Finite Group Databasebeta

← #29729784

Subgroups — #29729784

Order 15616.

764 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456195C211yesmaximal, characteristic, complemented
2C2×#16839957C211yesmaximal, characteristic
3#21454768C211yesmaximal, characteristic, complemented
4#21447176C212yesmaximal, complemented
5#21447074C212yesmaximal, complemented
6#21446728C212yesmaximal, complemented
7#21446658C211yesmaximal, characteristic, complemented
8#21446592C211yesmaximal, characteristic, complemented
9#21446480C212yesmaximal, complemented
10C4×#14519694C211yesmaximal, characteristic, complemented
11C61×#3077C211yesmaximal, characteristic, complemented
12C22×#11758199C2212yes—
13C2×#14519774C2211yescharacteristic
14#16840128—22no—
15#16840110—21no—
16#16840110—21no—
17#16839957—21no—
18#16839957—21no—
19#16839957—22no—
20#16839893—21no—
21#16839893—22no—
22Q8×#92418—21no—
23C2×#14519712C2212yes—
24#16839789C2212yes—
25C2×C4⋊#92418C2211yescharacteristic
26#16839766C2212yes—
27#16839766C2212yes—
28C2×#14519697C2212yes—
29C2×#14519694C2211yescharacteristic
30C2×#14519694C2211yescharacteristic
31C2×#14519693C2212yes—
32C2×#14519693C2212yes—
33#16839718C2212yes—
34C4×#11758194C2211yescharacteristic
35C4×#11758194C2211yescharacteristic
36#16839531C2211yescharacteristic
37#16839531C2211yescharacteristic
38#16839526C2212yes—
39C61×#533C2211yescharacteristic
40C2×C4×D4×C61C2211yescharacteristic
41C61×#478—22no—
42C61×#476—21no—
43C61×#474—21no—
44C61×#428C2212yes—
45C61×#423C2211yescharacteristic
46C61×#418C2212yes—
47C22×D244—21no—
48C22×D244—21no—
49C22×D244C2312yes—
50C2×#11758199—24no—
51C2×#11758199—22no—
52C2×#11758199—22no—
53C2×#11758199—42no—
54C2×#11758194C2311yescharacteristic
55C2×#11758194C2311yescharacteristic
56C2×#11758194C2311yescharacteristic
57C2×#11758194C2311yescharacteristic
58C22×#92418C2312yes—
59#14519774—21no—
60#14519774—21no—
61#14519774—21no—
62#14519774—21no—
63#14519712—42no—
64C4⋊#92418—22no—
65C4⋊#92418—22no—
66C4⋊#92418D411yescharacteristic
67C4⋊#92418D412yes—
68C4⋊#92418D411yescharacteristic
69#14519697—22no—
70#14519697—22no—
71#14519697—22no—
72#14519697—22no—
73#14519697—22no—
74#14519697—22no—
75#14519694—22no—
76#14519694—22no—
77#14519693—24no—
78#14519693—42no—
79#14519688—21no—
80#14519688—21no—
81#14519688—22no—
82C4×#92418—21no—
83C4×#92418—21no—
84C4×#92418—22no—
85C22×D4×C61C2311yescharacteristic
86C23×C4×C61—21no—
87C2×M16×C61C2312yes—
88C4⋊Q8×C61D411yescharacteristic
89C4⋊Q8×C61D411yescharacteristic
90#125×C61D412yes—
91C22⋊Q8×C61—21no—
92C22⋊Q8×C61—21no—
93C4×Q8×C61—21no—
94C4×Q8×C61—21no—
95C4×D4×C61—21no—
96C4×D4×C61—21no—
97C4×D4×C61—21no—
98C4×D4×C61—21no—
99#117×C61C2312yes—
100C2×C4⋊C4×C61C2311yescharacteristic
101C2×C22⋊C4×C61—21no—
102C2×C42×C61C2311yescharacteristic
103#107×C61—22no—
104#106×C61—22no—
105C4⋊C8×C61—21no—
106C4⋊C8×C61—21no—
107#102×C61—22no—
108#102×C61—22no—
109C24×C61—21no—
110C23×D61—22no—
111C2×Q8×C61—21no—
112C2×Q8×C61—21no—
113C2×D4×C61—21no—
114C2×D4×C61—21no—
115C2×D4×C61—21no—
116C2×D4×C61—21no—
117C2×D4×C61—21no—
118C2×D4×C61#4112yes—
119C22×C4×C61—21no—
120C22×C4×C61—41no—
121C22×C4×C61—41no—
122C22×C4×C61—82no—
123C22×C4×C61#4111yescharacteristic
124C22×C4×C61#4111yescharacteristic
125C22×C4×C61C2411yescharacteristic
126C2×D244—22no—
127C2×D244—22no—
128C2×D244—22no—
129C2×D244—22no—
130C2×D244—22no—
131C2×D244—22no—
132C2×D244—41no—
133C2×D244—41no—
134C2×D244—41no—
135C2×D244—41no—
136C2×D244—82no—
137C2×D244—82no—
138M16×C61—22no—
139M16×C61—22no—
140C2×C8×C61—22no—
141C4⋊C4×C61—22no—
142C4⋊C4×C61—22no—
143C4⋊C4×C61—21no—
144C4⋊C4×C61—21no—
145C4⋊C4×C61—21no—
146C4⋊C4×C61—21no—
147C4⋊C4×C61C2×D412yes—
148C4⋊C4×C61C2×D412yes—
149C22⋊C4×C61—22no—
150C22⋊C4×C61—41no—
151C22⋊C4×C61—41no—
152C42×C61—22no—
153C42×C61C2×D411yescharacteristic
154C42×C61C2×D411yescharacteristic
155C42×C61C2×D411yescharacteristic
156C42×C61C2×D411yescharacteristic
157#11758199—44no—
158#11758199—44no—
159#11758194—21no—
160#11758194—21no—
161#11758194—21no—
162#11758194—21no—
163#11758194—21no—
164#11758194—21no—
165#11758194—21no—
166#11758194#4112yes—
167C2×#92418—21no—
168C2×#92418—22no—
169C2×#92418—22no—
170C2×#92418—21no—
171C2×#92418—21no—
172C2×#92418—21no—
173C2×#92418C2×D412yes—
174C2×#92418C2×D412yes—
175C23×C61—22no—
176C23×C61—41no—
177C23×C61—41no—
178C23×C61—81no—
179C23×C61—81no—
180C23×C61C2×#4111yescharacteristic
181C22×D61—42no—
182C22×D61—42no—
183C22×D61—42no—
184C22×D61—82no—
185C22×D61—82no—
186Q8×C61—42no—
187Q8×C61—81no—
188D4×C61—22no—
189D4×C61—22no—
190D4×C61—41no—
191D4×C61—41no—
192C2×C4×C61—22no—
193C2×C4×C61—22no—
194C2×C4×C61—22no—
195C2×C4×C61—41no—
196C2×C4×C61—41no—
197C2×C4×C61—82no—
198C2×C4×C61—82no—
199C2×C4×C61—81no—
200C2×C4×C61#12111yescharacteristic
201C2×C4×C61#12111yescharacteristic
202C2×C4×C61#12111yescharacteristic
203C2×C4×C61#12111yescharacteristic
204C2×C4×C61C22×D411yescharacteristic
205C2×C4×C61C22×D411yescharacteristic
206C2×C4×C61C2×#4111yescharacteristic
207C2×C4×C61C2×#4111yescharacteristic
208C2×C4×C61H(5,𝔽2)11yescharacteristic
209C2×C4×C612−1+411yescharacteristic
210D244—42no—
211D244—42no—
212D244—42no—
213D244—42no—
214D244—82no—
215D244—82no—
216D244—82no—
217D244—82no—
218C8×C61—42no—
219#92418—22no—
220#92418—22no—
221#92418—22no—
222#92418—41no—
223#92418—41no—
224#92418—41no—
225#25312—611nomaximal, Sylow
226C22×C61—21no—
227C22×C61—21no—
228C22×C61—42no—
229C22×C61—82no—
230C22×C61—82no—
231C22×C61—81no—
232C22×C61—81no—
233C22×C61C2×#12111yescharacteristic
234C22×C61#52911yescharacteristic
235C22×C61#54211yescharacteristic
236C2×D61—82no—
237C2×D61—82no—
238C2×D61—82no—
239C2×D61—162no—
240C2×D61—162no—
241C4×C61—21no—
242C4×C61—21no—
243C4×C61—21no—
244C4×C61—42no—
245C4×C61—42no—
246C4×C61—81no—
247C4×C61#47212yes—
248C4×C61#54611yescharacteristic
249C4×C61#54811yescharacteristic
250C4×C61#54811yescharacteristic
251C4×C61#55011yescharacteristic
252#3138—611no—
253#3077D6111yescharacteristic, complemented
254C2×#459—611no—
255#2962—611no—
256#2063—612no—
257#2045—612no—
258#1978—612no—
259#1965—611no—
260#1950—611no—
261#1931—612no—
262C4×#100—611no—
263C2×C61—21no—
264C2×C61—21no—
265C2×C61—82no—
266C2×C61#242611yescharacteristic
267C2×C61C2×#47211yescharacteristic
268C2×C61#306811yescharacteristic
269D61—162no—
270C22×D8—612no—
271#533C2×D6111yescharacteristic
272C2×#127—611no—
273C2×C4×D4C2×D6111yescharacteristic
274#490—1222no—
275#486—1221no—
276#486—1221no—
277#478—22no—
278#476—21no—
279#474—21no—
280#459—1221no—
281#459—1222no—
282#459—1221no—
283#446—1222no—
284#446—1221no—
285C8×Q8—1221no—
286C2×#108—612no—
287#428C2×D6112yes—
288#424—612no—
289#423C2×D6111yescharacteristic
290C2×C4⋊C8—611no—
291#418—612no—
292#418—612no—
293#418C2×D6112yes—
294C2×#102—612no—
295C2×#100—611no—
296C2×#100—611no—
297C2×#100—612no—
298C2×#100—612no—
299#405—612no—
300C4×M16—611no—
301C4×M16—611no—
302#343—611no—
303#343—611no—
304#341—612no—
305C61#2531211yescharacteristic, complemented, Sylow
306C22×D4—612no—
307C22×D4—1221no—
308C22×D4—1221no—
309C22×D4C22×D6111yescharacteristic
310C23×C4—21no—
311C2×D8—1222no—
312C2×D8—1222no—
313C2×D8—1224no—
314C2×D8—2442no—
315C2×M16—611no—
316C2×M16—611no—
317C2×M16—611no—
318C2×M16—611no—
319C2×M16C22×D6112yes—
320C22×C8—612no—
321C4⋊Q8C22⋊D6111yescharacteristic
322C4⋊Q8C22⋊D6111yescharacteristic
323#127—1221no—
324#127—1221no—
325#127—1221no—
326#127—1221no—
327#125C22⋊D6112yes—
328C22⋊Q8—21no—
329C22⋊Q8—21no—
330C4×Q8—21no—
331C4×Q8—21no—
332C4×D4—21no—
333C4×D4—21no—
334C4×D4—21no—
335C4×D4—21no—
336#117C22×D6112yes—
337C2×C4⋊C4C22×D6111yescharacteristic
338C2×C22⋊C4—21no—
339C2×C42C22×D6111yescharacteristic
340#108—2442no—
341#107—22no—
342#106—22no—
343C4⋊C8—21no—
344C4⋊C8—21no—
345C4⋊C8—611no—
346C4⋊C8—611no—
347C4⋊C8—612no—
348C4⋊C8—1222no—
349C4⋊C8—1222no—
350#102—22no—
351#102—22no—
352#102—1222no—
353#102—1222no—
354#102—1222no—
355#102—1222no—
356#102—1222no—
357#102—1222no—
358#100—1224no—
359#100—1222no—
360#100—1222no—
361#100—2442no—
362#97—1222no—
363#97—1221no—
364#97—1221no—
365C4×C8—1222no—
366C4×C8—1221no—
367C4×C8—1221no—
368C24—21no—
369C24—1222no—
370C2×Q8—21no—
371C2×Q8—21no—
372C2×D4—21no—
373C2×D4—21no—
374C2×D4—21no—
375C2×D4—21no—
376C2×D4—21no—
377C2×D4—1222no—
378C2×D4—1222no—
379C2×D4—1222no—
380C2×D4—1222no—
381C2×D4—1222no—
382C2×D4—1222no—
383C2×D4—4882no—
384C2×D4—4882no—
385C2×D4—2441no—
386C2×D4—2441no—
387C2×D4—2441no—
388C2×D4—2441no—
389C2×D4#1175822612yes—
390C22×C4—21no—
391C22×C4—41no—
392C22×C4—41no—
393C22×C4—82no—
394C22×C4#1175822411yescharacteristic
395C22×C4#1175822411yescharacteristic
396C22×C4C23×D6111yescharacteristic
397D8—2444no—
398D8—2444no—
399M16—22no—
400M16—22no—
401M16—612no—
402M16—1221no—
403M16—1221no—
404M16—1221no—
405M16—1221no—
406M16—1221no—
407M16—1221no—
408M16—1221no—
409C2×C8—22no—
410C2×C8—612no—
411C2×C8—612no—
412C2×C8—1221no—
413C2×C8—1222no—
414C2×C8—1222no—
415C2×C8—1221no—
416C2×C8—1221no—
417C2×C8—1221no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4C2×C22⋊D6112yes—
425C4⋊C4C2×C22⋊D6112yes—
426C22⋊C4—22no—
427C22⋊C4—41no—
428C22⋊C4—41no—
429C42—22no—
430C42D4×D6111yescharacteristic
431C42D4×D6111yescharacteristic
432C42C2×C22⋊D6111yescharacteristic
433C42C2×C22⋊D6111yescharacteristic
434C23—22no—
435C23—41no—
436C23—41no—
437C23—81no—
438C23—81no—
439C23—4882no—
440C23—4882no—
441C23—2442no—
442C23—2442no—
443C23—2442no—
444C23C2×#1175822411yescharacteristic
445Q8—42no—
446Q8—81no—
447D4—22no—
448D4—22no—
449D4—41no—
450D4—41no—
451D4—4882no—
452D4—4882no—
453D4—4882no—
454D4—4882no—
455D4—2442no—
456D4—2442no—
457D4—2442no—
458D4—2442no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—82no—
465C2×C4—82no—
466C2×C4—81no—
467C2×C4#1451974911yescharacteristic
468C2×C4#1451974911yescharacteristic
469C2×C4#1451974911yescharacteristic
470C2×C4#1451974911yescharacteristic
471C2×C4C2×D4×D6111yescharacteristic
472C2×C4C22×C22⋊D6111yescharacteristic
473C2×C4#41×D6111yescharacteristic
474C2×C4C2×#1175822611yescharacteristic
475C2×C4#1451982311yescharacteristic
476C2×C4#1451982511yescharacteristic
477C8—42no—
478C8—1222no—
479C8—1222no—
480C8—1222no—
481C8—2441no—
482C8—2441no—
483C8—2441no—
484C22—21no—
485C22—21no—
486C22—42no—
487C22—82no—
488C22—82no—
489C22—81no—
490C22—81no—
491C22—9762no—
492C22—9762no—
493C22—4882no—
494C22—4882no—
495C22—4882no—
496C22C2×#1451974911yescharacteristic
497C22#1684029811yescharacteristic
498C22#1684038511yescharacteristic
499C4—21no—
500C4—21no—
501C4—21no—
502C4—42no—
503C4—42no—
504C4—81no—
505C4#1684003012yes—
506C4#1684040311yescharacteristic
507C4#1684042211yescharacteristic
508C4#1684042311yescharacteristic
509C4#1684043111yescharacteristic
510C2—21no—
511C2—21no—
512C2—82no—
513C2—9762no—
514C2#2144938711yescharacteristic
515C2C2×#1684003011yescharacteristic
516C2#2145554911yescharacteristic
subgroupG/H
centerC22C2×#14519749
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#3077C2
socleC22×C61C2×#121
prime radicalC2×#16839957C2
hypercenter#3077D61
hypocenterC61#25312
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3077

Complements

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

NH ≅ G/Ntype
1. #21456195C2semidirect
3. #21454768C2semidirect
4. #21447176C2semidirect
5. #21447074C2semidirect
6. #21446728C2semidirect
7. #21446658C2semidirect
8. #21446592C2semidirect
9. #21446480C2semidirect
10. C4×#14519694C2semidirect
11. C61×#3077C2semidirect
253. #3077D61semidirect
305. C61#25312semidirect

Maximal subgroups

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

subgroupindex
#214561952
C2×#168399572
#214547682
#214471762
#214470742
#214467282
#214466582
#214465922
#214464802
C4×#145196942
C61×#30772
#2531261