Finite Group Databasebeta

← D61⋊#1342 #30604720

Subgroups — D61⋊#1342 #30604720

Order 15616.

428 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 78 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
1D61⋊#349C211yesmaximal, characteristic
2D61⋊#338C211yesmaximal, characteristic
3#21460796C212yesmaximal, complemented
4#21460795C212yesmaximal, complemented
5#470×D61C211yesmaximal, characteristic
6C2×D61⋊M16—21no—
7D61⋊M32—21no—
8#16840659C2212yes—
9#16840658—21no—
10#16840631—21no—
11#16840631C2212yes—
12C2×Q16×D61C411yescharacteristic
13C2×M16×D61C2211yescharacteristic
14C22⋊Q8×D61—21no—
15#16840021C2211yescharacteristic
16#16840020C411yescharacteristic
17#16840019—21no—
18#16840018—21no—
19#16840017C2211yescharacteristic
20#106×D61C411yescharacteristic
21#103×D61—21no—
22C61×#470C411yescharacteristic
23C2×#11758213—41no—
24D61⋊M16—22no—
25D61⋊M16—22no—
26D61⋊M16—41no—
27D61⋊M16—41no—
28C2×#11758217—41no—
29C2×D61⋊C8—22no—
30#14519852—41no—
31#14519851—22no—
32D61⋊C16—41no—
33C2×Q8×D61—21no—
34C22×C4×D61D411yescharacteristic
35C2×Dic244C2×C411yescharacteristic
36C2×#11758202—21no—
37Q16×D61—41no—
38Q16×D61—41no—
39C2×#11758194D411yescharacteristic
40C2×#11758189D411yescharacteristic
41C2×#11758189C2311yescharacteristic
42M16×D61—41no—
43M16×D61—41no—
44C2×C8×D61C2×C411yescharacteristic
45C2×C8×D61D411yescharacteristic
46#14519757—21no—
47#14519756—21no—
48#14519755—41no—
49#14519754—41no—
50#14519753—21no—
51C4⋊C4×D61—21no—
52C4⋊C4×D61—41no—
53C22⋊C4×D61—41no—
54#14519709C2×C411yescharacteristic
55#14519708—21no—
56#14519702—21no—
57#14519701—21no—
58#14519700—21no—
59C2×Q16×C61C2×C411yescharacteristic
60C2×M16×C61C2×C411yescharacteristic
61C22⋊Q8×C61—21no—
62#106×C61C2×C411yescharacteristic
63#103×C61—21no—
64C23×D61SD1611yescharacteristic
65C2×Q8×C61—21no—
66C22×C4×C61C22⋊C411yescharacteristic
67C22×Dic61D811yescharacteristic
68Q8×D61—41no—
69Q8×D61—41no—
70Q8×D61—41no—
71Q8×D61—41no—
72C2×C4×D61—21no—
73C2×C4×D61—21no—
74C2×C4×D61—21no—
75C2×C4×D61—21no—
76C2×C4×D61—41no—
77C2×C4×D61—41no—
78C2×C4×D61C22⋊C411yescharacteristic
79C2×C4×D61D811yescharacteristic
80C2×C4×D61SD1611yescharacteristic
81C2×C4×D61C2×D411yescharacteristic
82C2×Dic122—21no—
83C2×Dic122—41no—
84#11758217—42no—
85#11758217—42no—
86C2×#92420—42no—
87#11758213—42no—
88#11758213—42no—
89D61⋊C8—24no—
90D61⋊C8—42no—
91Q16×C61—41no—
92M16×C61—41no—
93C2×C8×C61C22⋊C411yescharacteristic
94C2×C8×C61C22×C411yescharacteristic
95C4⋊C4×C61—21no—
96C4⋊C4×C61—41no—
97C22⋊C4×C61—41no—
98C22⋊Dic61—41no—
99#11758202—42no—
100#11758198—41no—
101#11758198—41no—
102C4⋊Dic61—21no—
103C4⋊Dic61—41no—
104#11758196—41no—
105#11758196—41no—
106#11758196—41no—
107#11758194—41no—
108C2×#92418C22⋊C411yescharacteristic
109C2×#92418C2×D411yescharacteristic
110Dic244—41no—
111#11758189—41no—
112#11758189—41no—
113C8×D61—21no—
114C8×D61—21no—
115C8×D61—21no—
116C8×D61—21no—
117#11758187—42no—
118C23×C61#10211yescharacteristic
119C22×D61—21no—
120C22×D61—21no—
121C22×D61—42no—
122C22×D61#10211yescharacteristic
123C22×D61C2×SD1611yescharacteristic
124Q8×C61—41no—
125Q8×C61—41no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61#10211yescharacteristic
131C2×C4×C61C2×C22⋊C411yescharacteristic
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61#10211yescharacteristic
137C2×Dic61C2×D811yescharacteristic
138C4×D61—21no—
139C4×D61—21no—
140C4×D61—21no—
141C4×D61—21no—
142C4×D61—21no—
143C4×D61—21no—
144C4×D61—82no—
145C4×D61—81no—
146C4×D61—81no—
147C4×D61#9911yescharacteristic
148C4×D61#9911yescharacteristic
149C4×D61#10411yescharacteristic
150C4×D61#10411yescharacteristic
151Dic122—41no—
152Dic122—41no—
153Dic122—81no—
154Dic122—81no—
155#92420—44no—
156C8×C61—21no—
157C8×C61—21no—
158#92418—21no—
159#92418—21no—
160C2×#1342—611nomaximal, Sylow
161C22×C61—21no—
162C22×C61—41no—
163C22×C61C2×#10211yescharacteristic
164C2×D61—22no—
165C2×D61—21no—
166C2×D61—42no—
167C2×D61—41no—
168C2×D61—81no—
169C2×D61#32711yescharacteristic
170C2×D61#32711yescharacteristic
171C4×C61—21no—
172C4×C61—81no—
173C4×C61—81no—
174C4×C61C2×#9911yescharacteristic
175C4×C61C2×#10411yescharacteristic
176Dic61—21no—
177Dic61—81no—
178Dic61—81no—
179Dic61#32711yescharacteristic
180Dic61#32711yescharacteristic
181C2×#470—611no—
182C2×#349—611no—
183C2×#338—611no—
184#1342—612no—
185#1342—612no—
186C2×C61—21no—
187C2×C61—41no—
188C2×C61C2×#32711yescharacteristic
189D61—21no—
190D61—41no—
191D61#134212yescomplemented
192C22×Q16—611no—
193C22×M16—611no—
194C22×M16—1221no—
195C2×C22⋊Q8—1221no—
196C2×M32—1221no—
197#470—611no—
198#470—611no—
199#470—611no—
200#470—1221no—
201#470—1221no—
202#470#692311yescharacteristic
203C2×#106—611no—
204C2×#103—1221no—
205#349—612no—
206#349—1221no—
207#338—612no—
208#338—1221no—
209C61C2×#134211yescharacteristic, complemented, Sylow
210C22×Q8—1221no—
211C23×C4—611no—
212C2×Q16—611no—
213C2×Q16—1221no—
214C2×Q16—2441no—
215C2×Q16—2441no—
216C2×Q16C2×#692311yescharacteristic
217C2×M16—611no—
218C2×M16—611no—
219C2×M16—611no—
220C2×M16—1222no—
221C2×M16—1222no—
222C2×M16—2441no—
223C2×M16—2441no—
224C2×M16—2441no—
225C2×M16—2441no—
226C2×M16—2441no—
227C2×M16—2441no—
228C2×M16C2×#692311yescharacteristic
229C22×C8—611no—
230C22×C8—611no—
231C22×C8—1222no—
232C22⋊Q8—21no—
233C22⋊Q8—1221no—
234C22⋊Q8—1221no—
235C22⋊Q8—1221no—
236C22⋊Q8—2441no—
237C22⋊Q8—2441no—
238C2×C4⋊C4—1221no—
239C2×C4⋊C4—2441no—
240C2×C22⋊C4—2441no—
241M32—1222no—
242M32—2441no—
243C2×C16—2441no—
244#106—611no—
245#106—1221no—
246#106C2×#692311yescharacteristic
247#103—21no—
248#103—1221no—
249#103—1221no—
250#103—1221no—
251C24—611no—
252C2×Q8—21no—
253C2×Q8—1221no—
254C2×Q8—2441no—
255C2×Q8—2441no—
256C2×Q8—2441no—
257C2×Q8—2441no—
258C2×Q8—2441no—
259C22×C4—611no—
260C22×C4—611no—
261C22×C4—611no—
262C22×C4—611no—
263C22×C4—611no—
264C22×C4—1221no—
265C22×C4—1221no—
266C22×C4—1221no—
267C22×C4—1221no—
268C22×C4—2441no—
269C22×C4—2441no—
270C22×C4C22⋊#692311yescharacteristic
271Q16—41no—
272Q16—2441no—
273Q16—2442no—
274M16—41no—
275M16—2441no—
276M16—2441no—
277M16—2441no—
278M16—2442no—
279M16—2442no—
280M16—2442no—
281M16—2442no—
282C2×C8—611no—
283C2×C8—611no—
284C2×C8—1221no—
285C2×C8—1221no—
286C2×C8—1221no—
287C2×C8—1221no—
288C2×C8—1224no—
289C2×C8—2442no—
290C2×C8—2442no—
291C2×C8C22⋊#692311yescharacteristic
292C2×C8C22×#692311yescharacteristic
293C4⋊C4—21no—
294C4⋊C4—41no—
295C4⋊C4—1221no—
296C4⋊C4—2441no—
297C4⋊C4—2441no—
298C4⋊C4—2441no—
299C4⋊C4—2441no—
300C22⋊C4—41no—
301C22⋊C4—2441no—
302C22⋊C4—2441no—
303C22⋊C4—2441no—
304C16—2442no—
305C23—611no—
306C23—611no—
307C23—1221no—
308C23—1221no—
309C23—2442no—
310C23#1451983911yescharacteristic
311Q8—41no—
312Q8—41no—
313Q8—4881no—
314Q8—4881no—
315Q8—2441no—
316Q8—2441no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—611no—
322C2×C4—611no—
323C2×C4—611no—
324C2×C4—611no—
325C2×C4—611no—
326C2×C4—611no—
327C2×C4—1221no—
328C2×C4—1221no—
329C2×C4—1221no—
330C2×C4—1221no—
331C2×C4—1221no—
332C2×C4—1221no—
333C2×C4—1221no—
334C2×C4—1221no—
335C2×C4—4881no—
336C2×C4—4881no—
337C2×C4—4882no—
338C2×C4—2441no—
339C2×C4—2441no—
340C2×C4#1451983911yescharacteristic
341C2×C4C2×C22⋊#692311yescharacteristic
342C8—21no—
343C8—21no—
344C8—1221no—
345C8—1221no—
346C8—2444no—
347C22—21no—
348C22—41no—
349C22—611no—
350C22—611no—
351C22—1222no—
352C22—1221no—
353C22—4881no—
354C22—2441no—
355C22—2442no—
356C22C2×#1451983911yescharacteristic
357C4—21no—
358C4—81no—
359C4—81no—
360C4—611no—
361C4—611no—
362C4—1221no—
363C4—4881no—
364C4—4881no—
365C4D61⋊#9911yescharacteristic
366C4D61⋊#10411yescharacteristic
367C2—21no—
368C2—41no—
369C2—612no—
370C2—1221no—
371C2—2441no—
372C2D61⋊#32711yescharacteristic
subgroupG/H
centerC2D61⋊#327
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#470C4
socleC2×C61C2×#327
prime radicalC23×D61SD16
cosocleC2×#11758189C23
hypercenter#470#6923
hypocenterC61C2×#1342
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #470

Complements

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

NH ≅ G/Ntype
3. #21460796C2semidirect
4. #21460795C2semidirect
191. D61#1342semidirect
209. C61C2×#1342semidirect

Maximal subgroups

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

subgroupindex
D61⋊#3492
D61⋊#3382
#214607962
#214607952
#470×D612
C2×#134261