Finite Group Databasebeta

← #29590935

Subgroups — #29590935

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#21451295C211yesmaximal, characteristic
2#21445898C211yesmaximal, characteristic, complemented
3#324×D61C211yesmaximal, characteristic, complemented
4#21443846C211yesmaximal, characteristic, complemented
5#21443823C211yesmaximal, characteristic, complemented
6#21443821C211yesmaximal, characteristic, complemented
7C61×#1353C211yesmaximal, characteristic, complemented
8C2×#14519752C411yescharacteristic
9C2×C4⋊C4×D61C2211yescharacteristic
10#16839725—21no—
11C22⋊C8×D61—21no—
12#16839700C411yescharacteristic
13#16839680C411yescharacteristic
14#16839679C2211yescharacteristic
15#16839654—21no—
16#16839651—21no—
17#16839640—21no—
18#16839640—21no—
19#16839609C411yescharacteristic
20#16839531C2211yescharacteristic
21#16839530—21no—
22#16839488C2211yescharacteristic
23#16839487—21no—
24C61×#400C2211yescharacteristic
25C61×#343C2211yescharacteristic
26C61×#324C2211yescharacteristic
27C22×D244—21no—
28C22×D244C2×C411yescharacteristic
29C22×C4×D61C2×C411yescharacteristic
30C22×C4×D61D411yescharacteristic
31C22×C4×D61D411yescharacteristic
32C2×#11758194—21no—
33C2×C8×D61—41no—
34#14519752—41no—
35#14519752—41no—
36C2×C4⋊Dic61D411yescharacteristic
37C2×#11758196C2×C411yescharacteristic
38C2×#11758196D411yescharacteristic
39C4⋊C4×D61—41no—
40C4⋊C4×D61—41no—
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×#11758198—21no—
45C2×#11758198—21no—
46C2×#11758198—21no—
47C2×C4×Dic61—21no—
48C22⋊#92418—21no—
49#14519689—41no—
50#14519689—41no—
51#14519689—41no—
52#14519684—21no—
53#14519684—21no—
54#14519684C2×C411yescharacteristic
55C2×M16×C61—21no—
56C2×C4⋊C4×C61C2×C411yescharacteristic
57C2×C4⋊C4×C61C2311yescharacteristic
58C22⋊C8×C61—21no—
59#95×C61—21no—
60#95×C61—21no—
61#95×C61C2×C411yescharacteristic
62C23×D61—21no—
63C23×D61C22⋊C411yescharacteristic
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61C22×C411yescharacteristic
67C22×C4×C61C2×D411yescharacteristic
68C22×C4×C61C2×D411yescharacteristic
69C22×Dic61—21no—
70C22×Dic61C22⋊C411yescharacteristic
71C22×Dic61C22⋊C411yescharacteristic
72C22×Dic61C22⋊C411yescharacteristic
73C2×D244—41no—
74C2×D244—42no—
75C2×D244—42no—
76C2×D244—41no—
77C2×D244—41no—
78C2×D244—81no—
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—
95C4⋊C4×C61—41no—
96#11758198—42no—
97#11758198—42no—
98#11758198—42no—
99#11758198—41no—
100#11758198—41no—
101#11758198—81no—
102#11758198—81no—
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×C61C2×C22⋊C411yescharacteristic
113C22×D61—21no—
114C22×D61—21no—
115C22×D61—22no—
116C22×D61—41no—
117C22×D61—41no—
118C22×D61—41no—
119C22×D61—41no—
120C22×D61—41no—
121C22×D61—41no—
122C22×D61—41no—
123C22×D61—41no—
124C22×D61#9911yescharacteristic
125C22×D61#9911yescharacteristic
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61#13511yescharacteristic
139C2×C4×C61#13511yescharacteristic
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—
150D244—82no—
151D244—82no—
152D244—82no—
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×C61C2×#9911yescharacteristic
169C22×C61#41611yescharacteristic
170C22×C61#42111yescharacteristic
171C2×D61—21no—
172C2×D61—21no—
173C2×D61—21no—
174C2×D61—21no—
175C2×D61—21no—
176C2×D61—42no—
177C2×D61—42no—
178C2×D61—81no—
179C2×D61—81no—
180C2×D61—81no—
181C2×D61—81no—
182C2×D61—81no—
183C2×D61—81no—
184C2×D61—81no—
185C2×D61#35512yes—
186C4×C61—21no—
187C4×C61—21no—
188C4×C61—41no—
189C4×C61—41no—
190C4×C61—81no—
191C4×C61—81no—
192Dic61—41no—
193Dic61—41no—
194Dic61—41no—
195Dic61—81no—
196#2591—611no—
197#1821—611no—
198C2×#324—611no—
199#1353—611no—
200#1353D6111yescharacteristic, complemented
201#1345—611no—
202#1345—611no—
203C2×C61—21no—
204C2×C61—21no—
205C2×C61#151611yescharacteristic
206C2×C61#212111yescharacteristic
207C2×C61C2×#35511yescharacteristic
208D61—22no—
209D61—41no—
210D61—161no—
211C2×#121—611no—
212C22×C4⋊C4—611no—
213#407—1221no—
214C2×C22⋊C8—1221no—
215#400—611no—
216#400C2×D6111yescharacteristic
217#394—611no—
218#394—611no—
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—611no—
232C22×D4—1221no—
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—2441no—
245C2×C4⋊C4—2441no—
246C2×C4⋊C4C4×D6111yescharacteristic
247C2×C4⋊C4C22×D6111yescharacteristic
248C2×C22⋊C4—1221no—
249C2×C22⋊C4—1221no—
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—21no—
261#95—21no—
262#95—611no—
263#95—1221no—
264#95—1221no—
265#95C4×D6111yescharacteristic
266C24—611no—
267C24—1221no—
268C2×D4—4881no—
269C2×D4—2441no—
270C2×D4—2441no—
271C2×D4—2441no—
272C2×D4—2442no—
273C2×D4—2442no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—611no—
277C22×C4—611no—
278C22×C4—611no—
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—41no—
305C4⋊C4—2441no—
306C4⋊C4—2441no—
307C4⋊C4—2441no—
308C22⋊C4—4881no—
309C22⋊C4—4881no—
310C22⋊C4—2442no—
311C22⋊C4—2442no—
312C22⋊C4—2442no—
313C22⋊C4—2441no—
314C22⋊C4—2441no—
315C42—4881no—
316C23—611no—
317C23—611no—
318C23—1222no—
319C23—1221no—
320C23—1221no—
321C23—2441no—
322C23—2441no—
323C23—2441no—
324C23—2441no—
325C23—2441no—
326C23—2441no—
327C23—2441no—
328C23—2441no—
329C23C22⋊C4×D6111yescharacteristic
330D4—4882no—
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—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—1221no—
346C2×C4—1221no—
347C2×C4—1221no—
348C2×C4—1221no—
349C2×C4—1221no—
350C2×C4—4881no—
351C2×C4—4881no—
352C2×C4—4881no—
353C2×C4—2441no—
354C2×C4—2441no—
355C2×C4—2441no—
356C2×C4—2441no—
357C2×C4—2442no—
358C2×C4—2441no—
359C2×C4—2441no—
360C2×C4—2441no—
361C2×C4—2441no—
362C2×C4—2441no—
363C2×C4#1451979811yescharacteristic
364C2×C4#1451980011yescharacteristic
365C8—81no—
366C8—81no—
367C8—4881no—
368C8—4881no—
369C22—21no—
370C22—21no—
371C22—612no—
372C22—1221no—
373C22—1221no—
374C22—1221no—
375C22—1221no—
376C22—1221no—
377C22—4881no—
378C22—4881no—
379C22—4881no—
380C22—4881no—
381C22—4881no—
382C22—4881no—
383C22—4881no—
384C22—2442no—
385C22—2442no—
386C22#99×D6111yescharacteristic
387C22#1683975711yescharacteristic
388C22#1683977711yescharacteristic
389C4—21no—
390C4—21no—
391C4—41no—
392C4—41no—
393C4—81no—
394C4—81no—
395C4—4881no—
396C4—2441no—
397C4—2441no—
398C4—2441no—
399C2—21no—
400C2—21no—
401C2—1222no—
402C2—9761no—
403C2—2441no—
404C2#2144437411yescharacteristic
405C2#2144746411yescharacteristic
406C2#355×D6111yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1353C2
socleC22×C61C2×#99
prime radicalC2×#14519752C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1353D61
hypocenterC61#11852
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1353

Complements

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

NH ≅ G/Ntype
2. #21445898C2semidirect
3. #324×D61C2semidirect
4. #21443846C2semidirect
5. #21443823C2semidirect
6. #21443821C2semidirect
7. C61×#1353C2semidirect
200. #1353D61semidirect
230. C61#11852semidirect

Maximal subgroups

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

subgroupindex
#214512952
#214458982
#324×D612
#214438462
#214438232
#214438212
C61×#13532
#1185261