Finite Group Databasebeta

← #29647851

Subgroups — #29647851

Order 15616.

942 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459684C211yesmaximal, characteristic
2#21448740C211yesmaximal, characteristic, complemented
3#21444384C211yesmaximal, characteristic, complemented
4#21444380C211yesmaximal, characteristic
5#21444358C214yesmaximal, complemented
6#21444345C214yesmaximal, complemented
7#21444319C211yesmaximal, characteristic, complemented
8#21444315C211yesmaximal, characteristic
9C61×#2983C211yesmaximal, characteristic, complemented
10#16840497C412yescomplemented
11#16840490C412yescomplemented
12#16840485C412yescomplemented
13#16840484—22no—
14#16840472C412yescomplemented
15#16840453—22no—
16#16840359—22no—
17#16840336—21no—
18#16840319C2211yescharacteristic
19#16840312C2211yescharacteristic
20#16840296C2214yes—
21#16840243—21no—
22C2×Q8×Dic61—21no—
23#16839661—21no—
24#16839661—22no—
25#16839628C2212yes—
26#16839628C2211yescharacteristic
27C4×C4⋊Dic61C2211yescharacteristic
28C4×C4⋊Dic61C2212yes—
29#16839500C2212yes—
30#16839500C2214yes—
31#16839500C2212yes—
32#16839497C2212yes—
33#16839497C2214yes—
34#16839497C2212yes—
35C2×C4×Q8×C61C2211yescharacteristic
36C61×#446—22no—
37C61×#446—22no—
38C61×#432C2214yes—
39C61×#431C2211yescharacteristic
40C61×#431C2211yescharacteristic
41C2×#11758222—21no—
42#14519777C2×C411yescharacteristic
43#14519777C2×C411yescharacteristic
44#14519777C2×C411yescharacteristic
45#14519775—22no—
46#14519774C2×C411yescharacteristic
47#14519772—24no—
48#14519771—24no—
49#14519769—21no—
50#14519769C2×C414yes—
51#14519767—24no—
52#14519766—22no—
53#14519765—21no—
54#14519765C2×C414yes—
55#14519762—24no—
56#14519760—24no—
57#14519756—21no—
58#14519756C2312yes—
59#14519755—24no—
60#14519753—22no—
61#14519753—22no—
62#14519751—21no—
63#14519751C2312yes—
64Q8×Dic61—44no—
65C4×Dic122—21no—
66C4×Dic122C2×C414yes—
67C4×Dic122C2×C412yes—
68#14519742—22no—
69C4×D244—21no—
70C4×D244C2×C412yes—
71C4×D244C2×C414yes—
72#14519739—22no—
73C4×C22⋊D61—24no—
74#14519736—21no—
75#14519735—22no—
76#14519734—24no—
77C2×C4⋊Dic61—22no—
78C2×C4⋊Dic61—21no—
79C2×C4⋊Dic61—22no—
80C2×C4⋊Dic61—21no—
81C4⋊C4×D61—22no—
82C2×C4×Dic61—22no—
83C2×C4×Dic61—21no—
84#14519684—22no—
85#14519684—21no—
86#14519684C2311yescharacteristic
87#14519684C2311yescharacteristic
88#14519684C2312yes—
89C22×Q8×C61D411yescharacteristic
90C4×Q8×C61C2×C412yes—
91C4×Q8×C61C2×C412yes—
92C4×Q8×C61D412yes—
93C4×Q8×C61D412yes—
94C2×C4⋊C4×C61D411yescharacteristic
95C2×C4⋊C4×C61D412yes—
96C2×C42×C61C2312yes—
97C2×C42×C61C2311yescharacteristic
98C4⋊C8×C61—21no—
99C4⋊C8×C61—21no—
100C4⋊C8×C61—24no—
101C22⋊C8×C61C2312yes—
102C22⋊C8×C61C2312yes—
103#97×C61—24no—
104C4×C8×C61—21no—
105C4×C8×C61—21no—
106C2×Q8×C61—22no—
107C2×Q8×C61—22no—
108C2×Q8×C61C22⋊C412yes—
109C2×Q8×C61C22⋊C412yes—
110C22×C4×C61C2×D412yes—
111C22×C4×C61C2×D412yes—
112C22×C4×C61C2×D411yescharacteristic
113C22×C4×C61C2×D411yescharacteristic
114C22×C4×C61C2411yescharacteristic
115C2×C22⋊D61—22no—
116C22×Dic61—21no—
117C22×Dic61—22no—
118C22×Dic61—21no—
119#11758222—42no—
120#11758222—42no—
121C2×D244—21no—
122C2×D244—21no—
123C2×D244C22×C412yes—
124C2×C4×D61—22no—
125C2×C4×D61—24no—
126C2×Dic122—21no—
127C2×Dic122—21no—
128C2×Dic122C22×C412yes—
129C2×C8×C61—22no—
130C2×C8×C61—22no—
131C4⋊C4×C61C22⋊C412yes—
132C4⋊C4×C61C22⋊C412yes—
133C4⋊C4×C61C22⋊C414yes—
134C4⋊C4×C61C22⋊C414yes—
135C42×C61C22×C411yescharacteristic
136C42×C61C22×C414yes—
137C42×C61C22×C411yescharacteristic
138C42×C61C2×D411yescharacteristic
139C42×C61C2×D411yescharacteristic
140C42×C61C2×D414yes—
141C22⋊Dic61—22no—
142#11758198—24no—
143#11758198—24no—
144#11758198—22no—
145#11758198—24no—
146#11758198—22no—
147C4⋊Dic61—21no—
148C4⋊Dic61—21no—
149C4⋊Dic61—21no—
150C4⋊Dic61—21no—
151C4⋊Dic61—42no—
152C4⋊Dic61—44no—
153C4⋊Dic61—44no—
154C4⋊Dic61—42no—
155C4⋊Dic61C22×C412yes—
156C4⋊Dic61C22×C412yes—
157#11758196—24no—
158#11758196—24no—
159#11758196—24no—
160#11758196—22no—
161#11758196—22no—
162C4×Dic61—24no—
163C4×Dic61—22no—
164C4×Dic61—44no—
165C4×Dic61—42no—
166C23×C61C22×D411yescharacteristic
167C22×D61—22no—
168Q8×C61—24no—
169Q8×C61—24no—
170C2×C4×C61—22no—
171C2×C4×C61—22no—
172C2×C4×C61—41no—
173C2×C4×C61—42no—
174C2×C4×C61—41no—
175C2×C4×C61C2×C22⋊C414yes—
176C2×C4×C61C2×C22⋊C411yescharacteristic
177C2×C4×C61C2×C22⋊C414yes—
178C2×C4×C61C2×C22⋊C411yescharacteristic
179C2×C4×C61C2×C22⋊C411yescharacteristic
180C2×C4×C61C2×C22⋊C411yescharacteristic
181C2×C4×C61AGL(1,ℤ/8)12yes—
182C2×C4×C61#13712yes—
183C2×C4×C61C23×C411yescharacteristic
184C2×C4×C61C22×D411yescharacteristic
185C22⋊D61—42no—
186C22⋊D61—42no—
187C2×Dic61—22no—
188C2×Dic61—22no—
189C2×Dic61—22no—
190C2×Dic61—22no—
191C2×Dic61—41no—
192C2×Dic61—41no—
193C2×Dic61—42no—
194C2×Dic61—41no—
195C2×Dic61—42no—
196C2×Dic61—41no—
197C2×Dic61—42no—
198C2×Dic61—41no—
199D244—42no—
200D244—42no—
201D244—81no—
202C4×D61—44no—
203C4×D61—84no—
204Dic122—42no—
205Dic122—42no—
206Dic122—81no—
207C8×C61—42no—
208C8×C61—42no—
209#17628—611nomaximal, Sylow
210C22×C61—21no—
211C22×C61—21no—
212C22×C61C22×C22⋊C411yescharacteristic
213C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
214C22×C61C2×#13711yescharacteristic
215C2×D61—42no—
216C2×D61—42no—
217C2×D61—42no—
218C4×C61—21no—
219C4×C61—21no—
220C4×C61—24no—
221C4×C61—21no—
222C4×C61—24no—
223C4×C61—21no—
224C4×C61#41712yes—
225C4×C61#41712yes—
226Dic61—42no—
227Dic61—42no—
228Dic61—42no—
229Dic61—42no—
230Dic61—82no—
231Dic61—81no—
232#3507—611no—
233#2983D6111yescharacteristic, complemented
234#2351—611no—
235#1518—611no—
236#1517—611no—
237#1512—614no—
238#1509—614no—
239#1503—611no—
240#1502—611no—
241C2×C61—21no—
242C2×C61—21no—
243C2×C61#288411yescharacteristic
244C2×C61C2×#41711yescharacteristic
245C2×C61#290111yescharacteristic
246D61—82no—
247#559—612no—
248#557—612no—
249#556—612no—
250#556—1222no—
251#554—612no—
252#552—1222no—
253#539—1222no—
254#536—1221no—
255#533—611no—
256#532—611no—
257#529—614no—
258#520—1221no—
259C2×C4×Q8—1221no—
260C2×C4×Q8C2×D6111yescharacteristic
261#446—22no—
262#446—22no—
263#432C2×D6114yes—
264#431C2×D6111yescharacteristic
265#431C2×D6111yescharacteristic
266#389—1221no—
267#389—1222no—
268#382—612no—
269#382—611no—
270C4×C4⋊C4—611no—
271C4×C4⋊C4—612no—
272#328—612no—
273#328—612no—
274#328—614no—
275#327—612no—
276#327—612no—
277#327—614no—
278C61#1762811yescharacteristic, complemented, Sylow
279C2×#41—1221no—
280C22×Q8D24411yescharacteristic
281C4⋊Q8—611no—
282C4⋊Q8—611no—
283C4⋊Q8—611no—
284C4⋊Q8—1222no—
285#127—611no—
286#126—1224no—
287#126—1224no—
288#125—614no—
289#125—1224no—
290#125—1221no—
291#124—614no—
292#124—1222no—
293#124—1221no—
294#123—1224no—
295#123—1224no—
296C22⋊Q8—612no—
297C22⋊Q8—1222no—
298C22⋊Q8—1222no—
299C22⋊Q8—1221no—
300C22⋊Q8—1224no—
301#121—612no—
302#121—1221no—
303C4×Q8—614no—
304C4×Q8—612no—
305C4×Q8—1222no—
306C4×Q8—1221no—
307C4×Q8—2444no—
308C4×Q8C4×D6112yes—
309C4×Q8C4×D6112yes—
310C4×Q8C22⋊D6112yes—
311C4×Q8C22⋊D6112yes—
312C4×D4—614no—
313C4×D4—612no—
314C4×D4—1224no—
315C4×D4—1222no—
316C4×D4—1221no—
317#117—1221no—
318#117—1222no—
319#117—1224no—
320C2×C4⋊C4—1222no—
321C2×C4⋊C4—1222no—
322C2×C4⋊C4—1221no—
323C2×C4⋊C4—1222no—
324C2×C4⋊C4—1221no—
325C2×C4⋊C4D24411yescharacteristic
326C2×C4⋊C4D24412yes—
327C2×C42—1222no—
328C2×C42—1221no—
329C2×C42C22×D6112yes—
330C2×C42C22×D6111yescharacteristic
331C4⋊C8—21no—
332C4⋊C8—21no—
333C4⋊C8—24no—
334C22⋊C8C22×D6112yes—
335C22⋊C8C22×D6112yes—
336#97—24no—
337C4×C8—21no—
338C4×C8—21no—
339#95—611no—
340#95—611no—
341#95—612no—
342#95—1222no—
343#95—1221no—
344#41—2442no—
345#41—2442no—
346C2×Q8—22no—
347C2×Q8—22no—
348C2×Q8—612no—
349C2×Q8—1221no—
350C2×Q8—1221no—
351C2×Q8#1175819812yes—
352C2×Q8#1175819812yes—
353C2×D4—612no—
354C2×D4—1222no—
355C2×D4—1221no—
356C2×D4—1221no—
357C22×C4—1221no—
358C22×C4—1224no—
359C22×C4—1222no—
360C22×C4—1222no—
361C22×C4—1221no—
362C22×C4C2×D24412yes—
363C22×C4C2×D24412yes—
364C22×C4C2×D24411yescharacteristic
365C22×C4C2×D24411yescharacteristic
366C22×C4C23×D6111yescharacteristic
367C2×C8—22no—
368C2×C8—22no—
369C4⋊C4—612no—
370C4⋊C4—612no—
371C4⋊C4—1222no—
372C4⋊C4—1221no—
373C4⋊C4—1224no—
374C4⋊C4—1224no—
375C4⋊C4—1222no—
376C4⋊C4—1224no—
377C4⋊C4—1221no—
378C4⋊C4—1221no—
379C4⋊C4—1221no—
380C4⋊C4—2444no—
381C4⋊C4—2444no—
382C4⋊C4—2442no—
383C4⋊C4—2442no—
384C4⋊C4#1175819812yes—
385C4⋊C4#1175819812yes—
386C4⋊C4#1175819814yes—
387C4⋊C4#1175819814yes—
388C22⋊C4—1222no—
389C22⋊C4—1222no—
390C22⋊C4—1224no—
391C22⋊C4—1224no—
392C22⋊C4—1222no—
393C22⋊C4—1224no—
394C42—1224no—
395C42—1222no—
396C42—2444no—
397C42—2442no—
398C42C2×C4×D6111yescharacteristic
399C42C2×C4×D6114yes—
400C42C2×C4×D6111yescharacteristic
401C42C2×C22⋊D6111yescharacteristic
402C42C2×C22⋊D6111yescharacteristic
403C42C2×C22⋊D6114yes—
404C23—1222no—
405C23C22×D24411yescharacteristic
406Q8—24no—
407Q8—24no—
408Q8—4881no—
409Q8—2442no—
410Q8—2442no—
411D4—4881no—
412D4—2442no—
413D4—2442no—
414D4—2442no—
415D4—2442no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—42no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—1222no—
422C2×C4—1222no—
423C2×C4—1222no—
424C2×C4—1222no—
425C2×C4—4884no—
426C2×C4—2442no—
427C2×C4—2441no—
428C2×C4—2442no—
429C2×C4—2441no—
430C2×C4—2442no—
431C2×C4—2441no—
432C2×C4—2441no—
433C2×C4—2441no—
434C2×C4—2444no—
435C2×C4C2×#1175819814yes—
436C2×C4C2×#1175819814yes—
437C2×C4C2×#1175819811yescharacteristic
438C2×C4C2×#1175819811yescharacteristic
439C2×C4C2×#1175819811yescharacteristic
440C2×C4C2×#1175819811yescharacteristic
441C2×C4#1451980512yes—
442C2×C4#1451981012yes—
443C2×C4C22×C4×D6111yescharacteristic
444C2×C4C22×C22⋊D6111yescharacteristic
445C8—42no—
446C8—42no—
447C22—21no—
448C22—21no—
449C22—2442no—
450C22—2442no—
451C22—2442no—
452C22C22×#1175819811yescharacteristic
453C22C2×#1451980511yescharacteristic
454C22C2×#1451981011yescharacteristic
455C4—24no—
456C4—21no—
457C4—21no—
458C4—21no—
459C4—21no—
460C4—24no—
461C4—4882no—
462C4—4881no—
463C4—2442no—
464C4—2442no—
465C4—2442no—
466C4—2442no—
467C4#1683976412yes—
468C4#1683976412yes—
469C2—21no—
470C2—21no—
471C2—4882no—
472C2#2145428211yescharacteristic
473C2C2×#1683976411yescharacteristic
474C2#2145436411yescharacteristic
subgroupG/H
centerC22C22×#11758198
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2983C2
socleC22×C61C22×C22⋊C4
prime radical#16840312C22
cosocleC22×C4×C61C24
hypercenter#2983D61
hypocenterC61#17628
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4×Q8 ◁ #2983

Complements

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

NH ≅ G/Ntype
2. #21448740C2semidirect
3. #21444384C2semidirect
5. #21444358C2semidirect
6. #21444345C2semidirect
7. #21444319C2semidirect
9. C61×#2983C2semidirect
10. #16840497C4semidirect
11. #16840490C4semidirect
12. #16840485C4semidirect
14. #16840472C4semidirect
233. #2983D61semidirect
278. C61#17628semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214596842
#214487402
#214443842
#214443802
#214443582
#214443452
#214443192
#214443152
C61×#29832
#1762861