Finite Group Databasebeta

← #29590933

Subgroups — #29590933

Order 15616.

438 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 71 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#21451293C211yesmaximal, characteristic
2#21445898C211yesmaximal, characteristic, complemented
3#324×D61C211yesmaximal, characteristic, complemented
4#21443847C211yesmaximal, characteristic, complemented
5#21443845C211yesmaximal, characteristic, complemented
6#21443822C211yesmaximal, characteristic, complemented
7C61×#1345C211yesmaximal, characteristic, complemented
8C2×#14519748C411yescharacteristic
9C2×C4⋊C4×D61C2211yescharacteristic
10#16839725—21no—
11C22⋊C8×D61—21no—
12#16839702C411yescharacteristic
13#16839701C2211yescharacteristic
14#16839676C411yescharacteristic
15#16839655—21no—
16#16839650—21no—
17#16839638—21no—
18#16839638—21no—
19#16839609C411yescharacteristic
20#16839531C2211yescharacteristic
21#16839530—21no—
22#16839488C2211yescharacteristic
23#16839487—21no—
24C61×#394C2211yescharacteristic
25C61×#343C2211yescharacteristic
26C61×#324C2211yescharacteristic
27C22×C22⋊D61—21no—
28C22×C4×D61C2×C411yescharacteristic
29C22×C4×D61D411yescharacteristic
30C22×C4×D61D411yescharacteristic
31C2×#11758194—21no—
32C2×C8×D61—41no—
33#14519748—41no—
34#14519748—41no—
35C2×C4⋊Dic61C2×C411yescharacteristic
36C2×C4⋊Dic61D411yescharacteristic
37C2×#11758196C2×C411yescharacteristic
38C2×#11758196D411yescharacteristic
39C4⋊C4×D61—41no—
40C4⋊C4×D61—41no—
41C2×C22⋊Dic61—21no—
42C2×C22⋊Dic61—21no—
43C2×C22⋊Dic61—21no—
44C2×#11758198—21no—
45C2×C4×Dic61—21no—
46C22⋊#92418—21no—
47#14519689—41no—
48#14519689—41no—
49#14519689—41no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684C2×C411yescharacteristic
55C22×D4×C61C2×C411yescharacteristic
56C2×M16×C61—21no—
57C2×C4⋊C4×C61C2311yescharacteristic
58C2×C22⋊C4×C61—21no—
59C2×C22⋊C4×C61—21no—
60C22⋊C8×C61—21no—
61#95×C61C2×C411yescharacteristic
62C24×C61—21no—
63C23×D61C22⋊C411yescharacteristic
64C2×D4×C61—41no—
65C2×D4×C61—81no—
66C22×C4×C61—21no—
67C22×C4×C61C22×C411yescharacteristic
68C22×C4×C61C2×D411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C2×C22⋊D61—42no—
71C2×C22⋊D61—42no—
72C2×C22⋊D61—41no—
73C2×C22⋊D61—41no—
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61C22⋊C411yescharacteristic
77C22×Dic61C22⋊C411yescharacteristic
78C22×Dic61C22⋊C411yescharacteristic
79C2×C4×D61—21no—
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×C4×D61—21no—
86C2×C4×D61—21no—
87C2×C4×D61—41no—
88C2×C4×D61—81no—
89C2×C4×D61—81no—
90M16×C61—41no—
91M16×C61—41no—
92C2×C8×C61—41no—
93C2×C8×C61—41no—
94C4⋊C4×C61—41no—
95C22⋊C4×C61—41no—
96C22⋊C4×C61—41no—
97C22⋊C4×C61—81no—
98C22⋊Dic61—42no—
99C22⋊Dic61—42no—
100C22⋊Dic61—81no—
101#11758198—42no—
102C4⋊Dic61—41no—
103C4⋊Dic61—41no—
104#11758196—41no—
105#11758196—41no—
106C4×Dic61—81no—
107#11758194—41no—
108#11758194—41no—
109C2×#92418—41no—
110C2×#92418—41no—
111C8×D61—82no—
112C23×C61—41no—
113C23×C61—41no—
114C23×C61—41no—
115C23×C61—41no—
116C23×C61—41no—
117C23×C61—41no—
118C23×C61—41no—
119C23×C61C2×C22⋊C411yescharacteristic
120C22×D61—21no—
121C22×D61—21no—
122C22×D61—22no—
123C22×D61—41no—
124C22×D61#9911yescharacteristic
125C22×D61#9911yescharacteristic
126D4×C61—82no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61#13511yescharacteristic
137C2×C4×C61#13511yescharacteristic
138C22⋊D61—82no—
139C22⋊D61—82no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C4×D61—41no—
154C4×D61—41no—
155C4×D61—41no—
156C4×D61—41no—
157C4×D61—42no—
158C4×D61—81no—
159C4×D61—81no—
160C4×D61—81no—
161C8×C61—81no—
162C8×C61—81no—
163#92418—81no—
164#92418—81no—
165#11852—611nomaximal, Sylow
166C22×C61—21no—
167C22×C61—21no—
168C22×C61—81no—
169C22×C61—81no—
170C22×C61—81no—
171C22×C61—81no—
172C22×C61—81no—
173C22×C61—81no—
174C22×C61—81no—
175C22×C61C2×#9911yescharacteristic
176C22×C61#41611yescharacteristic
177C22×C61#42111yescharacteristic
178C2×D61—21no—
179C2×D61—21no—
180C2×D61—21no—
181C2×D61—21no—
182C2×D61—21no—
183C2×D61—42no—
184C2×D61—42no—
185C2×D61#35512yes—
186C4×C61—21no—
187C4×C61—21no—
188C4×C61—41no—
189C4×C61—41no—
190C4×C61—81no—
191Dic61—41no—
192Dic61—41no—
193Dic61—41no—
194Dic61—81no—
195Dic61—81no—
196#2591—611no—
197#1821—611no—
198C2×#324—611no—
199#1353—611no—
200#1353—611no—
201#1345—611no—
202#1345D6111yescharacteristic, complemented
203C2×C61—21no—
204C2×C61—21no—
205C2×C61—161no—
206C2×C61#151611yescharacteristic
207C2×C61#212111yescharacteristic
208C2×C61C2×#35511yescharacteristic
209D61—22no—
210D61—41no—
211C2×#121—611no—
212C22×C4⋊C4—611no—
213#407—1221no—
214C2×C22⋊C8—1221no—
215#400—611no—
216#400—611no—
217#394—611no—
218#394C2×D6111yescharacteristic
219#388—1221no—
220#388—1221no—
221#386—1221no—
222#386—1221no—
223C4×C22⋊C4—611no—
224#343—611no—
225#343—1221no—
226#343C2×D6111yescharacteristic
227#324—611no—
228#324—1221no—
229#324C2×D6111yescharacteristic
230C61#1185211yescharacteristic, complemented, Sylow
231C22×D4—1221no—
232C22×D4C4×D6111yescharacteristic
233C23×C4—611no—
234C23×C4—611no—
235C23×C4—611no—
236C2×M16—21no—
237C2×M16—1221no—
238C22×C8—2441no—
239#121—2441no—
240#121—2441no—
241C2×C4⋊C4—611no—
242C2×C4⋊C4—611no—
243C2×C4⋊C4—611no—
244C2×C4⋊C4—611no—
245C2×C4⋊C4—2441no—
246C2×C4⋊C4—2441no—
247C2×C4⋊C4C22×D6111yescharacteristic
248C2×C22⋊C4—21no—
249C2×C22⋊C4—21no—
250C2×C22⋊C4—1221no—
251C2×C22⋊C4—1221no—
252C2×C22⋊C4—1221no—
253C2×C22⋊C4—1221no—
254C2×C42—1221no—
255C22⋊C8—21no—
256C22⋊C8—1221no—
257C22⋊C8—2441no—
258C22⋊C8—2441no—
259C22⋊C8—2441no—
260#95—611no—
261#95—1221no—
262#95—1221no—
263#95—1221no—
264#95—1221no—
265#95C4×D6111yescharacteristic
266C24—21no—
267C24—611no—
268C2×D4—41no—
269C2×D4—81no—
270C2×D4—2441no—
271C2×D4—2441no—
272C2×D4—2442no—
273C2×D4—2442no—
274C22×C4—21no—
275C22×C4—611no—
276C22×C4—611no—
277C22×C4—611no—
278C22×C4—1221no—
279C22×C4—1221no—
280C22×C4—1221no—
281C22×C4—1221no—
282C22×C4—1221no—
283C22×C4—1221no—
284C22×C4—1221no—
285C22×C4—1221no—
286C22×C4—1221no—
287C22×C4—1221no—
288C22×C4—4881no—
289C22×C4—4881no—
290C22×C4—2441no—
291C22×C4C2×C4×D6111yescharacteristic
292C22×C4D4×D6111yescharacteristic
293C22×C4D4×D6111yescharacteristic
294M16—41no—
295M16—41no—
296M16—2441no—
297M16—2441no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—4882no—
301C2×C8—2441no—
302C2×C8—2441no—
303C4⋊C4—41no—
304C4⋊C4—2441no—
305C4⋊C4—2441no—
306C4⋊C4—2441no—
307C4⋊C4—2441no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C22⋊C4—81no—
311C22⋊C4—4881no—
312C22⋊C4—2442no—
313C22⋊C4—2442no—
314C22⋊C4—2442no—
315C42—4881no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—611no—
324C23—611no—
325C23—1222no—
326C23—1221no—
327C23—1221no—
328C23—2441no—
329C23C22⋊C4×D6111yescharacteristic
330D4—82no—
331D4—4882no—
332D4—4882no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—1221no—
343C2×C4—1221no—
344C2×C4—1221no—
345C2×C4—1221no—
346C2×C4—1221no—
347C2×C4—4881no—
348C2×C4—4881no—
349C2×C4—4881no—
350C2×C4—2441no—
351C2×C4—2441no—
352C2×C4—2441no—
353C2×C4—2441no—
354C2×C4—2442no—
355C2×C4—2441no—
356C2×C4—2441no—
357C2×C4—2441no—
358C2×C4—2441no—
359C2×C4—2441no—
360C2×C4—2441no—
361C2×C4—2441no—
362C2×C4—2441no—
363C2×C4#1451979611yescharacteristic
364C2×C4#1451979811yescharacteristic
365C8—81no—
366C8—81no—
367C8—4881no—
368C8—4881no—
369C22—21no—
370C22—21no—
371C22—81no—
372C22—81no—
373C22—81no—
374C22—81no—
375C22—81no—
376C22—81no—
377C22—81no—
378C22—612no—
379C22—1221no—
380C22—1221no—
381C22—1221no—
382C22—1221no—
383C22—1221no—
384C22—2442no—
385C22—2442no—
386C22#99×D6111yescharacteristic
387C22#1683975511yescharacteristic
388C22#1683977711yescharacteristic
389C4—21no—
390C4—21no—
391C4—41no—
392C4—41no—
393C4—81no—
394C4—4881no—
395C4—4881no—
396C4—2441no—
397C4—2441no—
398C4—2441no—
399C2—21no—
400C2—21no—
401C2—161no—
402C2—1222no—
403C2—2441no—
404C2#2144437211yescharacteristic
405C2#2144746211yescharacteristic
406C2#355×D6111yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1345C2
socleC22×C61C2×#99
prime radicalC2×#14519748C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1345D61
hypocenterC61#11852
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1345

Complements

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

NH ≅ G/Ntype
2. #21445898C2semidirect
3. #324×D61C2semidirect
4. #21443847C2semidirect
5. #21443845C2semidirect
6. #21443822C2semidirect
7. C61×#1345C2semidirect
202. #1345D61semidirect
230. C61#11852semidirect

Maximal subgroups

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

subgroupindex
#214512932
#214458982
#324×D612
#214438472
#214438452
#214438222
C61×#13452
#1185261