Finite Group Databasebeta

← #21456720

Subgroups — #21456720

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#16840342C211yesmaximal, characteristic, complemented
2#16840340C211yesmaximal, characteristic, complemented
3#16840096C211yesmaximal, characteristic, complemented
4#16840095C211yesmaximal, characteristic, complemented
5#16840076C211yesmaximal, characteristic, complemented
6#16840074C211yesmaximal, characteristic, complemented
7#16840011C211yesmaximal, characteristic, complemented
8#16840005C211yesmaximal, characteristic, complemented
9#16840000C211yesmaximal, characteristic, complemented
10#16839997C211yesmaximal, characteristic, complemented
11#16839923C211yesmaximal, characteristic, complemented
12#16839907C211yesmaximal, characteristic, complemented
13#16839906C211yesmaximal, characteristic, complemented
14#16839727C211yesmaximal, characteristic, complemented
15C61×#452C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×#11758222C2211yescharacteristic
18C2×#11758201C2211yescharacteristic
19C2×#11758199C2211yescharacteristic
20C2×#11758189C2211yescharacteristic
21C2×C8×D61C2211yescharacteristic
22#14519756—21no—
23#14519755—21no—
24#14519753C2211yescharacteristic
25#14519753C2211yescharacteristic
26#14519753C2211yescharacteristic
27#14519752—21no—
28#14519752C2211yescharacteristic
29#14519751—21no—
30#14519751C2211yescharacteristic
31#14519750—21no—
32#14519750—21no—
33#14519749—21no—
34#14519749—21no—
35#14519748C2211yescharacteristic
36#14519748C2211yescharacteristic
37C2×C4⋊Dic61C2211yescharacteristic
38C4⋊C4×D61C2211yescharacteristic
39#14519711C2211yescharacteristic
40#14519711C2211yescharacteristic
41#14519710C2211yescharacteristic
42#14519710C2211yescharacteristic
43#14519701C2211yescharacteristic
44#14519701C2211yescharacteristic
45#14519701C2211yescharacteristic
46#14519699C2211yescharacteristic
47#14519699C2211yescharacteristic
48#14519698C2211yescharacteristic
49C22⋊#92418C2211yescharacteristic
50#14519689C2211yescharacteristic
51#14519689C2211yescharacteristic
52C2×#41×C61C2211yescharacteristic
53C2×Q16×C61C2211yescharacteristic
54C2×SD16×C61C2211yescharacteristic
55C22⋊Q8×C61C2211yescharacteristic
56#103×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic
58C22⋊C8×C61C2211yescharacteristic
59#41×C61—41no—
60#41×C61—41no—
61C2×Q8×C61C2311yescharacteristic
62C2×Q8×C61C2311yescharacteristic
63C2×D4×C61—21no—
64C2×D4×C61C2311yescharacteristic
65C22×C4×C61—21no—
66C22×C4×C61C2311yescharacteristic
67C2×C22⋊D61—21no—
68C2×C22⋊D61—21no—
69C2×C22⋊D61—21no—
70C2×C22⋊D61D411yescharacteristic
71C2×C22⋊D61D411yescharacteristic
72C22×Dic61—21no—
73#11758226—41no—
74#11758226—41no—
75#11758222—41no—
76#11758222—41no—
77C2×D244—21no—
78C2×D244—21no—
79C2×D244D411yescharacteristic
80C2×D244C2311yescharacteristic
81C2×C4×D61—21no—
82C2×C4×D61—21no—
83C2×C4×D61C2311yescharacteristic
84C2×C4×D61C2311yescharacteristic
85C2×Dic122D411yescharacteristic
86Q16×C61—41no—
87SD16×C61—41no—
88C2×C8×C61C2311yescharacteristic
89C2×C8×C61C2311yescharacteristic
90C4⋊C4×C61—21no—
91C4⋊C4×C61C2311yescharacteristic
92C22⋊C4×C61—21no—
93C22⋊Dic61—21no—
94C22⋊Dic61—21no—
95#11758201—41no—
96#11758199—41no—
97#11758198—21no—
98#11758198—21no—
99#11758198—21no—
100#11758198—21no—
101#11758198—21no—
102C4⋊Dic61—21no—
103C4⋊Dic61C2311yescharacteristic
104C4⋊Dic61C2311yescharacteristic
105C4⋊Dic61C2311yescharacteristic
106#11758196—21no—
107#11758196—21no—
108#11758196—21no—
109#11758196—21no—
110C2×#92418C2311yescharacteristic
111C2×#92418C2311yescharacteristic
112#11758189—41no—
113C8×D61—41no—
114C23×C61—21no—
115C23×C61C2×D411yescharacteristic
116C22×D61—21no—
117C22×D61C2×D411yescharacteristic
118C22×D61C2×D411yescharacteristic
119Q8×C61—21no—
120Q8×C61—21no—
121Q8×C61—21no—
122Q8×C61—21no—
123D4×C61—21no—
124D4×C61—21no—
125D4×C61—42no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—42no—
132C2×C4×C61C2×D411yescharacteristic
133C2×C4×C61C2411yescharacteristic
134C22⋊D61—41no—
135C22⋊D61—41no—
136C22⋊D61—81no—
137C22⋊D61—81no—
138C22⋊D61—81no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—81no—
143C2×Dic61C2×D411yescharacteristic
144C2×Dic61C2×D411yescharacteristic
145D244—21no—
146D244—21no—
147D244—41no—
148D244—42no—
149D244—81no—
150C4×D61—21no—
151C4×D61—21no—
152C4×D61—21no—
153C4×D61—21no—
154C4×D61—42no—
155C4×D61—81no—
156Dic122—41no—
157C8×C61—21no—
158C8×C61—21no—
159#92418—21no—
160#92418—21no—
161C22×C61—21no—
162C22×C61—21no—
163C22×C61—21no—
164C22×C61—41no—
165C22×C61—41no—
166C22×C61—41no—
167C22×C61C22×D411yescharacteristic
168C2×D61—21no—
169C2×D61—21no—
170C2×D61—21no—
171C2×D61—21no—
172C2×D61—21no—
173C2×D61—21no—
174C2×D61—41no—
175C2×D61—41no—
176C2×D61—41no—
177C4×C61—21no—
178C4×C61—41no—
179C4×C61—41no—
180C4×C61—41no—
181C4×C61H(5,𝔽2)11yescharacteristic
182C4×C61H(5,𝔽2)11yescharacteristic
183Dic61—21no—
184Dic61—21no—
185Dic61—41no—
186Dic61—41no—
187Dic61—41no—
188#3203—611nomaximal, Sylow
189C2×C61—41no—
190C2×C61—81no—
191C2×C61#53411yescharacteristic
192C2×C61#57611yescharacteristic
193C2×C61#57811yescharacteristic
194D61—41no—
195D61—41no—
196D61—81no—
197#537—611no—
198#537—611no—
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#452D6111yescharacteristic, complemented
209#449—611no—
210#449—611no—
211#408—611no—
212C61#320311yescharacteristic, complemented, Sylow
213C2×#41—611no—
214C2×#41—611no—
215C2×#41C2×D6111yescharacteristic
216C2×Q16C2×D6111yescharacteristic
217C2×SD16—611no—
218C2×SD16C2×D6111yescharacteristic
219C2×D8—611no—
220C2×M16—611no—
221C22×C8—611no—
222C22⋊Q8—611no—
223C22⋊Q8—611no—
224C22⋊Q8—611no—
225C22⋊Q8—1221no—
226C22⋊Q8—1221no—
227C22⋊Q8C2×D6111yescharacteristic
228#121—611no—
229#121—611no—
230#121—611no—
231#121—611no—
232#121—1221no—
233#121—1221no—
234#121—1221no—
235#121—1221no—
236#121—1221no—
237#121—1221no—
238C2×C4⋊C4—611no—
239C2×C4⋊C4—611no—
240#107—611no—
241#107—611no—
242#107—611no—
243#107—611no—
244#103—611no—
245#103—611no—
246#103—611no—
247#103C2×D6111yescharacteristic
248#102—611no—
249#102—611no—
250#102—611no—
251#102C2×D6111yescharacteristic
252C22⋊C8—611no—
253C22⋊C8—611no—
254C22⋊C8—611no—
255C22⋊C8C2×D6111yescharacteristic
256#41—41no—
257#41—41no—
258#41—2441no—
259#41—2441no—
260#41—2441no—
261#41—2441no—
262C2×Q8—611no—
263C2×Q8C22×D6111yescharacteristic
264C2×Q8C22×D6111yescharacteristic
265C2×D4—21no—
266C2×D4—611no—
267C2×D4—611no—
268C2×D4—611no—
269C2×D4—611no—
270C2×D4—1221no—
271C2×D4—1221no—
272C2×D4—1221no—
273C2×D4—1221no—
274C2×D4—1221no—
275C2×D4C22×D6111yescharacteristic
276C22×C4—21no—
277C22×C4—611no—
278C22×C4—611no—
279C22×C4—1221no—
280C22×C4—1221no—
281C22×C4—1221no—
282C22×C4C22×D6111yescharacteristic
283Q16—41no—
284SD16—41no—
285SD16—2441no—
286D8—2441no—
287M16—2441no—
288C2×C8—611no—
289C2×C8—611no—
290C2×C8—2441no—
291C2×C8C22×D6111yescharacteristic
292C2×C8C22×D6111yescharacteristic
293C4⋊C4—21no—
294C4⋊C4—611no—
295C4⋊C4—611no—
296C4⋊C4—611no—
297C4⋊C4—1221no—
298C4⋊C4—1221no—
299C4⋊C4—1221no—
300C4⋊C4—1221no—
301C4⋊C4—1221no—
302C4⋊C4C22×D6111yescharacteristic
303C22⋊C4—21no—
304C22⋊C4—1221no—
305C22⋊C4—1221no—
306C22⋊C4—1221no—
307C22⋊C4—1221no—
308C22⋊C4—1221no—
309C22⋊C4—1221no—
310C22⋊C4—1221no—
311C23—21no—
312C23—611no—
313C23—611no—
314C23—1221no—
315C23D4×D6111yescharacteristic
316Q8—21no—
317Q8—21no—
318Q8—21no—
319Q8—21no—
320Q8—2441no—
321D4—21no—
322D4—21no—
323D4—42no—
324D4—1221no—
325D4—1221no—
326D4—4881no—
327D4—4881no—
328D4—4881no—
329D4—4881no—
330D4—2441no—
331D4—2442no—
332D4—2441no—
333D4—2441no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—42no—
340C2×C4—611no—
341C2×C4—611no—
342C2×C4—1221no—
343C2×C4—1221no—
344C2×C4—1221no—
345C2×C4—1221no—
346C2×C4—1221no—
347C2×C4—1221no—
348C2×C4—1221no—
349C2×C4—4881no—
350C2×C4—4881no—
351C2×C4—2442no—
352C2×C4D4×D6111yescharacteristic
353C2×C4C23×D6111yescharacteristic
354C8—21no—
355C8—21no—
356C8—1221no—
357C8—1221no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—1221no—
365C22—1221no—
366C22—1221no—
367C22—1221no—
368C22—1221no—
369C22—1221no—
370C22—2441no—
371C22—2441no—
372C22—2441no—
373C22C2×D4×D6111yescharacteristic
374C4—21no—
375C4—41no—
376C4—41no—
377C4—41no—
378C4—1221no—
379C4—1221no—
380C4—2441no—
381C4—2441no—
382C4—2441no—
383C4#1451982211yescharacteristic
384C4#1451982211yescharacteristic
385C2—41no—
386C2—81no—
387C2—4881no—
388C2—2441no—
389C2—2441no—
390C2#1684032211yescharacteristic
391C2#1684056411yescharacteristic
392C2#1684057811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#452C2
socleC22×C61C22×D4
hypercenter#452D61
hypocenterC61#3203
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #16840342C2semidirect
2. #16840340C2semidirect
3. #16840096C2semidirect
4. #16840095C2semidirect
5. #16840076C2semidirect
6. #16840074C2semidirect
7. #16840011C2semidirect
8. #16840005C2semidirect
9. #16840000C2semidirect
10. #16839997C2semidirect
11. #16839923C2semidirect
12. #16839907C2semidirect
13. #16839906C2semidirect
14. #16839727C2semidirect
15. C61×#452C2semidirect
208. #452D61semidirect
212. C61#3203semidirect