Finite Group Databasebeta

← #21456716

Subgroups — #21456716

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#16840340C211yesmaximal, characteristic, complemented
2#16840097C211yesmaximal, characteristic, complemented
3#16840095C211yesmaximal, characteristic, complemented
4#16840075C211yesmaximal, characteristic, complemented
5#16840073C211yesmaximal, characteristic, complemented
6#16840010C211yesmaximal, characteristic, complemented
7#16840006C211yesmaximal, characteristic, complemented
8#16840001C211yesmaximal, characteristic, complemented
9#16839996C211yesmaximal, characteristic, complemented
10#16839924C211yesmaximal, characteristic, complemented
11#16839922C211yesmaximal, characteristic, complemented
12#16839907C211yesmaximal, characteristic, complemented
13#16839905C211yesmaximal, characteristic, complemented
14#16839729C211yesmaximal, characteristic, complemented
15C61×#537C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C2×#11758202C2211yescharacteristic
18C2×#11758200C2211yescharacteristic
19C2×#11758201C2211yescharacteristic
20C2×#11758199C2211yescharacteristic
21C2×#11758194C2211yescharacteristic
22C22×#92418C2211yescharacteristic
23#14519756C2211yescharacteristic
24#14519756C2211yescharacteristic
25#14519753—21no—
26#14519751C2211yescharacteristic
27#14519751C2211yescharacteristic
28#14519749—21no—
29#14519749—21no—
30#14519748—21no—
31C2×C4⋊Dic61C2211yescharacteristic
32#14519710C2211yescharacteristic
33#14519710C2211yescharacteristic
34#14519710C2211yescharacteristic
35#14519710C2211yescharacteristic
36#14519701C2211yescharacteristic
37#14519701C2211yescharacteristic
38#14519700C2211yescharacteristic
39#14519700C2211yescharacteristic
40#14519698C2211yescharacteristic
41#14519698C2211yescharacteristic
42#14519697C2211yescharacteristic
43#14519697C2211yescharacteristic
44C22⋊#92418C2211yescharacteristic
45C22⋊#92418C2211yescharacteristic
46C22⋊#92418C2211yescharacteristic
47C22⋊#92418C2211yescharacteristic
48C2×#41×C61C2211yescharacteristic
49C2×#41×C61C2211yescharacteristic
50C22⋊Q8×C61—21no—
51C22⋊Q8×C61C2211yescharacteristic
52C22⋊Q8×C61C2211yescharacteristic
53#121×C61—21no—
54#121×C61—21no—
55#121×C61—21no—
56#121×C61C2211yescharacteristic
57#121×C61C2211yescharacteristic
58C2×C4⋊C4×C61C2211yescharacteristic
59#41×C61—41no—
60#41×C61—41no—
61#41×C61—41no—
62#41×C61—41no—
63C2×Q8×C61D411yescharacteristic
64C2×Q8×C61C2311yescharacteristic
65C2×D4×C61—21no—
66C2×D4×C61—21no—
67C2×D4×C61—21no—
68C2×D4×C61D411yescharacteristic
69C2×D4×C61D411yescharacteristic
70C2×D4×C61D411yescharacteristic
71C2×D4×C61C2311yescharacteristic
72C22×C4×C61—21no—
73C22×C4×C61—21no—
74C22×C4×C61C2311yescharacteristic
75C22×C4×C61C2311yescharacteristic
76C22×C4×C61C2311yescharacteristic
77C2×C22⋊D61—21no—
78C2×C22⋊D61—21no—
79C2×C22⋊D61—21no—
80C22×Dic61—21no—
81#11758222—41no—
82#11758222—41no—
83C2×D244C2311yescharacteristic
84C2×C4×D61—21no—
85C2×Dic122C2311yescharacteristic
86C4⋊C4×C61—21no—
87C4⋊C4×C61—21no—
88C4⋊C4×C61—21no—
89C4⋊C4×C61C2311yescharacteristic
90C4⋊C4×C61C2311yescharacteristic
91C22⋊C4×C61—21no—
92C22⋊C4×C61—21no—
93C22⋊C4×C61—21no—
94C22⋊C4×C61—21no—
95C22⋊Dic61—21no—
96C22⋊Dic61—21no—
97#11758202—41no—
98#11758201—41no—
99#11758200—41no—
100#11758199—41no—
101#11758198—21no—
102#11758198—21no—
103C4⋊Dic61—21no—
104C4⋊Dic61C2311yescharacteristic
105C4⋊Dic61C2311yescharacteristic
106#11758196—21no—
107#11758196—21no—
108#11758194—41no—
109C2×#92418—41no—
110C2×#92418C2311yescharacteristic
111C2×#92418C2311yescharacteristic
112C2×#92418C2311yescharacteristic
113C2×#92418C2311yescharacteristic
114C23×C61—21no—
115C23×C61C2×D411yescharacteristic
116C23×C61C2×D411yescharacteristic
117C23×C61C2×D411yescharacteristic
118C22×D61—21no—
119Q8×C61—21no—
120Q8×C61—21no—
121Q8×C61—41no—
122D4×C61—21no—
123D4×C61—21no—
124D4×C61—41no—
125D4×C61—41no—
126D4×C61—41no—
127D4×C61—42no—
128D4×C61—81no—
129D4×C61—81no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—42no—
140C2×C4×C61—81no—
141C2×C4×C61C2×D411yescharacteristic
142C2×C4×C61C2×D411yescharacteristic
143C2×C4×C61C2×D411yescharacteristic
144C2×C4×C61C2411yescharacteristic
145C22⋊D61—42no—
146C22⋊D61—81no—
147C22⋊D61—81no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—81no—
152D244—21no—
153D244—21no—
154C4×D61—42no—
155Dic122—21no—
156Dic122—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×C61—41no—
171C22×C61—41no—
172C22×C61—41no—
173C22×C61C22×D411yescharacteristic
174C2×D61—41no—
175C2×D61—41no—
176C2×D61—41no—
177C4×C61—21no—
178C4×C61—21no—
179C4×C61—21no—
180C4×C61—41no—
181C4×C61—41no—
182C4×C61—41no—
183C4×C61H(5,𝔽2)11yescharacteristic
184C4×C61H(5,𝔽2)11yescharacteristic
185Dic61—41no—
186Dic61—41no—
187Dic61—41no—
188#3203—611nomaximal, Sylow
189C2×C61—41no—
190C2×C61—41no—
191C2×C61—41no—
192C2×C61—81no—
193C2×C61#53411yescharacteristic
194C2×C61#57611yescharacteristic
195C2×C61#57811yescharacteristic
196D61—81no—
197#537—611no—
198#537D6111yescharacteristic, complemented
199#484—611no—
200#484—611no—
201#480—611no—
202#480—611no—
203#468—611no—
204#468—611no—
205#467—611no—
206#466—611no—
207#452—611no—
208#452—611no—
209#449—611no—
210#449—611no—
211#408—611no—
212C61#320311yescharacteristic, complemented, Sylow
213C2×#41—611no—
214C2×#41C2×D6111yescharacteristic
215C2×#41C2×D6111yescharacteristic
216C2×Q16—611no—
217C2×SD16—611no—
218C2×SD16—611no—
219C2×D8—611no—
220C2×M16—611no—
221C22×C8—611no—
222C22⋊Q8—21no—
223C22⋊Q8—611no—
224C22⋊Q8—611no—
225C22⋊Q8—1221no—
226C22⋊Q8C2×D6111yescharacteristic
227C22⋊Q8C2×D6111yescharacteristic
228#121—21no—
229#121—21no—
230#121—21no—
231#121—611no—
232#121—611no—
233#121—1221no—
234#121—1221no—
235#121—1221no—
236#121C2×D6111yescharacteristic
237#121C2×D6111yescharacteristic
238C2×C4⋊C4—611no—
239C2×C4⋊C4C2×D6111yescharacteristic
240#107—611no—
241#107—611no—
242#107—611no—
243#107—611no—
244#103—611no—
245#103—611no—
246#103—611no—
247#103—611no—
248#102—611no—
249#102—611no—
250#102—611no—
251#102—611no—
252C22⋊C8—611no—
253C22⋊C8—611no—
254C22⋊C8—611no—
255C22⋊C8—611no—
256#41—41no—
257#41—41no—
258#41—41no—
259#41—41no—
260#41—2441no—
261#41—2441no—
262C2×Q8—611no—
263C2×Q8C22⋊D6111yescharacteristic
264C2×Q8C22×D6111yescharacteristic
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—611no—
269C2×D4—1221no—
270C2×D4—1221no—
271C2×D4—1221no—
272C2×D4C22⋊D6111yescharacteristic
273C2×D4C22⋊D6111yescharacteristic
274C2×D4C22⋊D6111yescharacteristic
275C2×D4C22×D6111yescharacteristic
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—1221no—
279C22×C4—1221no—
280C22×C4C22×D6111yescharacteristic
281C22×C4C22×D6111yescharacteristic
282C22×C4C22×D6111yescharacteristic
283Q16—2441no—
284SD16—2441no—
285SD16—2441no—
286D8—2441no—
287M16—2441no—
288C2×C8—611no—
289C2×C8—611no—
290C2×C8—611no—
291C2×C8—611no—
292C2×C8—2441no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—611no—
297C4⋊C4—611no—
298C4⋊C4—1221no—
299C4⋊C4—1221no—
300C4⋊C4—1221no—
301C4⋊C4C22×D6111yescharacteristic
302C4⋊C4C22×D6111yescharacteristic
303C22⋊C4—21no—
304C22⋊C4—21no—
305C22⋊C4—21no—
306C22⋊C4—21no—
307C22⋊C4—1221no—
308C22⋊C4—1221no—
309C22⋊C4—1221no—
310C22⋊C4—1221no—
311C23—21no—
312C23—1221no—
313C23C2×C22⋊D6111yescharacteristic
314C23C2×C22⋊D6111yescharacteristic
315C23C2×C22⋊D6111yescharacteristic
316Q8—21no—
317Q8—21no—
318Q8—41no—
319Q8—1221no—
320Q8—1221no—
321D4—21no—
322D4—21no—
323D4—41no—
324D4—41no—
325D4—41no—
326D4—42no—
327D4—81no—
328D4—81no—
329D4—1221no—
330D4—1221no—
331D4—4881no—
332D4—4881no—
333D4—2442no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—42no—
344C2×C4—81no—
345C2×C4—1221no—
346C2×C4—1221no—
347C2×C4—1221no—
348C2×C4—4881no—
349C2×C4—2442no—
350C2×C4C2×C22⋊D6111yescharacteristic
351C2×C4C2×C22⋊D6111yescharacteristic
352C2×C4C2×C22⋊D6111yescharacteristic
353C2×C4C23×D6111yescharacteristic
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—41no—
368C22—41no—
369C22—41no—
370C22—2441no—
371C22—2441no—
372C22—2441no—
373C22C22×C22⋊D6111yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—2441no—
381C4—2441no—
382C4—2441no—
383C4#1451982211yescharacteristic
384C4#1451982211yescharacteristic
385C2—41no—
386C2—41no—
387C2—41no—
388C2—81no—
389C2—4881no—
390C2#1684032111yescharacteristic
391C2#1684056511yescharacteristic
392C2#1684057711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#537C2
socleC22×C61C22×D4
hypercenter#537D61
hypocenterC61#3203
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×#41 ◁ #537

Complements

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

NH ≅ G/Ntype
1. #16840340C2semidirect
2. #16840097C2semidirect
3. #16840095C2semidirect
4. #16840075C2semidirect
5. #16840073C2semidirect
6. #16840010C2semidirect
7. #16840006C2semidirect
8. #16840001C2semidirect
9. #16839996C2semidirect
10. #16839924C2semidirect
11. #16839922C2semidirect
12. #16839907C2semidirect
13. #16839905C2semidirect
14. #16839729C2semidirect
15. C61×#537C2semidirect
198. #537D61semidirect
212. C61#3203semidirect