Finite Group Databasebeta

← #29590806

Subgroups — #29590806

Order 15616.

418 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 69 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#21451692C211yesmaximal, characteristic
2#21445806C211yesmaximal, characteristic
3#21444154C211yesmaximal, characteristic
4#21443844C211yesmaximal, characteristic, complemented
5#21443842C211yesmaximal, characteristic, complemented
6#21443819C211yesmaximal, characteristic, complemented
7C61×#1344C211yesmaximal, characteristic, complemented
8C2×#14519768C411yescharacteristic, complemented
9C2×#14519737C2211yescharacteristic
10C2×#14519691—21no—
11#16839724—21no—
12#16839699C411yescharacteristic, complemented
13#16839698C2211yescharacteristic
14#16839696—21no—
15#16839688C411yescharacteristic, complemented
16#16839677—21no—
17#16839637—21no—
18#16839636—21no—
19#16839629C411yescharacteristic, complemented
20#16839620—21no—
21#16839529C2211yescharacteristic
22#16839487—21no—
23#16839486C2211yescharacteristic
24C61×#397C2211yescharacteristic
25C61×#342C2211yescharacteristic
26C61×#323C2211yescharacteristic
27C22×C22⋊D61D411yescharacteristic
28C23×Dic61D411yescharacteristic
29C22×C4×D61D411yescharacteristic
30C2×#11758189—41no—
31#14519768—41no—
32#14519768—41no—
33#14519737—41no—
34#14519737—41no—
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61C2×C411yescharacteristic
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758196—41no—
41C2×#11758196D411yescharacteristic
42C2×C22⋊Dic61—21no—
43C2×C22⋊Dic61—21no—
44C2×#11758198—21no—
45C2×#11758198—21no—
46C2×#11758198C2×C411yescharacteristic
47C2×C4×Dic61C2×C411yescharacteristic
48#14519691—42no—
49C22⋊#92418—21no—
50#14519689—41no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684—41no—
55#14519684C2×C411yescharacteristic
56C2×C4⋊C4×C61C2×C411yescharacteristic
57C2×C22⋊C4×C61—21no—
58C2×C22⋊C4×C61—21no—
59C2×C22⋊C4×C61C2311yescharacteristic
60C22⋊C8×C61—21no—
61#95×C61—21no—
62#95×C61C2×C411yescharacteristic
63C24×C61C2×D411yescharacteristic
64C23×D61C22⋊C411yescharacteristic
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—41no—
68C22×C4×C61C22×C411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C2×C22⋊D61—21no—
71C2×C22⋊D61—21no—
72C2×C22⋊D61—41no—
73C2×C22⋊D61—41no—
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61—21no—
77C22×Dic61—21no—
78C22×Dic61—41no—
79C22×Dic61—81no—
80C22×Dic61C22⋊C411yescharacteristic
81C22×Dic61C22⋊C411yescharacteristic
82C22×Dic61C22⋊C411yescharacteristic
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×C4×D61—81no—
86C2×C8×C61—41no—
87C4⋊C4×C61—41no—
88C22⋊C4×C61—41no—
89C22⋊C4×C61—41no—
90C22⋊C4×C61—41no—
91C22⋊C4×C61—41no—
92C22⋊C4×C61—41no—
93C22⋊Dic61—41no—
94C22⋊Dic61—41no—
95C22⋊Dic61—81no—
96#11758198—41no—
97#11758198—42no—
98#11758198—81no—
99C4⋊Dic61—41no—
100C4⋊Dic61—41no—
101C4⋊Dic61—41no—
102C4⋊Dic61—81no—
103#11758196—41no—
104#11758196—42no—
105#11758196—81no—
106#11758196—82no—
107C4×Dic61—21no—
108C4×Dic61—21no—
109C2×#92418—41no—
110#11758189—82no—
111C23×C61—21no—
112C23×C61—21no—
113C23×C61—41no—
114C23×C61—41no—
115C23×C61C2×C22⋊C411yescharacteristic
116C23×C61AGL(1,ℤ/8)11yescharacteristic
117C23×C61#13711yescharacteristic
118C22×D61—21no—
119C22×D61—21no—
120C22×D61—21no—
121C22×D61—41no—
122C22×D61—41no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—81no—
134C2×C4×C61—81no—
135C2×C4×C61—81no—
136C22⋊D61—42no—
137C22⋊D61—42no—
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—41no—
143C2×Dic61—42no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—81no—
152C2×Dic61—81no—
153C2×Dic61—81no—
154C2×Dic61—81no—
155C2×Dic61#9911yescharacteristic
156C2×Dic61#9911yescharacteristic
157C4×D61—42no—
158C4×D61—81no—
159C8×C61—81no—
160#92418—81no—
161#11827—611nomaximal, Sylow
162C22×C61—21no—
163C22×C61—21no—
164C22×C61—21no—
165C22×C61—21no—
166C22×C61—41no—
167C22×C61—41no—
168C22×C61—41no—
169C22×C61—41no—
170C22×C61—81no—
171C22×C61C2×#9911yescharacteristic
172C22×C61#41711yescharacteristic
173C22×C61#42111yescharacteristic
174C2×D61—42no—
175C2×D61—41no—
176C2×D61—41no—
177C2×D61—41no—
178C2×D61—81no—
179C4×C61—41no—
180C4×C61—41no—
181C4×C61—81no—
182C4×C61—81no—
183C4×C61—161no—
184Dic61—21no—
185Dic61—21no—
186Dic61—41no—
187Dic61—41no—
188Dic61—81no—
189Dic61—81no—
190Dic61—161no—
191#2633—611no—
192#1799—611no—
193#1465—611no—
194#1352—611no—
195#1352—611no—
196#1344—611no—
197#1344D6111yescharacteristic, complemented
198C2×C61—21no—
199C2×C61—21no—
200C2×C61—41no—
201C2×C61—41no—
202C2×C61#151311yescharacteristic
203C2×C61#212311yescharacteristic
204C2×C61#212711yescharacteristic
205D61—81no—
206C2×#125—611no—
207C2×C4×D4—611no—
208C2×#99—1221no—
209#407—1221no—
210#399—611no—
211#399—611no—
212#398—1221no—
213#397—611no—
214#397C2×D6111yescharacteristic
215#394—1221no—
216#385—1221no—
217#385—1221no—
218#383—611no—
219#380—1221no—
220#342—611no—
221#342C2×D6111yescharacteristic
222#324—1221no—
223#323—611no—
224#323C2×D6111yescharacteristic
225C61#1182711yescharacteristic, complemented, Sylow
226C22×D4—611no—
227C23×C4—611no—
228C23×C4—611no—
229C2×M16—2441no—
230#125—2441no—
231#125—2441no—
232C4×D4—2441no—
233C4×D4—2441no—
234C2×C4⋊C4—611no—
235C2×C4⋊C4—611no—
236C2×C4⋊C4—1221no—
237C2×C4⋊C4—1221no—
238C2×C4⋊C4—1221no—
239C2×C4⋊C4—1221no—
240C2×C4⋊C4—2441no—
241C2×C4⋊C4C4×D6111yescharacteristic
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—611no—
245C2×C22⋊C4—1221no—
246C2×C22⋊C4—1221no—
247C2×C22⋊C4—1221no—
248C2×C22⋊C4—1221no—
249C2×C22⋊C4C22×D6111yescharacteristic
250C2×C42—611no—
251#99—2442no—
252C22⋊C8—21no—
253C22⋊C8—1221no—
254C22⋊C8—2441no—
255#95—21no—
256#95—611no—
257#95—1221no—
258#95—1221no—
259#95—1221no—
260#95—2441no—
261#95C4×D6111yescharacteristic
262C24—611no—
263C24D4×D6111yescharacteristic
264C2×D4—1221no—
265C2×D4—1221no—
266C2×D4—2441no—
267C2×D4—2441no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—41no—
271C22×C4—611no—
272C22×C4—611no—
273C22×C4—611no—
274C22×C4—1221no—
275C22×C4—1221no—
276C22×C4—1221no—
277C22×C4—1221no—
278C22×C4—1221no—
279C22×C4—1221no—
280C22×C4—4881no—
281C22×C4—4881no—
282C22×C4—2441no—
283C22×C4C2×C4×D6111yescharacteristic
284C22×C4D4×D6111yescharacteristic
285M16—4882no—
286C2×C8—41no—
287C2×C8—2441no—
288C4⋊C4—41no—
289C4⋊C4—4881no—
290C4⋊C4—4881no—
291C4⋊C4—4882no—
292C4⋊C4—2441no—
293C4⋊C4—2441no—
294C4⋊C4—2441no—
295C4⋊C4—2441no—
296C4⋊C4—2442no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—41no—
301C22⋊C4—41no—
302C22⋊C4—4881no—
303C22⋊C4—4881no—
304C22⋊C4—2441no—
305C22⋊C4—2442no—
306C22⋊C4—2441no—
307C22⋊C4—2441no—
308C42—1221no—
309C42—1221no—
310C23—21no—
311C23—21no—
312C23—41no—
313C23—41no—
314C23—1221no—
315C23—1221no—
316C23—1221no—
317C23—2441no—
318C23—2441no—
319C23C22⋊C4×D6111yescharacteristic
320C23#1451980111yescharacteristic
321C23#1451980611yescharacteristic
322D4—2442no—
323D4—2442no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—611no—
338C2×C4—611no—
339C2×C4—1221no—
340C2×C4—1221no—
341C2×C4—1221no—
342C2×C4—1221no—
343C2×C4—4881no—
344C2×C4—4881no—
345C2×C4—4881no—
346C2×C4—4881no—
347C2×C4—4881no—
348C2×C4—2442no—
349C2×C4—2441no—
350C2×C4—2442no—
351C2×C4—2441no—
352C2×C4—2441no—
353C2×C4—2441no—
354C2×C4—2441no—
355C2×C4—2441no—
356C2×C4—2441no—
357C2×C4—2441no—
358C8—81no—
359C8—4881no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—81no—
369C22—4881no—
370C22—2442no—
371C22—2441no—
372C22—2441no—
373C22—2441no—
374C22#99×D6111yescharacteristic
375C22#1683976011yescharacteristic
376C22#1683977711yescharacteristic
377C4—41no—
378C4—41no—
379C4—81no—
380C4—81no—
381C4—161no—
382C4—1221no—
383C4—1221no—
384C4—9761no—
385C4—4881no—
386C4—4881no—
387C4—2441no—
388C4—2441no—
389C2—21no—
390C2—21no—
391C2—41no—
392C2—41no—
393C2—4881no—
394C2#2144435911yescharacteristic
395C2#2144747111yescharacteristic
396C2#2144748711yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1344C2
socleC22×C61C2×#99
prime radicalC22×C22⋊D61D4
cosocleC2×C22⋊C4×C61C23
hypercenter#1344D61
hypocenterC61#11827
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1344

Complements

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

NH ≅ G/Ntype
4. #21443844C2semidirect
5. #21443842C2semidirect
6. #21443819C2semidirect
7. C61×#1344C2semidirect
8. C2×#14519768C4semidirect
12. #16839699C4semidirect
15. #16839688C4semidirect
19. #16839629C4semidirect
197. #1344D61semidirect
225. C61#11827semidirect

Maximal subgroups

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

subgroupindex
#214516922
#214458062
#214441542
#214438442
#214438422
#214438192
C61×#13442
#1182761