
81C2×Dic122C2×C411yescharacteristic
82M16×C61—41no—
83C2×C8×C61—41no—
84C2×C8×C61C2311yescharacteristic
85C2×C8×C61C2311yescharacteristic
86C2×C8×C61C2311yescharacteristic
87C2×C8×C61C2311yescharacteristic
88C22⋊Dic61C2×C411yescharacteristic
89C22⋊Dic61C2×C411yescharacteristic
90C22⋊Dic61C2×C411yescharacteristic
91C22⋊Dic61C2×C411yescharacteristic
92#11758198C2×C411yescharacteristic
93#11758198C2×C411yescharacteristic
94#11758198C2×C411yescharacteristic
95#11758198C2×C411yescharacteristic
96#11758196C2×C411yescharacteristic
97#11758196C2×C411yescharacteristic
98#11758196C2×C411yescharacteristic
99#11758196C2×C411yescharacteristic
100C4×Dic61C2×C411yescharacteristic
101C4×Dic61C2×C411yescharacteristic
102C4×Dic61C2311yescharacteristic
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
116C23×C61C22×C411yescharacteristic
117C22×D61C22×C411yescharacteristic
118C22×D61C22×C411yescharacteristic
119Q8×C61—41no—
120D4×C61—41no—
121D4×C61—41no—
122D4×C61—41no—
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×C61C22×C411yescharacteristic
130C2×C4×C61C22×C411yescharacteristic
131C2×C4×C61C22×C411yescharacteristic
132C2×C4×C61C2411yescharacteristic
133C22⋊D61—22no—
134C22⋊D61—22no—
135C22⋊D61—41no—
136C22⋊D61—41no—
137C22⋊D61—41no—
138C22⋊D61—41no—
139C2×Dic61—22no—
140C2×Dic61—41no—
141C2×Dic61C22×C411yescharacteristic
142C2×Dic61C22×C411yescharacteristic
143C2×Dic61C22×C411yescharacteristic
144C2×Dic61C22×C411yescharacteristic
145C2×Dic61C22×C411yescharacteristic
146C2×Dic61C22×C411yescharacteristic
147D244—41no—
148C4×D61—21no—
149C4×D61—21no—
150C4×D61—21no—
151C4×D61—21no—
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×C61—21no—
168C22×C61—21no—
169C22×C61—21no—
170C22×C61C23×C411yescharacteristic
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×C61H(5,𝔽2)11yescharacteristic
181C4×C61H(5,𝔽2)11yescharacteristic
182Dic61—21no—
183Dic61—21no—
184Dic61—21no—
185Dic61—21no—
186Dic61—21no—
187Dic61#13112yes—
188#2981—611nomaximal, Sylow
189C2×C61—41no—
190C2×C61—41no—
191C2×C61—41no—
192C2×C61#51811yescharacteristic
193C2×C61C2×#13111yescharacteristic
194C2×C61#56811yescharacteristic
195D61—41no—
196D61—41no—
197#532—611no—
198#436—611no—
199#436—611no—
200#435—611no—
201#435—611no—
202#435—611no—
203#435—611no—
204C8×D4—611no—
205C8×D4—611no—
206#432—611no—
207#431—611no—
208#408—611no—
209#408—611no—
210#408—611no—
211#408D6111yescharacteristic, complemented
212C61#298111yescharacteristic, complemented, Sylow
213C2×#41—611no—
214C2×#41C2×D6111yescharacteristic
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×D4—611no—
235C2×C42—611no—
236C4⋊C8—611no—
237C4⋊C8—611no—
238C4⋊C8—611no—
239C4⋊C8—611no—
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⋊C8C2×D6111yescharacteristic
249C22⋊C8C2×D6111yescharacteristic
250C22⋊C8C2×D6111yescharacteristic
251C22⋊C8C2×D6111yescharacteristic
252#97—611no—
253#97—611no—
254C4×C8—611no—
255C4×C8—611no—
256#41—41no—
257#41—41no—
258#41—2441no—
259#41—2441no—
260C2×Q8—611no—
261C2×Q8C4×D6111yescharacteristic
262C2×D4—611no—
263C2×D4—611no—
264C2×D4—611no—
265C2×D4—611no—
266C2×D4—611no—
267C2×D4—611no—
268C2×D4—611no—
269C2×D4C4×D6111yescharacteristic
270C2×D4C4×D6111yescharacteristic
271C2×D4C4×D6111yescharacteristic
272C22×C4—611no—
273C22×C4—611no—
274C22×C4—611no—
275C22×C4—611no—
276C22×C4C22×D6111yescharacteristic
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⋊C4—611no—
299C22⋊C4—611no—
300C22⋊C4—611no—
301C22⋊C4—611no—
302C22⋊C4—611no—
303C22⋊C4—611no—
304C22⋊C4—611no—
305C22⋊C4—611no—
306C22⋊C4—611no—
307C42—611no—
308C42—611no—
309C42—611no—
310C42—611no—
311C23—611no—
312C23—611no—
313C23C2×C4×D6111yescharacteristic
314C23C2×C4×D6111yescharacteristic
315C23C2×C4×D6111yescharacteristic
316Q8—41no—
317Q8—2441no—
318D4—41no—
319D4—41no—
320D4—41no—
321D4—1222no—
322D4—1222no—
323D4—2441no—
324D4—2441no—
325D4—2441no—
326D4—2441no—
327D4—2441no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—611no—
335C2×C4—611no—
336C2×C4—611no—
337C2×C4—611no—
338C2×C4—611no—
339C2×C4—611no—
340C2×C4—1222no—
341C2×C4—1221no—
342C2×C4—1221no—
343C2×C4—1221no—
344C2×C4—1221no—
345C2×C4—2441no—
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—21no—
365C22—21no—
366C22—21no—
367C22—1221no—
368C22—1221no—
369C22—1221no—
370C22—1221no—
371C22—1221no—
372C22—1221no—
373C22C22×C4×D6111yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—612no—
378C4—1221no—
379C4—1221no—
380C4—1221no—
381C4—1221no—
382C4—1221no—
383C4#1451982211yescharacteristic
384C4#1451982211yescharacteristic
385C2—41no—
386C2—41no—
387C2—41no—
388C2—2441no—
389C2—2441no—
390C2#1684023511yescharacteristic
391C2#131×D6111yescharacteristic
392C2#1684052711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D61
commutator, socleC22×C61C23×C4
FittingC61×#408C2
hypercenter#408D61
hypocenterC61#2981
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ #408

Complements

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

NH ≅ G/Ntype
2. #16839838C2semidirect
3. #16839837C2semidirect
4. #16839836C2semidirect
5. #16839833C2semidirect
6. #16839831C2semidirect
7. #16839830C2semidirect
8. C8×C22⋊D61C2semidirect
9. #16839825C2semidirect
10. #16839816C2semidirect
11. #16839812C2semidirect
12. #16839729C2semidirect
13. #16839727C2semidirect
14. #16839727C2semidirect
15. C61×#408C2semidirect
211. #408D61semidirect
212. C61#2981semidirect