Finite Group Databasebeta

← #29577336

Subgroups — #29577336

Order 15616.

548 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 111 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#21454848C211yesmaximal, characteristic
2#21450995C211yesmaximal, characteristic
3#21444390C212yesmaximal, complemented
4#21443697C212yesmaximal, complemented
5C61×#1799C211yesmaximal, characteristic
6C2×#14519756C2211yescharacteristic
7#16839834—24no—
8#16839819—21no—
9#16839726—21no—
10C2×C22⋊#92418C2212yes—
11#16839701C411yescharacteristic, complemented
12#16839698C411yescharacteristic, complemented
13#16839682C411yescharacteristic, complemented
14#16839674C411yescharacteristic, complemented
15#16839646—21no—
16#16839642—21no—
17#16839635—21no—
18#16839620—21no—
19C2×#14519684C2211yescharacteristic
20#16839498—24no—
21C2×C4×D4×C61C2211yescharacteristic
22C2×#99×C61—21no—
23C61×#380C2212yes—
24C61×#342—21no—
25C22×Dic122C2×C411yescharacteristic
26C23×Dic61—21no—
27C2×#11758194—22no—
28C22×#92418—22no—
29#14519756—22no—
30#14519756—22no—
31C2×C4⋊Dic61C2×C411yescharacteristic
32C2×#11758196—21no—
33C2×#11758196—21no—
34C2×#11758196—21no—
35C2×C22⋊Dic61—21no—
36C2×C22⋊Dic61—21no—
37C2×C22⋊Dic61—21no—
38C4⋊#92418—22no—
39C22⋊#92418—22no—
40C22⋊#92418—22no—
41C22⋊#92418D414yes—
42#14519688—22no—
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684C2×C411yescharacteristic
49#14519684C2×C411yescharacteristic
50C22×D4×C61D411yescharacteristic
51C23×C4×C61D411yescharacteristic
52C23×C4×C61C2311yescharacteristic
53C4×D4×C61—22no—
54C4×D4×C61—22no—
55C2×C4⋊C4×C61—22no—
56C2×C4⋊C4×C61C2×C411yescharacteristic
57C2×C22⋊C4×C61—22no—
58C2×C22⋊C4×C61C2×C411yescharacteristic
59C2×C22⋊C4×C61D411yescharacteristic
60C2×C42×C61D411yescharacteristic
61#99×C61—42no—
62#95×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—42no—
72C22×C4×C61—81no—
73C22×C4×C61—81no—
74C22×C4×C61C22⋊C411yescharacteristic
75C22×C4×C61C22⋊C411yescharacteristic
76C22×C4×C61C22⋊C411yescharacteristic
77C22×C4×C61C22×C411yescharacteristic
78C22×C4×C61C2×D412yes—
79C22×C4×C61C2×D411yescharacteristic
80C22×C4×C61#4112yes—
81C22×Dic61—21no—
82C22×Dic61—21no—
83C22×Dic61—21no—
84C22×Dic61—21no—
85C22×Dic61—42no—
86C22×Dic61—41no—
87C22×Dic61—41no—
88C22×Dic61—81no—
89C2×Dic122—22no—
90C2×Dic122—81no—
91C4⋊C4×C61—22no—
92C4⋊C4×C61—82no—
93C22⋊C4×C61—22no—
94C22⋊C4×C61—22no—
95C22⋊C4×C61—42no—
96C22⋊C4×C61—42no—
97C42×C61—21no—
98C42×C61—21no—
99C22⋊Dic61—42no—
100C22⋊Dic61—42no—
101C22⋊Dic61—81no—
102C4⋊Dic61—22no—
103#11758196—42no—
104#11758196—41no—
105#11758196—41no—
106#11758196—81no—
107#11758194—82no—
108C2×#92418—24no—
109C2×#92418—82no—
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×C61—82no—
138C2×C4×C61—82no—
139C2×C4×C61—82no—
140C2×C4×C61C4×D412yes—
141C2×C4×C61#12011yescharacteristic
142C2×C4×C61#12311yescharacteristic
143C2×Dic61—22no—
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—41no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—82no—
156C2×Dic61—82no—
157Dic122—82no—
158#92418—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—
183C4×C61—162no—
184Dic61—42no—
185Dic61—81no—
186Dic61—81no—
187Dic61—81no—
188#2973—611no—
189#2564—611no—
190#1799D6111yescharacteristic
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—1224no—
204#432—1221no—
205C2×#99—21no—
206#407—1221no—
207C2×C22⋊C8—612no—
208#400—611no—
209#399—611no—
210#395—611no—
211#393—611no—
212#387—1221no—
213#386—1221no—
214#385—1221no—
215#380—1221no—
216#380C2×D6112yes—
217C2×#95—611no—
218#342—21no—
219#328—1224no—
220C61#938511yescharacteristic, complemented, Sylow
221C22×Q8—611no—
222C22×D4C22⋊D6111yescharacteristic
223C23×C4—1221no—
224C23×C4D24411yescharacteristic
225C23×C4C22×D6111yescharacteristic
226C2×M16—1222no—
227C22×C8—1222no—
228C22⋊Q8—1222no—
229C22⋊Q8—1222no—
230C4×D4—22no—
231C4×D4—22no—
232C2×C4⋊C4—22no—
233C2×C4⋊C4—611no—
234C2×C4⋊C4—1221no—
235C2×C4⋊C4—1221no—
236C2×C4⋊C4—1221no—
237C2×C4⋊C4C4×D6111yescharacteristic
238C2×C22⋊C4—22no—
239C2×C22⋊C4—1221no—
240C2×C22⋊C4—1221no—
241C2×C22⋊C4—1221no—
242C2×C22⋊C4C4×D6111yescharacteristic
243C2×C22⋊C4C22⋊D6111yescharacteristic
244C2×C42D24411yescharacteristic
245C4⋊C8—1222no—
246#99—42no—
247C22⋊C8—614no—
248C22⋊C8—1222no—
249C22⋊C8—1222no—
250#97—1222no—
251#95—22no—
252#95—611no—
253#95—611no—
254#95—1221no—
255#95—1221no—
256#95—1221no—
257#95—1221no—
258#95—1221no—
259C24#1175819811yescharacteristic
260C24C2×C22⋊D6111yescharacteristic
261C2×Q8—1222no—
262C2×Q8—4881no—
263C2×D4—21no—
264C2×D4—22no—
265C2×D4—21no—
266C2×D4—22no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—42no—
270C22×C4—81no—
271C22×C4—81no—
272C22×C4—1221no—
273C22×C4—1221no—
274C22×C4—1221no—
275C22×C4—1221no—
276C22×C4—4881no—
277C22×C4—2442no—
278C22×C4—2441no—
279C22×C4—2441no—
280C22×C4#1175819811yescharacteristic
281C22×C4#1175819811yescharacteristic
282C22×C4#1175819811yescharacteristic
283C22×C4C2×C4×D6111yescharacteristic
284C22×C4C2×D24411yescharacteristic
285C22×C4D4×D6112yes—
286C22×C4#1175822412yes—
287M16—4882no—
288C2×C8—1224no—
289C2×C8—4882no—
290C4⋊C4—22no—
291C4⋊C4—82no—
292C4⋊C4—1222no—
293C4⋊C4—4881no—
294C4⋊C4—2442no—
295C4⋊C4—2441no—
296C4⋊C4—2441no—
297C22⋊C4—22no—
298C22⋊C4—22no—
299C22⋊C4—42no—
300C22⋊C4—42no—
301C22⋊C4—4881no—
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#1451974912yes—
315C23#1451980311yescharacteristic
316C23#1451980712yes—
317C23#1451980811yescharacteristic
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—82no—
335C2×C4—82no—
336C2×C4—82no—
337C2×C4—1222no—
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×C4#1451973712yes—
352C2×C4#1451974711yescharacteristic
353C2×C4#1451976111yescharacteristic
354C8—2444no—
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#1683963911yescharacteristic
368C22#1683976111yescharacteristic
369C22#1683977011yescharacteristic
370C22#1684000612yes—
371C22#1684001812yes—
372C4—21no—
373C4—21no—
374C4—22no—
375C4—41no—
376C4—41no—
377C4—41no—
378C4—162no—
379C4—4881no—
380C4—4881no—
381C4—4881no—
382C4—2442no—
383C2—22no—
384C2—21no—
385C2—21no—
386C2—22no—
387C2—81no—
388C2#2144620011yescharacteristic
389C2#2144625011yescharacteristic
390C2#2144635911yescharacteristic
subgroupG/H
centerC22#16839639
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1799C2
socleC22×C61#386
prime radicalC22×D4×C61D4
cosocleC23×C4×C61C23
hypercenter#1799D61
hypocenterC61#9385
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1799

Complements

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

NH ≅ G/Ntype
3. #21444390C2semidirect
4. #21443697C2semidirect
11. #16839701C4semidirect
12. #16839698C4semidirect
13. #16839682C4semidirect
14. #16839674C4semidirect
220. C61#9385semidirect

Maximal subgroups

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

subgroupindex
#214548482
#214509952
#214443902
#214436972
C61×#17992
#938561