Finite Group Databasebeta

← #29834861

Subgroups — #29834861

Order 15616.

556 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#21455469C211yesmaximal, characteristic
2#21454415C211yesmaximal, characteristic
3#21448030C211yesmaximal, characteristic, complemented
4#21448028C211yesmaximal, characteristic, complemented
5#21448025C211yesmaximal, characteristic, complemented
6#21448024C211yesmaximal, characteristic, complemented
7#21448021C211yesmaximal, characteristic, complemented
8#21448020C211yesmaximal, characteristic, complemented
9#21448018C211yesmaximal, characteristic, complemented
10#21447606C211yesmaximal, characteristic, complemented
11#21447602C211yesmaximal, characteristic, complemented
12#21447537C211yesmaximal, characteristic, complemented
13#358×D61C211yesmaximal, characteristic, complemented
14#21447431C211yesmaximal, characteristic
15C61×#2235C211yesmaximal, characteristic, complemented
16C2×Q16×D61C2211yescharacteristic
17C2×#14519783C2211yescharacteristic
18#16840335—21no—
19#16840243—21no—
20C2×#14519716C2211yescharacteristic
21C2×C16×D61C2211yescharacteristic
22#16840019—21no—
23#16840018—21no—
24#16840004C2211yescharacteristic
25#16840003C2211yescharacteristic
26#16840000C2211yescharacteristic
27#16839803—21no—
28#16839803—21no—
29#16839802—21no—
30#16839800C2211yescharacteristic
31#16839799C2211yescharacteristic
32#16839799C2211yescharacteristic
33#16839799C2211yescharacteristic
34#107×D61C2211yescharacteristic
35#107×D61C2211yescharacteristic
36#16839769—21no—
37#16839590C2211yescharacteristic
38#16839589C2211yescharacteristic
39#16839588C2211yescharacteristic
40#16839587C2211yescharacteristic
41#16839587C2211yescharacteristic
42#16839587C2211yescharacteristic
43#16839567C2211yescharacteristic
44#16839567C2211yescharacteristic
45#16839566C2211yescharacteristic
46#16839566C2211yescharacteristic
47#16839565C2211yescharacteristic
48#16839565C2211yescharacteristic
49C22⋊#11758185C2211yescharacteristic
50#16839541C2211yescharacteristic
51#16839541C2211yescharacteristic
52C61×#467C2211yescharacteristic
53C2×#107×C61C2211yescharacteristic
54C61×#367C2211yescharacteristic
55C61×#367C2211yescharacteristic
56C61×#358C2211yescharacteristic
57C61×#358C2211yescharacteristic
58C61×C22⋊C16C2211yescharacteristic
59C2×#11758222D411yescharacteristic
60C2×Q8×D61—21no—
61C2×Dic244C2311yescharacteristic
62C2×#11758202—21no—
63Q16×D61—22no—
64Q16×D61—22no—
65#14519783—22no—
66#14519783—22no—
67C2×#11758194D411yescharacteristic
68C2×#11758189D411yescharacteristic
69C2×#11758189D411yescharacteristic
70C2×C8×D61C2311yescharacteristic
71C2×C8×D61C2311yescharacteristic
72#14519776—41no—
73#14519763—41no—
74#14519762—41no—
75#14519759—41no—
76#14519757—21no—
77#14519756—21no—
78#14519753—21no—
79#14519742—41no—
80#14519739—41no—
81C4×C22⋊D61—41no—
82C4×C22⋊D61—41no—
83#14519736—21no—
84#14519735—21no—
85#14519735—21no—
86#14519735—21no—
87C4⋊C4×D61—21no—
88C4⋊C4×D61—21no—
89#14519716—22no—
90C2×#11758185C2311yescharacteristic
91C2×#11758185C2311yescharacteristic
92C16×D61—22no—
93#14519711C2311yescharacteristic
94#14519711C2311yescharacteristic
95#14519711C2311yescharacteristic
96#14519710—21no—
97#14519710—21no—
98#14519709—21no—
99#14519708—21no—
100#14519708—21no—
101#14519708—21no—
102#14519702—21no—
103#14519701—21no—
104#14519700—21no—
105C2×Q16×C61C2311yescharacteristic
106C22×C8×C61C2311yescharacteristic
107C22⋊Q8×C61—21no—
108C2×C4⋊C4×C61—21no—
109C2×C16×C61C2311yescharacteristic
110C2×C16×C61C2311yescharacteristic
111#107×C61—21no—
112#107×C61C2311yescharacteristic
113#107×C61C2311yescharacteristic
114#107×C61C2311yescharacteristic
115#103×C61—21no—
116C2×Q8×C61—21no—
117C22×C4×C61—41no—
118C22×C4×C61C2×D411yescharacteristic
119C2×C22⋊D61D811yescharacteristic
120C2×C22⋊D61D811yescharacteristic
121Q8×D61—42no—
122Q8×D61—42no—
123#11758222—22no—
124#11758222—22no—
125C2×D244D811yescharacteristic
126C2×C4×D61—41no—
127C2×C4×D61—41no—
128C2×C4×D61—41no—
129C2×C4×D61C2×D411yescharacteristic
130C2×C4×D61C2×D411yescharacteristic
131C2×Dic122—21no—
132C2×Dic122—41no—
133C2×Dic122D811yescharacteristic
134Q16×C61—21no—
135Q16×C61—21no—
136C2×C8×C61—21no—
137C2×C8×C61—21no—
138C2×C8×C61C2×D411yescharacteristic
139C2×C8×C61C2411yescharacteristic
140C4⋊C4×C61—21no—
141C4⋊C4×C61—21no—
142C4⋊C4×C61—21no—
143C4⋊C4×C61—41no—
144C4⋊C4×C61—41no—
145C22⋊C4×C61—41no—
146C22⋊Dic61—41no—
147C22⋊Dic61—41no—
148#11758202—42no—
149#11758198—41no—
150#11758198—41no—
151#11758198—41no—
152#11758198—41no—
153#11758198—41no—
154C4⋊Dic61—21no—
155C4⋊Dic61—21no—
156C4⋊Dic61—21no—
157C4⋊Dic61—41no—
158#11758196—41no—
159#11758196—41no—
160#11758196—41no—
161#11758196—41no—
162C4×Dic61—41no—
163C4×Dic61—41no—
164C4×Dic61—41no—
165C4×Dic61—41no—
166#11758194—22no—
167C2×#92418C2×D411yescharacteristic
168C2×#92418C2×D411yescharacteristic
169Dic244—21no—
170Dic244—21no—
171#11758189—22no—
172#11758189—22no—
173C8×D61—21no—
174C8×D61—21no—
175C8×D61#4112yes—
176C8×D61#4112yes—
177C16×C61—21no—
178C16×C61—21no—
179#11758185—21no—
180#11758185—21no—
181C23×C61C2×D811yescharacteristic
182C22×D61C2×D811yescharacteristic
183C22×D61C2×D811yescharacteristic
184Q8×C61—41no—
185Q8×C61—41no—
186C2×C4×C61—21no—
187C2×C4×C61—21no—
188C2×C4×C61—41no—
189C2×C4×C61—41no—
190C2×C4×C61—41no—
191C2×C4×C61—41no—
192C2×C4×C61—161no—
193C2×C4×C61C2×D811yescharacteristic
194C2×C4×C61C22×D411yescharacteristic
195C22⋊D61—22no—
196C22⋊D61—22no—
197C2×Dic61—41no—
198C2×Dic61—41no—
199C2×Dic61—41no—
200C2×Dic61—41no—
201C2×Dic61C2×D811yescharacteristic
202C2×Dic61C2×D811yescharacteristic
203D244—22no—
204C4×D61—21no—
205C4×D61—21no—
206C4×D61—82no—
207C4×D61—161no—
208C4×D61—161no—
209C4×D61#12312yes—
210C4×D61#13712yes—
211Dic122—22no—
212Dic122—41no—
213Dic122—41no—
214Dic122—82no—
215C8×C61—21no—
216C8×C61C2×#4111yescharacteristic
217C8×C61C2×#4111yescharacteristic
218#92418—21no—
219#92418#12312yes—
220#33651—611nomaximal, Sylow
221C22×C61—21no—
222C22×C61—21no—
223C22×C61—21no—
224C22×C61C22×D811yescharacteristic
225C2×D61—21no—
226C2×D61—21no—
227C2×D61—21no—
228C2×D61—21no—
229C2×D61—21no—
230C2×D61#48012yes—
231C4×C61—21no—
232C4×C61—81no—
233C4×C61—81no—
234C4×C61—81no—
235C4×C61—81no—
236C4×C61C2×#12311yescharacteristic
237C4×C61C2×#13711yescharacteristic
238Dic61—21no—
239Dic61—81no—
240Dic61—81no—
241Dic61—81no—
242Dic61—81no—
243Dic61#48012yes—
244#3059—611no—
245#2913—611no—
246#2237—611no—
247#2237—611no—
248#2237—611no—
249#2237—611no—
250#2236—611no—
251#2236—611no—
252#2235—611no—
253#2235D6111yescharacteristic, complemented
254#2159—611no—
255#2158—611no—
256#2141—611no—
257C2×#358—611no—
258#2113—611no—
259C2×C61—41no—
260C2×C61C2×#48011yescharacteristic
261C2×C61#341611yescharacteristic
262C2×C61#341711yescharacteristic
263D61—22no—
264D61—41no—
265C22×Q16—611no—
266C2×#131—611no—
267#536—1221no—
268#520—1221no—
269C2×M32—611no—
270C22×C16—611no—
271#470—1221no—
272#470—1221no—
273#467—611no—
274#467—611no—
275#467—611no—
276#467C2×D6111yescharacteristic
277#428—1221no—
278#428—1221no—
279#428—1221no—
280#427—611no—
281#427—611no—
282#427—611no—
283#427—611no—
284C2×#107—611no—
285C2×#107—611no—
286C2×#107C2×D6111yescharacteristic
287#419—1221no—
288#367—611no—
289#367—611no—
290#367C2×D6111yescharacteristic
291#367C2×D6111yescharacteristic
292#366—611no—
293#366—611no—
294#366—611no—
295#366—611no—
296#358—611no—
297#358—611no—
298#358—611no—
299#358—611no—
300#358—611no—
301#358—611no—
302#358C2×D6111yescharacteristic
303#358C2×D6111yescharacteristic
304C22⋊C16—611no—
305C22⋊C16—611no—
306C22⋊C16—611no—
307C22⋊C16C2×D6111yescharacteristic
308C61#3365111yescharacteristic, complemented, Sylow
309C2×#41—611no—
310C22×Q8—1221no—
311C2×Q16—611no—
312C2×Q16—1222no—
313C2×Q16—1222no—
314C2×Q16—1221no—
315C2×Q16C22×D6111yescharacteristic
316#131—1222no—
317#131—1222no—
318C2×M16—611no—
319C2×M16—611no—
320C2×M16—611no—
321C22×C8—611no—
322C22×C8—611no—
323C22×C8C22×D6111yescharacteristic
324C4⋊Q8—2441no—
325#124—2441no—
326#123—2441no—
327#123—2441no—
328C22⋊Q8—21no—
329C22⋊Q8—1221no—
330C22⋊Q8—1221no—
331C22⋊Q8—1221no—
332C4×Q8—2441no—
333C4×D4—2441no—
334C4×D4—2441no—
335C4×D4—2441no—
336#117—1221no—
337#117—1221no—
338#117—1221no—
339#117—1221no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—1221no—
342C2×C4⋊C4—1221no—
343M32—1222no—
344C2×C16—611no—
345C2×C16—611no—
346C2×C16—1222no—
347C2×C16C22×D6111yescharacteristic
348C2×C16C22×D6111yescharacteristic
349#107—21no—
350#107—611no—
351#107—611no—
352#107—611no—
353#107—1221no—
354#107—1221no—
355#107C22×D6111yescharacteristic
356#107C22×D6111yescharacteristic
357#107C22×D6111yescharacteristic
358#106—1221no—
359#106—1221no—
360#106—1221no—
361#106—1221no—
362#103—21no—
363#103—1221no—
364#103—1221no—
365#103—1221no—
366#41—1222no—
367#41—1222no—
368C2×Q8—21no—
369C2×Q8—611no—
370C2×Q8—1221no—
371C2×Q8—2441no—
372C2×Q8—2442no—
373C2×Q8—2442no—
374C2×D4—611no—
375C2×D4—611no—
376C2×D4—611no—
377C22×C4—41no—
378C22×C4—611no—
379C22×C4—611no—
380C22×C4—2441no—
381C22×C4—2441no—
382C22×C4—2441no—
383C22×C4D4×D6111yescharacteristic
384Q16—21no—
385Q16—21no—
386Q16—1221no—
387Q16—1221no—
388Q16—2442no—
389M16—1222no—
390M16—1222no—
391M16—1222no—
392C2×C8—21no—
393C2×C8—21no—
394C2×C8—611no—
395C2×C8—612no—
396C2×C8—612no—
397C2×C8—611no—
398C2×C8—1221no—
399C2×C8—1221no—
400C2×C8D4×D6111yescharacteristic
401C2×C8C23×D6111yescharacteristic
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—41no—
406C4⋊C4—41no—
407C4⋊C4—1221no—
408C4⋊C4—1221no—
409C4⋊C4—1221no—
410C4⋊C4—2441no—
411C4⋊C4—2441no—
412C4⋊C4—2441no—
413C4⋊C4—2441no—
414C4⋊C4—2441no—
415C22⋊C4—41no—
416C22⋊C4—2441no—
417C22⋊C4—2441no—
418C22⋊C4—2441no—
419C22⋊C4—2441no—
420C22⋊C4—2441no—
421C22⋊C4—2441no—
422C22⋊C4—2441no—
423C42—2441no—
424C42—2441no—
425C42—2441no—
426C42—2441no—
427C16—21no—
428C16—21no—
429C16—1221no—
430C16—1221no—
431C23—611no—
432C23—611no—
433C23D8×D6111yescharacteristic
434Q8—41no—
435Q8—41no—
436Q8—1222no—
437Q8—4882no—
438Q8—2441no—
439Q8—2441no—
440D4—1222no—
441D4—1222no—
442D4—1222no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—161no—
450C2×C4—611no—
451C2×C4—612no—
452C2×C4—612no—
453C2×C4—611no—
454C2×C4—1221no—
455C2×C4—1221no—
456C2×C4—9761no—
457C2×C4—9761no—
458C2×C4—4882no—
459C2×C4—2441no—
460C2×C4—2441no—
461C2×C4—2441no—
462C2×C4—2441no—
463C2×C4D8×D6111yescharacteristic
464C2×C4C2×D4×D6111yescharacteristic
465C8—21no—
466C8—612no—
467C8—1221no—
468C8#41×D6111yescharacteristic
469C8#41×D6111yescharacteristic
470C22—21no—
471C22—21no—
472C22—21no—
473C22—612no—
474C22—1221no—
475C22—1221no—
476C22—1221no—
477C22—1221no—
478C22—1221no—
479C22C2×D8×D6111yescharacteristic
480C4—21no—
481C4—81no—
482C4—81no—
483C4—81no—
484C4—81no—
485C4—612no—
486C4—1221no—
487C4—4881no—
488C4—4881no—
489C4—4881no—
490C4—4881no—
491C4#123×D6111yescharacteristic
492C4#137×D6111yescharacteristic
493C2—41no—
494C2—1222no—
495C2—2441no—
496C2#480×D6111yescharacteristic
497C2#2145896111yescharacteristic
498C2#2145897111yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2235C2
socleC22×C61C22×D8
prime radicalC2×#11758222D4
hypercenter#2235D61
hypocenterC61#33651
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2235

Complements

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

NH ≅ G/Ntype
3. #21448030C2semidirect
4. #21448028C2semidirect
5. #21448025C2semidirect
6. #21448024C2semidirect
7. #21448021C2semidirect
8. #21448020C2semidirect
9. #21448018C2semidirect
10. #21447606C2semidirect
11. #21447602C2semidirect
12. #21447537C2semidirect
13. #358×D61C2semidirect
15. C61×#2235C2semidirect
253. #2235D61semidirect
308. C61#33651semidirect

Maximal subgroups

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

subgroupindex
#214554692
#214544152
#214480302
#214480282
#214480252
#214480242
#214480212
#214480202
#214480182
#214476062
#214476022
#214475372
#358×D612
#214474312
C61×#22352
#3365161