Finite Group Databasebeta

← #29837081

Subgroups — #29837081

Order 15616.

536 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458189C211yesmaximal, characteristic
2#21457569C211yesmaximal, characteristic
3#21448064C211yesmaximal, characteristic, complemented
4#21448026C211yesmaximal, characteristic, complemented
5#21448015C211yesmaximal, characteristic, complemented
6#21447984C211yesmaximal, characteristic, complemented
7#21447924C211yesmaximal, characteristic, complemented
8#21447907C211yesmaximal, characteristic, complemented
9#21447751C211yesmaximal, characteristic, complemented
10#21447751C211yesmaximal, characteristic, complemented
11#21447688C211yesmaximal, characteristic, complemented
12#21447643C211yesmaximal, characteristic
13#21447537C211yesmaximal, characteristic, complemented
14#358×D61C211yesmaximal, characteristic, complemented
15C61×#2209C211yesmaximal, characteristic, complemented
16C2×Q16×D61C2211yescharacteristic
17C2×Q16×D61C2211yescharacteristic
18#16840453—21no—
19#16840427—21no—
20C2×#14519723C2211yescharacteristic
21C2×#14519716C2211yescharacteristic
22C2×C16×D61C2211yescharacteristic
23#16840164C2211yescharacteristic
24#16840101—21no—
25#16840091—21no—
26#16840069—21no—
27#16840000C2211yescharacteristic
28#16840000C2211yescharacteristic
29#16840000C2211yescharacteristic
30#16840000C2211yescharacteristic
31#16839969—21no—
32#16839916—21no—
33#16839916—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#16839566C2211yescharacteristic
46#16839566C2211yescharacteristic
47#16839566C2211yescharacteristic
48#16839565C2211yescharacteristic
49#16839541C2211yescharacteristic
50#16839541C2211yescharacteristic
51#16839538C2211yescharacteristic
52C2×Q32×C61C2211yescharacteristic
53C2×Q32×C61C2211yescharacteristic
54C61×#494C2211yescharacteristic
55C4×Q16×C61C2211yescharacteristic
56C61×C4⋊C16C2211yescharacteristic
57C61×#358C2211yescharacteristic
58C61×#358C2211yescharacteristic
59C2×Q8×D61—21no—
60C2×Q8×D61—21no—
61C2×Dic244C2311yescharacteristic
62C2×#11758202—21no—
63C2×#11758202—21no—
64Q16×D61—22no—
65Q16×D61—22no—
66Q16×D61—41no—
67Q16×D61—41no—
68C2×C8×D61C2311yescharacteristic
69C2×C8×D61C2311yescharacteristic
70#14519776—41no—
71#14519771—41no—
72#14519769—21no—
73#14519767—41no—
74#14519762—41no—
75#14519755—41no—
76#14519755—41no—
77#14519753—21no—
78#14519753—21no—
79#14519753—21no—
80#14519753—21no—
81C4×Dic122—21no—
82C4×D244D411yescharacteristic
83#14519739—41no—
84#14519735—21no—
85#14519734—41no—
86C4⋊C4×D61—21no—
87#14519723—22no—
88#14519716—41no—
89C2×#11758185C2311yescharacteristic
90C2×#11758185C2311yescharacteristic
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#14519701—21no—
102#14519701—21no—
103#14519701—21no—
104#14519689D411yescharacteristic
105#14519689D411yescharacteristic
106C2×Q16×C61—21no—
107C2×Q16×C61C2311yescharacteristic
108C2×Q16×C61C2311yescharacteristic
109C2×Q16×C61C2311yescharacteristic
110C4⋊Q8×C61—21no—
111C4×Q8×C61—21no—
112Q32×C61—41no—
113Q32×C61—41no—
114C2×C16×C61C2311yescharacteristic
115C2×C16×C61C2311yescharacteristic
116#107×C61C2311yescharacteristic
117#103×C61—21no—
118C4×C8×C61C2311yescharacteristic
119C2×Q8×C61—21no—
120C2×Q8×C61—21no—
121C2×Q8×C61—21no—
122Q8×D61—42no—
123Q8×D61—42no—
124Q8×D61—81no—
125Q8×D61—81no—
126C2×D244D811yescharacteristic
127C2×C4×D61—41no—
128C2×C4×D61—41no—
129C2×C4×D61—41no—
130C2×C4×D61C2×D411yescharacteristic
131C2×C4×D61C2×D411yescharacteristic
132C2×Dic122—21no—
133C2×Dic122—41no—
134C2×Dic122—41no—
135Q16×C61—21no—
136Q16×C61—21no—
137Q16×C61—21no—
138Q16×C61—21no—
139Q16×C61—21no—
140Q16×C61—21no—
141Q16×C61—81no—
142C2×C8×C61C2×D411yescharacteristic
143C2×C8×C61C2411yescharacteristic
144C4⋊C4×C61—21no—
145C4⋊C4×C61—41no—
146C4⋊C4×C61—41no—
147C4⋊C4×C61—41no—
148C42×C61—41no—
149C42×C61C2×D411yescharacteristic
150#11758202—42no—
151#11758202—42no—
152#11758198—41no—
153#11758198—41no—
154#11758198—41no—
155#11758198—41no—
156#11758198—41no—
157#11758198D811yescharacteristic
158#11758198D811yescharacteristic
159C4⋊Dic61—21no—
160C4⋊Dic61—21no—
161C4⋊Dic61—21no—
162C4⋊Dic61D811yescharacteristic
163#11758196—41no—
164#11758196—41no—
165#11758196—41no—
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—
185C22×D61C2×D811yescharacteristic
186C22×D61C2×D811yescharacteristic
187Q8×C61—41no—
188Q8×C61—41no—
189Q8×C61—41no—
190Q8×C61—41no—
191Q8×C61—41no—
192Q8×C61—41no—
193C2×C4×C61—41no—
194C2×C4×C61—41no—
195C2×C4×C61—41no—
196C2×C4×C61—41no—
197C2×C4×C61C2×D811yescharacteristic
198C2×C4×C61C2×D811yescharacteristic
199C2×C4×C61C22×D411yescharacteristic
200C2×Dic61—41no—
201C2×Dic61—41no—
202C2×Dic61—41no—
203C2×Dic61—41no—
204C2×Dic61C2×D811yescharacteristic
205C2×Dic61C2×D811yescharacteristic
206D244—22no—
207C4×D61—21no—
208C4×D61—21no—
209C4×D61—21no—
210C4×D61—21no—
211C4×D61—82no—
212C4×D61—82no—
213C4×D61—82no—
214Dic122—22no—
215Dic122—41no—
216Dic122—82no—
217Dic122—82no—
218C8×C61—21no—
219C8×C61C2×#4111yescharacteristic
220C8×C61H(5,𝔽2)11yescharacteristic
221#92418—21no—
222#92418—21no—
223#33879—611nomaximal, Sylow
224C22×C61C22×D811yescharacteristic
225C2×D61—21no—
226C2×D61—21no—
227C2×D61—21no—
228C2×D61—21no—
229C2×D61—21no—
230C2×D61#51012yes—
231C4×C61—21no—
232C4×C61—21no—
233C4×C61—81no—
234C4×C61—81no—
235C4×C61—81no—
236C4×C61—81no—
237C4×C61#54611yescharacteristic
238C4×C61#57711yescharacteristic
239Dic61—21no—
240Dic61—21no—
241Dic61—42no—
242Dic61—81no—
243Dic61—81no—
244Dic61—81no—
245#3336—611no—
246D4×Q16—611no—
247#2245—611no—
248#2237—611no—
249#2235—611no—
250#2229—611no—
251#2219—611no—
252#2216—611no—
253#2209D6111yescharacteristic, complemented
254#2188—611no—
255#2188—611no—
256#2176—611no—
257#2168—611no—
258#2141—611no—
259C2×#358—611no—
260C2×C61#329411yescharacteristic
261C2×C61C2×#51011yescharacteristic
262C2×C61#341711yescharacteristic
263D61—22no—
264D61—41no—
265C22×Q16—611no—
266C22×Q16—611no—
267#552—1221no—
268D4×Q8—1221no—
269C2×Q32—611no—
270C2×Q32C2×D6111yescharacteristic
271C2×Q32C2×D6111yescharacteristic
272C2×M32—611no—
273C22×C16—611no—
274#499—611no—
275#494C2×D6111yescharacteristic
276#485—1221no—
277#483—1221no—
278#479—1221no—
279#467—611no—
280#467—611no—
281#467—611no—
282#467—611no—
283#462—1221no—
284#451—1221no—
285#451—1221no—
286C4×Q16—611no—
287C4×Q16C2×D6111yescharacteristic
288C8×D4—611no—
289#427—611no—
290C2×#107—611no—
291#367—611no—
292#367—611no—
293#366—611no—
294C4⋊C16C2×D6111yescharacteristic
295#358—611no—
296#358—611no—
297#358—611no—
298#358—611no—
299#358—611no—
300#358—611no—
301#358—611no—
302#358—611no—
303#358C2×D6111yescharacteristic
304#358C2×D6111yescharacteristic
305C22⋊C16—611no—
306C22⋊C16—611no—
307#346—611no—
308C61#3387911yescharacteristic, complemented, Sylow
309C22×Q8—1221no—
310C22×Q8—1221no—
311C2×Q16—21no—
312C2×Q16—611no—
313C2×Q16—1221no—
314C2×Q16—1221no—
315C2×Q16—1222no—
316C2×Q16—1222no—
317C2×Q16—2441no—
318C2×Q16—2441no—
319C2×Q16C22×D6111yescharacteristic
320C2×Q16C22×D6111yescharacteristic
321C2×Q16C22×D6111yescharacteristic
322C22×C8—611no—
323C22×C8—611no—
324C4⋊Q8—21no—
325C4⋊Q8—2441no—
326#126—2441no—
327#125—1221no—
328#125—2441no—
329#123—2441no—
330C22⋊Q8—1221no—
331C22⋊Q8—1221no—
332C22⋊Q8—1221no—
333C22⋊Q8—1221no—
334C22⋊Q8—2441no—
335C22⋊Q8—2441no—
336C4×Q8—21no—
337C4×Q8—1221no—
338C4×D4—611no—
339C4×D4—2441no—
340#117—1221no—
341#117—2441no—
342C2×C4⋊C4—1221no—
343Q32—41no—
344Q32—41no—
345Q32—1222no—
346M32—2441no—
347C2×C16—611no—
348C2×C16—611no—
349C2×C16—2441no—
350C2×C16C22×D6111yescharacteristic
351C2×C16C22×D6111yescharacteristic
352#107—611no—
353#107—611no—
354#107—611no—
355#107—1221no—
356#107C22×D6111yescharacteristic
357#106—1221no—
358#106—1221no—
359C4⋊C8—611no—
360#103—21no—
361#103—1221no—
362#103—1221no—
363#103—1221no—
364#103—1221no—
365#103—1221no—
366C22⋊C8—611no—
367C22⋊C8—611no—
368C4×C8C22×D6111yescharacteristic
369C2×Q8—21no—
370C2×Q8—21no—
371C2×Q8—21no—
372C2×Q8—1221no—
373C2×Q8—4881no—
374C2×Q8—4881no—
375C2×Q8—2441no—
376C2×Q8—2441no—
377C2×Q8—2442no—
378C2×Q8—2442no—
379C2×D4—611no—
380C22×C4—611no—
381C22×C4—611no—
382C22×C4—2441no—
383C22×C4—2441no—
384C22×C4—2441no—
385Q16—21no—
386Q16—21no—
387Q16—21no—
388Q16—21no—
389Q16—21no—
390Q16—21no—
391Q16—81no—
392Q16—612no—
393Q16—1221no—
394Q16—2442no—
395Q16—2442no—
396C2×C8—611no—
397C2×C8—611no—
398C2×C8—1221no—
399C2×C8—1221no—
400C2×C8—1221no—
401C2×C8—1221no—
402C2×C8D4×D6111yescharacteristic
403C2×C8C23×D6111yescharacteristic
404C4⋊C4—21no—
405C4⋊C4—41no—
406C4⋊C4—41no—
407C4⋊C4—41no—
408C4⋊C4—611no—
409C4⋊C4—1221no—
410C4⋊C4—1221no—
411C4⋊C4—1221no—
412C4⋊C4—2441no—
413C4⋊C4—2441no—
414C4⋊C4—2441no—
415C4⋊C4—2441no—
416C4⋊C4—2441no—
417C4⋊C4—2441no—
418C4⋊C4—2441no—
419C4⋊C4—2441no—
420C22⋊C4—611no—
421C22⋊C4—611no—
422C22⋊C4—2441no—
423C22⋊C4—2441no—
424C22⋊C4—2441no—
425C22⋊C4—2441no—
426C22⋊C4—2441no—
427C42—41no—
428C42—2441no—
429C42—2441no—
430C42D4×D6111yescharacteristic
431C16—21no—
432C16—21no—
433C16—1221no—
434C16—1221no—
435C23—611no—
436C23—611no—
437Q8—41no—
438Q8—41no—
439Q8—41no—
440Q8—41no—
441Q8—41no—
442Q8—41no—
443Q8—1222no—
444Q8—4882no—
445Q8—4882no—
446Q8—2441no—
447D4—1222no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—611no—
453C2×C4—611no—
454C2×C4—1221no—
455C2×C4—1221no—
456C2×C4—1221no—
457C2×C4—1221no—
458C2×C4—4882no—
459C2×C4—4882no—
460C2×C4—4882no—
461C2×C4—2441no—
462C2×C4—2441no—
463C2×C4—2441no—
464C2×C4—2441no—
465C2×C4D8×D6111yescharacteristic
466C2×C4D8×D6111yescharacteristic
467C2×C4C2×D4×D6111yescharacteristic
468C8—21no—
469C8—1221no—
470C8—1221no—
471C8#41×D6111yescharacteristic
472C8#1451982211yescharacteristic
473C22—612no—
474C22—1221no—
475C22—1221no—
476C22—1221no—
477C22—1221no—
478C22—1221no—
479C22C2×D8×D6111yescharacteristic
480C4—21no—
481C4—21no—
482C4—81no—
483C4—81no—
484C4—81no—
485C4—81no—
486C4—1221no—
487C4—1221no—
488C4—4881no—
489C4—4881no—
490C4—4881no—
491C4—2442no—
492C4#1684040911yescharacteristic
493C4#1684057211yescharacteristic
494C2—1222no—
495C2—2441no—
496C2#2145763511yescharacteristic
497C2#510×D6111yescharacteristic
498C2#2145896811yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2209C2
socleC22×C61C22×D8
prime radicalC2×D244D8
hypercenter#2209D61
hypocenterC61#33879
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2209

Complements

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

NH ≅ G/Ntype
3. #21448064C2semidirect
4. #21448026C2semidirect
5. #21448015C2semidirect
6. #21447984C2semidirect
7. #21447924C2semidirect
8. #21447907C2semidirect
9. #21447751C2semidirect
10. #21447751C2semidirect
11. #21447688C2semidirect
13. #21447537C2semidirect
14. #358×D61C2semidirect
15. C61×#2209C2semidirect
253. #2209D61semidirect
308. C61#33879semidirect

Maximal subgroups

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

subgroupindex
#214581892
#214575692
#214480642
#214480262
#214480152
#214479842
#214479242
#214479072
#214477512
#214476882
#214476432
#214475372
#358×D612
C61×#22092
#3387961