Finite Group Databasebeta

← D61×#1393 #29594978

Subgroups — D61×#1393 #29594978

Order 15616.

1154 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 1154 conjugacy classes of subgroups — too many to draw. Only its 159 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
1C2×#99×D61C212yesmaximal
2#390×D61C211yesmaximal, characteristic
3#21443944C211yesmaximal, characteristic, complemented
4#21443943C212yesmaximal, complemented
5C61×#1393C211yesmaximal, characteristic, complemented
6C22×D4×D61C2211yescharacteristic
7C2×C4⋊C4×D61C411yescharacteristic, complemented
8C2×C22⋊C4×D61—22no—
9C2×C22⋊C4×D61—22no—
10C2×C42×D61C411yescharacteristic, complemented
11C2×#14519692C2212yes—
12C2×#14519691—22no—
13#99×D61—24no—
14#99×D61C418yescomplemented
15#16839665C2211yescharacteristic
16#16839664C411yescharacteristic, complemented
17#16839663C411yescharacteristic, complemented
18#16839662—22no—
19C2×#99×C61C2212yes—
20C61×#390C2211yescharacteristic
21C24×D61D412yes—
22C22×D244C2×C411yescharacteristic
23C22×C22⋊D61D412yes—
24C2×D4×D61—42no—
25C2×D4×D61—41no—
26C2×D4×D61—41no—
27C2×D4×D61C2×C414yes—
28C2×D4×D61D412yes—
29C2×D4×D61Q812yes—
30C22×C4×D61—21no—
31C22×C4×D61—21no—
32C22×C4×D61—42no—
33C22×C4×D61C2×C411yescharacteristic
34C2×C4⋊Dic61C2×C411yescharacteristic, complemented
35C2×#11758196—21no—
36C4⋊C4×D61—41no—
37C4⋊C4×D61—41no—
38C2×C22⋊Dic61—22no—
39C2×C22⋊Dic61—22no—
40C2×#11758198—22no—
41C2×#11758198—22no—
42C2×#11758198—42no—
43C22⋊C4×D61—28no—
44C22⋊C4×D61—48no—
45C22⋊C4×D61—44no—
46C2×C4×Dic61—21no—
47C2×C4×Dic61C2×C411yescharacteristic, complemented
48C42×D61—42no—
49#14519692—22no—
50#14519692C2×C414yescomplemented
51#14519691—28no—
52C22×D4×C61C2311yescharacteristic
53C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
54C2×C22⋊C4×C61—22no—
55C2×C22⋊C4×C61—22no—
56C2×C42×C61C2×C411yescharacteristic, complemented
57#99×C61—22no—
58#99×C61C2×C414yescomplemented
59C24×C61C2×D412yes—
60C23×D61—22no—
61C23×D61—24no—
62C23×D61—22no—
63C23×D61—44no—
64C23×D61—44no—
65C23×D61C22⋊C411yescharacteristic
66C23×D61C22⋊C414yes—
67C23×D61C22⋊C412yes—
68C23×D61C4⋊C414yes—
69C2×D4×C61—41no—
70C2×D4×C61—41no—
71C2×D4×C61C22×C412yes—
72C2×D4×C61C2×D411yescharacteristic
73C2×D4×C61C2×Q811yescharacteristic
74C22×C4×C61—21no—
75C22×C4×C61—21no—
76C22×C4×C61—42no—
77C22×C4×C61C22×C411yescharacteristic
78C2×C22⋊D61—42no—
79C2×C22⋊D61—42no—
80C2×C22⋊D61C22⋊C414yes—
81C2×C22⋊D61C4⋊C414yes—
82C22×Dic61—21no—
83C22×Dic61—21no—
84C22×Dic61—42no—
85C22×Dic61C22⋊C411yescharacteristic
86D4×D61—44no—
87D4×D61—44no—
88D4×D61—42no—
89D4×D61—42no—
90D4×D61—42no—
91D4×D61—42no—
92C2×D244—41no—
93C2×D244—41no—
94C2×D244C4212yes—
95C2×D244C4⋊C412yes—
96C2×C4×D61—22no—
97C2×C4×D61—21no—
98C2×C4×D61—21no—
99C2×C4×D61—24no—
100C2×C4×D61—42no—
101C2×C4×D61—42no—
102C2×C4×D61—44no—
103C2×C4×D61—48no—
104C2×C4×D61—41no—
105C2×C4×D61—41no—
106C2×C4×D61—84no—
107C2×C4×D61—84no—
108C2×C4×D61C4212yes—
109C2×C4×D61C4⋊C412yes—
110C4⋊C4×C61—41no—
111C22⋊C4×C61—24no—
112C22⋊C4×C61—44no—
113C22⋊C4×C61—42no—
114C42×C61—41no—
115C22⋊Dic61—24no—
116C22⋊Dic61—44no—
117C22⋊Dic61—42no—
118#11758198—44no—
119#11758198—44no—
120#11758198—48no—
121C4⋊Dic61—41no—
122#11758196—42no—
123C4×Dic61—42no—
124C4×Dic61—41no—
125C23×C61—22no—
126C23×C61—22no—
127C23×C61—42no—
128C23×C61—42no—
129C23×C61C2×C22⋊C411yescharacteristic
130C23×C61C2×C22⋊C412yes—
131C23×C61C2×C4⋊C412yes—
132C22×D61—22no—
133C22×D61—22no—
134C22×D61—22no—
135C22×D61—22no—
136C22×D61—24no—
137C22×D61—24no—
138C22×D61—24no—
139C22×D61—24no—
140C22×D61—48no—
141C22×D61—48no—
142C22×D61—44no—
143C22×D61—44no—
144C22×D61—42no—
145C22×D61—42no—
146C22×D61—88no—
147C22×D61—82no—
148C22×D61—82no—
149C22×D61#9512yes—
150C22×D61#9514yes—
151C22×D61#9911yescharacteristic
152C22×D61#9912yes—
153C22×D61#9911yescharacteristic
154D4×C61—42no—
155D4×C61—41no—
156D4×C61—41no—
157C2×C4×C61—21no—
158C2×C4×C61—21no—
159C2×C4×C61—22no—
160C2×C4×C61—41no—
161C2×C4×C61—41no—
162C2×C4×C61—44no—
163C2×C4×C61—42no—
164C2×C4×C61—41no—
165C2×C4×C61—82no—
166C2×C4×C61—82no—
167C2×C4×C61C2×C4211yescharacteristic
168C2×C4×C61C2×C4⋊C411yescharacteristic
169C22⋊D61—44no—
170C22⋊D61—44no—
171C2×Dic61—21no—
172C2×Dic61—21no—
173C2×Dic61—22no—
174C2×Dic61—41no—
175C2×Dic61—41no—
176C2×Dic61—44no—
177C2×Dic61—42no—
178C2×Dic61—41no—
179C2×Dic61—82no—
180C2×Dic61—82no—
181C2×Dic61#9512yes—
182D244—42no—
183D244—42no—
184C4×D61—22no—
185C4×D61—22no—
186C4×D61—22no—
187C4×D61—22no—
188C4×D61—48no—
189C4×D61—82no—
190C4×D61—816no—
191C4×D61—82no—
192C2×#1393—611nomaximal, Sylow
193C22×C61—21no—
194C22×C61—21no—
195C22×C61—22no—
196C22×C61—22no—
197C22×C61—42no—
198C22×C61—42no—
199C22×C61—42no—
200C22×C61—42no—
201C22×C61—82no—
202C22×C61C2×#9511yescharacteristic
203C22×C61C2×#9911yescharacteristic
204C22×C61C2×#9911yescharacteristic
205C2×D61—21no—
206C2×D61—21no—
207C2×D61—24no—
208C2×D61—24no—
209C2×D61—24no—
210C2×D61—42no—
211C2×D61—42no—
212C2×D61—48no—
213C2×D61—48no—
214C2×D61—44no—
215C2×D61—84no—
216C2×D61—84no—
217C2×D61—82no—
218C2×D61#34212yes—
219C2×D61#34212yes—
220C2×D61#35312yes—
221C2×D61#35412yes—
222C4×C61—21no—
223C4×C61—21no—
224C4×C61—42no—
225C4×C61—84no—
226C4×C61—81no—
227Dic61—22no—
228Dic61—42no—
229Dic61—84no—
230Dic61—81no—
231C22×#99—612no—
232C2×#390—611no—
233#1393—612no—
234#1393—611no—
235#1393D6111yescharacteristic, direct product factor
236C2×C61—21no—
237C2×C61—21no—
238C2×C61—42no—
239C2×C61—42no—
240C2×C61C2×#34211yescharacteristic
241C2×C61C2×#35311yescharacteristic
242C2×C61C2×#35411yescharacteristic
243D61—22no—
244D61—44no—
245D61#139314yesdirect product factor
246C23×D4—611no—
247C22×C4⋊C4—611no—
248C22×C22⋊C4—1222no—
249C22×C22⋊C4—1222no—
250C22×C42—611no—
251C2×#99—612no—
252C2×#99—618no—
253C2×#99—1224no—
254C2×#99—1222no—
255C2×#99C2×D6112yes—
256#390—611no—
257#390—611no—
258#390—611no—
259#390—1222no—
260#390C2×D6111yescharacteristic
261C61C2×#139311yescharacteristic, complemented, Sylow
262C25—612no—
263C22×D4—612no—
264C22×D4—614no—
265C22×D4—612no—
266C22×D4—612no—
267C22×D4—611no—
268C22×D4—2442no—
269C22×D4—2441no—
270C22×D4—2441no—
271C22×D4C22×D6111yescharacteristic
272C23×C4—611no—
273C23×C4—1221no—
274C23×C4—1221no—
275C23×C4—2442no—
276C2×C4⋊C4—611no—
277C2×C4⋊C4—1221no—
278C2×C4⋊C4—2441no—
279C2×C4⋊C4—2441no—
280C2×C4⋊C4C4×D6111yescharacteristic, complemented
281C2×C22⋊C4—22no—
282C2×C22⋊C4—22no—
283C2×C22⋊C4—1228no—
284C2×C22⋊C4—1222no—
285C2×C22⋊C4—1222no—
286C2×C22⋊C4—1222no—
287C2×C22⋊C4—1222no—
288C2×C22⋊C4—2448no—
289C2×C22⋊C4—2444no—
290C2×C22⋊C4—2442no—
291C2×C42—611no—
292C2×C42—1221no—
293C2×C42—2442no—
294C2×C42C4×D6111yescharacteristic, complemented
295#99—22no—
296#99—614no—
297#99—1228no—
298#99—1222no—
299#99C4×D6114yescomplemented
300C24—611no—
301C24—614no—
302C24—612no—
303C24—614no—
304C24—1222no—
305C24—1224no—
306C24—1222no—
307C24—2444no—
308C24—2444no—
309C24D4×D6112yes—
310C2×D4—41no—
311C2×D4—41no—
312C2×D4—614no—
313C2×D4—614no—
314C2×D4—612no—
315C2×D4—612no—
316C2×D4—2441no—
317C2×D4—2441no—
318C2×D4—2444no—
319C2×D4—2444no—
320C2×D4—2442no—
321C2×D4—2442no—
322C2×D4—2442no—
323C2×D4—2442no—
324C2×D4—2442no—
325C2×D4—2442no—
326C2×D4C2×C4×D6112yes—
327C2×D4D4×D6111yescharacteristic
328C2×D4Q8×D6111yescharacteristic
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—42no—
332C22×C4—611no—
333C22×C4—612no—
334C22×C4—612no—
335C22×C4—1222no—
336C22×C4—1221no—
337C22×C4—1221no—
338C22×C4—1224no—
339C22×C4—1221no—
340C22×C4—1221no—
341C22×C4—4884no—
342C22×C4—4884no—
343C22×C4—2441no—
344C22×C4—2441no—
345C22×C4—2448no—
346C22×C4—2444no—
347C22×C4—2442no—
348C22×C4—2442no—
349C22×C4—2442no—
350C22×C4C2×C4×D6111yescharacteristic
351C4⋊C4—41no—
352C4⋊C4—2441no—
353C4⋊C4—2442no—
354C22⋊C4—24no—
355C22⋊C4—44no—
356C22⋊C4—42no—
357C22⋊C4—1224no—
358C22⋊C4—2444no—
359C22⋊C4—2444no—
360C22⋊C4—2448no—
361C22⋊C4—2444no—
362C22⋊C4—2442no—
363C42—41no—
364C42—2441no—
365C42—2442no—
366C23—22no—
367C23—22no—
368C23—42no—
369C23—42no—
370C23—611no—
371C23—612no—
372C23—611no—
373C23—612no—
374C23—614no—
375C23—1222no—
376C23—1222no—
377C23—1224no—
378C23—1224no—
379C23—1224no—
380C23—1224no—
381C23—1222no—
382C23—1222no—
383C23—4882no—
384C23—4882no—
385C23—4888no—
386C23—2442no—
387C23—2442no—
388C23—2444no—
389C23—2444no—
390C23—2448no—
391C23—2448no—
392C23C22⋊C4×D6112yes—
393C23C22⋊C4×D6111yescharacteristic
394C23C4⋊C4×D6112yes—
395D4—42no—
396D4—41no—
397D4—41no—
398D4—2442no—
399D4—2442no—
400D4—2444no—
401D4—2444no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—22no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—44no—
408C2×C4—42no—
409C2×C4—41no—
410C2×C4—82no—
411C2×C4—82no—
412C2×C4—612no—
413C2×C4—1222no—
414C2×C4—1222no—
415C2×C4—1222no—
416C2×C4—1222no—
417C2×C4—1221no—
418C2×C4—1221no—
419C2×C4—1222no—
420C2×C4—4882no—
421C2×C4—4882no—
422C2×C4—48816no—
423C2×C4—4882no—
424C2×C4—4882no—
425C2×C4—2448no—
426C2×C4—2444no—
427C2×C4—2442no—
428C2×C4—2441no—
429C2×C4—2441no—
430C2×C4—2441no—
431C2×C4C42×D6111yescharacteristic
432C2×C4C4⋊C4×D6111yescharacteristic
433C22—21no—
434C22—21no—
435C22—22no—
436C22—22no—
437C22—42no—
438C22—42no—
439C22—42no—
440C22—42no—
441C22—82no—
442C22—612no—
443C22—612no—
444C22—612no—
445C22—612no—
446C22—1224no—
447C22—1224no—
448C22—1221no—
449C22—1221no—
450C22—1224no—
451C22—4882no—
452C22—4884no—
453C22—4884no—
454C22—2444no—
455C22—2448no—
456C22—2448no—
457C22—2442no—
458C22—2442no—
459C22#95×D6111yescharacteristic
460C22#99×D6111yescharacteristic
461C22#99×D6111yescharacteristic
462C4—21no—
463C4—21no—
464C4—42no—
465C4—84no—
466C4—81no—
467C4—1222no—
468C4—4884no—
469C4—4881no—
470C4—2442no—
471C2—21no—
472C2—21no—
473C2—42no—
474C2—42no—
475C2—614no—
476C2—1222no—
477C2—2444no—
478C2#342×D6111yescharacteristic
479C2#353×D6111yescharacteristic
480C2#354×D6111yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC2×C4×C61C2×C42
FrattiniC22×D4C22×D61
FittingC61×#1393C2
socleC22×C61C2×#99
prime radicalC22×D4×D61C22
cosocleC22×D4×C61C23
hypercenter#1393D61
hypocenterC61C2×#1393
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #1393

Complements

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

NH ≅ G/Ntype
3. #21443944C2semidirect
4. #21443943C2semidirect
5. C61×#1393C2semidirect
7. C2×C4⋊C4×D61C4semidirect
10. C2×C42×D61C4semidirect
14. #99×D61C4semidirect
16. #16839664C4semidirect
17. #16839663C4semidirect
34. C2×C4⋊Dic61C2×C4semidirect
47. C2×C4×Dic61C2×C4semidirect
50. #14519692C2×C4semidirect
53. C2×C4⋊C4×C61C2×C4semidirect
56. C2×C42×C61C2×C4semidirect
58. #99×C61C2×C4semidirect
235. #1393D61direct (N × H)
245. D61#1393direct (N × H)
261. C61C2×#1393semidirect
280. C2×C4⋊C4C4×D61semidirect
294. C2×C42C4×D61semidirect
299. #99C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#99×D612
#390×D612
#214439442
#214439432
C61×#13932
C2×#139361