Finite Group Databasebeta

← D61×#1321 #29589136

Subgroups — D61×#1321 #29589136

Order 15616.

518 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 91 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#408×D61C211yesmaximal, characteristic
2#349×D61C212yesmaximal, complemented
3#21443757C211yesmaximal, characteristic, complemented
4#21443756C212yesmaximal, complemented
5C61×#1321C211yesmaximal, characteristic, complemented
6C2×#41×D61C411yescharacteristic
7C2×M16×D61C2211yescharacteristic
8C22×C8×D61C411yescharacteristic
9M32×D61—22no—
10#16839730C2211yescharacteristic
11#16839729C411yescharacteristic
12#16839728C411yescharacteristic
13#16839727—22no—
14C22⋊C8×D61—22no—
15#16839544C2212yescomplemented
16#16839543—22no—
17C61×#408C2211yescharacteristic
18C61×#349C2212yescomplemented
19C2×#11758226C811yescharacteristic
20C2×#11758222—21no—
21C2×#11758222C2×C411yescharacteristic
22C2×#11758224—21no—
23C2×#11758224C811yescharacteristic
24#41×D61—41no—
25#41×D61—41no—
26#41×D61—41no—
27#41×D61—41no—
28C2×Q8×D61C811yescharacteristic
29C2×D4×D61—21no—
30C2×D4×D61C811yescharacteristic
31C22×C4×D61—21no—
32C22×C4×D61C2×C411yescharacteristic
33C2×#11758194C2×C411yescharacteristic
34C2×#11758189D412yes—
35M16×D61—41no—
36M16×D61—41no—
37C22×#92418C2×C411yescharacteristic
38C2×C8×D61—21no—
39C2×C8×D61—21no—
40C2×C8×D61—41no—
41C2×C8×D61—41no—
42C2×C8×D61D412yes—
43#14519717—22no—
44#14519716—42no—
45C16×D61—42no—
46C22⋊#92418—22no—
47#14519689—22no—
48#14519689—22no—
49C2×#41×C61C2×C411yescharacteristic
50C2×M16×C61C2311yescharacteristic
51C22×C8×C61C2×C411yescharacteristic
52M32×C61—22no—
53C22⋊C8×C61—22no—
54C23×D61—21no—
55C23×D61M1611yescharacteristic
56#41×C61—41no—
57#41×C61—41no—
58C2×Q8×C61C2×C811yescharacteristic
59C2×D4×C61—21no—
60C2×D4×C61C2×C811yescharacteristic
61C22×C4×C61—21no—
62C22×C4×C61C22×C411yescharacteristic
63C2×C22⋊D61—21no—
64C2×C22⋊D61—21no—
65C2×C22⋊D61—21no—
66C22×Dic61—21no—
67C22×Dic61M1611yescharacteristic
68#11758226—41no—
69#11758226—41no—
70Q8×D61—41no—
71Q8×D61—41no—
72#11758224—41no—
73#11758224—41no—
74#11758224—42no—
75#11758224—42no—
76D4×D61—41no—
77D4×D61—41no—
78D4×D61—42no—
79D4×D61—42no—
80#11758222—42no—
81#11758222—42no—
82#11758222—41no—
83#11758222—41no—
84C2×D244—21no—
85C2×D244C2×C811yescharacteristic
86C2×C4×D61—21no—
87C2×C4×D61—21no—
88C2×C4×D61—21no—
89C2×C4×D61—21no—
90C2×C4×D61—21no—
91C2×C4×D61—21no—
92C2×C4×D61—21no—
93C2×C4×D61—41no—
94C2×C4×D61—41no—
95C2×C4×D61—41no—
96C2×C4×D61—41no—
97C2×C4×D61C22⋊C411yescharacteristic
98C2×C4×D61C22⋊C411yescharacteristic
99C2×C4×D61C2×C811yescharacteristic
100C2×C4×D61C2×C811yescharacteristic
101C2×Dic122—21no—
102C2×Dic122C2×C811yescharacteristic
103M16×C61—41no—
104C2×C8×C61—21no—
105C2×C8×C61—41no—
106C2×C8×C61C2×D412yes—
107#11758194—41no—
108C2×#92418—21no—
109C2×#92418—41no—
110C2×#92418C22⋊C412yes—
111#11758189—42no—
112C8×D61—22no—
113C8×D61—22no—
114C8×D61—42no—
115C8×D61—41no—
116C8×D61—41no—
117C16×C61—42no—
118#11758185—42no—
119C23×C61—21no—
120C23×C61C2×M1611yescharacteristic
121C22×D61—21no—
122C22×D61—21no—
123C22×D61—21no—
124C22×D61—42no—
125C22×D61—44no—
126C22×D61—41no—
127C22×D61—41no—
128C22×D61C22⋊C811yescharacteristic
129C22×D61C22⋊C811yescharacteristic
130Q8×C61—41no—
131D4×C61—41no—
132D4×C61—42no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61C2×C22⋊C411yescharacteristic
139C2×C4×C61C22×C811yescharacteristic
140C22⋊D61—42no—
141C22⋊D61—42no—
142C22⋊D61—42no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61C22⋊C811yescharacteristic
149C2×Dic61C22⋊C811yescharacteristic
150D244—41no—
151D244—42no—
152C4×D61—21no—
153C4×D61—21no—
154C4×D61—21no—
155C4×D61—21no—
156C4×D61—21no—
157C4×D61—21no—
158C4×D61—41no—
159C4×D61—41no—
160C4×D61—41no—
161C4×D61—41no—
162C4×D61—41no—
163C4×D61—41no—
164C4×D61#9911yescharacteristic
165C4×D61#9911yescharacteristic
166C4×D61#10011yescharacteristic
167C4×D61#10011yescharacteristic
168Dic122—42no—
169Dic122—41no—
170C8×C61—22no—
171C8×C61—41no—
172#92418—22no—
173#92418—41no—
174C2×#1321—611nomaximal, Sylow
175C22×C61—21no—
176C22×C61—41no—
177C22×C61—42no—
178C22×C61—41no—
179C22×C61C2×C22⋊C811yescharacteristic
180C2×D61—22no—
181C2×D61—21no—
182C2×D61—42no—
183C2×D61—42no—
184C2×D61—41no—
185C2×D61—42no—
186C2×D61—41no—
187C2×D61—82no—
188C2×D61—82no—
189C2×D61#32311yescharacteristic
190C2×D61#32311yescharacteristic
191C4×C61—21no—
192C4×C61—41no—
193C4×C61C2×#9911yescharacteristic
194C4×C61C2×#10011yescharacteristic
195Dic61—21no—
196Dic61—41no—
197Dic61#32311yescharacteristic
198Dic61#32311yescharacteristic
199C2×#408—611no—
200C2×#349—612no—
201#1321—611no—
202#1321—612no—
203#1321D6111yescharacteristic, direct product factor
204C2×C61—21no—
205C2×C61—41no—
206C2×C61—81no—
207C2×C61C2×#32311yescharacteristic
208D61—21no—
209D61—41no—
210D61—81no—
211D61#132112yesdirect product factor
212C22×#41—611no—
213C22×M16—611no—
214C23×C8—611no—
215C2×M32—1222no—
216#408—611no—
217#408—611no—
218#408—611no—
219#408—1222no—
220#408C2×D6111yescharacteristic
221C2×C22⋊C8—1222no—
222#349—612no—
223#349—1222no—
224#349C2×D6112yescomplemented
225C61C2×#132111yescharacteristic, complemented, Sylow
226C2×#41—611no—
227C2×#41—611no—
228C2×#41—611no—
229C2×#41—1221no—
230C2×#41—1221no—
231C2×#41—2441no—
232C2×#41—2441no—
233C2×#41—2441no—
234C2×#41—2441no—
235C2×#41C4×D6111yescharacteristic
236C22×Q8—611no—
237C22×D4—611no—
238C22×D4—1221no—
239C23×C4—611no—
240C23×C4—1221no—
241C2×M16—611no—
242C2×M16—612no—
243C2×M16—2441no—
244C2×M16—2441no—
245C2×M16C22×D6111yescharacteristic
246C22×C8—612no—
247C22×C8—611no—
248C22×C8—1221no—
249C22×C8—1221no—
250C22×C8—2441no—
251C22×C8—2441no—
252C22×C8C4×D6111yescharacteristic
253M32—22no—
254M32—1222no—
255M32—2442no—
256C2×C16—2442no—
257C22⋊C8—22no—
258C22⋊C8—1222no—
259C22⋊C8—1222no—
260C22⋊C8—1222no—
261C24—611no—
262C24—1221no—
263#41—41no—
264#41—41no—
265#41—2441no—
266#41—2441no—
267#41—2442no—
268#41—2442no—
269#41—2442no—
270#41—2442no—
271#41—2441no—
272#41—2441no—
273#41—2441no—
274#41—2441no—
275C2×Q8—611no—
276C2×Q8—1221no—
277C2×Q8—2441no—
278C2×Q8—2441no—
279C2×Q8C8×D6111yescharacteristic
280C2×D4—21no—
281C2×D4—611no—
282C2×D4—1221no—
283C2×D4—1221no—
284C2×D4—1221no—
285C2×D4—1221no—
286C2×D4—2441no—
287C2×D4—2441no—
288C2×D4—2442no—
289C2×D4—2442no—
290C2×D4C8×D6111yescharacteristic
291C22×C4—21no—
292C22×C4—611no—
293C22×C4—611no—
294C22×C4—611no—
295C22×C4—611no—
296C22×C4—611no—
297C22×C4—1221no—
298C22×C4—1221no—
299C22×C4—1221no—
300C22×C4—1221no—
301C22×C4—1221no—
302C22×C4—1221no—
303C22×C4—1221no—
304C22×C4—1221no—
305C22×C4—2441no—
306C22×C4—2441no—
307C22×C4—2441no—
308C22×C4—2441no—
309C22×C4C2×C4×D6111yescharacteristic
310M16—41no—
311M16—2442no—
312M16—2441no—
313C2×C8—21no—
314C2×C8—41no—
315C2×C8—612no—
316C2×C8—1222no—
317C2×C8—1222no—
318C2×C8—1221no—
319C2×C8—2441no—
320C2×C8—2441no—
321C2×C8—2442no—
322C2×C8—2441no—
323C2×C8D4×D6112yes—
324C16—42no—
325C16—2442no—
326C23—21no—
327C23—611no—
328C23—611no—
329C23—1221no—
330C23—1221no—
331C23—1221no—
332C23—2441no—
333C23—2441no—
334C23—2444no—
335C23—2442no—
336C23M16×D6111yescharacteristic
337Q8—41no—
338Q8—2441no—
339Q8—2442no—
340D4—41no—
341D4—42no—
342D4—2441no—
343D4—2442no—
344D4—2442no—
345D4—2442no—
346D4—2442no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—611no—
353C2×C4—611no—
354C2×C4—611no—
355C2×C4—611no—
356C2×C4—611no—
357C2×C4—611no—
358C2×C4—1221no—
359C2×C4—1221no—
360C2×C4—1221no—
361C2×C4—1221no—
362C2×C4—1221no—
363C2×C4—1221no—
364C2×C4—1221no—
365C2×C4—1221no—
366C2×C4—1221no—
367C2×C4—2441no—
368C2×C4—2441no—
369C2×C4—2441no—
370C2×C4—2441no—
371C2×C4—2441no—
372C2×C4—2441no—
373C2×C4—2441no—
374C2×C4—2441no—
375C2×C4C22⋊C4×D6111yescharacteristic
376C2×C4C2×C8×D6111yescharacteristic
377C8—22no—
378C8—41no—
379C8—1222no—
380C8—2441no—
381C22—21no—
382C22—41no—
383C22—42no—
384C22—41no—
385C22—611no—
386C22—611no—
387C22—1222no—
388C22—1221no—
389C22—4882no—
390C22—4882no—
391C22—2442no—
392C22—2441no—
393C22—2442no—
394C22—2442no—
395C22—2441no—
396C22C22⋊C8×D6111yescharacteristic
397C4—21no—
398C4—41no—
399C4—611no—
400C4—611no—
401C4—1221no—
402C4—2441no—
403C4#99×D6111yescharacteristic
404C4#100×D6111yescharacteristic
405C2—21no—
406C2—41no—
407C2—81no—
408C2—612no—
409C2—1221no—
410C2—4881no—
411C2—2441no—
412C2#323×D6111yescharacteristic
subgroupG/H
centerC4#99×D61
commutatorC2×C4×C61C22×C8
FrattiniC2×M16C22×D61
FittingC61×#1321C2
socleC2×C61C2×#323
prime radicalC2×#41×D61C4
cosocleC2×M16×C61C23
hypercenter#1321D61
hypocenterC61C2×#1321
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #1321

Complements

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

NH ≅ G/Ntype
2. #349×D61C2semidirect
3. #21443757C2semidirect
4. #21443756C2semidirect
5. C61×#1321C2semidirect
15. #16839544C22semidirect
18. C61×#349C22semidirect
203. #1321D61direct (N × H)
211. D61#1321direct (N × H)
224. #349C2×D61semidirect
225. C61C2×#1321semidirect

Maximal subgroups

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

subgroupindex
#408×D612
#349×D612
#214437572
#214437562
C61×#13212
C2×#132161