Finite Group Databasebeta

← #29577726

Subgroups — #29577726

Order 15616.

536 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 95 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#21454903C211yesmaximal, characteristic, complemented
2#21450821C211yesmaximal, characteristic
3#21444532C211yesmaximal, characteristic
4#21444532C211yesmaximal, characteristic
5#21444162C211yesmaximal, characteristic, complemented
6#21443675C211yesmaximal, characteristic, complemented
7C61×#1285C211yesmaximal, characteristic, complemented
8C2×#14519774C2211yescharacteristic
9C2×#14519765C412yes—
10C2×C4×Dic122C2211yescharacteristic
11#16839891—22no—
12#16839890—22no—
13#16839819C2211yescharacteristic
14#16839819C2211yescharacteristic
15#16839816—21no—
16#16839812—21no—
17#16839680—21no—
18#16839680—21no—
19#16839664C412yes—
20#16839663—21no—
21#16839663—21no—
22#16839505—22no—
23#16839505—22no—
24#16839487—21no—
25#16839487—21no—
26C61×#432C2211yescharacteristic
27C61×#432C2211yescharacteristic
28C4×C4⋊C4×C61C2211yescharacteristic
29C22×Dic122C2×C411yescharacteristic
30C22×D244—21no—
31C22×D244—21no—
32C22×D244C2×C412yes—
33#14519774—21no—
34#14519774—21no—
35#14519774—21no—
36#14519774—21no—
37#14519765—44no—
38C4×Dic122—21no—
39C4×Dic122—21no—
40C4×Dic122—21no—
41C4×Dic122—21no—
42C2×C4⋊Dic61C2×C411yescharacteristic
43C2×#11758196D411yescharacteristic
44C2×#11758196D411yescharacteristic
45C2×#11758198—22no—
46C2×#11758198—22no—
47C2×#11758198—22no—
48C2×#11758198—22no—
49C2×C4×Dic61D411yescharacteristic
50C2×C4×Dic61D411yescharacteristic
51C4⋊#92418—21no—
52C4⋊#92418D412yes—
53#14519706—22no—
54#14519706—22no—
55C22⋊#92418—21no—
56C22⋊#92418—21no—
57#14519688—21no—
58#14519688—21no—
59#14519687—22no—
60C8×Dic61—22no—
61C2×C4⋊C4×C61—21no—
62C2×C42×C61C2×C412yes—
63C2×C42×C61C2311yescharacteristic
64C4⋊C8×C61—21no—
65C4⋊C8×C61D412yes—
66C22⋊C8×C61—21no—
67C22⋊C8×C61—21no—
68#97×C61—21no—
69#97×C61—21no—
70#95×C61—21no—
71C23×D61—22no—
72C22×C4×C61—22no—
73C22×C4×C61C22×C411yescharacteristic
74C22×C4×C61C2×D411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C22×Dic61C22⋊C411yescharacteristic
77C22×Dic61C22⋊C411yescharacteristic
78C22×Dic61C22⋊C411yescharacteristic
79C22×Dic61C22⋊C411yescharacteristic
80C2×D244—22no—
81C2×D244—22no—
82C2×D244—42no—
83C2×D244—42no—
84C2×D244—42no—
85C2×D244—42no—
86C2×D244—41no—
87C2×D244—41no—
88C2×D244—41no—
89C2×D244—41no—
90C2×D244—82no—
91C2×Dic122—21no—
92C2×Dic122—21no—
93C2×Dic122—22no—
94C2×Dic122—41no—
95C2×C8×C61—22no—
96C2×C8×C61—41no—
97C4⋊C4×C61—42no—
98C42×C61—42no—
99C42×C61C2×D411yescharacteristic
100C42×C61C2×D411yescharacteristic
101C42×C61#4111yescharacteristic
102C42×C61#4111yescharacteristic
103#11758198—44no—
104#11758198—44no—
105#11758198—82no—
106#11758198—82no—
107C4⋊Dic61—21no—
108C4⋊Dic61—21no—
109#11758196—21no—
110#11758196—21no—
111#11758196—21no—
112#11758196—21no—
113C4×Dic61—21no—
114C4×Dic61—21no—
115C4×Dic61—21no—
116C4×Dic61—21no—
117C2×#92418—22no—
118C2×#92418—41no—
119C23×C61C2×C22⋊C411yescharacteristic
120C22×D61—42no—
121C22×D61—42no—
122C22×D61—42no—
123C22×D61—42no—
124C22×D61—42no—
125C22×D61—42no—
126C22×D61—42no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—22no—
130C2×C4×C61—41no—
131C2×C4×C61—42no—
132C2×C4×C61—42no—
133C2×C4×C61—42no—
134C2×C4×C61C4×D411yescharacteristic
135C2×C4×C61C4×D411yescharacteristic
136C2×C4×C61#12011yescharacteristic
137C2×C4×C61#12111yescharacteristic
138C2×C4×C61#12111yescharacteristic
139C2×C4×C61#12311yescharacteristic
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61#10012yes—
150D244—82no—
151D244—82no—
152D244—82no—
153D244—82no—
154D244—82no—
155D244—82no—
156Dic122—42no—
157Dic122—42no—
158C8×C61—42no—
159C8×C61—81no—
160#92418—42no—
161#92418—81no—
162#9458—611nomaximal, Sylow
163C22×C61—21no—
164C22×C61—21no—
165C22×C61#38611yescharacteristic
166C22×C61C2×#10011yescharacteristic
167C22×C61#41311yescharacteristic
168C2×D61—82no—
169C2×D61—82no—
170C2×D61—82no—
171C2×D61—82no—
172C2×D61—82no—
173C2×D61—82no—
174C2×D61—82no—
175C4×C61—21no—
176C4×C61—21no—
177C4×C61—21no—
178C4×C61—21no—
179C4×C61—21no—
180C4×C61—82no—
181C4×C61#45412yes—
182Dic61—22no—
183Dic61—41no—
184Dic61—41no—
185Dic61—41no—
186#2983—611no—
187#2548—611no—
188#1555—611no—
189#1555—611no—
190#1467—611no—
191#1285—611no—
192#1285D6111yescharacteristic, complemented
193C2×C61—21no—
194C2×C61—21no—
195C2×C61#188811yescharacteristic
196C2×C61#190011yescharacteristic
197C2×C61#191011yescharacteristic
198D61—162no—
199C2×#127—611no—
200C2×#124—612no—
201C2×C4×Q8—611no—
202#446—1222no—
203#446—1222no—
204#432—611no—
205#432—611no—
206#432—1221no—
207#432C2×D6111yescharacteristic
208#432C2×D6111yescharacteristic
209#431—1221no—
210#394—1221no—
211#394—1221no—
212#390—612no—
213#390—1221no—
214#390—1221no—
215C4×C4⋊C4C2×D6111yescharacteristic
216#331—1222no—
217#331—1222no—
218#324—1221no—
219#324—1221no—
220C61#945811yescharacteristic, complemented, Sylow
221C22×Q8—611no—
222C22×D4—612no—
223C22×D4—1221no—
224C22×D4—1221no—
225#127—1221no—
226#127—1221no—
227#127—1221no—
228#127—1221no—
229#124—2444no—
230C4×Q8—1221no—
231C4×Q8—1221no—
232C4×Q8—1221no—
233C4×Q8—1221no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—611no—
236C2×C4⋊C4—611no—
237C2×C4⋊C4—611no—
238C2×C22⋊C4—1222no—
239C2×C22⋊C4—1222no—
240C2×C22⋊C4—1222no—
241C2×C22⋊C4—1222no—
242C2×C42—611no—
243C2×C42—611no—
244C2×C42C4×D6112yes—
245C2×C42C22×D6111yescharacteristic
246C4⋊C8—21no—
247C4⋊C8—612no—
248C4⋊C8—1222no—
249C4⋊C8—1222no—
250C4⋊C8—1221no—
251C4⋊C8D24412yes—
252C22⋊C8—21no—
253C22⋊C8—21no—
254C22⋊C8—1221no—
255C22⋊C8—1221no—
256#97—21no—
257#97—21no—
258#97—1222no—
259#97—1221no—
260#97—1221no—
261C4×C8—1222no—
262#95—21no—
263C24—1222no—
264C2×Q8—1222no—
265C2×Q8—1221no—
266C2×Q8—1221no—
267C2×Q8—2441no—
268C2×D4—1222no—
269C2×D4—1222no—
270C2×D4—4882no—
271C2×D4—2442no—
272C2×D4—2442no—
273C2×D4—2442no—
274C2×D4—2442no—
275C2×D4—2441no—
276C2×D4—2441no—
277C2×D4—2441no—
278C2×D4—2441no—
279C22×C4—22no—
280C22×C4—611no—
281C22×C4—611no—
282C22×C4—611no—
283C22×C4—611no—
284C22×C4C2×C4×D6111yescharacteristic
285C22×C4D4×D6111yescharacteristic
286C22×C4D4×D6111yescharacteristic
287C2×C8—22no—
288C2×C8—41no—
289C2×C8—1222no—
290C2×C8—2441no—
291C4⋊C4—42no—
292C4⋊C4—1221no—
293C4⋊C4—1221no—
294C4⋊C4—1221no—
295C4⋊C4—1221no—
296C4⋊C4—1221no—
297C4⋊C4—1221no—
298C22⋊C4—4882no—
299C22⋊C4—4882no—
300C22⋊C4—2444no—
301C22⋊C4—2444no—
302C42—42no—
303C42—1221no—
304C42—1221no—
305C42—1221no—
306C42—1221no—
307C42C2×D24411yescharacteristic
308C42#1175822211yescharacteristic
309C42D4×D6111yescharacteristic
310C42#1175822611yescharacteristic
311C23—2442no—
312C23—2442no—
313C23—2442no—
314C23—2442no—
315C23—2442no—
316C23—2442no—
317C23—2442no—
318C23C22⋊C4×D6111yescharacteristic
319Q8—2442no—
320Q8—2442no—
321D4—4882no—
322D4—4882no—
323D4—4882no—
324D4—4882no—
325D4—4882no—
326D4—4882no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—22no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—612no—
335C2×C4—1221no—
336C2×C4—1221no—
337C2×C4—1221no—
338C2×C4—1221no—
339C2×C4—1221no—
340C2×C4—1221no—
341C2×C4—1221no—
342C2×C4—2441no—
343C2×C4—2441no—
344C2×C4#1451973911yescharacteristic
345C2×C4C4×D24411yescharacteristic
346C2×C4#1451974711yescharacteristic
347C2×C4#1451975011yescharacteristic
348C2×C4#1451975211yescharacteristic
349C2×C4#1451976211yescharacteristic
350C8—42no—
351C8—81no—
352C8—4881no—
353C8—2442no—
354C22—21no—
355C22—21no—
356C22—4882no—
357C22—4882no—
358C22—4882no—
359C22—4882no—
360C22—4882no—
361C22—4882no—
362C22—4882no—
363C22#1683964011yescharacteristic
364C22#100×D6111yescharacteristic
365C22#1683974511yescharacteristic
366C4—21no—
367C4—21no—
368C4—21no—
369C4—21no—
370C4—21no—
371C4—82no—
372C4—1222no—
373C4—2441no—
374C4—2441no—
375C4—2441no—
376C4#1683993612yes—
377C2—21no—
378C2—21no—
379C2—9762no—
380C2#2144622111yescharacteristic
381C2#2144628111yescharacteristic
382C2#2144634511yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1285C2
socleC22×C61#386
prime radicalC2×#14519774C22
cosocleC2×C42×C61C23
hypercenter#1285D61
hypocenterC61#9458
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1285

Complements

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

NH ≅ G/Ntype
1. #21454903C2semidirect
5. #21444162C2semidirect
6. #21443675C2semidirect
7. C61×#1285C2semidirect
192. #1285D61semidirect
220. C61#9458semidirect

Maximal subgroups

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

subgroupindex
#214549032
#214508212
#214445322
#214441622
#214436752
C61×#12852
#945861