Finite Group Databasebeta

← #30599249

Subgroups — #30599249

Order 15616.

940 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 940 conjugacy classes of subgroups — too many to draw. Only its 116 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461642C211yesmaximal, characteristic
2#21460993C211yesmaximal, characteristic
3#21460692C212yesmaximal, complemented
4#21460692C212yesmaximal, complemented
5#380×D61C211yesmaximal, characteristic
6C22×C22⋊#6923—21no—
7C2×#14519834—21no—
8C2×#14519834C2212yes—
9C2×C22⋊#92420—21no—
10C2×(C2×#6923)⋊C4—21no—
11C2×(C2×#6923)⋊C4C2212yes—
12C23×C4×D61C2211yescharacteristic
13C2×C4⋊C4×D61C411yescharacteristic, complemented
14C2×C4⋊C4×D61C411yescharacteristic, complemented
15C2×C22⋊C4×D61—21no—
16#16839622C411yescharacteristic, complemented
17#16839621—21no—
18#16839620—21no—
19#16839619C2211yescharacteristic
20#16839619C2211yescharacteristic
21#95×D61—21no—
22C61×#380C411yescharacteristic, complemented
23C23×#6923—22no—
24C22×#92420—22no—
25C2×C22⋊#6923—24no—
26C2×C22⋊#6923—42no—
27C2×C22⋊#6923—42no—
28#14519834—24no—
29#14519834—42no—
30C22⋊#92420—42no—
31(C2×#6923)⋊C4—24no—
32(C2×#6923)⋊C4—42no—
33C24×D61D411yescharacteristic
34C23×Dic61D411yescharacteristic
35C22×C4×D61—24no—
36C22×C4×D61—21no—
37C22×C4×D61—21no—
38C22×C4×D61—42no—
39C22×C4×D61—42no—
40C22×C4×D61C2×C411yescharacteristic
41C22×C4×D61D411yescharacteristic
42C22×C4×D61D411yescharacteristic
43C22×C4×D61C2311yescharacteristic
44C2×C4⋊Dic61C2×C411yescharacteristic
45C2×C4⋊Dic61C2×C411yescharacteristic
46C2×#11758196—21no—
47C2×#11758196—21no—
48C4⋊C4×D61—42no—
49C4⋊C4×D61—42no—
50C2×C22⋊Dic61—21no—
51C2×#11758198—21no—
52C2×#11758198—21no—
53C22⋊C4×D61—42no—
54C22⋊C4×D61—42no—
55#14519684—21no—
56#14519684—21no—
57#14519684—21no—
58C23×C4×C61C2×C411yescharacteristic
59C2×C4⋊C4×C61C2×C411yescharacteristic
60C2×C4⋊C4×C61C2×C411yescharacteristic
61C2×C22⋊C4×C61—21no—
62#95×C61—21no—
63C24×C61C22⋊C411yescharacteristic
64C23×D61—22no—
65C23×D61—22no—
66C23×D61—22no—
67C23×D61—22no—
68C23×D61—41no—
69C23×D61—41no—
70C23×D61C22⋊C411yescharacteristic
71C23×D61D812yes—
72C23×D61SD1612yes—
73C23×D61C2×D411yescharacteristic
74C22×#6923—24no—
75C22×#6923—42no—
76C22×#6923—42no—
77C22×#6923—42no—
78C22×#6923—42no—
79C22×#6923—42no—
80C22×#6923—42no—
81C22×C4×C61—22no—
82C22×C4×C61—21no—
83C22×C4×C61—21no—
84C22×C4×C61—41no—
85C22×C4×C61—41no—
86C22×C4×C61C22⋊C411yescharacteristic
87C22×C4×C61C22×C411yescharacteristic
88C22×Dic61—22no—
89C22×Dic61—22no—
90C22×Dic61—21no—
91C22×Dic61—21no—
92C22×Dic61—41no—
93C22×Dic61C22⋊C411yescharacteristic
94C22×Dic61C2×D411yescharacteristic
95C2×C4×D61—22no—
96C2×C4×D61—22no—
97C2×C4×D61—22no—
98C2×C4×D61—22no—
99C2×C4×D61—22no—
100C2×C4×D61—22no—
101C2×C4×D61—22no—
102C2×C4×D61—416no—
103C2×C4×D61—41no—
104C2×C4×D61—41no—
105C2×C4×D61—41no—
106C2×C4×D61—41no—
107C2×C4×D61—42no—
108C2×C4×D61—42no—
109C2×C4×D61—42no—
110C2×C4×D61—42no—
111C2×C4×D61—42no—
112C2×C4×D61—42no—
113C2×C4×D61#4114yes—
114C22⋊#6923—48no—
115C2×#92420—42no—
116C2×#92420—42no—
117C2×#92420—42no—
118C4⋊C4×C61—41no—
119C4⋊C4×C61—41no—
120C22⋊C4×C61—42no—
121C22⋊Dic61—42no—
122#11758198—41no—
123#11758198—41no—
124#11758198—41no—
125#11758198—41no—
126C4⋊Dic61—41no—
127C4⋊Dic61—41no—
128#11758196—42no—
129#11758196—42no—
130C23×C61—21no—
131C23×C61—21no—
132C23×C61—21no—
133C23×C61—21no—
134C23×C61—21no—
135C23×C61—21no—
136C23×C61#10212yes—
137C23×C61C2×C22⋊C411yescharacteristic
138C22×D61—21no—
139C22×D61—21no—
140C22×D61—21no—
141C22×D61—21no—
142C22×D61—21no—
143C22×D61—21no—
144C22×D61—21no—
145C22×D61—21no—
146C22×D61—24no—
147C22×D61—24no—
148C22×D61—24no—
149C22×D61—24no—
150C22×D61—42no—
151C22×D61—42no—
152C22×D61—44no—
153C22×D61—44no—
154C22×D61—44no—
155C22×D61—44no—
156C22×D61#9912yes—
157C22×D61#10212yes—
158C22×D61#10412yes—
159C22×D61#12312yes—
160C22×D61C2×D811yescharacteristic
161C22×D61C2×SD1611yescharacteristic
162C22×D61#13712yes—
163C2×#6923—44no—
164C2×#6923—44no—
165C2×#6923—44no—
166C2×#6923—82no—
167C2×#6923—82no—
168C2×#6923—82no—
169C2×#6923—82no—
170C2×C4×C61—21no—
171C2×C4×C61—21no—
172C2×C4×C61—21no—
173C2×C4×C61—21no—
174C2×C4×C61—21no—
175C2×C4×C61—44no—
176C2×C4×C61—41no—
177C2×C4×C61—41no—
178C2×C4×C61—41no—
179C2×C4×C61—41no—
180C2×C4×C61—41no—
181C2×C4×C61—41no—
182C2×C4×C61#11712yes—
183C2×Dic61—21no—
184C2×Dic61—21no—
185C2×Dic61—21no—
186C2×Dic61—21no—
187C2×Dic61—44no—
188C2×Dic61—41no—
189C2×Dic61—41no—
190C2×Dic61—41no—
191C2×Dic61—41no—
192C2×Dic61—41no—
193C2×Dic61—41no—
194C2×Dic61#9912yes—
195C2×Dic61#12312yes—
196C4×D61—28no—
197C4×D61—44no—
198C4×D61—44no—
199C4×D61—44no—
200C4×D61—84no—
201C4×D61—84no—
202#92420—82no—
203#8712—611nomaximal, Sylow
204C22×C61—22no—
205C22×C61—22no—
206C22×C61—22no—
207C22×C61—41no—
208C22×C61—41no—
209C22×C61—41no—
210C22×C61—41no—
211C22×C61#38111yescharacteristic
212C22×C61C2×#9911yescharacteristic
213C22×C61C2×#9911yescharacteristic
214C22×C61C2×#10211yescharacteristic
215C22×C61#41911yescharacteristic
216C22×C61C2×#10411yescharacteristic
217C22×C61#42111yescharacteristic
218C2×D61—22no—
219C2×D61—22no—
220C2×D61—22no—
221C2×D61—22no—
222C2×D61—22no—
223C2×D61—21no—
224C2×D61—21no—
225C2×D61—22no—
226C2×D61—22no—
227C2×D61—22no—
228C2×D61—22no—
229C2×D61—22no—
230C2×D61—21no—
231C2×D61—21no—
232C2×D61—48no—
233C2×D61—48no—
234C2×D61#32714yes—
235C2×D61#48012yes—
236C2×D61#48312yes—
237#6923—84no—
238C4×C61—22no—
239C4×C61—41no—
240C4×C61—81no—
241C4×C61—81no—
242Dic61—22no—
243Dic61—22no—
244Dic61—81no—
245Dic61—81no—
246C2×#380—611no—
247#1779—611no—
248C22⋊#95—611no—
249#1294—612no—
250#1294—612no—
251C2×C61—42no—
252C2×C61C2×#32711yescharacteristic
253C2×C61#150811yescharacteristic
254C2×C61#151111yescharacteristic
255C2×C61#151911yescharacteristic
256C2×C61#181911yescharacteristic
257C2×C61#182311yescharacteristic
258C2×C61#182611yescharacteristic
259D61—22no—
260D61—24no—
261D61—22no—
262C24×C4—611no—
263C22×C4⋊C4—611no—
264C22×C4⋊C4—611no—
265C22×C22⋊C4—1221no—
266C22×C22⋊C4—1221no—
267C2×C22⋊C8—612no—
268C2×C22⋊C8—1221no—
269C2×C22⋊C8—1221no—
270#380—611no—
271#380—611no—
272#380—611no—
273#380—1221no—
274#380—1221no—
275#380#692311yescharacteristic, complemented
276C2×#95—612no—
277C2×#95—1221no—
278C2×#95—1221no—
279C61#871211yescharacteristic, complemented, Sylow
280C25—611no—
281C23×C4—611no—
282C23×C4—611no—
283C23×C4—611no—
284C23×C4—611no—
285C23×C4—611no—
286C23×C4—1224no—
287C23×C4—1221no—
288C23×C4—1221no—
289C23×C4—1222no—
290C23×C4—2442no—
291C23×C4—2442no—
292C23×C4C2×#692311yescharacteristic
293C22×C8—1222no—
294C2×C4⋊C4—611no—
295C2×C4⋊C4—611no—
296C2×C4⋊C4—1221no—
297C2×C4⋊C4—1221no—
298C2×C4⋊C4—2442no—
299C2×C4⋊C4—2442no—
300C2×C4⋊C4C2×#692311yescharacteristic
301C2×C4⋊C4C2×#692311yescharacteristic
302C2×C22⋊C4—21no—
303C2×C22⋊C4—1221no—
304C2×C22⋊C4—1221no—
305C2×C22⋊C4—1224no—
306C2×C22⋊C4—1221no—
307C2×C22⋊C4—2442no—
308C2×C22⋊C4—2442no—
309C2×C22⋊C4—2442no—
310C2×C22⋊C4—2442no—
311C22⋊C8—1224no—
312C22⋊C8—2442no—
313C22⋊C8—2442no—
314#95—21no—
315#95—1221no—
316#95—1221no—
317#95—1224no—
318#95—1221no—
319#95—2442no—
320C24—611no—
321C24—611no—
322C24—612no—
323C24—612no—
324C24—1222no—
325C24—1222no—
326C24—1222no—
327C24—1222no—
328C24—2441no—
329C24—2441no—
330C24C22⋊#692311yescharacteristic
331C22×C4—22no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—41no—
335C22×C4—41no—
336C22×C4—611no—
337C22×C4—611no—
338C22×C4—614no—
339C22×C4—1222no—
340C22×C4—1222no—
341C22×C4—1222no—
342C22×C4—1222no—
343C22×C4—1222no—
344C22×C4—1222no—
345C22×C4—1222no—
346C22×C4—1222no—
347C22×C4—1222no—
348C22×C4—1224no—
349C22×C4—1221no—
350C22×C4—1221no—
351C22×C4—2441no—
352C22×C4—2441no—
353C22×C4—2441no—
354C22×C4—2441no—
355C22×C4—24416no—
356C22×C4—2442no—
357C22×C4—2442no—
358C22×C4—2442no—
359C22×C4—2442no—
360C22×C4—2442no—
361C22×C4—2442no—
362C22×C4—2441no—
363C22×C4—2442no—
364C22×C4—2442no—
365C22×C4—2442no—
366C22×C4—2442no—
367C22×C4—2442no—
368C22×C4—2442no—
369C22×C4C22⋊#692311yescharacteristic
370C22×C4C22×#692311yescharacteristic
371C2×C8—2442no—
372C2×C8—2442no—
373C2×C8—2442no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4—2441no—
377C4⋊C4—2441no—
378C4⋊C4—2442no—
379C4⋊C4—2442no—
380C22⋊C4—42no—
381C22⋊C4—2441no—
382C22⋊C4—2441no—
383C22⋊C4—2441no—
384C22⋊C4—2441no—
385C22⋊C4—2448no—
386C22⋊C4—2442no—
387C23—21no—
388C23—21no—
389C23—21no—
390C23—21no—
391C23—21no—
392C23—21no—
393C23—612no—
394C23—612no—
395C23—612no—
396C23—611no—
397C23—611no—
398C23—612no—
399C23—612no—
400C23—1224no—
401C23—1224no—
402C23—1224no—
403C23—1224no—
404C23—1221no—
405C23—1221no—
406C23—1221no—
407C23—1221no—
408C23—1221no—
409C23—1221no—
410C23—1221no—
411C23—1221no—
412C23—2442no—
413C23—2442no—
414C23—2444no—
415C23—2444no—
416C23—2444no—
417C23—2444no—
418C23#1451983912yes—
419C23C2×C22⋊#692311yescharacteristic
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—44no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—612no—
433C2×C4—612no—
434C2×C4—1228no—
435C2×C4—1221no—
436C2×C4—1221no—
437C2×C4—1221no—
438C2×C4—1221no—
439C2×C4—4884no—
440C2×C4—4884no—
441C2×C4—4882no—
442C2×C4—4882no—
443C2×C4—4882no—
444C2×C4—4882no—
445C2×C4—2444no—
446C2×C4—2444no—
447C2×C4—2444no—
448C2×C4—2444no—
449C2×C4—2444no—
450C2×C4—2444no—
451C2×C4—2444no—
452C2×C4—2441no—
453C2×C4—2441no—
454C2×C4—2441no—
455C2×C4—2441no—
456C2×C4—2441no—
457C2×C4—2441no—
458C2×C4#1451985612yes—
459C8—4882no—
460C22—22no—
461C22—22no—
462C22—22no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—41no—
467C22—614no—
468C22—612no—
469C22—612no—
470C22—1221no—
471C22—1222no—
472C22—1221no—
473C22—1221no—
474C22—1221no—
475C22—1222no—
476C22—1222no—
477C22—1222no—
478C22—1222no—
479C22—1222no—
480C22—1222no—
481C22—1222no—
482C22—1222no—
483C22—1222no—
484C22—2448no—
485C22—2448no—
486C22#1684070511yescharacteristic
487C22D61⋊#9911yescharacteristic
488C22D61⋊#9911yescharacteristic
489C22C2×#1451983911yescharacteristic
490C22#1684075511yescharacteristic
491C22D61⋊#10411yescharacteristic
492C22#1684075911yescharacteristic
493C4—22no—
494C4—41no—
495C4—81no—
496C4—81no—
497C4—1222no—
498C4—1222no—
499C4—4884no—
500C4—4881no—
501C4—4881no—
502C2—42no—
503C2—1222no—
504C2—1224no—
505C2—1222no—
506C2D61⋊#32711yescharacteristic
507C2#2146121711yescharacteristic
508C2#2146122811yescharacteristic
509C2#2146125411yescharacteristic
510C2#2146171511yescharacteristic
511C2#2146172211yescharacteristic
512C2#2146172711yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#380C4
socleC23×C61C2×C22⋊C4
prime radicalC24×D61D4
cosocleC22×C4×D61C23
hypercenter#380#6923
hypocenterC61#8712
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
3. #21460692C2semidirect
4. #21460692C2semidirect
13. C2×C4⋊C4×D61C4semidirect
14. C2×C4⋊C4×D61C4semidirect
16. #16839622C4semidirect
22. C61×#380C4semidirect
275. #380#6923semidirect
279. C61#8712semidirect

Maximal subgroups

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

subgroupindex
#214616422
#214609932
#214606922
#380×D612
#871261