Finite Group Databasebeta

← #29710001

Subgroups — #29710001

Order 15616.

880 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14519751C211yesmaximal, characteristic
2#21447376C211yesmaximal, characteristic, complemented
3#21447348C211yesmaximal, characteristic, complemented
4#21447291C211yesmaximal, characteristic, complemented
5#21447245C212yesmaximal, complemented
6#21447223C211yesmaximal, characteristic, complemented
7#21447001C212yesmaximal
8C4×#14519710C212yesmaximal, complemented
9C4×#14519697C212yesmaximal, complemented
10C4×C22⋊#92418C211yesmaximal, characteristic, complemented
11C61×#2285C211yesmaximal, characteristic, complemented
12C2×#14519751C2211yescharacteristic
13C2×C4×D244C2211yescharacteristic
14C2×C4×C22⋊D61—21no—
15C2×#14519710C2212yes—
16C2×#14519710C2212yes—
17C2×#14519697C2212yes—
18C2×#14519697C2212yes—
19C2×C22⋊#92418C2212yes—
20C2×C4×#92418C2212yes—
21#16839664C2211yescharacteristic
22#16839660C2211yescharacteristic
23#16839653—21no—
24#16839641—21no—
25#16839622C2211yescharacteristic
26C4×C4⋊Dic61C2211yescharacteristic
27C4×#11758198—21no—
28#16839524C2212yes—
29#16839524C2212yes—
30#16839524C2212yes—
31#16839524C2212yes—
32#16839517C2211yescharacteristic
33#16839517C2211yescharacteristic
34C2×#117×C61—21no—
35C22×C42×C61C2211yescharacteristic
36C61×#384C2211yescharacteristic
37C61×#384C2211yescharacteristic
38C61×#382—21no—
39C61×#380—21no—
40C61×#380C2212yes—
41C4×C4⋊C4×C61—21no—
42C4×C4⋊C4×C61C2212yes—
43C22×D244C2311yescharacteristic
44C22×C22⋊D61—21no—
45C22×C4×D61—21no—
46C22×#92418C2312yes—
47C22×#92418C2312yes—
48#14519751—22no—
49#14519751—22no—
50C4×D244—24no—
51C4×C22⋊D61—44no—
52C2×C4⋊Dic61C2311yescharacteristic
53C2×C4⋊Dic61C2311yescharacteristic
54C2×C4⋊Dic61C2311yescharacteristic
55C2×#11758196—21no—
56C2×C22⋊Dic61—21no—
57C2×#11758198—21no—
58C2×#11758198—21no—
59C2×#11758198—21no—
60C2×#11758198—21no—
61C2×C4×Dic61—21no—
62#14519710—24no—
63#14519710—24no—
64#14519697—24no—
65#14519697—24no—
66C22⋊#92418—24no—
67C4×#92418—24no—
68#14519684—21no—
69#14519684—21no—
70#14519684—21no—
71C23×C4×C61D411yescharacteristic
72C23×C4×C61D411yescharacteristic
73C23×C4×C61C2311yescharacteristic
74#117×C61—44no—
75C2×C4⋊C4×C61—21no—
76C2×C4⋊C4×C61—21no—
77C2×C4⋊C4×C61—21no—
78C2×C4⋊C4×C61—21no—
79C2×C4⋊C4×C61C2312yes—
80C2×C4⋊C4×C61C2312yes—
81C2×C22⋊C4×C61—22no—
82C2×C42×C61—24no—
83C2×C42×C61—22no—
84C2×C42×C61D411yescharacteristic
85C2×C42×C61D411yescharacteristic
86C2×C42×C61C2311yescharacteristic
87C2×C42×C61C2311yescharacteristic
88#95×C61—22no—
89#95×C61—22no—
90C24×C61C2×D411yescharacteristic
91C23×D61—21no—
92C22×C4×C61—22no—
93C22×C4×C61—22no—
94C22×C4×C61—22no—
95C22×C4×C61—22no—
96C22×C4×C61—22no—
97C22×C4×C61—22no—
98C22×C4×C61—21no—
99C22×C4×C61—21no—
100C22×C4×C61—22no—
101C22×C4×C61—22no—
102C22×C4×C61—41no—
103C22×C4×C61D814yes—
104C22×C4×C61C2×D411yescharacteristic
105C22×C4×C61C2×D411yescharacteristic
106C22×C4×C61C2×D411yescharacteristic
107C22×C4×C61C2×D411yescharacteristic
108C22×C4×C61C2×D411yescharacteristic
109C22×C4×C61C2411yescharacteristic
110C2×C22⋊D61—24no—
111C2×C22⋊D61—42no—
112C2×C22⋊D61—42no—
113C22×Dic61—21no—
114C22×Dic61—21no—
115C22×Dic61—21no—
116C2×D244—22no—
117C2×D244—22no—
118C2×D244—21no—
119C2×D244#4112yes—
120C2×C4×D61—42no—
121C2×C4×D61—42no—
122C2×C4×D61—42no—
123C4⋊C4×C61—22no—
124C4⋊C4×C61—22no—
125C4⋊C4×C61—22no—
126C4⋊C4×C61—22no—
127C4⋊C4×C61—42no—
128C4⋊C4×C61—42no—
129C4⋊C4×C61—42no—
130C4⋊C4×C61—42no—
131C22⋊C4×C61—44no—
132C42×C61—22no—
133C42×C61—22no—
134C42×C61—22no—
135C42×C61—44no—
136C42×C61#4114yes—
137C22⋊Dic61—42no—
138#11758198—24no—
139#11758198—42no—
140#11758198—42no—
141#11758198—42no—
142C4⋊Dic61—21no—
143C4⋊Dic61—22no—
144C4⋊Dic61—22no—
145C4⋊Dic61#4112yes—
146#11758196—42no—
147C4×Dic61—42no—
148C2×#92418—22no—
149C2×#92418—22no—
150C2×#92418—22no—
151C2×#92418—22no—
152C2×#92418—22no—
153C2×#92418#4114yes—
154C23×C61—21no—
155C23×C61—21no—
156C23×C61—21no—
157C23×C61—21no—
158C23×C61—21no—
159C23×C61—21no—
160C23×C61C2×D812yes—
161C23×C61C22×D411yescharacteristic
162C22×D61—22no—
163C22×D61—41no—
164C22×D61—41no—
165C22×D61—41no—
166C22×D61—41no—
167C22×D61—41no—
168C22×D61—41no—
169C2×C4×C61—21no—
170C2×C4×C61—21no—
171C2×C4×C61—21no—
172C2×C4×C61—21no—
173C2×C4×C61—21no—
174C2×C4×C61—21no—
175C2×C4×C61—28no—
176C2×C4×C61—21no—
177C2×C4×C61—21no—
178C2×C4×C61—21no—
179C2×C4×C61—44no—
180C2×C4×C61—42no—
181C2×C4×C61—42no—
182C2×C4×C61—42no—
183C2×C4×C61—42no—
184C2×C4×C61—42no—
185C2×C4×C61—42no—
186C2×C4×C61—42no—
187C2×C4×C61—42no—
188C2×C4×C61#12312yes—
189C2×C4×C61#12312yes—
190C2×C4×C61C2×D812yes—
191C2×C4×C61C2×D812yes—
192C2×C4×C61#13512yes—
193C2×C4×C61#13712yes—
194C2×C4×C61C2×#4111yescharacteristic
195C2×C4×C61C2×#4111yescharacteristic
196C2×C4×C61C2×#4112yes—
197C2×C4×C61C2×#4112yes—
198C22⋊D61—48no—
199C2×Dic61—22no—
200C2×Dic61—41no—
201C2×Dic61—41no—
202C2×Dic61—41no—
203C2×Dic61—41no—
204C2×Dic61—41no—
205C2×Dic61—41no—
206C2×Dic61—41no—
207C2×Dic61—41no—
208D244—24no—
209D244—42no—
210C4×D61—84no—
211#92418—24no—
212#92418—42no—
213#23754—611nomaximal, Sylow
214C22×C61—22no—
215C22×C61—22no—
216C22×C61—22no—
217C22×C61—41no—
218C22×C61—41no—
219C22×C61—41no—
220C22×C61—41no—
221C22×C61C2×#12311yescharacteristic
222C22×C61#52511yescharacteristic
223C22×C61#53211yescharacteristic
224C22×C61C22×D811yescharacteristic
225C22×C61C2×#13511yescharacteristic
226C22×C61C2×#13711yescharacteristic
227C22×C61#57511yescharacteristic
228C2×D61—42no—
229C2×D61—42no—
230C2×D61—42no—
231C2×D61—81no—
232C2×D61—81no—
233C2×D61—81no—
234C2×D61—81no—
235C4×C61—22no—
236C4×C61—22no—
237C4×C61—22no—
238C4×C61—41no—
239C4×C61—82no—
240C4×C61—82no—
241C4×C61#48014yes—
242C4×C61#52912yes—
243C4×C61#52912yes—
244Dic61—42no—
245Dic61—81no—
246Dic61—81no—
247C4×#121—611no—
248#2285D6111yescharacteristic, complemented
249#2099—611no—
250#2093—611no—
251#2083—611no—
252#2075—612no—
253#2071—611no—
254#2033—612no—
255C4×#107—612no—
256C4×#102—612no—
257C4×C22⋊C8—611no—
258C2×C61—42no—
259C2×C61#239511yescharacteristic
260C2×C61C2×#48011yescharacteristic
261C2×C61#309111yescharacteristic
262C2×C61#310011yescharacteristic
263C2×C61#310711yescharacteristic
264C2×C61#316911yescharacteristic
265C2×C61#317211yescharacteristic
266D61—82no—
267C2×#121—611no—
268C2×C4×D4—611no—
269C2×C4×D4—1221no—
270C2×#117—21no—
271C22×C42C2×D6111yescharacteristic
272C2×#107—612no—
273C2×#107—612no—
274C2×#102—612no—
275C2×#102—612no—
276C2×C22⋊C8—612no—
277C2×C4×C8—612no—
278#390—611no—
279#389—611no—
280#388—1221no—
281#386—1221no—
282#384C2×D6111yescharacteristic
283#384C2×D6111yescharacteristic
284#382—21no—
285#380—21no—
286#380—611no—
287#380C2×D6112yes—
288C4×C4⋊C4—21no—
289C4×C4⋊C4—611no—
290C4×C4⋊C4C2×D6112yes—
291C4×C22⋊C4—1221no—
292#340—612no—
293#340—612no—
294#340—612no—
295#340—612no—
296#336—611no—
297#336—611no—
298C61#2375411yescharacteristic, complemented, Sylow
299C22×D4—611no—
300C22×D4—1221no—
301C23×C4—1221no—
302C23×C4C22⋊D6111yescharacteristic
303C23×C4C22⋊D6111yescharacteristic
304C23×C4C22×D6111yescharacteristic
305C22×C8—612no—
306C22×C8—612no—
307#121—1222no—
308#121—1222no—
309C4×D4—1224no—
310C4×D4—2444no—
311#117—44no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—611no—
317C2×C4⋊C4—611no—
318C2×C4⋊C4—611no—
319C2×C4⋊C4—1221no—
320C2×C4⋊C4C22×D6112yes—
321C2×C4⋊C4C22×D6112yes—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—1221no—
324C2×C22⋊C4—1221no—
325C2×C22⋊C4—1221no—
326C2×C22⋊C4—1221no—
327C2×C22⋊C4—1221no—
328C2×C42—24no—
329C2×C42—22no—
330C2×C42—1221no—
331C2×C42C22⋊D6111yescharacteristic
332C2×C42C22⋊D6111yescharacteristic
333C2×C42C22×D6111yescharacteristic
334C2×C42C22×D6111yescharacteristic
335#107—1224no—
336#107—1224no—
337#102—1224no—
338#102—1224no—
339C22⋊C8—1224no—
340C4×C8—1224no—
341#95—22no—
342#95—22no—
343#95—1221no—
344#95—1221no—
345#95—1221no—
346C24—1221no—
347C24C2×C22⋊D6111yescharacteristic
348C2×D4—612no—
349C2×D4—1224no—
350C2×D4—1222no—
351C2×D4—1221no—
352C2×D4—1222no—
353C2×D4—2442no—
354C2×D4—2442no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—41no—
366C22×C4—1221no—
367C22×C4—1221no—
368C22×C4—1221no—
369C22×C4—2442no—
370C22×C4—2442no—
371C22×C4—2442no—
372C22×C4#1175819914yes—
373C22×C4C2×C22⋊D6111yescharacteristic
374C22×C4C2×C22⋊D6111yescharacteristic
375C22×C4C2×C22⋊D6111yescharacteristic
376C22×C4C2×C22⋊D6111yescharacteristic
377C22×C4C2×C22⋊D6111yescharacteristic
378C22×C4C23×D6111yescharacteristic
379C2×C8—614no—
380C2×C8—1222no—
381C2×C8—1222no—
382C2×C8—1222no—
383C2×C8—1222no—
384C2×C8—1222no—
385C4⋊C4—22no—
386C4⋊C4—22no—
387C4⋊C4—22no—
388C4⋊C4—22no—
389C4⋊C4—42no—
390C4⋊C4—42no—
391C4⋊C4—42no—
392C4⋊C4—42no—
393C4⋊C4—612no—
394C4⋊C4—1221no—
395C4⋊C4—1222no—
396C4⋊C4—1222no—
397C4⋊C4—2442no—
398C22⋊C4—44no—
399C22⋊C4—1224no—
400C22⋊C4—2442no—
401C22⋊C4—2442no—
402C22⋊C4—2442no—
403C22⋊C4—2442no—
404C42—22no—
405C42—22no—
406C42—22no—
407C42—44no—
408C42—2442no—
409C42#1175822214yes—
410C23—21no—
411C23—21no—
412C23—21no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—1222no—
417C23—2441no—
418C23—2441no—
419C23—2441no—
420C23—2441no—
421C23—2441no—
422C23—2441no—
423C23C2×#1175819912yes—
424C23C22×C22⋊D6111yescharacteristic
425D4—1224no—
426D4—2448no—
427D4—2442no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—28no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—44no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—1222no—
448C2×C4—4884no—
449C2×C4—2441no—
450C2×C4—2441no—
451C2×C4—2441no—
452C2×C4—2441no—
453C2×C4—2441no—
454C2×C4—2441no—
455C2×C4—2441no—
456C2×C4—2441no—
457C2×C4#1451976012yes—
458C2×C4#1451976012yes—
459C2×C4C2×#1175819912yes—
460C2×C4C2×#1175819912yes—
461C2×C4#1451979712yes—
462C2×C4#1451980812yes—
463C2×C4#41×D6111yescharacteristic
464C2×C4#41×D6111yescharacteristic
465C2×C4#41×D6112yes—
466C2×C4C2×#1175822212yes—
467C8—1224no—
468C8—2442no—
469C22—22no—
470C22—22no—
471C22—22no—
472C22—41no—
473C22—41no—
474C22—41no—
475C22—41no—
476C22—4881no—
477C22—4881no—
478C22—4881no—
479C22—4881no—
480C22—2442no—
481C22—2442no—
482C22—2442no—
483C22C2×#1451976011yescharacteristic
484C22#1684026911yescharacteristic
485C22#1684030811yescharacteristic
486C22C22×#1175819911yescharacteristic
487C22C2×#1451979711yescharacteristic
488C22C2×#1451980811yescharacteristic
489C22#1684056011yescharacteristic
490C4—22no—
491C4—22no—
492C4—22no—
493C4—41no—
494C4—82no—
495C4—82no—
496C4—4881no—
497C4—4881no—
498C4—2442no—
499C4#1684007514yes—
500C4#1684029012yes—
501C4#1684029012yes—
502C2—42no—
503C2—4882no—
504C2#2144907611yescharacteristic
505C2C2×#1684007511yescharacteristic
506C2#2145573211yescharacteristic
507C2#2145581511yescharacteristic
508C2#2145588411yescharacteristic
509C2#2145639411yescharacteristic
510C2#2145641911yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2285C2
socleC23×C61C22×D4
prime radicalC2×#14519751C22
hypercenter#2285D61
hypocenterC61#23754
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ #2285

Complements

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

NH ≅ G/Ntype
2. #21447376C2semidirect
3. #21447348C2semidirect
4. #21447291C2semidirect
5. #21447245C2semidirect
6. #21447223C2semidirect
8. C4×#14519710C2semidirect
9. C4×#14519697C2semidirect
10. C4×C22⋊#92418C2semidirect
11. C61×#2285C2semidirect
248. #2285D61semidirect
298. C61#23754semidirect

Maximal subgroups

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

subgroupindex
C4×#145197512
#214473762
#214473482
#214472912
#214472452
#214472232
#214470012
C4×#145197102
C4×#145196972
C4×C22⋊#924182
C61×#22852
#2375461