Finite Group Databasebeta

← D61⋊#1321 #30603857

Subgroups — D61⋊#1321 #30603857

Order 15616.

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

normal subgroups only

This group has 518 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
1D61⋊#349C212yesmaximal, complemented
2#21460754C212yesmaximal, complemented
3#21460753C212yesmaximal, complemented
4#408×D61C211yesmaximal, characteristic
5D61⋊M32—22no—
6#16840659—22no—
7#16840658C2214yescomplemented
8C2×#41×D61C411yescharacteristic
9C2×M16×D61C2211yescharacteristic
10C22×C8×D61C411yescharacteristic
11#16839730C411yescharacteristic
12#16839729C2211yescharacteristic
13#16839728C2211yescharacteristic
14#16839727—22no—
15C22⋊C8×D61—22no—
16C61×#408C411yescharacteristic
17#14519852—42no—
18#14519851—24no—
19D61⋊C16—42no—
20C2×#11758226C811yescharacteristic
21C2×#11758222—21no—
22C2×#11758222C2×C411yescharacteristic
23C2×#11758224—21no—
24C2×#11758224C811yescharacteristic
25#41×D61—41no—
26#41×D61—41no—
27#41×D61—41no—
28#41×D61—41no—
29C2×Q8×D61C811yescharacteristic
30C2×D4×D61—21no—
31C2×D4×D61C811yescharacteristic
32C22×C4×D61—21no—
33C22×C4×D61C2×C411yescharacteristic
34C2×#11758194C2311yescharacteristic
35C2×#11758189D412yes—
36M16×D61—41no—
37M16×D61—41no—
38C22×#92418C2×C411yescharacteristic
39C2×C8×D61—21no—
40C2×C8×D61—21no—
41C2×C8×D61—41no—
42C2×C8×D61—41no—
43C2×C8×D61D412yes—
44C22⋊#92418—22no—
45#14519689—22no—
46#14519689—22no—
47C2×#41×C61C2×C411yescharacteristic
48C2×M16×C61C2×C411yescharacteristic
49C22×C8×C61C2×C411yescharacteristic
50C22⋊C8×C61—22no—
51C23×D61—21no—
52C23×D61M1611yescharacteristic
53#41×C61—41no—
54#41×C61—41no—
55C2×Q8×C61C2×C811yescharacteristic
56C2×D4×C61—21no—
57C2×D4×C61C2×C811yescharacteristic
58C22×C4×C61—21no—
59C22×C4×C61C22×C411yescharacteristic
60C2×C22⋊D61—21no—
61C2×C22⋊D61—21no—
62C2×C22⋊D61—21no—
63C22×Dic61—21no—
64C22×Dic61M1611yescharacteristic
65#11758226—41no—
66#11758226—41no—
67Q8×D61—41no—
68Q8×D61—41no—
69#11758224—41no—
70#11758224—41no—
71#11758224—42no—
72#11758224—42no—
73D4×D61—41no—
74D4×D61—41no—
75D4×D61—42no—
76D4×D61—42no—
77#11758222—42no—
78#11758222—42no—
79#11758222—41no—
80#11758222—41no—
81C2×D244—21no—
82C2×D244C2×C811yescharacteristic
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×C4×D61—21no—
86C2×C4×D61—21no—
87C2×C4×D61—21no—
88C2×C4×D61—21no—
89C2×C4×D61—21no—
90C2×C4×D61—41no—
91C2×C4×D61—41no—
92C2×C4×D61—41no—
93C2×C4×D61—41no—
94C2×C4×D61C22⋊C411yescharacteristic
95C2×C4×D61C22⋊C411yescharacteristic
96C2×C4×D61C2×C811yescharacteristic
97C2×C4×D61C2×C811yescharacteristic
98C2×Dic122—21no—
99C2×Dic122C2×C811yescharacteristic
100M16×C61—41no—
101C2×C8×C61—21no—
102C2×C8×C61—41no—
103C2×C8×C61C22⋊C412yes—
104#11758194—41no—
105C2×#92418—21no—
106C2×#92418—41no—
107C2×#92418C2×D412yes—
108#11758189—42no—
109C8×D61—22no—
110C8×D61—22no—
111C8×D61—42no—
112C8×D61—41no—
113C8×D61—41no—
114#11758187—44no—
115C23×C61—21no—
116C23×C61C2×M1611yescharacteristic
117C22×D61—21no—
118C22×D61—21no—
119C22×D61—21no—
120C22×D61—42no—
121C22×D61—44no—
122C22×D61—41no—
123C22×D61—41no—
124C22×D61C22⋊C811yescharacteristic
125C22×D61C22⋊C811yescharacteristic
126Q8×C61—41no—
127D4×C61—41no—
128D4×C61—42no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61C2×C22⋊C411yescharacteristic
135C2×C4×C61C22×C811yescharacteristic
136C22⋊D61—42no—
137C22⋊D61—42no—
138C22⋊D61—42no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61C22⋊C811yescharacteristic
145C2×Dic61C22⋊C811yescharacteristic
146D244—41no—
147D244—42no—
148C4×D61—21no—
149C4×D61—21no—
150C4×D61—21no—
151C4×D61—21no—
152C4×D61—21no—
153C4×D61—21no—
154C4×D61—41no—
155C4×D61—41no—
156C4×D61—41no—
157C4×D61—41no—
158C4×D61—41no—
159C4×D61—41no—
160C4×D61#9911yescharacteristic
161C4×D61#9911yescharacteristic
162C4×D61#10011yescharacteristic
163C4×D61#10011yescharacteristic
164Dic122—42no—
165Dic122—41no—
166C8×C61—22no—
167C8×C61—41no—
168#92418—22no—
169#92418—41no—
170C2×#1321—611nomaximal, Sylow
171C22×C61—21no—
172C22×C61—41no—
173C22×C61—42no—
174C22×C61—41no—
175C22×C61C2×C22⋊C811yescharacteristic
176C2×D61—22no—
177C2×D61—21no—
178C2×D61—42no—
179C2×D61—42no—
180C2×D61—41no—
181C2×D61—42no—
182C2×D61—41no—
183C2×D61—82no—
184C2×D61—82no—
185C2×D61#32311yescharacteristic
186C2×D61#32311yescharacteristic
187C4×C61—21no—
188C4×C61—41no—
189C4×C61C2×#9911yescharacteristic
190C4×C61C2×#10011yescharacteristic
191Dic61—21no—
192Dic61—41no—
193Dic61#32311yescharacteristic
194Dic61#32311yescharacteristic
195C2×#408—611no—
196C2×#349—612no—
197#1321—612no—
198#1321—612no—
199C2×C61—21no—
200C2×C61—41no—
201C2×C61—81no—
202C2×C61C2×#32311yescharacteristic
203D61—21no—
204D61—41no—
205D61—81no—
206D61#132112yescomplemented
207C22×#41—611no—
208C22×M16—611no—
209C23×C8—611no—
210C2×M32—1222no—
211#408—611no—
212#408—611no—
213#408—611no—
214#408—1222no—
215#408#692311yescharacteristic
216C2×C22⋊C8—1222no—
217#349—614no—
218#349—1222no—
219C61C2×#132111yescharacteristic, complemented, Sylow
220C2×#41—611no—
221C2×#41—611no—
222C2×#41—611no—
223C2×#41—1221no—
224C2×#41—1221no—
225C2×#41—2441no—
226C2×#41—2441no—
227C2×#41—2441no—
228C2×#41—2441no—
229C2×#41C2×#692311yescharacteristic
230C22×Q8—611no—
231C22×D4—611no—
232C22×D4—1221no—
233C23×C4—611no—
234C23×C4—1221no—
235C2×M16—611no—
236C2×M16—612no—
237C2×M16—2441no—
238C2×M16—2441no—
239C2×M16C2×#692311yescharacteristic
240C22×C8—612no—
241C22×C8—611no—
242C22×C8—1221no—
243C22×C8—1221no—
244C22×C8—2441no—
245C22×C8—2441no—
246C22×C8C2×#692311yescharacteristic
247M32—1224no—
248M32—2442no—
249C2×C16—2442no—
250C22⋊C8—22no—
251C22⋊C8—1222no—
252C22⋊C8—1222no—
253C22⋊C8—1222no—
254C24—611no—
255C24—1221no—
256#41—41no—
257#41—41no—
258#41—2441no—
259#41—2441no—
260#41—2442no—
261#41—2442no—
262#41—2442no—
263#41—2442no—
264#41—2441no—
265#41—2441no—
266#41—2441no—
267#41—2441no—
268C2×Q8—611no—
269C2×Q8—1221no—
270C2×Q8—2441no—
271C2×Q8—2441no—
272C2×Q8D61⋊C811yescharacteristic
273C2×D4—21no—
274C2×D4—611no—
275C2×D4—1221no—
276C2×D4—1221no—
277C2×D4—1221no—
278C2×D4—1221no—
279C2×D4—2441no—
280C2×D4—2441no—
281C2×D4—2442no—
282C2×D4—2442no—
283C2×D4D61⋊C811yescharacteristic
284C22×C4—21no—
285C22×C4—611no—
286C22×C4—611no—
287C22×C4—611no—
288C22×C4—611no—
289C22×C4—611no—
290C22×C4—1221no—
291C22×C4—1221no—
292C22×C4—1221no—
293C22×C4—1221no—
294C22×C4—1221no—
295C22×C4—1221no—
296C22×C4—1221no—
297C22×C4—1221no—
298C22×C4—2441no—
299C22×C4—2441no—
300C22×C4—2441no—
301C22×C4—2441no—
302C22×C4C22×#692311yescharacteristic
303M16—41no—
304M16—2442no—
305M16—2441no—
306C2×C8—21no—
307C2×C8—41no—
308C2×C8—612no—
309C2×C8—1222no—
310C2×C8—1222no—
311C2×C8—1221no—
312C2×C8—2441no—
313C2×C8—2441no—
314C2×C8—2442no—
315C2×C8—2441no—
316C2×C8C22⋊#692312yes—
317C16—2444no—
318C23—21no—
319C23—611no—
320C23—611no—
321C23—1221no—
322C23—1221no—
323C23—1221no—
324C23—2441no—
325C23—2441no—
326C23—2444no—
327C23—2442no—
328C23D61⋊M1611yescharacteristic
329Q8—41no—
330Q8—2441no—
331Q8—2442no—
332D4—41no—
333D4—42no—
334D4—2441no—
335D4—2442no—
336D4—2442no—
337D4—2442no—
338D4—2442no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—611no—
345C2×C4—611no—
346C2×C4—611no—
347C2×C4—611no—
348C2×C4—611no—
349C2×C4—611no—
350C2×C4—1221no—
351C2×C4—1221no—
352C2×C4—1221no—
353C2×C4—1221no—
354C2×C4—1221no—
355C2×C4—1221no—
356C2×C4—1221no—
357C2×C4—1221no—
358C2×C4—1221no—
359C2×C4—2441no—
360C2×C4—2441no—
361C2×C4—2441no—
362C2×C4—2441no—
363C2×C4—2441no—
364C2×C4—2441no—
365C2×C4—2441no—
366C2×C4—2441no—
367C2×C4C2×C22⋊#692311yescharacteristic
368C2×C4C2×D61⋊C811yescharacteristic
369C8—22no—
370C8—41no—
371C8—1222no—
372C8—2441no—
373C22—21no—
374C22—41no—
375C22—42no—
376C22—41no—
377C22—611no—
378C22—611no—
379C22—1222no—
380C22—1221no—
381C22—4882no—
382C22—4882no—
383C22—2442no—
384C22—2441no—
385C22—2442no—
386C22—2442no—
387C22—2441no—
388C22D61⋊(C22⋊C8)11yescharacteristic
389C4—21no—
390C4—41no—
391C4—611no—
392C4—611no—
393C4—1221no—
394C4—2441no—
395C4D61⋊#9911yescharacteristic
396C4D61⋊#10011yescharacteristic
397C2—21no—
398C2—41no—
399C2—81no—
400C2—612no—
401C2—1221no—
402C2—4881no—
403C2—2441no—
404C2D61⋊#32311yescharacteristic
subgroupG/H
centerC4D61⋊#99
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC61×#408C4
socleC2×C61C2×#323
prime radicalC2×#41×D61C4
cosocleC2×#11758194C23
hypercenter#408#6923
hypocenterC61C2×#1321
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #408

Complements

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

NH ≅ G/Ntype
1. D61⋊#349C2semidirect
2. #21460754C2semidirect
3. #21460753C2semidirect
7. #16840658C22semidirect
206. D61#1321semidirect
219. C61C2×#1321semidirect

Maximal subgroups

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

subgroupindex
D61⋊#3492
#214607542
#214607532
#408×D612
C2×#132161