Finite Group Databasebeta

← #29590580

Subgroups — #29590580

Order 15616.

532 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 83 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#21450775C211yesmaximal, characteristic
2C4×#14519692C211yesmaximal, characteristic, complemented
3#21443820C212yesmaximal, complemented
4#21443817C212yesmaximal, complemented
5C61×#1466C211yesmaximal, characteristic, complemented
6C2×#14519751C411yescharacteristic, complemented
7C2×#14519749—21no—
8C2×#14519692—21no—
9#16839692C411yescharacteristic, complemented
10#16839687C2211yescharacteristic
11#16839679C411yescharacteristic, complemented
12#16839671C2211yescharacteristic
13#16839653—21no—
14#16839641—21no—
15#16839639—21no—
16C4×C22⋊Dic61—21no—
17C2×#14519684C411yescharacteristic, complemented
18#16839529C2212yes—
19C2×C4×D4×C61C2211yescharacteristic
20C61×#432—21no—
21C61×#323—21no—
22C61×#323C2212yes—
23C22×D244C2×C411yescharacteristic
24C22×C22⋊D61—21no—
25C22×C22⋊D61—21no—
26C23×Dic61—21no—
27#14519751—41no—
28#14519751—41no—
29#14519749—44no—
30C2×C4⋊Dic61C2×C411yescharacteristic
31C2×#11758196—21no—
32C2×C22⋊Dic61—22no—
33C2×C22⋊Dic61—21no—
34C2×#11758198—21no—
35C2×#11758198—21no—
36C2×#11758198—21no—
37C2×#11758198—21no—
38C2×C4×Dic61—41no—
39#14519692—24no—
40#14519684—21no—
41#14519684—21no—
42#14519684—21no—
43#14519684—41no—
44#14519684C2×C411yescharacteristic
45#14519684C2×C411yescharacteristic
46C22×D4×C61D411yescharacteristic
47C23×C4×C61C2×C411yescharacteristic
48C23×C4×C61D411yescharacteristic
49C4×D4×C61—41no—
50C4×D4×C61—41no—
51C2×C4⋊C4×C61C2×C411yescharacteristic
52C2×C22⋊C4×C61D411yescharacteristic
53C2×C22⋊C4×C61C2311yescharacteristic
54C2×C42×C61D411yescharacteristic
55C4⋊C8×C61—41no—
56C22⋊C8×C61—22no—
57#97×C61—41no—
58C24×C61C22⋊C411yescharacteristic
59C24×C61C2×D411yescharacteristic
60C23×D61—21no—
61C2×D4×C61—22no—
62C2×D4×C61—22no—
63C2×D4×C61—41no—
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61—81no—
69C22×C4×C61—81no—
70C22×C4×C61C22⋊C411yescharacteristic
71C22×C4×C61C22⋊C411yescharacteristic
72C22×C4×C61C22⋊C411yescharacteristic
73C22×C4×C61C22×C411yescharacteristic
74C22×C4×C61C2×D411yescharacteristic
75C2×C22⋊D61—42no—
76C2×C22⋊D61—42no—
77C2×C22⋊D61—42no—
78C2×C22⋊D61—42no—
79C2×C22⋊D61—42no—
80C2×C22⋊D61—81no—
81C22×Dic61—21no—
82C22×Dic61—21no—
83C22×Dic61—21no—
84C22×Dic61—42no—
85C22×Dic61—42no—
86C22×Dic61—42no—
87C22×Dic61—81no—
88C2×D244—41no—
89C2×D244—81no—
90C2×C8×C61—42no—
91C4⋊C4×C61—41no—
92C22⋊C4×C61—41no—
93C22⋊C4×C61—41no—
94C42×C61—21no—
95C42×C61—21no—
96C22⋊Dic61—24no—
97C22⋊Dic61—42no—
98C22⋊Dic61—42no—
99#11758198—42no—
100#11758198—42no—
101#11758198—41no—
102#11758198—41no—
103#11758198—81no—
104C4⋊Dic61—41no—
105#11758196—42no—
106C4×Dic61—82no—
107C23×C61—21no—
108C23×C61—21no—
109C23×C61—21no—
110C23×C61—21no—
111C23×C61—41no—
112C23×C61—41no—
113C23×C61—41no—
114C23×C61—41no—
115C23×C61#10412yes—
116C23×C61C2×C22⋊C411yescharacteristic
117C23×C61AGL(1,ℤ/8)12yes—
118C22×D61—41no—
119C22×D61—41no—
120C22×D61—41no—
121C22×D61—41no—
122C22×D61—41no—
123C22×D61—41no—
124C22×D61—41no—
125D4×C61—44no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—41no—
133C2×C4×C61—42no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—81no—
138C2×C4×C61—81no—
139C2×C4×C61—81no—
140C2×C4×C61#9911yescharacteristic
141C2×C4×C61#9911yescharacteristic
142C22⋊D61—84no—
143C22⋊D61—84no—
144C2×Dic61—22no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—44no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—84no—
155C2×Dic61—82no—
156C2×Dic61—82no—
157D244—82no—
158C8×C61—82no—
159#11775—611nomaximal, Sylow
160C22×C61—21no—
161C22×C61—21no—
162C22×C61—22no—
163C22×C61—22no—
164C22×C61—42no—
165C22×C61—42no—
166C22×C61—42no—
167C22×C61—41no—
168C22×C61—41no—
169C22×C61—41no—
170C22×C61—41no—
171C22×C61—81no—
172C22×C61C2×#9911yescharacteristic
173C22×C61#41811yescharacteristic
174C22×C61C2×#10411yescharacteristic
175C2×D61—81no—
176C2×D61—81no—
177C2×D61—81no—
178C2×D61—81no—
179C2×D61—81no—
180C2×D61—81no—
181C2×D61—81no—
182C4×C61—21no—
183C4×C61—21no—
184C4×C61—41no—
185C4×C61—41no—
186C4×C61—41no—
187C4×C61—41no—
188Dic61—42no—
189Dic61—81no—
190Dic61—84no—
191Dic61—81no—
192#2543—611no—
193C4×#99—611no—
194#1466D6111yescharacteristic, complemented
195#1344—612no—
196#1343—612no—
197C2×C61—21no—
198C2×C61—21no—
199C2×C61—42no—
200C2×C61—42no—
201C2×C61#150711yescharacteristic
202C2×C61#212111yescharacteristic
203C2×C61#212611yescharacteristic
204D61—161no—
205C2×#121—611no—
206C2×#121—1221no—
207C2×C4×D4C2×D6111yescharacteristic
208#432—21no—
209C2×#99—1221no—
210#398—611no—
211#397—611no—
212#394—611no—
213#392—611no—
214#388—1221no—
215#386—1221no—
216#386—1221no—
217C4×C22⋊C4—1221no—
218C2×#95—611no—
219#342—612no—
220#323—21no—
221#323C2×D6112yes—
222C61#1177511yescharacteristic, complemented, Sylow
223C22×D4—611no—
224C22×D4—1221no—
225C22×D4—1221no—
226C22×D4D24411yescharacteristic
227C23×C4—1221no—
228C23×C4C4×D6111yescharacteristic
229C23×C4D24411yescharacteristic
230#121—2444no—
231#121—2441no—
232#121—2441no—
233C4×D4—41no—
234C4×D4—41no—
235C2×C4⋊C4—611no—
236C2×C4⋊C4—1221no—
237C2×C4⋊C4C4×D6111yescharacteristic
238C2×C22⋊C4—1222no—
239C2×C22⋊C4—1221no—
240C2×C22⋊C4—1221no—
241C2×C22⋊C4—1221no—
242C2×C22⋊C4—1221no—
243C2×C22⋊C4—1221no—
244C2×C22⋊C4C22⋊D6111yescharacteristic
245C2×C22⋊C4C22×D6111yescharacteristic
246C2×C42—2441no—
247C2×C42C22⋊D6111yescharacteristic
248C4⋊C8—41no—
249#99—1224no—
250C22⋊C8—22no—
251#97—41no—
252#95—611no—
253#95—611no—
254#95—1221no—
255#95—1221no—
256#95—1221no—
257#95—2441no—
258C24—1221no—
259C24#1175819811yescharacteristic
260C24C2×D24411yescharacteristic
261C2×D4—22no—
262C2×D4—22no—
263C2×D4—41no—
264C2×D4—4881no—
265C2×D4—4881no—
266C2×D4—2441no—
267C2×D4—2442no—
268C2×D4—2442no—
269C2×D4—2442no—
270C2×D4—2442no—
271C2×D4—2442no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—81no—
277C22×C4—81no—
278C22×C4—1221no—
279C22×C4—1221no—
280C22×C4—1221no—
281C22×C4—4881no—
282C22×C4—2442no—
283C22×C4—2442no—
284C22×C4—2442no—
285C22×C4#1175819811yescharacteristic
286C22×C4#1175819811yescharacteristic
287C22×C4#1175819811yescharacteristic
288C22×C4C2×C4×D6111yescharacteristic
289C22×C4C2×C22⋊D6111yescharacteristic
290C2×C8—42no—
291C4⋊C4—41no—
292C4⋊C4—2441no—
293C4⋊C4—2442no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C22⋊C4—1224no—
297C22⋊C4—4881no—
298C22⋊C4—2442no—
299C22⋊C4—2442no—
300C22⋊C4—2442no—
301C22⋊C4—2442no—
302C22⋊C4—2441no—
303C22⋊C4—2441no—
304C42—21no—
305C42—21no—
306C42—4882no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—21no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—2441no—
316C23—2441no—
317C23—2441no—
318C23—2441no—
319C23—2441no—
320C23—2441no—
321C23—2441no—
322C23#1451970312yes—
323C23C2×#1175819811yescharacteristic
324C23#1451980512yes—
325D4—44no—
326D4—4882no—
327D4—4884no—
328D4—4884no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—81no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4—1222no—
344C2×C4—4882no—
345C2×C4—4882no—
346C2×C4—4884no—
347C2×C4—2444no—
348C2×C4—2441no—
349C2×C4—2441no—
350C2×C4—2441no—
351C2×C4—2441no—
352C2×C4—2441no—
353C2×C4—2441no—
354C2×C4—2441no—
355C2×C4—2441no—
356C2×C4#1451969111yescharacteristic
357C2×C4#1451969111yescharacteristic
358C8—82no—
359C22—21no—
360C22—21no—
361C22—22no—
362C22—22no—
363C22—42no—
364C22—42no—
365C22—42no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—81no—
371C22—4881no—
372C22—4881no—
373C22—4881no—
374C22—4881no—
375C22—4881no—
376C22—4881no—
377C22—4881no—
378C22C2×#1451969111yescharacteristic
379C22#1683976811yescharacteristic
380C22C2×#1451970311yescharacteristic
381C4—21no—
382C4—21no—
383C4—41no—
384C4—41no—
385C4—41no—
386C4—41no—
387C4—4881no—
388C4—4884no—
389C4—4881no—
390C4—2442no—
391C2—21no—
392C2—21no—
393C2—42no—
394C2—42no—
395C2—9761no—
396C2#2144433611yescharacteristic
397C2#2144746611yescharacteristic
398C2#2144748211yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1466C2
socleC22×C61C2×#99
prime radical#21450775C2
cosocleC2×C22⋊C4×C61C23
hypercenter#1466D61
hypocenterC61#11775
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1466

Complements

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

NH ≅ G/Ntype
2. C4×#14519692C2semidirect
3. #21443820C2semidirect
4. #21443817C2semidirect
5. C61×#1466C2semidirect
6. C2×#14519751C4semidirect
9. #16839692C4semidirect
11. #16839679C4semidirect
17. C2×#14519684C4semidirect
194. #1466D61semidirect
222. C61#11775semidirect

Maximal subgroups

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

subgroupindex
#214507752
C4×#145196922
#214438202
#214438172
C61×#14662
#1177561