Finite Group Databasebeta

← D61×#1352 #29590286

Subgroups — D61×#1352 #29590286

Order 15616.

712 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 712 conjugacy classes of subgroups — too many to draw. Only its 91 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#399×D61C211yesmaximal, characteristic
2#342×D61C211yesmaximal, characteristic
3#323×D61C211yesmaximal, characteristic
4#21443844C211yesmaximal, characteristic, complemented
5#21443843C211yesmaximal, characteristic, complemented
6#21443842C211yesmaximal, characteristic, complemented
7C61×#1352C211yesmaximal, characteristic, complemented
8C2×C4⋊C4×D61—21no—
9C2×C4⋊C4×D61C411yescharacteristic, complemented
10C2×C22⋊C4×D61—21no—
11C2×C22⋊C4×D61—21no—
12C2×C22⋊C4×D61C2211yescharacteristic
13C22⋊C8×D61—21no—
14#16839699C411yescharacteristic, complemented
15#16839698—21no—
16#16839698C2211yescharacteristic
17#16839697—21no—
18#16839697C411yescharacteristic, complemented
19#95×D61C411yescharacteristic, complemented
20#16839529C2211yescharacteristic
21#16839528—21no—
22#16839486C2211yescharacteristic
23#16839485—21no—
24C61×#399C2211yescharacteristic
25C61×#342C2211yescharacteristic
26C61×#323C2211yescharacteristic
27C24×D61D411yescharacteristic
28C22×C4×D61—21no—
29C22×C4×D61—21no—
30C22×C4×D61—41no—
31C22×C4×D61C2×C411yescharacteristic
32C22×C4×D61D411yescharacteristic
33C2×C8×D61—41no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61C2×C411yescharacteristic, complemented
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×#11758196—21no—
39C4⋊C4×D61—41no—
40C4⋊C4×D61—41no—
41C4⋊C4×D61—44no—
42C2×C22⋊Dic61—21no—
43C2×C22⋊Dic61—21no—
44C2×C22⋊Dic61D411yescharacteristic
45C2×#11758198—21no—
46C2×#11758198—21no—
47C2×#11758198—41no—
48C2×#11758198C2×C411yescharacteristic
49C2×#11758198D411yescharacteristic
50C22⋊C4×D61—24no—
51C22⋊C4×D61—41no—
52C22⋊C4×D61—41no—
53C22⋊C4×D61—44no—
54C22⋊C4×D61—42no—
55C22⋊#92418—21no—
56#14519689—41no—
57#14519684—21no—
58#14519684C2×C411yescharacteristic, complemented
59C2×C4⋊C4×C61—21no—
60C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
61C2×C22⋊C4×C61—21no—
62C2×C22⋊C4×C61—21no—
63C2×C22⋊C4×C61C2311yescharacteristic
64C22⋊C8×C61—21no—
65#95×C61C2×C411yescharacteristic, complemented
66C24×C61C2×D411yescharacteristic
67C23×D61—21no—
68C23×D61—21no—
69C23×D61—22no—
70C23×D61—42no—
71C23×D61—42no—
72C23×D61C22⋊C411yescharacteristic
73C23×D61C22⋊C411yescharacteristic
74C23×D61SD1612yes—
75C23×D61Q1612yes—
76C22×C4×C61—21no—
77C22×C4×C61—21no—
78C22×C4×C61—41no—
79C22×C4×C61C22×C411yescharacteristic
80C22×C4×C61C2×D411yescharacteristic
81C22×Dic61—21no—
82C22×Dic61—21no—
83C22×Dic61—41no—
84C22×Dic61C22⋊C411yescharacteristic
85C22×Dic61C22⋊C411yescharacteristic
86C2×C4×D61—24no—
87C2×C4×D61—21no—
88C2×C4×D61—21no—
89C2×C4×D61—21no—
90C2×C4×D61—21no—
91C2×C4×D61—42no—
92C2×C4×D61—42no—
93C2×C4×D61—42no—
94C2×C4×D61—42no—
95C2×C4×D61—42no—
96C2×C4×D61—42no—
97C2×C4×D61—44no—
98C2×C4×D61—41no—
99C2×C4×D61—41no—
100C2×C4×D61—82no—
101C2×C4×D61—82no—
102C2×C8×C61—41no—
103C4⋊C4×C61—42no—
104C4⋊C4×C61—41no—
105C22⋊C4×C61—22no—
106C22⋊C4×C61—41no—
107C22⋊C4×C61—42no—
108C22⋊C4×C61—41no—
109C22⋊Dic61—22no—
110C22⋊Dic61—41no—
111C22⋊Dic61—42no—
112C22⋊Dic61—41no—
113#11758198—41no—
114#11758198—41no—
115#11758198—42no—
116#11758198—42no—
117#11758198—44no—
118C4⋊Dic61—42no—
119C4⋊Dic61—41no—
120#11758196—42no—
121#11758196—42no—
122#11758196—42no—
123C2×#92418—41no—
124C8×D61—82no—
125C23×C61—21no—
126C23×C61—21no—
127C23×C61—41no—
128C23×C61—41no—
129C23×C61C2×C22⋊C411yescharacteristic
130C23×C61C2×SD1611yescharacteristic
131C23×C61C2×Q1611yescharacteristic
132C22×D61—22no—
133C22×D61—22no—
134C22×D61—21no—
135C22×D61—21no—
136C22×D61—22no—
137C22×D61—22no—
138C22×D61—22no—
139C22×D61—22no—
140C22×D61—44no—
141C22×D61—44no—
142C22×D61—42no—
143C22×D61—42no—
144C22×D61—41no—
145C22×D61—41no—
146C22×D61—84no—
147C22×D61—81no—
148C22×D61—81no—
149C22×D61#9911yescharacteristic
150C22×D61#9911yescharacteristic
151C22×D61#10312yes—
152C22×D61#10312yes—
153C22×D61#10412yes—
154C2×C4×C61—22no—
155C2×C4×C61—21no—
156C2×C4×C61—21no—
157C2×C4×C61—41no—
158C2×C4×C61—41no—
159C2×C4×C61—41no—
160C2×C4×C61—41no—
161C2×C4×C61—41no—
162C2×C4×C61—42no—
163C2×C4×C61—41no—
164C2×C4×C61—41no—
165C2×C4×C61—81no—
166C2×C4×C61—81no—
167C2×Dic61—22no—
168C2×Dic61—21no—
169C2×Dic61—21no—
170C2×Dic61—41no—
171C2×Dic61—41no—
172C2×Dic61—41no—
173C2×Dic61—41no—
174C2×Dic61—41no—
175C2×Dic61—42no—
176C2×Dic61—41no—
177C2×Dic61—41no—
178C2×Dic61—81no—
179C2×Dic61—81no—
180C4×D61—48no—
181C4×D61—42no—
182C4×D61—42no—
183C4×D61—42no—
184C4×D61—81no—
185C4×D61—82no—
186C4×D61—88no—
187C4×D61—82no—
188C8×C61—81no—
189#92418—81no—
190C2×#1352—611nomaximal, Sylow
191C22×C61—21no—
192C22×C61—21no—
193C22×C61—21no—
194C22×C61—21no—
195C22×C61—41no—
196C22×C61—41no—
197C22×C61—41no—
198C22×C61—41no—
199C22×C61—81no—
200C22×C61C2×#9911yescharacteristic
201C22×C61C2×#10311yescharacteristic
202C22×C61C2×#10411yescharacteristic
203C2×D61—21no—
204C2×D61—21no—
205C2×D61—24no—
206C2×D61—24no—
207C2×D61—22no—
208C2×D61—41no—
209C2×D61—41no—
210C2×D61—44no—
211C2×D61—44no—
212C2×D61—42no—
213C2×D61—82no—
214C2×D61—82no—
215C2×D61—81no—
216C2×D61#32812yes—
217C2×D61#32812yes—
218C2×D61#35212yes—
219C2×D61#35312yes—
220C4×C61—42no—
221C4×C61—41no—
222C4×C61—41no—
223C4×C61—82no—
224C4×C61—81no—
225Dic61—42no—
226Dic61—41no—
227Dic61—41no—
228Dic61—82no—
229Dic61—81no—
230C2×#399—611no—
231C2×#342—611no—
232C2×#323—611no—
233#1352—611no—
234#1352—611no—
235#1352—611no—
236#1352D6111yescharacteristic, direct product factor
237C2×C61—21no—
238C2×C61—21no—
239C2×C61—41no—
240C2×C61—41no—
241C2×C61C2×#32811yescharacteristic
242C2×C61C2×#35211yescharacteristic
243C2×C61C2×#35311yescharacteristic
244D61—22no—
245D61—42no—
246D61#135214yesdirect product factor
247C22×C4⋊C4—611no—
248C22×C4⋊C4—1221no—
249C22×C22⋊C4—611no—
250C22×C22⋊C4—1221no—
251C22×C22⋊C4—1221no—
252C2×C22⋊C8—1221no—
253#399—611no—
254#399—611no—
255#399—611no—
256#399—1221no—
257#399—1221no—
258#399C2×D6111yescharacteristic
259C2×#95—611no—
260#342—611no—
261#342—1221no—
262#342C2×D6111yescharacteristic
263#323—611no—
264#323—1221no—
265#323C2×D6111yescharacteristic
266C61C2×#135211yescharacteristic, complemented, Sylow
267C25—611no—
268C23×C4—611no—
269C23×C4—611no—
270C23×C4—1221no—
271C23×C4—1221no—
272C23×C4—2441no—
273C22×C8—2441no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—611no—
276C2×C4⋊C4—1221no—
277C2×C4⋊C4—1221no—
278C2×C4⋊C4—1221no—
279C2×C4⋊C4—1221no—
280C2×C4⋊C4—2441no—
281C2×C4⋊C4—2441no—
282C2×C4⋊C4—2444no—
283C2×C4⋊C4C4×D6111yescharacteristic, complemented
284C2×C22⋊C4—21no—
285C2×C22⋊C4—21no—
286C2×C22⋊C4—611no—
287C2×C22⋊C4—611no—
288C2×C22⋊C4—611no—
289C2×C22⋊C4—1224no—
290C2×C22⋊C4—1221no—
291C2×C22⋊C4—1221no—
292C2×C22⋊C4—1221no—
293C2×C22⋊C4—1221no—
294C2×C22⋊C4—2441no—
295C2×C22⋊C4—2441no—
296C2×C22⋊C4—2444no—
297C2×C22⋊C4—2442no—
298C2×C22⋊C4—2441no—
299C2×C22⋊C4C22×D6111yescharacteristic
300C22⋊C8—21no—
301C22⋊C8—1221no—
302C22⋊C8—2441no—
303#95—611no—
304#95—1221no—
305#95C4×D6111yescharacteristic, complemented
306C24—611no—
307C24—611no—
308C24—612no—
309C24—612no—
310C24—1222no—
311C24—1221no—
312C24—1221no—
313C24—2442no—
314C24—2442no—
315C24D4×D6111yescharacteristic
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—41no—
319C22×C4—611no—
320C22×C4—611no—
321C22×C4—1221no—
322C22×C4—1221no—
323C22×C4—1221no—
324C22×C4—1221no—
325C22×C4—1224no—
326C22×C4—1221no—
327C22×C4—1221no—
328C22×C4—4882no—
329C22×C4—4882no—
330C22×C4—2441no—
331C22×C4—2441no—
332C22×C4—2444no—
333C22×C4—2442no—
334C22×C4—2442no—
335C22×C4—2442no—
336C22×C4—2442no—
337C22×C4—2442no—
338C22×C4—2442no—
339C22×C4—2441no—
340C22×C4C2×C4×D6111yescharacteristic
341C22×C4D4×D6111yescharacteristic
342C2×C8—41no—
343C2×C8—4882no—
344C2×C8—2441no—
345C4⋊C4—41no—
346C4⋊C4—42no—
347C4⋊C4—2441no—
348C4⋊C4—2442no—
349C4⋊C4—2442no—
350C4⋊C4—2442no—
351C4⋊C4—2442no—
352C22⋊C4—22no—
353C22⋊C4—41no—
354C22⋊C4—42no—
355C22⋊C4—41no—
356C22⋊C4—1222no—
357C22⋊C4—2441no—
358C22⋊C4—2441no—
359C22⋊C4—2442no—
360C22⋊C4—2442no—
361C22⋊C4—2444no—
362C22⋊C4—2441no—
363C22⋊C4—2442no—
364C22⋊C4—2441no—
365C23—21no—
366C23—21no—
367C23—41no—
368C23—41no—
369C23—611no—
370C23—611no—
371C23—612no—
372C23—612no—
373C23—612no—
374C23—1222no—
375C23—1222no—
376C23—1222no—
377C23—1222no—
378C23—1222no—
379C23—1222no—
380C23—1221no—
381C23—1221no—
382C23—4881no—
383C23—4881no—
384C23—4884no—
385C23—2441no—
386C23—2441no—
387C23—2442no—
388C23—2442no—
389C23—2444no—
390C23—2444no—
391C23C22⋊C4×D6111yescharacteristic
392C23SD16×D6111yescharacteristic
393C23Q16×D6111yescharacteristic
394C2×C4—22no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—42no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—81no—
406C2×C4—81no—
407C2×C4—1222no—
408C2×C4—1221no—
409C2×C4—1221no—
410C2×C4—4881no—
411C2×C4—4882no—
412C2×C4—4882no—
413C2×C4—4888no—
414C2×C4—4881no—
415C2×C4—4881no—
416C2×C4—2442no—
417C2×C4—2442no—
418C2×C4—2448no—
419C2×C4—2442no—
420C2×C4—2442no—
421C2×C4—2441no—
422C2×C4—2441no—
423C2×C4—2441no—
424C2×C4—2441no—
425C2×C4—2441no—
426C2×C4—2441no—
427C2×C4—2441no—
428C8—81no—
429C8—4881no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—41no—
435C22—41no—
436C22—41no—
437C22—41no—
438C22—81no—
439C22—612no—
440C22—612no—
441C22—612no—
442C22—612no—
443C22—1224no—
444C22—1224no—
445C22—1221no—
446C22—1221no—
447C22—1222no—
448C22—4881no—
449C22—4882no—
450C22—4882no—
451C22—2442no—
452C22—2444no—
453C22—2444no—
454C22—2441no—
455C22—2441no—
456C22#99×D6111yescharacteristic
457C22#103×D6111yescharacteristic
458C22#104×D6111yescharacteristic
459C4—42no—
460C4—41no—
461C4—41no—
462C4—82no—
463C4—81no—
464C4—4882no—
465C4—4881no—
466C4—2442no—
467C4—2441no—
468C4—2441no—
469C2—21no—
470C2—21no—
471C2—41no—
472C2—41no—
473C2—614no—
474C2—1222no—
475C2—2442no—
476C2#328×D6111yescharacteristic
477C2#352×D6111yescharacteristic
478C2#353×D6111yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1352C2
socleC22×C61C2×#99
prime radicalC24×D61D4
cosocleC2×C22⋊C4×C61C23
hypercenter#1352D61
hypocenterC61C2×#1352
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1352

Complements

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

NH ≅ G/Ntype
4. #21443844C2semidirect
5. #21443843C2semidirect
6. #21443842C2semidirect
7. C61×#1352C2semidirect
9. C2×C4⋊C4×D61C4semidirect
14. #16839699C4semidirect
18. #16839697C4semidirect
19. #95×D61C4semidirect
35. C2×C4⋊Dic61C2×C4semidirect
58. #14519684C2×C4semidirect
60. C2×C4⋊C4×C61C2×C4semidirect
65. #95×C61C2×C4semidirect
236. #1352D61direct (N × H)
246. D61#1352direct (N × H)
266. C61C2×#1352semidirect
283. C2×C4⋊C4C4×D61semidirect
305. #95C4×D61semidirect

Maximal subgroups

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

subgroupindex
#399×D612
#342×D612
#323×D612
#214438442
#214438432
#214438422
C61×#13522
C2×#135261