Finite Group Databasebeta

← #29837021

Subgroups — #29837021

Order 15616.

580 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458168C211yesmaximal, characteristic, complemented
2#21457559C211yesmaximal, characteristic, complemented
3#21448055C211yesmaximal, characteristic, complemented
4#21448020C211yesmaximal, characteristic, complemented
5#21447998C211yesmaximal, characteristic, complemented
6#21447972C211yesmaximal, characteristic, complemented
7#21447929C211yesmaximal, characteristic, complemented
8#21447902C211yesmaximal, characteristic, complemented
9#21447739C211yesmaximal, characteristic, complemented
10#21447734C211yesmaximal, characteristic, complemented
11#21447683C211yesmaximal, characteristic, complemented
12#21447643C211yesmaximal, characteristic, complemented
13#21447528C211yesmaximal, characteristic, complemented
14#358×D61C211yesmaximal, characteristic, complemented
15C61×#2210C211yesmaximal, characteristic, complemented
16C2×#14519796C2211yescharacteristic
17C2×Q16×D61C2211yescharacteristic
18#16840420—21no—
19#16840417—21no—
20C2×#14519721C2211yescharacteristic
21C2×#14519716C2211yescharacteristic
22C2×C16×D61C2211yescharacteristic
23#16840167C2211yescharacteristic
24#16840074—21no—
25#16840074—21no—
26#16840042—21no—
27#16840000C2211yescharacteristic
28#16839995C2211yescharacteristic
29#16839995C2211yescharacteristic
30#16839995C2211yescharacteristic
31#16839981—21no—
32#16839921—21no—
33#16839899—21no—
34C4×Dic244C2211yescharacteristic
35C8×D244C2211yescharacteristic
36#107×D61C2211yescharacteristic
37#107×D61C2211yescharacteristic
38#16839588C2211yescharacteristic
39#16839588C2211yescharacteristic
40#16839587C2211yescharacteristic
41#16839567C2211yescharacteristic
42#16839567C2211yescharacteristic
43#16839566C2211yescharacteristic
44#16839566C2211yescharacteristic
45#16839565C2211yescharacteristic
46#16839563C2211yescharacteristic
47#16839563C2211yescharacteristic
48#16839563C2211yescharacteristic
49#16839541C2211yescharacteristic
50#16839541C2211yescharacteristic
51#16839538C2211yescharacteristic
52C2×SD32×C61C2211yescharacteristic
53C2×D16×C61C2211yescharacteristic
54C61×#495C2211yescharacteristic
55C4×D8×C61C2211yescharacteristic
56C61×C4⋊C16C2211yescharacteristic
57C61×#358C2211yescharacteristic
58C61×#357C2211yescharacteristic
59C2×#11758222—41no—
60C2×#11758224—21no—
61C2×Q8×D61—21no—
62#14519796—22no—
63#14519796—41no—
64C2×Dic244C2311yescharacteristic
65C2×#11758202—21no—
66Q16×D61—22no—
67Q16×D61—41no—
68C2×#11758200—21no—
69C2×C8×D61C2311yescharacteristic
70C2×C8×D61C2311yescharacteristic
71#14519777—21no—
72#14519763—41no—
73#14519759—41no—
74#14519759—41no—
75#14519756—41no—
76#14519754—41no—
77#14519753—21no—
78#14519750—41no—
79#14519748—21no—
80#14519748—21no—
81#14519748—21no—
82C4×Dic122—21no—
83C4×D244D411yescharacteristic
84#14519737—41no—
85C4⋊C4×D61—21no—
86C4⋊C4×D61—21no—
87#14519721—22no—
88#14519716—41no—
89C2×#11758185C2311yescharacteristic
90C2×#11758185C2311yescharacteristic
91C16×D61—41no—
92#14519711—21no—
93#14519711C2311yescharacteristic
94#14519711C2311yescharacteristic
95#14519711C2311yescharacteristic
96#14519710—21no—
97#14519710—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—
132#11758222—84no—
133C2×D244D811yescharacteristic
134C2×C4×D61—41no—
135C2×C4×D61—41no—
136C2×C4×D61—41no—
137C2×C4×D61C2×D411yescharacteristic
138C2×C4×D61C2×D411yescharacteristic
139C2×Dic122—21no—
140C2×Dic122—41no—
141C2×Dic122—41no—
142Q16×C61—21no—
143Q16×C61—21no—
144SD16×C61—81no—
145D8×C61—21no—
146D8×C61—21no—
147D8×C61—21no—
148D8×C61—21no—
149C2×C8×C61C2×D411yescharacteristic
150C2×C8×C61C2411yescharacteristic
151C4⋊C4×C61—21no—
152C22⋊C4×C61—41no—
153C22⋊C4×C61—41no—
154C22⋊C4×C61—41no—
155C42×C61C2×D411yescharacteristic
156C22⋊Dic61—41no—
157C22⋊Dic61—41no—
158C22⋊Dic61—41no—
159#11758202—42no—
160#11758200—42no—
161#11758198—41no—
162#11758198D811yescharacteristic
163#11758198D811yescharacteristic
164C4⋊Dic61—21no—
165C4⋊Dic61—21no—
166C4⋊Dic61—21no—
167C4⋊Dic61—41no—
168C4⋊Dic61D811yescharacteristic
169#11758196—41no—
170#11758196—41no—
171#11758196—41no—
172#11758196—41no—
173C4×Dic61—41no—
174C2×#92418C2×D411yescharacteristic
175C2×#92418C2×D411yescharacteristic
176Dic244—21no—
177Dic244#4112yescomplemented
178C8×D61—21no—
179C8×D61—21no—
180C8×D61—21no—
181C8×D61—21no—
182C16×C61—21no—
183C16×C61—21no—
184#11758185—21no—
185#11758185—21no—
186C23×C61—41no—
187C23×C61—41no—
188C22×D61C2×D811yescharacteristic
189C22×D61C2×D811yescharacteristic
190Q8×C61—41no—
191Q8×C61—41no—
192D4×C61—41no—
193D4×C61—41no—
194D4×C61—41no—
195D4×C61—41no—
196C2×C4×C61—41no—
197C2×C4×C61—41no—
198C2×C4×C61—82no—
199C2×C4×C61C2×D811yescharacteristic
200C2×C4×C61C2×D811yescharacteristic
201C2×C4×C61C22×D411yescharacteristic
202C22⋊D61—82no—
203C22⋊D61—82no—
204C22⋊D61—82no—
205C22⋊D61—82no—
206C2×Dic61—41no—
207C2×Dic61—41no—
208C2×Dic61—41no—
209C2×Dic61—41no—
210C2×Dic61—82no—
211C2×Dic61C2×D811yescharacteristic
212C2×Dic61C2×D811yescharacteristic
213D244—22no—
214C4×D61—21no—
215C4×D61—21no—
216C4×D61—21no—
217C4×D61—21no—
218C4×D61—82no—
219C4×D61—82no—
220C4×D61—82no—
221Dic122—22no—
222Dic122—41no—
223Dic122—82no—
224Dic122—82no—
225C8×C61—21no—
226C8×C61C2×#4111yescharacteristic
227C8×C61H(5,𝔽2)11yescharacteristic
228#92418—21no—
229#92418—21no—
230#33875—611nomaximal, Sylow
231C22×C61—81no—
232C22×C61—81no—
233C22×C61—81no—
234C22×C61—81no—
235C22×C61—81no—
236C22×C61—81no—
237C22×C61C22×D811yescharacteristic
238C2×D61—21no—
239C2×D61—21no—
240C2×D61—21no—
241C2×D61—21no—
242C2×D61—21no—
243C2×D61#50912yes—
244C4×C61—21no—
245C4×C61—21no—
246C4×C61—81no—
247C4×C61—81no—
248C4×C61#54611yescharacteristic
249C4×C61#57711yescharacteristic
250Dic61—21no—
251Dic61—21no—
252Dic61—42no—
253Dic61—81no—
254Dic61—81no—
255Dic61—81no—
256#3334—611no—
257#3285—611no—
258#2243—611no—
259#2236—611no—
260#2232—611no—
261#2227—611no—
262#2220—611no—
263#2215—611no—
264#2210D6111yescharacteristic, complemented
265#2186—611no—
266#2185—611no—
267#2175—611no—
268#2168—611no—
269#2139—611no—
270C2×#358—611no—
271C2×C61—161no—
272C2×C61—161no—
273C2×C61#329411yescharacteristic
274C2×C61C2×#50911yescharacteristic
275C2×C61#341711yescharacteristic
276D61—22no—
277D61—41no—
278C2×#135—611no—
279C22×Q16—611no—
280#548—1221no—
281#547—1221no—
282C2×SD32—611no—
283C2×SD32C2×D6111yescharacteristic
284C2×D16C2×D6111yescharacteristic
285C2×M32—611no—
286C22×C16—611no—
287#500—611no—
288#495C2×D6111yescharacteristic
289#480—1221no—
290#480—1221no—
291#474—1221no—
292#467—611no—
293#466—611no—
294#466—611no—
295#466—611no—
296#464—1221no—
297#452—1221no—
298#448—1221no—
299C4×Q16—611no—
300C4×D8C2×D6111yescharacteristic
301C8×D4—611no—
302C2×#107—611no—
303C2×#107—611no—
304#366—611no—
305#366—611no—
306#366—611no—
307C4⋊C16C2×D6111yescharacteristic
308#358—611no—
309#358—611no—
310#358—611no—
311#358—611no—
312#358—611no—
313#358C2×D6111yescharacteristic
314#357—611no—
315#357—611no—
316#357—611no—
317#357C2×D6111yescharacteristic
318C22⋊C16—611no—
319C22⋊C16—611no—
320#346—611no—
321C61#3387511yescharacteristic, complemented, Sylow
322C2×#41—1221no—
323C2×#41—2441no—
324C22×Q8—1221no—
325#135—1222no—
326#135—2441no—
327C2×Q16—611no—
328C2×Q16—1221no—
329C2×Q16—1222no—
330C2×Q16—2441no—
331C2×Q16C22×D6111yescharacteristic
332C2×SD16—21no—
333C2×SD16—1221no—
334C2×D8C22×D6111yescharacteristic
335C2×D8C22×D6111yescharacteristic
336C22×C8—611no—
337C22×C8—611no—
338C4⋊Q8—1221no—
339#124—21no—
340#124—2441no—
341#123—2441no—
342#123—2441no—
343C22⋊Q8—1221no—
344C22⋊Q8—2441no—
345C22⋊Q8—2441no—
346#121—1221no—
347#121—1221no—
348#121—1221no—
349#121—2441no—
350C4×Q8—1221no—
351C4×D4—21no—
352C4×D4—611no—
353C4×D4—2441no—
354C2×C4⋊C4—1221no—
355C2×C4⋊C4—1221no—
356SD32—41no—
357SD32—1222no—
358D16—41no—
359M32—2441no—
360C2×C16—611no—
361C2×C16—611no—
362C2×C16—2441no—
363C2×C16C22×D6111yescharacteristic
364C2×C16C22×D6111yescharacteristic
365#107—611no—
366#107—611no—
367#107—611no—
368#107—1221no—
369#107—1221no—
370#107—1221no—
371#107C22×D6111yescharacteristic
372C4⋊C8—611no—
373#103—1221no—
374#103—1221no—
375#102—21no—
376#102—1221no—
377#102—1221no—
378#102—1221no—
379C22⋊C8—611no—
380C22⋊C8—611no—
381C4×C8C22×D6111yescharacteristic
382#41—4884no—
383#41—4881no—
384#41—2442no—
385C2×Q8—21no—
386C2×Q8—1221no—
387C2×Q8—4881no—
388C2×Q8—2441no—
389C2×Q8—2442no—
390C2×Q8—2441no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—611no—
394C2×D4—2441no—
395C2×D4—2441no—
396C2×D4—2441no—
397C2×D4—2441no—
398C22×C4—41no—
399C22×C4—611no—
400C22×C4—611no—
401C22×C4—2441no—
402C22×C4—2441no—
403C22×C4—2441no—
404C22×C4—2441no—
405Q16—21no—
406Q16—21no—
407Q16—612no—
408Q16—1221no—
409Q16—2442no—
410SD16—81no—
411SD16—2442no—
412D8—21no—
413D8—21no—
414D8—21no—
415D8—21no—
416C2×C8—611no—
417C2×C8—611no—
418C2×C8—1221no—
419C2×C8—1221no—
420C2×C8—1221no—
421C2×C8—1221no—
422C2×C8D4×D6111yescharacteristic
423C2×C8C23×D6111yescharacteristic
424C4⋊C4—21no—
425C4⋊C4—611no—
426C4⋊C4—1221no—
427C4⋊C4—1221no—
428C4⋊C4—1221no—
429C4⋊C4—2441no—
430C4⋊C4—2441no—
431C4⋊C4—2441no—
432C4⋊C4—2441no—
433C4⋊C4—2441no—
434C22⋊C4—41no—
435C22⋊C4—41no—
436C22⋊C4—41no—
437C22⋊C4—611no—
438C22⋊C4—611no—
439C22⋊C4—2441no—
440C22⋊C4—2441no—
441C22⋊C4—2441no—
442C22⋊C4—2441no—
443C42—2441no—
444C42D4×D6111yescharacteristic
445C16—21no—
446C16—21no—
447C16—1221no—
448C16—1221no—
449C23—41no—
450C23—41no—
451C23—611no—
452C23—611no—
453Q8—41no—
454Q8—41no—
455Q8—1222no—
456Q8—4882no—
457Q8—4882no—
458Q8—2441no—
459D4—41no—
460D4—41no—
461D4—41no—
462D4—41no—
463D4—1222no—
464D4—4882no—
465D4—4882no—
466D4—4882no—
467D4—4882no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—82no—
471C2×C4—611no—
472C2×C4—611no—
473C2×C4—1221no—
474C2×C4—1221no—
475C2×C4—1221no—
476C2×C4—1221no—
477C2×C4—4882no—
478C2×C4—4882no—
479C2×C4—4882no—
480C2×C4—4882no—
481C2×C4—2441no—
482C2×C4—2441no—
483C2×C4—2441no—
484C2×C4—2441no—
485C2×C4D8×D6111yescharacteristic
486C2×C4D8×D6111yescharacteristic
487C2×C4C2×D4×D6111yescharacteristic
488C8—21no—
489C8—1221no—
490C8—1221no—
491C8#41×D6111yescharacteristic
492C8#1451982211yescharacteristic
493C22—81no—
494C22—81no—
495C22—81no—
496C22—81no—
497C22—81no—
498C22—81no—
499C22—612no—
500C22—1221no—
501C22—1221no—
502C22—1221no—
503C22—1221no—
504C22—1221no—
505C22C2×D8×D6111yescharacteristic
506C4—21no—
507C4—21no—
508C4—81no—
509C4—81no—
510C4—1221no—
511C4—1221no—
512C4—4881no—
513C4—4881no—
514C4—4881no—
515C4—2442no—
516C4#1684040911yescharacteristic
517C4#1684057211yescharacteristic
518C2—161no—
519C2—161no—
520C2—1222no—
521C2—2441no—
522C2#2145763511yescharacteristic
523C2#509×D6111yescharacteristic
524C2#2145896911yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2210C2
socleC22×C61C22×D8
hypercenter#2210D61
hypocenterC61#33875
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. #21458168C2semidirect
2. #21457559C2semidirect
3. #21448055C2semidirect
4. #21448020C2semidirect
5. #21447998C2semidirect
6. #21447972C2semidirect
7. #21447929C2semidirect
8. #21447902C2semidirect
9. #21447739C2semidirect
10. #21447734C2semidirect
11. #21447683C2semidirect
12. #21447643C2semidirect
13. #21447528C2semidirect
14. #358×D61C2semidirect
15. C61×#2210C2semidirect
177. Dic244#41semidirect
264. #2210D61semidirect
321. C61#33875semidirect

Maximal subgroups

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

subgroupindex
#214581682
#214575592
#214480552
#214480202
#214479982
#214479722
#214479292
#214479022
#214477392
#214477342
#214476832
#214476432
#214475282
#358×D612
C61×#22102
#3387561