Finite Group Databasebeta

← #30604737

Subgroups — #30604737

Order 15616.

670 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 670 conjugacy classes of subgroups — too many to draw. Only its 80 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#21461516C211yesmaximal, characteristic, complemented
2D61⋊#323C211yesmaximal, characteristic, complemented
3#21460800C212yesmaximal, complemented
4#21460797C212yesmaximal, complemented
5#21451552C211yesmaximal, characteristic
6C22×C22⋊#6923—21no—
7D61⋊(C22⋊C8)—21no—
8#16840640—21no—
9#16840640C2212yes—
10#16840606C2212yes—
11#16840605—21no—
12C2×#14519748C411yescharacteristic, complemented
13C2×#14519745—21no—
14C2×C22⋊C4×D61C2211yescharacteristic
15#16839689C2211yescharacteristic
16#16839687C411yescharacteristic, complemented
17#16839677—21no—
18#16839676—21no—
19#16839670C2211yescharacteristic
20#16839638—21no—
21#16839621C411yescharacteristic, complemented
22C61×#392C411yescharacteristic, complemented
23C23×#6923—41no—
24C2×D61⋊C8—41no—
25C2×C22⋊#6923—24no—
26C2×C22⋊#6923—22no—
27C2×C22⋊#6923—41no—
28C2×C22⋊#6923—42no—
29#14519834—41no—
30C22⋊#92420—22no—
31C24×D61D411yescharacteristic
32C22×C22⋊D61—21no—
33C22×C22⋊D61—21no—
34C22×C4×D61C2×C411yescharacteristic
35C22×C4×D61D411yescharacteristic
36#14519748—41no—
37#14519748—41no—
38#14519745—42no—
39#14519745—42no—
40C2×C4⋊Dic61C2×C411yescharacteristic, complemented
41C2×#11758196—21no—
42C2×C22⋊Dic61—21no—
43C2×C22⋊Dic61—21no—
44C2×C22⋊Dic61—21no—
45C2×C22⋊Dic61D411yescharacteristic
46C2×#11758198—21no—
47C2×#11758198—21no—
48C2×#11758198D411yescharacteristic
49C2×#11758198C2311yescharacteristic
50C22⋊C4×D61—41no—
51C22⋊C4×D61—41no—
52#14519684—21no—
53#14519684—21no—
54#14519684C2×C411yescharacteristic, complemented
55C22×D4×C61—21no—
56C22×D4×C61C2×C411yescharacteristic, complemented
57C2×C22⋊C4×C61—21no—
58C2×C22⋊C4×C61C2×C411yescharacteristic
59#95×C61C2×C411yescharacteristic, complemented
60C24×C61—21no—
61C24×C61C22⋊C411yescharacteristic
62C23×D61—21no—
63C23×D61—21no—
64C23×D61—22no—
65C23×D61—81no—
66C23×D61—81no—
67C23×D61C22⋊C411yescharacteristic
68C23×D61D812yes—
69C23×D61SD1612yes—
70C23×D61C2×D411yescharacteristic
71C22×#6923—42no—
72C22×#6923—44no—
73C22×#6923—82no—
74C22×#6923—82no—
75C2×D4×C61—41no—
76C2×D4×C61—42no—
77C2×D4×C61—81no—
78C2×D4×C61—81no—
79C2×D4×C61—81no—
80C22×C4×C61—21no—
81C22×C4×C61C22⋊C411yescharacteristic
82C22×C4×C61C22×C411yescharacteristic
83C2×C22⋊D61—41no—
84C2×C22⋊D61—41no—
85C2×C22⋊D61—42no—
86C2×C22⋊D61—42no—
87C2×C22⋊D61—41no—
88C2×C22⋊D61—41no—
89C2×C22⋊D61—81no—
90C2×C22⋊D61—81no—
91C22×Dic61—21no—
92C22×Dic61—21no—
93C22×Dic61C22⋊C411yescharacteristic
94C22×Dic61C2×D411yescharacteristic
95C2×C4×D61—21no—
96C2×C4×D61—21no—
97C2×C4×D61—21no—
98C2×C4×D61—21no—
99C2×C4×D61—81no—
100C2×C4×D61—81no—
101C22⋊#6923—24no—
102C22⋊#6923—44no—
103C22⋊#6923—42no—
104C2×#92420—42no—
105D61⋊C8—82no—
106C22⋊C4×C61—41no—
107C22⋊C4×C61—81no—
108C22⋊Dic61—41no—
109C22⋊Dic61—42no—
110C22⋊Dic61—42no—
111C22⋊Dic61—81no—
112#11758198—41no—
113#11758198—41no—
114#11758198—42no—
115#11758198—41no—
116#11758198—41no—
117C4⋊Dic61—41no—
118#11758196—81no—
119C23×C61—21no—
120C23×C61—21no—
121C23×C61—41no—
122C23×C61—41no—
123C23×C61—41no—
124C23×C61—41no—
125C23×C61—41no—
126C23×C61—41no—
127C23×C61—41no—
128C23×C61—41no—
129C23×C61—41no—
130C23×C61#10212yes—
131C23×C61C2×C22⋊C411yescharacteristic
132C22×D61—21no—
133C22×D61—21no—
134C22×D61—22no—
135C22×D61—22no—
136C22×D61—22no—
137C22×D61—22no—
138C22×D61—41no—
139C22×D61—41no—
140C22×D61—42no—
141C22×D61—42no—
142C22×D61—41no—
143C22×D61—41no—
144C22×D61—81no—
145C22×D61—81no—
146C22×D61—82no—
147C22×D61—82no—
148C22×D61—84no—
149C22×D61#9911yescharacteristic
150C22×D61#9911yescharacteristic
151C22×D61#10212yes—
152C22×D61#10412yes—
153C22×D61C2×D811yescharacteristic
154C22×D61C2×SD1611yescharacteristic
155C2×#6923—44no—
156C2×#6923—88no—
157C2×#6923—82no—
158C2×#6923—82no—
159D4×C61—82no—
160D4×C61—84no—
161C2×C4×C61—21no—
162C2×C4×C61—21no—
163C2×C4×C61—41no—
164C2×C4×C61—41no—
165C2×C4×C61—41no—
166C2×C4×C61—41no—
167C2×C4×C61—41no—
168C22⋊D61—82no—
169C22⋊D61—82no—
170C22⋊D61—82no—
171C22⋊D61—82no—
172C2×Dic61—21no—
173C2×Dic61—21no—
174C2×Dic61—41no—
175C2×Dic61—41no—
176C2×Dic61—41no—
177C2×Dic61—41no—
178C2×Dic61—41no—
179C2×Dic61—41no—
180C2×Dic61—41no—
181C2×Dic61—41no—
182C4×D61—42no—
183C4×D61—81no—
184C4×D61—81no—
185C4×D61—81no—
186#92420—82no—
187#11692—611nomaximal, Sylow
188C22×C61—21no—
189C22×C61—21no—
190C22×C61—22no—
191C22×C61—42no—
192C22×C61—41no—
193C22×C61—41no—
194C22×C61—81no—
195C22×C61—81no—
196C22×C61—81no—
197C22×C61—81no—
198C22×C61—81no—
199C22×C61—81no—
200C22×C61—81no—
201C22×C61—81no—
202C22×C61C2×#9911yescharacteristic
203C22×C61C2×#10211yescharacteristic
204C22×C61C2×#10411yescharacteristic
205C2×D61—21no—
206C2×D61—21no—
207C2×D61—21no—
208C2×D61—21no—
209C2×D61—21no—
210C2×D61—21no—
211C2×D61—42no—
212C2×D61—42no—
213C2×D61—44no—
214C2×D61—44no—
215C2×D61—41no—
216C2×D61—41no—
217C2×D61—41no—
218C2×D61—41no—
219C2×D61—82no—
220C2×D61—82no—
221C2×D61—81no—
222C2×D61#32712yes—
223C2×D61#32712yes—
224#6923—84no—
225C4×C61—41no—
226C4×C61—41no—
227C4×C61—81no—
228Dic61—41no—
229Dic61—41no—
230Dic61—81no—
231Dic61—81no—
232#2617—611no—
233C2×#342—611no—
234C2×#323—611no—
235#1344—612no—
236#1343—612no—
237C2×C61—21no—
238C2×C61—21no—
239C2×C61—42no—
240C2×C61—161no—
241C2×C61C2×#32711yescharacteristic
242C2×C61#212111yescharacteristic
243C2×C61#212711yescharacteristic
244D61—22no—
245D61—22no—
246D61—41no—
247D61—41no—
248C2×#121—611no—
249C2×#120—1221no—
250C22×C22⋊C4—611no—
251C22×C22⋊C4—1221no—
252C2×C22⋊C8—1221no—
253#397—611no—
254#397—611no—
255#394—1221no—
256#394—1221no—
257#392—611no—
258#392#692311yescharacteristic, complemented
259#386—1221no—
260#380—611no—
261#342—612no—
262#342—1221no—
263#323—612no—
264#323—1221no—
265C61#1169211yescharacteristic, complemented, Sylow
266C25—611no—
267C22×D4—21no—
268C22×D4—1221no—
269C22×D4—1221no—
270C22×D4C2×#692311yescharacteristic, complemented
271C23×C4—611no—
272C23×C4—611no—
273C23×C4—2441no—
274C22×C8—2441no—
275#121—2441no—
276#121—2441no—
277#120—2442no—
278#120—2442no—
279C2×C4⋊C4—611no—
280C2×C4⋊C4—1221no—
281C2×C22⋊C4—21no—
282C2×C22⋊C4—611no—
283C2×C22⋊C4—611no—
284C2×C22⋊C4—611no—
285C2×C22⋊C4—1222no—
286C2×C22⋊C4—1224no—
287C2×C22⋊C4—1221no—
288C2×C22⋊C4—1221no—
289C2×C22⋊C4—1221no—
290C2×C22⋊C4—1221no—
291C2×C22⋊C4—1221no—
292C2×C22⋊C4—2441no—
293C2×C22⋊C4—2441no—
294C2×C22⋊C4—2442no—
295C2×C22⋊C4—2441no—
296C2×C22⋊C4C2×#692311yescharacteristic
297C22⋊C8—1222no—
298C22⋊C8—2441no—
299#95—611no—
300#95—1221no—
301#95—1221no—
302#95C2×#692311yescharacteristic, complemented
303C24—21no—
304C24—611no—
305C24—612no—
306C24—612no—
307C24—611no—
308C24—1222no—
309C24—1221no—
310C24—1221no—
311C24—4881no—
312C24—4881no—
313C24C22⋊#692311yescharacteristic
314C2×D4—41no—
315C2×D4—42no—
316C2×D4—81no—
317C2×D4—81no—
318C2×D4—81no—
319C2×D4—4881no—
320C2×D4—4881no—
321C2×D4—2442no—
322C2×D4—2441no—
323C2×D4—2441no—
324C2×D4—2441no—
325C2×D4—2441no—
326C2×D4—2442no—
327C22×C4—21no—
328C22×C4—611no—
329C22×C4—611no—
330C22×C4—1221no—
331C22×C4—1221no—
332C22×C4—1221no—
333C22×C4—1221no—
334C22×C4—1221no—
335C22×C4—1221no—
336C22×C4—4881no—
337C22×C4—4881no—
338C22×C4—4882no—
339C22×C4—4882no—
340C22×C4—2444no—
341C22×C4—2442no—
342C22×C4C22⋊#692311yescharacteristic
343C22×C4C22×#692311yescharacteristic
344C2×C8—4882no—
345C2×C8—2442no—
346C4⋊C4—4881no—
347C4⋊C4—2441no—
348C22⋊C4—41no—
349C22⋊C4—81no—
350C22⋊C4—1224no—
351C22⋊C4—4881no—
352C22⋊C4—2441no—
353C22⋊C4—2441no—
354C22⋊C4—2442no—
355C22⋊C4—2441no—
356C22⋊C4—2441no—
357C22⋊C4—2441no—
358C22⋊C4—2442no—
359C22⋊C4—2442no—
360C22⋊C4—2444no—
361C22⋊C4—2442no—
362C23—21no—
363C23—21no—
364C23—41no—
365C23—41no—
366C23—41no—
367C23—41no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23—41no—
372C23—41no—
373C23—611no—
374C23—611no—
375C23—612no—
376C23—612no—
377C23—611no—
378C23—611no—
379C23—1222no—
380C23—1222no—
381C23—1222no—
382C23—1222no—
383C23—1221no—
384C23—1221no—
385C23—4881no—
386C23—4881no—
387C23—4882no—
388C23—4882no—
389C23—4884no—
390C23—2441no—
391C23—2441no—
392C23—2441no—
393C23—2441no—
394C23—2442no—
395C23—2442no—
396C23#1451983912yes—
397C23C2×C22⋊#692311yescharacteristic
398D4—82no—
399D4—84no—
400D4—4882no—
401D4—4882no—
402D4—4882no—
403D4—4882no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—1221no—
412C2×C4—1221no—
413C2×C4—4881no—
414C2×C4—4881no—
415C2×C4—4881no—
416C2×C4—4888no—
417C2×C4—4882no—
418C2×C4—4882no—
419C2×C4—2442no—
420C2×C4—2441no—
421C2×C4—2441no—
422C2×C4—2444no—
423C2×C4—2441no—
424C2×C4—2441no—
425C2×C4—2441no—
426C2×C4—2441no—
427C2×C4—2441no—
428C2×C4—2441no—
429C8—4882no—
430C22—21no—
431C22—21no—
432C22—22no—
433C22—42no—
434C22—41no—
435C22—41no—
436C22—81no—
437C22—81no—
438C22—81no—
439C22—81no—
440C22—81no—
441C22—81no—
442C22—81no—
443C22—81no—
444C22—612no—
445C22—612no—
446C22—1221no—
447C22—1221no—
448C22—1221no—
449C22—1221no—
450C22—1221no—
451C22—1221no—
452C22—4881no—
453C22—4882no—
454C22—4882no—
455C22—2442no—
456C22—2442no—
457C22—2441no—
458C22—2441no—
459C22—2444no—
460C22—2444no—
461C22—2441no—
462C22—2441no—
463C22D61⋊#9911yescharacteristic
464C22C2×#1451983911yescharacteristic
465C22D61⋊#10411yescharacteristic
466C4—41no—
467C4—41no—
468C4—81no—
469C4—4881no—
470C4—4884no—
471C4—4881no—
472C4—2441no—
473C4—2441no—
474C2—21no—
475C2—21no—
476C2—42no—
477C2—161no—
478C2—1222no—
479C2—1222no—
480C2—2441no—
481C2—2441no—
482C2D61⋊#32711yescharacteristic
483C2#2146207511yescharacteristic
484C2#2146209511yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#392C4
socleC22×C61C2×#99
prime radical#21451552C2
cosocleC2×#11758198C23
hypercenter#392#6923
hypocenterC61#11692
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #392

Complements

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

NH ≅ G/Ntype
1. #21461516C2semidirect
2. D61⋊#323C2semidirect
3. #21460800C2semidirect
4. #21460797C2semidirect
12. C2×#14519748C4semidirect
16. #16839687C4semidirect
21. #16839621C4semidirect
22. C61×#392C4semidirect
40. C2×C4⋊Dic61C2×C4semidirect
54. #14519684C2×C4semidirect
56. C22×D4×C61C2×C4semidirect
59. #95×C61C2×C4semidirect
258. #392#6923semidirect
265. C61#11692semidirect
270. C22×D4C2×#6923semidirect
302. #95C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214615162
D61⋊#3232
#214608002
#214607972
#214515522
#1169261