Finite Group Databasebeta

← #30611721

Subgroups — #30611721

Order 15616.

1016 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#431C212yesmaximal, complemented
2#21461324C212yesmaximal, complemented
3#21461322C212yesmaximal, complemented
4#21461320C214yesmaximal, complemented
5#21461316C214yesmaximal, complemented
6#21459112C211yesmaximal, characteristic
7#16840781—22no—
8#16840780C2214yes—
9#16840779C2214yes—
10#16840778—22no—
11D61⋊(C4⋊C8)C2214yes—
12D61⋊(C22⋊C8)—22no—
13C4×D61⋊C8—22no—
14#16840622C2214yescomplemented
15#16840621C2218yescomplemented
16#16840620C2214yescomplemented
17#16840316C2212yes—
18#16840315C2211yescharacteristic
19#16840309C2212yes—
20#16840308C2211yescharacteristic
21#16840299C412yes—
22#16840294C412yes—
23#16840292—22no—
24#16840290—22no—
25#16840274C411yescharacteristic
26#16840271—22no—
27#16840269C411yescharacteristic
28C4×#11758222—22no—
29C4×#11758222C411yescharacteristic
30C2×C42×D61C2211yescharacteristic
31C4×#41×C61C411yescharacteristic
32C2×D61⋊C8—24no—
33#14519844C2318yes—
34C4⋊#92420—24no—
35#14519834—24no—
36C22⋊#92420—24no—
37C4×#92420—24no—
38C4×#92420—24no—
39C2×#11758222—22no—
40C2×#11758222C2×C411yescharacteristic
41C22×C4×D61C2×C411yescharacteristic
42C22×C4×D61D412yes—
43#14519776C2312yes—
44#14519775C2311yescharacteristic
45#14519773C2311yescharacteristic
46#14519772—22no—
47#14519770—22no—
48#14519768C2×C412yes—
49#14519767—22no—
50#14519766C2×C411yescharacteristic
51#14519764C2×C411yescharacteristic
52#14519763—22no—
53#14519762—22no—
54#14519761—21no—
55#14519759—22no—
56#14519758—21no—
57#14519757C2×C412yes—
58#14519755—22no—
59#14519754—22no—
60#14519753C2×C412yes—
61#14519752C2×C412yes—
62#14519750—22no—
63#14519749—22no—
64#14519748C2×C412yes—
65#14519747—21no—
66#14519745—21no—
67C4×Dic122—22no—
68C4×Dic122—22no—
69C4×Dic122C2×C412yes—
70C4×D244—22no—
71C4×D244—22no—
72C4×D244C2×C412yes—
73C4×C22⋊D61—22no—
74C4×C22⋊D61—22no—
75C4×C22⋊D61—22no—
76C4×C22⋊D61—22no—
77C4×C22⋊D61—22no—
78#14519736—22no—
79#14519736C2×C411yescharacteristic
80#14519734—22no—
81#14519734—21no—
82#14519734—22no—
83C2×C4×Dic61D412yes—
84C2×C4×Dic61C2311yescharacteristic
85C42×D61—21no—
86C42×D61C2×C412yes—
87C42×D61D412yes—
88C42×D61D412yes—
89C42×D61C2312yes—
90C2×#41×C61C2×C411yescharacteristic
91C4×Q8×C61C2×C412yes—
92C4×D4×C61—22no—
93C4×D4×C61C2×C412yes—
94#117×C61—21no—
95#117×C61C2×C411yescharacteristic
96C2×C42×C61—21no—
97C2×C42×C61C2×C411yescharacteristic
98C23×D61C22⋊C411yescharacteristic
99#41×C61—42no—
100C2×Q8×C61C22×C411yescharacteristic
101C2×D4×C61—21no—
102C2×D4×C61C22×C411yescharacteristic
103C22×C4×C61—22no—
104C22×C4×C61—21no—
105C22×C4×C61C22⋊C412yes—
106C22×C4×C61C22×C411yescharacteristic
107C2×C22⋊D61—21no—
108C2×C22⋊D61—22no—
109C2×C22⋊D61—22no—
110C22×Dic61C22⋊C411yescharacteristic
111C22×Dic61C2×D412yes—
112#11758222—48no—
113#11758222—42no—
114C2×D244—22no—
115C2×D244C22×C411yescharacteristic
116C2×C4×D61—28no—
117C2×C4×D61—22no—
118C2×C4×D61—21no—
119C2×C4×D61—42no—
120C2×C4×D61C22⋊C412yes—
121C2×C4×D61C22⋊C412yes—
122C2×C4×D61C22⋊C412yes—
123C2×C4×D61C22×C412yes—
124C2×C4×D61C2×D412yes—
125C2×C4×D61C2×D412yes—
126C2×Dic122—22no—
127C2×Dic122C22×C411yescharacteristic
128C2×#92420—28no—
129D61⋊C8—48no—
130C4⋊C4×C61—22no—
131C4⋊C4×C61C22×C412yes—
132C22⋊C4×C61—21no—
133C22⋊C4×C61—22no—
134C42×C61—21no—
135C42×C61—22no—
136C42×C61C22⋊C411yescharacteristic
137C42×C61C22⋊C411yescharacteristic
138C42×C61C22×C412yes—
139C22⋊Dic61—21no—
140C22⋊Dic61—22no—
141C22⋊Dic61—22no—
142#11758198—22no—
143#11758198—22no—
144#11758198—22no—
145#11758198—22no—
146#11758198—22no—
147C4⋊Dic61—22no—
148C4⋊Dic61—22no—
149C4⋊Dic61C22×C412yes—
150#11758196—22no—
151#11758196—22no—
152#11758196—22no—
153#11758196—22no—
154#11758196—22no—
155C4×Dic61—22no—
156C4×Dic61—21no—
157C4×Dic61C22⋊C412yes—
158C4×Dic61C22⋊C412yes—
159C4×Dic61C22×C411yescharacteristic
160C4×Dic61C2×D412yes—
161C4×Dic61C2×D412yes—
162C4×Dic61C2×D412yes—
163C4×Dic61C2411yescharacteristic
164C23×C61—21no—
165C23×C61C2×C22⋊C411yescharacteristic
166C22×D61—24no—
167C22×D61—21no—
168C22×D61—41no—
169C22×D61C2×C22⋊C412yes—
170Q8×C61—41no—
171D4×C61—41no—
172D4×C61—42no—
173C2×C4×C61—22no—
174C2×C4×C61—24no—
175C2×C4×C61—21no—
176C2×C4×C61—22no—
177C2×C4×C61—42no—
178C2×C4×C61—44no—
179C2×C4×C61C2×C22⋊C412yes—
180C2×C4×C61C2×C22⋊C411yescharacteristic
181C2×C4×C61C2×C22⋊C412yes—
182C2×C4×C61C23×C411yescharacteristic
183C22⋊D61—42no—
184C22⋊D61—44no—
185C22⋊D61—44no—
186C2×Dic61—24no—
187C2×Dic61—21no—
188C2×Dic61—22no—
189C2×Dic61—41no—
190C2×Dic61C2×C22⋊C412yes—
191C2×Dic61C2×C22⋊C412yes—
192C2×Dic61C22×D412yes—
193D244—41no—
194D244—44no—
195C4×D61—24no—
196C4×D61—24no—
197C4×D61—24no—
198C4×D61—24no—
199C4×D61—42no—
200C4×D61—42no—
201C4×D61—44no—
202C4×D61#13518yes—
203Dic122—44no—
204Dic122—41no—
205#92420—48no—
206#17700—611nomaximal, Sylow
207C22×C61—21no—
208C22×C61—22no—
209C22×C61—41no—
210C22×C61—42no—
211C22×C61C22×C22⋊C411yescharacteristic
212C2×D61—22no—
213C2×D61—22no—
214C2×D61—44no—
215C2×D61—41no—
216C2×D61—42no—
217C2×D61#41614yes—
218C4×C61—21no—
219C4×C61—22no—
220C4×C61—41no—
221C4×C61—42no—
222C4×C61#41312yes—
223C4×C61#41614yes—
224Dic61—22no—
225Dic61—22no—
226Dic61—41no—
227Dic61—42no—
228Dic61C2×#13514yes—
229#3444—611no—
230C2×#431—612no—
231#1544—612no—
232#1543—612no—
233#1542—614no—
234#1540—614no—
235C2×C61—41no—
236C2×C61—81no—
237C2×C61C2×#41311yescharacteristic
238C2×C61C2×#41612yes—
239D61—24no—
240D61—81no—
241#533—611no—
242#533—612no—
243#532—612no—
244#532—611no—
245#529—612no—
246#529—612no—
247#529—1222no—
248#529—1222no—
249#525—611no—
250#525—611no—
251#525—1222no—
252C4×#41—611no—
253C4×#41—1222no—
254C4×#41#692311yescharacteristic
255C22×C42—611no—
256#431—614no—
257#431—614no—
258#431—1222no—
259#431—1222no—
260C2×C4⋊C8—614no—
261C2×C22⋊C8—1222no—
262C2×C4×C8—1222no—
263#333—614no—
264#332—618no—
265#331—614no—
266C61#1770011yescharacteristic, complemented, Sylow
267C2×#41—611no—
268C2×#41—1222no—
269C2×#41C2×#692311yescharacteristic
270C23×C4—612no—
271C23×C4—611no—
272C22×C8—1224no—
273C4⋊Q8—612no—
274C4⋊Q8—611no—
275#127—611no—
276#126—1222no—
277#126—1222no—
278#125—612no—
279#125—1222no—
280#124—611no—
281#124—611no—
282#124—1222no—
283#123—1221no—
284#123—1222no—
285#123—1222no—
286#123—1221no—
287C22⋊Q8—612no—
288C22⋊Q8—612no—
289C22⋊Q8—1222no—
290C22⋊Q8—1222no—
291#121—612no—
292#121—612no—
293#121—1222no—
294#121—1222no—
295#120—1221no—
296#120—1221no—
297C4×Q8—612no—
298C4×Q8—1222no—
299C4×Q8—1222no—
300C4×Q8C2×#692312yes—
301C4×D4—22no—
302C4×D4—612no—
303C4×D4—1222no—
304C4×D4—1222no—
305C4×D4—1222no—
306C4×D4—1222no—
307C4×D4—1222no—
308C4×D4—1222no—
309C4×D4—1222no—
310C4×D4C2×#692312yes—
311#117—21no—
312#117—611no—
313#117—1222no—
314#117—1222no—
315#117—1222no—
316#117—1221no—
317#117C2×#692311yescharacteristic
318C2×C42—21no—
319C2×C42—612no—
320C2×C42—611no—
321C2×C42—612no—
322C2×C42—612no—
323C2×C42—612no—
324C2×C42—612no—
325C2×C42—1221no—
326C2×C42C2×#692311yescharacteristic
327C4⋊C8—618no—
328C4⋊C8—1224no—
329C22⋊C8—1224no—
330C22⋊C8—1224no—
331C4×C8—1224no—
332C4×C8—1224no—
333C24—611no—
334#41—42no—
335#41—2442no—
336#41—2448no—
337C2×Q8—611no—
338C2×Q8—1222no—
339C2×Q8C22×#692311yescharacteristic
340C2×D4—21no—
341C2×D4—611no—
342C2×D4—1222no—
343C2×D4—1222no—
344C2×D4—1222no—
345C2×D4—1221no—
346C2×D4C22×#692311yescharacteristic
347C22×C4—21no—
348C22×C4—22no—
349C22×C4—612no—
350C22×C4—612no—
351C22×C4—611no—
352C22×C4—612no—
353C22×C4—612no—
354C22×C4—612no—
355C22×C4—612no—
356C22×C4—612no—
357C22×C4—1228no—
358C22×C4—1222no—
359C22×C4—1221no—
360C22×C4—2442no—
361C22×C4C22⋊#692312yes—
362C22×C4C22×#692311yescharacteristic
363C2×C8—1228no—
364C2×C8—2448no—
365C4⋊C4—22no—
366C4⋊C4—612no—
367C4⋊C4—1222no—
368C4⋊C4—1222no—
369C4⋊C4—1222no—
370C4⋊C4—1222no—
371C4⋊C4—1222no—
372C4⋊C4—1222no—
373C4⋊C4—1222no—
374C4⋊C4C22×#692312yes—
375C22⋊C4—21no—
376C22⋊C4—22no—
377C22⋊C4—1222no—
378C22⋊C4—1222no—
379C22⋊C4—1222no—
380C22⋊C4—1222no—
381C22⋊C4—1222no—
382C22⋊C4—1222no—
383C22⋊C4—1221no—
384C22⋊C4—1222no—
385C42—21no—
386C42—22no—
387C42—612no—
388C42—612no—
389C42—612no—
390C42—612no—
391C42—612no—
392C42—611no—
393C42—611no—
394C42—1221no—
395C42—1222no—
396C42C22⋊#692311yescharacteristic
397C42C22⋊#692311yescharacteristic
398C42C22×#692312yes—
399C23—21no—
400C23—612no—
401C23—1224no—
402C23—1221no—
403C23—2441no—
404C23C2×C22⋊#692311yescharacteristic
405Q8—41no—
406Q8—2441no—
407Q8—2444no—
408D4—41no—
409D4—42no—
410D4—2441no—
411D4—2444no—
412D4—2444no—
413D4—2442no—
414D4—2444no—
415C2×C4—22no—
416C2×C4—24no—
417C2×C4—22no—
418C2×C4—21no—
419C2×C4—42no—
420C2×C4—44no—
421C2×C4—612no—
422C2×C4—618no—
423C2×C4—612no—
424C2×C4—612no—
425C2×C4—1224no—
426C2×C4—1224no—
427C2×C4—1224no—
428C2×C4—1224no—
429C2×C4—1224no—
430C2×C4—1222no—
431C2×C4—1221no—
432C2×C4—2442no—
433C2×C4—2441no—
434C2×C4—2442no—
435C2×C4—2444no—
436C2×C4C2×C22⋊#692312yes—
437C2×C4C2×C22⋊#692311yescharacteristic
438C2×C4C2×C22⋊#692312yes—
439C2×C4C23×#692311yescharacteristic
440C8—2448no—
441C22—21no—
442C22—22no—
443C22—41no—
444C22—42no—
445C22—614no—
446C22—1222no—
447C22—1222no—
448C22—2444no—
449C22—2441no—
450C22—2442no—
451C22C22×C22⋊#692311yescharacteristic
452C4—21no—
453C4—22no—
454C4—41no—
455C4—42no—
456C4—614no—
457C4—1222no—
458C4—1222no—
459C4—2441no—
460C4—2442no—
461C4#1684074812yes—
462C4#1684075214yes—
463C2—41no—
464C2—81no—
465C2—1224no—
466C2—4881no—
467C2C2×#1684074811yescharacteristic
468C2C2×#1684075212yes—
subgroupG/H
centerC42C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC4×#41×C61C4
socleC22×C61C22×C22⋊C4
prime radical#21459112C2
cosocleC4×Dic61C24
hypercenterC4×#41#6923
hypocenterC61#17700
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C42 ◁ C2×C42 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
1. D61⋊#431C2semidirect
2. #21461324C2semidirect
3. #21461322C2semidirect
4. #21461320C2semidirect
5. #21461316C2semidirect
14. #16840622C22semidirect
15. #16840621C22semidirect
16. #16840620C22semidirect
266. C61#17700semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4312
#214613242
#214613222
#214613202
#214613162
#214591122
#1770061