Finite Group Databasebeta

← #29577338

Subgroups — #29577338

Order 15616.

548 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 115 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#21450995C211yesmaximal, characteristic
2#21445807C211yesmaximal, characteristic
3#21444392C212yesmaximal, complemented
4#21443699C212yesmaximal, complemented
5C61×#2973C211yesmaximal, characteristic
6C2×#14519756C2211yescharacteristic
7C2×#14519692—21no—
8#16839701C411yescharacteristic, complemented
9#16839698C411yescharacteristic, complemented
10#16839682C411yescharacteristic, complemented
11#16839674C411yescharacteristic, complemented
12#16839646—21no—
13#16839642—21no—
14#16839635—21no—
15#16839622C2212yes—
16#16839620—21no—
17C2×#14519684C2211yescharacteristic
18#16839529—21no—
19#16839500—24no—
20C2×C4×D4×C61C2211yescharacteristic
21C61×#435—24no—
22C61×#432—21no—
23C61×#407—21no—
24C2×C22⋊C8×C61C2212yes—
25C22×Dic122C2×C411yescharacteristic
26C23×Dic61—21no—
27#14519756—22no—
28#14519756—22no—
29C2×C4⋊Dic61—22no—
30C2×C4⋊Dic61C2×C411yescharacteristic
31C2×#11758196—21no—
32C2×#11758196—21no—
33C2×#11758196—21no—
34C2×C22⋊Dic61—21no—
35C2×C22⋊Dic61—21no—
36C2×C22⋊Dic61—22no—
37C2×C22⋊Dic61—21no—
38#14519692—42no—
39#14519684—21no—
40#14519684—21no—
41#14519684—21no—
42#14519684—21no—
43#14519684—21no—
44#14519684—22no—
45#14519684C2×C411yescharacteristic
46#14519684C2×C411yescharacteristic
47C22×D4×C61D411yescharacteristic
48C23×C4×C61D411yescharacteristic
49C23×C4×C61C2311yescharacteristic
50C2×M16×C61—22no—
51C22×C8×C61—22no—
52C4×D4×C61—22no—
53C4×D4×C61—22no—
54C2×C4⋊C4×C61C2×C411yescharacteristic
55C2×C22⋊C4×C61C2×C411yescharacteristic
56C2×C22⋊C4×C61D411yescharacteristic
57C2×C42×C61D411yescharacteristic
58C4⋊C8×C61—22no—
59C22⋊C8×C61—22no—
60C22⋊C8×C61—22no—
61C22⋊C8×C61D414yes—
62#97×C61—22no—
63C24×C61C22⋊C411yescharacteristic
64C24×C61C2×D411yescharacteristic
65C2×D4×C61—22no—
66C2×D4×C61—21no—
67C2×D4×C61—21no—
68C2×D4×C61—22no—
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61—81no—
72C22×C4×C61—81no—
73C22×C4×C61C22⋊C411yescharacteristic
74C22×C4×C61C22⋊C411yescharacteristic
75C22×C4×C61C22⋊C411yescharacteristic
76C22×C4×C61C22×C411yescharacteristic
77C22×C4×C61C2×D412yes—
78C22×C4×C61C2×D411yescharacteristic
79C22×C4×C61#4112yes—
80C22×Dic61—21no—
81C22×Dic61—21no—
82C22×Dic61—21no—
83C22×Dic61—21no—
84C22×Dic61—42no—
85C22×Dic61—41no—
86C22×Dic61—41no—
87C22×Dic61—42no—
88C22×Dic61—81no—
89C2×Dic122—22no—
90C2×Dic122—81no—
91M16×C61—82no—
92C2×C8×C61—24no—
93C2×C8×C61—82no—
94C4⋊C4×C61—22no—
95C22⋊C4×C61—22no—
96C22⋊C4×C61—22no—
97C42×C61—21no—
98C42×C61—21no—
99C22⋊Dic61—42no—
100C22⋊Dic61—42no—
101C22⋊Dic61—42no—
102C22⋊Dic61—42no—
103C22⋊Dic61—81no—
104C4⋊Dic61—22no—
105C4⋊Dic61—82no—
106#11758196—42no—
107#11758196—41no—
108#11758196—41no—
109#11758196—81no—
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×C61#12112yes—
119C23×C61AGL(1,ℤ/8)11yescharacteristic
120C23×C61#13711yescharacteristic
121C23×C61#13712yes—
122D4×C61—42no—
123D4×C61—42no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—42no—
130C2×C4×C61—42no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—42no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—81no—
137C2×C4×C61C4×D412yes—
138C2×C4×C61#12011yescharacteristic
139C2×C4×C61#12311yescharacteristic
140C2×Dic61—22no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—82no—
153C2×Dic61—82no—
154C2×Dic61—82no—
155C2×Dic61—82no—
156C2×Dic61—82no—
157Dic122—82no—
158C8×C61—44no—
159#9385—611nomaximal, Sylow
160C22×C61—21no—
161C22×C61—22no—
162C22×C61—21no—
163C22×C61—22no—
164C22×C61—41no—
165C22×C61—41no—
166C22×C61—42no—
167C22×C61—42no—
168C22×C61—41no—
169C22×C61—41no—
170C22×C61—41no—
171C22×C61—81no—
172C22×C61#38611yescharacteristic
173C22×C61#41711yescharacteristic
174C22×C61#41911yescharacteristic
175C22×C61#46812yes—
176C22×C61#47012yes—
177C4×C61—21no—
178C4×C61—22no—
179C4×C61—21no—
180C4×C61—41no—
181C4×C61—41no—
182C4×C61—41no—
183Dic61—42no—
184Dic61—81no—
185Dic61—81no—
186Dic61—81no—
187Dic61—162no—
188#2973D6111yescharacteristic
189#2564—611no—
190#1799—611no—
191#1520—612no—
192#1294—612no—
193C2×C61—21no—
194C2×C61—22no—
195C2×C61—21no—
196C2×C61—22no—
197C2×C61—81no—
198C2×C61#188411yescharacteristic
199C2×C61#189411yescharacteristic
200C2×C61#191311yescharacteristic
201C2×C22⋊Q8—611no—
202C2×C4×D4C2×D6111yescharacteristic
203#435—24no—
204#432—21no—
205C2×#99—1221no—
206#407—21no—
207C2×C22⋊C8C2×D6112yes—
208#400—611no—
209#399—611no—
210#395—611no—
211#393—611no—
212#387—1221no—
213#386—1221no—
214#385—1221no—
215#380—612no—
216#380—1221no—
217C2×#95—611no—
218#342—1221no—
219#328—1224no—
220C61#938511yescharacteristic, complemented, Sylow
221C22×Q8—611no—
222C22×D4D24411yescharacteristic
223C23×C4—1221no—
224C23×C4C22⋊D6111yescharacteristic
225C23×C4C22×D6111yescharacteristic
226C2×M16—22no—
227C22×C8—22no—
228C22⋊Q8—1222no—
229C22⋊Q8—1222no—
230C4×D4—22no—
231C4×D4—22no—
232C2×C4⋊C4—611no—
233C2×C4⋊C4—1221no—
234C2×C4⋊C4—1222no—
235C2×C4⋊C4—1221no—
236C2×C4⋊C4—1221no—
237C2×C4⋊C4C4×D6111yescharacteristic
238C2×C22⋊C4—1221no—
239C2×C22⋊C4—1221no—
240C2×C22⋊C4—1221no—
241C2×C22⋊C4—1222no—
242C2×C22⋊C4C4×D6111yescharacteristic
243C2×C22⋊C4D24411yescharacteristic
244C2×C42C22⋊D6111yescharacteristic
245C4⋊C8—22no—
246#99—2442no—
247C22⋊C8—22no—
248C22⋊C8—22no—
249C22⋊C8C22⋊D6114yes—
250#97—22no—
251#95—611no—
252#95—611no—
253#95—1221no—
254#95—1221no—
255#95—1221no—
256#95—1221no—
257#95—1221no—
258#95—1222no—
259C24#1175819811yescharacteristic
260C24C2×D24411yescharacteristic
261C2×Q8—1222no—
262C2×Q8—4881no—
263C2×D4—21no—
264C2×D4—22no—
265C2×D4—22no—
266C2×D4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—81no—
270C22×C4—81no—
271C22×C4—1221no—
272C22×C4—1221no—
273C22×C4—1221no—
274C22×C4—1221no—
275C22×C4—4881no—
276C22×C4—2442no—
277C22×C4—2442no—
278C22×C4—2441no—
279C22×C4—2441no—
280C22×C4#1175819811yescharacteristic
281C22×C4#1175819811yescharacteristic
282C22×C4#1175819811yescharacteristic
283C22×C4C2×C4×D6111yescharacteristic
284C22×C4#1175822212yes—
285C22×C4C2×C22⋊D6112yes—
286C22×C4C2×C22⋊D6111yescharacteristic
287M16—82no—
288C2×C8—24no—
289C2×C8—82no—
290C4⋊C4—22no—
291C4⋊C4—1222no—
292C4⋊C4—4882no—
293C4⋊C4—4881no—
294C4⋊C4—2442no—
295C4⋊C4—2441no—
296C4⋊C4—2441no—
297C22⋊C4—22no—
298C22⋊C4—22no—
299C22⋊C4—4881no—
300C22⋊C4—2442no—
301C22⋊C4—2442no—
302C22⋊C4—2442no—
303C22⋊C4—2442no—
304C42—21no—
305C42—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23C2×#1175819811yescharacteristic
314C23#1451975112yes—
315C23#1451980511yescharacteristic
316C23#1451981012yes—
317C23#1451981011yescharacteristic
318Q8—4882no—
319D4—42no—
320D4—42no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—42no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—81no—
334C2×C4—1222no—
335C2×C4—4882no—
336C2×C4—4882no—
337C2×C4—4882no—
338C2×C4—4882no—
339C2×C4—4882no—
340C2×C4—2441no—
341C2×C4—2441no—
342C2×C4—2441no—
343C2×C4—2441no—
344C2×C4—2441no—
345C2×C4—2441no—
346C2×C4—2441no—
347C2×C4—2441no—
348C2×C4—2441no—
349C2×C4—2441no—
350C2×C4—2441no—
351C2×C4C4×C22⋊D6112yes—
352C2×C4#1451974611yescharacteristic
353C2×C4#1451976011yescharacteristic
354C8—44no—
355C22—21no—
356C22—22no—
357C22—21no—
358C22—22no—
359C22—41no—
360C22—41no—
361C22—42no—
362C22—42no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—81no—
367C22#1683964111yescharacteristic
368C22#1683976411yescharacteristic
369C22#1683977211yescharacteristic
370C22#1684000812yes—
371C22#1684002012yes—
372C4—21no—
373C4—21no—
374C4—22no—
375C4—41no—
376C4—41no—
377C4—41no—
378C4—9762no—
379C4—4881no—
380C4—4881no—
381C4—4881no—
382C4—2442no—
383C2—22no—
384C2—21no—
385C2—21no—
386C2—22no—
387C2—81no—
388C2#2144620211yescharacteristic
389C2#2144625211yescharacteristic
390C2#2144636111yescharacteristic
subgroupG/H
centerC22#16839641
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#2973C2
socleC22×C61#386
prime radicalC22×D4×C61D4
cosocleC23×C4×C61C23
hypercenter#2973D61
hypocenterC61#9385
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2973

Complements

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

NH ≅ G/Ntype
3. #21444392C2semidirect
4. #21443699C2semidirect
8. #16839701C4semidirect
9. #16839698C4semidirect
10. #16839682C4semidirect
11. #16839674C4semidirect
220. C61#9385semidirect

Maximal subgroups

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

subgroupindex
#214509952
#214458072
#214443922
#214436992
C61×#29732
#938561