Finite Group Databasebeta

← #29590632

Subgroups — #29590632

Order 15616.

516 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 73 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#21450767C211yesmaximal, characteristic
2#21445606C211yesmaximal, characteristic
3#21444154C211yesmaximal, characteristic
4#21443844C211yesmaximal, characteristic, complemented
5#21443843C211yesmaximal, characteristic, complemented
6#21443842C211yesmaximal, characteristic, complemented
7C61×#1352C211yesmaximal, characteristic, complemented
8C2×#14519776C411yescharacteristic, complemented
9C2×#14519755—21no—
10C2×#14519754—21no—
11C2×#14519737C2211yescharacteristic
12C2×#14519691—21no—
13#16839724—21no—
14#16839699C411yescharacteristic, complemented
15#16839698C2211yescharacteristic
16#16839697C411yescharacteristic, complemented
17#16839662—21no—
18#16839631—21no—
19#16839613C411yescharacteristic, complemented
20C22⋊C4×Dic61—21no—
21#16839529C2211yescharacteristic
22#16839487—21no—
23#16839486C2211yescharacteristic
24C61×#399C2211yescharacteristic
25C61×#342C2211yescharacteristic
26C61×#323C2211yescharacteristic
27C22×Dic122—21no—
28C22×C22⋊D61D411yescharacteristic
29C23×Dic61D411yescharacteristic
30C22×C4×D61D411yescharacteristic
31C2×#11758189—41no—
32#14519776—41no—
33#14519776—41no—
34#14519755—44no—
35#14519754—44no—
36#14519737—41no—
37#14519737—41no—
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61C2×C411yescharacteristic
40C2×#11758196—21no—
41C2×#11758196—21no—
42C2×#11758196—21no—
43C2×#11758196—21no—
44C2×#11758196D411yescharacteristic
45C2×C22⋊Dic61—21no—
46C2×C22⋊Dic61—21no—
47C2×#11758198—21no—
48C2×#11758198—21no—
49C2×#11758198C2×C411yescharacteristic
50C2×C4×Dic61—21no—
51C2×C4×Dic61—41no—
52C2×C4×Dic61C2×C411yescharacteristic
53#14519691—24no—
54C22⋊#92418—21no—
55#14519689—41no—
56#14519684—41no—
57#14519684C2×C411yescharacteristic
58C2×C4⋊C4×C61—21no—
59C2×C4⋊C4×C61C2×C411yescharacteristic
60C2×C22⋊C4×C61—21no—
61C2×C22⋊C4×C61—21no—
62C2×C22⋊C4×C61C2311yescharacteristic
63C22⋊C8×C61—21no—
64#95×C61C2×C411yescharacteristic
65C24×C61C2×D411yescharacteristic
66C23×D61C22⋊C411yescharacteristic
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61—41no—
70C22×C4×C61C22×C411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C2×C22⋊D61—21no—
73C2×C22⋊D61—21no—
74C2×C22⋊D61—22no—
75C2×C22⋊D61—41no—
76C22×Dic61—21no—
77C22×Dic61—21no—
78C22×Dic61—21no—
79C22×Dic61—21no—
80C22×Dic61—42no—
81C22×Dic61—41no—
82C22×Dic61C22⋊C411yescharacteristic
83C22×Dic61C22⋊C411yescharacteristic
84C22×Dic61C22⋊C411yescharacteristic
85C2×C4×D61—21no—
86C2×C4×D61—21no—
87C2×C4×D61—42no—
88C2×Dic122—42no—
89C2×Dic122—42no—
90C2×Dic122—41no—
91C2×Dic122—41no—
92C2×C8×C61—41no—
93C4⋊C4×C61—42no—
94C4⋊C4×C61—41no—
95C22⋊C4×C61—22no—
96C22⋊C4×C61—41no—
97C22⋊C4×C61—42no—
98C22⋊C4×C61—41no—
99C22⋊Dic61—22no—
100C22⋊Dic61—42no—
101C22⋊Dic61—41no—
102#11758198—41no—
103#11758198—42no—
104#11758198—42no—
105C4⋊Dic61—42no—
106C4⋊Dic61—41no—
107#11758196—24no—
108#11758196—41no—
109#11758196—42no—
110#11758196—42no—
111#11758196—42no—
112C4×Dic61—21no—
113C4×Dic61—21no—
114C4×Dic61—42no—
115C4×Dic61—82no—
116C2×#92418—41no—
117#11758189—82no—
118C23×C61—21no—
119C23×C61—21no—
120C23×C61—41no—
121C23×C61—41no—
122C23×C61C2×C22⋊C411yescharacteristic
123C23×C61#13711yescharacteristic
124C23×C61#13711yescharacteristic
125C22×D61—21no—
126C22×D61—21no—
127C22×D61—21no—
128C22×D61—41no—
129C22×D61—41no—
130C2×C4×C61—22no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—42no—
140C2×C4×C61—41no—
141C2×C4×C61—81no—
142C2×C4×C61—81no—
143C22⋊D61—42no—
144C22⋊D61—42no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—22no—
148C2×Dic61—22no—
149C2×Dic61—21no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—42no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—42no—
157C2×Dic61—41no—
158C2×Dic61—81no—
159C2×Dic61—81no—
160C2×Dic61—81no—
161C2×Dic61#9911yescharacteristic
162C2×Dic61#9911yescharacteristic
163C2×Dic61#10412yes—
164C4×D61—42no—
165C4×D61—81no—
166Dic122—82no—
167Dic122—82no—
168C8×C61—81no—
169#92418—81no—
170#11788—611nomaximal, Sylow
171C22×C61—21no—
172C22×C61—21no—
173C22×C61—21no—
174C22×C61—21no—
175C22×C61—41no—
176C22×C61—41no—
177C22×C61—41no—
178C22×C61—41no—
179C22×C61—81no—
180C22×C61C2×#9911yescharacteristic
181C22×C61#41911yescharacteristic
182C22×C61C2×#10411yescharacteristic
183C2×D61—42no—
184C2×D61—41no—
185C2×D61—41no—
186C2×D61—41no—
187C2×D61—81no—
188C4×C61—42no—
189C4×C61—41no—
190C4×C61—41no—
191C4×C61—82no—
192C4×C61—81no—
193Dic61—21no—
194Dic61—22no—
195Dic61—42no—
196Dic61—41no—
197Dic61—82no—
198Dic61—81no—
199Dic61#35312yes—
200#2542—611no—
201C4×#99—611no—
202#1465—611no—
203#1352—611no—
204#1352—611no—
205#1352—611no—
206#1352D6111yescharacteristic, complemented
207C2×C61—21no—
208C2×C61—21no—
209C2×C61—41no—
210C2×C61—41no—
211C2×C61#150811yescharacteristic
212C2×C61#212311yescharacteristic
213C2×C61C2×#35311yescharacteristic
214D61—81no—
215C2×C4⋊Q8—611no—
216C2×C22⋊Q8—1221no—
217C2×C22⋊Q8—1221no—
218C2×C4×D4—611no—
219C2×#99—1221no—
220#407—1221no—
221#399—611no—
222#399—611no—
223#399—611no—
224#399C2×D6111yescharacteristic
225#390—1221no—
226#384—1221no—
227C4×C4⋊C4—611no—
228C4×C22⋊C4—1221no—
229#342—611no—
230#342C2×D6111yescharacteristic
231#324—1221no—
232#323—611no—
233#323C2×D6111yescharacteristic
234C61#1178811yescharacteristic, complemented, Sylow
235C22×Q8—1221no—
236C22×D4—611no—
237C23×C4—611no—
238C23×C4—611no—
239C2×M16—2441no—
240C4⋊Q8—2441no—
241C4⋊Q8—2441no—
242C22⋊Q8—2444no—
243C22⋊Q8—2444no—
244C4×D4—2441no—
245C4×D4—2441no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—611no—
248C2×C4⋊C4—611no—
249C2×C4⋊C4—1221no—
250C2×C4⋊C4—1221no—
251C2×C4⋊C4—1221no—
252C2×C4⋊C4—1221no—
253C2×C4⋊C4—1221no—
254C2×C4⋊C4C4×D6111yescharacteristic
255C2×C22⋊C4—21no—
256C2×C22⋊C4—21no—
257C2×C22⋊C4—611no—
258C2×C22⋊C4—1221no—
259C2×C22⋊C4—1221no—
260C2×C22⋊C4—1221no—
261C2×C22⋊C4—1221no—
262C2×C22⋊C4C22×D6111yescharacteristic
263C2×C42—611no—
264C2×C42—1221no—
265C2×C42—2441no—
266#99—1224no—
267C22⋊C8—21no—
268C22⋊C8—1221no—
269C22⋊C8—2441no—
270#95—611no—
271#95—2441no—
272#95C4×D6111yescharacteristic
273C24—611no—
274C24D4×D6111yescharacteristic
275C2×Q8—2441no—
276C2×Q8—2441no—
277C2×Q8—2442no—
278C2×Q8—2442no—
279C2×D4—1222no—
280C2×D4—1221no—
281C2×D4—1221no—
282C2×D4—2441no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—41no—
286C22×C4—611no—
287C22×C4—611no—
288C22×C4—611no—
289C22×C4—1221no—
290C22×C4—1221no—
291C22×C4—1221no—
292C22×C4—1221no—
293C22×C4—1221no—
294C22×C4—1221no—
295C22×C4—2442no—
296C22×C4—2442no—
297C22×C4—2441no—
298C22×C4C2×C4×D6111yescharacteristic
299C22×C4D4×D6111yescharacteristic
300M16—4882no—
301C2×C8—41no—
302C2×C8—2441no—
303C4⋊C4—41no—
304C4⋊C4—42no—
305C4⋊C4—1224no—
306C4⋊C4—2441no—
307C4⋊C4—2441no—
308C4⋊C4—2442no—
309C4⋊C4—2442no—
310C4⋊C4—2442no—
311C4⋊C4—2442no—
312C22⋊C4—22no—
313C22⋊C4—41no—
314C22⋊C4—42no—
315C22⋊C4—41no—
316C22⋊C4—1222no—
317C22⋊C4—2441no—
318C22⋊C4—2442no—
319C22⋊C4—2442no—
320C22⋊C4—2442no—
321C22⋊C4—2441no—
322C42—1221no—
323C42—1221no—
324C42—4882no—
325C42—2442no—
326C23—21no—
327C23—21no—
328C23—41no—
329C23—41no—
330C23—1221no—
331C23—1221no—
332C23—1221no—
333C23—2441no—
334C23—2441no—
335C23C22⋊C4×D6111yescharacteristic
336C23#1451980611yescharacteristic
337C23#1451980911yescharacteristic
338Q8—4882no—
339Q8—4882no—
340D4—2442no—
341D4—2442no—
342C2×C4—22no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—42no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—81no—
354C2×C4—81no—
355C2×C4—611no—
356C2×C4—611no—
357C2×C4—612no—
358C2×C4—1222no—
359C2×C4—1221no—
360C2×C4—1221no—
361C2×C4—1222no—
362C2×C4—1221no—
363C2×C4—4881no—
364C2×C4—4881no—
365C2×C4—4881no—
366C2×C4—4881no—
367C2×C4—2442no—
368C2×C4—2442no—
369C2×C4—2442no—
370C2×C4—2441no—
371C2×C4—2441no—
372C2×C4—2441no—
373C2×C4—2441no—
374C2×C4—2441no—
375C2×C4—2441no—
376C8—81no—
377C8—4881no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—81no—
387C22—4881no—
388C22—2442no—
389C22—2441no—
390C22—2441no—
391C22—2441no—
392C22#99×D6111yescharacteristic
393C22#1683976911yescharacteristic
394C22#104×D6111yescharacteristic
395C4—42no—
396C4—41no—
397C4—41no—
398C4—82no—
399C4—81no—
400C4—612no—
401C4—1221no—
402C4—1222no—
403C4—4882no—
404C4—4881no—
405C4—2442no—
406C4—2441no—
407C2—21no—
408C2—21no—
409C2—41no—
410C2—41no—
411C2—4881no—
412C2#2144433711yescharacteristic
413C2#2144747111yescharacteristic
414C2#353×D6111yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1352C2
socleC22×C61C2×#99
prime radicalC22×C22⋊D61D4
cosocleC2×C22⋊C4×C61C23
hypercenter#1352D61
hypocenterC61#11788
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1352

Complements

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

NH ≅ G/Ntype
4. #21443844C2semidirect
5. #21443843C2semidirect
6. #21443842C2semidirect
7. C61×#1352C2semidirect
8. C2×#14519776C4semidirect
14. #16839699C4semidirect
16. #16839697C4semidirect
19. #16839613C4semidirect
206. #1352D61semidirect
234. C61#11788semidirect

Maximal subgroups

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

subgroupindex
#214507672
#214456062
#214441542
#214438442
#214438432
#214438422
C61×#13522
#1178861