Finite Group Databasebeta

← #21457444

Subgroups — #21457444

Order 7808.

498 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519804C211yesmaximal, characteristic, complemented
2#16840423C211yesmaximal, characteristic, complemented
3#16840400C211yesmaximal, characteristic, complemented
4#16840147C211yesmaximal, characteristic, complemented
5#16840017C211yesmaximal, characteristic, complemented
6#16840015C211yesmaximal, characteristic, complemented
7#16839986C211yesmaximal, characteristic, complemented
8#16839979C211yesmaximal, characteristic, complemented
9#16839923C211yesmaximal, characteristic, complemented
10#16839911C211yesmaximal, characteristic, complemented
11#16839907C211yesmaximal, characteristic, complemented
12#16839901C211yesmaximal, characteristic, complemented
13SD16×Dic61C211yesmaximal, characteristic, complemented
14#16839838C211yesmaximal, characteristic, complemented
15C2×#137×C61C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×D4×D61C2211yescharacteristic
18#14519804—24no—
19C2×#11758201C2211yescharacteristic
20C2×#11758201C2211yescharacteristic
21C2×#11758201C2211yescharacteristic, complemented
22C2×D488C2211yescharacteristic
23C2×#11758199C2211yescharacteristic
24C2×#11758189C2211yescharacteristic
25#14519766—21no—
26#14519766C2211yescharacteristic
27#14519766C2211yescharacteristic, complemented
28#14519760—21no—
29#14519753—21no—
30#14519753C2211yescharacteristic
31#14519753C2211yescharacteristic
32#14519751—21no—
33#14519751C2211yescharacteristic
34#14519751C2211yescharacteristic, complemented
35#14519749—21no—
36#14519745—21no—
37Q8×Dic61C2211yescharacteristic, complemented
38D4×Dic61C2211yescharacteristic
39C4×C22⋊D61—21no—
40C4×C22⋊D61C2211yescharacteristic
41C2×#11758198—21no—
42#14519709C2211yescharacteristic, complemented
43#14519706C2211yescharacteristic, complemented
44#14519701C2211yescharacteristic, complemented
45#14519701C2211yescharacteristic, complemented
46#14519701C2211yescharacteristic, complemented
47#14519699C2211yescharacteristic
48#14519699C2211yescharacteristic, complemented
49#14519698C2211yescharacteristic
50C22⋊#92418C2211yescharacteristic, complemented
51#14519689C2211yescharacteristic
52C8×Dic61C2211yescharacteristic, complemented
53C2×#41×C61C2211yescharacteristic
54C22×Q8×C61C2211yescharacteristic, complemented
55#137×C61—24no—
56C2×Q16×C61C2211yescharacteristic, complemented
57C2×Q16×C61C2211yescharacteristic, complemented
58C2×SD16×C61C2211yescharacteristic
59C2×SD16×C61C2211yescharacteristic
60C2×M16×C61C2211yescharacteristic, complemented
61C23×D61—21no—
62#41×C61—22no—
63#41×C61—41no—
64C2×Q8×C61—21no—
65C2×Q8×C61—22no—
66C2×Q8×C61—41no—
67C2×Q8×C61C2311yescharacteristic
68C2×Q8×C61C2311yescharacteristic
69C2×Q8×C61C2311yescharacteristic
70C2×D4×C61—21no—
71C2×D4×C61C2311yescharacteristic
72C22×C4×C61—21no—
73C22×C4×C61—21no—
74C22×C4×C61C2311yescharacteristic
75C2×C22⋊D61—21no—
76C2×C22⋊D61—21no—
77C2×C22⋊D61—21no—
78C2×C22⋊D61D411yescharacteristic
79C22×Dic61—21no—
80#11758226—22no—
81#11758226—41no—
82D4×D61—22no—
83D4×D61—41no—
84C2×D244—21no—
85C2×D244C2311yescharacteristic
86C2×D244C2311yescharacteristic
87C2×C4×D61—21no—
88C2×C4×D61C2311yescharacteristic
89Q16×C61—22no—
90Q16×C61—22no—
91SD16×C61—22no—
92SD16×C61D414yescomplemented
93M16×C61—22no—
94C2×C8×C61C2311yescharacteristic
95C2×C8×C61C2311yescharacteristic
96C22⋊Dic61—21no—
97C22⋊Dic61D411yescharacteristic
98#11758201—22no—
99#11758201—41no—
100#11758201—41no—
101#11758199—22no—
102#11758198—21no—
103#11758198—21no—
104#11758198—21no—
105#11758198—21no—
106#11758198—21no—
107#11758198—21no—
108#11758198—21no—
109#11758198—21no—
110#11758198D411yescharacteristic
111C4⋊Dic61—21no—
112C4⋊Dic61C2311yescharacteristic
113C4⋊Dic61C2311yescharacteristic
114#11758196—21no—
115#11758196—21no—
116#11758196D411yescharacteristic
117C4×Dic61—21no—
118C4×Dic61C2311yescharacteristic
119C2×#92418C2311yescharacteristic
120C2×#92418C2311yescharacteristic
121D488—22no—
122#11758189—22no—
123C23×C61—21no—
124C23×C61C2×D411yescharacteristic
125C22×D61—21no—
126C22×D61—21no—
127C22×D61—42no—
128C22×D61—42no—
129C22×D61—81no—
130C22×D61C2×D411yescharacteristic
131Q8×C61—21no—
132Q8×C61—21no—
133Q8×C61—21no—
134Q8×C61—21no—
135Q8×C61—21no—
136Q8×C61—42no—
137Q8×C61C2×D412yes—
138D4×C61—21no—
139D4×C61—42no—
140D4×C61C2×D412yes—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—42no—
147C2×C4×C61—42no—
148C2×C4×C61C2×D411yescharacteristic
149C2×C4×C61C2411yescharacteristic
150C22⋊D61—41no—
151C22⋊D61—42no—
152C22⋊D61—42no—
153C22⋊D61—81no—
154C2×Dic61—21no—
155C2×Dic61—21no—
156C2×Dic61—81no—
157C2×Dic61C2×D411yescharacteristic
158C2×Dic61C2×D411yescharacteristic
159C2×Dic61C2×D411yescharacteristic
160D244—21no—
161D244—21no—
162D244—21no—
163D244—21no—
164D244—42no—
165C4×D61—21no—
166C4×D61—21no—
167C4×D61—42no—
168C8×C61—21no—
169C8×C61C2×D412yes—
170#92418—21no—
171#92418—21no—
172C22×C61—22no—
173C22×C61—21no—
174C22×C61—21no—
175C22×C61—21no—
176C22×C61—41no—
177C22×C61—41no—
178C22×C61C22×D411yescharacteristic
179C2×D61—21no—
180C2×D61—21no—
181C2×D61—21no—
182C2×D61—41no—
183C2×D61—41no—
184C2×D61—41no—
185C2×D61—41no—
186C2×D61—41no—
187C2×D61—41no—
188C2×D61—84no—
189C4×C61—22no—
190C4×C61—21no—
191C4×C61—41no—
192C4×C61—41no—
193C4×C61C22×D411yescharacteristic
194C4×C61H(5,𝔽2)11yescharacteristic
195Dic61—21no—
196Dic61—21no—
197Dic61—21no—
198Dic61—41no—
199Dic61—41no—
200#3275—611nomaximal, Sylow
201C2×C61—42no—
202C2×C61—41no—
203C2×C61D4211yescharacteristic
204C2×C61#57511yescharacteristic
205C2×C61#57711yescharacteristic
206D61—41no—
207D61—81no—
208D61—81no—
209C2×#137D6111yescharacteristic, complemented
210C2×AGL(1,ℤ/8)—611no—
211#548—611no—
212#546—611no—
213#495—611no—
214#470—611no—
215#469—611no—
216#464—611no—
217#463—611no—
218#452—611no—
219#450—611no—
220#449—611no—
221#448—611no—
222C4×SD16—611no—
223#436—611no—
224C61#327511yescharacteristic, complemented, Sylow
225C2×#41—611no—
226C2×#41C2×D6111yescharacteristic
227C22×Q8C2×D6111yescharacteristic, complemented
228C22×D4—611no—
229#137—24no—
230AGL(1,ℤ/8)—1224no—
231C2×Q16C2×D6111yescharacteristic, complemented
232C2×Q16C2×D6111yescharacteristic, complemented
233C2×SD16—611no—
234C2×SD16—611no—
235C2×SD16—611no—
236C2×SD16C2×D6111yescharacteristic
237C2×SD16C2×D6111yescharacteristic
238C2×D8—611no—
239C2×D8—611no—
240C2×M16—611no—
241C2×M16C2×D6111yescharacteristic, complemented
242#124—611no—
243#124—611no—
244#124—1221no—
245#123—1221no—
246C22⋊Q8—611no—
247C22⋊Q8—611no—
248C22⋊Q8—1221no—
249#121—611no—
250#121—611no—
251#121—1221no—
252#121—1221no—
253#120—1221no—
254C4×Q8—611no—
255C4×D4—611no—
256C4×D4—611no—
257C4×D4—1221no—
258C2×C22⋊C4—1221no—
259#106—611no—
260C4⋊C8—611no—
261#103—611no—
262#103—611no—
263#103—611no—
264#102—611no—
265#102—611no—
266#102—611no—
267C22⋊C8—611no—
268C22⋊C8—611no—
269C4×C8—611no—
270C24—1221no—
271#41—22no—
272#41—41no—
273#41—1222no—
274#41—2441no—
275C2×Q8—21no—
276C2×Q8—22no—
277C2×Q8—41no—
278C2×Q8C22×D6111yescharacteristic
279C2×Q8C22×D6111yescharacteristic
280C2×Q8C22×D6111yescharacteristic
281C2×D4—21no—
282C2×D4—611no—
283C2×D4—611no—
284C2×D4—611no—
285C2×D4—1221no—
286C2×D4—1221no—
287C2×D4—1222no—
288C2×D4—1221no—
289C2×D4—1221no—
290C2×D4—2441no—
291C2×D4C22×D6111yescharacteristic
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—611no—
295C22×C4—1221no—
296C22×C4—1221no—
297C22×C4C22×D6111yescharacteristic
298Q16—22no—
299Q16—22no—
300SD16—22no—
301SD16—1222no—
302SD16—2441no—
303SD16—2441no—
304SD16C22⋊D6114yescomplemented
305D8—1222no—
306D8—1222no—
307M16—22no—
308M16—1222no—
309C2×C8—611no—
310C2×C8—611no—
311C2×C8C22×D6111yescharacteristic
312C2×C8C22×D6111yescharacteristic
313C4⋊C4—611no—
314C4⋊C4—611no—
315C4⋊C4—611no—
316C4⋊C4—1221no—
317C4⋊C4—1221no—
318C4⋊C4—1221no—
319C22⋊C4—611no—
320C22⋊C4—611no—
321C22⋊C4—1221no—
322C22⋊C4—1221no—
323C22⋊C4—1221no—
324C22⋊C4—1221no—
325C22⋊C4—1221no—
326C22⋊C4—1221no—
327C22⋊C4—1221no—
328C22⋊C4—1221no—
329C22⋊C4—1221no—
330C42—611no—
331C42—1221no—
332C23—21no—
333C23—611no—
334C23—1221no—
335C23—1221no—
336C23—4881no—
337C23—2442no—
338C23—2442no—
339C23D4×D6111yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—21no—
343Q8—21no—
344Q8—21no—
345Q8—42no—
346Q8C2×C22⋊D6112yes—
347D4—21no—
348D4—42no—
349D4—1221no—
350D4—1221no—
351D4—1221no—
352D4—1221no—
353D4—4881no—
354D4—2442no—
355D4—2441no—
356D4—2442no—
357D4—2442no—
358D4C2×C22⋊D6112yes—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—611no—
367C2×C4—611no—
368C2×C4—611no—
369C2×C4—1221no—
370C2×C4—1221no—
371C2×C4—1221no—
372C2×C4—1221no—
373C2×C4—4881no—
374C2×C4—2442no—
375C2×C4D4×D6111yescharacteristic
376C2×C4C23×D6111yescharacteristic
377C8—21no—
378C8—1221no—
379C8—1221no—
380C8C2×C22⋊D6112yes—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—22no—
385C22—41no—
386C22—41no—
387C22—1221no—
388C22—1221no—
389C22—1221no—
390C22—4884no—
391C22—2441no—
392C22—2441no—
393C22—2441no—
394C22—2441no—
395C22—2441no—
396C22—2441no—
397C22C2×D4×D6111yescharacteristic
398C4—21no—
399C4—22no—
400C4—41no—
401C4—41no—
402C4—1221no—
403C4—1221no—
404C4—1221no—
405C4—2441no—
406C4—2441no—
407C4C22×C22⋊D6111yescharacteristic
408C4#1451982211yescharacteristic
409C2—41no—
410C2—42no—
411C2—4881no—
412C2—4881no—
413C2—2441no—
414C2D4×C22⋊D6111yescharacteristic
415C2#1684056111yescharacteristic
416C2#1684057111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×#137×C61C2
socleC22×C61C22×D4
hypercenterC2×#137D61
hypocenterC61#3275
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×#14519804C2semidirect
2. #16840423C2semidirect
3. #16840400C2semidirect
4. #16840147C2semidirect
5. #16840017C2semidirect
6. #16840015C2semidirect
7. #16839986C2semidirect
8. #16839979C2semidirect
9. #16839923C2semidirect
10. #16839911C2semidirect
11. #16839907C2semidirect
12. #16839901C2semidirect
13. SD16×Dic61C2semidirect
14. #16839838C2semidirect
15. C2×#137×C61C2semidirect
21. C2×#11758201C22semidirect
27. #14519766C22semidirect
34. #14519751C22semidirect
37. Q8×Dic61C22semidirect
42. #14519709C22semidirect
43. #14519706C22semidirect
44. #14519701C22semidirect
45. #14519701C22semidirect
46. #14519701C22semidirect
48. #14519699C22semidirect
50. C22⋊#92418C22semidirect
52. C8×Dic61C22semidirect
54. C22×Q8×C61C22semidirect
56. C2×Q16×C61C22semidirect
57. C2×Q16×C61C22semidirect
60. C2×M16×C61C22semidirect
92. SD16×C61D4semidirect
209. C2×#137D61semidirect
224. C61#3275semidirect
227. C22×Q8C2×D61semidirect
231. C2×Q16C2×D61semidirect
232. C2×Q16C2×D61semidirect
241. C2×M16C2×D61semidirect
304. SD16C22⋊D61semidirect