Finite Group Databasebeta

← D61×#1320 #29589130

Subgroups — D61×#1320 #29589130

Order 15616.

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

normal subgroups only

This group has 626 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#407×D61C211yesmaximal, characteristic
2#349×D61C212yesmaximal, complemented
3#21443755C211yesmaximal, characteristic, complemented
4#21443754C212yesmaximal, complemented
5C61×#1320C211yesmaximal, characteristic, complemented
6C23×C4×D61C411yescharacteristic
7C2×M16×D61C411yescharacteristic
8C2×M16×D61C2211yescharacteristic
9M32×D61—22no—
10#16839726C411yescharacteristic
11#16839725C411yescharacteristic
12#16839725C2211yescharacteristic
13#16839724—22no—
14C22⋊C8×D61—22no—
15#16839544C2212yescomplemented
16#16839543—22no—
17C61×#407C2211yescharacteristic
18C61×#349C2212yescomplemented
19C24×D61C811yescharacteristic
20C23×Dic61C811yescharacteristic
21C22×C4×D61—21no—
22C22×C4×D61—21no—
23C22×C4×D61—21no—
24C22×C4×D61—21no—
25C22×C4×D61—41no—
26C22×C4×D61—41no—
27C22×C4×D61—41no—
28C22×C4×D61—41no—
29C22×C4×D61C811yescharacteristic
30C22×C4×D61C811yescharacteristic
31C22×C4×D61C2×C411yescharacteristic
32C22×C4×D61C2×C411yescharacteristic
33C2×#11758194C2×C411yescharacteristic
34C2×#11758194C2×C411yescharacteristic
35C2×#11758189—21no—
36C2×#11758189D412yes—
37M16×D61—41no—
38M16×D61—41no—
39M16×D61—41no—
40M16×D61—41no—
41C2×C8×D61—21no—
42C2×C8×D61D412yes—
43#14519717—22no—
44#14519716—42no—
45C16×D61—42no—
46C22⋊#92418—22no—
47#14519689—22no—
48#14519689—22no—
49C23×C4×C61C2×C411yescharacteristic
50C2×M16×C61C2×C411yescharacteristic
51C2×M16×C61C2311yescharacteristic
52M32×C61—22no—
53C22⋊C8×C61—22no—
54C24×C61C2×C811yescharacteristic
55C23×D61—21no—
56C23×D61—21no—
57C23×D61—41no—
58C23×D61—41no—
59C23×D61—44no—
60C23×D61C2×C811yescharacteristic
61C23×D61C2×C811yescharacteristic
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61—41no—
65C22×C4×C61—41no—
66C22×C4×C61C2×C811yescharacteristic
67C22×C4×C61C22×C411yescharacteristic
68C22×Dic61—21no—
69C22×Dic61—21no—
70C22×Dic61—41no—
71C22×Dic61—41no—
72C22×Dic61C2×C811yescharacteristic
73C22×Dic61C2×C811yescharacteristic
74C2×C4×D61—21no—
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×C4×D61—21no—
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×C4×D61—42no—
85C2×C4×D61—42no—
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—41no—
93C2×C4×D61—41no—
94C2×C4×D61—41no—
95C2×C4×D61—41no—
96C2×C4×D61—41no—
97C2×C4×D61—41no—
98C2×C4×D61—41no—
99C2×C4×D61—41no—
100C2×C4×D61C22⋊C411yescharacteristic
101C2×C4×D61C22⋊C411yescharacteristic
102C2×C4×D61M1611yescharacteristic
103C2×C4×D61M1611yescharacteristic
104M16×C61—41no—
105M16×C61—41no—
106C2×C8×C61—21no—
107C2×C8×C61C2×D412yes—
108#11758194—41no—
109#11758194—41no—
110C2×#92418—21no—
111C2×#92418C22⋊C412yes—
112#11758189—42no—
113#11758189—42no—
114C8×D61—22no—
115C8×D61—22no—
116C8×D61—41no—
117C8×D61—41no—
118C16×C61—42no—
119#11758185—42no—
120C23×C61—21no—
121C23×C61—41no—
122C23×C61—42no—
123C23×C61C22×C811yescharacteristic
124C22×D61—24no—
125C22×D61—21no—
126C22×D61—21no—
127C22×D61—21no—
128C22×D61—42no—
129C22×D61—42no—
130C22×D61—42no—
131C22×D61—42no—
132C22×D61—42no—
133C22×D61—42no—
134C22×D61—44no—
135C22×D61—44no—
136C22×D61—44no—
137C22×D61—41no—
138C22×D61—41no—
139C22×D61—41no—
140C22×D61—44no—
141C22×D61C22⋊C811yescharacteristic
142C22×D61C22⋊C811yescharacteristic
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—42no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61C2×C22⋊C411yescharacteristic
151C2×C4×C61C2×M1611yescharacteristic
152C2×Dic61—21no—
153C2×Dic61—21no—
154C2×Dic61—21no—
155C2×Dic61—42no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61C22⋊C811yescharacteristic
160C2×Dic61C22⋊C811yescharacteristic
161C4×D61—21no—
162C4×D61—21no—
163C4×D61—21no—
164C4×D61—21no—
165C4×D61—21no—
166C4×D61—21no—
167C4×D61—42no—
168C4×D61—42no—
169C4×D61—42no—
170C4×D61—41no—
171C4×D61—41no—
172C4×D61—41no—
173C4×D61—41no—
174C4×D61—41no—
175C4×D61—41no—
176C4×D61#9911yescharacteristic
177C4×D61#9911yescharacteristic
178C4×D61#10011yescharacteristic
179C4×D61#10011yescharacteristic
180C8×C61—22no—
181C8×C61—41no—
182#92418—22no—
183#92418—41no—
184C2×#1320—611nomaximal, Sylow
185C22×C61—22no—
186C22×C61—21no—
187C22×C61—41no—
188C22×C61—41no—
189C22×C61—42no—
190C22×C61—42no—
191C22×C61—41no—
192C22×C61C2×C22⋊C811yescharacteristic
193C2×D61—22no—
194C2×D61—22no—
195C2×D61—21no—
196C2×D61—44no—
197C2×D61—42no—
198C2×D61—41no—
199C2×D61—48no—
200C2×D61—42no—
201C2×D61—41no—
202C2×D61—44no—
203C2×D61—42no—
204C2×D61—41no—
205C2×D61—42no—
206C2×D61#32311yescharacteristic
207C2×D61#32311yescharacteristic
208C4×C61—21no—
209C4×C61—41no—
210C4×C61C2×#9911yescharacteristic
211C4×C61C2×#10011yescharacteristic
212Dic61—21no—
213Dic61—41no—
214Dic61#32311yescharacteristic
215Dic61#32311yescharacteristic
216C2×#407—611no—
217C2×#349—612no—
218#1320—611no—
219#1320—612no—
220#1320D6111yescharacteristic, direct product factor
221C2×C61—21no—
222C2×C61—42no—
223C2×C61—41no—
224C2×C61C2×#32311yescharacteristic
225D61—21no—
226D61—42no—
227D61—41no—
228D61#132012yesdirect product factor
229C24×C4—611no—
230C22×M16—611no—
231C22×M16—611no—
232C2×M32—1222no—
233#407—611no—
234#407—611no—
235#407—611no—
236#407—1222no—
237#407C2×D6111yescharacteristic
238C2×C22⋊C8—1222no—
239#349—612no—
240#349—1222no—
241#349C2×D6112yescomplemented
242C61C2×#132011yescharacteristic, complemented, Sylow
243C25—611no—
244C23×C4—611no—
245C23×C4—611no—
246C23×C4—611no—
247C23×C4—611no—
248C23×C4—611no—
249C23×C4—1221no—
250C23×C4—1221no—
251C23×C4—1221no—
252C23×C4—1221no—
253C23×C4—2441no—
254C23×C4—2441no—
255C23×C4—2441no—
256C23×C4—2441no—
257C23×C4C4×D6111yescharacteristic
258C2×M16—611no—
259C2×M16—612no—
260C2×M16—611no—
261C2×M16—1221no—
262C2×M16—2441no—
263C2×M16—2441no—
264C2×M16—2441no—
265C2×M16—2441no—
266C2×M16C4×D6111yescharacteristic
267C2×M16C22×D6111yescharacteristic
268C22×C8—612no—
269C22×C8—1221no—
270M32—22no—
271M32—1222no—
272M32—2442no—
273C2×C16—2442no—
274C22⋊C8—22no—
275C22⋊C8—1222no—
276C22⋊C8—1222no—
277C22⋊C8—1222no—
278C24—611no—
279C24—611no—
280C24—1221no—
281C24—1221no—
282C24—2441no—
283C24—2441no—
284C24—2444no—
285C24C8×D6111yescharacteristic
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—41no—
289C22×C4—41no—
290C22×C4—611no—
291C22×C4—611no—
292C22×C4—611no—
293C22×C4—611no—
294C22×C4—611no—
295C22×C4—611no—
296C22×C4—1221no—
297C22×C4—1221no—
298C22×C4—1221no—
299C22×C4—1221no—
300C22×C4—1221no—
301C22×C4—1221no—
302C22×C4—1221no—
303C22×C4—1221no—
304C22×C4—1221no—
305C22×C4—1221no—
306C22×C4—1221no—
307C22×C4—1221no—
308C22×C4—2441no—
309C22×C4—2441no—
310C22×C4—2441no—
311C22×C4—2441no—
312C22×C4—2441no—
313C22×C4—2441no—
314C22×C4—2442no—
315C22×C4—2442no—
316C22×C4—2442no—
317C22×C4—2442no—
318C22×C4—2442no—
319C22×C4—2442no—
320C22×C4—2441no—
321C22×C4—2441no—
322C22×C4—2441no—
323C22×C4—2441no—
324C22×C4—2441no—
325C22×C4—2441no—
326C22×C4C8×D6111yescharacteristic
327C22×C4C2×C4×D6111yescharacteristic
328M16—41no—
329M16—41no—
330M16—2442no—
331M16—2442no—
332M16—2441no—
333M16—2441no—
334C2×C8—21no—
335C2×C8—612no—
336C2×C8—1222no—
337C2×C8—1222no—
338C2×C8—1221no—
339C2×C8—2441no—
340C2×C8—2441no—
341C2×C8D4×D6112yes—
342C16—42no—
343C16—2442no—
344C23—21no—
345C23—41no—
346C23—42no—
347C23—611no—
348C23—611no—
349C23—1221no—
350C23—1221no—
351C23—1224no—
352C23—1221no—
353C23—2441no—
354C23—2442no—
355C23—2441no—
356C23—2441no—
357C23—2442no—
358C23—2442no—
359C23—2442no—
360C23—2442no—
361C23—2442no—
362C23—2444no—
363C23—2444no—
364C23—2444no—
365C23—2444no—
366C23C2×C8×D6111yescharacteristic
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—42no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—611no—
375C2×C4—611no—
376C2×C4—611no—
377C2×C4—611no—
378C2×C4—611no—
379C2×C4—611no—
380C2×C4—1221no—
381C2×C4—1221no—
382C2×C4—1221no—
383C2×C4—1221no—
384C2×C4—1221no—
385C2×C4—1221no—
386C2×C4—1221no—
387C2×C4—1221no—
388C2×C4—1221no—
389C2×C4—2442no—
390C2×C4—2441no—
391C2×C4—2441no—
392C2×C4—2442no—
393C2×C4—2441no—
394C2×C4—2441no—
395C2×C4—2442no—
396C2×C4—2441no—
397C2×C4—2441no—
398C2×C4—2442no—
399C2×C4—2441no—
400C2×C4—2441no—
401C2×C4—2441no—
402C2×C4C22⋊C4×D6111yescharacteristic
403C2×C4M16×D6111yescharacteristic
404C8—22no—
405C8—41no—
406C8—1222no—
407C8—2441no—
408C22—22no—
409C22—21no—
410C22—41no—
411C22—41no—
412C22—42no—
413C22—42no—
414C22—41no—
415C22—611no—
416C22—611no—
417C22—1222no—
418C22—1222no—
419C22—1221no—
420C22—2441no—
421C22—2441no—
422C22—2442no—
423C22—2444no—
424C22—2442no—
425C22—2444no—
426C22—2442no—
427C22—2442no—
428C22—2448no—
429C22—2441no—
430C22C22⋊C8×D6111yescharacteristic
431C4—21no—
432C4—41no—
433C4—611no—
434C4—611no—
435C4—1221no—
436C4—2441no—
437C4#99×D6111yescharacteristic
438C4#100×D6111yescharacteristic
439C2—21no—
440C2—42no—
441C2—41no—
442C2—612no—
443C2—1221no—
444C2—2442no—
445C2—2441no—
446C2#323×D6111yescharacteristic
subgroupG/H
centerC4#99×D61
commutatorC23×C61C22×C8
FrattiniC2×M16C22×D61
FittingC61×#1320C2
socleC2×C61C2×#323
prime radicalC24×D61C8
cosocleC2×M16×C61C23
hypercenter#1320D61
hypocenterC61C2×#1320
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #1320

Complements

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

NH ≅ G/Ntype
2. #349×D61C2semidirect
3. #21443755C2semidirect
4. #21443754C2semidirect
5. C61×#1320C2semidirect
15. #16839544C22semidirect
18. C61×#349C22semidirect
220. #1320D61direct (N × H)
228. D61#1320direct (N × H)
241. #349C2×D61semidirect
242. C61C2×#1320semidirect

Maximal subgroups

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

subgroupindex
#407×D612
#349×D612
#214437552
#214437542
C61×#13202
C2×#132061