Finite Group Databasebeta

← D61⋊#1352 #30604810

Subgroups — D61⋊#1352 #30604810

Order 15616.

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

normal subgroups only

This group has 712 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#21460816C212yesmaximal, complemented
4#21460815C212yesmaximal, complemented
5#399×D61C211yesmaximal, characteristic
6C22×C22⋊#6923—21no—
7D61⋊(C22⋊C8)—21no—
8#16840640—21no—
9#16840640C2212yes—
10#16840606C2212yes—
11#16840605—21no—
12C2×C4⋊C4×D61—21no—
13C2×C4⋊C4×D61C411yescharacteristic, complemented
14C2×C22⋊C4×D61—21no—
15C2×C22⋊C4×D61C2211yescharacteristic
16#16839699C2211yescharacteristic
17#16839698—21no—
18#16839698C411yescharacteristic, complemented
19#16839697—21no—
20#16839697C2211yescharacteristic
21#95×D61C411yescharacteristic, complemented
22C61×#399C411yescharacteristic, 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⋊Dic61—21no—
37C2×C4⋊Dic61C2×C411yescharacteristic, complemented
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758196—21no—
41C4⋊C4×D61—41no—
42C4⋊C4×D61—41no—
43C4⋊C4×D61—44no—
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—
52C22⋊C4×D61—44no—
53#14519684—21no—
54#14519684C2×C411yescharacteristic, complemented
55C2×C4⋊C4×C61—21no—
56C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
57C2×C22⋊C4×C61—21no—
58C2×C22⋊C4×C61C2×C411yescharacteristic
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×D61SD1612yes—
68C23×D61Q1612yes—
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—24no—
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×C4×D61—21no—
86C2×C4×D61—21no—
87C2×C4×D61—42no—
88C2×C4×D61—42no—
89C2×C4×D61—42no—
90C2×C4×D61—42no—
91C2×C4×D61—42no—
92C2×C4×D61—42no—
93C2×C4×D61—41no—
94C2×C4×D61—41no—
95C22⋊#6923—24no—
96C22⋊#6923—44no—
97C22⋊#6923—42no—
98C2×#92420—42no—
99D61⋊C8—82no—
100C4⋊C4×C61—42no—
101C4⋊C4×C61—41no—
102C22⋊C4×C61—41no—
103C22⋊C4×C61—42no—
104C22⋊Dic61—41no—
105C22⋊Dic61—42no—
106#11758198—41no—
107#11758198—41no—
108#11758198—42no—
109#11758198—42no—
110C4⋊Dic61—42no—
111C4⋊Dic61—41no—
112#11758196—42no—
113#11758196—42no—
114#11758196—42no—
115C23×C61—21no—
116C23×C61—21no—
117C23×C61—41no—
118C23×C61—41no—
119C23×C61#10312yes—
120C23×C61C2×C22⋊C411yescharacteristic
121C22×D61—22no—
122C22×D61—22no—
123C22×D61—21no—
124C22×D61—21no—
125C22×D61—22no—
126C22×D61—22no—
127C22×D61—22no—
128C22×D61—22no—
129C22×D61—44no—
130C22×D61—44no—
131C22×D61—42no—
132C22×D61—42no—
133C22×D61—41no—
134C22×D61—41no—
135C22×D61—84no—
136C22×D61—81no—
137C22×D61—81no—
138C22×D61#9911yescharacteristic
139C22×D61#9911yescharacteristic
140C22×D61#10312yes—
141C22×D61#10412yes—
142C22×D61C2×SD1611yescharacteristic
143C22×D61C2×Q1611yescharacteristic
144C2×#6923—44no—
145C2×#6923—82no—
146C2×#6923—82no—
147C2×#6923—88no—
148C2×C4×C61—22no—
149C2×C4×C61—21no—
150C2×C4×C61—21no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61—41no—
154C2×C4×C61—41no—
155C2×C4×C61—41no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×Dic61—22no—
159C2×Dic61—21no—
160C2×Dic61—21no—
161C2×Dic61—41no—
162C2×Dic61—41no—
163C2×Dic61—41no—
164C2×Dic61—41no—
165C2×Dic61—41no—
166C2×Dic61—41no—
167C2×Dic61—41no—
168C4×D61—48no—
169C4×D61—42no—
170C4×D61—42no—
171C4×D61—42no—
172C4×D61—81no—
173C4×D61—82no—
174C4×D61—82no—
175#92420—82no—
176C2×#1352—611nomaximal, Sylow
177C22×C61—21no—
178C22×C61—21no—
179C22×C61—22no—
180C22×C61—42no—
181C22×C61—41no—
182C22×C61—41no—
183C22×C61—81no—
184C22×C61C2×#9911yescharacteristic
185C22×C61C2×#10311yescharacteristic
186C22×C61C2×#10411yescharacteristic
187C2×D61—21no—
188C2×D61—21no—
189C2×D61—24no—
190C2×D61—24no—
191C2×D61—21no—
192C2×D61—21no—
193C2×D61—41no—
194C2×D61—41no—
195C2×D61—44no—
196C2×D61—44no—
197C2×D61—41no—
198C2×D61—41no—
199C2×D61—82no—
200C2×D61—82no—
201C2×D61—81no—
202C2×D61#32812yes—
203C2×D61#32812yes—
204C2×D61#35212yes—
205C2×D61#35312yes—
206#6923—84no—
207C4×C61—42no—
208C4×C61—41no—
209C4×C61—41no—
210C4×C61—81no—
211Dic61—42no—
212Dic61—41no—
213Dic61—41no—
214Dic61—81no—
215C2×#399—611no—
216C2×#342—611no—
217C2×#323—611no—
218#1352—612no—
219#1352—612no—
220C2×C61—21no—
221C2×C61—21no—
222C2×C61—42no—
223C2×C61C2×#32811yescharacteristic
224C2×C61C2×#35211yescharacteristic
225C2×C61C2×#35311yescharacteristic
226D61—22no—
227D61—41no—
228D61—41no—
229D61#135214yescomplemented
230C22×C4⋊C4—611no—
231C22×C4⋊C4—1221no—
232C22×C22⋊C4—611no—
233C22×C22⋊C4—1221no—
234C22×C22⋊C4—1221no—
235C2×C22⋊C8—1221no—
236#399—611no—
237#399—611no—
238#399—611no—
239#399—1221no—
240#399—1221no—
241#399#692311yescharacteristic, complemented
242C2×#95—611no—
243#342—612no—
244#342—1221no—
245#323—612no—
246#323—1221no—
247C61C2×#135211yescharacteristic, complemented, Sylow
248C25—611no—
249C23×C4—611no—
250C23×C4—611no—
251C23×C4—1221no—
252C23×C4—1221no—
253C23×C4—2441no—
254C22×C8—2441no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—611no—
257C2×C4⋊C4—1221no—
258C2×C4⋊C4—1221no—
259C2×C4⋊C4—1221no—
260C2×C4⋊C4—1221no—
261C2×C4⋊C4—2441no—
262C2×C4⋊C4—2441no—
263C2×C4⋊C4—2444no—
264C2×C4⋊C4C2×#692311yescharacteristic, complemented
265C2×C22⋊C4—21no—
266C2×C22⋊C4—611no—
267C2×C22⋊C4—611no—
268C2×C22⋊C4—611no—
269C2×C22⋊C4—1222no—
270C2×C22⋊C4—1224no—
271C2×C22⋊C4—1221no—
272C2×C22⋊C4—1221no—
273C2×C22⋊C4—1221no—
274C2×C22⋊C4—2441no—
275C2×C22⋊C4—2441no—
276C2×C22⋊C4—2444no—
277C2×C22⋊C4—2442no—
278C2×C22⋊C4—2441no—
279C2×C22⋊C4C2×#692311yescharacteristic
280C22⋊C8—1222no—
281C22⋊C8—2441no—
282#95—611no—
283#95—1221no—
284#95C2×#692311yescharacteristic, complemented
285C24—611no—
286C24—612no—
287C24—612no—
288C24—611no—
289C24—1222no—
290C24—1221no—
291C24—1221no—
292C24—2442no—
293C24—2442no—
294C24C22⋊#692311yescharacteristic
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—611no—
298C22×C4—611no—
299C22×C4—1221no—
300C22×C4—1221no—
301C22×C4—1221no—
302C22×C4—1221no—
303C22×C4—1224no—
304C22×C4—1221no—
305C22×C4—1221no—
306C22×C4—4882no—
307C22×C4—4882no—
308C22×C4—2441no—
309C22×C4—2441no—
310C22×C4—2442no—
311C22×C4—2442no—
312C22×C4—2442no—
313C22×C4—2442no—
314C22×C4—2442no—
315C22×C4—2442no—
316C22×C4—2444no—
317C22×C4—2442no—
318C22×C4C22⋊#692311yescharacteristic
319C22×C4C22×#692311yescharacteristic
320C2×C8—4882no—
321C2×C8—2442no—
322C4⋊C4—41no—
323C4⋊C4—42no—
324C4⋊C4—2441no—
325C4⋊C4—2442no—
326C4⋊C4—2442no—
327C4⋊C4—2442no—
328C4⋊C4—2442no—
329C22⋊C4—41no—
330C22⋊C4—42no—
331C22⋊C4—1224no—
332C22⋊C4—2441no—
333C22⋊C4—2441no—
334C22⋊C4—2442no—
335C22⋊C4—2442no—
336C22⋊C4—2441no—
337C22⋊C4—2442no—
338C22⋊C4—2442no—
339C22⋊C4—2444no—
340C23—21no—
341C23—21no—
342C23—41no—
343C23—41no—
344C23—611no—
345C23—611no—
346C23—612no—
347C23—612no—
348C23—611no—
349C23—611no—
350C23—1222no—
351C23—1222no—
352C23—1222no—
353C23—1222no—
354C23—1222no—
355C23—1222no—
356C23—1221no—
357C23—1221no—
358C23—4881no—
359C23—4881no—
360C23—4884no—
361C23—2441no—
362C23—2441no—
363C23—2442no—
364C23—2442no—
365C23—2444no—
366C23—2444no—
367C23#1451984012yes—
368C23C2×C22⋊#692311yescharacteristic
369C2×C4—22no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—1222no—
380C2×C4—1221no—
381C2×C4—1221no—
382C2×C4—4881no—
383C2×C4—4882no—
384C2×C4—4882no—
385C2×C4—4888no—
386C2×C4—4882no—
387C2×C4—4882no—
388C2×C4—2442no—
389C2×C4—2442no—
390C2×C4—2448no—
391C2×C4—2442no—
392C2×C4—2441no—
393C2×C4—2441no—
394C2×C4—2444no—
395C2×C4—2441no—
396C2×C4—2441no—
397C2×C4—2441no—
398C2×C4—2441no—
399C2×C4—2441no—
400C8—4882no—
401C22—21no—
402C22—21no—
403C22—22no—
404C22—42no—
405C22—41no—
406C22—41no—
407C22—81no—
408C22—612no—
409C22—612no—
410C22—612no—
411C22—612no—
412C22—1224no—
413C22—1224no—
414C22—1221no—
415C22—1221no—
416C22—1221no—
417C22—1221no—
418C22—4881no—
419C22—4882no—
420C22—4882no—
421C22—2441no—
422C22—2441no—
423C22—2444no—
424C22—2444no—
425C22—2441no—
426C22—2441no—
427C22D61⋊#9911yescharacteristic
428C22C2×#1451984011yescharacteristic
429C22D61⋊#10411yescharacteristic
430C4—42no—
431C4—41no—
432C4—41no—
433C4—81no—
434C4—4884no—
435C4—4881no—
436C4—2442no—
437C4—2441no—
438C4—2441no—
439C2—21no—
440C2—21no—
441C2—42no—
442C2—614no—
443C2—1222no—
444C2—2441no—
445C2—2441no—
446C2D61⋊#32811yescharacteristic
447C2D61⋊#35211yescharacteristic
448C2D61⋊#35311yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#399C4
socleC22×C61C2×#99
prime radicalC24×D61D4
cosocleC2×#11758198C23
hypercenter#399#6923
hypocenterC61C2×#1352
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #399

Complements

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

NH ≅ G/Ntype
3. #21460816C2semidirect
4. #21460815C2semidirect
13. C2×C4⋊C4×D61C4semidirect
18. #16839698C4semidirect
21. #95×D61C4semidirect
22. C61×#399C4semidirect
37. C2×C4⋊Dic61C2×C4semidirect
54. #14519684C2×C4semidirect
56. C2×C4⋊C4×C61C2×C4semidirect
59. #95×C61C2×C4semidirect
229. D61#1352semidirect
241. #399#6923semidirect
247. C61C2×#1352semidirect
264. C2×C4⋊C4C2×#6923semidirect
284. #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
#214608162
#214608152
#399×D612
C2×#135261