Finite Group Databasebeta

← #29665484

Subgroups — #29665484

Order 15616.

662 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456947C211yesmaximal, characteristic, complemented
2#21455628C211yesmaximal, characteristic, complemented
3#21455276C211yesmaximal, characteristic
4#21454928C211yesmaximal, characteristic, complemented
5#21445238C212yesmaximal, complemented
6#21445231C212yesmaximal, complemented
7#21445204C212yesmaximal, complemented
8#21445197C212yesmaximal, complemented
9#21444589C211yesmaximal, characteristic, complemented
10#21444494C211yesmaximal, characteristic, complemented
11C2×C61×#333C211yesmaximal, characteristic, complemented
12C2×#14519799—21no—
13#16840312C2211yescharacteristic
14C4×#11758222C2211yescharacteristic
15#16840158C2212yes—
16#16840110C2212yes—
17#16840080—22no—
18#16840054C2212yes—
19#16840049—21no—
20#16840049—21no—
21#16840049C2212yes—
22#16840044—21no—
23#16840039—21no—
24#16839985—21no—
25#16839978—21no—
26#16839973C2211yescharacteristic
27#16839968C2211yescharacteristic
28#16839963C2211yescharacteristic
29#16839958C2211yescharacteristic
30#16839886C2212yes—
31#16839827C2212yes—
32C8×C22⋊D61—22no—
33#16839815C2211yescharacteristic
34#16839814—21no—
35#16839802—21no—
36#16839786C2211yescharacteristic
37C4⋊C8×D61—21no—
38#16839761—21no—
39#16839759—21no—
40#16839512C2212yes—
41#16839512C2212yes—
42#16839507C2212yes—
43#16839505C2212yes—
44C2×C4⋊Q8×C61C2211yescharacteristic
45C2×C4⋊C8×C61C2211yescharacteristic
46C2×C4⋊C8×C61C2211yescharacteristic
47C61×#333C2212yes—
48C61×#333C2212yes—
49C2×#11758222—21no—
50C2×#11758222D411yescharacteristic
51#14519799—44no—
52C2×Dic244—21no—
53C2×#11758190—21no—
54C2×#11758190—21no—
55C2×D488—21no—
56C2×#11758194—21no—
57C2×C8×D61—22no—
58#14519777C2311yescharacteristic
59#14519774C2311yescharacteristic
60#14519765—21no—
61#14519751—21no—
62#14519751—21no—
63C4×Dic122D411yescharacteristic
64C4×Dic122C2311yescharacteristic
65C4×D244—21no—
66C4×D244—21no—
67C4×D244D411yescharacteristic
68C4×D244C2311yescharacteristic
69C4×C22⋊D61—21no—
70C4×C22⋊D61—21no—
71#14519736D411yescharacteristic
72#14519734—21no—
73C42×D61—21no—
74#14519710—22no—
75#14519708—22no—
76#14519708—22no—
77#14519708—22no—
78C4⋊#92418—21no—
79C4⋊#92418D411yescharacteristic
80C4⋊#92418D411yescharacteristic
81C4⋊#92418C2312yes—
82#14519706—22no—
83#14519702—21no—
84#14519702—21no—
85#14519700—22no—
86#14519699—21no—
87#14519699—21no—
88#14519697—22no—
89#14519697—22no—
90#14519697—22no—
91C22⋊#92418D412yes—
92#14519689—22no—
93C4×#92418C2312yes—
94C8×Dic61—22no—
95C22×Q8×C61—21no—
96C22×C8×C61—21no—
97C22×C8×C61—21no—
98C4⋊Q8×C61—21no—
99C4⋊Q8×C61—21no—
100C4⋊Q8×C61—21no—
101C4⋊Q8×C61C2312yes—
102C2×C4⋊C4×C61—21no—
103C2×C4⋊C4×C61—21no—
104C2×C42×C61C2311yescharacteristic
105C4⋊C8×C61—21no—
106C4⋊C8×C61—21no—
107C4⋊C8×C61C2311yescharacteristic
108C4⋊C8×C61C2311yescharacteristic
109C4⋊C8×C61C2312yes—
110C2×Q8×C61—22no—
111C2×Q8×C61—41no—
112C2×Q8×C61—82no—
113C22×C4×C61—41no—
114C22×C4×C61C2×D411yescharacteristic
115C22×C4×C61C2×D411yescharacteristic
116C22×C4×C61#4111yescharacteristic
117C2×C22⋊D61—21no—
118C2×C22⋊D61—41no—
119#11758222—22no—
120#11758222—42no—
121#11758222—42no—
122#11758222SD1614yes—
123C2×D244—21no—
124C2×D244—21no—
125C2×D244—21no—
126C2×D244C2×D411yescharacteristic
127C2×C4×D61—21no—
128C2×C4×D61—21no—
129C2×C4×D61—21no—
130C2×C4×D61—41no—
131C2×Dic122—21no—
132C2×Dic122C2×D411yescharacteristic
133C2×C8×C61—22no—
134C2×C8×C61—21no—
135C2×C8×C61—21no—
136C2×C8×C61—42no—
137C2×C8×C61—81no—
138C4⋊C4×C61—22no—
139C4⋊C4×C61—22no—
140C4⋊C4×C61—41no—
141C4⋊C4×C61—41no—
142C42×C61C2×D411yescharacteristic
143C42×C61C2×D411yescharacteristic
144C42×C61#4111yescharacteristic
145C42×C61C2411yescharacteristic
146C22⋊Dic61—21no—
147#11758198—21no—
148#11758198—21no—
149#11758198—41no—
150#11758198—41no—
151C4⋊Dic61—21no—
152C4⋊Dic61—21no—
153C4⋊Dic61C2×D411yescharacteristic
154C4⋊Dic61C2×D411yescharacteristic
155#11758196—21no—
156#11758196—21no—
157C4×Dic61—21no—
158C4×Dic61—21no—
159C4×Dic61—21no—
160#11758194—42no—
161C2×#92418—22no—
162C2×#92418C2×D412yes—
163C2×#92418C2×D412yes—
164Dic244—42no—
165D488—42no—
166#11758190—42no—
167#11758190—42no—
168C8×D61—82no—
169C23×C61#12111yescharacteristic
170C22×D61—21no—
171C22×D61—41no—
172Q8×C61—82no—
173Q8×C61—82no—
174C2×C4×C61—21no—
175C2×C4×C61—21no—
176C2×C4×C61—41no—
177C2×C4×C61—42no—
178C2×C4×C61—82no—
179C2×C4×C61#12111yescharacteristic
180C2×C4×C61#12111yescharacteristic
181C2×C4×C61#12111yescharacteristic
182C2×C4×C61C2×SD1612yes—
183C2×C4×C61#13512yes—
184C2×C4×C61C22×D411yescharacteristic
185C2×C4×C61C22×D411yescharacteristic
186C2×C4×C61C2×#4111yescharacteristic
187C22⋊D61—24no—
188C22⋊D61—82no—
189C2×Dic61—21no—
190C2×Dic61—21no—
191C2×Dic61—21no—
192C2×Dic61—41no—
193D244—21no—
194D244—41no—
195D244—41no—
196D244—41no—
197D244—41no—
198D244—81no—
199D244C2×SD1612yes—
200C4×D61—24no—
201C4×D61—41no—
202C4×D61—41no—
203C4×D61—81no—
204C4×D61—82no—
205Dic122—21no—
206Dic122—41no—
207Dic122—41no—
208Dic122C2×SD1612yes—
209C8×C61—41no—
210C8×C61—41no—
211C8×C61—42no—
212#92418—22no—
213#92418—22no—
214#92418—42no—
215#19414—611nomaximal, Sylow
216C22×C61—21no—
217C22×C61—21no—
218C22×C61#46512yes—
219C22×C61C2×#12111yescharacteristic
220C2×D61—22no—
221C2×D61—41no—
222C2×D61—41no—
223C2×D61—81no—
224C2×D61—81no—
225C2×D61—81no—
226C4×C61—21no—
227C4×C61—21no—
228C4×C61—21no—
229C4×C61—82no—
230C4×C61#46512yes—
231C4×C61C22×SD1611yescharacteristic
232C4×C61C2×#13511yescharacteristic
233C4×C61#57711yescharacteristic
234C4×C61#57811yescharacteristic
235Dic61—22no—
236Dic61—41no—
237Dic61—41no—
238Dic61—81no—
239#3227—611no—
240#3079—611no—
241#3035—611no—
242#2988—611no—
243#1678—612no—
244#1677—612no—
245#1672—612no—
246#1671—612no—
247#1570—611no—
248#1547—611no—
249C2×#333D6111yescharacteristic, complemented
250C2×C61—22no—
251C2×C61#304611yescharacteristic
252C2×C61C2×#46511yescharacteristic
253C2×C61#306811yescharacteristic
254D61—42no—
255D61—161no—
256C2×#135—1221no—
257#532—611no—
258C2×C4⋊Q8C2×D6111yescharacteristic
259C4×#41—611no—
260#498—612no—
261#486—612no—
262#481—1222no—
263#477—612no—
264#476—612no—
265#476—1221no—
266#476—1221no—
267#475—1221no—
268#474—1221no—
269#464—1221no—
270#463—1221no—
271#462—611no—
272#461—611no—
273#460—611no—
274#459—611no—
275C8×Q8—612no—
276C8×D4—612no—
277C8×D4—1222no—
278#431—611no—
279#431—1221no—
280#428—1221no—
281#423—611no—
282C2×C4⋊C8—1221no—
283C2×C4⋊C8C2×D6111yescharacteristic
284C2×C4⋊C8C2×D6111yescharacteristic
285#417—1221no—
286#416—1221no—
287#334—612no—
288#334—612no—
289#333C2×D6112yes—
290#333C2×D6112yes—
291#332—612no—
292#331—612no—
293C61#1941411yescharacteristic, complemented, Sylow
294C2×#41—611no—
295C2×#41—1221no—
296C22×Q8—21no—
297#135—2444no—
298C2×Q16—1221no—
299C2×SD16—1221no—
300C2×SD16—1221no—
301C2×D8—1221no—
302C2×M16—1221no—
303C22×C8—21no—
304C22×C8—21no—
305C22×C8—1222no—
306C4⋊Q8—21no—
307C4⋊Q8—21no—
308C4⋊Q8—21no—
309C4⋊Q8—611no—
310C4⋊Q8C22×D6112yes—
311#127—611no—
312#124—1221no—
313#121—1221no—
314#121—1221no—
315C4×Q8—611no—
316C4×Q8—611no—
317C4×D4—611no—
318C4×D4—611no—
319C4×D4—1221no—
320C4×D4—1221no—
321C4×D4—1221no—
322C4×D4—1221no—
323#117—611no—
324#117—1221no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C42—1221no—
328C2×C42C22×D6111yescharacteristic
329#107—1222no—
330#106—1222no—
331#106—1222no—
332#106—1222no—
333C4⋊C8—21no—
334C4⋊C8—21no—
335C4⋊C8—611no—
336C4⋊C8—611no—
337C4⋊C8—612no—
338C4⋊C8—1222no—
339C4⋊C8—1221no—
340C4⋊C8C22×D6112yes—
341C4⋊C8C22×D6111yescharacteristic
342C4⋊C8C22×D6111yescharacteristic
343#103—1222no—
344#103—1221no—
345#103—1221no—
346#102—1222no—
347#102—1222no—
348#102—1222no—
349#102—1221no—
350#102—1221no—
351C22⋊C8—612no—
352C22⋊C8—1222no—
353C4×C8—612no—
354C4×C8—1222no—
355#41—614no—
356#41—1222no—
357#41—2442no—
358#41—2442no—
359C2×Q8—22no—
360C2×Q8—41no—
361C2×Q8—82no—
362C2×Q8—611no—
363C2×Q8—1221no—
364C2×D4—611no—
365C2×D4—1221no—
366C2×D4—1221no—
367C2×D4—1221no—
368C2×D4—1221no—
369C2×D4—2441no—
370C22×C4—41no—
371C22×C4—1221no—
372C22×C4—1221no—
373C22×C4—1221no—
374C22×C4—2441no—
375C22×C4#1175822211yescharacteristic
376C22×C4D4×D6111yescharacteristic
377C22×C4D4×D6111yescharacteristic
378Q16—2442no—
379SD16—2442no—
380SD16—2442no—
381D8—2442no—
382M16—2442no—
383C2×C8—22no—
384C2×C8—21no—
385C2×C8—21no—
386C2×C8—42no—
387C2×C8—81no—
388C2×C8—612no—
389C2×C8—612no—
390C2×C8—1222no—
391C2×C8—4882no—
392C4⋊C4—22no—
393C4⋊C4—22no—
394C4⋊C4—41no—
395C4⋊C4—41no—
396C4⋊C4—611no—
397C4⋊C4—611no—
398C4⋊C4—1221no—
399C4⋊C4—1221no—
400C4⋊C4—1221no—
401C4⋊C4—1221no—
402C22⋊C4—1221no—
403C22⋊C4—1221no—
404C22⋊C4—1221no—
405C22⋊C4—2441no—
406C22⋊C4—2441no—
407C42—1221no—
408C42—1221no—
409C42—1221no—
410C42#1175822211yescharacteristic
411C42D4×D6111yescharacteristic
412C42D4×D6111yescharacteristic
413C42C23×D6111yescharacteristic
414C23—1221no—
415C23—2441no—
416C23#1451975011yescharacteristic
417Q8—82no—
418Q8—82no—
419Q8—612no—
420Q8—1221no—
421Q8—2441no—
422Q8—2441no—
423D4—612no—
424D4—1224no—
425D4—1221no—
426D4—4881no—
427D4—4882no—
428D4—2441no—
429D4—2441no—
430D4—2441no—
431D4—2441no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—41no—
435C2×C4—42no—
436C2×C4—82no—
437C2×C4—1221no—
438C2×C4—1224no—
439C2×C4—1221no—
440C2×C4—1221no—
441C2×C4—4881no—
442C2×C4—4882no—
443C2×C4—2441no—
444C2×C4—2441no—
445C2×C4—2441no—
446C2×C4#1451975011yescharacteristic
447C2×C4#1451975011yescharacteristic
448C2×C4#1451975011yescharacteristic
449C2×C4SD16×D6112yes—
450C2×C4#1451980012yes—
451C2×C4C2×D4×D6111yescharacteristic
452C2×C4C2×D4×D6111yescharacteristic
453C2×C4C2×#1175822211yescharacteristic
454C8—41no—
455C8—41no—
456C8—42no—
457C8—1222no—
458C8—1222no—
459C8—2442no—
460C22—21no—
461C22—21no—
462C22—1222no—
463C22—4881no—
464C22—4881no—
465C22—4881no—
466C22—2441no—
467C22—2441no—
468C22#1683999412yes—
469C22C2×#1451975011yescharacteristic
470C4—21no—
471C4—21no—
472C4—21no—
473C4—82no—
474C4—1222no—
475C4—4881no—
476C4—2441no—
477C4—2441no—
478C4#1683999412yes—
479C4C2×SD16×D6111yescharacteristic
480C4C2×#1451980011yescharacteristic
481C4#1684056811yescharacteristic
482C4#1684057511yescharacteristic
483C2—22no—
484C2—9761no—
485C2—2442no—
486C2#2145537411yescharacteristic
487C2C2×#1683999411yescharacteristic
488C2#2145554611yescharacteristic
subgroupG/H
centerC22C2×#14519750
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×#333C2
socleC22×C61C2×#121
prime radical#21455276C2
hypercenterC2×#333D61
hypocenterC61#19414
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#333

Complements

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

NH ≅ G/Ntype
1. #21456947C2semidirect
2. #21455628C2semidirect
4. #21454928C2semidirect
5. #21445238C2semidirect
6. #21445231C2semidirect
7. #21445204C2semidirect
8. #21445197C2semidirect
9. #21444589C2semidirect
10. #21444494C2semidirect
11. C2×C61×#333C2semidirect
249. C2×#333D61semidirect
293. C61#19414semidirect

Maximal subgroups

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

subgroupindex
#214569472
#214556282
#214552762
#214549282
#214452382
#214452312
#214452042
#214451972
#214445892
#214444942
C2×C61×#3332
#1941461