Finite Group Databasebeta

← #21456900

Subgroups — #21456900

Order 7808.

364 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840372C211yesmaximal, characteristic, complemented
2#16840333C211yesmaximal, characteristic
3#16840153C211yesmaximal, characteristic, complemented
4#16840140C211yesmaximal, characteristic, complemented
5#16840129C211yesmaximal, characteristic, complemented
6#16840115C211yesmaximal, characteristic, complemented
7#16839983C211yesmaximal, characteristic, complemented
8#16839982C211yesmaximal, characteristic, complemented
9#16839971C211yesmaximal, characteristic, complemented
10#16839970C211yesmaximal, characteristic, complemented
11#16839924C211yesmaximal, characteristic
12#16839920C211yesmaximal, characteristic, complemented
13#16839917C211yesmaximal, characteristic, complemented
14#16839820C211yesmaximal, characteristic, complemented
15C61×#452C211yesmaximal, characteristic
16C22×Dic122C2211yescharacteristic
17C2×Dic244C2211yescharacteristic
18C2×Dic244C2211yescharacteristic
19C2×#11758202C2211yescharacteristic
20C2×#11758202C2211yescharacteristic
21C2×#11758202C2211yescharacteristic
22C2×#11758200C2211yescharacteristic
23#14519775C2211yescharacteristic
24#14519775C2211yescharacteristic
25#14519775C2211yescharacteristic
26#14519770—21no—
27#14519770—21no—
28#14519768—21no—
29#14519768C2211yescharacteristic
30#14519767—21no—
31#14519764C2211yescharacteristic
32#14519764C2211yescharacteristic
33#14519758—21no—
34#14519758—21no—
35#14519756—21no—
36#14519756—21no—
37#14519756C2211yescharacteristic
38Q8×Dic61C2211yescharacteristic
39#14519742C2211yescharacteristic
40#14519736C2211yescharacteristic
41#14519706C2211yescharacteristic
42#14519706C2211yescharacteristic
43#14519702C2211yescharacteristic
44#14519702C2211yescharacteristic
45#14519701C2211yescharacteristic
46#14519700C2211yescharacteristic
47#14519700C2211yescharacteristic
48#14519698C2211yescharacteristic
49C22⋊#92418C2211yescharacteristic
50#14519687C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
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
67C22×Dic61—21no—
68C2×Dic122—21no—
69C2×Dic122—41no—
70C2×Dic122—41no—
71C2×Dic122C2311yescharacteristic
72C2×Dic122C2311yescharacteristic
73C2×Dic122C2311yescharacteristic
74Q16×C61—41no—
75SD16×C61—41no—
76C2×C8×C61C2311yescharacteristic
77C2×C8×C61C2311yescharacteristic
78C4⋊C4×C61—21no—
79C4⋊C4×C61C2311yescharacteristic
80C22⋊C4×C61—21no—
81C22⋊Dic61—21no—
82C22⋊Dic61—21no—
83C22⋊Dic61—21no—
84C22⋊Dic61—21no—
85C22⋊Dic61—21no—
86C22⋊Dic61D411yescharacteristic
87C22⋊Dic61D411yescharacteristic
88#11758202—41no—
89#11758202—41no—
90#11758202—41no—
91#11758200—41no—
92C4⋊Dic61—21no—
93C4⋊Dic61—21no—
94C4⋊Dic61D411yescharacteristic
95C4⋊Dic61D411yescharacteristic
96C4⋊Dic61C2311yescharacteristic
97#11758196—21no—
98#11758196—21no—
99#11758196—21no—
100#11758196—21no—
101#11758196—21no—
102#11758196—21no—
103#11758196—21no—
104#11758196—21no—
105#11758196—21no—
106C4×Dic61—21no—
107C4×Dic61—21no—
108C4×Dic61C2311yescharacteristic
109C4×Dic61C2311yescharacteristic
110C2×#92418C2311yescharacteristic
111C2×#92418C2311yescharacteristic
112Dic244—41no—
113Dic244—41no—
114C23×C61—21no—
115C23×C61C2×D411yescharacteristic
116Q8×C61—21no—
117Q8×C61—21no—
118Q8×C61—21no—
119Q8×C61—21no—
120D4×C61—21no—
121D4×C61—21no—
122D4×C61—42no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—42no—
129C2×C4×C61C2×D411yescharacteristic
130C2×C4×C61C2411yescharacteristic
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—42no—
136C2×Dic61C2×D411yescharacteristic
137C2×Dic61C2×D411yescharacteristic
138C2×Dic61C2×D411yescharacteristic
139C2×Dic61C2×D411yescharacteristic
140Dic122—21no—
141Dic122—21no—
142Dic122—21no—
143Dic122—21no—
144Dic122—21no—
145Dic122—21no—
146Dic122—42no—
147C8×C61—21no—
148C8×C61—21no—
149#92418—21no—
150#92418—21no—
151C22×C61—21no—
152C22×C61—21no—
153C22×C61—21no—
154C22×C61—41no—
155C22×C61—41no—
156C22×C61—41no—
157C22×C61C22×D411yescharacteristic
158C4×C61—21no—
159C4×C61—41no—
160C4×C61—41no—
161C4×C61—41no—
162C4×C61H(5,𝔽2)11yescharacteristic
163C4×C61H(5,𝔽2)11yescharacteristic
164Dic61—21no—
165Dic61—21no—
166Dic61—21no—
167Dic61—21no—
168Dic61—41no—
169Dic61—41no—
170Dic61—41no—
171Dic61—41no—
172#3223—611nomaximal, Sylow
173C2×C61—41no—
174C2×C61—81no—
175C2×C61#53511yescharacteristic
176C2×C61#57811yescharacteristic
177C2×C61#57811yescharacteristic
178#541—611no—
179#536—611no—
180#497—611no—
181#494—611no—
182#491—611no—
183#488—611no—
184#464—611no—
185#464—611no—
186#462—611no—
187#462—611no—
188#452—611no—
189#452D6111yescharacteristic
190#451—611no—
191#451—611no—
192#433—611no—
193C61#322311yescharacteristic, complemented, Sylow
194C2×#41C2×D6111yescharacteristic
195C22×Q8—611no—
196C2×Q16—611no—
197C2×Q16—611no—
198C2×Q16—611no—
199C2×Q16—611no—
200C2×Q16—611no—
201C2×Q16C2×D6111yescharacteristic
202C2×SD16—611no—
203C2×SD16C2×D6111yescharacteristic
204C4⋊Q8—611no—
205C4⋊Q8—611no—
206C4⋊Q8—611no—
207#126—1221no—
208#126—1221no—
209#125—611no—
210#125—1221no—
211#125—1221no—
212#124—611no—
213#124—611no—
214#123—1221no—
215#123—1221no—
216C22⋊Q8—611no—
217C22⋊Q8—1221no—
218C22⋊Q8—1221no—
219C22⋊Q8C2×D6111yescharacteristic
220C4×Q8—611no—
221C4×Q8—611no—
222#117—611no—
223C4⋊C8—611no—
224C4⋊C8—611no—
225#103—611no—
226#103—611no—
227#103—611no—
228#103—611no—
229#103—611no—
230#103C2×D6111yescharacteristic
231#102—611no—
232#102C2×D6111yescharacteristic
233C22⋊C8—611no—
234C22⋊C8C2×D6111yescharacteristic
235#97—611no—
236C4×C8—611no—
237#41—41no—
238#41—41no—
239C2×Q8—611no—
240C2×Q8—611no—
241C2×Q8—611no—
242C2×Q8—1221no—
243C2×Q8—2441no—
244C2×Q8—2441no—
245C2×Q8C22×D6111yescharacteristic
246C2×Q8C22×D6111yescharacteristic
247C2×D4—21no—
248C2×D4C22×D6111yescharacteristic
249C22×C4—21no—
250C22×C4—1221no—
251C22×C4C22×D6111yescharacteristic
252Q16—41no—
253Q16—2441no—
254Q16—2441no—
255Q16—2441no—
256Q16—2441no—
257Q16—2441no—
258SD16—41no—
259SD16—2441no—
260C2×C8—611no—
261C2×C8—611no—
262C2×C8C22×D6111yescharacteristic
263C2×C8C22×D6111yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—611no—
266C4⋊C4—611no—
267C4⋊C4—611no—
268C4⋊C4—1221no—
269C4⋊C4—1221no—
270C4⋊C4—1221no—
271C4⋊C4—1221no—
272C4⋊C4—1221no—
273C4⋊C4—1221no—
274C4⋊C4—1221no—
275C4⋊C4—1221no—
276C4⋊C4—1221no—
277C4⋊C4—1221no—
278C4⋊C4—1221no—
279C4⋊C4C22×D6111yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—611no—
282C22⋊C4—611no—
283C22⋊C4—1221no—
284C22⋊C4—1221no—
285C22⋊C4—1221no—
286C22⋊C4—1221no—
287C22⋊C4—1221no—
288C42—611no—
289C42—611no—
290C42—1221no—
291C42—1221no—
292C23—21no—
293C23D4×D6111yescharacteristic
294Q8—21no—
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—1221no—
299Q8—1221no—
300Q8—1221no—
301Q8—1221no—
302Q8—1221no—
303Q8—1221no—
304Q8—2442no—
305D4—21no—
306D4—21no—
307D4—42no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—611no—
315C2×C4—611no—
316C2×C4—611no—
317C2×C4—611no—
318C2×C4—1221no—
319C2×C4—1221no—
320C2×C4—1221no—
321C2×C4—1221no—
322C2×C4—2442no—
323C2×C4D4×D6111yescharacteristic
324C2×C4C23×D6111yescharacteristic
325C8—21no—
326C8—21no—
327C8—1221no—
328C8—1221no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22C2×D4×D6111yescharacteristic
336C4—21no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—1221no—
341C4—1221no—
342C4—1221no—
343C4—1221no—
344C4—2441no—
345C4—2441no—
346C4—2441no—
347C4—2441no—
348C4#1451982211yescharacteristic
349C4#1451982211yescharacteristic
350C2—41no—
351C2—81no—
352C2#1684032711yescharacteristic
353C2#1684057611yescharacteristic
354C2#1684057811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#452C2
socleC22×C61C22×D4
hypercenter#452D61
hypocenterC61#3223
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. #16840372C2semidirect
3. #16840153C2semidirect
4. #16840140C2semidirect
5. #16840129C2semidirect
6. #16840115C2semidirect
7. #16839983C2semidirect
8. #16839982C2semidirect
9. #16839971C2semidirect
10. #16839970C2semidirect
12. #16839920C2semidirect
13. #16839917C2semidirect
14. #16839820C2semidirect
193. C61#3223semidirect