Finite Group Databasebeta

← #29582072

Subgroups — #29582072

Order 15616.

496 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 103 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#21456972C211yesmaximal, characteristic, complemented
2#21455618C211yesmaximal, characteristic
3C2×#16840043C211yesmaximal, characteristic
4#21444501C211yesmaximal, characteristic, complemented
5#21444221C211yesmaximal, characteristic, complemented
6#21444139C211yesmaximal, characteristic
7C61×#1301C211yesmaximal, characteristic, complemented
8#16840319C2211yescharacteristic
9C2×#14519777C2211yescharacteristic
10C2×C4×D244C2211yescharacteristic
11#16840167—21no—
12#16840113—21no—
13#16840098—22no—
14#16840063—22no—
15#16840058—22no—
16#16840053—21no—
17#16840043—21no—
18#16840043—22no—
19#16840043—22no—
20#16839815C2211yescharacteristic
21#16839804—21no—
22C2×#14519711—21no—
23#16839768—21no—
24C2×#14519699—21no—
25#16839510—22no—
26#16839492—22no—
27#16839485—22no—
28C61×#431C2211yescharacteristic
29C61×#423C2211yescharacteristic
30C2×C4⋊C8×C61C2211yescharacteristic
31C22×Dic122—21no—
32C22×D244D411yescharacteristic
33C22×C4×D61—21no—
34#14519777—21no—
35#14519777—21no—
36#14519777—21no—
37#14519777D412yes—
38#14519777D411yescharacteristic
39#14519777D411yescharacteristic
40#14519769—21no—
41#14519756—21no—
42#14519756—21no—
43C4×Dic122—21no—
44C4×Dic122—21no—
45C4×D244—21no—
46C4×D244—21no—
47C4×D244—21no—
48C4×D244—21no—
49#14519736—21no—
50C2×C4⋊Dic61—21no—
51C2×C4⋊Dic61—21no—
52C2×C4⋊Dic61D411yescharacteristic
53C2×#11758198—21no—
54#14519711—24no—
55#14519711—22no—
56#14519711—24no—
57#14519709—22no—
58C4⋊#92418—21no—
59#14519702—24no—
60#14519699—24no—
61#14519699—22no—
62#14519699—22no—
63C22⋊#92418—21no—
64C4×#92418—21no—
65C2×M16×C61—21no—
66C22×C8×C61—21no—
67C2×C42×C61C2311yescharacteristic
68C4⋊C8×C61—21no—
69C4⋊C8×C61—21no—
70C4⋊C8×C61—21no—
71C4⋊C8×C61D412yes—
72C4⋊C8×C61D412yes—
73C22⋊C8×C61D412yes—
74C4×C8×C61—21no—
75C23×D61—21no—
76C22×C4×C61C2×D411yescharacteristic
77C22×C4×C61C2×D411yescharacteristic
78C22×C4×C61#4111yescharacteristic
79C22×Dic61—21no—
80C22×Dic61—41no—
81C2×D244—21no—
82C2×D244—21no—
83C2×D244—21no—
84C2×D244—21no—
85C2×D244—21no—
86C2×D244Q1612yes—
87C2×C4×D61—41no—
88C2×C4×D61—41no—
89C2×C4×D61—82no—
90C2×Dic122—21no—
91C2×Dic122—21no—
92C2×Dic122—22no—
93C2×Dic122—41no—
94C2×Dic122—82no—
95M16×C61—41no—
96M16×C61—41no—
97C2×C8×C61—22no—
98C2×C8×C61—22no—
99C2×C8×C61—22no—
100C2×C8×C61—41no—
101C2×C8×C61—41no—
102C42×C61C2×D411yescharacteristic
103C42×C61C2×D411yescharacteristic
104C42×C61C2×D411yescharacteristic
105C42×C61C2×D411yescharacteristic
106C22⋊Dic61—41no—
107#11758198—41no—
108#11758198—41no—
109C4⋊Dic61—21no—
110C4⋊Dic61—22no—
111C4⋊Dic61—21no—
112C4⋊Dic61—22no—
113C4⋊Dic61—21no—
114C4⋊Dic61—21no—
115C4⋊Dic61—21no—
116C4⋊Dic61—21no—
117C4⋊Dic61—41no—
118C4⋊Dic61—41no—
119#11758196—41no—
120#11758196—41no—
121C4×Dic61—41no—
122C2×#92418—41no—
123C23×C61#12111yescharacteristic
124C22×D61—22no—
125C22×D61—41no—
126C22×D61—41no—
127C22×D61—81no—
128C22×D61—81no—
129C2×C4×C61—22no—
130C2×C4×C61—41no—
131C2×C4×C61#12011yescharacteristic
132C2×C4×C61#12011yescharacteristic
133C2×C4×C61#12011yescharacteristic
134C2×C4×C61#12111yescharacteristic
135C2×C4×C61#12111yescharacteristic
136C2×C4×C61#12711yescharacteristic
137C2×C4×C61C2×Q1611yescharacteristic
138C2×C4×C61#13511yescharacteristic
139C2×C4×C61#13711yescharacteristic
140C2×C4×C61#13711yescharacteristic
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—42no—
144C2×Dic61—41no—
145C2×Dic61—82no—
146C2×Dic61—81no—
147D244—22no—
148D244—22no—
149D244—41no—
150D244—41no—
151C4×D61—82no—
152C4×D61—82no—
153Dic122—42no—
154Dic122—42no—
155Dic122—82no—
156Dic122—82no—
157C8×C61—42no—
158C8×C61—42no—
159C8×C61—42no—
160#92418—81no—
161#10190—611nomaximal, Sylow
162C22×C61—21no—
163C22×C61—21no—
164C22×C61#39211yescharacteristic
165C22×C61#46711yescharacteristic
166C22×C61#47011yescharacteristic
167C2×D61—42no—
168C2×D61—82no—
169C2×D61—81no—
170C2×D61—81no—
171C2×D61—82no—
172C4×C61—21no—
173C4×C61—21no—
174C4×C61—21no—
175C4×C61#45111yescharacteristic
176C4×C61#45111yescharacteristic
177C4×C61#45211yescharacteristic
178C4×C61#45211yescharacteristic
179C4×C61#47212yes—
180Dic61—81no—
181Dic61—81no—
182Dic61—82no—
183Dic61—81no—
184#3230—611no—
185#3077—611no—
186C2×#474—611no—
187#1548—611no—
188#1481—611no—
189#1460—611no—
190#1301D6111yescharacteristic, complemented
191C2×C61—21no—
192C2×C61—21no—
193C2×C61#200111yescharacteristic
194C2×C61#200911yescharacteristic
195C2×C61#201811yescharacteristic
196D61—82no—
197#533—611no—
198C2×C4⋊Q8—611no—
199C2×C4×D4—611no—
200#500—1221no—
201#487—1221no—
202#484—1222no—
203#478—1222no—
204#477—1222no—
205#476—1221no—
206#474—1221no—
207#474—1222no—
208#474—1222no—
209#431—611no—
210#431C2×D6111yescharacteristic
211#428—1221no—
212C2×#107—1221no—
213#423C2×D6111yescharacteristic
214C2×C4⋊C8C2×D6111yescharacteristic
215#418—1221no—
216C2×#102—1221no—
217#333—1222no—
218Q8⋊C8—1222no—
219#323—1222no—
220C61#1019011yescharacteristic, complemented, Sylow
221C22×Q8—1221no—
222C22×D4—611no—
223C23×C4—1221no—
224C2×M16—21no—
225C22×C8—21no—
226C4⋊Q8—612no—
227C4⋊Q8—611no—
228C4⋊Q8—611no—
229C4⋊Q8—1221no—
230C4⋊Q8—1221no—
231C4⋊Q8—1221no—
232#125—1221no—
233C22⋊Q8—1221no—
234C22⋊Q8—1221no—
235C4×Q8—1221no—
236C4×Q8—1221no—
237C4×D4—1221no—
238C4×D4—1221no—
239C4×D4—1221no—
240C4×D4—1221no—
241#117—1221no—
242C2×C4⋊C4—611no—
243C2×C4⋊C4—1221no—
244C2×C4⋊C4—1221no—
245C2×C22⋊C4—1221no—
246C2×C42C22×D6111yescharacteristic
247#107—1224no—
248#107—1222no—
249#107—1224no—
250#106—1222no—
251C4⋊C8—21no—
252C4⋊C8—21no—
253C4⋊C8—21no—
254C4⋊C8—1221no—
255C4⋊C8D24412yes—
256C4⋊C8D24412yes—
257#103—1224no—
258#102—1224no—
259#102—1222no—
260#102—1222no—
261C22⋊C8—1221no—
262C22⋊C8D24412yes—
263C4×C8—21no—
264C4×C8—1221no—
265C24—1221no—
266C2×Q8—1221no—
267C2×Q8—1222no—
268C2×Q8—1221no—
269C2×Q8—4882no—
270C2×Q8—2441no—
271C2×D4—612no—
272C2×D4—1221no—
273C2×D4—1221no—
274C2×D4—1221no—
275C2×D4—1221no—
276C2×D4—1221no—
277C22×C4—1221no—
278C22×C4—4882no—
279C22×C4—2441no—
280C22×C4—2441no—
281C22×C4—2441no—
282C22×C4C2×D24411yescharacteristic
283C22×C4D4×D6111yescharacteristic
284C22×C4#1175822611yescharacteristic
285M16—41no—
286M16—41no—
287C2×C8—22no—
288C2×C8—22no—
289C2×C8—22no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—2441no—
293C4⋊C4—1221no—
294C4⋊C4—1222no—
295C4⋊C4—1221no—
296C4⋊C4—1222no—
297C4⋊C4—1221no—
298C4⋊C4—1221no—
299C4⋊C4—1221no—
300C4⋊C4—1221no—
301C4⋊C4—2441no—
302C4⋊C4—2441no—
303C4⋊C4—2441no—
304C4⋊C4—2441no—
305C22⋊C4—2441no—
306C22⋊C4—2441no—
307C22⋊C4—2441no—
308C42—2441no—
309C42C2×D24411yescharacteristic
310C42C2×D24411yescharacteristic
311C42D4×D6111yescharacteristic
312C42D4×D6111yescharacteristic
313C23—1222no—
314C23—4881no—
315C23—4881no—
316C23—2441no—
317C23—2441no—
318C23#1451975211yescharacteristic
319Q8—4882no—
320Q8—4882no—
321Q8—2442no—
322Q8—2442no—
323D4—1222no—
324D4—1222no—
325D4—2441no—
326D4—2441no—
327C2×C4—22no—
328C2×C4—41no—
329C2×C4—4882no—
330C2×C4—4882no—
331C2×C4—4882no—
332C2×C4—4881no—
333C2×C4—2441no—
334C2×C4—2441no—
335C2×C4—2441no—
336C2×C4—2442no—
337C2×C4#1451974711yescharacteristic
338C2×C4#1451974711yescharacteristic
339C2×C4#1451974711yescharacteristic
340C2×C4#1451975211yescharacteristic
341C2×C4#1451975211yescharacteristic
342C2×C4#1451977411yescharacteristic
343C2×C4Q16×D6111yescharacteristic
344C2×C4#1451979611yescharacteristic
345C2×C4#1451980611yescharacteristic
346C2×C4#1451980611yescharacteristic
347C8—42no—
348C8—42no—
349C8—42no—
350C8—4881no—
351C22—21no—
352C22—21no—
353C22—4882no—
354C22—4882no—
355C22—4881no—
356C22—4881no—
357C22—2442no—
358C22#1683967211yescharacteristic
359C22#1684000411yescharacteristic
360C22#1684002111yescharacteristic
361C4—21no—
362C4—21no—
363C4—21no—
364C4—4881no—
365C4—4882no—
366C4—4881no—
367C4—4881no—
368C4#1683991911yescharacteristic
369C4#1683991911yescharacteristic
370C4#1683992511yescharacteristic
371C4#1683992511yescharacteristic
372C4#1684003312yes—
373C2—21no—
374C2—21no—
375C2—4882no—
376C2#2144683011yescharacteristic
377C2#2144688211yescharacteristic
378C2#2144692911yescharacteristic
subgroupG/H
centerC22#16839672
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1301C2
socleC22×C61#392
prime radicalC22×D244D4
hypercenter#1301D61
hypocenterC61#10190
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1301

Complements

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

NH ≅ G/Ntype
1. #21456972C2semidirect
4. #21444501C2semidirect
5. #21444221C2semidirect
7. C61×#1301C2semidirect
190. #1301D61semidirect
220. C61#10190semidirect

Maximal subgroups

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

subgroupindex
#214569722
#214556182
C2×#168400432
#214445012
#214442212
#214441392
C61×#13012
#1019061