Finite Group Databasebeta

← D61⋊#1344 #30604730

Subgroups — D61⋊#1344 #30604730

Order 15616.

668 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 668 conjugacy classes of subgroups — too many to draw. Only its 88 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
2D61⋊#323C211yesmaximal, characteristic
3#21460800C212yesmaximal, complemented
4#21460799C212yesmaximal, complemented
5#397×D61C211yesmaximal, characteristic
6C22×C22⋊#6923—21no—
7D61⋊(C22⋊C8)—21no—
8#16840640—21no—
9#16840640C2212yes—
10#16840606C2212yes—
11#16840605—21no—
12C2×C4⋊C4×D61C411yescharacteristic, complemented
13C2×C22⋊C4×D61—21no—
14C2×C22⋊C4×D61C2211yescharacteristic
15#16839691—21no—
16#16839690—21no—
17#16839689C2211yescharacteristic
18#16839688C2211yescharacteristic
19#16839687C411yescharacteristic, complemented
20#95×D61—21no—
21#95×D61C411yescharacteristic, complemented
22C61×#397C411yescharacteristic, 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×C4×D61—21no—
33C22×C4×D61—21no—
34C22×C4×D61C2×C411yescharacteristic
35C22×C4×D61D411yescharacteristic
36C2×C4⋊Dic61C2×C411yescharacteristic, complemented
37C2×#11758196—21no—
38C4⋊C4×D61—41no—
39C4⋊C4×D61—41no—
40C2×C22⋊Dic61—21no—
41C2×C22⋊Dic61D411yescharacteristic
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×#11758198D411yescharacteristic
45C2×#11758198C2311yescharacteristic
46C22⋊C4×D61—41no—
47C22⋊C4×D61—41no—
48C22⋊C4×D61—42no—
49C22⋊C4×D61—42no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684C2×C411yescharacteristic, complemented
55C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
56C2×C22⋊C4×C61—21no—
57C2×C22⋊C4×C61C2×C411yescharacteristic
58#95×C61—21no—
59#95×C61C2×C411yescharacteristic, complemented
60C24×C61C22⋊C411yescharacteristic
61C23×D61—21no—
62C23×D61—21no—
63C23×D61—22no—
64C23×D61—42no—
65C23×D61—42no—
66C23×D61C22⋊C411yescharacteristic
67C23×D61D812yes—
68C23×D61SD1612yes—
69C23×D61C2×D411yescharacteristic
70C22×#6923—42no—
71C22×#6923—44no—
72C22×#6923—82no—
73C22×#6923—82no—
74C22×C4×C61—21no—
75C22×C4×C61—21no—
76C22×C4×C61C22⋊C411yescharacteristic
77C22×C4×C61C22×C411yescharacteristic
78C22×Dic61—21no—
79C22×Dic61—21no—
80C22×Dic61C22⋊C411yescharacteristic
81C22×Dic61C2×D411yescharacteristic
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×C4×D61—21no—
86C2×C4×D61—42no—
87C2×C4×D61—42no—
88C2×C4×D61—42no—
89C2×C4×D61—42no—
90C2×C4×D61—41no—
91C2×C4×D61—41no—
92C2×C4×D61—42no—
93C2×C4×D61—42no—
94C2×C4×D61—42no—
95C22⋊#6923—24no—
96C22⋊#6923—44no—
97C22⋊#6923—42no—
98C2×#92420—42no—
99D61⋊C8—82no—
100C4⋊C4×C61—41no—
101C22⋊C4×C61—41no—
102C22⋊C4×C61—42no—
103C22⋊Dic61—41no—
104C22⋊Dic61—42no—
105#11758198—41no—
106#11758198—41no—
107#11758198—41no—
108#11758198—41no—
109#11758198—41no—
110#11758198—41no—
111C4⋊Dic61—41no—
112#11758196—42no—
113C23×C61—21no—
114C23×C61—21no—
115C23×C61—41no—
116C23×C61—41no—
117C23×C61#10212yes—
118C23×C61C2×C22⋊C411yescharacteristic
119C22×D61—22no—
120C22×D61—22no—
121C22×D61—21no—
122C22×D61—21no—
123C22×D61—22no—
124C22×D61—22no—
125C22×D61—22no—
126C22×D61—22no—
127C22×D61—44no—
128C22×D61—44no—
129C22×D61—42no—
130C22×D61—42no—
131C22×D61—41no—
132C22×D61—41no—
133C22×D61—84no—
134C22×D61—81no—
135C22×D61—81no—
136C22×D61#9911yescharacteristic
137C22×D61#9911yescharacteristic
138C22×D61#10212yes—
139C22×D61#10412yes—
140C22×D61C2×D811yescharacteristic
141C22×D61C2×SD1611yescharacteristic
142C2×#6923—44no—
143C2×#6923—82no—
144C2×#6923—82no—
145C2×#6923—88no—
146C2×C4×C61—21no—
147C2×C4×C61—21no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61—41no—
154C2×C4×C61—41no—
155C2×C4×C61—41no—
156C2×Dic61—21no—
157C2×Dic61—21no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61—41no—
163C2×Dic61—41no—
164C2×Dic61—41no—
165C2×Dic61—41no—
166C4×D61—42no—
167C4×D61—42no—
168C4×D61—42no—
169C4×D61—81no—
170C4×D61—84no—
171C4×D61—82no—
172C4×D61—82no—
173#92420—82no—
174C2×#1344—611nomaximal, Sylow
175C22×C61—21no—
176C22×C61—21no—
177C22×C61—22no—
178C22×C61—42no—
179C22×C61—41no—
180C22×C61—41no—
181C22×C61—81no—
182C22×C61C2×#9911yescharacteristic
183C22×C61C2×#10211yescharacteristic
184C22×C61C2×#10411yescharacteristic
185C2×D61—21no—
186C2×D61—21no—
187C2×D61—24no—
188C2×D61—24no—
189C2×D61—21no—
190C2×D61—21no—
191C2×D61—41no—
192C2×D61—41no—
193C2×D61—44no—
194C2×D61—44no—
195C2×D61—41no—
196C2×D61—41no—
197C2×D61—82no—
198C2×D61—82no—
199C2×D61—81no—
200C2×D61#32712yes—
201C2×D61#32712yes—
202C2×D61#35212yes—
203C2×D61#35412yes—
204#6923—84no—
205C4×C61—41no—
206C4×C61—41no—
207C4×C61—81no—
208C4×C61—81no—
209Dic61—41no—
210Dic61—41no—
211Dic61—81no—
212Dic61—81no—
213C2×#397—611no—
214C2×#342—611no—
215C2×#323—611no—
216#1344—612no—
217#1344—612no—
218C2×C61—21no—
219C2×C61—21no—
220C2×C61—42no—
221C2×C61C2×#32711yescharacteristic
222C2×C61C2×#35211yescharacteristic
223C2×C61C2×#35411yescharacteristic
224D61—22no—
225D61—41no—
226D61—41no—
227D61#134414yescomplemented
228C22×C4⋊C4—611no—
229C22×C22⋊C4—611no—
230C22×C22⋊C4—1221no—
231C22×C22⋊C4—1221no—
232C2×C22⋊C8—1221no—
233#397—611no—
234#397—611no—
235#397—611no—
236#397—1221no—
237#397—1221no—
238#397#692311yescharacteristic, complemented
239C2×#95—611no—
240C2×#95—1221no—
241#342—612no—
242#342—1221no—
243#323—612no—
244#323—1221no—
245C61C2×#134411yescharacteristic, complemented, Sylow
246C25—611no—
247C23×C4—611no—
248C23×C4—611no—
249C23×C4—1221no—
250C23×C4—1221no—
251C23×C4—2441no—
252C22×C8—2441no—
253C2×C4⋊C4—611no—
254C2×C4⋊C4—1221no—
255C2×C4⋊C4—2441no—
256C2×C4⋊C4—2441no—
257C2×C4⋊C4C2×#692311yescharacteristic, complemented
258C2×C22⋊C4—21no—
259C2×C22⋊C4—611no—
260C2×C22⋊C4—611no—
261C2×C22⋊C4—611no—
262C2×C22⋊C4—1222no—
263C2×C22⋊C4—1224no—
264C2×C22⋊C4—1221no—
265C2×C22⋊C4—1221no—
266C2×C22⋊C4—1221no—
267C2×C22⋊C4—2441no—
268C2×C22⋊C4—2441no—
269C2×C22⋊C4—2442no—
270C2×C22⋊C4—2442no—
271C2×C22⋊C4—2442no—
272C2×C22⋊C4—2441no—
273C2×C22⋊C4C2×#692311yescharacteristic
274C22⋊C8—1222no—
275C22⋊C8—2441no—
276#95—21no—
277#95—611no—
278#95—1221no—
279#95—1221no—
280#95—1221no—
281#95—1221no—
282#95C2×#692311yescharacteristic, complemented
283C24—611no—
284C24—612no—
285C24—612no—
286C24—611no—
287C24—1222no—
288C24—1221no—
289C24—1221no—
290C24—2442no—
291C24—2442no—
292C24C22⋊#692311yescharacteristic
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—611no—
296C22×C4—611no—
297C22×C4—1221no—
298C22×C4—1221no—
299C22×C4—1221no—
300C22×C4—1221no—
301C22×C4—1221no—
302C22×C4—1221no—
303C22×C4—4882no—
304C22×C4—4882no—
305C22×C4—2442no—
306C22×C4—2442no—
307C22×C4—2441no—
308C22×C4—2441no—
309C22×C4—2442no—
310C22×C4—2442no—
311C22×C4—2442no—
312C22×C4—2442no—
313C22×C4—2442no—
314C22×C4—2444no—
315C22×C4—2442no—
316C22×C4C22⋊#692311yescharacteristic
317C22×C4C22×#692311yescharacteristic
318C2×C8—4882no—
319C2×C8—2442no—
320C4⋊C4—41no—
321C4⋊C4—2441no—
322C4⋊C4—2442no—
323C22⋊C4—41no—
324C22⋊C4—42no—
325C22⋊C4—1224no—
326C22⋊C4—2441no—
327C22⋊C4—2441no—
328C22⋊C4—2441no—
329C22⋊C4—2441no—
330C22⋊C4—2441no—
331C22⋊C4—2441no—
332C22⋊C4—2441no—
333C22⋊C4—2442no—
334C22⋊C4—2444no—
335C22⋊C4—2442no—
336C23—21no—
337C23—21no—
338C23—41no—
339C23—41no—
340C23—611no—
341C23—611no—
342C23—612no—
343C23—612no—
344C23—611no—
345C23—611no—
346C23—1222no—
347C23—1222no—
348C23—1222no—
349C23—1222no—
350C23—1222no—
351C23—1222no—
352C23—1221no—
353C23—1221no—
354C23—4881no—
355C23—4881no—
356C23—4884no—
357C23—2441no—
358C23—2441no—
359C23—2442no—
360C23—2442no—
361C23—2444no—
362C23—2444no—
363C23#1451983912yes—
364C23C2×C22⋊#692311yescharacteristic
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—1221no—
376C2×C4—1221no—
377C2×C4—4881no—
378C2×C4—4882no—
379C2×C4—4882no—
380C2×C4—4884no—
381C2×C4—4888no—
382C2×C4—4882no—
383C2×C4—4882no—
384C2×C4—2442no—
385C2×C4—2442no—
386C2×C4—2442no—
387C2×C4—2441no—
388C2×C4—2441no—
389C2×C4—2444no—
390C2×C4—2441no—
391C2×C4—2441no—
392C2×C4—2441no—
393C2×C4—2441no—
394C2×C4—2441no—
395C2×C4—2441no—
396C8—4882no—
397C22—21no—
398C22—21no—
399C22—22no—
400C22—42no—
401C22—41no—
402C22—41no—
403C22—81no—
404C22—612no—
405C22—612no—
406C22—612no—
407C22—612no—
408C22—1224no—
409C22—1224no—
410C22—1221no—
411C22—1221no—
412C22—1221no—
413C22—1221no—
414C22—4881no—
415C22—4882no—
416C22—4882no—
417C22—2441no—
418C22—2441no—
419C22—2444no—
420C22—2444no—
421C22—2441no—
422C22—2441no—
423C22D61⋊#9911yescharacteristic
424C22C2×#1451983911yescharacteristic
425C22D61⋊#10411yescharacteristic
426C4—41no—
427C4—41no—
428C4—81no—
429C4—81no—
430C4—4881no—
431C4—4884no—
432C4—4881no—
433C4—2441no—
434C4—2441no—
435C2—21no—
436C2—21no—
437C2—42no—
438C2—614no—
439C2—1222no—
440C2—2441no—
441C2—2441no—
442C2D61⋊#32711yescharacteristic
443C2D61⋊#35211yescharacteristic
444C2D61⋊#35411yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#397C4
socleC22×C61C2×#99
prime radicalC24×D61D4
cosocleC2×#11758198C23
hypercenter#397#6923
hypocenterC61C2×#1344
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #397

Complements

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

NH ≅ G/Ntype
3. #21460800C2semidirect
4. #21460799C2semidirect
12. C2×C4⋊C4×D61C4semidirect
19. #16839687C4semidirect
21. #95×D61C4semidirect
22. C61×#397C4semidirect
36. C2×C4⋊Dic61C2×C4semidirect
54. #14519684C2×C4semidirect
55. C2×C4⋊C4×C61C2×C4semidirect
59. #95×C61C2×C4semidirect
227. D61#1344semidirect
238. #397#6923semidirect
245. C61C2×#1344semidirect
257. C2×C4⋊C4C2×#6923semidirect
282. #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
#214607992
#397×D612
C2×#134461