Finite Group Databasebeta

← D61×#1406 #29600290

Subgroups — D61×#1406 #29600290

Order 15616.

468 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 61 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#496×D61C211yesmaximal, characteristic
2#355×D61C211yesmaximal, characteristic, complemented
3#354×D61C211yesmaximal, characteristic, complemented
4#21443977C211yesmaximal, characteristic, complemented
5#21443976C211yesmaximal, characteristic, complemented
6#21443975C211yesmaximal, characteristic, complemented
7C61×#1406C211yesmaximal, characteristic, complemented
8C2×SD16×D61—21no—
9C2×D8×D61—21no—
10#127×D61C411yescharacteristic, complemented
11#124×D61C2211yescharacteristic
12#16840152C2211yescharacteristic
13#16840151C411yescharacteristic, complemented
14#16840150—21no—
15#16840149C411yescharacteristic, complemented
16#16840148—21no—
17#101×D61—21no—
18#99×D61—21no—
19#97×D61C411yescharacteristic, complemented
20#16839559C2211yescharacteristic, complemented
21#16839558—21no—
22#16839557C2211yescharacteristic, complemented
23#16839556—21no—
24C61×#496C2211yescharacteristic
25C61×#355C2211yescharacteristic, complemented
26C61×#354C2211yescharacteristic, complemented
27C2×Q8×D61D411yescharacteristic
28C2×D4×D61—21no—
29C2×D4×D61—41no—
30C2×D4×D61D411yescharacteristic
31C2×#11758190—21no—
32C2×#11758200—21no—
33C2×#11758201—21no—
34SD16×D61—42no—
35SD16×D61—42no—
36C2×D488—21no—
37C2×#11758199—21no—
38C2×#11758199—21no—
39D8×D61—42no—
40D8×D61—42no—
41M16×D61—41no—
42C2×C8×D61—21no—
43#14519774C2×C411yescharacteristic, complemented
44#14519773—21no—
45#14519773—41no—
46#14519766D411yescharacteristic
47#14519765C2×C411yescharacteristic
48#14519764D411yescharacteristic
49#14519763—41no—
50C22⋊C4×D61—41no—
51C22⋊C4×D61—41no—
52C42×D61C2×C411yescharacteristic
53#14519696—21no—
54#14519695—41no—
55#14519692—21no—
56#14519691—41no—
57#14519688C2×C411yescharacteristic, complemented
58#14519687—21no—
59C2×SD16×C61—21no—
60C2×D8×C61—21no—
61#127×C61C2×C411yescharacteristic, complemented
62#124×C61C2311yescharacteristic
63#101×C61—21no—
64#99×C61—21no—
65#97×C61C2×C411yescharacteristic, complemented
66C23×D61—21no—
67C23×D61—41no—
68C2×Q8×C61C2×D411yescharacteristic
69C2×D4×C61—21no—
70C2×D4×C61—41no—
71C2×D4×C61C2×D411yescharacteristic
72C2×C22⋊D61—21no—
73C2×C22⋊D61—42no—
74C2×C22⋊D61—41no—
75Q8×D61—41no—
76Q8×D61—41no—
77D4×D61—41no—
78D4×D61—41no—
79D4×D61—41no—
80D4×D61—41no—
81D4×D61—41no—
82D4×D61—41no—
83D4×D61—84no—
84C2×D244—21no—
85C2×D244—41no—
86C2×D244C22⋊C411yescharacteristic
87C2×C4×D61—21no—
88C2×C4×D61—21no—
89C2×C4×D61—81no—
90C2×C4×D61C22⋊C411yescharacteristic
91C2×Dic122—21no—
92C2×Dic122C22⋊C411yescharacteristic
93SD16×C61—42no—
94D8×C61—42no—
95M16×C61—41no—
96C2×C8×C61—21no—
97C22⋊C4×C61—41no—
98C22⋊C4×C61—41no—
99C42×C61C22×C411yescharacteristic
100C22⋊Dic61—41no—
101C22⋊Dic61—41no—
102#11758201—42no—
103#11758200—42no—
104#11758199—42no—
105#11758199—42no—
106#11758198—41no—
107#11758198—41no—
108#11758198—81no—
109C4×Dic61—21no—
110C4×Dic61C22⋊C411yescharacteristic
111#11758194—41no—
112C2×#92418—21no—
113D488—42no—
114#11758190—42no—
115#11758189—81no—
116C8×D61—22no—
117C8×D61—22no—
118C8×D61—81no—
119C23×C61—21no—
120C23×C61—41no—
121C22×D61—21no—
122C22×D61—41no—
123C22×D61—41no—
124C22×D61—41no—
125C22×D61—82no—
126C22×D61—84no—
127C22×D61—81no—
128C22×D61—81no—
129C22×D61#9911yescharacteristic
130Q8×C61—41no—
131D4×C61—41no—
132D4×C61—41no—
133D4×C61—41no—
134D4×C61—82no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61—81no—
138C2×C4×C61C2×C22⋊C411yescharacteristic
139C22⋊D61—81no—
140C22⋊D61—81no—
141C22⋊D61—81no—
142C22⋊D61—84no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—81no—
146C2×Dic61#9911yescharacteristic
147D244—41no—
148D244—41no—
149D244—41no—
150D244—82no—
151C4×D61—21no—
152C4×D61—21no—
153C4×D61—42no—
154C4×D61—41no—
155C4×D61—41no—
156C4×D61—162no—
157Dic122—41no—
158Dic122—81no—
159C8×C61—22no—
160C8×C61—81no—
161#92418—22no—
162#92418—81no—
163C2×#1406—611nomaximal, Sylow
164C22×C61—41no—
165C22×C61—81no—
166C22×C61—82no—
167C22×C61—81no—
168C22×C61C2×#9911yescharacteristic
169C2×D61—22no—
170C2×D61—41no—
171C2×D61—82no—
172C2×D61—81no—
173C2×D61—82no—
174C2×D61—81no—
175C2×D61—161no—
176C2×D61—162no—
177C2×D61—162no—
178C2×D61#35311yescharacteristic
179C2×D61#35311yescharacteristic
180C4×C61—21no—
181C4×C61—41no—
182C4×C61—41no—
183C4×C61—161no—
184Dic61—21no—
185Dic61—41no—
186Dic61—41no—
187Dic61—161no—
188C2×#496—611no—
189C2×#355—611no—
190C2×#354—611no—
191#1406—611no—
192#1406—611no—
193#1406—611no—
194#1406D6111yescharacteristic, direct product factor
195C2×C61—21no—
196C2×C61—81no—
197C2×C61—161no—
198C2×C61C2×#35311yescharacteristic
199D61—21no—
200D61—81no—
201D61—161no—
202D61#140612yesdirect product factor
203C22×SD16—1221no—
204C22×D8—1221no—
205C2×#127—611no—
206C2×#124—611no—
207#496—611no—
208#496—611no—
209#496—611no—
210#496—1221no—
211#496—1221no—
212#496C2×D6111yescharacteristic
213C2×#101—1221no—
214C2×#99—1221no—
215C2×#97—611no—
216#355—611no—
217#355—1221no—
218#355C2×D6111yescharacteristic, complemented
219#354—611no—
220#354—1221no—
221#354C2×D6111yescharacteristic, complemented
222C61C2×#140611yescharacteristic, complemented, Sylow
223C22×Q8—611no—
224C22×D4—611no—
225C22×D4—1221no—
226C22×D4—2441no—
227C2×SD16—21no—
228C2×SD16—1221no—
229C2×SD16—1221no—
230C2×SD16—1221no—
231C2×SD16—2442no—
232C2×SD16—2442no—
233C2×D8—21no—
234C2×D8—1221no—
235C2×D8—1221no—
236C2×D8—1221no—
237C2×D8—2442no—
238C2×D8—2442no—
239C2×M16—2441no—
240C22×C8—1221no—
241#127—611no—
242#127—1221no—
243#127—2441no—
244#127C4×D6111yescharacteristic, complemented
245#124—611no—
246#124—611no—
247#124—611no—
248#124—2441no—
249#124C22×D6111yescharacteristic
250C2×C22⋊C4—2441no—
251C2×C22⋊C4—2441no—
252C2×C42—611no—
253#101—21no—
254#101—1221no—
255#101—2441no—
256#99—21no—
257#99—1221no—
258#99—2441no—
259#97—611no—
260#97—1221no—
261#97C4×D6111yescharacteristic, complemented
262C24—1221no—
263C24—2441no—
264C2×Q8—611no—
265C2×Q8—1221no—
266C2×Q8—2441no—
267C2×Q8—2441no—
268C2×Q8D4×D6111yescharacteristic
269C2×D4—21no—
270C2×D4—41no—
271C2×D4—611no—
272C2×D4—1221no—
273C2×D4—1221no—
274C2×D4—4884no—
275C2×D4—2441no—
276C2×D4—2441no—
277C2×D4—2441no—
278C2×D4—2441no—
279C2×D4—2441no—
280C2×D4—2441no—
281C2×D4—2441no—
282C2×D4—2441no—
283C2×D4—2442no—
284C2×D4D4×D6111yescharacteristic
285C22×C4—611no—
286C22×C4—1221no—
287C22×C4—1221no—
288C22×C4—4881no—
289SD16—42no—
290SD16—2442no—
291SD16—2442no—
292SD16—2442no—
293D8—42no—
294D8—2442no—
295D8—2442no—
296D8—2442no—
297M16—41no—
298M16—4881no—
299M16—2441no—
300C2×C8—21no—
301C2×C8—1222no—
302C2×C8—1222no—
303C2×C8—1221no—
304C2×C8—4881no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C22⋊C4—4881no—
308C22⋊C4—2441no—
309C22⋊C4—2441no—
310C22⋊C4—2441no—
311C22⋊C4—2441no—
312C42—611no—
313C42—1221no—
314C42C2×C4×D6111yescharacteristic
315C23—21no—
316C23—41no—
317C23—611no—
318C23—1221no—
319C23—4881no—
320C23—4881no—
321C23—4884no—
322C23—4882no—
323C23—2441no—
324C23—2441no—
325C23—2441no—
326Q8—41no—
327Q8—4881no—
328Q8—2441no—
329D4—41no—
330D4—41no—
331D4—41no—
332D4—82no—
333D4—4882no—
334D4—4881no—
335D4—4881no—
336D4—4881no—
337D4—4884no—
338D4—2441no—
339D4—2441no—
340D4—2441no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—81no—
344C2×C4—611no—
345C2×C4—1221no—
346C2×C4—1221no—
347C2×C4—1221no—
348C2×C4—1221no—
349C2×C4—9762no—
350C2×C4—4881no—
351C2×C4—2441no—
352C2×C4—2441no—
353C2×C4—2442no—
354C2×C4C22⋊C4×D6111yescharacteristic
355C8—22no—
356C8—81no—
357C8—1222no—
358C8—4881no—
359C22—41no—
360C22—81no—
361C22—82no—
362C22—81no—
363C22—611no—
364C22—611no—
365C22—1222no—
366C22—9761no—
367C22—9762no—
368C22—9762no—
369C22—4882no—
370C22—4881no—
371C22—4882no—
372C22—4881no—
373C22—2441no—
374C22#99×D6111yescharacteristic
375C4—21no—
376C4—41no—
377C4—41no—
378C4—161no—
379C4—1221no—
380C4—9761no—
381C4—2441no—
382C4—2441no—
383C2—21no—
384C2—81no—
385C2—161no—
386C2—612no—
387C2—1221no—
388C2—9761no—
389C2—4881no—
390C2#353×D6111yescharacteristic
subgroupG/H
centerC2#353×D61
commutatorC42×C61C22×C4
Frattini#124C22×D61
FittingC61×#1406C2
socleC2×C61C2×#353
prime radical#496×D61C2
cosocle#124×C61C23
hypercenter#1406D61
hypocenterC61C2×#1406
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #124 ◁ #1406

Complements

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

NH ≅ G/Ntype
2. #355×D61C2semidirect
3. #354×D61C2semidirect
4. #21443977C2semidirect
5. #21443976C2semidirect
6. #21443975C2semidirect
7. C61×#1406C2semidirect
10. #127×D61C4semidirect
13. #16840151C4semidirect
15. #16840149C4semidirect
19. #97×D61C4semidirect
20. #16839559C22semidirect
22. #16839557C22semidirect
25. C61×#355C22semidirect
26. C61×#354C22semidirect
43. #14519774C2×C4semidirect
57. #14519688C2×C4semidirect
61. #127×C61C2×C4semidirect
65. #97×C61C2×C4semidirect
194. #1406D61direct (N × H)
202. D61#1406direct (N × H)
218. #355C2×D61semidirect
221. #354C2×D61semidirect
222. C61C2×#1406semidirect
244. #127C4×D61semidirect
261. #97C4×D61semidirect

Maximal subgroups

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

subgroupindex
#496×D612
#355×D612
#354×D612
#214439772
#214439762
#214439752
C61×#14062
C2×#140661