Finite Group Databasebeta

← D61⋊#1354 #30604830

Subgroups — D61⋊#1354 #30604830

Order 15616.

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

normal subgroups only

This group has 652 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
1#21461522C211yesmaximal, characteristic
2D61⋊#324C211yesmaximal, characteristic
3#21460820C212yesmaximal, complemented
4#21460819C212yesmaximal, complemented
5#395×D61C211yesmaximal, characteristic
6C2×D61⋊M16—21no—
7D61⋊(C22⋊C8)—21no—
8#16840642—21no—
9#16840642C2212yes—
10#16840608C2212yes—
11#16840607—21no—
12C22×Q8×D61C411yescharacteristic
13C2×C4⋊C4×D61—21no—
14C2×C4⋊C4×D61C2211yescharacteristic
15#16839683—21no—
16#16839683C2211yescharacteristic
17#16839682—21no—
18#16839682C411yescharacteristic
19#16839681C2211yescharacteristic
20#95×D61—21no—
21#95×D61C411yescharacteristic
22C61×#395C411yescharacteristic
23C2×#11758213—41no—
24D61⋊M16—24no—
25D61⋊M16—42no—
26C2×#11758217—22no—
27C2×D61⋊C8—41no—
28C2×D61⋊C8—41no—
29#14519834—41no—
30C22⋊#92420—22no—
31C22×Dic122—21no—
32C22×Dic122C2×C411yescharacteristic
33C2×Q8×D61—44no—
34C2×Q8×D61—41no—
35C2×Q8×D61—41no—
36C22×C4×D61—21no—
37C22×C4×D61—21no—
38C22×C4×D61C2×C411yescharacteristic
39C22×C4×D61D411yescharacteristic
40C22×C4×D61D411yescharacteristic
41C2×C4⋊Dic61—21no—
42C2×C4⋊Dic61D411yescharacteristic
43C2×#11758196—21no—
44C2×#11758196—21no—
45C2×#11758196D411yescharacteristic
46C2×#11758196C2311yescharacteristic
47C4⋊C4×D61—41no—
48C4⋊C4×D61—41no—
49C4⋊C4×D61—44no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684C2×C411yescharacteristic
55C22×Q8×C61C2×C411yescharacteristic
56C2×C4⋊C4×C61—21no—
57C2×C4⋊C4×C61C2×C411yescharacteristic
58#95×C61—21no—
59#95×C61C2×C411yescharacteristic
60C23×D61C22⋊C411yescharacteristic
61C2×Q8×C61—42no—
62C2×Q8×C61—41no—
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61C22⋊C411yescharacteristic
66C22×C4×C61C22⋊C411yescharacteristic
67C22×C4×C61C22×C411yescharacteristic
68C22×Dic61—21no—
69C22×Dic61—21no—
70C22×Dic61C22⋊C411yescharacteristic
71C22×Dic61C2×D411yescharacteristic
72C22×Dic61C2×D411yescharacteristic
73Q8×D61—44no—
74Q8×D61—44no—
75Q8×D61—44no—
76Q8×D61—44no—
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×C4×D61—22no—
80C2×C4×D61—24no—
81C2×C4×D61—24no—
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×C4×D61—21no—
86C2×C4×D61—42no—
87C2×C4×D61—42no—
88C2×C4×D61—41no—
89C2×C4×D61—41no—
90C2×C4×D61—42no—
91C2×C4×D61—42no—
92C2×C4×D61—42no—
93C2×C4×D61SD1612yes—
94C2×C4×D61Q1612yes—
95C2×Dic122—42no—
96C2×Dic122—42no—
97C2×Dic122—42no—
98C2×Dic122—41no—
99C2×Dic122—42no—
100#11758217—24no—
101#11758217—42no—
102C2×#92420—42no—
103C2×#92420—42no—
104#11758213—44no—
105D61⋊C8—44no—
106D61⋊C8—82no—
107C4⋊C4×C61—41no—
108C4⋊C4×C61—42no—
109C4⋊Dic61—41no—
110C4⋊Dic61—42no—
111#11758196—41no—
112#11758196—41no—
113#11758196—42no—
114#11758196—42no—
115C23×C61C2×C22⋊C411yescharacteristic
116C22×D61—22no—
117C22×D61—22no—
118C22×D61#9911yescharacteristic
119C22×D61#9911yescharacteristic
120C22×D61#10312yes—
121C22×D61#10412yes—
122Q8×C61—42no—
123Q8×C61—42no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—22no—
127C2×C4×C61—22no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61#10312yes—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—22no—
140C2×Dic61—22no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61C2×SD1611yescharacteristic
150C2×Dic61C2×Q1611yescharacteristic
151C4×D61—22no—
152C4×D61—22no—
153C4×D61—22no—
154C4×D61—22no—
155C4×D61—48no—
156C4×D61—42no—
157C4×D61—44no—
158C4×D61—42no—
159C4×D61—44no—
160C4×D61—42no—
161C4×D61—81no—
162Dic122—48no—
163Dic122—42no—
164Dic122—42no—
165#92420—44no—
166#92420—82no—
167C2×#1354—611nomaximal, Sylow
168C22×C61—21no—
169C22×C61—21no—
170C22×C61C2×#9911yescharacteristic
171C22×C61C2×#10311yescharacteristic
172C22×C61C2×#10411yescharacteristic
173C2×D61—21no—
174C2×D61—21no—
175C2×D61—24no—
176C2×D61—24no—
177C2×D61#32812yes—
178C2×D61#32812yes—
179C2×D61AΣL(1,𝔽16)12yes—
180C2×D61#35612yes—
181C4×C61—22no—
182C4×C61—42no—
183C4×C61—42no—
184C4×C61—41no—
185C4×C61—41no—
186Dic61—21no—
187Dic61—21no—
188Dic61—42no—
189Dic61—41no—
190Dic61—41no—
191Dic61—42no—
192C2×#395—611no—
193C2×#343—611no—
194C2×#324—611no—
195#1354—612no—
196#1354—612no—
197C2×C61—21no—
198C2×C61—21no—
199C2×C61C2×#32811yescharacteristic
200C2×C61C2×AΣL(1,𝔽16)11yescharacteristic
201C2×C61C2×#35611yescharacteristic
202D61—22no—
203D61#135414yescomplemented
204C23×Q8—611no—
205C22×M16—1221no—
206C22×C4⋊C4—611no—
207C22×C4⋊C4—1221no—
208C2×C22⋊C8—1221no—
209#395—611no—
210#395—611no—
211#395—611no—
212#395—1221no—
213#395—1221no—
214#395#692311yescharacteristic
215C2×#95—611no—
216C2×#95—1221no—
217#343—612no—
218#343—1221no—
219#324—612no—
220#324—1221no—
221C61C2×#135411yescharacteristic, complemented, Sylow
222C22×Q8—611no—
223C22×Q8—1221no—
224C22×Q8—2444no—
225C22×Q8—2441no—
226C22×Q8—2441no—
227C22×Q8C2×#692311yescharacteristic
228C23×C4—611no—
229C23×C4—611no—
230C23×C4—611no—
231C23×C4—1221no—
232C23×C4—1221no—
233C2×M16—1222no—
234C2×M16—1224no—
235C2×M16—2442no—
236C2×M16—2441no—
237C22×C8—2441no—
238C22×C8—2441no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—611no—
241C2×C4⋊C4—611no—
242C2×C4⋊C4—611no—
243C2×C4⋊C4—1221no—
244C2×C4⋊C4—1221no—
245C2×C4⋊C4—1221no—
246C2×C4⋊C4—2441no—
247C2×C4⋊C4—2441no—
248C2×C4⋊C4—2444no—
249C2×C4⋊C4C2×#692311yescharacteristic
250C22⋊C8—1222no—
251C22⋊C8—2441no—
252#95—21no—
253#95—611no—
254#95—1221no—
255#95—1221no—
256#95—1221no—
257#95—1221no—
258#95C2×#692311yescharacteristic
259C24—611no—
260C2×Q8—42no—
261C2×Q8—41no—
262C2×Q8—2442no—
263C2×Q8—2441no—
264C2×Q8—2442no—
265C2×Q8—2442no—
266C2×Q8—2442no—
267C2×Q8—2444no—
268C2×Q8—2444no—
269C2×Q8—2444no—
270C2×Q8—2444no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—611no—
274C22×C4—612no—
275C22×C4—612no—
276C22×C4—611no—
277C22×C4—611no—
278C22×C4—1221no—
279C22×C4—1221no—
280C22×C4—1222no—
281C22×C4—1221no—
282C22×C4—1221no—
283C22×C4—1221no—
284C22×C4—1221no—
285C22×C4—1224no—
286C22×C4—1224no—
287C22×C4—1221no—
288C22×C4—1221no—
289C22×C4—2442no—
290C22×C4—2441no—
291C22×C4—2441no—
292C22×C4—2442no—
293C22×C4—2442no—
294C22×C4—2442no—
295C22×C4—2442no—
296C22×C4C22⋊#692311yescharacteristic
297C22×C4C22⋊#692311yescharacteristic
298C22×C4C22×#692311yescharacteristic
299M16—1224no—
300M16—2442no—
301M16—2444no—
302C2×C8—4882no—
303C2×C8—2442no—
304C2×C8—2444no—
305C2×C8—2442no—
306C4⋊C4—41no—
307C4⋊C4—42no—
308C4⋊C4—2441no—
309C4⋊C4—2441no—
310C4⋊C4—2441no—
311C4⋊C4—2442no—
312C4⋊C4—2442no—
313C4⋊C4—2442no—
314C23—611no—
315C23—611no—
316C23—612no—
317C23—612no—
318C23—1222no—
319C23—1222no—
320C23C2×C22⋊#692311yescharacteristic
321Q8—42no—
322Q8—42no—
323Q8—2442no—
324Q8—2448no—
325Q8—2442no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—611no—
339C2×C4—611no—
340C2×C4—1222no—
341C2×C4—1222no—
342C2×C4—1222no—
343C2×C4—1222no—
344C2×C4—1221no—
345C2×C4—1221no—
346C2×C4—1222no—
347C2×C4—1222no—
348C2×C4—1221no—
349C2×C4—1221no—
350C2×C4—4881no—
351C2×C4—2442no—
352C2×C4—2444no—
353C2×C4—2442no—
354C2×C4—2448no—
355C2×C4—2444no—
356C2×C4—2442no—
357C2×C4—2441no—
358C2×C4—2441no—
359C2×C4—2441no—
360C2×C4—2441no—
361C2×C4—2441no—
362C2×C4—2441no—
363C2×C4#1451984012yes—
364C8—4882no—
365C8—2444no—
366C22—21no—
367C22—21no—
368C22—612no—
369C22—612no—
370C22—612no—
371C22—612no—
372C22—1224no—
373C22—1224no—
374C22—1221no—
375C22—1221no—
376C22D61⋊#9911yescharacteristic
377C22C2×#1451984011yescharacteristic
378C22D61⋊#10411yescharacteristic
379C4—22no—
380C4—42no—
381C4—42no—
382C4—41no—
383C4—41no—
384C4—1221no—
385C4—1221no—
386C4—2442no—
387C4—2441no—
388C4—2442no—
389C4—2441no—
390C2—21no—
391C2—21no—
392C2—614no—
393C2—1222no—
394C2D61⋊#32811yescharacteristic
395C2D61⋊AΣL(1,𝔽16)11yescharacteristic
396C2D61⋊#35611yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#395C4
socleC22×C61C2×#99
prime radicalC23×D61C22⋊C4
cosocleC2×#11758196C23
hypercenter#395#6923
hypocenterC61C2×#1354
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #395

Complements

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

NH ≅ G/Ntype
3. #21460820C2semidirect
4. #21460819C2semidirect
203. D61#1354semidirect
221. C61C2×#1354semidirect

Maximal subgroups

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

subgroupindex
#214615222
D61⋊#3242
#214608202
#214608192
#395×D612
C2×#135461