Finite Group Databasebeta

← #29568817

Subgroups — #29568817

Order 15616.

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

normal subgroups only

This group has 504 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#21452835C211yesmaximal, characteristic
2#21446957C211yesmaximal, characteristic, complemented
3#21446902C211yesmaximal, characteristic
4#21443644C211yesmaximal, characteristic, complemented
5#21443642C211yesmaximal, characteristic, complemented
6#21443639C211yesmaximal, characteristic
7C61×#2058C211yesmaximal, characteristic, complemented
8C22×#11758201—21no—
9C2×#14519755—21no—
10C2×#14519701—21no—
11C2×#14519700—21no—
12#16839697—21no—
13#16839696—21no—
14#16839684—21no—
15#16839668C2211yescharacteristic
16#16839664C2211yescharacteristic
17#16839640—21no—
18#16839633—21no—
19#16839524—21no—
20#16839517C2211yescharacteristic
21#16839517C2211yescharacteristic
22C2×C4⋊Q8×C61C2211yescharacteristic
23C2×#106×C61—21no—
24C61×#389C2211yescharacteristic
25C61×#340—21no—
26C61×#336C2211yescharacteristic
27C22×Dic122D411yescharacteristic
28C22×D244D411yescharacteristic
29C22×C4×D61—21no—
30C2×#11758201—42no—
31C2×#11758201—42no—
32C2×#11758201—42no—
33C22×#92418—21no—
34C22×#92418—21no—
35#14519755—42no—
36#14519755—42no—
37C2×C4⋊Dic61D411yescharacteristic
38C2×C4⋊Dic61D411yescharacteristic
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×#11758196—21no—
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×#11758198—21no—
45C2×#11758198—21no—
46C2×#11758198—21no—
47#14519701—42no—
48#14519700—42no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52C22×Q8×C61—21no—
53C22×C8×C61—21no—
54C4⋊Q8×C61—42no—
55C2×C4⋊C4×C61—21no—
56C2×C4⋊C4×C61—21no—
57C2×C4⋊C4×C61—21no—
58C2×C4⋊C4×C61D411yescharacteristic
59C2×C4⋊C4×C61D411yescharacteristic
60C2×C42×C61C2311yescharacteristic
61#106×C61—42no—
62#95×C61—21no—
63C23×D61—21no—
64C2×Q8×C61—22no—
65C2×Q8×C61—41no—
66C2×Q8×C61—41no—
67C2×Q8×C61—41no—
68C2×Q8×C61—41no—
69C2×Q8×C61—41no—
70C22×C4×C61—21no—
71C22×C4×C61—21no—
72C22×C4×C61—41no—
73C22×C4×C61C2×D411yescharacteristic
74C22×C4×C61C2×D411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C22×Dic61—21no—
77C22×Dic61—21no—
78C22×Dic61—21no—
79C2×D244—21no—
80C2×D244—41no—
81C2×D244—41no—
82C2×D244SD1612yes—
83C2×C4×D61—42no—
84C2×C4×D61—81no—
85C2×C4×D61—81no—
86C2×Dic122—21no—
87C2×Dic122—41no—
88C2×Dic122—41no—
89C2×Dic122SD1612yescomplemented
90C2×C8×C61—22no—
91C2×C8×C61—41no—
92C2×C8×C61—41no—
93C4⋊C4×C61—22no—
94C4⋊C4×C61—22no—
95C4⋊C4×C61—21no—
96C4⋊C4×C61—21no—
97C4⋊C4×C61—41no—
98C4⋊C4×C61—41no—
99C4⋊C4×C61—41no—
100C4⋊C4×C61—41no—
101C4⋊C4×C61—41no—
102C42×C61—41no—
103#11758201—48no—
104#11758198—42no—
105#11758198—41no—
106#11758198—41no—
107#11758198—41no—
108#11758198—41no—
109#11758198—81no—
110#11758198—81no—
111C4⋊Dic61—41no—
112C4⋊Dic61—41no—
113#11758196—42no—
114#11758196—42no—
115#11758196—81no—
116C2×#92418—22no—
117C2×#92418—41no—
118C2×#92418—41no—
119C2×#92418—41no—
120C2×#92418—41no—
121C2×#92418—41no—
122C23×C61#12011yescharacteristic
123C22×D61—22no—
124C22×D61—41no—
125C22×D61—41no—
126C22×D61—41no—
127C22×D61—41no—
128C22×D61—41no—
129C22×D61—41no—
130Q8×C61—42no—
131Q8×C61—42no—
132Q8×C61—81no—
133Q8×C61—81no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—42no—
146C2×C4×C61—41no—
147C2×C4×C61—81no—
148C2×C4×C61—81no—
149C2×C4×C61C2×SD1611yescharacteristic
150C2×C4×C61C2×SD1611yescharacteristic
151C2×C4×C61#13511yescharacteristic
152C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C61#13711yescharacteristic
154C2×C4×C61#13711yescharacteristic
155C2×Dic61—22no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61—41no—
163C2×Dic61—41no—
164D244—42no—
165D244—81no—
166C4×D61—84no—
167Dic122—42no—
168Dic122—81no—
169C8×C61—42no—
170#92418—42no—
171#92418—81no—
172#7753—611nomaximal, Sylow
173C22×C61#44811yescharacteristic
174C22×C61#45011yescharacteristic
175C22×C61#45211yescharacteristic
176C22×C61#45311yescharacteristic
177C22×C61#45511yescharacteristic
178C22×C61#45611yescharacteristic
179C22×C61B(4,𝔽2)11yescharacteristic
180C2×D61—42no—
181C2×D61—42no—
182C2×D61—42no—
183C2×D61—81no—
184C2×D61—81no—
185C2×D61—81no—
186C2×D61—81no—
187C4×C61—21no—
188C4×C61—21no—
189C4×C61—21no—
190C4×C61—21no—
191C4×C61—21no—
192C4×C61—21no—
193C4×C61—82no—
194C4×C61—81no—
195C4×C61—81no—
196Dic61—42no—
197Dic61—81no—
198Dic61—81no—
199#2732—611no—
200#2058D6111yescharacteristic, complemented
201#2024—611no—
202#2013—611no—
203#1272—611no—
204#1271—611no—
205#1270—611no—
206C2×C61#159611yescharacteristic
207C2×C61#160111yescharacteristic
208C2×C61#160311yescharacteristic
209C2×C61#163111yescharacteristic
210C2×C61#164311yescharacteristic
211C2×C61#165111yescharacteristic
212C2×C61#166111yescharacteristic
213D61—82no—
214C22×SD16—1221no—
215C2×C4⋊Q8C2×D6111yescharacteristic
216C2×C22⋊Q8—1221no—
217C2×#106—21no—
218C2×#103—1221no—
219C2×#103—1221no—
220#399—1221no—
221#398—1221no—
222#396—1221no—
223#391—611no—
224#390—611no—
225#389C2×D6111yescharacteristic
226#386—1221no—
227#385—1221no—
228#340—21no—
229#340—1221no—
230#336—611no—
231#336—611no—
232#336C2×D6111yescharacteristic
233C61#775311yescharacteristic, complemented, Sylow
234C22×Q8—21no—
235C22×Q8—611no—
236C22×D4—611no—
237C23×C4—1221no—
238C2×SD16—2442no—
239C2×SD16—2442no—
240C2×SD16—2442no—
241C22×C8—21no—
242C22×C8—1221no—
243C22×C8—1221no—
244C4⋊Q8—42no—
245C22⋊Q8—2442no—
246C22⋊Q8—2442no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—611no—
251C2×C4⋊C4—611no—
252C2×C4⋊C4—1221no—
253C2×C4⋊C4—1221no—
254C2×C4⋊C4—1221no—
255C2×C4⋊C4C22⋊D6111yescharacteristic
256C2×C4⋊C4C22⋊D6111yescharacteristic
257C2×C22⋊C4—1221no—
258C2×C22⋊C4—1221no—
259C2×C22⋊C4—1221no—
260C2×C22⋊C4—1221no—
261C2×C22⋊C4—1221no—
262C2×C42C22×D6111yescharacteristic
263#106—42no—
264#103—2442no—
265#103—2442no—
266#95—21no—
267#95—1221no—
268#95—1221no—
269#95—1221no—
270C24—1221no—
271C2×Q8—22no—
272C2×Q8—41no—
273C2×Q8—41no—
274C2×Q8—41no—
275C2×Q8—41no—
276C2×Q8—41no—
277C2×Q8—612no—
278C2×Q8—1221no—
279C2×Q8—2441no—
280C2×Q8—2441no—
281C2×D4—612no—
282C2×D4—1221no—
283C2×D4—2441no—
284C2×D4—2441no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—41no—
288C22×C4—1221no—
289C22×C4—1221no—
290C22×C4—1221no—
291C22×C4—4881no—
292C22×C4—4881no—
293C22×C4—2442no—
294C22×C4D4×D6111yescharacteristic
295C22×C4D4×D6111yescharacteristic
296C22×C4C2×C22⋊D6111yescharacteristic
297SD16—2448no—
298C2×C8—22no—
299C2×C8—41no—
300C2×C8—41no—
301C2×C8—1222no—
302C2×C8—2441no—
303C2×C8—2441no—
304C2×C8—2441no—
305C2×C8—2441no—
306C2×C8—2441no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—4881no—
317C4⋊C4—2441no—
318C4⋊C4—2441no—
319C4⋊C4—2442no—
320C4⋊C4—2442no—
321C22⋊C4—4881no—
322C22⋊C4—4881no—
323C22⋊C4—2442no—
324C22⋊C4—2441no—
325C22⋊C4—2441no—
326C22⋊C4—2441no—
327C22⋊C4—2441no—
328C42—41no—
329C23—1222no—
330C23—2441no—
331C23—2441no—
332C23—2441no—
333C23—2441no—
334C23—2441no—
335C23—2441no—
336C23#1451974511yescharacteristic
337Q8—42no—
338Q8—42no—
339Q8—81no—
340Q8—81no—
341Q8—4881no—
342Q8—2442no—
343D4—4881no—
344D4—2442no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—41no—
352C2×C4—42no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4—1222no—
361C2×C4—4884no—
362C2×C4—2441no—
363C2×C4—2441no—
364C2×C4—2441no—
365C2×C4—2441no—
366C2×C4—2441no—
367C2×C4—2441no—
368C2×C4—2441no—
369C2×C4—2441no—
370C2×C4SD16×D6111yescharacteristic
371C2×C4SD16×D6111yescharacteristic
372C2×C4#1451979711yescharacteristic
373C2×C4#1451980411yescharacteristic
374C2×C4#1451980611yescharacteristic
375C2×C4#1451980811yescharacteristic
376C8—42no—
377C8—4881no—
378C8—2442no—
379C22—4881no—
380C22—4881no—
381C22—4881no—
382C22—4881no—
383C22—2442no—
384C22—2442no—
385C22—2442no—
386C22#1683989911yescharacteristic
387C22#1683991111yescharacteristic
388C22#1683992211yescharacteristic
389C22#1683992811yescharacteristic
390C22#1683993811yescharacteristic
391C22#1683994411yescharacteristic
392C22#1683994811yescharacteristic
393C4—21no—
394C4—21no—
395C4—21no—
396C4—21no—
397C4—21no—
398C4—21no—
399C4—81no—
400C4—82no—
401C4—81no—
402C4—4881no—
403C4—4881no—
404C4—2442no—
405C2—4882no—
406C2#2144474011yescharacteristic
407C2#2144476911yescharacteristic
408C2#2144478011yescharacteristic
409C2#2144494511yescharacteristic
410C2#2144502511yescharacteristic
411C2#2144507911yescharacteristic
412C2#2144513411yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#2058C2
socleC23×C61#120
prime radicalC22×D244D4
hypercenter#2058D61
hypocenterC61#7753
LCSG ▷ C2×C42×C61 ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2058

Complements

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

NH ≅ G/Ntype
2. #21446957C2semidirect
4. #21443644C2semidirect
5. #21443642C2semidirect
7. C61×#2058C2semidirect
89. C2×Dic122SD16semidirect
200. #2058D61semidirect
233. C61#7753semidirect

Maximal subgroups

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

subgroupindex
#214528352
#214469572
#214469022
#214436442
#214436422
#214436392
C61×#20582
#775361