Finite Group Databasebeta

← #30599252

Subgroups — #30599252

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—44no—
54#14519684—21no—
55#14519684—21no—
56#14519684—21no—
57C23×C4×C61C2×C411yescharacteristic
58C2×C4⋊C4×C61C2×C411yescharacteristic
59C2×C4⋊C4×C61C2×C411yescharacteristic
60C2×C22⋊C4×C61—21no—
61#95×C61—21no—
62C24×C61C22⋊C411yescharacteristic
63C23×D61—22no—
64C23×D61—22no—
65C23×D61—22no—
66C23×D61—22no—
67C23×D61—41no—
68C23×D61—41no—
69C23×D61C22⋊C411yescharacteristic
70C23×D61SD1612yes—
71C23×D61Q1612yes—
72C23×D61C2×D411yescharacteristic
73C22×#6923—24no—
74C22×#6923—42no—
75C22×#6923—42no—
76C22×#6923—42no—
77C22×#6923—42no—
78C22×#6923—42no—
79C22×#6923—42no—
80C22×C4×C61—22no—
81C22×C4×C61—21no—
82C22×C4×C61—21no—
83C22×C4×C61—41no—
84C22×C4×C61—41no—
85C22×C4×C61C22⋊C411yescharacteristic
86C22×C4×C61C22×C411yescharacteristic
87C22×Dic61—22no—
88C22×Dic61—22no—
89C22×Dic61—21no—
90C22×Dic61—21no—
91C22×Dic61—41no—
92C22×Dic61C22⋊C411yescharacteristic
93C22×Dic61C2×D411yescharacteristic
94C2×C4×D61—22no—
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—416no—
102C2×C4×D61—41no—
103C2×C4×D61—41no—
104C2×C4×D61—41no—
105C2×C4×D61—41no—
106C2×C4×D61—42no—
107C2×C4×D61—42no—
108C2×C4×D61—42no—
109C2×C4×D61—42no—
110C2×C4×D61—42no—
111C2×C4×D61—42no—
112C2×C4×D61#4114yes—
113C22⋊#6923—48no—
114C2×#92420—42no—
115C2×#92420—42no—
116C2×#92420—42no—
117C4⋊C4×C61—41no—
118C4⋊C4×C61—41no—
119C22⋊C4×C61—42no—
120C22⋊Dic61—42no—
121#11758198—42no—
122#11758198—42no—
123C4⋊Dic61—41no—
124C4⋊Dic61—41no—
125#11758196—42no—
126#11758196—42no—
127C23×C61—21no—
128C23×C61—21no—
129C23×C61—21no—
130C23×C61—21no—
131C23×C61—21no—
132C23×C61—21no—
133C23×C61#10312yes—
134C23×C61C2×C22⋊C411yescharacteristic
135C22×D61—21no—
136C22×D61—21no—
137C22×D61—21no—
138C22×D61—21no—
139C22×D61—21no—
140C22×D61—21no—
141C22×D61—21no—
142C22×D61—21no—
143C22×D61—24no—
144C22×D61—24no—
145C22×D61—24no—
146C22×D61—24no—
147C22×D61—42no—
148C22×D61—42no—
149C22×D61—44no—
150C22×D61—44no—
151C22×D61—44no—
152C22×D61—44no—
153C22×D61#9912yes—
154C22×D61#10312yes—
155C22×D61#10412yes—
156C22×D61#12312yes—
157C22×D61C2×SD1611yescharacteristic
158C22×D61C2×Q1611yescharacteristic
159C22×D61AGL(1,ℤ/8)12yes—
160C2×#6923—44no—
161C2×#6923—44no—
162C2×#6923—44no—
163C2×#6923—82no—
164C2×#6923—82no—
165C2×#6923—82no—
166C2×#6923—82no—
167C2×C4×C61—21no—
168C2×C4×C61—21no—
169C2×C4×C61—21no—
170C2×C4×C61—21no—
171C2×C4×C61—21no—
172C2×C4×C61—44no—
173C2×C4×C61—41no—
174C2×C4×C61—41no—
175C2×C4×C61—41no—
176C2×C4×C61—41no—
177C2×C4×C61—41no—
178C2×C4×C61—41no—
179C2×C4×C61#11712yes—
180C2×Dic61—21no—
181C2×Dic61—21no—
182C2×Dic61—21no—
183C2×Dic61—21no—
184C2×Dic61—44no—
185C2×Dic61—41no—
186C2×Dic61—41no—
187C2×Dic61—41no—
188C2×Dic61—41no—
189C2×Dic61—41no—
190C2×Dic61—41no—
191C2×Dic61#9912yes—
192C2×Dic61#12312yes—
193C4×D61—28no—
194C4×D61—44no—
195C4×D61—44no—
196C4×D61—44no—
197C4×D61—84no—
198C4×D61—84no—
199#92420—82no—
200#8713—611nomaximal, Sylow
201C22×C61—22no—
202C22×C61—22no—
203C22×C61—22no—
204C22×C61—41no—
205C22×C61—41no—
206C22×C61—41no—
207C22×C61—41no—
208C22×C61#38111yescharacteristic
209C22×C61C2×#9911yescharacteristic
210C22×C61C2×#9911yescharacteristic
211C22×C61C2×#10311yescharacteristic
212C22×C61#41811yescharacteristic
213C22×C61C2×#10411yescharacteristic
214C22×C61#42111yescharacteristic
215C2×D61—22no—
216C2×D61—22no—
217C2×D61—22no—
218C2×D61—22no—
219C2×D61—22no—
220C2×D61—21no—
221C2×D61—21no—
222C2×D61—22no—
223C2×D61—22no—
224C2×D61—22no—
225C2×D61—22no—
226C2×D61—21no—
227C2×D61—22no—
228C2×D61—21no—
229C2×D61—48no—
230C2×D61—48no—
231C2×D61#32814yes—
232C2×D61#48112yes—
233C2×D61#48412yes—
234#6923—84no—
235C4×C61—22no—
236C4×C61—41no—
237C4×C61—81no—
238C4×C61—81no—
239Dic61—22no—
240Dic61—22no—
241Dic61—81no—
242Dic61—81no—
243C2×#380—611no—
244#1779—611no—
245C22⋊#95—611no—
246#1294—612no—
247#1294—612no—
248C2×C61—42no—
249C2×C61C2×#32811yescharacteristic
250C2×C61#150711yescharacteristic
251C2×C61#151011yescharacteristic
252C2×C61#152011yescharacteristic
253C2×C61#181911yescharacteristic
254C2×C61#182411yescharacteristic
255C2×C61#182611yescharacteristic
256D61—22no—
257D61—24no—
258D61—22no—
259C24×C4—611no—
260C22×C4⋊C4—611no—
261C22×C4⋊C4—611no—
262C22×C22⋊C4—1221no—
263C22×C22⋊C4—1221no—
264C2×C22⋊C8—612no—
265C2×C22⋊C8—1221no—
266C2×C22⋊C8—1221no—
267#380—611no—
268#380—611no—
269#380—611no—
270#380—1221no—
271#380—1221no—
272#380#692311yescharacteristic, complemented
273C2×#95—612no—
274C2×#95—1221no—
275C2×#95—1221no—
276C61#871311yescharacteristic, complemented, Sylow
277C25—611no—
278C23×C4—611no—
279C23×C4—611no—
280C23×C4—611no—
281C23×C4—611no—
282C23×C4—611no—
283C23×C4—1224no—
284C23×C4—1221no—
285C23×C4—1221no—
286C23×C4—1222no—
287C23×C4—2442no—
288C23×C4—2442no—
289C23×C4C2×#692311yescharacteristic
290C22×C8—1222no—
291C2×C4⋊C4—611no—
292C2×C4⋊C4—611no—
293C2×C4⋊C4—1221no—
294C2×C4⋊C4—1221no—
295C2×C4⋊C4—2442no—
296C2×C4⋊C4—2442no—
297C2×C4⋊C4C2×#692311yescharacteristic
298C2×C4⋊C4C2×#692311yescharacteristic
299C2×C22⋊C4—21no—
300C2×C22⋊C4—1221no—
301C2×C22⋊C4—1221no—
302C2×C22⋊C4—1224no—
303C2×C22⋊C4—1221no—
304C2×C22⋊C4—2444no—
305C2×C22⋊C4—2442no—
306C2×C22⋊C4—2442no—
307C22⋊C8—1224no—
308C22⋊C8—2442no—
309C22⋊C8—2442no—
310#95—21no—
311#95—1221no—
312#95—1221no—
313#95—1224no—
314#95—1221no—
315#95—2442no—
316C24—611no—
317C24—611no—
318C24—612no—
319C24—612no—
320C24—1222no—
321C24—1222no—
322C24—1222no—
323C24—1222no—
324C24—2441no—
325C24—2441no—
326C24C22⋊#692311yescharacteristic
327C22×C4—22no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—611no—
333C22×C4—611no—
334C22×C4—614no—
335C22×C4—1222no—
336C22×C4—1222no—
337C22×C4—1222no—
338C22×C4—1222no—
339C22×C4—1222no—
340C22×C4—1222no—
341C22×C4—1222no—
342C22×C4—1222no—
343C22×C4—1222no—
344C22×C4—1224no—
345C22×C4—1221no—
346C22×C4—1221no—
347C22×C4—2441no—
348C22×C4—2441no—
349C22×C4—2441no—
350C22×C4—2441no—
351C22×C4—24416no—
352C22×C4—2442no—
353C22×C4—2442no—
354C22×C4—2442no—
355C22×C4—2442no—
356C22×C4—2442no—
357C22×C4—2442no—
358C22×C4—2441no—
359C22×C4—2442no—
360C22×C4—2442no—
361C22×C4—2442no—
362C22×C4—2442no—
363C22×C4—2442no—
364C22×C4—2442no—
365C22×C4C22⋊#692311yescharacteristic
366C22×C4C22×#692311yescharacteristic
367C2×C8—2442no—
368C2×C8—2442no—
369C2×C8—2442no—
370C4⋊C4—41no—
371C4⋊C4—41no—
372C4⋊C4—2441no—
373C4⋊C4—2441no—
374C4⋊C4—2442no—
375C4⋊C4—2442no—
376C22⋊C4—42no—
377C22⋊C4—2442no—
378C22⋊C4—2442no—
379C22⋊C4—2442no—
380C22⋊C4—2448no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—612no—
388C23—612no—
389C23—612no—
390C23—611no—
391C23—611no—
392C23—612no—
393C23—612no—
394C23—1224no—
395C23—1224no—
396C23—1224no—
397C23—1224no—
398C23—1221no—
399C23—1221no—
400C23—1221no—
401C23—1221no—
402C23—1221no—
403C23—1221no—
404C23—1221no—
405C23—1221no—
406C23—2442no—
407C23—2442no—
408C23—2444no—
409C23—2444no—
410C23—2444no—
411C23—2444no—
412C23#1451984012yes—
413C23C2×C22⋊#692311yescharacteristic
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—44no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—612no—
427C2×C4—612no—
428C2×C4—1228no—
429C2×C4—1221no—
430C2×C4—1221no—
431C2×C4—1221no—
432C2×C4—1221no—
433C2×C4—4884no—
434C2×C4—4884no—
435C2×C4—4882no—
436C2×C4—4882no—
437C2×C4—4882no—
438C2×C4—4882no—
439C2×C4—2444no—
440C2×C4—2444no—
441C2×C4—2444no—
442C2×C4—2444no—
443C2×C4—2444no—
444C2×C4—2444no—
445C2×C4—2444no—
446C2×C4—2441no—
447C2×C4—2441no—
448C2×C4—2441no—
449C2×C4—2441no—
450C2×C4—2441no—
451C2×C4—2441no—
452C2×C4#1451985612yes—
453C8—4882no—
454C22—22no—
455C22—22no—
456C22—22no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—614no—
462C22—612no—
463C22—612no—
464C22—1221no—
465C22—1222no—
466C22—1221no—
467C22—1221no—
468C22—1221no—
469C22—1222no—
470C22—1222no—
471C22—1222no—
472C22—1222no—
473C22—1222no—
474C22—1222no—
475C22—1222no—
476C22—1222no—
477C22—1222no—
478C22—2448no—
479C22—2448no—
480C22#1684070511yescharacteristic
481C22D61⋊#9911yescharacteristic
482C22D61⋊#9911yescharacteristic
483C22C2×#1451984011yescharacteristic
484C22#1684075411yescharacteristic
485C22D61⋊#10411yescharacteristic
486C22#1684075911yescharacteristic
487C4—22no—
488C4—41no—
489C4—81no—
490C4—81no—
491C4—1222no—
492C4—1222no—
493C4—4884no—
494C4—4881no—
495C4—4881no—
496C2—42no—
497C2—1222no—
498C2—1224no—
499C2—1222no—
500C2D61⋊#32811yescharacteristic
501C2#2146121411yescharacteristic
502C2#2146122511yescharacteristic
503C2#2146125711yescharacteristic
504C2#2146171511yescharacteristic
505C2#2146172311yescharacteristic
506C2#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#8713
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
272. #380#6923semidirect
276. C61#8713semidirect

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
#871361