Finite Group Databasebeta

← #29836909

Subgroups — #29836909

Order 15616.

546 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458186C211yesmaximal, characteristic, complemented
2#21457559C211yesmaximal, characteristic
3#21448026C211yesmaximal, characteristic, complemented
4#21447998C211yesmaximal, characteristic, complemented
5#21447980C211yesmaximal, characteristic, complemented
6#21447914C211yesmaximal, characteristic, complemented
7#21447909C211yesmaximal, characteristic, complemented
8#21447878C211yesmaximal, characteristic, complemented
9#21447760C211yesmaximal, characteristic, complemented
10#21447754C211yesmaximal, characteristic, complemented
11C4×Dic488C211yesmaximal, characteristic, complemented
12C16×D244C211yesmaximal, characteristic, complemented
13#21447523C211yesmaximal, characteristic, complemented
14#358×D61C211yesmaximal, characteristic, complemented
15C61×#2242C211yesmaximal, characteristic, complemented
16C2×#14519796C2211yescharacteristic
17C2×Q16×D61C2211yescharacteristic
18#16840450—21no—
19#16840420—21no—
20C2×Dic488C2211yescharacteristic
21C2×#14519723C2211yescharacteristic
22C2×#14519721C2211yescharacteristic
23C2×C16×D61C2211yescharacteristic
24C2×C16×D61C2211yescharacteristic
25#16840106—21no—
26#16840094—21no—
27#16840066—21no—
28#16840004C2211yescharacteristic
29#16840004C2211yescharacteristic
30#16840000C2211yescharacteristic
31#16839995C2211yescharacteristic
32#16839981—21no—
33#16839921—21no—
34#16839899—21no—
35C4×Dic244C2211yescharacteristic
36C4×Dic244C2211yescharacteristic
37C8×D244C2211yescharacteristic
38#16839799C2211yescharacteristic
39#107×D61C2211yescharacteristic
40#16839589C2211yescharacteristic
41#16839588C2211yescharacteristic
42#16839587C2211yescharacteristic
43C4⋊#11758185C2211yescharacteristic
44#16839567C2211yescharacteristic
45#16839567C2211yescharacteristic
46#16839566C2211yescharacteristic
47#16839565C2211yescharacteristic
48#16839565C2211yescharacteristic
49#16839563C2211yescharacteristic
50#16839541C2211yescharacteristic
51#16839541C2211yescharacteristic
52C61×#499C2211yescharacteristic
53C61×#495C2211yescharacteristic
54C61×#358C2211yescharacteristic
55C61×#358C2211yescharacteristic
56C61×#357C2211yescharacteristic
57C61×#357C2211yescharacteristic
58C4×C16×C61C2211yescharacteristic
59C2×#11758224—21no—
60C2×Q8×D61—21no—
61#14519796—22no—
62#14519796—41no—
63C2×Dic244C2311yescharacteristic
64C2×Dic244C2311yescharacteristic
65C2×#11758202—21no—
66Q16×D61—22no—
67Q16×D61—41no—
68C2×#11758200—21no—
69C2×C8×D61C2311yescharacteristic
70C2×C8×D61C2311yescharacteristic
71#14519772—41no—
72#14519768—41no—
73#14519763—41no—
74#14519762—41no—
75#14519757—21no—
76#14519757—21no—
77#14519754—41no—
78#14519753—21no—
79#14519750—41no—
80#14519748—21no—
81C4×Dic122—21no—
82C4×Dic122—21no—
83C4×D244D411yescharacteristic
84#14519737—41no—
85#14519735—21no—
86#14519735—41no—
87C4⋊C4×D61—21no—
88Dic488—22no—
89#14519723—41no—
90#14519721—41no—
91C2×#11758185C2311yescharacteristic
92C2×#11758185C2311yescharacteristic
93C16×D61—41no—
94C16×D61—41no—
95#14519711C2311yescharacteristic
96#14519711C2311yescharacteristic
97#14519710—21no—
98#14519708—21no—
99C4⋊#92418D411yescharacteristic
100#14519702—21no—
101#14519702—21no—
102#14519701—21no—
103#14519700—21no—
104#14519700—21no—
105#14519698—21no—
106#14519689D411yescharacteristic
107#14519689D411yescharacteristic
108C2×Q16×C61C2311yescharacteristic
109C2×SD16×C61—21no—
110C2×D8×C61C2311yescharacteristic
111#125×C61—21no—
112#124×C61—21no—
113C2×C16×C61C2311yescharacteristic
114C2×C16×C61C2311yescharacteristic
115#107×C61C2311yescharacteristic
116#107×C61C2311yescharacteristic
117#106×C61—21no—
118C4×C8×C61C2311yescharacteristic
119C2×Q8×C61—21no—
120C2×D4×C61—21no—
121C2×C22⋊D61—41no—
122C2×C22⋊D61—41no—
123C22×Dic61—41no—
124Q8×D61—42no—
125Q8×D61—81no—
126#11758224—42no—
127#11758224—81no—
128C2×D244D811yescharacteristic
129C2×C4×D61—41no—
130C2×C4×D61—41no—
131C2×C4×D61C2×D411yescharacteristic
132C2×C4×D61C2×D411yescharacteristic
133C2×Dic122—21no—
134C2×Dic122—21no—
135C2×Dic122—41no—
136Q16×C61—21no—
137Q16×C61—21no—
138SD16×C61—81no—
139D8×C61—21no—
140D8×C61—21no—
141C2×C8×C61C2×D411yescharacteristic
142C2×C8×C61C2411yescharacteristic
143C4⋊C4×C61—21no—
144C4⋊C4×C61—21no—
145C4⋊C4×C61—41no—
146C4⋊C4×C61—41no—
147C22⋊C4×C61—41no—
148C22⋊C4×C61—41no—
149C42×C61C2×D411yescharacteristic
150C22⋊Dic61—41no—
151#11758202—42no—
152#11758200—42no—
153#11758198—41no—
154#11758198—41no—
155#11758198—41no—
156#11758198—41no—
157#11758198D811yescharacteristic
158#11758198D811yescharacteristic
159C4⋊Dic61—21no—
160C4⋊Dic61—21no—
161C4⋊Dic61—41no—
162C4⋊Dic61—41no—
163C4⋊Dic61D811yescharacteristic
164#11758196—41no—
165#11758196—41no—
166#11758196—41no—
167#11758196—41no—
168C4×Dic61—41no—
169C4×Dic61—41no—
170C4×Dic61—41no—
171C2×#92418C2×D411yescharacteristic
172C2×#92418C2×D411yescharacteristic
173Dic244—21no—
174Dic244—21no—
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—
186C22×D61C2×D811yescharacteristic
187C22×D61C2×D811yescharacteristic
188Q8×C61—41no—
189Q8×C61—41no—
190D4×C61—41no—
191D4×C61—41no—
192C2×C4×C61—41no—
193C2×C4×C61—41no—
194C2×C4×C61—41no—
195C2×C4×C61C2×D811yescharacteristic
196C2×C4×C61C2×D811yescharacteristic
197C2×C4×C61C22×D411yescharacteristic
198C22⋊D61—82no—
199C22⋊D61—82no—
200C2×Dic61—41no—
201C2×Dic61—41no—
202C2×Dic61—41no—
203C2×Dic61—41no—
204C2×Dic61—82no—
205C2×Dic61C2×D811yescharacteristic
206C2×Dic61C2×D811yescharacteristic
207D244—22no—
208C4×D61—21no—
209C4×D61—21no—
210C4×D61—21no—
211C4×D61—21no—
212C4×D61—82no—
213C4×D61—82no—
214Dic122—22no—
215Dic122—41no—
216Dic122—41no—
217Dic122—41no—
218Dic122—82no—
219C8×C61—21no—
220C8×C61C2×#4111yescharacteristic
221C8×C61H(5,𝔽2)11yescharacteristic
222#92418—21no—
223#92418—21no—
224#33867—611nomaximal, Sylow
225C22×C61—81no—
226C22×C61—81no—
227C22×C61—81no—
228C22×C61C22×D811yescharacteristic
229C2×D61—21no—
230C2×D61—21no—
231C2×D61—21no—
232C2×D61—21no—
233C2×D61—21no—
234C2×D61#50812yes—
235C4×C61—21no—
236C4×C61—21no—
237C4×C61—81no—
238C4×C61—81no—
239C4×C61—81no—
240C4×C61#54611yescharacteristic
241C4×C61#57711yescharacteristic
242Dic61—21no—
243Dic61—21no—
244Dic61—42no—
245Dic61—81no—
246Dic61—81no—
247Dic61—81no—
248#3336—611no—
249#3285—611no—
250#2242D6111yescharacteristic, complemented
251#2237—611no—
252#2232—611no—
253#2229—611no—
254#2217—611no—
255#2216—611no—
256#2211—611no—
257#2189—611no—
258#2188—611no—
259C4×Q32—611no—
260D4×C16—611no—
261#2138—611no—
262C2×#358—611no—
263C2×C61—161no—
264C2×C61#329411yescharacteristic
265C2×C61C2×#50811yescharacteristic
266C2×C61#341711yescharacteristic
267D61—22no—
268D61—41no—
269C2×#135—611no—
270C22×Q16—611no—
271#552—1221no—
272#548—1221no—
273C2×Q32—611no—
274C2×Q32—611no—
275C2×SD32—611no—
276C22×C16—611no—
277C22×C16—611no—
278#499C2×D6111yescharacteristic
279#495C2×D6111yescharacteristic
280#485—1221no—
281#483—1221no—
282#479—1221no—
283#467—611no—
284#467—611no—
285#467—611no—
286#466—611no—
287#464—1221no—
288#452—1221no—
289#448—1221no—
290C4×Q16—611no—
291C4×Q16—611no—
292C8×D4—611no—
293#427—611no—
294C2×#107—611no—
295#367—611no—
296#366—611no—
297#366—611no—
298C4⋊C16—611no—
299#358—611no—
300#358—611no—
301#358—611no—
302#358—611no—
303#358—611no—
304#358C2×D6111yescharacteristic
305#358C2×D6111yescharacteristic
306#357—611no—
307#357C2×D6111yescharacteristic
308#357C2×D6111yescharacteristic
309C22⋊C16—611no—
310C22⋊C16—611no—
311C4×C16C2×D6111yescharacteristic
312C61#3386711yescharacteristic, complemented, Sylow
313C2×#41—1221no—
314C22×Q8—1221no—
315#135—1222no—
316#135—2441no—
317C2×Q16—611no—
318C2×Q16—611no—
319C2×Q16—1221no—
320C2×Q16—1222no—
321C2×Q16—2441no—
322C2×Q16C22×D6111yescharacteristic
323C2×SD16—21no—
324C2×SD16—1221no—
325C2×D8C22×D6111yescharacteristic
326C22×C8—611no—
327C22×C8—611no—
328#126—2441no—
329#125—21no—
330#125—2441no—
331#124—21no—
332#124—2441no—
333#123—2441no—
334C22⋊Q8—1221no—
335C22⋊Q8—1221no—
336C22⋊Q8—1221no—
337C22⋊Q8—2441no—
338#121—1221no—
339#121—2441no—
340C4×Q8—1221no—
341C4×Q8—1221no—
342C4×D4—611no—
343C4×D4—2441no—
344#117—1221no—
345#117—2441no—
346C2×C4⋊C4—1221no—
347Q32—1222no—
348Q32—2441no—
349SD32—2441no—
350C2×C16—611no—
351C2×C16—611no—
352C2×C16—2441no—
353C2×C16—2441no—
354C2×C16C22×D6111yescharacteristic
355C2×C16C22×D6111yescharacteristic
356#107—611no—
357#107—611no—
358#107—1221no—
359#107C22×D6111yescharacteristic
360#107C22×D6111yescharacteristic
361#106—21no—
362#106—1221no—
363C4⋊C8—611no—
364#103—1221no—
365#103—1221no—
366#103—1221no—
367#103—1221no—
368#103—1221no—
369#102—1221no—
370C22⋊C8—611no—
371C22⋊C8—611no—
372C4×C8C22×D6111yescharacteristic
373#41—4881no—
374#41—2442no—
375C2×Q8—21no—
376C2×Q8—1221no—
377C2×Q8—1221no—
378C2×Q8—4881no—
379C2×Q8—2441no—
380C2×Q8—2442no—
381C2×D4—21no—
382C2×D4—611no—
383C2×D4—2441no—
384C2×D4—2441no—
385C22×C4—611no—
386C22×C4—611no—
387C22×C4—2441no—
388C22×C4—2441no—
389C22×C4—2441no—
390Q16—21no—
391Q16—21no—
392Q16—612no—
393Q16—1221no—
394Q16—1221no—
395Q16—1221no—
396Q16—2442no—
397SD16—81no—
398SD16—2442no—
399D8—21no—
400D8—21no—
401C2×C8—611no—
402C2×C8—611no—
403C2×C8—1221no—
404C2×C8—1221no—
405C2×C8—1221no—
406C2×C8—1221no—
407C2×C8D4×D6111yescharacteristic
408C2×C8C23×D6111yescharacteristic
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—41no—
412C4⋊C4—41no—
413C4⋊C4—611no—
414C4⋊C4—1221no—
415C4⋊C4—1221no—
416C4⋊C4—2441no—
417C4⋊C4—2441no—
418C4⋊C4—2441no—
419C4⋊C4—2441no—
420C4⋊C4—2441no—
421C4⋊C4—2441no—
422C22⋊C4—41no—
423C22⋊C4—41no—
424C22⋊C4—611no—
425C22⋊C4—611no—
426C22⋊C4—2441no—
427C22⋊C4—2441no—
428C22⋊C4—2441no—
429C22⋊C4—2441no—
430C22⋊C4—2441no—
431C42—2441no—
432C42—2441no—
433C42—2441no—
434C42D4×D6111yescharacteristic
435C16—21no—
436C16—21no—
437C16—1221no—
438C16—1221no—
439C23—41no—
440C23—611no—
441C23—611no—
442Q8—41no—
443Q8—41no—
444Q8—1222no—
445Q8—4882no—
446Q8—2441no—
447Q8—2441no—
448Q8—2441no—
449D4—41no—
450D4—41no—
451D4—1222no—
452D4—4882no—
453D4—4882no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—611no—
458C2×C4—611no—
459C2×C4—1221no—
460C2×C4—1221no—
461C2×C4—1221no—
462C2×C4—1221no—
463C2×C4—4882no—
464C2×C4—4882no—
465C2×C4—4882no—
466C2×C4—2441no—
467C2×C4—2441no—
468C2×C4—2441no—
469C2×C4—2441no—
470C2×C4D8×D6111yescharacteristic
471C2×C4D8×D6111yescharacteristic
472C2×C4C2×D4×D6111yescharacteristic
473C8—21no—
474C8—1221no—
475C8—1221no—
476C8#41×D6111yescharacteristic
477C8#1451982311yescharacteristic
478C22—81no—
479C22—81no—
480C22—81no—
481C22—612no—
482C22—1221no—
483C22—1221no—
484C22—1221no—
485C22—1221no—
486C22—1221no—
487C22C2×D8×D6111yescharacteristic
488C4—21no—
489C4—21no—
490C4—81no—
491C4—81no—
492C4—81no—
493C4—1221no—
494C4—1221no—
495C4—4881no—
496C4—4881no—
497C4—4881no—
498C4—2442no—
499C4#1684040511yescharacteristic
500C4#1684056811yescharacteristic
501C2—161no—
502C2—1222no—
503C2—2441no—
504C2#2145763111yescharacteristic
505C2#508×D6111yescharacteristic
506C2#2145896911yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2242C2
socleC22×C61C22×D8
prime radical#21457559C2
hypercenter#2242D61
hypocenterC61#33867
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2242

Complements

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

NH ≅ G/Ntype
1. #21458186C2semidirect
3. #21448026C2semidirect
4. #21447998C2semidirect
5. #21447980C2semidirect
6. #21447914C2semidirect
7. #21447909C2semidirect
8. #21447878C2semidirect
9. #21447760C2semidirect
10. #21447754C2semidirect
11. C4×Dic488C2semidirect
12. C16×D244C2semidirect
13. #21447523C2semidirect
14. #358×D61C2semidirect
15. C61×#2242C2semidirect
250. #2242D61semidirect
312. C61#33867semidirect

Maximal subgroups

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

subgroupindex
#214581862
#214575592
#214480262
#214479982
#214479802
#214479142
#214479092
#214478782
#214477602
#214477542
C4×Dic4882
C16×D2442
#214475232
#358×D612
C61×#22422
#3386761