Finite Group Databasebeta

← #29721490

Subgroups — #29721490

Order 15616.

674 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455635C211yesmaximal, characteristic
2C2×#16840058C211yesmaximal, characteristic, complemented
3C4×#14519810C211yesmaximal, characteristic
4#21454484C211yesmaximal, characteristic
5#21447261C212yesmaximal
6#21447120C212yesmaximal
7#21446808C211yesmaximal, characteristic, complemented
8#21446605C212yesmaximal, complemented
9#21446475C212yesmaximal, complemented
10#21445812C211yesmaximal, characteristic, complemented
11C61×#1950C211yesmaximal, characteristic, complemented
12C2×#14519810C2211yescharacteristic
13C2×#14519777C2211yescharacteristic
14C4×#11758222C2211yescharacteristic
15C2×C4×Dic122C2211yescharacteristic
16#16840058—21no—
17#16840058—21no—
18#16840058—21no—
19#16840058—22no—
20#16840053—21no—
21#16840048—21no—
22#16840043—21no—
23#16839870—21no—
24#16839864—21no—
25C4×Dic244—21no—
26C4×#11758190—21no—
27#16839822—22no—
28#16839818—21no—
29#16839814—21no—
30#16839804C2212yes—
31#16839804C2211yescharacteristic
32C2×#14519711C2212yes—
33#16839786C2211yescharacteristic
34#16839772C2211yescharacteristic
35#16839764C2212yes—
36#16839764C2211yescharacteristic
37C2×#14519702C2212yes—
38C2×#14519695C2212yes—
39#16839728C2212yes—
40#16839717C2212yes—
41#16839530C2212yes—
42#16839530C2212yes—
43#16839530C2212yes—
44C2×#108×C61C2212yes—
45C61×#423C2211yescharacteristic
46C2×C4⋊C8×C61C2211yescharacteristic
47C4×M16×C61C2211yescharacteristic
48C61×#341C2212yes—
49C2×#11758222C2311yescharacteristic
50C22×Dic122—21no—
51C22×Dic122C2311yescharacteristic
52#14519810—22no—
53#14519810—22no—
54C2×Dic244—21no—
55C2×#11758190—21no—
56C2×#11758194C2312yes—
57#14519777—21no—
58#14519777—21no—
59#14519777—21no—
60#14519777—21no—
61C4×Dic122—21no—
62C4×Dic122—21no—
63C4×Dic122—21no—
64C4×Dic122—21no—
65C4×Dic122D411yescharacteristic
66C4×Dic122D411yescharacteristic
67C4×D244D411yescharacteristic
68C4×D244D411yescharacteristic
69C4×C22⋊D61—21no—
70C4×C22⋊D61—21no—
71#14519736C2311yescharacteristic
72#14519734—21no—
73C2×C4⋊Dic61—21no—
74C2×C4⋊Dic61C2311yescharacteristic
75C2×C4⋊Dic61C2312yes—
76C2×#11758196—21no—
77C2×C4×Dic61—21no—
78C42×D61—21no—
79#14519711—22no—
80#14519711—22no—
81#14519711—22no—
82#14519711—21no—
83#14519709—22no—
84#14519709—21no—
85C4⋊#92418—21no—
86C4⋊#92418—21no—
87#14519702—22no—
88#14519702—21no—
89#14519702—22no—
90#14519702—22no—
91#14519702—21no—
92#14519702—21no—
93#14519699—22no—
94#14519699—21no—
95#14519695—24no—
96#14519689—22no—
97#14519689—22no—
98#14519687—22no—
99C8×Dic61—22no—
100C2×M16×C61C2312yes—
101C2×M16×C61C2311yescharacteristic
102C2×M16×C61C2311yescharacteristic
103C22×C8×C61C2312yes—
104C2×C42×C61C2311yescharacteristic
105#108×C61—24no—
106C4⋊C8×C61—21no—
107C4⋊C8×C61—21no—
108C4⋊C8×C61D411yescharacteristic
109C4⋊C8×C61D411yescharacteristic
110C4⋊C8×C61D412yes—
111#97×C61—21no—
112C4×C8×C61—21no—
113C22×C4×C61#4111yescharacteristic
114C22×C4×C61#4111yescharacteristic
115C22×C4×C61C2411yescharacteristic
116C2×C22⋊D61—21no—
117C22×Dic61—21no—
118C22×Dic61—22no—
119C22×Dic61—21no—
120#11758222—21no—
121#11758222—21no—
122#11758222—21no—
123#11758222—21no—
124C2×D244C2×D411yescharacteristic
125C2×C4×D61—21no—
126C2×C4×D61—21no—
127C2×C4×D61—21no—
128C2×Dic122—21no—
129C2×Dic122—21no—
130C2×Dic122—21no—
131C2×Dic122—21no—
132C2×Dic122—21no—
133C2×Dic122—41no—
134C2×Dic122—41no—
135C2×Dic122—82no—
136C2×Dic122C2×D411yescharacteristic
137C2×Dic122#4112yes—
138M16×C61—21no—
139M16×C61—22no—
140M16×C61—22no—
141M16×C61—21no—
142M16×C61—21no—
143M16×C61#4112yes—
144C2×C8×C61—21no—
145C2×C8×C61—22no—
146C2×C8×C61—22no—
147C2×C8×C61—21no—
148C2×C8×C61—22no—
149C2×C8×C61C2×D412yes—
150C2×C8×C61C2×D412yes—
151C42×C61C2×D411yescharacteristic
152C42×C61C2×D411yescharacteristic
153C42×C61C2×D411yescharacteristic
154C42×C61C2×D411yescharacteristic
155C22⋊Dic61—21no—
156#11758198—21no—
157#11758198—21no—
158C4⋊Dic61—21no—
159C4⋊Dic61—22no—
160C4⋊Dic61—22no—
161C4⋊Dic61—21no—
162C4⋊Dic61—41no—
163C4⋊Dic61—41no—
164C4⋊Dic61C2×D411yescharacteristic
165C4⋊Dic61C2×D411yescharacteristic
166#11758196—21no—
167#11758196—21no—
168#11758196—41no—
169#11758196—41no—
170C4×Dic61—21no—
171C4×Dic61—21no—
172C4×Dic61—21no—
173C4×Dic61—41no—
174C4×Dic61—41no—
175#11758194—22no—
176#11758194—22no—
177C2×#92418—22no—
178Dic244—24no—
179#11758190—24no—
180C23×C61C2×#4111yescharacteristic
181C22×D61—21no—
182C2×C4×C61—22no—
183C2×C4×C61—41no—
184C2×C4×C61#12111yescharacteristic
185C2×C4×C61#12111yescharacteristic
186C2×C4×C61#12111yescharacteristic
187C2×C4×C61#12111yescharacteristic
188C2×C4×C61C22×D411yescharacteristic
189C2×C4×C61C22×D411yescharacteristic
190C2×C4×C61C2×#4111yescharacteristic
191C2×C4×C61C2×#4111yescharacteristic
192C2×C4×C612−1+411yescharacteristic
193C2×C4×C612−1+411yescharacteristic
194C22⋊D61—41no—
195C22⋊D61—41no—
196C2×Dic61—21no—
197C2×Dic61—21no—
198C2×Dic61—21no—
199C2×Dic61—22no—
200C2×Dic61—41no—
201C2×Dic61—41no—
202C2×Dic61—41no—
203C2×Dic61—42no—
204C2×Dic61—82no—
205C2×Dic61—81no—
206D244—21no—
207D244—21no—
208C4×D61—41no—
209C4×D61—41no—
210C4×D61—42no—
211C4×D61—81no—
212Dic122—22no—
213Dic122—21no—
214Dic122—21no—
215Dic122—22no—
216Dic122—41no—
217Dic122—41no—
218Dic122—82no—
219Dic122—82no—
220C8×C61—22no—
221C8×C61—22no—
222C8×C61—22no—
223C8×C61—42no—
224C8×C61—41no—
225#92418—42no—
226#24722—611nomaximal, Sylow
227C22×C61—21no—
228C22×C61—21no—
229C22×C61C2×#12111yescharacteristic
230C22×C61#55211yescharacteristic
231C22×C61#55611yescharacteristic
232C2×D61—41no—
233C2×D61—41no—
234C2×D61—41no—
235C4×C61—21no—
236C4×C61—21no—
237C4×C61—21no—
238C4×C61#47312yes—
239C4×C61#52511yescharacteristic
240C4×C61#53611yescharacteristic
241C4×C61#54711yescharacteristic
242C4×C61#54811yescharacteristic
243Dic61—42no—
244Dic61—41no—
245Dic61—41no—
246Dic61—41no—
247Dic61—82no—
248Dic61—81no—
249#3079—611no—
250C2×#477—611no—
251C4×#137—611no—
252#2925—611no—
253#2078—612no—
254#2052—612no—
255#1997—611no—
256#1952—612no—
257#1950D6111yescharacteristic, complemented
258#1930—612no—
259#1801—611no—
260C2×C61—21no—
261C2×C61—21no—
262C2×C61#241511yescharacteristic
263C2×C61C2×#47311yescharacteristic
264C2×C61#306811yescharacteristic
265D61—81no—
266C2×#137—611no—
267C2×C4⋊Q8—611no—
268C4×#41—611no—
269C2×C4×Q8—611no—
270#477—1221no—
271#477—1221no—
272#477—1221no—
273#477—1222no—
274#476—1221no—
275#475—1221no—
276#474—1221no—
277#441—1221no—
278#440—1221no—
279C4×Q16—1221no—
280C4×SD16—1221no—
281#433—1222no—
282#432—1221no—
283#431—1221no—
284C2×#108C2×D6112yes—
285#428—612no—
286#428—611no—
287C2×#107—612no—
288#423—611no—
289#423C2×D6111yescharacteristic
290C2×C4⋊C8C2×D6111yescharacteristic
291#419—611no—
292#417—612no—
293#417—611no—
294C2×#103—612no—
295C2×#101—612no—
296#408—612no—
297#405—612no—
298C4×M16C2×D6111yescharacteristic
299#343—612no—
300#343—612no—
301#343—612no—
302#341C2×D6112yes—
303C61#2472211yescharacteristic, complemented, Sylow
304C2×#41—611no—
305C22×Q8—611no—
306C22×Q8—1221no—
307#137—1222no—
308#137—1222no—
309C2×Q16—1221no—
310C2×SD16—1221no—
311C2×M16—612no—
312C2×M16C22×D6111yescharacteristic
313C2×M16C22×D6112yes—
314C2×M16C22×D6111yescharacteristic
315C22×C8C22×D6112yes—
316C4⋊Q8—1221no—
317C4⋊Q8—1221no—
318C4⋊Q8—1221no—
319C4⋊Q8—1221no—
320C4×Q8—611no—
321C4×Q8—611no—
322C4×Q8—1221no—
323C4×Q8—1221no—
324C4×Q8—1221no—
325C4×Q8—1221no—
326C4×D4—611no—
327C4×D4—611no—
328C4×D4—1221no—
329C4×D4—1221no—
330#117—611no—
331#117—1221no—
332C2×C4⋊C4—611no—
333C2×C4⋊C4—612no—
334C2×C4⋊C4—1221no—
335C2×C4⋊C4—1221no—
336C2×C42—1221no—
337C2×C42—1221no—
338C2×C42C22×D6111yescharacteristic
339#108—24no—
340#107—1221no—
341#107—1222no—
342#107—1222no—
343#107—1222no—
344#106—1221no—
345#106—1222no—
346C4⋊C8—21no—
347C4⋊C8—21no—
348C4⋊C8—1221no—
349C4⋊C8—1221no—
350C4⋊C8D24411yescharacteristic
351C4⋊C8D24411yescharacteristic
352C4⋊C8D24412yes—
353#103—1221no—
354#103—1221no—
355#103—1221no—
356#103—1222no—
357#103—1222no—
358#103—1222no—
359#102—1221no—
360#102—1222no—
361#101—1224no—
362C22⋊C8—1222no—
363C22⋊C8—1222no—
364#97—21no—
365#97—1222no—
366C4×C8—21no—
367C4×C8—1222no—
368#41—1221no—
369#41—1221no—
370#41—1221no—
371#41—1221no—
372C2×Q8—611no—
373C2×Q8—612no—
374C2×Q8—1221no—
375C2×Q8—1221no—
376C2×Q8—1221no—
377C2×Q8—1221no—
378C2×Q8—1221no—
379C2×Q8—4882no—
380C2×Q8—2441no—
381C2×Q8—2441no—
382C2×D4—611no—
383C2×D4—1221no—
384C22×C4—1221no—
385C22×C4—1221no—
386C22×C4—1221no—
387C22×C4—1221no—
388C22×C4—1221no—
389C22×C4—1222no—
390C22×C4#1175822611yescharacteristic
391C22×C4#1175822611yescharacteristic
392C22×C4C23×D6111yescharacteristic
393Q16—1224no—
394SD16—1224no—
395M16—21no—
396M16—22no—
397M16—22no—
398M16—21no—
399M16—21no—
400M16—1222no—
401M16—1222no—
402M16#1175822412yes—
403C2×C8—21no—
404C2×C8—22no—
405C2×C8—22no—
406C2×C8—21no—
407C2×C8—22no—
408C2×C8—1222no—
409C2×C8C2×D24412yes—
410C2×C8C2×D24412yes—
411C4⋊C4—611no—
412C4⋊C4—611no—
413C4⋊C4—1221no—
414C4⋊C4—1221no—
415C4⋊C4—1221no—
416C4⋊C4—1222no—
417C4⋊C4—1222no—
418C4⋊C4—1221no—
419C4⋊C4—2441no—
420C4⋊C4—2441no—
421C4⋊C4—2441no—
422C4⋊C4—2441no—
423C22⋊C4—1221no—
424C22⋊C4—1221no—
425C22⋊C4—1221no—
426C42—1221no—
427C42—1221no—
428C42—1221no—
429C42—2441no—
430C42—2441no—
431C42C2×D24411yescharacteristic
432C42C2×D24411yescharacteristic
433C42D4×D6111yescharacteristic
434C42D4×D6111yescharacteristic
435C23—1221no—
436C23C2×#1175822611yescharacteristic
437Q8—1222no—
438Q8—1221no—
439Q8—1221no—
440Q8—1222no—
441Q8—4882no—
442Q8—4882no—
443Q8—2441no—
444Q8—2441no—
445D4—1221no—
446D4—1221no—
447D4—2441no—
448D4—2441no—
449C2×C4—22no—
450C2×C4—41no—
451C2×C4—1222no—
452C2×C4—1221no—
453C2×C4—1221no—
454C2×C4—1221no—
455C2×C4—4881no—
456C2×C4—4881no—
457C2×C4—4882no—
458C2×C4—2441no—
459C2×C4—2442no—
460C2×C4—2441no—
461C2×C4—2441no—
462C2×C4—2442no—
463C2×C4—2441no—
464C2×C4—2441no—
465C2×C4#1451975211yescharacteristic
466C2×C4#1451975211yescharacteristic
467C2×C4#1451975211yescharacteristic
468C2×C4#1451975211yescharacteristic
469C2×C4C2×D4×D6111yescharacteristic
470C2×C4C22×D24411yescharacteristic
471C2×C4#41×D6111yescharacteristic
472C2×C4C2×#1175822411yescharacteristic
473C2×C4#1451982411yescharacteristic
474C2×C4#1451982511yescharacteristic
475C8—22no—
476C8—22no—
477C8—22no—
478C8—42no—
479C8—41no—
480C8—2442no—
481C22—21no—
482C22—21no—
483C22—2441no—
484C22—2441no—
485C22—2441no—
486C22C2×#1451975211yescharacteristic
487C22#1684045011yescharacteristic
488C22#1684048611yescharacteristic
489C4—21no—
490C4—21no—
491C4—21no—
492C4—4881no—
493C4—4882no—
494C4—2441no—
495C4—2442no—
496C4—2441no—
497C4—2441no—
498C4#1684003812yes—
499C4#1684027211yescharacteristic
500C4#1684033511yescharacteristic
501C4#1684041611yescharacteristic
502C4#1684042411yescharacteristic
503C2—21no—
504C2—21no—
505C2—4881no—
506C2#2144924611yescharacteristic
507C2C2×#1684003811yescharacteristic
508C2#2145554811yescharacteristic
subgroupG/H
centerC22C2×#14519752
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1950C2
socleC22×C61C2×#121
prime radicalC2×#11758222C23
hypercenter#1950D61
hypocenterC61#24722
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1950

Complements

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

NH ≅ G/Ntype
2. C2×#16840058C2semidirect
7. #21446808C2semidirect
8. #21446605C2semidirect
9. #21446475C2semidirect
10. #21445812C2semidirect
11. C61×#1950C2semidirect
257. #1950D61semidirect
303. C61#24722semidirect

Maximal subgroups

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

subgroupindex
#214556352
C2×#168400582
C4×#145198102
#214544842
#214472612
#214471202
#214468082
#214466052
#214464752
#214458122
C61×#19502
#2472261