Finite Group Databasebeta

← #29677286

Subgroups — #29677286

Order 15616.

560 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458749C211yesmaximal, characteristic, complemented
2#21458629C211yesmaximal, characteristic
3#21458622C211yesmaximal, characteristic, complemented
4#21445418C211yesmaximal, characteristic
5#21445375C211yesmaximal, characteristic, complemented
6#21445357C211yesmaximal, characteristic
7#21445325C211yesmaximal, characteristic, complemented
8#21445288C211yesmaximal, characteristic
9#21445038C211yesmaximal, characteristic, complemented
10#21445005C211yesmaximal, characteristic
11#21444977C211yesmaximal, characteristic, complemented
12#21444914C211yesmaximal, characteristic
13#21444716C211yesmaximal, characteristic, complemented
14#21444714C211yesmaximal, characteristic, complemented
15C61×#3400C211yesmaximal, characteristic
16Q8×Dic122C2211yescharacteristic
17#16840491C2211yescharacteristic
18#16840170—21no—
19#16840160C2211yescharacteristic
20#16840132—21no—
21#16840121—21no—
22#16840114C2211yescharacteristic
23#16840114C2211yescharacteristic
24#16840108C2211yescharacteristic
25#16840108C2211yescharacteristic
26#16840067—21no—
27#16840066—21no—
28#16840057C2211yescharacteristic
29#16840057C2211yescharacteristic
30#16840047C2211yescharacteristic
31#16840045—21no—
32#16840044C2211yescharacteristic
33#16840042—21no—
34#16839981—21no—
35#16839972—21no—
36#16839972C2211yescharacteristic
37#16839959C2211yescharacteristic
38#16839893C2211yescharacteristic
39#16839893C2211yescharacteristic
40#16839892C2211yescharacteristic
41#16839869—21no—
42#16839867—21no—
43#16839862—21no—
44C4×#11758202C2211yescharacteristic
45#16839515C2211yescharacteristic
46#16839514C2211yescharacteristic
47#16839510C2211yescharacteristic
48#16839508C2211yescharacteristic
49#16839507C2211yescharacteristic
50#16839506C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic
52Q8⋊#92418C2211yescharacteristic
53Q8⋊#92418C2211yescharacteristic
54#16839492C2211yescharacteristic
55C8×#92418C2211yescharacteristic
56C61×#559C2211yescharacteristic
57C61×#557C2211yescharacteristic
58C61×#497—21no—
59C61×#492C2211yescharacteristic
60C61×#464—21no—
61C61×#462C2211yescharacteristic
62C61×#461—21no—
63C61×#460C2211yescharacteristic
64C61×#446C2211yescharacteristic
65C61×#440—21no—
66C4×Q16×C61C2211yescharacteristic
67C2×#11758202—21no—
68C2×#11758202D411yescharacteristic
69C2×#11758200—21no—
70#14519777—21no—
71#14519777—21no—
72#14519777C2311yescharacteristic
73#14519777C2311yescharacteristic
74#14519776—21no—
75#14519776—41no—
76#14519768—21no—
77#14519768—41no—
78Q8×Dic61—21no—
79Q8×Dic61—21no—
80C4×Dic122—21no—
81C4×Dic122—21no—
82C4×Dic122C2311yescharacteristic
83#14519710—21no—
84#14519710—21no—
85#14519710D411yescharacteristic
86#14519709—21no—
87#14519709—21no—
88#14519708—21no—
89#14519708—21no—
90C4⋊#92418—21no—
91C4⋊#92418—21no—
92C4⋊#92418C2311yescharacteristic
93C4⋊#92418C2311yescharacteristic
94C4⋊#92418C2311yescharacteristic
95#14519706—21no—
96#14519701—21no—
97#14519701—21no—
98#14519701—21no—
99#14519701D411yescharacteristic
100#14519700—21no—
101#14519700—21no—
102#14519700—21no—
103#14519700—21no—
104#14519700—41no—
105#14519700D411yescharacteristic
106#14519698—21no—
107#14519698—21no—
108#14519698—21no—
109#14519698—41no—
110#14519688—21no—
111#14519688—21no—
112#14519687—21no—
113C4×#92418C2311yescharacteristic
114C4×#92418C2311yescharacteristic
115C2×Q16×C61—21no—
116C2×Q16×C61D411yescharacteristic
117C2×SD16×C61—21no—
118C2×SD16×C61—21no—
119C2×SD16×C61—21no—
120C4⋊Q8×C61—21no—
121C4⋊Q8×C61C2311yescharacteristic
122#127×C61C2311yescharacteristic
123#125×C61—21no—
124#125×C61—41no—
125#124×C61—21no—
126#124×C61—21no—
127#123×C61—41no—
128C4×Q8×C61—21no—
129C4×Q8×C61—21no—
130C4×Q8×C61C2311yescharacteristic
131C4×Q8×C61C2311yescharacteristic
132C4×Q8×C61C2311yescharacteristic
133C4×D4×C61—21no—
134C4×D4×C61—21no—
135#107×C61D411yescharacteristic
136C4⋊C8×C61—21no—
137C4⋊C8×C61C2311yescharacteristic
138#103×C61—21no—
139#103×C61D411yescharacteristic
140#103×C61D411yescharacteristic
141#102×C61—21no—
142#97×C61—21no—
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61—21no—
145C2×Q8×C61C2×D411yescharacteristic
146C2×Q8×C61C2×D411yescharacteristic
147C2×Q8×C61C2×D411yescharacteristic
148C2×D4×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C22×C4×C61—41no—
152C2×Dic122—21no—
153C2×Dic122—21no—
154C2×Dic122—41no—
155C2×Dic122C2×D411yescharacteristic
156Q16×C61—22no—
157Q16×C61—81no—
158SD16×C61—42no—
159SD16×C61—81no—
160SD16×C61—81no—
161C2×C8×C61—21no—
162C2×C8×C61C2×D411yescharacteristic
163C2×C8×C61C2×D411yescharacteristic
164C4⋊C4×C61—21no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—41no—
170C4⋊C4×C61—41no—
171C4⋊C4×C61—41no—
172C4⋊C4×C61C2×D411yescharacteristic
173C4⋊C4×C61C2×D411yescharacteristic
174C4⋊C4×C61C2×D411yescharacteristic
175C22⋊C4×C61—41no—
176C22⋊C4×C61—41no—
177C22⋊C4×C61—41no—
178C42×C61—21no—
179C42×C61—21no—
180C42×C61—21no—
181C42×C61—41no—
182C42×C61C2411yescharacteristic
183#11758202—41no—
184#11758202—42no—
185#11758200—42no—
186C4⋊Dic61—21no—
187C4⋊Dic61—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61—41no—
191C4⋊Dic61—41no—
192C4⋊Dic61—41no—
193C4⋊Dic61C2×D411yescharacteristic
194#11758196—21no—
195#11758196—41no—
196#11758196—41no—
197C4×Dic61—21no—
198C4×Dic61—41no—
199C4×Dic61—41no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418C2×D411yescharacteristic
205C2×#92418C2×D411yescharacteristic
206C23×C61—41no—
207Q8×C61—21no—
208Q8×C61—21no—
209Q8×C61—21no—
210Q8×C61—21no—
211Q8×C61—21no—
212Q8×C61—21no—
213Q8×C61—41no—
214Q8×C61—41no—
215D4×C61—41no—
216D4×C61—41no—
217D4×C61—41no—
218D4×C61—41no—
219D4×C61—81no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—41no—
227C2×C4×C61—161no—
228C2×C4×C61C22×D411yescharacteristic
229C2×C4×C61C22×D411yescharacteristic
230C2×C4×C61H(5,𝔽2)11yescharacteristic
231C2×Dic61—21no—
232C2×Dic61—21no—
233C2×Dic61—41no—
234C2×Dic61—41no—
235Dic122—21no—
236Dic122—21no—
237Dic122—41no—
238Dic122—41no—
239Dic122—81no—
240Dic122—161no—
241C8×C61—21no—
242C8×C61—41no—
243C8×C61#13712yes—
244#92418—21no—
245#92418—21no—
246#92418—41no—
247#92418—41no—
248#92418—41no—
249#92418—41no—
250#20320—611nomaximal, Sylow
251C22×C61—81no—
252C22×C61—81no—
253C22×C61—81no—
254C22×C61D4211yescharacteristic
255C4×C61—21no—
256C4×C61—41no—
257C4×C61—41no—
258C4×C61—41no—
259C4×C61—41no—
260C4×C61—41no—
261C4×C61—41no—
262C4×C61—81no—
263C4×C61C2×#13711yescharacteristic
264C4×C61#57511yescharacteristic
265C4×C61#57711yescharacteristic
266C4×C61#57811yescharacteristic
267Dic61—41no—
268Dic61—41no—
269Dic61—81no—
270Dic61—81no—
271#3400D6111yescharacteristic
272#3387—611no—
273#3375—611no—
274#3374—611no—
275#1708—611no—
276#1700—611no—
277#1698—611no—
278#1692—611no—
279#1686—611no—
280#1645—611no—
281#1640—611no—
282#1636—611no—
283#1626—611no—
284#1591—611no—
285#1591—611no—
286C2×C61—161no—
287C2×C61#327711yescharacteristic
288C2×C61#327811yescharacteristic
289C2×C61#329011yescharacteristic
290#559C2×D6111yescharacteristic
291Q82—611no—
292#557—611no—
293#557C2×D6111yescharacteristic
294#501—1221no—
295#498—611no—
296#497—21no—
297#492C2×D6111yescharacteristic
298#491—1221no—
299#489—1221no—
300#487—611no—
301#487—611no—
302#486—611no—
303#486—611no—
304#479—1221no—
305#479—1221no—
306#477—611no—
307#477—611no—
308#475—611no—
309#475—611no—
310#475—1221no—
311#474—1221no—
312#464—21no—
313#464—1221no—
314#462—611no—
315#462—1221no—
316#462C2×D6111yescharacteristic
317#461—21no—
318#460—611no—
319#460C2×D6111yescharacteristic
320#446—611no—
321#446—611no—
322#446—611no—
323#446C2×D6111yescharacteristic
324#441—1221no—
325#441—1221no—
326#440—21no—
327#440—1221no—
328C4×Q16—611no—
329C4×Q16C2×D6111yescharacteristic
330#335—611no—
331#335—611no—
332#333—611no—
333#332—611no—
334#332—611no—
335#331—611no—
336Q8⋊C8—611no—
337Q8⋊C8—611no—
338Q8⋊C8—611no—
339Q8⋊C8—611no—
340C82—611no—
341C61#2032011yescharacteristic, complemented, Sylow
342C2×Q16—21no—
343C2×Q16—611no—
344C2×Q16—1221no—
345C2×Q16C22⋊D6111yescharacteristic
346C2×SD16—21no—
347C2×SD16—21no—
348C2×SD16—21no—
349C2×SD16—1221no—
350C4⋊Q8—21no—
351C4⋊Q8—611no—
352C4⋊Q8—611no—
353C4⋊Q8—1221no—
354C4⋊Q8—1221no—
355C4⋊Q8—1221no—
356C4⋊Q8—2441no—
357C4⋊Q8C22×D6111yescharacteristic
358#127C22×D6111yescharacteristic
359#125—21no—
360#125—41no—
361#125—1221no—
362#125—2441no—
363#124—21no—
364#124—21no—
365#123—41no—
366C4×Q8—21no—
367C4×Q8—21no—
368C4×Q8—611no—
369C4×Q8—1221no—
370C4×Q8—1221no—
371C4×Q8—1221no—
372C4×Q8—1221no—
373C4×Q8C22×D6111yescharacteristic
374C4×Q8C22×D6111yescharacteristic
375C4×Q8C22×D6111yescharacteristic
376C4×D4—21no—
377C4×D4—21no—
378#107—611no—
379#107—1221no—
380#107—1221no—
381#107C22⋊D6111yescharacteristic
382#106—1221no—
383#106—1221no—
384#106—1221no—
385#106—1221no—
386C4⋊C8—21no—
387C4⋊C8—611no—
388C4⋊C8—611no—
389C4⋊C8—611no—
390C4⋊C8—1221no—
391C4⋊C8—1221no—
392C4⋊C8—1221no—
393C4⋊C8C22×D6111yescharacteristic
394#103—21no—
395#103—611no—
396#103—611no—
397#103—1221no—
398#103—1221no—
399#103—1221no—
400#103—1221no—
401#103—1221no—
402#103—1221no—
403#103—1221no—
404#103—2441no—
405#103C22⋊D6111yescharacteristic
406#103C22⋊D6111yescharacteristic
407#102—21no—
408#102—1221no—
409#102—1221no—
410#102—1221no—
411#102—2441no—
412#97—21no—
413#97—1221no—
414#97—1221no—
415#97—1221no—
416C4×C8—611no—
417C4×C8—611no—
418C4×C8C22×D6111yescharacteristic
419C2×Q8—21no—
420C2×Q8—611no—
421C2×Q8—1221no—
422C2×Q8—1221no—
423C2×Q8—2441no—
424C2×Q8D4×D6111yescharacteristic
425C2×Q8C2×C22⋊D6111yescharacteristic
426C2×Q8C2×C22⋊D6111yescharacteristic
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C22×C4—41no—
431Q16—22no—
432Q16—81no—
433Q16—2441no—
434Q16—2442no—
435SD16—42no—
436SD16—81no—
437SD16—81no—
438SD16—2442no—
439C2×C8—21no—
440C2×C8—611no—
441C2×C8—611no—
442C2×C8—1221no—
443C2×C8—1221no—
444C2×C8—1221no—
445C2×C8—1221no—
446C2×C8C2×C22⋊D6111yescharacteristic
447C2×C8C2×C22⋊D6111yescharacteristic
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—41no—
454C4⋊C4—41no—
455C4⋊C4—41no—
456C4⋊C4—611no—
457C4⋊C4—1221no—
458C4⋊C4—1221no—
459C4⋊C4—1221no—
460C4⋊C4—1221no—
461C4⋊C4—1221no—
462C4⋊C4—2441no—
463C4⋊C4—2441no—
464C4⋊C4—2441no—
465C4⋊C4—2441no—
466C4⋊C4—2441no—
467C4⋊C4D4×D6111yescharacteristic
468C4⋊C4C2×C22⋊D6111yescharacteristic
469C4⋊C4C2×C22⋊D6111yescharacteristic
470C22⋊C4—41no—
471C22⋊C4—41no—
472C22⋊C4—41no—
473C42—21no—
474C42—21no—
475C42—21no—
476C42—41no—
477C42—1221no—
478C42—2441no—
479C42—2441no—
480C42C23×D6111yescharacteristic
481C23—41no—
482Q8—21no—
483Q8—21no—
484Q8—21no—
485Q8—21no—
486Q8—21no—
487Q8—21no—
488Q8—41no—
489Q8—41no—
490Q8—1221no—
491Q8—1221no—
492Q8—9761no—
493Q8—4881no—
494Q8—2441no—
495Q8—2441no—
496D4—41no—
497D4—41no—
498D4—41no—
499D4—41no—
500D4—81no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—41no—
508C2×C4—161no—
509C2×C4—1221no—
510C2×C4—1221no—
511C2×C4—2441no—
512C2×C4—2441no—
513C2×C4C2×D4×D6111yescharacteristic
514C2×C4C22×C22⋊D6111yescharacteristic
515C2×C4#1451982211yescharacteristic
516C8—21no—
517C8—41no—
518C8—1221no—
519C8—1221no—
520C8—2441no—
521C8—2441no—
522C8—2441no—
523C8—2441no—
524C8#1451980712yes—
525C22—81no—
526C22—81no—
527C22—81no—
528C22D4×C22⋊D6111yescharacteristic
529C4—21no—
530C4—41no—
531C4—41no—
532C4—41no—
533C4—41no—
534C4—41no—
535C4—41no—
536C4—81no—
537C4—4881no—
538C4—4881no—
539C4—2441no—
540C4—2441no—
541C4C2×#1451980711yescharacteristic
542C4#1684056111yescharacteristic
543C4#1684057311yescharacteristic
544C4#1684057811yescharacteristic
545C2—161no—
546C2#2145747011yescharacteristic
547C2#2145748511yescharacteristic
548C2#2145759911yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3400C2
socleC22×C61D42
prime radical#127×C61C23
hypercenter#3400D61
hypocenterC61#20320
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3400

Complements

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

NH ≅ G/Ntype
1. #21458749C2semidirect
3. #21458622C2semidirect
5. #21445375C2semidirect
7. #21445325C2semidirect
9. #21445038C2semidirect
11. #21444977C2semidirect
13. #21444716C2semidirect
14. #21444714C2semidirect
341. C61#20320semidirect

Maximal subgroups

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

subgroupindex
#214587492
#214586292
#214586222
#214454182
#214453752
#214453572
#214453252
#214452882
#214450382
#214450052
#214449772
#214449142
#214447162
#214447142
C61×#34002
#2032061