Finite Group Databasebeta

← #29836932

Subgroups — #29836932

Order 15616.

558 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458223C211yesmaximal, characteristic, complemented
2#21457559C211yesmaximal, characteristic, complemented
3#21448050C211yesmaximal, characteristic, complemented
4#21448026C211yesmaximal, characteristic, complemented
5#21448003C211yesmaximal, characteristic, complemented
6#21447984C211yesmaximal, characteristic, complemented
7#21447912C211yesmaximal, characteristic, complemented
8#21447902C211yesmaximal, characteristic, complemented
9#21447739C211yesmaximal, characteristic, complemented
10#21447734C211yesmaximal, characteristic, complemented
11C4×#14519721C211yesmaximal, characteristic, complemented
12#21447638C211yesmaximal, characteristic, complemented
13#21447523C211yesmaximal, characteristic, complemented
14#358×D61C211yesmaximal, characteristic, complemented
15C61×#2210C211yesmaximal, characteristic, complemented
16C2×#14519796C2211yescharacteristic
17C2×Q16×D61C2211yescharacteristic
18#16840462—21no—
19#16840420—21no—
20C2×#14519721C2211yescharacteristic
21C2×C16×D61C2211yescharacteristic
22C2×C16×D61C2211yescharacteristic
23#16840164C2211yescharacteristic
24#16840085—21no—
25#16840079—21no—
26#16840062—21no—
27#16840000C2211yescharacteristic
28#16839995C2211yescharacteristic
29#16839995C2211yescharacteristic
30#16839995C2211yescharacteristic
31#16839981—21no—
32#16839921—21no—
33#16839899—21no—
34C4×Dic244C2211yescharacteristic
35C8×D244C2211yescharacteristic
36#16839799C2211yescharacteristic
37#107×D61C2211yescharacteristic
38#16839590C2211yescharacteristic
39#16839589C2211yescharacteristic
40#16839588C2211yescharacteristic
41#16839567C2211yescharacteristic
42#16839567C2211yescharacteristic
43#16839566C2211yescharacteristic
44#16839566C2211yescharacteristic
45#16839565C2211yescharacteristic
46#16839563C2211yescharacteristic
47#16839563C2211yescharacteristic
48#16839563C2211yescharacteristic
49#16839541C2211yescharacteristic
50#16839541C2211yescharacteristic
51C4×#11758185C2211yescharacteristic
52C2×SD32×C61C2211yescharacteristic
53C2×D16×C61C2211yescharacteristic
54C61×#495C2211yescharacteristic
55C4×D8×C61C2211yescharacteristic
56C61×C4⋊C16C2211yescharacteristic
57C61×#358C2211yescharacteristic
58C61×#357C2211yescharacteristic
59C2×#11758224—21no—
60C2×Q8×D61—21no—
61#14519796—22no—
62#14519796—41no—
63C2×Dic244C2311yescharacteristic
64C2×#11758202—21no—
65Q16×D61—22no—
66Q16×D61—41no—
67C2×#11758200—21no—
68C2×C8×D61C2311yescharacteristic
69C2×C8×D61C2311yescharacteristic
70#14519770—41no—
71#14519769—21no—
72#14519763—41no—
73#14519760—41no—
74#14519754—41no—
75#14519753—21no—
76#14519750—41no—
77#14519750—41no—
78#14519748—21no—
79#14519748—21no—
80#14519748—21no—
81C4×Dic122—21no—
82C4×D244D411yescharacteristic
83C4×C22⋊D61—41no—
84#14519737—41no—
85#14519735—21no—
86C4⋊C4×D61—21no—
87#14519721—22no—
88C2×#11758185C2311yescharacteristic
89C2×#11758185C2311yescharacteristic
90C16×D61—41no—
91C16×D61—41no—
92#14519711C2311yescharacteristic
93#14519711C2311yescharacteristic
94#14519711C2311yescharacteristic
95#14519710—21no—
96#14519709—21no—
97#14519708—21no—
98C4⋊#92418D411yescharacteristic
99#14519702—21no—
100#14519701—21no—
101#14519698—21no—
102#14519698—21no—
103#14519698—21no—
104#14519689D411yescharacteristic
105#14519689D411yescharacteristic
106C2×Q16×C61C2311yescharacteristic
107C2×SD16×C61—21no—
108C2×D8×C61C2311yescharacteristic
109C2×D8×C61C2311yescharacteristic
110#124×C61—21no—
111C4×D4×C61—21no—
112SD32×C61—41no—
113D16×C61—41no—
114C2×C16×C61C2311yescharacteristic
115C2×C16×C61C2311yescharacteristic
116#107×C61C2311yescharacteristic
117#102×C61—21no—
118C4×C8×C61C2311yescharacteristic
119C2×Q8×C61—21no—
120C2×D4×C61—21no—
121C2×D4×C61—21no—
122C22×C4×C61—41no—
123C2×C22⋊D61—41no—
124C2×C22⋊D61—41no—
125C2×C22⋊D61—41no—
126C2×C22⋊D61—41no—
127C22×Dic61—41no—
128Q8×D61—42no—
129Q8×D61—81no—
130#11758224—42no—
131#11758224—81no—
132C2×D244D811yescharacteristic
133C2×C4×D61—41no—
134C2×C4×D61—41no—
135C2×C4×D61C2×D411yescharacteristic
136C2×C4×D61C2×D411yescharacteristic
137C2×Dic122—21no—
138C2×Dic122—41no—
139Q16×C61—21no—
140Q16×C61—21no—
141SD16×C61—81no—
142D8×C61—21no—
143D8×C61—21no—
144D8×C61—21no—
145D8×C61—21no—
146C2×C8×C61C2×D411yescharacteristic
147C2×C8×C61C2411yescharacteristic
148C4⋊C4×C61—21no—
149C22⋊C4×C61—41no—
150C22⋊C4×C61—41no—
151C22⋊C4×C61—41no—
152C42×C61C2×D411yescharacteristic
153C22⋊Dic61—41no—
154C22⋊Dic61—41no—
155C22⋊Dic61—41no—
156#11758202—42no—
157#11758200—42no—
158#11758198—41no—
159#11758198—41no—
160#11758198D811yescharacteristic
161#11758198D811yescharacteristic
162C4⋊Dic61—21no—
163C4⋊Dic61—21no—
164C4⋊Dic61—21no—
165C4⋊Dic61D811yescharacteristic
166#11758196—41no—
167#11758196—41no—
168#11758196—41no—
169#11758196—41no—
170#11758196—41no—
171C4×Dic61—41no—
172C4×Dic61—41no—
173C2×#92418C2×D411yescharacteristic
174C2×#92418C2×D411yescharacteristic
175Dic244—21no—
176Dic244#4112yes—
177C8×D61—21no—
178C8×D61—21no—
179C8×D61—21no—
180C8×D61—21no—
181C16×C61—21no—
182C16×C61—21no—
183#11758185—21no—
184#11758185—21no—
185C23×C61—41no—
186C23×C61—41no—
187C22×D61C2×D811yescharacteristic
188C22×D61C2×D811yescharacteristic
189Q8×C61—41no—
190Q8×C61—41no—
191D4×C61—41no—
192D4×C61—41no—
193D4×C61—41no—
194D4×C61—41no—
195C2×C4×C61—41no—
196C2×C4×C61—41no—
197C2×C4×C61—161no—
198C2×C4×C61C2×D811yescharacteristic
199C2×C4×C61C2×D811yescharacteristic
200C2×C4×C61C22×D411yescharacteristic
201C22⋊D61—82no—
202C22⋊D61—82no—
203C22⋊D61—82no—
204C22⋊D61—161no—
205C2×Dic61—41no—
206C2×Dic61—41no—
207C2×Dic61—41no—
208C2×Dic61—41no—
209C2×Dic61—82no—
210C2×Dic61C2×D811yescharacteristic
211C2×Dic61C2×D811yescharacteristic
212D244—22no—
213C4×D61—21no—
214C4×D61—21no—
215C4×D61—21no—
216C4×D61—21no—
217C4×D61—82no—
218C4×D61—161no—
219Dic122—22no—
220Dic122—41no—
221Dic122—82no—
222C8×C61—21no—
223C8×C61C2×#4111yescharacteristic
224C8×C61H(5,𝔽2)11yescharacteristic
225#92418—21no—
226#92418—21no—
227#33868—611nomaximal, Sylow
228C22×C61—81no—
229C22×C61—81no—
230C22×C61—81no—
231C22×C61—81no—
232C22×C61—81no—
233C22×C61—81no—
234C22×C61C22×D811yescharacteristic
235C2×D61—21no—
236C2×D61—21no—
237C2×D61—21no—
238C2×D61—21no—
239C2×D61—21no—
240C2×D61#50812yes—
241C4×C61—21no—
242C4×C61—21no—
243C4×C61—81no—
244C4×C61—81no—
245C4×C61#54611yescharacteristic
246C4×C61#57711yescharacteristic
247Dic61—21no—
248Dic61—21no—
249Dic61—42no—
250Dic61—81no—
251Dic61—81no—
252Dic61—81no—
253#3339—611no—
254#3285—611no—
255#2242—611no—
256#2237—611no—
257#2233—611no—
258#2229—611no—
259#2217—611no—
260#2215—611no—
261#2210D6111yescharacteristic, complemented
262#2186—611no—
263#2185—611no—
264C4×SD32—611no—
265D4×C16—611no—
266#2138—611no—
267C2×#358—611no—
268C2×C61—161no—
269C2×C61—161no—
270C2×C61#329411yescharacteristic
271C2×C61C2×#50811yescharacteristic
272C2×C61#341611yescharacteristic
273D61—22no—
274D61—41no—
275C2×#135—611no—
276C22×Q16—611no—
277#553—1221no—
278#548—1221no—
279C2×SD32—611no—
280C2×SD32C2×D6111yescharacteristic
281C2×D16C2×D6111yescharacteristic
282C22×C16—611no—
283C22×C16—611no—
284#499—611no—
285#495C2×D6111yescharacteristic
286#482—1221no—
287#481—1221no—
288#478—1221no—
289#467—611no—
290#466—611no—
291#466—611no—
292#466—611no—
293#464—1221no—
294#452—1221no—
295#448—1221no—
296C4×Q16—611no—
297C4×D8C2×D6111yescharacteristic
298C8×D4—611no—
299#427—611no—
300C2×#107—611no—
301#367—611no—
302#367—611no—
303#366—611no—
304C4⋊C16C2×D6111yescharacteristic
305#358—611no—
306#358—611no—
307#358—611no—
308#358—611no—
309#358—611no—
310#358C2×D6111yescharacteristic
311#357—611no—
312#357—611no—
313#357—611no—
314#357C2×D6111yescharacteristic
315C22⋊C16—611no—
316C22⋊C16—611no—
317C4×C16—611no—
318C61#3386811yescharacteristic, complemented, Sylow
319C2×#41—1221no—
320C22×Q8—1221no—
321#135—1222no—
322#135—2441no—
323C2×Q16—611no—
324C2×Q16—1221no—
325C2×Q16—1222no—
326C2×Q16—2441no—
327C2×Q16C22×D6111yescharacteristic
328C2×SD16—21no—
329C2×SD16—1221no—
330C2×D8C22×D6111yescharacteristic
331C2×D8C22×D6111yescharacteristic
332C22×C8—611no—
333C22×C8—611no—
334#126—2441no—
335#125—1221no—
336#124—21no—
337#124—2441no—
338#123—2441no—
339C22⋊Q8—1221no—
340C22⋊Q8—2441no—
341#121—1221no—
342#121—1221no—
343#121—1221no—
344#121—2441no—
345#121—2441no—
346C4×Q8—1221no—
347C4×D4—21no—
348C4×D4—611no—
349C4×D4—2441no—
350C4×D4—2441no—
351#117—1221no—
352C2×C4⋊C4—1221no—
353SD32—41no—
354SD32—1222no—
355D16—41no—
356C2×C16—611no—
357C2×C16—611no—
358C2×C16—2441no—
359C2×C16—2441no—
360C2×C16C22×D6111yescharacteristic
361C2×C16C22×D6111yescharacteristic
362#107—611no—
363#107—611no—
364#107—611no—
365#107—1221no—
366#107C22×D6111yescharacteristic
367#106—1221no—
368#106—1221no—
369C4⋊C8—611no—
370#103—1221no—
371#103—1221no—
372#102—21no—
373#102—1221no—
374#102—1221no—
375#102—1221no—
376C22⋊C8—611no—
377C22⋊C8—611no—
378C4×C8C22×D6111yescharacteristic
379#41—4881no—
380#41—2442no—
381C2×Q8—21no—
382C2×Q8—1221no—
383C2×Q8—4881no—
384C2×Q8—2441no—
385C2×Q8—2442no—
386C2×D4—21no—
387C2×D4—21no—
388C2×D4—611no—
389C2×D4—2441no—
390C2×D4—2441no—
391C2×D4—2441no—
392C2×D4—2441no—
393C22×C4—41no—
394C22×C4—611no—
395C22×C4—611no—
396C22×C4—2441no—
397C22×C4—2441no—
398C22×C4—2441no—
399Q16—21no—
400Q16—21no—
401Q16—612no—
402Q16—1221no—
403Q16—2442no—
404SD16—81no—
405SD16—2442no—
406D8—21no—
407D8—21no—
408D8—21no—
409D8—21no—
410C2×C8—611no—
411C2×C8—611no—
412C2×C8—1221no—
413C2×C8—1221no—
414C2×C8—1221no—
415C2×C8—1221no—
416C2×C8D4×D6111yescharacteristic
417C2×C8C23×D6111yescharacteristic
418C4⋊C4—21no—
419C4⋊C4—611no—
420C4⋊C4—1221no—
421C4⋊C4—1221no—
422C4⋊C4—1221no—
423C4⋊C4—2441no—
424C4⋊C4—2441no—
425C4⋊C4—2441no—
426C4⋊C4—2441no—
427C4⋊C4—2441no—
428C22⋊C4—41no—
429C22⋊C4—41no—
430C22⋊C4—41no—
431C22⋊C4—611no—
432C22⋊C4—611no—
433C22⋊C4—2441no—
434C22⋊C4—2441no—
435C22⋊C4—2441no—
436C22⋊C4—2441no—
437C22⋊C4—2441no—
438C42—2441no—
439C42—2441no—
440C42D4×D6111yescharacteristic
441C16—21no—
442C16—21no—
443C16—1221no—
444C16—1221no—
445C23—41no—
446C23—41no—
447C23—611no—
448C23—611no—
449Q8—41no—
450Q8—41no—
451Q8—1222no—
452Q8—4882no—
453Q8—2441no—
454D4—41no—
455D4—41no—
456D4—41no—
457D4—41no—
458D4—1222no—
459D4—9761no—
460D4—4882no—
461D4—4882no—
462D4—4882no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—161no—
466C2×C4—611no—
467C2×C4—611no—
468C2×C4—1221no—
469C2×C4—1221no—
470C2×C4—1221no—
471C2×C4—1221no—
472C2×C4—9761no—
473C2×C4—4882no—
474C2×C4—4882no—
475C2×C4—2441no—
476C2×C4—2441no—
477C2×C4—2441no—
478C2×C4—2441no—
479C2×C4D8×D6111yescharacteristic
480C2×C4D8×D6111yescharacteristic
481C2×C4C2×D4×D6111yescharacteristic
482C8—21no—
483C8—1221no—
484C8—1221no—
485C8#41×D6111yescharacteristic
486C8#1451982211yescharacteristic
487C22—81no—
488C22—81no—
489C22—81no—
490C22—81no—
491C22—81no—
492C22—81no—
493C22—612no—
494C22—1221no—
495C22—1221no—
496C22—1221no—
497C22—1221no—
498C22—1221no—
499C22C2×D8×D6111yescharacteristic
500C4—21no—
501C4—21no—
502C4—81no—
503C4—81no—
504C4—1221no—
505C4—1221no—
506C4—4881no—
507C4—4881no—
508C4—4881no—
509C4—2442no—
510C4#1684040911yescharacteristic
511C4#1684057211yescharacteristic
512C2—161no—
513C2—161no—
514C2—1222no—
515C2—2441no—
516C2#2145763511yescharacteristic
517C2#508×D6111yescharacteristic
518C2#2145896511yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2210C2
socleC22×C61C22×D8
hypercenter#2210D61
hypocenterC61#33868
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2210

Complements

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

NH ≅ G/Ntype
1. #21458223C2semidirect
2. #21457559C2semidirect
3. #21448050C2semidirect
4. #21448026C2semidirect
5. #21448003C2semidirect
6. #21447984C2semidirect
7. #21447912C2semidirect
8. #21447902C2semidirect
9. #21447739C2semidirect
10. #21447734C2semidirect
11. C4×#14519721C2semidirect
12. #21447638C2semidirect
13. #21447523C2semidirect
14. #358×D61C2semidirect
15. C61×#2210C2semidirect
261. #2210D61semidirect
318. C61#33868semidirect

Maximal subgroups

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

subgroupindex
#214582232
#214575592
#214480502
#214480262
#214480032
#214479842
#214479122
#214479022
#214477392
#214477342
C4×#145197212
#214476382
#214475232
#358×D612
C61×#22102
#3386861