Finite Group Databasebeta

← #29577771

Subgroups — #29577771

Order 15616.

738 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454841C211yesmaximal, characteristic
2#21449185C211yesmaximal, characteristic
3#21445804C211yesmaximal, characteristic
4#21445755C211yesmaximal, characteristic, complemented
5#21445753C211yesmaximal, characteristic, complemented
6#21443686C211yesmaximal, characteristic, complemented
7C61×#1289C211yesmaximal, characteristic, complemented
8C23×Dic122C2211yescharacteristic
9C2×#14519757—21no—
10C2×C4×C22⋊D61C2211yescharacteristic
11C8×C22⋊D61—22no—
12#16839825—22no—
13#16839812—21no—
14C2×#14519702—22no—
15C2×#14519700—22no—
16C2×#14519691—21no—
17C2×C22⋊#92418C2211yescharacteristic
18C22⋊C8×D61—21no—
19#16839683C412yescomplemented
20#16839675C412yescomplemented
21#16839667—21no—
22#16839639—21no—
23#16839637—21no—
24#16839622C2211yescharacteristic
25#16839528—21no—
26C2×C22⋊C8×C61C2211yescharacteristic
27C61×#380C2211yescharacteristic
28C61×#380C2211yescharacteristic
29C22×Dic122—21no—
30C22×Dic122—21no—
31C22×Dic122—21no—
32C22×Dic122—21no—
33C22×Dic122—21no—
34C22×Dic122—44no—
35C22×Dic122C2×C412yes—
36C22×C22⋊D61D411yescharacteristic
37C23×Dic61—21no—
38C22×C4×D61D411yescharacteristic
39C22×#92418D412yes—
40C2×C8×D61—22no—
41#14519757—44no—
42C4×C22⋊D61—21no—
43C4×C22⋊D61—21no—
44C4×C22⋊D61—21no—
45C4×C22⋊D61—21no—
46C2×C4⋊Dic61—22no—
47C2×C4⋊Dic61—21no—
48C2×#11758196C2×C411yescharacteristic
49C2×C22⋊Dic61—21no—
50C2×C22⋊Dic61D411yescharacteristic
51C2×#11758198—22no—
52C2×#11758198C2×C411yescharacteristic
53C2×C4×Dic61D411yescharacteristic
54#14519706—22no—
55#14519702—44no—
56#14519700—44no—
57#14519691—42no—
58C22⋊#92418—21no—
59C22⋊#92418—21no—
60#14519689—22no—
61C8×Dic61—22no—
62#14519684—22no—
63#14519684—22no—
64#14519684—21no—
65C23×C4×C61C2311yescharacteristic
66C22×C8×C61D412yes—
67C2×C4⋊C4×C61—21no—
68C2×C4⋊C4×C61—21no—
69C2×C22⋊C4×C61—21no—
70C2×C22⋊C4×C61—21no—
71C22⋊C8×C61—21no—
72C22⋊C8×C61—21no—
73#95×C61—21no—
74#95×C61C2×C412yes—
75C24×C61C2×D411yescharacteristic
76C23×D61C22⋊C411yescharacteristic
77C22×C4×C61—22no—
78C22×C4×C61—42no—
79C22×C4×C61—41no—
80C22×C4×C61C22×C411yescharacteristic
81C22×C4×C61C2×D411yescharacteristic
82C22×C4×C61C2×D411yescharacteristic
83C22×C4×C61C2×D411yescharacteristic
84C22×C4×C61#4111yescharacteristic
85C22×C4×C61#4111yescharacteristic
86C2×C22⋊D61—21no—
87C2×C22⋊D61—21no—
88C2×C22⋊D61—21no—
89C2×C22⋊D61—21no—
90C2×C22⋊D61SD1612yes—
91C2×C22⋊D61Q1612yes—
92C22×Dic61—22no—
93C22×Dic61—44no—
94C22×Dic61—41no—
95C22×Dic61—41no—
96C22×Dic61—41no—
97C22×Dic61C22⋊C411yescharacteristic
98C22×Dic61C22⋊C411yescharacteristic
99C22×Dic61C22⋊C411yescharacteristic
100C2×C4×D61—21no—
101C2×C4×D61—21no—
102C2×C4×D61—42no—
103C2×Dic122—24no—
104C2×Dic122—24no—
105C2×Dic122—22no—
106C2×Dic122—22no—
107C2×Dic122—24no—
108C2×Dic122—44no—
109C2×Dic122—44no—
110C2×Dic122—44no—
111C2×Dic122—42no—
112C2×Dic122—42no—
113C2×Dic122—42no—
114C2×Dic122—41no—
115C2×Dic122—41no—
116C2×C8×C61—22no—
117C2×C8×C61—42no—
118C4⋊C4×C61—42no—
119C4⋊C4×C61—42no—
120C22⋊C4×C61—41no—
121C22⋊C4×C61—41no—
122C22⋊C4×C61—41no—
123C22⋊C4×C61—41no—
124C22⋊Dic61—21no—
125C22⋊Dic61—21no—
126C22⋊Dic61—41no—
127C22⋊Dic61—41no—
128#11758198—21no—
129#11758198—21no—
130#11758198—44no—
131C4⋊Dic61—44no—
132C4⋊Dic61—42no—
133#11758196—21no—
134#11758196—21no—
135C4×Dic61—21no—
136C4×Dic61—21no—
137C2×#92418—22no—
138C2×#92418—42no—
139C8×D61—82no—
140C23×C61—41no—
141C23×C61—41no—
142C23×C61C2×C22⋊C411yescharacteristic
143C23×C61#12111yescharacteristic
144C23×C61#12111yescharacteristic
145C23×C61C2×SD1611yescharacteristic
146C23×C61C2×Q1611yescharacteristic
147C23×C61#13511yescharacteristic
148C23×C61#13511yescharacteristic
149C22×D61—21no—
150C22×D61—21no—
151C22×D61—41no—
152C22×D61—41no—
153C22×D61#10312yescomplemented
154C2×C4×C61—22no—
155C2×C4×C61—22no—
156C2×C4×C61—22no—
157C2×C4×C61—41no—
158C2×C4×C61—41no—
159C2×C4×C61—41no—
160C2×C4×C61—42no—
161C2×C4×C61—42no—
162C2×C4×C61—42no—
163C2×C4×C61—81no—
164C2×C4×C61—81no—
165C2×C4×C61—81no—
166C2×C4×C61C4×D411yescharacteristic
167C2×C4×C61C4×D411yescharacteristic
168C2×C4×C61#12011yescharacteristic
169C2×C4×C61#12311yescharacteristic
170C22⋊D61—22no—
171C22⋊D61—22no—
172C22⋊D61—22no—
173C22⋊D61—22no—
174C2×Dic61—21no—
175C2×Dic61—21no—
176C2×Dic61—24no—
177C2×Dic61—21no—
178C2×Dic61—21no—
179C2×Dic61—44no—
180C2×Dic61—44no—
181C2×Dic61—42no—
182C2×Dic61—42no—
183C2×Dic61—41no—
184C2×Dic61—41no—
185C2×Dic61—81no—
186C2×Dic61—81no—
187C2×Dic61—81no—
188C2×Dic61#10312yescomplemented
189C4×D61—42no—
190C4×D61—81no—
191Dic122—24no—
192Dic122—24no—
193Dic122—42no—
194Dic122—42no—
195Dic122—44no—
196Dic122—44no—
197C8×C61—42no—
198#92418—42no—
199#9467—611nomaximal, Sylow
200C22×C61—21no—
201C22×C61—21no—
202C22×C61—21no—
203C22×C61—21no—
204C22×C61—21no—
205C22×C61—21no—
206C22×C61—41no—
207C22×C61—41no—
208C22×C61—41no—
209C22×C61—41no—
210C22×C61#38611yescharacteristic
211C22×C61C2×#10311yescharacteristic
212C22×C61#41611yescharacteristic
213C22×C61#46511yescharacteristic
214C22×C61#46511yescharacteristic
215C22×C61#46711yescharacteristic
216C22×C61#46711yescharacteristic
217C2×D61—22no—
218C2×D61—41no—
219C2×D61—41no—
220C2×D61—42no—
221C2×D61—81no—
222C4×C61—21no—
223C4×C61—21no—
224C4×C61—21no—
225C4×C61—82no—
226C4×C61—161no—
227C4×C61B(4,𝔽2)12yes—
228Dic61—22no—
229Dic61—44no—
230Dic61—41no—
231Dic61—41no—
232Dic61—161no—
233#2972—611no—
234#2409—611no—
235#1799—611no—
236#1787—611no—
237#1787—611no—
238#1289—611no—
239#1289D6111yescharacteristic, complemented
240C2×C61—21no—
241C2×C61—21no—
242C2×C61—21no—
243C2×C61—21no—
244C2×C61—21no—
245C2×C61—21no—
246C2×C61#188911yescharacteristic
247C2×C61#189211yescharacteristic
248C2×C61#190911yescharacteristic
249D61—42no—
250C23×Q8—611no—
251C2×C22⋊Q8—1221no—
252C2×C4×D4—611no—
253C8×D4—1222no—
254C8×D4—1222no—
255#431—1221no—
256C2×#103—1222no—
257C2×#103—1222no—
258C2×#99—1221no—
259C2×C22⋊C8—611no—
260C2×C22⋊C8—1221no—
261C2×C22⋊C8C2×D6111yescharacteristic
262#395—612no—
263#393—612no—
264#391—1221no—
265#386—1221no—
266#385—1221no—
267#380—611no—
268#380C2×D6111yescharacteristic
269#380C2×D6111yescharacteristic
270#342—1221no—
271C61#946711yescharacteristic, complemented, Sylow
272C22×Q8—612no—
273C22×Q8—1221no—
274C22×Q8—1221no—
275C22×Q8—1221no—
276C22×Q8—1221no—
277C22×Q8—1221no—
278C22×Q8—2444no—
279C22×D4—611no—
280C23×C4—611no—
281C23×C4—1221no—
282C23×C4C22×D6111yescharacteristic
283C22×C8—612no—
284C22×C8—1222no—
285C22×C8D24412yes—
286C22⋊Q8—2444no—
287C4×D4—1221no—
288C4×D4—1221no—
289C4×D4—1221no—
290C4×D4—1221no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—611no—
294C2×C4⋊C4—1222no—
295C2×C4⋊C4—1221no—
296C2×C22⋊C4—21no—
297C2×C22⋊C4—21no—
298C2×C22⋊C4—611no—
299C2×C22⋊C4—611no—
300C2×C22⋊C4—1222no—
301C2×C22⋊C4—1221no—
302C2×C42—611no—
303C4⋊C8—1222no—
304#103—2444no—
305#103—2444no—
306#99—2442no—
307C22⋊C8—21no—
308C22⋊C8—21no—
309C22⋊C8—1222no—
310C22⋊C8—1221no—
311C22⋊C8—1221no—
312C4×C8—1222no—
313#95—21no—
314#95—1222no—
315#95—1222no—
316#95—1221no—
317#95C4×D6112yes—
318C24—611no—
319C24D4×D6111yescharacteristic
320C2×Q8—1224no—
321C2×Q8—1224no—
322C2×Q8—1224no—
323C2×Q8—1222no—
324C2×Q8—1222no—
325C2×Q8—2442no—
326C2×Q8—2442no—
327C2×Q8—2442no—
328C2×Q8—2444no—
329C2×Q8—2444no—
330C2×Q8—2444no—
331C2×Q8—2441no—
332C2×Q8—2441no—
333C2×D4—612no—
334C2×D4—612no—
335C2×D4—1221no—
336C2×D4—1221no—
337C2×D4—1221no—
338C2×D4—1221no—
339C22×C4—22no—
340C22×C4—42no—
341C22×C4—41no—
342C22×C4—611no—
343C22×C4—611no—
344C22×C4—611no—
345C22×C4—1222no—
346C22×C4—1221no—
347C22×C4—1221no—
348C22×C4—2442no—
349C22×C4—2444no—
350C22×C4—2441no—
351C22×C4—2441no—
352C22×C4—2441no—
353C22×C4C2×C4×D6111yescharacteristic
354C22×C4C2×D24411yescharacteristic
355C22×C4#1175822211yescharacteristic
356C22×C4D4×D6111yescharacteristic
357C22×C4D4×D6111yescharacteristic
358C22×C4#1175822611yescharacteristic
359C2×C8—22no—
360C2×C8—42no—
361C2×C8—1222no—
362C2×C8—4882no—
363C2×C8—2442no—
364C4⋊C4—42no—
365C4⋊C4—42no—
366C4⋊C4—1221no—
367C4⋊C4—1221no—
368C4⋊C4—2442no—
369C4⋊C4—2444no—
370C22⋊C4—41no—
371C22⋊C4—41no—
372C22⋊C4—41no—
373C22⋊C4—41no—
374C22⋊C4—1221no—
375C22⋊C4—1221no—
376C22⋊C4—1221no—
377C22⋊C4—1221no—
378C22⋊C4—2444no—
379C22⋊C4—2441no—
380C22⋊C4—2441no—
381C42—1221no—
382C42—1221no—
383C23—41no—
384C23—41no—
385C23—612no—
386C23—1221no—
387C23—1221no—
388C23—2441no—
389C23—2441no—
390C23C22⋊C4×D6111yescharacteristic
391C23#1451975011yescharacteristic
392C23#1451975211yescharacteristic
393C23SD16×D6111yescharacteristic
394C23Q16×D6111yescharacteristic
395C23#1451979611yescharacteristic
396C23#1451979811yescharacteristic
397Q8—1224no—
398Q8—1224no—
399Q8—2444no—
400Q8—2442no—
401Q8—2442no—
402Q8—2444no—
403D4—1222no—
404D4—1222no—
405D4—1222no—
406D4—1222no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—81no—
417C2×C4—81no—
418C2×C4—81no—
419C2×C4—612no—
420C2×C4—1221no—
421C2×C4—1221no—
422C2×C4—1224no—
423C2×C4—1221no—
424C2×C4—1221no—
425C2×C4—4881no—
426C2×C4—4881no—
427C2×C4—4881no—
428C2×C4—4881no—
429C2×C4—2442no—
430C2×C4—2444no—
431C2×C4—2444no—
432C2×C4—2442no—
433C2×C4—2442no—
434C2×C4—2441no—
435C2×C4—2441no—
436C2×C4#1451973911yescharacteristic
437C2×C4C4×D24411yescharacteristic
438C2×C4#1451974711yescharacteristic
439C2×C4#1451976211yescharacteristic
440C8—42no—
441C8—2442no—
442C22—21no—
443C22—21no—
444C22—21no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—41no—
449C22—41no—
450C22—41no—
451C22—41no—
452C22—1222no—
453C22—4881no—
454C22—2442no—
455C22—2441no—
456C22—2441no—
457C22#1683964011yescharacteristic
458C22#103×D6111yescharacteristic
459C22#1683975511yescharacteristic
460C22#1683999011yescharacteristic
461C22#1683999211yescharacteristic
462C22#1684000211yescharacteristic
463C22#1684000411yescharacteristic
464C4—21no—
465C4—21no—
466C4—21no—
467C4—82no—
468C4—161no—
469C4—1222no—
470C4—9761no—
471C4—2441no—
472C4—2444no—
473C4—2441no—
474C4#1683995012yes—
475C2—21no—
476C2—21no—
477C2—21no—
478C2—21no—
479C2—21no—
480C2—21no—
481C2—2442no—
482C2#2144622611yescharacteristic
483C2#2144624111yescharacteristic
484C2#2144634011yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1289C2
socleC22×C61#386
prime radicalC22×C22⋊D61D4
cosocleC23×C4×C61C23
hypercenter#1289D61
hypocenterC61#9467
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1289

Complements

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

NH ≅ G/Ntype
4. #21445755C2semidirect
5. #21445753C2semidirect
6. #21443686C2semidirect
7. C61×#1289C2semidirect
19. #16839683C4semidirect
20. #16839675C4semidirect
153. C22×D61#103semidirect
188. C2×Dic61#103semidirect
239. #1289D61semidirect
271. C61#9467semidirect

Maximal subgroups

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

subgroupindex
#214548412
#214491852
#214458042
#214457552
#214457532
#214436862
C61×#12892
#946761