Finite Group Databasebeta

← D61×#1341 #29590165

Subgroups — D61×#1341 #29590165

Order 15616.

480 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 81 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#469×D61C211yesmaximal, characteristic
2#349×D61C211yesmaximal, characteristic, complemented
3#338×D61C211yesmaximal, characteristic, complemented
4#21443811C211yesmaximal, characteristic, complemented
5#21443810C211yesmaximal, characteristic, complemented
6#21443809C211yesmaximal, characteristic, complemented
7C61×#1341C211yesmaximal, characteristic, complemented
8C2×D8×D61C411yescharacteristic
9C2×M16×D61—21no—
10C2×M16×D61C2211yescharacteristic
11#121×D61—21no—
12M32×D61—21no—
13#16840016C411yescharacteristic
14#16840015C2211yescharacteristic
15#16840014—21no—
16#16840013—21no—
17#16840012C411yescharacteristic
18#106×D61C411yescharacteristic
19#102×D61—21no—
20#16839544C2211yescharacteristic, complemented
21#16839543—21no—
22#16839520—21no—
23#16839520C2211yescharacteristic, complemented
24C61×#469C2211yescharacteristic
25C61×#349C2211yescharacteristic, complemented
26C61×#338C2211yescharacteristic, complemented
27C2×D4×D61—21no—
28C2×D4×D61—41no—
29C22×C4×D61D411yescharacteristic
30C2×D488C2×C411yescharacteristic
31C2×#11758199—21no—
32D8×D61—41no—
33D8×D61—41no—
34C2×#11758194—21no—
35C2×#11758194D411yescharacteristic
36C2×#11758189—22no—
37C2×#11758189C2×C411yescharacteristic
38C2×#11758189D411yescharacteristic
39M16×D61—41no—
40M16×D61—41no—
41M16×D61—41no—
42M16×D61—41no—
43M16×D61—41no—
44M16×D61—41no—
45C2×C8×D61—22no—
46C2×C8×D61C2×C411yescharacteristic
47C2×C8×D61D411yescharacteristic
48#14519752—21no—
49#14519751—21no—
50#14519750—41no—
51#14519749—41no—
52#14519748—21no—
53C4⋊C4×D61—21no—
54C22⋊C4×D61—41no—
55#14519717—21no—
56#14519716—41no—
57C16×D61—41no—
58#14519709C2×C411yescharacteristic
59#14519708—21no—
60#14519699—21no—
61#14519698—21no—
62#14519697—21no—
63C2×D8×C61C2×C411yescharacteristic
64C2×M16×C61—21no—
65C2×M16×C61C2311yescharacteristic
66#121×C61—21no—
67M32×C61—21no—
68#106×C61C2×C411yescharacteristic
69#102×C61—21no—
70C23×D61—41no—
71C23×D61SD1611yescharacteristic
72C2×D4×C61—21no—
73C2×D4×C61—41no—
74C22×C4×C61C2×D411yescharacteristic
75C2×C22⋊D61—41no—
76C2×C22⋊D61—41no—
77C2×C22⋊D61—41no—
78C22×Dic61SD1611yescharacteristic
79D4×D61—41no—
80D4×D61—41no—
81D4×D61—41no—
82D4×D61—41no—
83D4×D61—84no—
84C2×D244—21no—
85C2×D244—41no—
86C2×C4×D61—21no—
87C2×C4×D61—21no—
88C2×C4×D61—21no—
89C2×C4×D61—21no—
90C2×C4×D61—41no—
91C2×C4×D61C22⋊C411yescharacteristic
92C2×C4×D61C22⋊C411yescharacteristic
93C2×C4×D61D811yescharacteristic
94C2×C4×D61D811yescharacteristic
95D8×C61—41no—
96M16×C61—41no—
97M16×C61—41no—
98M16×C61—41no—
99C2×C8×C61—22no—
100C2×C8×C61C22×C411yescharacteristic
101C2×C8×C61C2×D411yescharacteristic
102C4⋊C4×C61—21no—
103C22⋊C4×C61—41no—
104C22⋊Dic61—41no—
105#11758199—42no—
106#11758198—41no—
107#11758198—41no—
108C4⋊Dic61—21no—
109#11758196—41no—
110#11758194—41no—
111#11758194—41no—
112#11758194—41no—
113C2×#92418—22no—
114C2×#92418C22⋊C411yescharacteristic
115C2×#92418C22⋊C411yescharacteristic
116D488—41no—
117#11758189—41no—
118#11758189—41no—
119#11758189—42no—
120#11758189—42no—
121C8×D61—21no—
122C8×D61—21no—
123C8×D61—21no—
124C8×D61—21no—
125C8×D61—42no—
126C8×D61—42no—
127C16×C61—41no—
128#11758185—41no—
129C23×C61—41no—
130C23×C61C2×SD1611yescharacteristic
131C22×D61—21no—
132C22×D61—21no—
133C22×D61—42no—
134C22×D61—41no—
135C22×D61—82no—
136C22×D61—82no—
137C22×D61—81no—
138C22×D61—81no—
139C22×D61#10211yescharacteristic
140C22×D61#10211yescharacteristic
141D4×C61—41no—
142D4×C61—41no—
143D4×C61—82no—
144C2×C4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—41no—
147C2×C4×C61C2×C22⋊C411yescharacteristic
148C2×C4×C61C2×D811yescharacteristic
149C22⋊D61—82no—
150C22⋊D61—82no—
151C22⋊D61—81no—
152C22⋊D61—81no—
153C2×Dic61—21no—
154C2×Dic61—21no—
155C2×Dic61—41no—
156C2×Dic61#10211yescharacteristic
157C2×Dic61#10211yescharacteristic
158D244—41no—
159D244—41no—
160D244—82no—
161C4×D61—21no—
162C4×D61—21no—
163C4×D61—21no—
164C4×D61—21no—
165C4×D61—21no—
166C4×D61—21no—
167C4×D61—82no—
168C4×D61#9911yescharacteristic
169C4×D61#9911yescharacteristic
170C4×D61#10411yescharacteristic
171C4×D61#10411yescharacteristic
172C8×C61—21no—
173C8×C61—21no—
174C8×C61—42no—
175#92418—21no—
176#92418—21no—
177#92418—42no—
178C2×#1341—611nomaximal, Sylow
179C22×C61—21no—
180C22×C61—41no—
181C22×C61—81no—
182C22×C61—81no—
183C22×C61—81no—
184C22×C61C2×#10211yescharacteristic
185C2×D61—22no—
186C2×D61—21no—
187C2×D61—42no—
188C2×D61—41no—
189C2×D61—81no—
190C2×D61—81no—
191C2×D61—81no—
192C2×D61—81no—
193C2×D61—162no—
194C2×D61—162no—
195C2×D61#32711yescharacteristic
196C2×D61#32711yescharacteristic
197C4×C61—21no—
198C4×C61—81no—
199C4×C61C2×#9911yescharacteristic
200C4×C61C2×#10411yescharacteristic
201Dic61—21no—
202Dic61—81no—
203Dic61#32711yescharacteristic
204Dic61#32711yescharacteristic
205C2×#469—611no—
206C2×#349—611no—
207C2×#338—611no—
208#1341—611no—
209#1341—611no—
210#1341—611no—
211#1341D6111yescharacteristic, direct product factor
212C2×C61—21no—
213C2×C61—41no—
214C2×C61—161no—
215C2×C61C2×#32711yescharacteristic
216D61—21no—
217D61—41no—
218D61—161no—
219D61#134112yesdirect product factor
220C22×D8—611no—
221C22×M16—611no—
222C22×M16—1221no—
223C2×#121—1221no—
224C2×M32—1221no—
225#469—611no—
226#469—611no—
227#469—611no—
228#469—1221no—
229#469—1221no—
230#469C2×D6111yescharacteristic
231C2×#106—611no—
232C2×#102—1221no—
233#349—611no—
234#349—1221no—
235#349C2×D6111yescharacteristic, complemented
236#338—611no—
237#338—1221no—
238#338C2×D6111yescharacteristic, complemented
239C61C2×#134111yescharacteristic, complemented, Sylow
240C22×D4—1221no—
241C22×D4—2441no—
242C23×C4—611no—
243C2×D8—611no—
244C2×D8—1221no—
245C2×D8—2441no—
246C2×D8—2441no—
247C2×D8C4×D6111yescharacteristic
248C2×M16—21no—
249C2×M16—611no—
250C2×M16—611no—
251C2×M16—611no—
252C2×M16—1222no—
253C2×M16—1221no—
254C2×M16—2441no—
255C2×M16—2441no—
256C2×M16—2441no—
257C2×M16—2441no—
258C2×M16—2441no—
259C2×M16—2441no—
260C2×M16C22×D6111yescharacteristic
261C22×C8—611no—
262C22×C8—611no—
263C22×C8—1222no—
264#121—21no—
265#121—1221no—
266#121—1221no—
267#121—1221no—
268#121—2441no—
269#121—2441no—
270C2×C4⋊C4—1221no—
271C2×C22⋊C4—2441no—
272M32—21no—
273M32—1221no—
274M32—2441no—
275C2×C16—2441no—
276#106—611no—
277#106—1221no—
278#106C4×D6111yescharacteristic
279#102—21no—
280#102—1221no—
281#102—1221no—
282#102—1221no—
283C24—611no—
284C24—2441no—
285C2×D4—21no—
286C2×D4—41no—
287C2×D4—1221no—
288C2×D4—4884no—
289C2×D4—2441no—
290C2×D4—2441no—
291C2×D4—2441no—
292C2×D4—2441no—
293C2×D4—2441no—
294C2×D4—2441no—
295C2×D4—2441no—
296C2×D4—2441no—
297C22×C4—611no—
298C22×C4—611no—
299C22×C4—611no—
300C22×C4—611no—
301C22×C4—611no—
302C22×C4—1221no—
303C22×C4—1221no—
304C22×C4—1221no—
305C22×C4—1221no—
306C22×C4—2441no—
307C22×C4D4×D6111yescharacteristic
308D8—41no—
309D8—2441no—
310D8—2442no—
311M16—41no—
312M16—41no—
313M16—41no—
314M16—2441no—
315M16—2441no—
316M16—2442no—
317M16—2442no—
318M16—2441no—
319M16—2441no—
320M16—2441no—
321C2×C8—22no—
322C2×C8—611no—
323C2×C8—611no—
324C2×C8—1221no—
325C2×C8—1221no—
326C2×C8—1221no—
327C2×C8—1221no—
328C2×C8—1222no—
329C2×C8—2442no—
330C2×C8—2442no—
331C2×C8C2×C4×D6111yescharacteristic
332C2×C8D4×D6111yescharacteristic
333C4⋊C4—21no—
334C4⋊C4—1221no—
335C4⋊C4—2441no—
336C22⋊C4—41no—
337C22⋊C4—2441no—
338C22⋊C4—2441no—
339C22⋊C4—2441no—
340C16—41no—
341C16—2441no—
342C23—41no—
343C23—611no—
344C23—611no—
345C23—1221no—
346C23—1221no—
347C23—4881no—
348C23—4881no—
349C23—4882no—
350C23—4882no—
351C23—2442no—
352C23—2441no—
353C23SD16×D6111yescharacteristic
354D4—41no—
355D4—41no—
356D4—82no—
357D4—4882no—
358D4—4881no—
359D4—4881no—
360D4—4882no—
361D4—4882no—
362D4—2441no—
363D4—2441no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—41no—
367C2×C4—611no—
368C2×C4—611no—
369C2×C4—611no—
370C2×C4—611no—
371C2×C4—611no—
372C2×C4—611no—
373C2×C4—1221no—
374C2×C4—1221no—
375C2×C4—1221no—
376C2×C4—1221no—
377C2×C4—1221no—
378C2×C4—1221no—
379C2×C4—1221no—
380C2×C4—1221no—
381C2×C4—4882no—
382C2×C4—2441no—
383C2×C4C22⋊C4×D6111yescharacteristic
384C2×C4D8×D6111yescharacteristic
385C8—21no—
386C8—21no—
387C8—42no—
388C8—1221no—
389C8—1221no—
390C8—2442no—
391C22—21no—
392C22—41no—
393C22—81no—
394C22—81no—
395C22—81no—
396C22—611no—
397C22—611no—
398C22—1222no—
399C22—1221no—
400C22—9762no—
401C22—9762no—
402C22—4881no—
403C22—4881no—
404C22—4881no—
405C22—4881no—
406C22—2441no—
407C22—2442no—
408C22#102×D6111yescharacteristic
409C4—21no—
410C4—81no—
411C4—611no—
412C4—611no—
413C4—1221no—
414C4—4881no—
415C4#99×D6111yescharacteristic
416C4#104×D6111yescharacteristic
417C2—21no—
418C2—41no—
419C2—161no—
420C2—612no—
421C2—1221no—
422C2—9761no—
423C2—2441no—
424C2#327×D6111yescharacteristic
subgroupG/H
centerC2#327×D61
commutatorC2×C8×C61C22×C4
FrattiniC2×M16C22×D61
FittingC61×#1341C2
socleC2×C61C2×#327
prime radical#469×D61C2
cosocleC2×M16×C61C23
hypercenter#1341D61
hypocenterC61C2×#1341
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #1341

Complements

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

NH ≅ G/Ntype
2. #349×D61C2semidirect
3. #338×D61C2semidirect
4. #21443811C2semidirect
5. #21443810C2semidirect
6. #21443809C2semidirect
7. C61×#1341C2semidirect
20. #16839544C22semidirect
23. #16839520C22semidirect
25. C61×#349C22semidirect
26. C61×#338C22semidirect
211. #1341D61direct (N × H)
219. D61#1341direct (N × H)
235. #349C2×D61semidirect
238. #338C2×D61semidirect
239. C61C2×#1341semidirect

Maximal subgroups

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

subgroupindex
#469×D612
#349×D612
#338×D612
#214438112
#214438102
#214438092
C61×#13412
C2×#134161