Finite Group Databasebeta

← #29667646

Subgroups — #29667646

Order 15616.

590 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457146C211yesmaximal, characteristic
2#21457040C211yesmaximal, characteristic, complemented
3#21456940C211yesmaximal, characteristic, complemented
4#21454975C211yesmaximal, characteristic, complemented
5#21445362C211yesmaximal, characteristic, complemented
6#21445355C211yesmaximal, characteristic, complemented
7#21445346C211yesmaximal, characteristic, complemented
8#21445341C211yesmaximal, characteristic, complemented
9#21445238C211yesmaximal, characteristic, complemented
10#21445231C211yesmaximal, characteristic, complemented
11#21445222C211yesmaximal, characteristic, complemented
12#21445217C211yesmaximal, characteristic, complemented
13#21444602C211yesmaximal, characteristic, complemented
14#21444512C211yesmaximal, characteristic, complemented
15C2×C61×#333C211yesmaximal, characteristic, complemented
16#16840312C2211yescharacteristic
17#16840296C2211yescharacteristic
18#16840168—21no—
19#16840165C2211yescharacteristic
20#16840165C2211yescharacteristic
21#16840124—21no—
22#16840110C2211yescharacteristic
23#16840110C2211yescharacteristic
24#16840092—21no—
25#16840075—21no—
26#16840075—21no—
27#16840075—21no—
28#16840063—21no—
29#16840058C2211yescharacteristic
30#16840054C2211yescharacteristic
31#16840054C2211yescharacteristic
32#16840053C2211yescharacteristic
33#16840049C2211yescharacteristic
34#16840049C2211yescharacteristic
35#16840039—21no—
36#16840039—21no—
37#16839998—21no—
38#16839991—21no—
39#16839978—21no—
40#16839963C2211yescharacteristic
41#16839958C2211yescharacteristic
42#16839889C2211yescharacteristic
43#16839886C2211yescharacteristic
44#16839839C2211yescharacteristic
45#16839833—21no—
46#16839827C2211yescharacteristic
47C8×C22⋊D61—21no—
48#16839822—21no—
49#16839819C2211yescharacteristic
50#16839815C2211yescharacteristic
51#16839787—21no—
52#16839514C2211yescharacteristic
53#16839514C2211yescharacteristic
54#16839512C2211yescharacteristic
55#16839512C2211yescharacteristic
56#16839510C2211yescharacteristic
57#16839510C2211yescharacteristic
58#16839505C2211yescharacteristic
59#16839505C2211yescharacteristic
60C2×C4⋊Q8×C61C2211yescharacteristic
61C2×C4⋊C8×C61C2211yescharacteristic
62C2×C4⋊C8×C61C2211yescharacteristic
63C61×#333C2211yescharacteristic
64C61×#333C2211yescharacteristic
65C61×#333C2211yescharacteristic
66C61×#333C2211yescharacteristic
67C2×#11758222—21no—
68C2×#11758190—21no—
69C2×D488—21no—
70C2×#11758189—21no—
71C2×C8×D61—21no—
72#14519777C2311yescharacteristic
73#14519774C2311yescharacteristic
74#14519771—21no—
75#14519769D411yescharacteristic
76#14519765—21no—
77#14519765D411yescharacteristic
78#14519760—21no—
79#14519756D411yescharacteristic
80#14519751—21no—
81#14519751—21no—
82#14519751D411yescharacteristic
83C4×Dic122C2311yescharacteristic
84C4×D244—21no—
85C4×D244—21no—
86C4×D244C2311yescharacteristic
87C4×C22⋊D61—21no—
88#14519734—21no—
89#14519711—21no—
90#14519710—21no—
91#14519710—21no—
92#14519710—21no—
93#14519710—21no—
94#14519710—21no—
95#14519710—21no—
96#14519709—21no—
97#14519708—21no—
98#14519708—21no—
99C4⋊#92418D411yescharacteristic
100C4⋊#92418D411yescharacteristic
101C4⋊#92418C2311yescharacteristic
102C4⋊#92418C2311yescharacteristic
103#14519706—21no—
104#14519706—21no—
105#14519702—21no—
106#14519700—21no—
107#14519700—21no—
108#14519699—21no—
109#14519699—21no—
110#14519699—21no—
111#14519697—21no—
112#14519697—21no—
113#14519697—21no—
114#14519697—21no—
115#14519697—21no—
116#14519697—21no—
117C22⋊#92418—21no—
118C22⋊#92418D411yescharacteristic
119C22⋊#92418D411yescharacteristic
120#14519689—21no—
121#14519689—21no—
122#14519688—21no—
123#14519687—21no—
124C4×#92418C2311yescharacteristic
125C4×#92418C2311yescharacteristic
126C8×Dic61—21no—
127C22×Q8×C61—21no—
128C22×C8×C61—21no—
129C22×C8×C61—21no—
130C4⋊Q8×C61—21no—
131C4⋊Q8×C61—21no—
132C4⋊Q8×C61—21no—
133C4⋊Q8×C61C2311yescharacteristic
134C4⋊Q8×C61C2311yescharacteristic
135C2×C4⋊C4×C61—21no—
136C2×C4⋊C4×C61—21no—
137C2×C42×C61C2311yescharacteristic
138C4⋊C8×C61—21no—
139C4⋊C8×C61—21no—
140C4⋊C8×C61C2311yescharacteristic
141C4⋊C8×C61C2311yescharacteristic
142C4⋊C8×C61C2311yescharacteristic
143C4⋊C8×C61C2311yescharacteristic
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61—41no—
147C2×Q8×C61—82no—
148C22×C4×C61—41no—
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61#4111yescharacteristic
152C2×C22⋊D61—21no—
153C2×C22⋊D61—41no—
154#11758222—82no—
155C2×D244—21no—
156C2×D244—21no—
157C2×D244—21no—
158C2×D244C2×D411yescharacteristic
159C2×C4×D61—21no—
160C2×C4×D61—41no—
161C2×Dic122—21no—
162C2×Dic122C2×D411yescharacteristic
163C2×C8×C61—21no—
164C2×C8×C61—21no—
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61—81no—
168C2×C8×C61—81no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—41no—
174C4⋊C4×C61—41no—
175C42×C61C2×D411yescharacteristic
176C42×C61C2×D411yescharacteristic
177C42×C61#4111yescharacteristic
178C42×C61C2411yescharacteristic
179C22⋊Dic61—21no—
180#11758198—21no—
181#11758198—21no—
182#11758198—21no—
183#11758198—21no—
184#11758198—41no—
185#11758198—41no—
186C4⋊Dic61—21no—
187C4⋊Dic61—21no—
188C4⋊Dic61C2×D411yescharacteristic
189C4⋊Dic61C2×D411yescharacteristic
190#11758196—21no—
191#11758196—21no—
192#11758196—21no—
193#11758196—21no—
194C4×Dic61—21no—
195C2×#92418—21no—
196C2×#92418—21no—
197C2×#92418C2×D411yescharacteristic
198C2×#92418C2×D411yescharacteristic
199C2×#92418C2×D411yescharacteristic
200C2×#92418C2×D411yescharacteristic
201D488—81no—
202#11758190—81no—
203#11758189—81no—
204C8×D61—81no—
205C23×C61#12111yescharacteristic
206C22×D61—21no—
207C22×D61—41no—
208Q8×C61—82no—
209Q8×C61—81no—
210Q8×C61—81no—
211C2×C4×C61—22no—
212C2×C4×C61—21no—
213C2×C4×C61—21no—
214C2×C4×C61—21no—
215C2×C4×C61—21no—
216C2×C4×C61—41no—
217C2×C4×C61—41no—
218C2×C4×C61—82no—
219C2×C4×C61#12111yescharacteristic
220C2×C4×C61#12111yescharacteristic
221C2×C4×C61#12111yescharacteristic
222C2×C4×C61C22×D411yescharacteristic
223C2×C4×C61C22×D411yescharacteristic
224C2×C4×C61C2×#4111yescharacteristic
225C22⋊D61—42no—
226C22⋊D61—82no—
227C2×Dic61—21no—
228C2×Dic61—21no—
229C2×Dic61—21no—
230C2×Dic61—41no—
231D244—21no—
232D244—21no—
233D244—41no—
234D244—41no—
235D244—41no—
236D244—41no—
237D244—81no—
238C4×D61—41no—
239C4×D61—41no—
240C4×D61—82no—
241Dic122—21no—
242Dic122—21no—
243Dic122—81no—
244C8×C61—41no—
245C8×C61—41no—
246C8×C61—41no—
247C8×C61—41no—
248#92418—21no—
249#92418—21no—
250#92418—21no—
251#92418—21no—
252#92418—41no—
253#92418—41no—
254#19591—611nomaximal, Sylow
255C22×C61—21no—
256C22×C61—21no—
257C22×C61#47212yes—
258C22×C61C2×#12111yescharacteristic
259C2×D61—41no—
260C2×D61—41no—
261C2×D61—41no—
262C2×D61—81no—
263C2×D61—81no—
264C2×D61—81no—
265C4×C61—21no—
266C4×C61—21no—
267C4×C61—21no—
268C4×C61—21no—
269C4×C61—81no—
270C4×C61—81no—
271C4×C61#57711yescharacteristic
272C4×C61#57711yescharacteristic
273C4×C61#57811yescharacteristic
274C4×C61#57811yescharacteristic
275Dic61—41no—
276Dic61—41no—
277Dic61—41no—
278Dic61—81no—
279#3247—611no—
280#3238—611no—
281#3226—611no—
282#2994—611no—
283#1698—611no—
284#1697—611no—
285#1696—611no—
286#1695—611no—
287#1678—611no—
288#1677—611no—
289#1676—611no—
290#1675—611no—
291#1573—611no—
292#1551—611no—
293C2×#333D6111yescharacteristic, complemented
294C2×C61—22no—
295C2×C61#304611yescharacteristic
296C2×C61#306311yescharacteristic
297C2×C61C2×#47211yescharacteristic
298D61—81no—
299D61—161no—
300#532—611no—
301C2×C4⋊Q8C2×D6111yescharacteristic
302#529—611no—
303#501—1221no—
304#500—611no—
305#500—611no—
306#489—1221no—
307#486—611no—
308#486—611no—
309#483—1221no—
310#480—1221no—
311#480—1221no—
312#480—1221no—
313#478—1221no—
314#477—611no—
315#477—611no—
316#477—611no—
317#476—611no—
318#476—611no—
319#476—611no—
320#474—1221no—
321#474—1221no—
322#466—1221no—
323#465—1221no—
324#463—1221no—
325#460—611no—
326#459—611no—
327#446—611no—
328C8×Q8—611no—
329#436—611no—
330#435—1221no—
331C8×D4—611no—
332C8×D4—1221no—
333#433—1221no—
334#432—611no—
335#431—611no—
336#424—1221no—
337C2×C4⋊C8C2×D6111yescharacteristic
338C2×C4⋊C8C2×D6111yescharacteristic
339#335—611no—
340#335—611no—
341#334—611no—
342#334—611no—
343#333—611no—
344#333—611no—
345#333C2×D6111yescharacteristic
346#333C2×D6111yescharacteristic
347#333C2×D6111yescharacteristic
348#333C2×D6111yescharacteristic
349#331—611no—
350#331—611no—
351C61#1959111yescharacteristic, complemented, Sylow
352C2×#41—1221no—
353C22×Q8—21no—
354C2×SD16—1221no—
355C2×D8—1221no—
356C2×M16—1221no—
357C22×C8—21no—
358C22×C8—21no—
359C22×C8—1221no—
360C4⋊Q8—21no—
361C4⋊Q8—21no—
362C4⋊Q8—21no—
363C4⋊Q8—611no—
364C4⋊Q8C22×D6111yescharacteristic
365C4⋊Q8C22×D6111yescharacteristic
366#127—611no—
367#126—1221no—
368#125—611no—
369#124—611no—
370#124—1221no—
371#123—1221no—
372C22⋊Q8—611no—
373#121—611no—
374#121—1221no—
375#121—1221no—
376C4×Q8—611no—
377C4×D4—611no—
378C4×D4—1221no—
379C4×D4—1221no—
380C4×D4—1221no—
381#117—1221no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C42C22×D6111yescharacteristic
385#107—1221no—
386#107—1221no—
387#107—1221no—
388#107—1221no—
389#107—1221no—
390#107—1221no—
391#107—1221no—
392#106—1221no—
393#106—1221no—
394#106—1221no—
395C4⋊C8—21no—
396C4⋊C8—21no—
397C4⋊C8—611no—
398C4⋊C8—611no—
399C4⋊C8—611no—
400C4⋊C8—611no—
401C4⋊C8—1221no—
402C4⋊C8—1221no—
403C4⋊C8C22×D6111yescharacteristic
404C4⋊C8C22×D6111yescharacteristic
405C4⋊C8C22×D6111yescharacteristic
406C4⋊C8C22×D6111yescharacteristic
407#103—1221no—
408#103—1221no—
409#103—1221no—
410#102—1221no—
411#102—1221no—
412#102—1221no—
413#102—1221no—
414#102—1221no—
415#102—1221no—
416#102—1221no—
417#102—1221no—
418#102—1221no—
419C22⋊C8—611no—
420C22⋊C8—611no—
421C22⋊C8—1221no—
422C22⋊C8—1221no—
423C22⋊C8—1221no—
424#97—1221no—
425#97—1221no—
426C4×C8—611no—
427C4×C8—611no—
428C4×C8—1221no—
429#41—4882no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—41no—
433C2×Q8—82no—
434C2×Q8—611no—
435C2×Q8—1221no—
436C2×D4—611no—
437C2×D4—1221no—
438C2×D4—1221no—
439C2×D4—1221no—
440C2×D4—1221no—
441C2×D4—2441no—
442C22×C4—41no—
443C22×C4—1221no—
444C22×C4—2441no—
445C22×C4#1175822211yescharacteristic
446C22×C4D4×D6111yescharacteristic
447C22×C4D4×D6111yescharacteristic
448SD16—4881no—
449D8—4881no—
450M16—4881no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—81no—
456C2×C8—81no—
457C2×C8—611no—
458C2×C8—611no—
459C2×C8—611no—
460C2×C8—611no—
461C2×C8—1221no—
462C2×C8—1221no—
463C2×C8—4881no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—41no—
469C4⋊C4—41no—
470C4⋊C4—611no—
471C4⋊C4—611no—
472C4⋊C4—1221no—
473C4⋊C4—1221no—
474C4⋊C4—1221no—
475C4⋊C4—1221no—
476C4⋊C4—1221no—
477C4⋊C4—1221no—
478C22⋊C4—1221no—
479C22⋊C4—1221no—
480C22⋊C4—1221no—
481C22⋊C4—1221no—
482C22⋊C4—1221no—
483C22⋊C4—2441no—
484C22⋊C4—2441no—
485C42—1221no—
486C42#1175822211yescharacteristic
487C42D4×D6111yescharacteristic
488C42D4×D6111yescharacteristic
489C42C23×D6111yescharacteristic
490C23—1221no—
491C23—2441no—
492C23#1451975011yescharacteristic
493Q8—81no—
494Q8—81no—
495Q8—82no—
496Q8—1221no—
497Q8—1221no—
498Q8—4881no—
499D4—1221no—
500D4—1221no—
501D4—4881no—
502D4—4882no—
503D4—2442no—
504D4—2441no—
505D4—2441no—
506D4—2441no—
507D4—2441no—
508C2×C4—22no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—82no—
516C2×C4—1221no—
517C2×C4—1221no—
518C2×C4—1221no—
519C2×C4—4882no—
520C2×C4—2441no—
521C2×C4—2441no—
522C2×C4—2441no—
523C2×C4#1451975011yescharacteristic
524C2×C4#1451975011yescharacteristic
525C2×C4#1451975011yescharacteristic
526C2×C4C2×D4×D6111yescharacteristic
527C2×C4C2×D4×D6111yescharacteristic
528C2×C4C2×#1175822211yescharacteristic
529C8—41no—
530C8—41no—
531C8—41no—
532C8—41no—
533C8—1221no—
534C8—1221no—
535C8—1221no—
536C8—1221no—
537C8—2441no—
538C8—2441no—
539C22—21no—
540C22—21no—
541C22—4881no—
542C22—4881no—
543C22—4881no—
544C22—2441no—
545C22—2441no—
546C22—2441no—
547C22#1684003112yes—
548C22C2×#1451975011yescharacteristic
549C4—21no—
550C4—21no—
551C4—21no—
552C4—21no—
553C4—81no—
554C4—81no—
555C4—4881no—
556C4—2441no—
557C4—2441no—
558C4—2441no—
559C4#1684056811yescharacteristic
560C4#1684056811yescharacteristic
561C4#1684057511yescharacteristic
562C4#1684057511yescharacteristic
563C2—22no—
564C2—9761no—
565C2—4881no—
566C2#2145537411yescharacteristic
567C2#2145550811yescharacteristic
568C2C2×#1684003111yescharacteristic
subgroupG/H
centerC22C2×#14519750
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×#333C2
socleC22×C61C2×#121
prime radical#21457146C2
hypercenterC2×#333D61
hypocenterC61#19591
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#333

Complements

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

NH ≅ G/Ntype
2. #21457040C2semidirect
3. #21456940C2semidirect
4. #21454975C2semidirect
5. #21445362C2semidirect
6. #21445355C2semidirect
7. #21445346C2semidirect
8. #21445341C2semidirect
9. #21445238C2semidirect
10. #21445231C2semidirect
11. #21445222C2semidirect
12. #21445217C2semidirect
13. #21444602C2semidirect
14. #21444512C2semidirect
15. C2×C61×#333C2semidirect
293. C2×#333D61semidirect
351. C61#19591semidirect

Maximal subgroups

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

subgroupindex
#214571462
#214570402
#214569402
#214549752
#214453622
#214453552
#214453462
#214453412
#214452382
#214452312
#214452222
#214452172
#214446022
#214445122
C2×C61×#3332
#1959161