Finite Group Databasebeta

← #29590572

Subgroups — #29590572

Order 15616.

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

normal subgroups only

This group has 544 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#21450716C211yesmaximal, characteristic
2#21444157C211yesmaximal, characteristic, complemented
3#21443818C212yesmaximal, complemented
4#21443815C212yesmaximal, complemented
5C4×#99×C61C211yesmaximal, characteristic, complemented
6C2×#14519748—21no—
7C2×C4×D244C411yescharacteristic, complemented
8#16839726—21no—
9#16839687C411yescharacteristic, complemented
10#16839687C2211yescharacteristic
11#16839671C411yescharacteristic, complemented
12#16839671C2211yescharacteristic
13#16839641—21no—
14#16839641—21no—
15#16839628C411yescharacteristic, complemented
16#16839619—21no—
17#16839488—21no—
18#16839486C2212yes—
19C2×C4×D4×C61C2211yescharacteristic
20C2×#99×C61—21no—
21C4×C22⋊C4×C61—21no—
22C61×#342C2212yes—
23C22×D244C2×C411yescharacteristic
24C22×C22⋊D61—21no—
25C22×C22⋊D61—21no—
26C22×C4×D61—21no—
27C2×#11758194—41no—
28#14519748—44no—
29C4×D244—41no—
30C4×D244—41no—
31C2×C4⋊Dic61—21no—
32C2×C4⋊Dic61C2×C411yescharacteristic
33C2×C22⋊Dic61—21no—
34C2×C22⋊Dic61—21no—
35C2×#11758198—21no—
36C2×#11758198—21no—
37C2×#11758198—21no—
38C22⋊#92418—22no—
39C22⋊#92418—41no—
40#14519684—21no—
41#14519684—21no—
42#14519684—21no—
43#14519684C2×C411yescharacteristic
44#14519684C2×C411yescharacteristic
45C22×D4×C61D411yescharacteristic
46C23×C4×C61D411yescharacteristic
47C23×C4×C61D411yescharacteristic
48C4×D4×C61—41no—
49C4×D4×C61—41no—
50C2×C4⋊C4×C61D411yescharacteristic
51C2×C22⋊C4×C61—22no—
52C2×C22⋊C4×C61C2×C411yescharacteristic
53C2×C22⋊C4×C61C2311yescharacteristic
54C2×C42×C61—41no—
55C2×C42×C61C2×C411yescharacteristic
56#99×C61—24no—
57#95×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—42no—
69C22×C4×C61—81no—
70C22×C4×C61—81no—
71C22×C4×C61C22⋊C411yescharacteristic
72C22×C4×C61C22⋊C411yescharacteristic
73C22×C4×C61C22⋊C411yescharacteristic
74C22×C4×C61C22×C411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C2×C22⋊D61—42no—
77C2×C22⋊D61—42no—
78C2×C22⋊D61—42no—
79C2×C22⋊D61—42no—
80C2×C22⋊D61—81no—
81C2×C22⋊D61—81no—
82C22×Dic61—21no—
83C22×Dic61—21no—
84C22×Dic61—21no—
85C2×D244—41no—
86C2×D244—42no—
87C2×C4×D61—42no—
88C2×C4×D61—42no—
89C2×C4×D61—42no—
90C4⋊C4×C61—41no—
91C22⋊C4×C61—24no—
92C22⋊C4×C61—41no—
93C22⋊C4×C61—41no—
94C22⋊C4×C61—42no—
95C42×C61—21no—
96C42×C61—21no—
97C42×C61—82no—
98C22⋊Dic61—42no—
99C22⋊Dic61—42no—
100#11758198—41no—
101#11758198—41no—
102#11758198—81no—
103#11758198—81no—
104C4⋊Dic61—42no—
105C4⋊Dic61—41no—
106#11758194—82no—
107C2×#92418—42no—
108C23×C61—21no—
109C23×C61—21no—
110C23×C61—21no—
111C23×C61—21no—
112C23×C61—21no—
113C23×C61—41no—
114C23×C61—41no—
115C23×C61—41no—
116C23×C61—41no—
117C23×C61C2×C22⋊C411yescharacteristic
118C23×C61AGL(1,ℤ/8)12yes—
119C22×D61—22no—
120C22×D61—41no—
121C22×D61—41no—
122C22×D61—41no—
123C22×D61—41no—
124C22×D61—41no—
125C22×D61—41no—
126D4×C61—44no—
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—42no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—44no—
139C2×C4×C61—81no—
140C2×C4×C61—81no—
141C2×C4×C61—82no—
142C2×C4×C61—82no—
143C2×C4×C61#9911yescharacteristic
144C2×C4×C61#9911yescharacteristic
145C2×C4×C61#10412yes—
146C22⋊D61—84no—
147C22⋊D61—84no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157D244—42no—
158D244—42no—
159C4×D61—84no—
160#92418—82no—
161#11774—611nomaximal, Sylow
162C22×C61—21no—
163C22×C61—21no—
164C22×C61—22no—
165C22×C61—42no—
166C22×C61—42no—
167C22×C61—41no—
168C22×C61—41no—
169C22×C61—41no—
170C22×C61—41no—
171C22×C61—41no—
172C22×C61—81no—
173C22×C61—81no—
174C22×C61C2×#9911yescharacteristic
175C22×C61#41811yescharacteristic
176C22×C61C2×#10411yescharacteristic
177C2×D61—42no—
178C2×D61—42no—
179C2×D61—42no—
180C2×D61—81no—
181C2×D61—81no—
182C2×D61—81no—
183C2×D61—81no—
184C4×C61—21no—
185C4×C61—21no—
186C4×C61—22no—
187C4×C61—41no—
188C4×C61—41no—
189C4×C61—41no—
190C4×C61—84no—
191Dic61—81no—
192Dic61—81no—
193Dic61—81no—
194#2535—611no—
195C4×#99D6111yescharacteristic, complemented
196#1465—611no—
197#1344—612no—
198#1343—612no—
199C2×C61—21no—
200C2×C61—21no—
201C2×C61—42no—
202C2×C61—81no—
203C2×C61#150711yescharacteristic
204C2×C61#212011yescharacteristic
205C2×C61#212711yescharacteristic
206D61—82no—
207C2×#121—1221no—
208C2×C4×D4—611no—
209C2×C4×D4C2×D6111yescharacteristic
210C2×#99—21no—
211#407—1221no—
212#397—611no—
213#397—611no—
214#392—611no—
215#392—611no—
216#386—1221no—
217#386—1221no—
218#382—611no—
219#380—1221no—
220C4×C22⋊C4—21no—
221#342C2×D6112yes—
222#324—1221no—
223#323—612no—
224C61#1177411yescharacteristic, complemented, Sylow
225C22×D4—611no—
226C22×D4—1221no—
227C22×D4—1221no—
228C22×D4C22⋊D6111yescharacteristic
229C23×C4—1221no—
230C23×C4D24411yescharacteristic
231C23×C4C22⋊D6111yescharacteristic
232C2×M16—2441no—
233#121—2444no—
234C4×D4—41no—
235C4×D4—41no—
236C4×D4—2441no—
237C4×D4—2441no—
238C2×C4⋊C4—611no—
239C2×C4⋊C4—1221no—
240C2×C4⋊C4D24411yescharacteristic
241C2×C22⋊C4—22no—
242C2×C22⋊C4—1221no—
243C2×C22⋊C4—1221no—
244C2×C22⋊C4—1221no—
245C2×C22⋊C4—1221no—
246C2×C22⋊C4—1221no—
247C2×C22⋊C4C4×D6111yescharacteristic
248C2×C22⋊C4C22×D6111yescharacteristic
249C2×C42—41no—
250C2×C42C4×D6111yescharacteristic
251#99—24no—
252C22⋊C8—1222no—
253C22⋊C8—2441no—
254#95—41no—
255#95—611no—
256#95—611no—
257#95—1221no—
258#95—1221no—
259#95—1221no—
260C24—1221no—
261C24#1175819811yescharacteristic
262C24C2×C22⋊D6111yescharacteristic
263C2×D4—22no—
264C2×D4—22no—
265C2×D4—41no—
266C2×D4—4881no—
267C2×D4—4881no—
268C2×D4—2441no—
269C2×D4—2442no—
270C2×D4—2442no—
271C2×D4—2442no—
272C2×D4—2442no—
273C2×D4—2442no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—42no—
279C22×C4—81no—
280C22×C4—81no—
281C22×C4—1221no—
282C22×C4—1221no—
283C22×C4—1221no—
284C22×C4—2442no—
285C22×C4—2442no—
286C22×C4—2442no—
287C22×C4#1175819811yescharacteristic
288C22×C4#1175819811yescharacteristic
289C22×C4#1175819811yescharacteristic
290C22×C4C2×C4×D6111yescharacteristic
291C22×C4C2×D24411yescharacteristic
292M16—4882no—
293C2×C8—2442no—
294C4⋊C4—41no—
295C4⋊C4—2441no—
296C4⋊C4—2442no—
297C22⋊C4—24no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—42no—
301C22⋊C4—4881no—
302C22⋊C4—4881no—
303C22⋊C4—2442no—
304C22⋊C4—2442no—
305C22⋊C4—2441no—
306C22⋊C4—2441no—
307C42—21no—
308C42—21no—
309C42—82no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—1222no—
320C23—2441no—
321C23—2441no—
322C23—2441no—
323C23—2441no—
324C23—2441no—
325C23—2441no—
326C23C2×#1175819811yescharacteristic
327C23#1451980212yes—
328D4—44no—
329D4—4884no—
330D4—4884no—
331D4—2442no—
332D4—2442no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—44no—
345C2×C4—81no—
346C2×C4—81no—
347C2×C4—82no—
348C2×C4—82no—
349C2×C4—4884no—
350C2×C4—2441no—
351C2×C4—2441no—
352C2×C4—2441no—
353C2×C4—2441no—
354C2×C4—2441no—
355C2×C4—2441no—
356C2×C4—2441no—
357C2×C4—2441no—
358C2×C4—2441no—
359C2×C4#1451969111yescharacteristic
360C2×C4#1451969111yescharacteristic
361C2×C4#1451970512yes—
362C8—4882no—
363C22—21no—
364C22—21no—
365C22—22no—
366C22—42no—
367C22—42no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—81no—
374C22—81no—
375C22—4881no—
376C22—4881no—
377C22—4881no—
378C22—4881no—
379C22—2442no—
380C22—2442no—
381C22—2442no—
382C22C2×#1451969111yescharacteristic
383C22#1683976611yescharacteristic
384C22C2×#1451970511yescharacteristic
385C4—21no—
386C4—21no—
387C4—22no—
388C4—41no—
389C4—41no—
390C4—41no—
391C4—84no—
392C4—4881no—
393C4—4881no—
394C4—4881no—
395C2—21no—
396C2—21no—
397C2—42no—
398C2—81no—
399C2—4882no—
400C2#2144433411yescharacteristic
401C2#2144745811yescharacteristic
402C2#2144748611yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC4×#99×C61C2
socleC22×C61C2×#99
prime radical#21450716C2
cosocleC2×C22⋊C4×C61C23
hypercenterC4×#99D61
hypocenterC61#11774
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
2. #21444157C2semidirect
3. #21443818C2semidirect
4. #21443815C2semidirect
5. C4×#99×C61C2semidirect
7. C2×C4×D244C4semidirect
9. #16839687C4semidirect
11. #16839671C4semidirect
15. #16839628C4semidirect
195. C4×#99D61semidirect
224. C61#11774semidirect

Maximal subgroups

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

subgroupindex
#214507162
#214441572
#214438182
#214438152
C4×#99×C612
#1177461