Finite Group Databasebeta

← #21457986

Subgroups — #21457986

Order 7808.

388 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840460C211yesmaximal, characteristic
2Q8×C22⋊D61C211yesmaximal, characteristic, complemented
3#16840129C211yesmaximal, characteristic, complemented
4#16840101C211yesmaximal, characteristic, complemented
5#16840097C211yesmaximal, characteristic, complemented
6#16840067C211yesmaximal, characteristic, complemented
7#16840011C211yesmaximal, characteristic, complemented
8#16839991C211yesmaximal, characteristic, complemented
9#16839966C211yesmaximal, characteristic, complemented
10#16839902C211yesmaximal, characteristic, complemented
11#16839901C211yesmaximal, characteristic, complemented
12#16839865C211yesmaximal, characteristic, complemented
13#16839833C211yesmaximal, characteristic, complemented
14#16839769C211yesmaximal, characteristic, complemented
15C2×#103×C61C211yesmaximal, characteristic, complemented
16C2×Q8×D61C2211yescharacteristic
17C2×#11758190C2211yescharacteristic
18C2×#11758201C2211yescharacteristic
19C2×#11758201C2211yescharacteristic
20C2×#11758189C2211yescharacteristic
21#14519775—21no—
22#14519775C2211yescharacteristic
23#14519772—21no—
24#14519768C2211yescharacteristic
25#14519762—21no—
26#14519756—21no—
27#14519756C2211yescharacteristic
28#14519753—21no—
29#14519753C2211yescharacteristic
30#14519752C2211yescharacteristic
31#14519751—21no—
32#14519751C2211yescharacteristic
33Q8×Dic61C2211yescharacteristic
34#14519739C2211yescharacteristic
35C4×C22⋊D61—21no—
36C4×C22⋊D61—21no—
37C4×C22⋊D61C2211yescharacteristic
38#14519735C2211yescharacteristic
39#14519710C2211yescharacteristic
40#14519710C2211yescharacteristic
41#14519709C2211yescharacteristic
42#14519706C2211yescharacteristic
43#14519702C2211yescharacteristic
44#14519701C2211yescharacteristic
45#14519701C2211yescharacteristic
46#14519700C2211yescharacteristic
47#14519700C2211yescharacteristic
48#14519699C2211yescharacteristic
49C22⋊#92418C2211yescharacteristic
50#14519689C2211yescharacteristic
51#14519687C2211yescharacteristic
52C22×Q8×C61C2211yescharacteristic
53C22×C8×C61C2211yescharacteristic
54C2×C4⋊C4×C61C2211yescharacteristic
55#103×C61C2211yescharacteristic
56#103×C61C2211yescharacteristic
57#103×C61C2211yescharacteristic
58#103×C61C2211yescharacteristic
59C2×Q8×C61—21no—
60C2×Q8×C61—22no—
61C2×Q8×C61—41no—
62C2×Q8×C61C2311yescharacteristic
63C2×Q8×C61C2311yescharacteristic
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61C2311yescharacteristic
67C2×C22⋊D61—21no—
68C2×C22⋊D61D411yescharacteristic
69Q8×D61—22no—
70Q8×D61—41no—
71C2×D244—21no—
72C2×D244C2311yescharacteristic
73C2×C4×D61—21no—
74C2×C4×D61—21no—
75C2×C4×D61C2311yescharacteristic
76C2×Dic122—21no—
77C2×Dic122C2311yescharacteristic
78C2×C8×C61—41no—
79C2×C8×C61C2311yescharacteristic
80C2×C8×C61C2311yescharacteristic
81C4⋊C4×C61—21no—
82C4⋊C4×C61C2311yescharacteristic
83C4⋊C4×C61C2311yescharacteristic
84C22⋊Dic61—21no—
85C22⋊Dic61D411yescharacteristic
86#11758201—22no—
87#11758201—41no—
88#11758198—21no—
89#11758198—21no—
90#11758198—21no—
91#11758198—21no—
92#11758198—21no—
93#11758198D411yescharacteristic
94C4⋊Dic61—21no—
95C4⋊Dic61—21no—
96C4⋊Dic61C2311yescharacteristic
97C4⋊Dic61C2311yescharacteristic
98#11758196—21no—
99#11758196—21no—
100#11758196—21no—
101#11758196—21no—
102#11758196—21no—
103#11758196D411yescharacteristic
104C4×Dic61—21no—
105C4×Dic61—21no—
106C4×Dic61C2311yescharacteristic
107C2×#92418C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109#11758190—41no—
110#11758189—41no—
111C23×C61C2×D411yescharacteristic
112C22×D61—21no—
113C22×D61C2×D411yescharacteristic
114Q8×C61—21no—
115Q8×C61—21no—
116Q8×C61—21no—
117Q8×C61—42no—
118Q8×C61#4112yes—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—42no—
126C2×C4×C61—81no—
127C2×C4×C61C2×D411yescharacteristic
128C2×C4×C61C2411yescharacteristic
129C22⋊D61—22no—
130C22⋊D61—42no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61C2×D411yescharacteristic
135C2×Dic61C2×D411yescharacteristic
136C2×Dic61C2×D411yescharacteristic
137D244—21no—
138D244—21no—
139D244—81no—
140C4×D61—21no—
141C4×D61—21no—
142C4×D61—42no—
143C4×D61—81no—
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#13712yes—
154C22×C61C22×D411yescharacteristic
155C2×D61—21no—
156C2×D61—21no—
157C2×D61—21no—
158C2×D61—41no—
159C2×D61—41no—
160C2×D61—41no—
161C4×C61—22no—
162C4×C61—21no—
163C4×C61—41no—
164C4×C61—41no—
165C4×C61—41no—
166C4×C61C2×#4111yescharacteristic
167C4×C61H(5,𝔽2)11yescharacteristic
168Dic61—21no—
169Dic61—21no—
170Dic61—21no—
171Dic61—41no—
172Dic61—41no—
173Dic61—41no—
174#3320—611nomaximal, Sylow
175C2×C61—22no—
176C2×C61#54611yescharacteristic
177C2×C61C2×#13711yescharacteristic
178C2×C61#57711yescharacteristic
179D61—41no—
180D61—81no—
181#553—611no—
182D4×Q8—611no—
183#491—611no—
184#485—611no—
185#484—611no—
186#479—611no—
187#468—611no—
188#465—611no—
189#461—611no—
190#448—611no—
191#448—611no—
192#440—611no—
193#435—611no—
194#419—611no—
195C2×#103D6111yescharacteristic, complemented
196C61#332011yescharacteristic, complemented, Sylow
197C22×Q8—611no—
198C22×Q8C2×D6111yescharacteristic
199C2×SD16—611no—
200C2×SD16—611no—
201C2×SD16—611no—
202C2×M16—611no—
203C22×C8C2×D6111yescharacteristic
204C4⋊Q8—611no—
205C4⋊Q8—1221no—
206#126—1221no—
207#125—611no—
208#123—1221no—
209C22⋊Q8—611no—
210C22⋊Q8—611no—
211C22⋊Q8—1221no—
212C22⋊Q8—1221no—
213#121—611no—
214#121—611no—
215#121—1221no—
216C4×Q8—611no—
217C4×D4—611no—
218C4×D4—611no—
219C4×D4—1221no—
220C4×D4—1221no—
221#117—611no—
222C2×C4⋊C4C2×D6111yescharacteristic
223#107—611no—
224#107—611no—
225#106—611no—
226C4⋊C8—611no—
227#103—611no—
228#103—611no—
229#103—611no—
230#103—611no—
231#103—611no—
232#103C2×D6111yescharacteristic
233#103C2×D6111yescharacteristic
234#103C2×D6111yescharacteristic
235#103C2×D6111yescharacteristic
236#102—611no—
237C22⋊C8—611no—
238C22⋊C8—611no—
239#97—611no—
240C2×Q8—21no—
241C2×Q8—22no—
242C2×Q8—41no—
243C2×Q8—611no—
244C2×Q8—1221no—
245C2×Q8—1222no—
246C2×Q8—2441no—
247C2×Q8C22×D6111yescharacteristic
248C2×Q8C22×D6111yescharacteristic
249C2×D4—611no—
250C2×D4—611no—
251C2×D4—1221no—
252C2×D4—1221no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—611no—
256C22×C4—1221no—
257C22×C4—1221no—
258C22×C4C22×D6111yescharacteristic
259SD16—1222no—
260SD16—2441no—
261SD16—2441no—
262M16—2441no—
263C2×C8—41no—
264C2×C8—611no—
265C2×C8—611no—
266C2×C8C22×D6111yescharacteristic
267C2×C8C22×D6111yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—611no—
270C4⋊C4—611no—
271C4⋊C4—611no—
272C4⋊C4—1221no—
273C4⋊C4—1221no—
274C4⋊C4—1221no—
275C4⋊C4—1221no—
276C4⋊C4—1221no—
277C4⋊C4—1221no—
278C4⋊C4—1221no—
279C4⋊C4C22×D6111yescharacteristic
280C4⋊C4C22×D6111yescharacteristic
281C22⋊C4—611no—
282C22⋊C4—611no—
283C22⋊C4—1221no—
284C22⋊C4—1221no—
285C22⋊C4—1221no—
286C22⋊C4—1221no—
287C22⋊C4—1221no—
288C22⋊C4—1221no—
289C42—611no—
290C42—1221no—
291C42—1221no—
292C23—611no—
293C23—1221no—
294C23D4×D6111yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—42no—
299Q8—1221no—
300Q8—1221no—
301Q8—2442no—
302Q8#1175822212yes—
303D4—1222no—
304D4—1221no—
305D4—1221no—
306D4—4881no—
307D4—2442no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—42no—
315C2×C4—81no—
316C2×C4—611no—
317C2×C4—611no—
318C2×C4—611no—
319C2×C4—1221no—
320C2×C4—1221no—
321C2×C4—1221no—
322C2×C4—1221no—
323C2×C4—1221no—
324C2×C4—4881no—
325C2×C4—2442no—
326C2×C4D4×D6111yescharacteristic
327C2×C4C23×D6111yescharacteristic
328C8—21no—
329C8—21no—
330C8—1221no—
331C8—1221no—
332C22—21no—
333C22—21no—
334C22—1221no—
335C22—1221no—
336C22—1221no—
337C22—2441no—
338C22—2441no—
339C22—2441no—
340C22#1451980912yes—
341C22C2×D4×D6111yescharacteristic
342C4—21no—
343C4—22no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—1221no—
348C4—1221no—
349C4—1221no—
350C4—2441no—
351C4—2441no—
352C4—2441no—
353C4C2×#1175822211yescharacteristic
354C4#1451982211yescharacteristic
355C2—22no—
356C2—4881no—
357C2—2441no—
358C2#1684040211yescharacteristic
359C2C2×#1451980911yescharacteristic
360C2#1684056811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×#103×C61C2
socleC22×C61C22×D4
hypercenterC2×#103D61
hypocenterC61#3320
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
2. Q8×C22⋊D61C2semidirect
3. #16840129C2semidirect
4. #16840101C2semidirect
5. #16840097C2semidirect
6. #16840067C2semidirect
7. #16840011C2semidirect
8. #16839991C2semidirect
9. #16839966C2semidirect
10. #16839902C2semidirect
11. #16839901C2semidirect
12. #16839865C2semidirect
13. #16839833C2semidirect
14. #16839769C2semidirect
15. C2×#103×C61C2semidirect
195. C2×#103D61semidirect
196. C61#3320semidirect