Finite Group Databasebeta

← #29670241

Subgroups — #29670241

Order 15616.

590 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458714C211yesmaximal, characteristic
2#21458682C211yesmaximal, characteristic
3#21458213C211yesmaximal, characteristic, complemented
4#21445499C211yesmaximal, characteristic, complemented
5#21445345C211yesmaximal, characteristic, complemented
6#21445267C211yesmaximal, characteristic, complemented
7#21445218C211yesmaximal, characteristic, complemented
8#21445199C211yesmaximal, characteristic, complemented
9#21445031C211yesmaximal, characteristic, complemented
10#21444984C211yesmaximal, characteristic, complemented
11#21444953C211yesmaximal, characteristic, complemented
12#21444952C211yesmaximal, characteristic, complemented
13#21444670C211yesmaximal, characteristic, complemented
14#21444641C211yesmaximal, characteristic
15C61×#3299C211yesmaximal, characteristic, complemented
16#16840472C2211yescharacteristic
17#16840472C2211yescharacteristic
18#16840168—21no—
19#16840167C2211yescharacteristic
20#16840165C2211yescharacteristic
21#16840161—21no—
22#16840158C2211yescharacteristic
23#16840141C2211yescharacteristic
24#16840114C2211yescharacteristic
25#16840096—21no—
26#16840096—21no—
27#16840062—21no—
28#16840062—21no—
29#16840059—21no—
30#16840057C2211yescharacteristic
31#16840057C2211yescharacteristic
32#16840052C2211yescharacteristic
33#16840052C2211yescharacteristic
34#16840049—21no—
35#16840049C2211yescharacteristic
36#16840039C2211yescharacteristic
37#16840000—21no—
38#16839893C2211yescharacteristic
39Q8×#92418C2211yescharacteristic
40#16839872—21no—
41C4×#11758199—21no—
42C4×#11758199C2211yescharacteristic
43C8×D244C2211yescharacteristic
44#107×D61—21no—
45#16839515C2211yescharacteristic
46#16839512C2211yescharacteristic
47#16839511C2211yescharacteristic
48#16839510C2211yescharacteristic
49#16839510C2211yescharacteristic
50#16839508C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic
52Q8⋊#92418C2211yescharacteristic
53D4⋊#92418C2211yescharacteristic
54#16839489C2211yescharacteristic
55#16839484C2211yescharacteristic
56C61×#554C2211yescharacteristic
57D4×Q8×C61C2211yescharacteristic
58C61×#487C2211yescharacteristic
59C61×#484—21no—
60C61×#477C2211yescharacteristic
61C61×#467—21no—
62C61×#462C2211yescharacteristic
63C61×#451—21no—
64C4×Q16×C61C2211yescharacteristic
65C8×D4×C61C2211yescharacteristic
66C2×#103×C61—21no—
67C2×#11758202—41no—
68C2×#11758199D411yescharacteristic
69C2×C8×D61—21no—
70#14519777C2311yescharacteristic
71#14519777C2311yescharacteristic
72#14519769—21no—
73#14519769—21no—
74#14519755—41no—
75#14519755—41no—
76#14519753—21no—
77#14519753—21no—
78C4×D244—21no—
79C4×D244—21no—
80C4×D244C2311yescharacteristic
81C4⋊C4×D61—21no—
82C4⋊C4×D61—21no—
83#14519711—21no—
84#14519711—21no—
85#14519710—21no—
86#14519710—21no—
87#14519710—21no—
88#14519710—21no—
89#14519710—21no—
90#14519710D411yescharacteristic
91#14519708—21no—
92#14519708—21no—
93#14519708—21no—
94#14519708—21no—
95#14519708—21no—
96C4⋊#92418—21no—
97C4⋊#92418—21no—
98C4⋊#92418C2311yescharacteristic
99C4⋊#92418C2311yescharacteristic
100C4⋊#92418C2311yescharacteristic
101#14519701—21no—
102#14519701—21no—
103#14519700—41no—
104#14519698—21no—
105#14519698—21no—
106#14519698D411yescharacteristic
107#14519697—21no—
108#14519697—21no—
109#14519697D411yescharacteristic
110#14519689—21no—
111#14519688—21no—
112C4×#92418—21no—
113C4×#92418C2311yescharacteristic
114C4×#92418C2311yescharacteristic
115C22×Q8×C61—21no—
116C2×Q16×C61—21no—
117C2×Q16×C61D411yescharacteristic
118C22×C8×C61—21no—
119C4⋊Q8×C61—21no—
120C4⋊Q8×C61C2311yescharacteristic
121C4⋊Q8×C61C2311yescharacteristic
122#125×C61—21no—
123C22⋊Q8×C61—21no—
124C22⋊Q8×C61—21no—
125C22⋊Q8×C61—41no—
126C22⋊Q8×C61—41no—
127C4×Q8×C61C2311yescharacteristic
128C4×Q8×C61C2311yescharacteristic
129C4×D4×C61—21no—
130C4×D4×C61—21no—
131C4×D4×C61C2311yescharacteristic
132C2×C4⋊C4×C61—21no—
133#107×C61—21no—
134#107×C61D411yescharacteristic
135C4⋊C8×C61C2311yescharacteristic
136#103×C61—21no—
137#103×C61—21no—
138#103×C61—21no—
139#103×C61—21no—
140#103×C61D411yescharacteristic
141#103×C61D411yescharacteristic
142C22⋊C8×C61—21no—
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61—41no—
147C2×Q8×C61—42no—
148C2×Q8×C61—81no—
149C2×Q8×C61C2×D411yescharacteristic
150C2×Q8×C61C2×D411yescharacteristic
151C2×D4×C61C2×D411yescharacteristic
152C22×C4×C61—21no—
153C22×C4×C61—41no—
154C22×C4×C61—41no—
155C2×D244C2×D411yescharacteristic
156C2×C4×D61—21no—
157C2×C4×D61—41no—
158C2×C4×D61—41no—
159C2×Dic122—21no—
160C2×Dic122—21no—
161Q16×C61—41no—
162Q16×C61—81no—
163C2×C8×C61—21no—
164C2×C8×C61—81no—
165C2×C8×C61C2×D411yescharacteristic
166C2×C8×C61C2×D411yescharacteristic
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—41no—
174C4⋊C4×C61—41no—
175C4⋊C4×C61—41no—
176C4⋊C4×C61C2×D411yescharacteristic
177C4⋊C4×C61C2×D411yescharacteristic
178C4⋊C4×C61C2×D411yescharacteristic
179C22⋊C4×C61—21no—
180C22⋊C4×C61—41no—
181C22⋊C4×C61—41no—
182C42×C61—21no—
183C42×C61—21no—
184C42×C61C2411yescharacteristic
185#11758202—82no—
186#11758199Q1614yescomplemented
187#11758198—21no—
188#11758198—41no—
189#11758198—41no—
190C4⋊Dic61—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61—21no—
194C4⋊Dic61C2×D411yescharacteristic
195#11758196—41no—
196#11758196—41no—
197#11758196—41no—
198#11758196—41no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418C2×D411yescharacteristic
204C2×#92418C2×D411yescharacteristic
205C8×D61—42no—
206C23×C61—21no—
207C22×D61—21no—
208Q8×C61—21no—
209Q8×C61—21no—
210Q8×C61—21no—
211Q8×C61—21no—
212Q8×C61—41no—
213Q8×C61—41no—
214Q8×C61—81no—
215Q8×C61—82no—
216D4×C61—21no—
217D4×C61C2×Q1612yes—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—41no—
224C2×C4×C61—41no—
225C2×C4×C61—41no—
226C2×C4×C61—41no—
227C2×C4×C61—82no—
228C2×C4×C61—161no—
229C2×C4×C61C22×D411yescharacteristic
230C2×C4×C61C22×D411yescharacteristic
231C2×C4×C61H(5,𝔽2)11yescharacteristic
232C2×Dic61—21no—
233C2×Dic61—41no—
234C2×Dic61—41no—
235D244—21no—
236D244C2×Q1612yes—
237C4×D61—41no—
238C4×D61—41no—
239C4×D61—161no—
240C4×D61—161no—
241Dic122—81no—
242Dic122—81no—
243C8×C61—21no—
244C8×C61—21no—
245C8×C61—41no—
246#92418—21no—
247#92418—41no—
248#92418—41no—
249#92418—41no—
250#92418—41no—
251#92418C2×Q1612yes—
252#19814—611nomaximal, Sylow
253C22×C61—22no—
254C22×C61—41no—
255C22×C61—41no—
256C22×C61D4211yescharacteristic
257C2×D61—22no—
258C2×D61—41no—
259C2×D61—41no—
260C4×C61—21no—
261C4×C61—41no—
262C4×C61—41no—
263C4×C61—41no—
264C4×C61—41no—
265C4×C61—41no—
266C4×C61—81no—
267C4×C61—81no—
268C4×C61C22×Q1611yescharacteristic
269C4×C61#57511yescharacteristic
270C4×C61#57711yescharacteristic
271C4×C61#57811yescharacteristic
272Dic61—41no—
273Dic61—81no—
274Dic61—81no—
275#3384—611no—
276#3380—611no—
277#3338—611no—
278#3299D6111yescharacteristic, complemented
279#1723—611no—
280#1696—611no—
281#1683—611no—
282#1675—611no—
283#1672—611no—
284#1644—611no—
285#1637—611no—
286#1632—611no—
287#1632—611no—
288#1584—611no—
289#1580—611no—
290C2×C61—42no—
291C2×C61#326711yescharacteristic
292C2×C61D4×Q1611yescharacteristic
293C2×C61#328811yescharacteristic
294D61—42no—
295#554—611no—
296#554—611no—
297#554C2×D6111yescharacteristic
298D4×Q8C2×D6111yescharacteristic
299#501—1221no—
300#500—611no—
301#500—611no—
302#499—1221no—
303#498—611no—
304#494—611no—
305#487—611no—
306#487C2×D6111yescharacteristic
307#484—21no—
308#484—1221no—
309#484—1221no—
310#478—1221no—
311#478—1221no—
312#478—1221no—
313#477—611no—
314#477—611no—
315#477C2×D6111yescharacteristic
316#476—611no—
317#476—611no—
318#476—611no—
319#476—1221no—
320#474—611no—
321#467—21no—
322#467—1221no—
323#462C2×D6111yescharacteristic
324#451—21no—
325#446—611no—
326C8×Q8—611no—
327#442—1221no—
328C4×Q16C2×D6111yescharacteristic
329C4×D8—611no—
330C4×D8—1221no—
331C8×D4—611no—
332C8×D4C2×D6111yescharacteristic
333C2×#107—1221no—
334C2×#103—21no—
335#335—611no—
336#334—611no—
337#333—611no—
338#333—611no—
339#333—611no—
340#332—611no—
341Q8⋊C8—611no—
342Q8⋊C8—611no—
343D4⋊C8—611no—
344D4⋊C8—611no—
345#322—611no—
346C61#1981411yescharacteristic, complemented, Sylow
347C22×Q8—21no—
348C2×Q16—21no—
349C2×Q16—2441no—
350C2×Q16C22⋊D6111yescharacteristic
351C2×D8—611no—
352C22×C8—21no—
353C22×C8—1221no—
354C4⋊Q8—21no—
355C4⋊Q8—611no—
356C4⋊Q8—611no—
357C4⋊Q8C22×D6111yescharacteristic
358C4⋊Q8C22×D6111yescharacteristic
359#125—21no—
360#125—1221no—
361#125—1221no—
362C22⋊Q8—21no—
363C22⋊Q8—21no—
364C22⋊Q8—41no—
365C22⋊Q8—41no—
366C22⋊Q8—1221no—
367C22⋊Q8—1221no—
368C22⋊Q8—2441no—
369C22⋊Q8—2441no—
370C4×Q8C22×D6111yescharacteristic
371C4×Q8C22×D6111yescharacteristic
372C4×D4—21no—
373C4×D4—21no—
374C4×D4—611no—
375C4×D4—1221no—
376C4×D4—1221no—
377C4×D4C22×D6111yescharacteristic
378C2×C4⋊C4—21no—
379C2×C4⋊C4—1221no—
380C2×C4⋊C4—1221no—
381#107—21no—
382#107—611no—
383#107—1221no—
384#107—1221no—
385#107—1221no—
386#107—1221no—
387#107—1221no—
388#107—1221no—
389#107—1221no—
390#107C22⋊D6111yescharacteristic
391#106—1221no—
392#106—1221no—
393#106—1221no—
394#106—1221no—
395#106—1221no—
396C4⋊C8—611no—
397C4⋊C8—611no—
398C4⋊C8—611no—
399C4⋊C8—1221no—
400C4⋊C8—1221no—
401C4⋊C8C22×D6111yescharacteristic
402#103—21no—
403#103—21no—
404#103—21no—
405#103—21no—
406#103—1221no—
407#103—1221no—
408#103—2441no—
409#103C22⋊D6111yescharacteristic
410#103C22⋊D6111yescharacteristic
411#102—611no—
412#102—611no—
413#102—1221no—
414#102—1221no—
415#102—1221no—
416#102—1221no—
417C22⋊C8—21no—
418C22⋊C8—1221no—
419#97—1221no—
420C4×C8—611no—
421C4×C8—611no—
422C4×C8—1221no—
423C4×C8C22×D6111yescharacteristic
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—41no—
427C2×Q8—42no—
428C2×Q8—81no—
429C2×Q8—1221no—
430C2×Q8—1221no—
431C2×Q8C2×C22⋊D6111yescharacteristic
432C2×Q8C2×C22⋊D6111yescharacteristic
433C2×D4—611no—
434C2×D4D4×D6111yescharacteristic
435C22×C4—21no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—1221no—
439C22×C4—2441no—
440C22×C4—2441no—
441Q16—41no—
442Q16—81no—
443Q16—4882no—
444D8—614no—
445C2×C8—21no—
446C2×C8—81no—
447C2×C8—611no—
448C2×C8—611no—
449C2×C8—1221no—
450C2×C8—1221no—
451C2×C8—1221no—
452C2×C8—1221no—
453C2×C8—2442no—
454C2×C8C2×C22⋊D6111yescharacteristic
455C2×C8C2×C22⋊D6111yescharacteristic
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—611no—
466C4⋊C4—1221no—
467C4⋊C4—1221no—
468C4⋊C4—1221no—
469C4⋊C4—1221no—
470C4⋊C4—2441no—
471C4⋊C4—2441no—
472C4⋊C4—2441no—
473C4⋊C4—2441no—
474C4⋊C4D4×D6111yescharacteristic
475C4⋊C4C2×C22⋊D6111yescharacteristic
476C4⋊C4C2×C22⋊D6111yescharacteristic
477C22⋊C4—21no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—1221no—
481C22⋊C4—2441no—
482C22⋊C4—2441no—
483C42—21no—
484C42—21no—
485C42C23×D6111yescharacteristic
486C23—21no—
487C23—1221no—
488Q8—21no—
489Q8—21no—
490Q8—21no—
491Q8—21no—
492Q8—41no—
493Q8—41no—
494Q8—81no—
495Q8—82no—
496Q8—4881no—
497Q8—4881no—
498D4—21no—
499D4—612no—
500D4—1221no—
501D4Q16×D6112yes—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—82no—
512C2×C4—161no—
513C2×C4—1221no—
514C2×C4—9761no—
515C2×C4—9761no—
516C2×C4—2441no—
517C2×C4—2441no—
518C2×C4—2441no—
519C2×C4—2441no—
520C2×C4C2×D4×D6111yescharacteristic
521C2×C4C22×C22⋊D6111yescharacteristic
522C2×C4#1451982211yescharacteristic
523C8—21no—
524C8—21no—
525C8—41no—
526C8—612no—
527C8—1221no—
528C8—2441no—
529C8—2441no—
530C8—2441no—
531C8—2441no—
532C22—22no—
533C22—41no—
534C22—41no—
535C22—1222no—
536C22—2441no—
537C22—2441no—
538C22D4×C22⋊D6111yescharacteristic
539C4—21no—
540C4—41no—
541C4—41no—
542C4—41no—
543C4—41no—
544C4—41no—
545C4—81no—
546C4—81no—
547C4—4881no—
548C4—4881no—
549C4—2441no—
550C4C2×Q16×D6111yescharacteristic
551C4#1684056011yescharacteristic
552C4#1684057311yescharacteristic
553C4#1684057511yescharacteristic
554C2—42no—
555C2—2442no—
556C2#2145734011yescharacteristic
557C2Q16×C22⋊D6111yescharacteristic
558C2#2145758111yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3299C2
socleC22×C61D42
prime radicalC2×#11758199D4
hypercenter#3299D61
hypocenterC61#19814
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3299

Complements

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

NH ≅ G/Ntype
3. #21458213C2semidirect
4. #21445499C2semidirect
5. #21445345C2semidirect
6. #21445267C2semidirect
7. #21445218C2semidirect
8. #21445199C2semidirect
9. #21445031C2semidirect
10. #21444984C2semidirect
11. #21444953C2semidirect
12. #21444952C2semidirect
13. #21444670C2semidirect
15. C61×#3299C2semidirect
186. #11758199Q16semidirect
278. #3299D61semidirect
346. C61#19814semidirect

Maximal subgroups

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

subgroupindex
#214587142
#214586822
#214582132
#214454992
#214453452
#214452672
#214452182
#214451992
#214450312
#214449842
#214449532
#214449522
#214446702
#214446412
C61×#32992
#1981461