Finite Group Databasebeta

← #29574018

Subgroups — #29574018

Order 15616.

692 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21448416C211yesmaximal, characteristic
2#21446014C211yesmaximal, characteristic, complemented
3#21446006C211yesmaximal, characteristic, complemented
4C2×#16839485C211yesmaximal, characteristic
5#21444065C211yesmaximal, characteristic
6#21443698C211yesmaximal, characteristic, complemented
7C61×#1294C211yesmaximal, characteristic, complemented
8C22×C4⋊Dic61C2211yescharacteristic
9C22×#11758198—21no—
10C22×#11758198C2211yescharacteristic
11C2×#14519710—21no—
12C2×#14519709—21no—
13C2×C22⋊#92418C2211yescharacteristic
14#16839654—21no—
15#16839654—21no—
16#16839652—21no—
17#16839652—21no—
18#16839622C2211yescharacteristic
19#16839617—21no—
20C22⋊C4×Dic61—21no—
21C2×#14519684—21no—
22#16839525—21no—
23#16839524—21no—
24#16839485C414yescomplemented
25C2×C22⋊C8×C61C2211yescharacteristic
26C61×#380C2211yescharacteristic
27C2×#95×C61C2211yescharacteristic
28C24×D61D411yescharacteristic
29C23×Dic61—21no—
30C23×Dic61D411yescharacteristic
31C22×#92418—21no—
32C2×C4⋊Dic61—21no—
33C2×C4⋊Dic61—21no—
34C2×C4⋊Dic61—42no—
35C2×C4⋊Dic61D411yescharacteristic
36C2×C4⋊Dic61D411yescharacteristic
37C2×C22⋊Dic61—21no—
38C2×#11758198—21no—
39C2×#11758198—21no—
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×#11758198—21no—
45C2×#11758198—21no—
46C2×#11758198—42no—
47C2×#11758198—42no—
48C2×#11758198—42no—
49C2×#11758198C2×C412yes—
50C2×#11758198Q812yes—
51C2×C4×Dic61—21no—
52C2×C4×Dic61—21no—
53#14519710—42no—
54#14519709—42no—
55C22⋊#92418—21no—
56C22⋊#92418C2×C412yes—
57#14519684—21no—
58#14519684—21no—
59#14519684—21no—
60#14519684—42no—
61C23×C4×C61—21no—
62C23×C4×C61C2311yescharacteristic
63C22×C8×C61—21no—
64C2×C4⋊C4×C61D411yescharacteristic
65C2×C4⋊C4×C61D411yescharacteristic
66C2×C22⋊C4×C61—21no—
67C22⋊C8×C61—21no—
68C22⋊C8×C61C2×C412yes—
69#95×C61—21no—
70#95×C61—21no—
71#95×C61—21no—
72C24×C61C2×D411yescharacteristic
73C23×D61—21no—
74C23×D61—21no—
75C23×D61—21no—
76C23×D61—21no—
77C23×D61—21no—
78C23×D61—21no—
79C23×D61—41no—
80C23×D61—41no—
81C23×D61—41no—
82C23×D61—41no—
83C23×D61C4⋊C412yes—
84C22×C4×C61—22no—
85C22×C4×C61—21no—
86C22×C4×C61—21no—
87C22×C4×C61—41no—
88C22×C4×C61—41no—
89C22×C4×C61—41no—
90C22×C4×C61—41no—
91C22×C4×C61—41no—
92C22×C4×C61—41no—
93C22×C4×C61—41no—
94C22×C4×C61—41no—
95C22×C4×C61C22×C411yescharacteristic
96C22×C4×C61C2×D411yescharacteristic
97C22×C4×C61C2×D411yescharacteristic
98C22×C4×C61C2×Q811yescharacteristic
99C22×C4×C61#4111yescharacteristic
100C22×C4×C61#4111yescharacteristic
101C22×Dic61—21no—
102C22×Dic61—21no—
103C22×Dic61—22no—
104C22×Dic61—21no—
105C22×Dic61—21no—
106C22×Dic61—41no—
107C22×Dic61—41no—
108C22×Dic61—41no—
109C22×Dic61—41no—
110C22×Dic61—41no—
111C22×Dic61—41no—
112C22×Dic61—41no—
113C22×Dic61—41no—
114C22×Dic61C4⋊C412yes—
115C2×C8×C61—22no—
116C2×C8×C61—41no—
117C2×C8×C61—41no—
118C4⋊C4×C61—41no—
119C4⋊C4×C61—41no—
120C22⋊C4×C61—41no—
121C22⋊C4×C61—41no—
122C22⋊Dic61—41no—
123C22⋊Dic61—41no—
124#11758198—22no—
125#11758198—22no—
126#11758198—22no—
127#11758198—22no—
128#11758198—48no—
129#11758198—81no—
130#11758198—81no—
131#11758198—81no—
132#11758198—81no—
133C4⋊Dic61—22no—
134C4⋊Dic61—22no—
135C4⋊Dic61—41no—
136C4⋊Dic61—41no—
137C4⋊Dic61—41no—
138C4⋊Dic61—41no—
139C4×Dic61—81no—
140C4×Dic61—81no—
141C2×#92418—22no—
142C2×#92418—41no—
143C2×#92418—41no—
144C23×C61—21no—
145C23×C61—21no—
146C23×C61—21no—
147C23×C61—21no—
148C23×C61C2×C4⋊C411yescharacteristic
149C23×C61#12011yescharacteristic
150C23×C61#12311yescharacteristic
151C23×C61#13511yescharacteristic
152C23×C61#13511yescharacteristic
153C23×C61AGL(1,ℤ/8)11yescharacteristic
154C23×C61#13711yescharacteristic
155C22×D61—22no—
156C22×D61—22no—
157C22×D61—22no—
158C22×D61—42no—
159C22×D61—42no—
160C22×D61—42no—
161C22×D61—42no—
162C22×D61—42no—
163C22×D61—42no—
164C22×D61—41no—
165C22×D61—41no—
166C22×D61—41no—
167C22×D61—41no—
168C22×D61—41no—
169C22×D61—41no—
170C22×D61—41no—
171C22×D61—41no—
172C22×D61—81no—
173C22×D61—81no—
174C22×D61—81no—
175C22×D61—81no—
176C22×D61—81no—
177C22×D61—81no—
178C2×C4×C61—21no—
179C2×C4×C61—21no—
180C2×C4×C61—21no—
181C2×C4×C61—21no—
182C2×C4×C61—41no—
183C2×C4×C61—41no—
184C2×C4×C61—41no—
185C2×C4×C61—41no—
186C2×C4×C61—42no—
187C2×C4×C61—42no—
188C2×C4×C61—42no—
189C2×C4×C61—41no—
190C2×C4×C61—41no—
191C2×C4×C61—41no—
192C2×C4×C61—41no—
193C2×C4×C61—41no—
194C2×C4×C61—41no—
195C2×C4×C61—81no—
196C2×C4×C61—81no—
197C2×C4×C61—81no—
198C2×C4×C61—81no—
199C2×C4×C61C4×D411yescharacteristic
200C2×C4×C61C4×D411yescharacteristic
201C2×C4×C61C22⋊Q811yescharacteristic
202C2×C4×C61C22⋊Q811yescharacteristic
203C2×Dic61—22no—
204C2×Dic61—41no—
205C2×Dic61—41no—
206C2×Dic61—42no—
207C2×Dic61—42no—
208C2×Dic61—42no—
209C2×Dic61—41no—
210C2×Dic61—41no—
211C2×Dic61—41no—
212C2×Dic61—41no—
213C2×Dic61—42no—
214C2×Dic61—41no—
215C2×Dic61—41no—
216C2×Dic61—81no—
217C2×Dic61—81no—
218C2×Dic61—81no—
219C2×Dic61—81no—
220C2×Dic61—81no—
221C8×C61—42no—
222#92418—42no—
223#8858—611nomaximal, Sylow
224C22×C61—21no—
225C22×C61—21no—
226C22×C61—21no—
227C22×C61—21no—
228C22×C61—21no—
229C22×C61—21no—
230C22×C61—21no—
231C22×C61—21no—
232C22×C61—21no—
233C22×C61—21no—
234C22×C61—21no—
235C22×C61—21no—
236C22×C61#38511yescharacteristic
237C22×C61#42711yescharacteristic
238C22×C61#42811yescharacteristic
239C22×C61#44911yescharacteristic
240C22×C61#45211yescharacteristic
241C22×C61#45311yescharacteristic
242C22×C61#45511yescharacteristic
243C22×C61B(4,𝔽2)11yescharacteristic
244C22×C61#45811yescharacteristic
245C22×C61#48211yescharacteristic
246C22×C61#48511yescharacteristic
247C2×D61—44no—
248C2×D61—42no—
249C2×D61—42no—
250C2×D61—42no—
251C2×D61—82no—
252C2×D61—82no—
253C2×D61—81no—
254C2×D61—81no—
255C2×D61—81no—
256C2×D61—81no—
257C2×D61—82no—
258C4×C61—21no—
259C4×C61—21no—
260C4×C61—21no—
261C4×C61—21no—
262C4×C61—82no—
263C4×C61—81no—
264C4×C61—81no—
265Dic61—42no—
266Dic61—82no—
267Dic61—81no—
268Dic61—81no—
269#2312—611no—
270#1853—611no—
271#1852—611no—
272C2×#323—611no—
273#1439—611no—
274#1294—611no—
275#1294D6111yescharacteristic, complemented
276C2×C61—21no—
277C2×C61—21no—
278C2×C61—21no—
279C2×C61—21no—
280C2×C61#160011yescharacteristic
281C2×C61#160611yescharacteristic
282C2×C61#161211yescharacteristic
283C2×C61#161811yescharacteristic
284C2×C61#185411yescharacteristic
285C2×C61#185611yescharacteristic
286C2×C61#186711yescharacteristic
287D61—82no—
288C22×C4⋊C4—611no—
289C22×C22⋊C4—611no—
290C22×C22⋊C4—1221no—
291C2×#107—1221no—
292C2×#106—1221no—
293C2×C22⋊C8—611no—
294C2×C22⋊C8C2×D6111yescharacteristic
295#388—1221no—
296#388—1221no—
297#388—1221no—
298#388—1221no—
299#380—611no—
300#380C2×D6111yescharacteristic
301#379—1221no—
302C4×C22⋊C4—1221no—
303C2×#95—1221no—
304C2×#95C2×D6111yescharacteristic
305#340—1221no—
306#340—1221no—
307#323—614no—
308C61#885811yescharacteristic, complemented, Sylow
309C25—611no—
310C23×C4—21no—
311C23×C4—611no—
312C23×C4—1221no—
313C23×C4C22×D6111yescharacteristic
314C22×C8—21no—
315C22×C8—1221no—
316C2×C4⋊C4—611no—
317C2×C4⋊C4—611no—
318C2×C4⋊C4—1221no—
319C2×C4⋊C4—1221no—
320C2×C4⋊C4—2442no—
321C2×C4⋊C4D24411yescharacteristic
322C2×C4⋊C4D24411yescharacteristic
323C2×C22⋊C4—21no—
324C2×C22⋊C4—612no—
325C2×C22⋊C4—612no—
326C2×C22⋊C4—1221no—
327C2×C22⋊C4—1221no—
328C2×C22⋊C4—1221no—
329C2×C22⋊C4—1221no—
330C2×C22⋊C4—1221no—
331C2×C22⋊C4—1221no—
332C2×C22⋊C4—1221no—
333C2×C22⋊C4—1221no—
334C2×C22⋊C4—1221no—
335C2×C22⋊C4—2442no—
336C2×C22⋊C4—2442no—
337C2×C22⋊C4—2442no—
338C2×C42—1221no—
339C2×C42—1221no—
340#107—2442no—
341#106—2442no—
342C22⋊C8—21no—
343C22⋊C8—612no—
344C22⋊C8—1221no—
345C22⋊C8C4×D6112yes—
346#95—21no—
347#95—21no—
348#95—21no—
349#95—1221no—
350#95—1221no—
351#95—1221no—
352#95—2442no—
353C24—612no—
354C24—1221no—
355C24—1221no—
356C24—1221no—
357C24—1221no—
358C24—1221no—
359C24—1221no—
360C24—2441no—
361C24—2441no—
362C24—2441no—
363C24—2441no—
364C24D4×D6111yescharacteristic
365C22×C4—22no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—41no—
369C22×C4—41no—
370C22×C4—41no—
371C22×C4—41no—
372C22×C4—41no—
373C22×C4—41no—
374C22×C4—41no—
375C22×C4—41no—
376C22×C4—612no—
377C22×C4—1221no—
378C22×C4—1221no—
379C22×C4—1222no—
380C22×C4—1221no—
381C22×C4—1221no—
382C22×C4—2441no—
383C22×C4—2441no—
384C22×C4—2441no—
385C22×C4—2441no—
386C22×C4—2441no—
387C22×C4—2441no—
388C22×C4—2441no—
389C22×C4—2441no—
390C22×C4C2×C4×D6111yescharacteristic
391C22×C4C2×D24411yescharacteristic
392C22×C4#1175822211yescharacteristic
393C22×C4D4×D6111yescharacteristic
394C22×C4#1175822411yescharacteristic
395C22×C4Q8×D6111yescharacteristic
396C2×C8—22no—
397C2×C8—41no—
398C2×C8—41no—
399C2×C8—1222no—
400C2×C8—2441no—
401C2×C8—2441no—
402C4⋊C4—41no—
403C4⋊C4—41no—
404C4⋊C4—1222no—
405C4⋊C4—1222no—
406C4⋊C4—2441no—
407C4⋊C4—2441no—
408C4⋊C4—2441no—
409C4⋊C4—2441no—
410C22⋊C4—41no—
411C22⋊C4—41no—
412C22⋊C4—1222no—
413C22⋊C4—1222no—
414C22⋊C4—1222no—
415C22⋊C4—1222no—
416C22⋊C4—4881no—
417C22⋊C4—4881no—
418C22⋊C4—4881no—
419C22⋊C4—4881no—
420C22⋊C4—2448no—
421C22⋊C4—2441no—
422C22⋊C4—2441no—
423C42—4881no—
424C42—4881no—
425C23—21no—
426C23—21no—
427C23—21no—
428C23—21no—
429C23—1222no—
430C23—1222no—
431C23—1222no—
432C23—4881no—
433C23—4881no—
434C23—4881no—
435C23—4881no—
436C23—4881no—
437C23—4881no—
438C23—2442no—
439C23—2442no—
440C23—2442no—
441C23—2442no—
442C23—2442no—
443C23—2442no—
444C23—2441no—
445C23—2441no—
446C23—2441no—
447C23—2441no—
448C23—2441no—
449C23—2441no—
450C23—2441no—
451C23—2441no—
452C23C4⋊C4×D6111yescharacteristic
453C23#1451974711yescharacteristic
454C23#1451975911yescharacteristic
455C23#1451979811yescharacteristic
456C23#1451979811yescharacteristic
457C23#1451980111yescharacteristic
458C23#1451980911yescharacteristic
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—81no—
477C2×C4—81no—
478C2×C4—81no—
479C2×C4—81no—
480C2×C4—1222no—
481C2×C4—4881no—
482C2×C4—4881no—
483C2×C4—4881no—
484C2×C4—4881no—
485C2×C4—4881no—
486C2×C4—2442no—
487C2×C4—2442no—
488C2×C4—2441no—
489C2×C4—2441no—
490C2×C4—2442no—
491C2×C4—2441no—
492C2×C4—2441no—
493C2×C4—2441no—
494C2×C4—2441no—
495C2×C4—2441no—
496C2×C4—2441no—
497C2×C4—2442no—
498C2×C4#1451973711yescharacteristic
499C2×C4C4×D24411yescharacteristic
500C2×C4#1451975511yescharacteristic
501C2×C4#1451975711yescharacteristic
502C8—42no—
503C8—2442no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—21no—
514C22—21no—
515C22—21no—
516C22—4882no—
517C22—4882no—
518C22—4882no—
519C22—4881no—
520C22—4881no—
521C22—4881no—
522C22—4881no—
523C22—2444no—
524C22—2442no—
525C22—2442no—
526C22—2442no—
527C22#1683963611yescharacteristic
528C22#1683979711yescharacteristic
529C22#1683980311yescharacteristic
530C22#1683990811yescharacteristic
531C22#1683992711yescharacteristic
532C22#1683993111yescharacteristic
533C22#1683994111yescharacteristic
534C22#1683995011yescharacteristic
535C22#1683995311yescharacteristic
536C22#1684008511yescharacteristic
537C22#1684010111yescharacteristic
538C4—21no—
539C4—21no—
540C4—21no—
541C4—21no—
542C4—82no—
543C4—81no—
544C4—81no—
545C4—4881no—
546C4—4882no—
547C4—4881no—
548C4—2442no—
549C2—21no—
550C2—21no—
551C2—21no—
552C2—21no—
553C2—4882no—
554C2#2144476611yescharacteristic
555C2#2144480211yescharacteristic
556C2#2144483411yescharacteristic
557C2#2144487011yescharacteristic
558C2#2144601911yescharacteristic
559C2#2144603011yescharacteristic
560C2#2144610111yescharacteristic
subgroupG/H
centerC23#14519747
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1294C2
socleC23×C61#120
prime radicalC24×D61D4
cosocleC23×C4×C61C23
hypercenter#1294D61
hypocenterC61#8858
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
2. #21446014C2semidirect
3. #21446006C2semidirect
6. #21443698C2semidirect
7. C61×#1294C2semidirect
24. #16839485C4semidirect
275. #1294D61semidirect
308. C61#8858semidirect

Maximal subgroups

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

subgroupindex
#214484162
#214460142
#214460062
C2×#168394852
#214440652
#214436982
C61×#12942
#885861