Finite Group Databasebeta

← #30607577

Subgroups — #30607577

Order 15616.

516 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 84 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#21462578C211yesmaximal, characteristic, complemented
2D61⋊#361C211yesmaximal, characteristic, complemented
3#21462128C211yesmaximal, characteristic, complemented
4#21461980C211yesmaximal, characteristic, complemented
5#21460881C211yesmaximal, characteristic, complemented
6#21460872C211yesmaximal, characteristic, complemented
7C2×D16×D61C211yesmaximal, characteristic
8#16840829—21no—
9D61⋊M32C2211yescharacteristic
10#16840803—22no—
11D8×#6923—22no—
12D61⋊#108C2211yescharacteristic
13#16840772C2211yescharacteristic
14#16840754—21no—
15#16840754—21no—
16D61⋊#100—21no—
17#16840725C2211yescharacteristic
18#16840680—22no—
19#16840674—22no—
20C2×D8×D61C2211yescharacteristic
21C2×D8×D61C2211yescharacteristic
22C2×D976C411yescharacteristic, complemented
23C2×#14519718C411yescharacteristic, complemented
24C2×#14519718C411yescharacteristic, complemented
25D16×D61—22no—
26D16×D61—22no—
27C2×C16×D61C2211yescharacteristic
28C2×D16×C61C411yescharacteristic, complemented
29D61⋊M16—21no—
30D61⋊M16D411yescharacteristic
31D4×#6923—24no—
32D4×#6923—42no—
33#14519856—21no—
34#14519856D411yescharacteristic
35C2×C22⋊#6923—42no—
36#14519852—21no—
37#14519851—21no—
38D61⋊C16—21no—
39#14519848—21no—
40#14519847—21no—
41#14519846D412yes—
42#14519845—21no—
43#14519839—24no—
44#14519839—42no—
45#14519837—42no—
46#14519831—21no—
47C8×#6923—21no—
48C2×D4×D61—21no—
49C2×D4×D61—21no—
50C2×D488C2×C411yescharacteristic
51C2×D488C2×C411yescharacteristic, complemented
52C2×#11758199—21no—
53C2×#11758199—21no—
54D8×D61—21no—
55D8×D61—21no—
56D8×D61—21no—
57D8×D61—21no—
58D8×D61—21no—
59D8×D61—21no—
60D8×D61D412yes—
61D8×D61D412yes—
62C2×C8×D61C2311yescharacteristic
63D976—22no—
64#14519718—22no—
65#14519718—22no—
66C2×#11758185C2×C411yescharacteristic, complemented
67C16×D61—21no—
68C16×D61—21no—
69C2×D8×C61C2×C411yescharacteristic
70C2×D8×C61C2×C411yescharacteristic, complemented
71D16×C61—22no—
72C2×C16×C61C2×C411yescharacteristic, complemented
73C23×D61—41no—
74C23×D61—41no—
75C22×#6923—44no—
76C2×D4×C61—21no—
77C2×D4×C61—21no—
78C2×C22⋊D61—41no—
79C2×C22⋊D61—41no—
80D4×D61—22no—
81D4×D61—22no—
82D4×D61—41no—
83D4×D61—41no—
84D4×D61—41no—
85D4×D61—41no—
86D4×D61—41no—
87D4×D61—41no—
88C2×D244—21no—
89C2×D244—21no—
90C2×C4×D61C2×D411yescharacteristic
91C22⋊#6923—21no—
92C22⋊#6923—44no—
93C22⋊#6923—41no—
94#11758217—21no—
95#11758217—41no—
96C4⋊#6923—22no—
97C4⋊#6923D812yes—
98C4×#6923—21no—
99C4×#6923—41no—
100#11758213—21no—
101#11758213—41no—
102D61⋊C8—21no—
103D61⋊C8—41no—
104D8×C61—21no—
105D8×C61—21no—
106D8×C61—21no—
107D8×C61C22⋊C412yes—
108C2×C8×C61C22×C411yescharacteristic
109#11758199—22no—
110#11758199—22no—
111#11758199—41no—
112#11758199—41no—
113C2×#92418#4111yescharacteristic
114D488—21no—
115D488—21no—
116D488—21no—
117D488C22⋊C412yes—
118C8×D61C2×D411yescharacteristic
119C8×D61C2×D411yescharacteristic
120C8×D61C2×D411yescharacteristic
121C8×D61#4111yescharacteristic
122#11758187—41no—
123C16×C61—21no—
124#11758185—21no—
125C23×C61—41no—
126C23×C61—41no—
127C22×D61—41no—
128C22×D61—42no—
129C22×D61—42no—
130C22×D61—41no—
131C22×D61—81no—
132C22×D61—81no—
133C22×D61—162no—
134C22×D61—162no—
135C22×D61AGL(1,ℤ/8)11yescharacteristic
136C2×#6923—22no—
137C2×#6923—42no—
138C2×#6923—164no—
139D4×C61—22no—
140D4×C61—41no—
141D4×C61—41no—
142D4×C61—41no—
143C2×C4×C61C4×D411yescharacteristic
144C22⋊D61—42no—
145C22⋊D61—42no—
146C22⋊D61—81no—
147C22⋊D61—81no—
148C2×Dic61AGL(1,ℤ/8)11yescharacteristic
149D244—22no—
150D244—41no—
151D244—41no—
152D244—41no—
153C4×D61#12011yescharacteristic
154C4×D61#12111yescharacteristic
155C4×D61C2×D811yescharacteristic
156C4×D61#13511yescharacteristic
157#92420—41no—
158#92420—81no—
159C8×C61C2×C22⋊C411yescharacteristic
160C8×C61C4×D411yescharacteristic
161#92418#12111yescharacteristic
162#92418#12311yescharacteristic
163#13017—611nomaximal, Sylow
164C22×C61—42no—
165C22×C61—81no—
166C22×C61—161no—
167C22×C61—161no—
168C22×C61#44211yescharacteristic
169C2×D61—22no—
170C2×D61—42no—
171C2×D61—84no—
172C2×D61—81no—
173C2×D61—162no—
174C2×D61—162no—
175C2×D61—161no—
176C2×D61—162no—
177C2×D61—161no—
178C2×D61#44711yescharacteristic
179C2×D61#46311yescharacteristic
180#6923—42no—
181#6923—82no—
182C4×C61#38611yescharacteristic
183C4×C61C4×D811yescharacteristic
184Dic61#44911yescharacteristic
185Dic61#45911yescharacteristic
186C22×D16—611no—
187#2948—611no—
188C2×#361—611no—
189#2140—611no—
190#1978—611no—
191#1382—611no—
192#1379—611no—
193C2×C61—21no—
194C2×C61—82no—
195C2×C61—161no—
196C2×C61#187911yescharacteristic
197D61—21no—
198D61—82no—
199D61—161no—
200D61#219212yes—
201C22×D8—611no—
202C22×D8—611no—
203#518—1221no—
204C2×D16—611no—
205C2×D16—611no—
206C2×D16—611no—
207C2×D16—1222no—
208C2×D16—1222no—
209C2×D16#692311yescharacteristic, complemented
210C2×M32—611no—
211C22×C16—611no—
212#442—1222no—
213C4×D8—1222no—
214C2×#108—611no—
215#427—611no—
216#418—1221no—
217#418—1221no—
218C2×#100—1221no—
219#405—611no—
220#361—1222no—
221#357—1222no—
222C61#1301711yescharacteristic, complemented, Sylow
223C22×D4—1221no—
224C22×D4—1221no—
225C2×D8—612no—
226C2×D8—612no—
227C2×D8—611no—
228C2×D8—611no—
229C2×D8—1221no—
230C2×D8—1221no—
231C2×D8—1221no—
232C2×D8—1221no—
233C2×D8—1221no—
234C2×D8—1221no—
235C2×D8—1221no—
236C2×D8—1221no—
237C2×D8C2×#692311yescharacteristic
238C2×D8C2×#692311yescharacteristic, complemented
239C2×M16—611no—
240C2×M16—1221no—
241C22×C8—611no—
242C4×D4—1224no—
243C4×D4—2442no—
244#117—611no—
245#117—1221no—
246C2×C22⋊C4—2442no—
247D16—22no—
248D16—1222no—
249D16—1222no—
250D16—1222no—
251M32—1221no—
252M32—1221no—
253C2×C16—611no—
254C2×C16—1221no—
255C2×C16—1221no—
256C2×C16—1221no—
257C2×C16C2×#692311yescharacteristic, complemented
258#108—1221no—
259#108—1221no—
260#107—612no—
261#106—1221no—
262#102—1224no—
263#102—2442no—
264#100—2442no—
265#97—1221no—
266C4×C8—1221no—
267C24—2441no—
268C24—2441no—
269C2×D4—21no—
270C2×D4—21no—
271C2×D4—1222no—
272C2×D4—1222no—
273C2×D4—1221no—
274C2×D4—1221no—
275C2×D4—2441no—
276C2×D4—2441no—
277C2×D4—2441no—
278C2×D4—2441no—
279C2×D4—2441no—
280C2×D4—2441no—
281C2×D4—2441no—
282C2×D4—2441no—
283C22×C4—611no—
284C22×C4—2444no—
285D8—21no—
286D8—21no—
287D8—21no—
288D8—612no—
289D8—1222no—
290D8—1222no—
291D8—1221no—
292D8—1221no—
293D8—1221no—
294D8—2441no—
295D8—2441no—
296D8C22⋊#692312yes—
297M16—1221no—
298M16—1221no—
299M16—2441no—
300M16—2441no—
301C2×C8—611no—
302C2×C8—611no—
303C2×C8—611no—
304C2×C8—611no—
305C2×C8—611no—
306C2×C8—1221no—
307C2×C8—2441no—
308C2×C8C22×#692311yescharacteristic
309C4⋊C4—612no—
310C4⋊C4—1222no—
311C22⋊C4—1221no—
312C22⋊C4—2444no—
313C22⋊C4—2441no—
314C42—1221no—
315C42—2441no—
316C16—21no—
317C16—1221no—
318C16—2441no—
319C23—41no—
320C23—41no—
321C23—611no—
322C23—9762no—
323C23—9762no—
324C23—4881no—
325C23—4881no—
326C23—2442no—
327C23—2442no—
328C23—2441no—
329C23—2441no—
330D4—22no—
331D4—41no—
332D4—41no—
333D4—41no—
334D4—1222no—
335D4—4881no—
336D4—4881no—
337D4—2442no—
338D4—2442no—
339D4—2441no—
340D4—2441no—
341D4—2441no—
342C2×C4—611no—
343C2×C4—611no—
344C2×C4—611no—
345C2×C4—611no—
346C2×C4—611no—
347C2×C4—1222no—
348C2×C4—9764no—
349C2×C4—2442no—
350C2×C4D4×#692311yescharacteristic
351C8—611no—
352C8—611no—
353C8—4881no—
354C8—2441no—
355C8C2×C22⋊#692311yescharacteristic
356C8D4×#692311yescharacteristic
357C22—42no—
358C22—81no—
359C22—161no—
360C22—161no—
361C22—611no—
362C22—611no—
363C22—1222no—
364C22—9761no—
365C22—9761no—
366C22—9762no—
367C22—9762no—
368C22—9762no—
369C22—4884no—
370C22—4881no—
371C22—2442no—
372C22#1684080311yescharacteristic
373C4—611no—
374C4—611no—
375C4—4882no—
376C4—2442no—
377C4#1684071011yescharacteristic
378C4D8×#692311yescharacteristic
379C2—21no—
380C2—82no—
381C2—161no—
382C2—612no—
383C2—1221no—
384C2—9761no—
385C2—4882no—
386C2#2146181411yescharacteristic
subgroupG/H
centerC2#21461814
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC2×D16×C61C4
socleC2×C61#1879
prime radicalC2×D16×D61C2
cosocleC2×C8×D61C23
hypercenterC2×D16#6923
hypocenterC61#13017
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×D16

Complements

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

NH ≅ G/Ntype
1. #21462578C2semidirect
2. D61⋊#361C2semidirect
3. #21462128C2semidirect
4. #21461980C2semidirect
5. #21460881C2semidirect
6. #21460872C2semidirect
22. C2×D976C4semidirect
23. C2×#14519718C4semidirect
24. C2×#14519718C4semidirect
28. C2×D16×C61C4semidirect
51. C2×D488C2×C4semidirect
66. C2×#11758185C2×C4semidirect
70. C2×D8×C61C2×C4semidirect
72. C2×C16×C61C2×C4semidirect
209. C2×D16#6923semidirect
222. C61#13017semidirect
238. C2×D8C2×#6923semidirect
257. C2×C16C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214625782
D61⋊#3612
#214621282
#214619802
#214608812
#214608722
C2×D16×D612
#1301761