Finite Group Databasebeta

← D61×#1344 #29590182

Subgroups — D61×#1344 #29590182

Order 15616.

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

normal subgroups only

This group has 668 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#397×D61C211yesmaximal, characteristic
2#342×D61C211yesmaximal, characteristic
3#323×D61C211yesmaximal, characteristic
4#21443820C211yesmaximal, characteristic, complemented
5#21443819C211yesmaximal, characteristic, complemented
6#21443818C211yesmaximal, characteristic, complemented
7C61×#1344C211yesmaximal, characteristic, complemented
8C2×C4⋊C4×D61C411yescharacteristic, complemented
9C2×C22⋊C4×D61—21no—
10C2×C22⋊C4×D61—21no—
11C2×C22⋊C4×D61C2211yescharacteristic
12C22⋊C8×D61—21no—
13#16839691—21no—
14#16839690—21no—
15#16839689C411yescharacteristic, complemented
16#16839688C411yescharacteristic, complemented
17#16839687C2211yescharacteristic
18#95×D61—21no—
19#95×D61C411yescharacteristic, complemented
20#16839529C2211yescharacteristic
21#16839528—21no—
22#16839486C2211yescharacteristic
23#16839485—21no—
24C61×#397C2211yescharacteristic
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⋊Dic61C2×C411yescharacteristic, complemented
35C2×#11758196—21no—
36C4⋊C4×D61—41no—
37C4⋊C4×D61—41no—
38C2×C22⋊Dic61—21no—
39C2×C22⋊Dic61—21no—
40C2×C22⋊Dic61D411yescharacteristic
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×#11758198—41no—
44C2×#11758198C2×C411yescharacteristic
45C2×#11758198D411yescharacteristic
46C22⋊C4×D61—24no—
47C22⋊C4×D61—41no—
48C22⋊C4×D61—41no—
49C22⋊C4×D61—42no—
50C22⋊C4×D61—42no—
51C22⋊C4×D61—42no—
52C22⋊#92418—21no—
53#14519689—41no—
54#14519684—21no—
55#14519684—21no—
56#14519684—21no—
57#14519684—21no—
58#14519684C2×C411yescharacteristic, complemented
59C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
60C2×C22⋊C4×C61—21no—
61C2×C22⋊C4×C61—21no—
62C2×C22⋊C4×C61C2311yescharacteristic
63C22⋊C8×C61—21no—
64#95×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×D61D812yes—
75C23×D61SD1612yes—
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—21no—
87C2×C4×D61—21no—
88C2×C4×D61—21no—
89C2×C4×D61—21no—
90C2×C4×D61—42no—
91C2×C4×D61—42no—
92C2×C4×D61—42no—
93C2×C4×D61—42no—
94C2×C4×D61—44no—
95C2×C4×D61—41no—
96C2×C4×D61—41no—
97C2×C4×D61—42no—
98C2×C4×D61—42no—
99C2×C4×D61—42no—
100C2×C4×D61—82no—
101C2×C4×D61—82no—
102C2×C8×C61—41no—
103C4⋊C4×C61—41no—
104C22⋊C4×C61—22no—
105C22⋊C4×C61—41no—
106C22⋊C4×C61—41no—
107C22⋊C4×C61—41no—
108C22⋊C4×C61—41no—
109C22⋊Dic61—22no—
110C22⋊Dic61—41no—
111C22⋊Dic61—41no—
112C22⋊Dic61—41no—
113C22⋊Dic61—41no—
114#11758198—41no—
115#11758198—41no—
116#11758198—44no—
117#11758198—42no—
118#11758198—42no—
119C4⋊Dic61—41no—
120#11758196—42no—
121C2×#92418—41no—
122C8×D61—82no—
123C23×C61—21no—
124C23×C61—21no—
125C23×C61—41no—
126C23×C61—41no—
127C23×C61C2×C22⋊C411yescharacteristic
128C23×C61C2×D811yescharacteristic
129C23×C61C2×SD1611yescharacteristic
130C22×D61—22no—
131C22×D61—22no—
132C22×D61—21no—
133C22×D61—21no—
134C22×D61—22no—
135C22×D61—22no—
136C22×D61—22no—
137C22×D61—22no—
138C22×D61—44no—
139C22×D61—44no—
140C22×D61—42no—
141C22×D61—42no—
142C22×D61—41no—
143C22×D61—41no—
144C22×D61—84no—
145C22×D61—81no—
146C22×D61—81no—
147C22×D61#9911yescharacteristic
148C22×D61#9911yescharacteristic
149C22×D61#10212yes—
150C22×D61#10212yes—
151C22×D61#10412yes—
152C2×C4×C61—21no—
153C2×C4×C61—21no—
154C2×C4×C61—41no—
155C2×C4×C61—41no—
156C2×C4×C61—42no—
157C2×C4×C61—41no—
158C2×C4×C61—41no—
159C2×C4×C61—41no—
160C2×C4×C61—41no—
161C2×C4×C61—41no—
162C2×C4×C61—41no—
163C2×C4×C61—81no—
164C2×C4×C61—81no—
165C2×Dic61—21no—
166C2×Dic61—21no—
167C2×Dic61—41no—
168C2×Dic61—41no—
169C2×Dic61—42no—
170C2×Dic61—41no—
171C2×Dic61—41no—
172C2×Dic61—41no—
173C2×Dic61—41no—
174C2×Dic61—41no—
175C2×Dic61—41no—
176C2×Dic61—81no—
177C2×Dic61—81no—
178C4×D61—42no—
179C4×D61—42no—
180C4×D61—42no—
181C4×D61—81no—
182C4×D61—84no—
183C4×D61—88no—
184C4×D61—82no—
185C4×D61—82no—
186C8×C61—81no—
187#92418—81no—
188C2×#1344—611nomaximal, Sylow
189C22×C61—21no—
190C22×C61—21no—
191C22×C61—21no—
192C22×C61—21no—
193C22×C61—41no—
194C22×C61—41no—
195C22×C61—41no—
196C22×C61—41no—
197C22×C61—81no—
198C22×C61C2×#9911yescharacteristic
199C22×C61C2×#10211yescharacteristic
200C22×C61C2×#10411yescharacteristic
201C2×D61—21no—
202C2×D61—21no—
203C2×D61—24no—
204C2×D61—24no—
205C2×D61—22no—
206C2×D61—41no—
207C2×D61—41no—
208C2×D61—44no—
209C2×D61—44no—
210C2×D61—42no—
211C2×D61—82no—
212C2×D61—82no—
213C2×D61—81no—
214C2×D61#32712yes—
215C2×D61#32712yes—
216C2×D61#35212yes—
217C2×D61#35412yes—
218C4×C61—41no—
219C4×C61—41no—
220C4×C61—81no—
221C4×C61—82no—
222C4×C61—81no—
223Dic61—41no—
224Dic61—41no—
225Dic61—81no—
226Dic61—82no—
227Dic61—81no—
228C2×#397—611no—
229C2×#342—611no—
230C2×#323—611no—
231#1344—611no—
232#1344—611no—
233#1344—611no—
234#1344D6111yescharacteristic, direct product factor
235C2×C61—21no—
236C2×C61—21no—
237C2×C61—41no—
238C2×C61—41no—
239C2×C61C2×#32711yescharacteristic
240C2×C61C2×#35211yescharacteristic
241C2×C61C2×#35411yescharacteristic
242D61—22no—
243D61—42no—
244D61#134414yesdirect product factor
245C22×C4⋊C4—611no—
246C22×C22⋊C4—611no—
247C22×C22⋊C4—1221no—
248C22×C22⋊C4—1221no—
249C2×C22⋊C8—1221no—
250#397—611no—
251#397—611no—
252#397—611no—
253#397—1221no—
254#397—1221no—
255#397C2×D6111yescharacteristic
256C2×#95—611no—
257C2×#95—1221no—
258#342—611no—
259#342—1221no—
260#342C2×D6111yescharacteristic
261#323—611no—
262#323—1221no—
263#323C2×D6111yescharacteristic
264C61C2×#134411yescharacteristic, complemented, Sylow
265C25—611no—
266C23×C4—611no—
267C23×C4—611no—
268C23×C4—1221no—
269C23×C4—1221no—
270C23×C4—2441no—
271C22×C8—2441no—
272C2×C4⋊C4—611no—
273C2×C4⋊C4—1221no—
274C2×C4⋊C4—2441no—
275C2×C4⋊C4—2441no—
276C2×C4⋊C4C4×D6111yescharacteristic, complemented
277C2×C22⋊C4—21no—
278C2×C22⋊C4—21no—
279C2×C22⋊C4—611no—
280C2×C22⋊C4—611no—
281C2×C22⋊C4—611no—
282C2×C22⋊C4—1224no—
283C2×C22⋊C4—1221no—
284C2×C22⋊C4—1221no—
285C2×C22⋊C4—1221no—
286C2×C22⋊C4—1221no—
287C2×C22⋊C4—2441no—
288C2×C22⋊C4—2441no—
289C2×C22⋊C4—2442no—
290C2×C22⋊C4—2442no—
291C2×C22⋊C4—2442no—
292C2×C22⋊C4—2441no—
293C2×C22⋊C4C22×D6111yescharacteristic
294C22⋊C8—21no—
295C22⋊C8—1221no—
296C22⋊C8—2441no—
297#95—21no—
298#95—611no—
299#95—1221no—
300#95—1221no—
301#95—1221no—
302#95—1221no—
303#95C4×D6111yescharacteristic, complemented
304C24—611no—
305C24—611no—
306C24—612no—
307C24—612no—
308C24—1222no—
309C24—1221no—
310C24—1221no—
311C24—2442no—
312C24—2442no—
313C24D4×D6111yescharacteristic
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—41no—
317C22×C4—611no—
318C22×C4—611no—
319C22×C4—1221no—
320C22×C4—1221no—
321C22×C4—1221no—
322C22×C4—1221no—
323C22×C4—1221no—
324C22×C4—1221no—
325C22×C4—4882no—
326C22×C4—4882no—
327C22×C4—2442no—
328C22×C4—2442no—
329C22×C4—2441no—
330C22×C4—2441no—
331C22×C4—2442no—
332C22×C4—2444no—
333C22×C4—2442no—
334C22×C4—2442no—
335C22×C4—2442no—
336C22×C4—2442no—
337C22×C4—2441no—
338C22×C4C2×C4×D6111yescharacteristic
339C22×C4D4×D6111yescharacteristic
340C2×C8—41no—
341C2×C8—4882no—
342C2×C8—2441no—
343C4⋊C4—41no—
344C4⋊C4—2441no—
345C4⋊C4—2442no—
346C22⋊C4—22no—
347C22⋊C4—41no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C22⋊C4—1222no—
352C22⋊C4—2441no—
353C22⋊C4—2441no—
354C22⋊C4—2442no—
355C22⋊C4—2442no—
356C22⋊C4—2444no—
357C22⋊C4—2441no—
358C22⋊C4—2441no—
359C22⋊C4—2441no—
360C22⋊C4—2441no—
361C23—21no—
362C23—21no—
363C23—41no—
364C23—41no—
365C23—611no—
366C23—611no—
367C23—612no—
368C23—612no—
369C23—612no—
370C23—1222no—
371C23—1222no—
372C23—1222no—
373C23—1222no—
374C23—1222no—
375C23—1222no—
376C23—1221no—
377C23—1221no—
378C23—4881no—
379C23—4881no—
380C23—4884no—
381C23—2441no—
382C23—2441no—
383C23—2442no—
384C23—2442no—
385C23—2444no—
386C23—2444no—
387C23C22⋊C4×D6111yescharacteristic
388C23D8×D6111yescharacteristic
389C23SD16×D6111yescharacteristic
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—42no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4—1221no—
404C2×C4—1221no—
405C2×C4—4881no—
406C2×C4—4882no—
407C2×C4—4882no—
408C2×C4—4884no—
409C2×C4—4888no—
410C2×C4—4881no—
411C2×C4—4881no—
412C2×C4—2442no—
413C2×C4—2442no—
414C2×C4—2442no—
415C2×C4—2442no—
416C2×C4—2441no—
417C2×C4—2441no—
418C2×C4—2441no—
419C2×C4—2441no—
420C2×C4—2441no—
421C2×C4—2441no—
422C2×C4—2441no—
423C2×C4—2441no—
424C8—81no—
425C8—4881no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—21no—
430C22—41no—
431C22—41no—
432C22—41no—
433C22—41no—
434C22—81no—
435C22—612no—
436C22—612no—
437C22—612no—
438C22—612no—
439C22—1224no—
440C22—1224no—
441C22—1221no—
442C22—1221no—
443C22—1222no—
444C22—4881no—
445C22—4882no—
446C22—4882no—
447C22—2442no—
448C22—2444no—
449C22—2444no—
450C22—2441no—
451C22—2441no—
452C22#99×D6111yescharacteristic
453C22#102×D6111yescharacteristic
454C22#104×D6111yescharacteristic
455C4—41no—
456C4—41no—
457C4—81no—
458C4—82no—
459C4—81no—
460C4—4881no—
461C4—4882no—
462C4—4881no—
463C4—2441no—
464C4—2441no—
465C2—21no—
466C2—21no—
467C2—41no—
468C2—41no—
469C2—614no—
470C2—1222no—
471C2—2442no—
472C2#327×D6111yescharacteristic
473C2#352×D6111yescharacteristic
474C2#354×D6111yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1344C2
socleC22×C61C2×#99
prime radicalC24×D61D4
cosocleC2×C22⋊C4×C61C23
hypercenter#1344D61
hypocenterC61C2×#1344
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1344

Complements

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

NH ≅ G/Ntype
4. #21443820C2semidirect
5. #21443819C2semidirect
6. #21443818C2semidirect
7. C61×#1344C2semidirect
8. C2×C4⋊C4×D61C4semidirect
15. #16839689C4semidirect
16. #16839688C4semidirect
19. #95×D61C4semidirect
34. C2×C4⋊Dic61C2×C4semidirect
58. #14519684C2×C4semidirect
59. C2×C4⋊C4×C61C2×C4semidirect
65. #95×C61C2×C4semidirect
234. #1344D61direct (N × H)
244. D61#1344direct (N × H)
264. C61C2×#1344semidirect
276. C2×C4⋊C4C4×D61semidirect
303. #95C4×D61semidirect

Maximal subgroups

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

subgroupindex
#397×D612
#342×D612
#323×D612
#214438202
#214438192
#214438182
C61×#13442
C2×#134461