Finite Group Databasebeta

← #21456901

Subgroups — #21456901

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#16840370C211yesmaximal, characteristic, complemented
2#16840337C211yesmaximal, characteristic
3#16840155C211yesmaximal, characteristic, complemented
4#16840140C211yesmaximal, characteristic, complemented
5#16840129C211yesmaximal, characteristic, complemented
6#16840118C211yesmaximal, characteristic, complemented
7#16839985C211yesmaximal, characteristic, complemented
8#16839984C211yesmaximal, characteristic, complemented
9#16839969C211yesmaximal, characteristic, complemented
10#16839927C211yesmaximal, characteristic
11#16839923C211yesmaximal, characteristic
12#16839919C211yesmaximal, characteristic, complemented
13#16839916C211yesmaximal, characteristic, complemented
14#16839822C211yesmaximal, characteristic, complemented
15C61×#462C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×Q8×D61C2211yescharacteristic
18C2×Dic244C2211yescharacteristic
19C2×#11758202C2211yescharacteristic
20C2×#11758202C2211yescharacteristic
21C2×#11758202C2211yescharacteristic
22C2×#11758190C2211yescharacteristic
23C2×#11758201C2211yescharacteristic
24#14519775C2211yescharacteristic
25#14519775C2211yescharacteristic
26#14519772—21no—
27#14519771—21no—
28#14519769—21no—
29#14519768C2211yescharacteristic
30#14519767—21no—
31#14519766C2211yescharacteristic
32#14519765C2211yescharacteristic
33#14519762—21no—
34#14519762—21no—
35#14519757C2211yescharacteristic
36#14519755—21no—
37#14519755—21no—
38#14519753C2211yescharacteristic
39C4×Dic122C2211yescharacteristic
40#14519734C2211yescharacteristic
41C4⋊#92418C2211yescharacteristic
42#14519702C2211yescharacteristic
43#14519701C2211yescharacteristic
44#14519701C2211yescharacteristic
45#14519700C2211yescharacteristic
46#14519699C2211yescharacteristic
47#14519697C2211yescharacteristic
48#14519689C2211yescharacteristic
49#14519689C2211yescharacteristic
50#14519687C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52C2×Q16×C61C2211yescharacteristic
53C2×Q16×C61C2211yescharacteristic
54C4⋊Q8×C61C2211yescharacteristic
55C4×Q8×C61C2211yescharacteristic
56C4⋊C8×C61C2211yescharacteristic
57#103×C61C2211yescharacteristic
58#103×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60C2×Q8×C61C2311yescharacteristic
61C2×Q8×C61C2311yescharacteristic
62#11758226—41no—
63#11758226—41no—
64Q8×D61—41no—
65Q8×D61—41no—
66C2×D244—21no—
67C2×D244C2311yescharacteristic
68C2×C4×D61—21no—
69C2×C4×D61—21no—
70C2×C4×D61C2311yescharacteristic
71C2×Dic122—21no—
72C2×Dic122C2311yescharacteristic
73C2×Dic122C2311yescharacteristic
74Q16×C61—41no—
75Q16×C61—41no—
76C2×C8×C61C2311yescharacteristic
77C2×C8×C61C2311yescharacteristic
78C4⋊C4×C61—21no—
79C4⋊C4×C61—21no—
80C4⋊C4×C61—21no—
81C4⋊C4×C61C2311yescharacteristic
82C42×C61—21no—
83C42×C61C2311yescharacteristic
84#11758202—41no—
85#11758202—41no—
86#11758202—41no—
87#11758201—41no—
88#11758198—21no—
89#11758198—21no—
90#11758198—21no—
91#11758198—21no—
92#11758198—21no—
93#11758198—21no—
94#11758198D411yescharacteristic
95#11758198D411yescharacteristic
96C4⋊Dic61—21no—
97C4⋊Dic61—21no—
98C4⋊Dic61C2311yescharacteristic
99#11758196—21no—
100#11758196—21no—
101#11758196—21no—
102#11758196—21no—
103#11758196—21no—
104#11758196—21no—
105#11758196—21no—
106#11758196D411yescharacteristic
107#11758196D411yescharacteristic
108C4×Dic61—21no—
109C4×Dic61C2311yescharacteristic
110C2×#92418C2311yescharacteristic
111C2×#92418C2311yescharacteristic
112Dic244—41no—
113#11758190—41no—
114C22×D61—21no—
115C22×D61C2×D411yescharacteristic
116Q8×C61—21no—
117Q8×C61—21no—
118Q8×C61—21no—
119Q8×C61—21no—
120Q8×C61—21no—
121Q8×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61C2×D411yescharacteristic
127C2×C4×C61C2×D411yescharacteristic
128C2×C4×C61C2411yescharacteristic
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61C2×D411yescharacteristic
133C2×Dic61C2×D411yescharacteristic
134C2×Dic61C2×D411yescharacteristic
135D244—21no—
136D244—21no—
137D244—42no—
138C4×D61—21no—
139C4×D61—21no—
140C4×D61—42no—
141C4×D61—42no—
142Dic122—21no—
143Dic122—21no—
144Dic122—21no—
145Dic122—21no—
146Dic122—42no—
147C8×C61—21no—
148C8×C61—21no—
149#92418—21no—
150#92418—21no—
151C22×C61C22×D411yescharacteristic
152C2×D61—21no—
153C2×D61—21no—
154C2×D61—21no—
155C2×D61—41no—
156C2×D61—41no—
157C2×D61—41no—
158C4×C61—21no—
159C4×C61—21no—
160C4×C61—41no—
161C4×C61—41no—
162C4×C61—41no—
163C4×C61—41no—
164C4×C61H(5,𝔽2)11yescharacteristic
165C4×C61H(5,𝔽2)11yescharacteristic
166Dic61—21no—
167Dic61—21no—
168Dic61—21no—
169Dic61—41no—
170Dic61—41no—
171Dic61—41no—
172#3223—611nomaximal, Sylow
173C2×C61#53511yescharacteristic
174C2×C61#57811yescharacteristic
175C2×C61#57811yescharacteristic
176D61—41no—
177D61—81no—
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#462D6111yescharacteristic, complemented
188#452—611no—
189#452—611no—
190#451—611no—
191#451—611no—
192#433—611no—
193C61#322311yescharacteristic, complemented, Sylow
194C2×#41—611no—
195C22×Q8—611no—
196C2×Q16—611no—
197C2×Q16—611no—
198C2×Q16—611no—
199C2×Q16—611no—
200C2×Q16C2×D6111yescharacteristic
201C2×Q16C2×D6111yescharacteristic
202C2×SD16—611no—
203C2×SD16—611no—
204C4⋊Q8—611no—
205C4⋊Q8—611no—
206C4⋊Q8C2×D6111yescharacteristic
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—611no—
218C22⋊Q8—1221no—
219C22⋊Q8—1221no—
220C4×Q8—611no—
221C4×Q8C2×D6111yescharacteristic
222#117—611no—
223C4⋊C8—611no—
224C4⋊C8C2×D6111yescharacteristic
225#103—611no—
226#103—611no—
227#103—611no—
228#103—611no—
229#103C2×D6111yescharacteristic
230#103C2×D6111yescharacteristic
231#102—611no—
232#102—611no—
233C22⋊C8—611no—
234C22⋊C8—611no—
235#97—611no—
236C4×C8—611no—
237#41—2441no—
238#41—2441no—
239C2×Q8—611no—
240C2×Q8—611no—
241C2×Q8—1221no—
242C2×Q8—2441no—
243C2×Q8—2441no—
244C2×Q8C22×D6111yescharacteristic
245C2×Q8C22×D6111yescharacteristic
246C2×Q8C22×D6111yescharacteristic
247C2×D4—611no—
248C2×D4—1221no—
249C22×C4—611no—
250C22×C4—1221no—
251C22×C4—1221no—
252Q16—41no—
253Q16—41no—
254Q16—2441no—
255Q16—2441no—
256Q16—2441no—
257Q16—2441no—
258SD16—2441no—
259SD16—2441no—
260C2×C8—611no—
261C2×C8—611no—
262C2×C8C22×D6111yescharacteristic
263C2×C8C22×D6111yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—611no—
268C4⋊C4—611no—
269C4⋊C4—611no—
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—611no—
281C22⋊C4—611no—
282C22⋊C4—1221no—
283C22⋊C4—1221no—
284C22⋊C4—1221no—
285C22⋊C4—1221no—
286C22⋊C4—1221no—
287C22⋊C4—1221no—
288C42—21no—
289C42—611no—
290C42—1221no—
291C42C22×D6111yescharacteristic
292C23—611no—
293C23—1221no—
294Q8—21no—
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—21no—
299Q8—21no—
300Q8—1221no—
301Q8—1221no—
302Q8—1221no—
303Q8—1221no—
304Q8—2442no—
305D4—1221no—
306D4—1221no—
307D4—2442no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—611no—
313C2×C4—611no—
314C2×C4—611no—
315C2×C4—1221no—
316C2×C4—1221no—
317C2×C4—1221no—
318C2×C4—1221no—
319C2×C4—1221no—
320C2×C4—2442no—
321C2×C4—2442no—
322C2×C4D4×D6111yescharacteristic
323C2×C4D4×D6111yescharacteristic
324C2×C4C23×D6111yescharacteristic
325C8—21no—
326C8—21no—
327C8—1221no—
328C8—1221no—
329C22—1221no—
330C22—1221no—
331C22—1221no—
332C22—2441no—
333C22—2441no—
334C22—2441no—
335C22C2×D4×D6111yescharacteristic
336C4—21no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—1221no—
343C4—1221no—
344C4—1221no—
345C4—2441no—
346C4—2441no—
347C4—2441no—
348C4#1451982211yescharacteristic
349C4#1451982311yescharacteristic
350C2—4881no—
351C2—2441no—
352C2#1684032811yescharacteristic
353C2#1684057511yescharacteristic
354C2#1684057811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#462C2
socleC22×C61C22×D4
hypercenter#462D61
hypocenterC61#3223
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
1. #16840370C2semidirect
3. #16840155C2semidirect
4. #16840140C2semidirect
5. #16840129C2semidirect
6. #16840118C2semidirect
7. #16839985C2semidirect
8. #16839984C2semidirect
9. #16839969C2semidirect
12. #16839919C2semidirect
13. #16839916C2semidirect
14. #16839822C2semidirect
15. C61×#462C2semidirect
187. #462D61semidirect
193. C61#3223semidirect