Finite Group Databasebeta

← #21456922

Subgroups — #21456922

Order 7808.

376 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840338C211yesmaximal, characteristic, complemented
2#16840157C211yesmaximal, characteristic, complemented
3#16840144C211yesmaximal, characteristic, complemented
4#16840124C211yesmaximal, characteristic, complemented
5#16840114C211yesmaximal, characteristic, complemented
6#16839984C211yesmaximal, characteristic, complemented
7#16839977C211yesmaximal, characteristic, complemented
8#16839972C211yesmaximal, characteristic, complemented
9#16839967C211yesmaximal, characteristic, complemented
10#16839922C211yesmaximal, characteristic, complemented
11#16839917C211yesmaximal, characteristic, complemented
12#16839905C211yesmaximal, characteristic
13#16839900C211yesmaximal, characteristic, complemented
14#16839823C211yesmaximal, characteristic, complemented
15C61×#542C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C22×Dic122C2211yescharacteristic
18C2×#11758202C2211yescharacteristic
19C2×#11758202C2211yescharacteristic
20C2×#11758202C2211yescharacteristic
21C2×#11758200C2211yescharacteristic
22C2×#11758200C2211yescharacteristic
23C2×#11758200C2211yescharacteristic
24C2×#11758201C2211yescharacteristic
25C2×#11758199C2211yescharacteristic
26#14519777C2211yescharacteristic
27#14519777C2211yescharacteristic
28#14519765C2211yescharacteristic
29#14519765C2211yescharacteristic
30#14519761—21no—
31#14519761—21no—
32#14519757—21no—
33#14519757—21no—
34C4⋊#92418C2211yescharacteristic
35C4⋊#92418C2211yescharacteristic
36#14519700C2211yescharacteristic
37#14519700C2211yescharacteristic
38#14519700C2211yescharacteristic
39#14519700C2211yescharacteristic
40#14519700C2211yescharacteristic
41#14519700C2211yescharacteristic
42#14519697C2211yescharacteristic
43#14519697C2211yescharacteristic
44C22⋊#92418C2211yescharacteristic
45C22⋊#92418C2211yescharacteristic
46#14519688C2211yescharacteristic
47C4×#92418C2211yescharacteristic
48C4⋊Q8×C61C2211yescharacteristic
49#126×C61—21no—
50#124×C61—21no—
51#124×C61C2211yescharacteristic
52#123×C61—21no—
53C22⋊Q8×C61—21no—
54C22⋊Q8×C61C2211yescharacteristic
55#121×C61C2211yescharacteristic
56C4×Q8×C61C2211yescharacteristic
57C4×D4×C61C2211yescharacteristic
58#117×C61C2211yescharacteristic
59C2×Q8×C61—21no—
60C2×Q8×C61C2311yescharacteristic
61C2×D4×C61—21no—
62C2×D4×C61C2311yescharacteristic
63C22×C4×C61—21no—
64C22×C4×C61C2311yescharacteristic
65C2×C22⋊D61—21no—
66C22×Dic61—21no—
67#11758222—41no—
68#11758222—41no—
69C2×D244C2311yescharacteristic
70C2×C4×D61—21no—
71C2×Dic122—21no—
72C2×Dic122—41no—
73C2×Dic122—41no—
74C2×Dic122C2311yescharacteristic
75C2×Dic122C2311yescharacteristic
76C2×Dic122C2311yescharacteristic
77C4⋊C4×C61—21no—
78C4⋊C4×C61—21no—
79C4⋊C4×C61—21no—
80C4⋊C4×C61D411yescharacteristic
81C4⋊C4×C61D411yescharacteristic
82C4⋊C4×C61C2311yescharacteristic
83C4⋊C4×C61C2311yescharacteristic
84C22⋊C4×C61—21no—
85C22⋊C4×C61—21no—
86C22⋊C4×C61—21no—
87C22⋊C4×C61—21no—
88C22⋊C4×C61—21no—
89C22⋊C4×C61D411yescharacteristic
90C22⋊C4×C61D411yescharacteristic
91C42×C61—21no—
92C42×C61C2311yescharacteristic
93C42×C61C2311yescharacteristic
94#11758202—41no—
95#11758202—41no—
96#11758202—41no—
97#11758201—41no—
98#11758200—41no—
99#11758200—41no—
100#11758200—41no—
101#11758199—41no—
102#11758198—21no—
103#11758198—21no—
104#11758198—21no—
105#11758198—21no—
106C4⋊Dic61—21no—
107C4⋊Dic61—21no—
108C4⋊Dic61—21no—
109C4⋊Dic61—21no—
110C2×#92418C2311yescharacteristic
111C2×#92418C2311yescharacteristic
112C2×#92418C2311yescharacteristic
113C2×#92418C2311yescharacteristic
114C23×C61—21no—
115C23×C61C2×D411yescharacteristic
116C22×D61—21no—
117Q8×C61—21no—
118Q8×C61—21no—
119Q8×C61—81no—
120D4×C61—21no—
121D4×C61—21no—
122D4×C61—81no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—81no—
129C2×C4×C61C2×D411yescharacteristic
130C2×C4×C61C2×D411yescharacteristic
131C2×C4×C61C2×D411yescharacteristic
132C2×C4×C61C2×D411yescharacteristic
133C2×C4×C61C2×D411yescharacteristic
134C2×C4×C61C2411yescharacteristic
135C22⋊D61—42no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—42no—
140D244—21no—
141D244—21no—
142C4×D61—42no—
143Dic122—21no—
144Dic122—21no—
145Dic122—21no—
146Dic122—21no—
147Dic122—21no—
148Dic122—21no—
149Dic122—42no—
150#92418—21no—
151#92418—21no—
152#92418—21no—
153#92418—21no—
154C22×C61—21no—
155C22×C61—21no—
156C22×C61—21no—
157C22×C61—41no—
158C22×C61—41no—
159C22×C61—41no—
160C22×C61C22×D411yescharacteristic
161C2×D61—41no—
162C2×D61—41no—
163C2×D61—41no—
164C4×C61—21no—
165C4×C61—21no—
166C4×C61—21no—
167C4×C61—21no—
168C4×C61—21no—
169C4×C61—41no—
170C4×C61—41no—
171C4×C61—41no—
172C4×C61H(5,𝔽2)11yescharacteristic
173C4×C61H(5,𝔽2)11yescharacteristic
174Dic61—41no—
175Dic61—41no—
176Dic61—41no—
177#3225—611nomaximal, Sylow
178C2×C61—41no—
179C2×C61—81no—
180C2×C61#53511yescharacteristic
181C2×C61#57711yescharacteristic
182C2×C61#57811yescharacteristic
183D61—81no—
184#542D6111yescharacteristic, complemented
185#536—611no—
186#497—611no—
187#495—611no—
188#489—611no—
189#487—611no—
190#464—611no—
191#463—611no—
192#462—611no—
193#461—611no—
194#452—611no—
195#451—611no—
196#449—611no—
197#448—611no—
198#433—611no—
199C61#322511yescharacteristic, complemented, Sylow
200C2×#41—611no—
201C22×Q8—611no—
202C2×Q16—611no—
203C2×Q16—611no—
204C2×Q16—611no—
205C2×SD16—611no—
206C2×SD16—611no—
207C2×SD16—611no—
208C2×SD16—611no—
209C2×D8—611no—
210C4⋊Q8—611no—
211C4⋊Q8—611no—
212C4⋊Q8C2×D6111yescharacteristic
213#126—21no—
214#124—21no—
215#124—611no—
216#124—611no—
217#124C2×D6111yescharacteristic
218#123—21no—
219#123—1221no—
220#123—1221no—
221C22⋊Q8—21no—
222C22⋊Q8—1221no—
223C22⋊Q8—1221no—
224C22⋊Q8C2×D6111yescharacteristic
225#121C2×D6111yescharacteristic
226C4×Q8C2×D6111yescharacteristic
227C4×D4C2×D6111yescharacteristic
228#117C2×D6111yescharacteristic
229C4⋊C8—611no—
230C4⋊C8—611no—
231#103—611no—
232#103—611no—
233#103—611no—
234#103—611no—
235#103—611no—
236#103—611no—
237#102—611no—
238#102—611no—
239C22⋊C8—611no—
240C22⋊C8—611no—
241#97—611no—
242C4×C8—611no—
243#41—2441no—
244#41—2441no—
245C2×Q8—21no—
246C2×Q8—611no—
247C2×Q8—611no—
248C2×Q8—611no—
249C2×Q8—1221no—
250C2×Q8—2441no—
251C2×Q8—2441no—
252C2×Q8C22×D6111yescharacteristic
253C2×D4—21no—
254C2×D4—611no—
255C2×D4—1221no—
256C2×D4C22×D6111yescharacteristic
257C22×C4—21no—
258C22×C4—1221no—
259C22×C4—1221no—
260C22×C4C22×D6111yescharacteristic
261Q16—2441no—
262Q16—2441no—
263Q16—2441no—
264SD16—2441no—
265SD16—2441no—
266SD16—2441no—
267SD16—2441no—
268D8—2441no—
269C2×C8—611no—
270C2×C8—611no—
271C2×C8—611no—
272C2×C8—611no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—1221no—
277C4⋊C4—1221no—
278C4⋊C4—1221no—
279C4⋊C4—1221no—
280C4⋊C4C22⋊D6111yescharacteristic
281C4⋊C4C22⋊D6111yescharacteristic
282C4⋊C4C22×D6111yescharacteristic
283C4⋊C4C22×D6111yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—1221no—
290C22⋊C4—1221no—
291C22⋊C4—1221no—
292C22⋊C4—1221no—
293C22⋊C4C22⋊D6111yescharacteristic
294C22⋊C4C22⋊D6111yescharacteristic
295C42—21no—
296C42C22×D6111yescharacteristic
297C42C22×D6111yescharacteristic
298C23—21no—
299C23—1221no—
300C23C2×C22⋊D6111yescharacteristic
301Q8—21no—
302Q8—21no—
303Q8—81no—
304Q8—1221no—
305Q8—1221no—
306Q8—1221no—
307Q8—1221no—
308Q8—1221no—
309Q8—1221no—
310Q8—2442no—
311D4—21no—
312D4—21no—
313D4—81no—
314D4—1221no—
315D4—1221no—
316D4—2442no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—81no—
323C2×C4—1221no—
324C2×C4—1221no—
325C2×C4—1221no—
326C2×C4—2442no—
327C2×C4—2442no—
328C2×C4C2×C22⋊D6111yescharacteristic
329C2×C4C2×C22⋊D6111yescharacteristic
330C2×C4C2×C22⋊D6111yescharacteristic
331C2×C4C2×C22⋊D6111yescharacteristic
332C2×C4C2×C22⋊D6111yescharacteristic
333C2×C4C23×D6111yescharacteristic
334C8—1221no—
335C8—1221no—
336C8—1221no—
337C8—1221no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—2441no—
345C22—2441no—
346C22—2441no—
347C22C22×C22⋊D6111yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—2441no—
357C4—2441no—
358C4—2441no—
359C4#1451982311yescharacteristic
360C4#1451982311yescharacteristic
361C2—41no—
362C2—81no—
363C2—4881no—
364C2#1684032611yescharacteristic
365C2#1684057311yescharacteristic
366C2#1684057711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#542C2
socleC22×C61C22×D4
hypercenter#542D61
hypocenterC61#3225
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #16840338C2semidirect
2. #16840157C2semidirect
3. #16840144C2semidirect
4. #16840124C2semidirect
5. #16840114C2semidirect
6. #16839984C2semidirect
7. #16839977C2semidirect
8. #16839972C2semidirect
9. #16839967C2semidirect
10. #16839922C2semidirect
11. #16839917C2semidirect
13. #16839900C2semidirect
14. #16839823C2semidirect
15. C61×#542C2semidirect
184. #542D61semidirect
199. C61#3225semidirect