Finite Group Databasebeta

← #30607597

Subgroups — #30607597

Order 15616.

498 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 82 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
2#21462141C211yesmaximal, characteristic, complemented
3#21462128C211yesmaximal, characteristic, complemented
4#21461978C211yesmaximal, characteristic, complemented
5#21460887C211yesmaximal, characteristic, complemented
6#21460868C211yesmaximal, characteristic, complemented
7C2×#16840199C211yesmaximal, characteristic
8#16840829—21no—
9D61⋊M32C2211yescharacteristic
10#16840803—22no—
11D8×#6923—22no—
12#16840772C2211yescharacteristic
13#16840772C2211yescharacteristic
14#16840761—21no—
15#16840754—21no—
16#16840743—21no—
17#16840725C2211yescharacteristic
18#16840679—22no—
19#16840674—22no—
20C2×#14519800C2211yescharacteristic
21C2×D8×D61C2211yescharacteristic
22#16840199—22no—
23#16840199—22no—
24C2×#14519720C411yescharacteristic, complemented
25C2×D976C411yescharacteristic, complemented
26C2×#14519718C411yescharacteristic, complemented
27C2×#14519716C2211yescharacteristic
28C2×SD32×C61C411yescharacteristic, complemented
29D61⋊M16D411yescharacteristic
30D4×#6923—24no—
31D4×#6923—42no—
32#14519856—21no—
33#14519856—21no—
34#14519856D411yescharacteristic
35C2×C22⋊#6923—42no—
36#14519852—21no—
37#14519851—21no—
38D61⋊C16—21no—
39#14519846—21no—
40#14519846—21no—
41#14519845—21no—
42#14519845D412yes—
43#14519842—42no—
44#14519839—24no—
45#14519836—42no—
46#14519831—21no—
47C8×#6923—21no—
48C2×#11758226—21no—
49C2×D4×D61—21no—
50#14519800—21no—
51#14519800—21no—
52#14519800—21no—
53#14519800—21no—
54C2×#11758201—21no—
55C2×D488C2×C411yescharacteristic
56C2×D488C2×C411yescharacteristic, complemented
57C2×#11758199—21no—
58D8×D61—21no—
59D8×D61—21no—
60D8×D61D412yes—
61D8×D61D412yes—
62C2×C8×D61C2311yescharacteristic
63#14519720—22no—
64D976—22no—
65#14519718—22no—
66#14519716—21no—
67#14519716—21no—
68C2×#11758185C2×C411yescharacteristic, complemented
69C2×Q16×C61C2×C411yescharacteristic, complemented
70C2×D8×C61C2×C411yescharacteristic
71SD32×C61—22no—
72C2×C16×C61C2×C411yescharacteristic, complemented
73C23×D61—41no—
74C22×#6923—44no—
75C2×Q8×C61—21no—
76C2×D4×C61—21no—
77C2×C22⋊D61—41no—
78#11758226—41no—
79#11758226—41no—
80#11758226—41no—
81#11758226—41no—
82D4×D61—22no—
83D4×D61—22no—
84D4×D61—41no—
85D4×D61—41no—
86C2×D244—21no—
87C2×D244—21no—
88C2×D244—41no—
89C2×C4×D61—41no—
90C2×C4×D61C2×D411yescharacteristic
91C22⋊#6923—44no—
92C22⋊#6923—41no—
93C22⋊#6923—41no—
94C22⋊#6923D812yes—
95#11758217—21no—
96C4⋊#6923—22no—
97C4⋊#6923—21no—
98C4⋊#6923—41no—
99C4×#6923—21no—
100C4×#6923—41no—
101C4×#6923—41no—
102#11758213—21no—
103D61⋊C8—21no—
104Q16×C61—21no—
105Q16×C61—21no—
106D8×C61—21no—
107D8×C61C22⋊C412yes—
108C2×C8×C61C22×C411yescharacteristic
109#11758201—41no—
110#11758201—41no—
111#11758199—22no—
112#11758199—22no—
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—
126C22×D61—41no—
127C22×D61—42no—
128C22×D61—42no—
129C22×D61—41no—
130C22×D61—162no—
131C22×D61C2×D811yescharacteristic
132C2×#6923—22no—
133C2×#6923—42no—
134C2×#6923—81no—
135C2×#6923—164no—
136Q8×C61—41no—
137Q8×C61—41no—
138D4×C61—22no—
139D4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61C4×D411yescharacteristic
142C22⋊D61—42no—
143C22⋊D61—42no—
144C2×Dic61#13511yescharacteristic
145D244—22no—
146D244—41no—
147D244—41no—
148D244—41no—
149D244—81no—
150D244—81no—
151C4×D61—81no—
152C4×D61—81no—
153C4×D61#12011yescharacteristic
154C4×D61#12111yescharacteristic
155C4×D61AGL(1,ℤ/8)11yescharacteristic
156C4×D61AGL(1,ℤ/8)11yescharacteristic
157#92420—41no—
158C8×C61C2×C22⋊C411yescharacteristic
159C8×C61C4×D411yescharacteristic
160#92418#12111yescharacteristic
161#92418#12311yescharacteristic
162#13033—611nomaximal, Sylow
163C22×C61—42no—
164C22×C61—161no—
165C22×C61C4×D811yescharacteristic
166C2×D61—41no—
167C2×D61—42no—
168C2×D61—84no—
169C2×D61—81no—
170C2×D61—162no—
171C2×D61—161no—
172C2×D61—161no—
173C2×D61#44711yescharacteristic
174C2×D61#45911yescharacteristic
175#6923—42no—
176#6923—82no—
177#6923—161no—
178C4×C61—81no—
179C4×C61#38611yescharacteristic
180C4×C61#44211yescharacteristic
181Dic61#44911yescharacteristic
182Dic61#46311yescharacteristic
183C2×#509—611no—
184#2948—611no—
185#2145—611no—
186#2140—611no—
187#1976—611no—
188#1384—611no—
189#1378—611no—
190C2×C61—21no—
191C2×C61—82no—
192C2×C61#187911yescharacteristic
193D61—21no—
194D61—21no—
195D61—82no—
196D61—161no—
197C2×#135—611no—
198C22×D8—611no—
199#518—1221no—
200#509—1222no—
201#509—1222no—
202C2×SD32—611no—
203C2×SD32#692311yescharacteristic, complemented
204C2×D16—611no—
205C2×D16—611no—
206C2×M32—611no—
207C2×M32—611no—
208#442—1222no—
209C4×D8—1222no—
210#427—611no—
211#427—611no—
212#421—1221no—
213#418—1221no—
214#410—1221no—
215#405—611no—
216#360—1222no—
217#357—1222no—
218C61#1303311yescharacteristic, complemented, Sylow
219C2×#41—1221no—
220C22×D4—1221no—
221#135—1221no—
222#135—1221no—
223#135—1221no—
224#135—1221no—
225C2×Q16C2×#692311yescharacteristic, complemented
226C2×SD16—1221no—
227C2×D8—612no—
228C2×D8—612no—
229C2×D8—611no—
230C2×D8—611no—
231C2×D8—1221no—
232C2×D8—1221no—
233C2×D8—1221no—
234C2×D8C2×#692311yescharacteristic
235C2×M16—611no—
236C22×C8—611no—
237C4×D4—1224no—
238C4×D4—2442no—
239#117—611no—
240#117—1221no—
241#117—1221no—
242C2×C22⋊C4—2442no—
243SD32—22no—
244SD32—1222no—
245D16—1222no—
246D16—1222no—
247M32—1221no—
248M32—1221no—
249M32—1221no—
250M32—1221no—
251C2×C16—611no—
252C2×C16—1221no—
253C2×C16C2×#692311yescharacteristic, complemented
254#107—1221no—
255#107—1221no—
256#106—612no—
257#106—1221no—
258#104—2442no—
259#102—1224no—
260#99—2442no—
261#97—1221no—
262C4×C8—1221no—
263C24—2441no—
264#41—2441no—
265#41—2441no—
266#41—2441no—
267#41—2441no—
268C2×Q8—21no—
269C2×D4—21no—
270C2×D4—1222no—
271C2×D4—1222no—
272C2×D4—1221no—
273C2×D4—1221no—
274C2×D4—2441no—
275C2×D4—2441no—
276C2×D4—2441no—
277C2×D4—2441no—
278C22×C4—611no—
279C22×C4—2441no—
280C22×C4—2444no—
281Q16—21no—
282Q16—21no—
283SD16—2441no—
284SD16—2441no—
285D8—21no—
286D8—612no—
287D8—1222no—
288D8—1222no—
289D8—1221no—
290D8—1221no—
291D8—1221no—
292D8C22⋊#692312yes—
293M16—1221no—
294M16—1221no—
295C2×C8—611no—
296C2×C8—611no—
297C2×C8—611no—
298C2×C8—611no—
299C2×C8—611no—
300C2×C8—1221no—
301C2×C8C22×#692311yescharacteristic
302C4⋊C4—1221no—
303C4⋊C4—1222no—
304C4⋊C4—2441no—
305C22⋊C4—612no—
306C22⋊C4—2444no—
307C22⋊C4—2441no—
308C22⋊C4—2441no—
309C42—1221no—
310C42—2441no—
311C42—2441no—
312C16—21no—
313C16—1221no—
314C16—2441no—
315C23—41no—
316C23—611no—
317C23—9762no—
318C23—2442no—
319C23—2442no—
320C23—2441no—
321C23—2441no—
322Q8—41no—
323Q8—41no—
324D4—22no—
325D4—41no—
326D4—1222no—
327D4—4881no—
328D4—4881no—
329D4—2442no—
330D4—2442no—
331D4—2441no—
332D4—2441no—
333D4—2441no—
334C2×C4—41no—
335C2×C4—611no—
336C2×C4—611no—
337C2×C4—611no—
338C2×C4—611no—
339C2×C4—611no—
340C2×C4—1222no—
341C2×C4—9764no—
342C2×C4—4881no—
343C2×C4—4881no—
344C2×C4—4881no—
345C2×C4—2442no—
346C2×C4D4×#692311yescharacteristic
347C8—611no—
348C8—611no—
349C8—2441no—
350C8C2×C22⋊#692311yescharacteristic
351C8D4×#692311yescharacteristic
352C22—42no—
353C22—161no—
354C22—611no—
355C22—611no—
356C22—9761no—
357C22—9761no—
358C22—9762no—
359C22—4884no—
360C22—4881no—
361C22—2441no—
362C22—2442no—
363C22D8×#692311yescharacteristic
364C4—81no—
365C4—611no—
366C4—611no—
367C4—9761no—
368C4—4882no—
369C4—2442no—
370C4#1684071011yescharacteristic
371C4#1684080311yescharacteristic
372C2—21no—
373C2—82no—
374C2—1221no—
375C2—1221no—
376C2—9761no—
377C2—4882no—
378C2#2146181411yescharacteristic
subgroupG/H
centerC2#21461814
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC2×SD32×C61C4
socleC2×C61#1879
prime radicalC2×#16840199C2
cosocleC2×C8×D61C23
hypercenterC2×SD32#6923
hypocenterC61#13033
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
1. #21462578C2semidirect
2. #21462141C2semidirect
3. #21462128C2semidirect
4. #21461978C2semidirect
5. #21460887C2semidirect
6. #21460868C2semidirect
24. C2×#14519720C4semidirect
25. C2×D976C4semidirect
26. C2×#14519718C4semidirect
28. C2×SD32×C61C4semidirect
56. C2×D488C2×C4semidirect
68. C2×#11758185C2×C4semidirect
69. C2×Q16×C61C2×C4semidirect
72. C2×C16×C61C2×C4semidirect
203. C2×SD32#6923semidirect
218. C61#13033semidirect
225. C2×Q16C2×#6923semidirect
253. C2×C16C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214625782
#214621412
#214621282
#214619782
#214608872
#214608682
C2×#168401992
#1303361