Finite Group Databasebeta

← #29647846

Subgroups — #29647846

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#21454904C211yesmaximal, characteristic, complemented
3#21444382C211yesmaximal, characteristic, complemented
4#21444378C211yesmaximal, characteristic
5#21444355C214yesmaximal, complemented
6#21444342C214yesmaximal, complemented
7#21444317C211yesmaximal, characteristic, complemented
8#21444313C211yesmaximal, characteristic
9C61×#2351C211yesmaximal, 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—
22#16839893—22no—
23#16839893—22no—
24#16839819C2214yes—
25#16839815C2211yescharacteristic
26#16839815C2211yescharacteristic
27#16839498C2212yes—
28#16839498C2214yes—
29#16839498C2212yes—
30#16839495C2212yes—
31#16839495C2214yes—
32#16839495C2212yes—
33C2×C4×Q8×C61—21no—
34C2×C4×Q8×C61C2211yescharacteristic
35C61×#389—21no—
36C61×#389—22no—
37C61×#382C2212yes—
38C61×#382C2211yescharacteristic
39C4×C4⋊C4×C61C2211yescharacteristic
40C4×C4⋊C4×C61C2212yes—
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—
64C4×Dic122—21no—
65C4×Dic122C2×C414yes—
66C4×Dic122C2×C412yes—
67#14519742—22no—
68C4×D244—21no—
69C4×D244C2×C412yes—
70C4×D244C2×C414yes—
71#14519739—22no—
72C4×C22⋊D61—24no—
73#14519736—21no—
74#14519735—22no—
75#14519734—24no—
76C4⋊C4×D61—22no—
77C4⋊#92418—21no—
78C4⋊#92418—21no—
79C4⋊#92418—24no—
80C22⋊#92418C2312yes—
81C22⋊#92418C2312yes—
82#14519688—24no—
83C4×#92418—21no—
84C4×#92418—21no—
85C22×Q8×C61D411yescharacteristic
86C4×Q8×C61—44no—
87C4×Q8×C61C2×C412yes—
88C4×Q8×C61C2×C412yes—
89C4×Q8×C61D412yes—
90C4×Q8×C61D412yes—
91C2×C4⋊C4×C61—22no—
92C2×C4⋊C4×C61—21no—
93C2×C4⋊C4×C61—22no—
94C2×C4⋊C4×C61—21no—
95C2×C4⋊C4×C61D411yescharacteristic
96C2×C4⋊C4×C61D412yes—
97C2×C42×C61—22no—
98C2×C42×C61—21no—
99C2×C42×C61C2312yes—
100C2×C42×C61C2311yescharacteristic
101#95×C61—22no—
102#95×C61—21no—
103#95×C61C2311yescharacteristic
104#95×C61C2311yescharacteristic
105#95×C61C2312yes—
106C2×Q8×C61—22no—
107C2×Q8×C61—22no—
108C2×Q8×C61C22⋊C412yes—
109C2×Q8×C61C22⋊C412yes—
110C22×C4×C61—21no—
111C22×C4×C61—22no—
112C22×C4×C61—21no—
113C22×C4×C61C2×D412yes—
114C22×C4×C61C2×D412yes—
115C22×C4×C61C2×D411yescharacteristic
116C22×C4×C61C2×D411yescharacteristic
117C22×C4×C61C2411yescharacteristic
118C2×C22⋊D61—22no—
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—
129C4⋊C4×C61—42no—
130C4⋊C4×C61—44no—
131C4⋊C4×C61—44no—
132C4⋊C4×C61—42no—
133C4⋊C4×C61C22⋊C412yes—
134C4⋊C4×C61C22⋊C412yes—
135C4⋊C4×C61C22⋊C414yes—
136C4⋊C4×C61C22⋊C414yes—
137C42×C61—44no—
138C42×C61—42no—
139C42×C61C22×C411yescharacteristic
140C42×C61C22×C414yes—
141C42×C61C22×C411yescharacteristic
142C42×C61C2×D411yescharacteristic
143C42×C61C2×D411yescharacteristic
144C42×C61C2×D414yes—
145C22⋊Dic61—22no—
146#11758198—24no—
147#11758198—24no—
148#11758198—22no—
149#11758198—24no—
150#11758198—22no—
151C4⋊Dic61—21no—
152C4⋊Dic61—21no—
153C4⋊Dic61—21no—
154C4⋊Dic61—21no—
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—
164C2×#92418—22no—
165C2×#92418—22no—
166C23×C61C22×D411yescharacteristic
167C22×D61—22no—
168Q8×C61—24no—
169Q8×C61—24no—
170C2×C4×C61—22no—
171C2×C4×C61—22no—
172C2×C4×C61—22no—
173C2×C4×C61—41no—
174C2×C4×C61—42no—
175C2×C4×C61—41no—
176C2×C4×C61—41no—
177C2×C4×C61—41no—
178C2×C4×C61—42no—
179C2×C4×C61—41no—
180C2×C4×C61—42no—
181C2×C4×C61—41no—
182C2×C4×C61—42no—
183C2×C4×C61—41no—
184C2×C4×C61C2×C22⋊C414yes—
185C2×C4×C61C2×C22⋊C411yescharacteristic
186C2×C4×C61C2×C22⋊C414yes—
187C2×C4×C61C2×C22⋊C411yescharacteristic
188C2×C4×C61C2×C22⋊C411yescharacteristic
189C2×C4×C61C2×C22⋊C411yescharacteristic
190C2×C4×C61AGL(1,ℤ/8)12yes—
191C2×C4×C61#13712yes—
192C2×C4×C61C23×C411yescharacteristic
193C2×C4×C61C22×D411yescharacteristic
194C22⋊D61—42no—
195C22⋊D61—42no—
196C2×Dic61—22no—
197C2×Dic61—22no—
198C2×Dic61—22no—
199D244—42no—
200D244—42no—
201D244—81no—
202C4×D61—44no—
203C4×D61—84no—
204Dic122—42no—
205Dic122—42no—
206Dic122—81no—
207#92418—42no—
208#92418—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—42no—
225C4×C61—82no—
226C4×C61—81no—
227C4×C61#41712yes—
228C4×C61#41712yes—
229Dic61—42no—
230Dic61—42no—
231Dic61—42no—
232#3507—611no—
233#2983—611no—
234#2351D6111yescharacteristic, complemented
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—21no—
260C2×C4×Q8C2×D6111yescharacteristic
261#446—1222no—
262#446—1222no—
263#432—614no—
264#431—611no—
265#431—611no—
266#389—21no—
267#389—22no—
268#382C2×D6112yes—
269#382C2×D6111yescharacteristic
270C4×C4⋊C4C2×D6111yescharacteristic
271C4×C4⋊C4C2×D6112yes—
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×Q8C22⋊D6111yescharacteristic
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—44no—
304C4×Q8—614no—
305C4×Q8—612no—
306C4×Q8—1222no—
307C4×Q8—1221no—
308C4×Q8C4×D6112yes—
309C4×Q8C4×D6112yes—
310C4×Q8D24412yes—
311C4×Q8D24412yes—
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—22no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—1222no—
325C2×C4⋊C4C22⋊D6111yescharacteristic
326C2×C4⋊C4C22⋊D6112yes—
327C2×C42—22no—
328C2×C42—21no—
329C2×C42C22×D6112yes—
330C2×C42C22×D6111yescharacteristic
331C4⋊C8—1221no—
332C4⋊C8—1221no—
333C4⋊C8—1224no—
334C22⋊C8—612no—
335C22⋊C8—612no—
336#97—1224no—
337C4×C8—1221no—
338C4×C8—1221no—
339#95—22no—
340#95—21no—
341#95C22×D6111yescharacteristic
342#95C22×D6111yescharacteristic
343#95C22×D6112yes—
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—21no—
358C22×C4—22no—
359C22×C4—21no—
360C22×C4—1224no—
361C22×C4—1222no—
362C22×C4C2×C22⋊D6112yes—
363C22×C4C2×C22⋊D6112yes—
364C22×C4C2×C22⋊D6111yescharacteristic
365C22×C4C2×C22⋊D6111yescharacteristic
366C22×C4C23×D6111yescharacteristic
367C2×C8—1222no—
368C2×C8—1222no—
369C4⋊C4—44no—
370C4⋊C4—44no—
371C4⋊C4—42no—
372C4⋊C4—42no—
373C4⋊C4—612no—
374C4⋊C4—612no—
375C4⋊C4—1222no—
376C4⋊C4—1221no—
377C4⋊C4—1224no—
378C4⋊C4—1224no—
379C4⋊C4—1222no—
380C4⋊C4—1224no—
381C4⋊C4—1221no—
382C4⋊C4—1221no—
383C4⋊C4—1221no—
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—44no—
395C42—42no—
396C42—1224no—
397C42—1222no—
398C42C2×C4×D6111yescharacteristic
399C42C2×C4×D6114yes—
400C42C2×C4×D6111yescharacteristic
401C42C2×D24411yescharacteristic
402C42C2×D24411yescharacteristic
403C42C2×D24414yes—
404C23—1222no—
405C23C22×C22⋊D6111yescharacteristic
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—22no—
419C2×C4—42no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—42no—
425C2×C4—41no—
426C2×C4—42no—
427C2×C4—41no—
428C2×C4—42no—
429C2×C4—41no—
430C2×C4—1222no—
431C2×C4—1222no—
432C2×C4—1222no—
433C2×C4—4884no—
434C2×C4—2444no—
435C2×C4C2×#1175819814yes—
436C2×C4C2×#1175819814yes—
437C2×C4C2×#1175819811yescharacteristic
438C2×C4C2×#1175819811yescharacteristic
439C2×C4C2×#1175819811yescharacteristic
440C2×C4C2×#1175819811yescharacteristic
441C2×C4#1451980312yes—
442C2×C4#1451980812yes—
443C2×C4C22×C4×D6111yescharacteristic
444C2×C4C22×D24411yescharacteristic
445C8—2442no—
446C8—2442no—
447C22—21no—
448C22—21no—
449C22—2442no—
450C22—2442no—
451C22—2442no—
452C22C22×#1175819811yescharacteristic
453C22C2×#1451980311yescharacteristic
454C22C2×#1451980811yescharacteristic
455C4—24no—
456C4—21no—
457C4—21no—
458C4—21no—
459C4—21no—
460C4—24no—
461C4—42no—
462C4—82no—
463C4—81no—
464C4—2442no—
465C4—2442no—
466C4—2442no—
467C4#1683976112yes—
468C4#1683976112yes—
469C2—21no—
470C2—21no—
471C2—4882no—
472C2#2145428211yescharacteristic
473C2C2×#1683976111yescharacteristic
474C2#2145436711yescharacteristic
subgroupG/H
centerC22C22×#11758198
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2351C2
socleC22×C61C22×C22⋊C4
prime radical#16840312C22
cosocleC22×C4×C61C24
hypercenter#2351D61
hypocenterC61#17628
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4×Q8 ◁ #2351

Complements

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

NH ≅ G/Ntype
2. #21454904C2semidirect
3. #21444382C2semidirect
5. #21444355C2semidirect
6. #21444342C2semidirect
7. #21444317C2semidirect
9. C61×#2351C2semidirect
10. #16840497C4semidirect
11. #16840490C4semidirect
12. #16840485C4semidirect
14. #16840472C4semidirect
234. #2351D61semidirect
278. C61#17628semidirect

Maximal subgroups

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

subgroupindex
#214596842
#214549042
#214443822
#214443782
#214443552
#214443422
#214443172
#214443132
C61×#23512
#1762861