Finite Group Databasebeta

← #29577325

Subgroups — #29577325

Order 15616.

570 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454841C211yesmaximal, characteristic
2#21451001C211yesmaximal, characteristic
3#21445804C211yesmaximal, characteristic
4#21444391C211yesmaximal, characteristic, complemented
5#21443699C211yesmaximal, characteristic, complemented
6#21443697C211yesmaximal, characteristic, complemented
7C61×#1520C211yesmaximal, characteristic, complemented
8C2×C4×C22⋊D61C2211yescharacteristic
9C8×C22⋊D61—22no—
10#16839825—22no—
11#16839812—21no—
12C2×#14519691—21no—
13C2×C22⋊#92418C2211yescharacteristic
14C22⋊C8×D61—21no—
15#16839700C411yescharacteristic, complemented
16#16839697C411yescharacteristic, complemented
17#16839681C411yescharacteristic, complemented
18#16839673C411yescharacteristic, complemented
19#16839643—21no—
20#16839639—21no—
21#16839633—21no—
22#16839622C2211yescharacteristic
23#16839620—21no—
24C2×#14519684C2211yescharacteristic
25#16839528—21no—
26#16839499—22no—
27C2×C22⋊Q8×C61C2211yescharacteristic
28C2×C22⋊C8×C61C2211yescharacteristic
29C61×#380C2211yescharacteristic
30C61×#328—22no—
31C22×C22⋊D61D411yescharacteristic
32C23×Dic61—21no—
33C22×C4×D61D411yescharacteristic
34C22×#92418—21no—
35C2×C8×D61—22no—
36C4×C22⋊D61—21no—
37C4×C22⋊D61—21no—
38C4×C22⋊D61—21no—
39C4×C22⋊D61—21no—
40C2×C4⋊Dic61—21no—
41C2×#11758196—21no—
42C2×#11758196—21no—
43C2×#11758196C2×C411yescharacteristic
44C2×C22⋊Dic61—21no—
45C2×C22⋊Dic61D411yescharacteristic
46C2×#11758198—21no—
47C2×#11758198—21no—
48C2×#11758198C2×C411yescharacteristic
49C2×C4×Dic61D411yescharacteristic
50#14519706—22no—
51#14519691—42no—
52C22⋊#92418—21no—
53C22⋊#92418D412yes—
54#14519689—22no—
55C8×Dic61—22no—
56#14519684—21no—
57#14519684—21no—
58#14519684—21no—
59#14519684—21no—
60#14519684—21no—
61#14519684—21no—
62#14519684C2×C411yescharacteristic
63#14519684C2×C411yescharacteristic
64C22×Q8×C61C2×C411yescharacteristic
65C23×C4×C61C2311yescharacteristic
66C22×C8×C61—21no—
67C22⋊Q8×C61—21no—
68C22⋊Q8×C61—21no—
69C22⋊Q8×C61—21no—
70C22⋊Q8×C61—21no—
71C2×C4⋊C4×C61—21no—
72C2×C4⋊C4×C61—21no—
73C2×C4⋊C4×C61C2×C411yescharacteristic
74C2×C22⋊C4×C61—21no—
75C2×C22⋊C4×C61—21no—
76C22⋊C8×C61—21no—
77C22⋊C8×C61D412yes—
78#95×C61—21no—
79C24×C61C2×D411yescharacteristic
80C23×D61C22⋊C411yescharacteristic
81C2×Q8×C61—21no—
82C2×Q8×C61—21no—
83C2×Q8×C61—81no—
84C22×C4×C61—21no—
85C22×C4×C61—21no—
86C22×C4×C61—41no—
87C22×C4×C61—81no—
88C22×C4×C61C22×C411yescharacteristic
89C22×C4×C61C2×D411yescharacteristic
90C22×C4×C61C2×D411yescharacteristic
91C22×C4×C61C2×D411yescharacteristic
92C22×C4×C61#4111yescharacteristic
93C22×C4×C61#4111yescharacteristic
94C2×C22⋊D61—21no—
95C2×C22⋊D61—21no—
96C2×C22⋊D61—21no—
97C2×C22⋊D61—21no—
98C2×C22⋊D61SD1612yes—
99C2×C22⋊D61Q1612yes—
100C22×Dic61—21no—
101C22×Dic61—21no—
102C22×Dic61—42no—
103C22×Dic61—41no—
104C22×Dic61—41no—
105C22×Dic61—41no—
106C22×Dic61—81no—
107C22×Dic61C22⋊C411yescharacteristic
108C22×Dic61C22⋊C411yescharacteristic
109C22×Dic61C22⋊C411yescharacteristic
110C2×C4×D61—21no—
111C2×C4×D61—21no—
112C2×C4×D61—81no—
113C2×C8×C61—22no—
114C2×C8×C61—81no—
115C4⋊C4×C61—21no—
116C4⋊C4×C61—21no—
117C4⋊C4×C61—41no—
118C4⋊C4×C61—41no—
119C4⋊C4×C61—81no—
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—42no—
131#11758198—81no—
132C4⋊Dic61—81no—
133#11758196—21no—
134#11758196—21no—
135#11758196—42no—
136#11758196—81no—
137C4×Dic61—21no—
138C4×Dic61—21no—
139C2×#92418—22no—
140C2×#92418—81no—
141C8×D61—82no—
142C23×C61—41no—
143C23×C61—41no—
144C23×C61C2×C22⋊C411yescharacteristic
145C23×C61#12111yescharacteristic
146C23×C61#12111yescharacteristic
147C23×C61C2×SD1611yescharacteristic
148C23×C61C2×Q1611yescharacteristic
149C23×C61#13511yescharacteristic
150C23×C61#13511yescharacteristic
151C22×D61—21no—
152C22×D61—21no—
153C22×D61—41no—
154C22×D61—41no—
155C22×D61#10312yes—
156Q8×C61—81no—
157Q8×C61—81no—
158C2×C4×C61—41no—
159C2×C4×C61—41no—
160C2×C4×C61—41no—
161C2×C4×C61—41no—
162C2×C4×C61—41no—
163C2×C4×C61—41no—
164C2×C4×C61—41no—
165C2×C4×C61—41no—
166C2×C4×C61—41no—
167C2×C4×C61—41no—
168C2×C4×C61—41no—
169C2×C4×C61—41no—
170C2×C4×C61—81no—
171C2×C4×C61—81no—
172C2×C4×C61—81no—
173C2×C4×C61C4×D411yescharacteristic
174C2×C4×C61C4×D411yescharacteristic
175C2×C4×C61#12011yescharacteristic
176C2×C4×C61#12311yescharacteristic
177C22⋊D61—22no—
178C22⋊D61—22no—
179C22⋊D61—22no—
180C22⋊D61—22no—
181C2×Dic61—21no—
182C2×Dic61—21no—
183C2×Dic61—22no—
184C2×Dic61—21no—
185C2×Dic61—21no—
186C2×Dic61—41no—
187C2×Dic61—41no—
188C2×Dic61—41no—
189C2×Dic61—41no—
190C2×Dic61—41no—
191C2×Dic61—41no—
192C2×Dic61—41no—
193C2×Dic61—82no—
194C2×Dic61—82no—
195C2×Dic61—81no—
196C2×Dic61—81no—
197C2×Dic61—81no—
198C2×Dic61#10312yes—
199C4×D61—42no—
200C4×D61—81no—
201C8×C61—42no—
202#92418—42no—
203#9383—611nomaximal, Sylow
204C22×C61—21no—
205C22×C61—21no—
206C22×C61—21no—
207C22×C61—21no—
208C22×C61—21no—
209C22×C61—21no—
210C22×C61—41no—
211C22×C61—41no—
212C22×C61—41no—
213C22×C61—41no—
214C22×C61#38611yescharacteristic
215C22×C61C2×#10311yescharacteristic
216C22×C61#41611yescharacteristic
217C22×C61#46511yescharacteristic
218C22×C61#46511yescharacteristic
219C22×C61#46711yescharacteristic
220C22×C61#46711yescharacteristic
221C2×D61—22no—
222C2×D61—41no—
223C2×D61—41no—
224C2×D61—42no—
225C2×D61—81no—
226C4×C61—21no—
227C4×C61—21no—
228C4×C61—21no—
229C4×C61—21no—
230C4×C61—81no—
231C4×C61—81no—
232C4×C61—161no—
233Dic61—22no—
234Dic61—42no—
235Dic61—41no—
236Dic61—41no—
237Dic61—81no—
238Dic61—161no—
239#2972—611no—
240#2564—611no—
241#1799—611no—
242#1520—611no—
243#1520D6111yescharacteristic, complemented
244#1294—611no—
245#1294—611no—
246C2×C61—21no—
247C2×C61—21no—
248C2×C61—21no—
249C2×C61—21no—
250C2×C61—21no—
251C2×C61—21no—
252C2×C61#188411yescharacteristic
253C2×C61#189211yescharacteristic
254C2×C61#191311yescharacteristic
255D61—42no—
256C2×C22⋊Q8C2×D6111yescharacteristic
257C2×C4×D4—611no—
258C8×D4—1222no—
259C8×D4—1222no—
260#431—1221no—
261C2×#99—1221no—
262C2×C22⋊C8—611no—
263C2×C22⋊C8—1221no—
264C2×C22⋊C8C2×D6111yescharacteristic
265#400—611no—
266#399—611no—
267#395—611no—
268#393—611no—
269#387—1221no—
270#386—1221no—
271#385—1221no—
272#380—611no—
273#380—1221no—
274#380C2×D6111yescharacteristic
275C2×#95—611no—
276#342—1221no—
277#328—22no—
278#328—1222no—
279C61#938311yescharacteristic, complemented, Sylow
280C22×Q8C4×D6111yescharacteristic
281C22×D4—611no—
282C23×C4—611no—
283C23×C4—1221no—
284C23×C4C22×D6111yescharacteristic
285C22×C8—21no—
286C22×C8—1222no—
287C22×C8—1221no—
288C22⋊Q8—21no—
289C22⋊Q8—21no—
290C22⋊Q8—21no—
291C22⋊Q8—21no—
292C4×D4—1221no—
293C4×D4—1221no—
294C4×D4—1221no—
295C4×D4—1221no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—611no—
299C2×C4⋊C4—1221no—
300C2×C4⋊C4—1221no—
301C2×C4⋊C4—1221no—
302C2×C4⋊C4C4×D6111yescharacteristic
303C2×C22⋊C4—21no—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—611no—
306C2×C22⋊C4—611no—
307C2×C22⋊C4—1221no—
308C2×C22⋊C4—1221no—
309C2×C22⋊C4—1221no—
310C2×C42—611no—
311C4⋊C8—1222no—
312#99—2442no—
313C22⋊C8—21no—
314C22⋊C8—612no—
315C22⋊C8—1222no—
316C22⋊C8—1221no—
317C22⋊C8C22⋊D6112yes—
318C4×C8—1222no—
319#95—21no—
320#95—611no—
321#95—611no—
322#95—1221no—
323#95—1221no—
324#95—1221no—
325#95—1221no—
326#95—1221no—
327#95—1221no—
328C24—611no—
329C24D4×D6111yescharacteristic
330C2×Q8—21no—
331C2×Q8—21no—
332C2×Q8—81no—
333C2×D4—612no—
334C2×D4—612no—
335C2×D4—1221no—
336C2×D4—1221no—
337C2×D4—1221no—
338C2×D4—1221no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—41no—
342C22×C4—81no—
343C22×C4—611no—
344C22×C4—611no—
345C22×C4—611no—
346C22×C4—1221no—
347C22×C4—1221no—
348C22×C4—1221no—
349C22×C4—1221no—
350C22×C4—4881no—
351C22×C4—4881no—
352C22×C4—2442no—
353C22×C4—2441no—
354C22×C4—2441no—
355C22×C4—2441no—
356C22×C4C2×C4×D6111yescharacteristic
357C22×C4#1175822211yescharacteristic
358C22×C4D4×D6111yescharacteristic
359C22×C4D4×D6111yescharacteristic
360C22×C4#1175822411yescharacteristic
361C22×C4C2×C22⋊D6111yescharacteristic
362C2×C8—22no—
363C2×C8—81no—
364C2×C8—1222no—
365C2×C8—4882no—
366C2×C8—4881no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—41no—
370C4⋊C4—41no—
371C4⋊C4—81no—
372C4⋊C4—1221no—
373C4⋊C4—1221no—
374C4⋊C4—4881no—
375C4⋊C4—4881no—
376C4⋊C4—2442no—
377C22⋊C4—41no—
378C22⋊C4—41no—
379C22⋊C4—41no—
380C22⋊C4—41no—
381C22⋊C4—1221no—
382C22⋊C4—1221no—
383C22⋊C4—1221no—
384C22⋊C4—1221no—
385C22⋊C4—4881no—
386C22⋊C4—2442no—
387C22⋊C4—2441no—
388C22⋊C4—2441no—
389C42—1221no—
390C42—1221no—
391C23—41no—
392C23—41no—
393C23—612no—
394C23—1221no—
395C23—1221no—
396C23—2441no—
397C23—2441no—
398C23C22⋊C4×D6111yescharacteristic
399C23#1451974811yescharacteristic
400C23#1451975011yescharacteristic
401C23SD16×D6111yescharacteristic
402C23Q16×D6111yescharacteristic
403C23#1451979811yescharacteristic
404C23#1451980011yescharacteristic
405Q8—81no—
406Q8—81no—
407D4—1222no—
408D4—1222no—
409D4—1222no—
410D4—1222no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—81no—
424C2×C4—81no—
425C2×C4—81no—
426C2×C4—612no—
427C2×C4—1221no—
428C2×C4—1221no—
429C2×C4—1222no—
430C2×C4—1221no—
431C2×C4—1221no—
432C2×C4—4881no—
433C2×C4—4881no—
434C2×C4—4881no—
435C2×C4—4881no—
436C2×C4—4882no—
437C2×C4—4882no—
438C2×C4—2442no—
439C2×C4—2441no—
440C2×C4—2441no—
441C2×C4—2441no—
442C2×C4—2441no—
443C2×C4—2441no—
444C2×C4—2441no—
445C2×C4—2441no—
446C2×C4#1451973711yescharacteristic
447C2×C4C4×C22⋊D6111yescharacteristic
448C2×C4#1451974511yescharacteristic
449C2×C4#1451975911yescharacteristic
450C8—42no—
451C8—2442no—
452C22—21no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—1222no—
463C22—4881no—
464C22—2442no—
465C22—2441no—
466C22—2441no—
467C22#1683963811yescharacteristic
468C22#103×D6111yescharacteristic
469C22#1683975711yescharacteristic
470C22#1683998811yescharacteristic
471C22#1683999411yescharacteristic
472C22#1684000011yescharacteristic
473C22#1684000211yescharacteristic
474C4—21no—
475C4—21no—
476C4—21no—
477C4—21no—
478C4—81no—
479C4—81no—
480C4—161no—
481C4—1222no—
482C4—9761no—
483C4—4881no—
484C4—2442no—
485C4—2441no—
486C4—2441no—
487C2—21no—
488C2—21no—
489C2—21no—
490C2—21no—
491C2—21no—
492C2—21no—
493C2—2442no—
494C2#2144619911yescharacteristic
495C2#2144623911yescharacteristic
496C2#2144635811yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1520C2
socleC22×C61#386
prime radicalC22×C22⋊D61D4
cosocleC23×C4×C61C23
hypercenter#1520D61
hypocenterC61#9383
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1520

Complements

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

NH ≅ G/Ntype
4. #21444391C2semidirect
5. #21443699C2semidirect
6. #21443697C2semidirect
7. C61×#1520C2semidirect
15. #16839700C4semidirect
16. #16839697C4semidirect
17. #16839681C4semidirect
18. #16839673C4semidirect
243. #1520D61semidirect
279. C61#9383semidirect

Maximal subgroups

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

subgroupindex
#214548412
#214510012
#214458042
#214443912
#214436992
#214436972
C61×#15202
#938361