Finite Group Databasebeta

← #21454697

Subgroups — #21454697

Order 7808.

484 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519798C211yesmaximal, characteristic
2#16840244C211yesmaximal, characteristic, complemented
3#16840241C211yesmaximal, characteristic, complemented
4#16839872C211yesmaximal, characteristic, complemented
5#16839871C211yesmaximal, characteristic, complemented
6#16839867C211yesmaximal, characteristic, complemented
7#16839866C211yesmaximal, characteristic, complemented
8C4×#11758190C211yesmaximal, characteristic, complemented
9SD16×Dic61C211yesmaximal, characteristic, complemented
10#16839849C211yesmaximal, characteristic, complemented
11#106×D61C211yesmaximal, characteristic, complemented
12#16839762C211yesmaximal, characteristic, complemented
13#16839760C211yesmaximal, characteristic, complemented
14#16839716C211yesmaximal, characteristic, complemented
15C4×SD16×C61C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×#11758224C2211yescharacteristic
18#14519798C418yescomplemented
19C2×#11758202C2211yescharacteristic
20C2×#11758190C2211yescharacteristic
21C2×#11758199C2211yescharacteristic
22C2×#11758189C2211yescharacteristic
23C2×C8×D61C2211yescharacteristic
24Q8×Dic61C2211yescharacteristic
25C4×Dic122C2211yescharacteristic
26#14519742C2211yescharacteristic
27C4×D244—21no—
28C4×D244C2211yescharacteristic
29D4×Dic61C2211yescharacteristic
30#14519739—21no—
31#14519739C2211yescharacteristic
32C4×C22⋊D61—21no—
33#14519737—21no—
34#14519734—21no—
35#14519734C2211yescharacteristic
36#14519733—21no—
37C2×#11758196—21no—
38C4⋊C4×D61—21no—
39C4⋊C4×D61C2211yescharacteristic
40C4⋊C4×D61C2211yescharacteristic
41#14519709C2211yescharacteristic
42#14519708C2211yescharacteristic
43#14519708C2211yescharacteristic
44#14519702C2211yescharacteristic
45#14519701C2211yescharacteristic
46#14519700C2211yescharacteristic
47#14519699C2211yescharacteristic
48#14519698C2211yescharacteristic
49#14519697C2211yescharacteristic
50#14519688C2211yescharacteristic
51#14519687C2211yescharacteristic
52C8×Dic61C2211yescharacteristic
53C2×SD16×C61C2211yescharacteristic
54C4×Q8×C61C2211yescharacteristic
55C4×D4×C61C2211yescharacteristic
56#106×C61C2211yescharacteristic
57#103×C61C2211yescharacteristic
58#102×C61C2211yescharacteristic
59C4×C8×C61C2211yescharacteristic
60C2×Q8×C61C2311yescharacteristic
61C2×D4×C61C2311yescharacteristic
62C22×C4×C61—21no—
63C2×C22⋊D61—21no—
64C22×Dic61—21no—
65C22×Dic61—21no—
66#11758226—22no—
67#11758226C2×C414yescomplemented
68#11758224—22no—
69#11758224C2×C414yescomplemented
70C2×D244—21no—
71C2×D244C2311yescharacteristic
72C2×C4×D61—21no—
73C2×C4×D61—21no—
74C2×C4×D61—21no—
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C2×C4×D61C2311yescharacteristic
78C2×Dic122C2311yescharacteristic
79SD16×C61C2×C414yescomplemented
80C2×C8×C61C2311yescharacteristic
81C2×C8×C61C2311yescharacteristic
82C4⋊C4×C61—21no—
83C4⋊C4×C61C2311yescharacteristic
84C4⋊C4×C61C2311yescharacteristic
85C22⋊C4×C61—21no—
86C42×C61—21no—
87C42×C61C2311yescharacteristic
88C22⋊Dic61—21no—
89#11758202C2×C414yescomplemented
90#11758199C2×C414yescomplemented
91#11758198—21no—
92#11758198—21no—
93#11758198D411yescharacteristic
94#11758198D411yescharacteristic
95C4⋊Dic61—21no—
96C4⋊Dic61C2311yescharacteristic
97C4⋊Dic61C2311yescharacteristic
98#11758196—21no—
99#11758196—21no—
100#11758196—21no—
101#11758196—21no—
102#11758196D411yescharacteristic
103#11758196D411yescharacteristic
104C4×Dic61—21no—
105C4×Dic61—21no—
106C4×Dic61—21no—
107C4×Dic61C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110#11758190C2×C414yescomplemented
111#11758189—22no—
112C8×D61C2×C414yescomplemented
113C23×C61—21no—
114C22×D61—21no—
115C22×D61C2×D411yescharacteristic
116Q8×C61—21no—
117Q8×C61C22×C412yes—
118D4×C61—21no—
119D4×C61C22×C412yes—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—81no—
124C2×C4×C61C2×D411yescharacteristic
125C2×C4×C61C2×D411yescharacteristic
126C2×C4×C61C2411yescharacteristic
127C22⋊D61—24no—
128C2×Dic61—21no—
129C2×Dic61—24no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—81no—
133C2×Dic61C2×D411yescharacteristic
134C2×Dic61C2×D411yescharacteristic
135C2×Dic61C2×D411yescharacteristic
136D244—24no—
137D244—21no—
138D244C22×C412yes—
139C4×D61—24no—
140C4×D61—81no—
141C4×D61—81no—
142C4×D61—81no—
143C4×D61—81no—
144C4×D61C22×C412yes—
145C4×D61#4112yes—
146Dic122—21no—
147Dic122C22×C412yes—
148C8×C61—21no—
149C8×C61C22×C412yes—
150#92418—21no—
151#92418C22×C412yes—
152C22×C61—22no—
153C22×C61—41no—
154C22×C61—41no—
155C22×C61C22×D411yescharacteristic
156C2×D61—21no—
157C2×D61—21no—
158C2×D61—22no—
159C2×D61—41no—
160C2×D61—41no—
161C2×D61C4×D412yes—
162C4×C61—22no—
163C4×C61—21no—
164C4×C61—21no—
165C4×C61—41no—
166C4×C61—41no—
167C4×C61C23×C411yescharacteristic
168C4×C61C2×#4111yescharacteristic
169Dic61—22no—
170Dic61—21no—
171Dic61—21no—
172Dic61—41no—
173Dic61—41no—
174Dic61C4×D412yes—
175#2952—611nomaximal, Sylow
176C2×C61—42no—
177C2×C61C2×C4×D411yescharacteristic
178C2×C61#57711yescharacteristic
179C2×C61#57711yescharacteristic
180D61—22no—
181D61—42no—
182C2×#135—611no—
183#520—611no—
184#520—611no—
185#442—611no—
186#442—611no—
187#441—611no—
188#441—611no—
189C4×SD16—611no—
190C4×SD16—611no—
191C4×SD16—611no—
192C4×SD16D6111yescharacteristic, complemented
193C2×#106—611no—
194#417—611no—
195#417—611no—
196#405—611no—
197C61#295211yescharacteristic, complemented, Sylow
198C2×#41—611no—
199C2×#41—611no—
200#135—618no—
201C2×Q16—611no—
202C2×SD16—611no—
203C2×SD16C2×D6111yescharacteristic
204C2×D8—611no—
205C2×M16—611no—
206C22×C8—611no—
207C4×Q8—611no—
208C4×Q8—611no—
209C4×Q8—611no—
210C4×Q8C2×D6111yescharacteristic
211C4×D4—611no—
212C4×D4—611no—
213C4×D4—611no—
214C4×D4—1221no—
215C4×D4—1221no—
216C4×D4—1221no—
217C4×D4—1221no—
218C4×D4C2×D6111yescharacteristic
219#117—611no—
220#117—1221no—
221#117—1221no—
222C2×C4⋊C4—611no—
223C2×C4⋊C4—611no—
224C2×C4⋊C4—1221no—
225C2×C4⋊C4—1221no—
226#106—611no—
227#106—611no—
228#106—611no—
229#106C2×D6111yescharacteristic
230#103—611no—
231#103—611no—
232#103—611no—
233#103C2×D6111yescharacteristic
234#102—611no—
235#102—611no—
236#102—611no—
237#102C2×D6111yescharacteristic
238#97—611no—
239#97—611no—
240C4×C8—611no—
241C4×C8C2×D6111yescharacteristic
242#41—614no—
243#41—614no—
244#41—1222no—
245#41—1222no—
246C2×Q8—611no—
247C2×Q8C22×D6111yescharacteristic
248C2×D4—611no—
249C2×D4—1221no—
250C2×D4—1221no—
251C2×D4C22×D6111yescharacteristic
252C22×C4—21no—
253C22×C4—611no—
254C22×C4—1221no—
255C22×C4—1221no—
256C22×C4—1221no—
257C22×C4—1221no—
258C22×C4—1221no—
259C22×C4—1221no—
260C22×C4—1221no—
261Q16—614no—
262SD16—614no—
263SD16C4×D6114yescomplemented
264D8—614no—
265M16—1222no—
266C2×C8—611no—
267C2×C8—614no—
268C2×C8—611no—
269C2×C8C22×D6111yescharacteristic
270C2×C8C22×D6111yescharacteristic
271C4⋊C4—21no—
272C4⋊C4—611no—
273C4⋊C4—611no—
274C4⋊C4—611no—
275C4⋊C4—611no—
276C4⋊C4—1221no—
277C4⋊C4—1221no—
278C4⋊C4—1221no—
279C4⋊C4—1221no—
280C4⋊C4—1221no—
281C4⋊C4C22×D6111yescharacteristic
282C4⋊C4C22×D6111yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—611no—
285C22⋊C4—611no—
286C22⋊C4—1221no—
287C22⋊C4—1221no—
288C22⋊C4—1221no—
289C42—21no—
290C42—611no—
291C42—1221no—
292C42—1221no—
293C42—1221no—
294C42C22×D6111yescharacteristic
295C23—21no—
296C23—611no—
297C23—1221no—
298Q8—21no—
299Q8—612no—
300Q8—1221no—
301Q8C2×C4×D6112yes—
302D4—21no—
303D4—612no—
304D4—1224no—
305D4—1224no—
306D4—1221no—
307D4C2×C4×D6112yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—81no—
312C2×C4—611no—
313C2×C4—612no—
314C2×C4—612no—
315C2×C4—611no—
316C2×C4—611no—
317C2×C4—1224no—
318C2×C4—1224no—
319C2×C4—1221no—
320C2×C4—1221no—
321C2×C4—1221no—
322C2×C4—4881no—
323C2×C4—4881no—
324C2×C4—4881no—
325C2×C4—4881no—
326C2×C4—4881no—
327C2×C4D4×D6111yescharacteristic
328C2×C4D4×D6111yescharacteristic
329C2×C4C23×D6111yescharacteristic
330C8—21no—
331C8—612no—
332C8—1221no—
333C8C2×C4×D6112yes—
334C22—22no—
335C22—41no—
336C22—41no—
337C22—612no—
338C22—1221no—
339C22—1221no—
340C22—1222no—
341C22—2441no—
342C22—2441no—
343C22C2×D4×D6111yescharacteristic
344C4—22no—
345C4—21no—
346C4—21no—
347C4—41no—
348C4—41no—
349C4—612no—
350C4—1222no—
351C4—1221no—
352C4—1221no—
353C4—2441no—
354C4—2441no—
355C4C22×C4×D6111yescharacteristic
356C4#41×D6111yescharacteristic
357C2—42no—
358C2—1222no—
359C2—2442no—
360C2C4×D4×D6111yescharacteristic
361C2#1684056811yescharacteristic
362C2#1684056911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC4×C61C23×C4
FrattiniC2×C4C23×D61
FittingC4×SD16×C61C2
socleC22×C61C22×D4
hypercenterC4×SD16D61
hypocenterC61#2952
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
2. #16840244C2semidirect
3. #16840241C2semidirect
4. #16839872C2semidirect
5. #16839871C2semidirect
6. #16839867C2semidirect
7. #16839866C2semidirect
8. C4×#11758190C2semidirect
9. SD16×Dic61C2semidirect
10. #16839849C2semidirect
11. #106×D61C2semidirect
12. #16839762C2semidirect
13. #16839760C2semidirect
14. #16839716C2semidirect
15. C4×SD16×C61C2semidirect
18. #14519798C4semidirect
67. #11758226C2×C4semidirect
69. #11758224C2×C4semidirect
79. SD16×C61C2×C4semidirect
89. #11758202C2×C4semidirect
90. #11758199C2×C4semidirect
110. #11758190C2×C4semidirect
112. C8×D61C2×C4semidirect
192. C4×SD16D61semidirect
197. C61#2952semidirect
263. SD16C4×D61semidirect