Finite Group Databasebeta

← #29597069

Subgroups — #29597069

Order 15616.

590 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D976C211yesmaximal, characteristic
2C2×C4×D488C211yesmaximal, characteristic, complemented
3C2×#16839564C211yesmaximal, characteristic, complemented
4C2×#16839564C211yesmaximal, characteristic, complemented
5#21446685C211yesmaximal, characteristic, complemented
6#21443911C211yesmaximal, characteristic, complemented
7C61×#1374C211yesmaximal, characteristic, complemented
8C22×D488C2211yescharacteristic
9C22×D488C2211yescharacteristic
10C2×C4×D244—21no—
11C2×D976—22no—
12C2×D976—22no—
13C2×D976C414yescomplemented
14C4×D488—22no—
15C4×D488—22no—
16C2×#14519711C2211yescharacteristic
17C2×#14519711C2211yescharacteristic
18C2×#14519699—21no—
19C2×#14519699—21no—
20#16839664—21no—
21#16839564—22no—
22#16839564—22no—
23C22×C16×C61C2211yescharacteristic
24C22×C16×C61C2211yescharacteristic
25C2×C4×C8×C61C2211yescharacteristic
26C22×D244—21no—
27C22×D244—21no—
28C22×C4×D61—41no—
29C2×D488—21no—
30C2×D488—21no—
31C2×D488—21no—
32C2×D488—21no—
33C2×D488—21no—
34C2×D488—21no—
35C2×D488—21no—
36C2×D488—21no—
37C2×D488C2×C412yes—
38C2×D488C2×C412yescomplemented
39C2×D488D412yes—
40C2×D488D412yes—
41C4×D244—24no—
42C4×D244—42no—
43C2×C4⋊Dic61—21no—
44C2×C4⋊Dic61—21no—
45C2×#11758198—41no—
46C2×#11758198—41no—
47C2×#11758198—41no—
48D976—28no—
49#14519711—21no—
50#14519711—21no—
51#14519711—21no—
52#14519711D412yes—
53#14519699—24no—
54#14519699—42no—
55C22×C8×C61D411yescharacteristic
56C22×C8×C61C2311yescharacteristic
57C2×C42×C61D411yescharacteristic
58C2×C16×C61—21no—
59C2×C16×C61—21no—
60C2×C16×C61—21no—
61C2×C16×C61—21no—
62C2×C16×C61—21no—
63C2×C16×C61C2×C412yescomplemented
64C4×C8×C61—21no—
65C4×C8×C61—21no—
66C23×D61—41no—
67C23×D61—41no—
68C22×C4×C61D811yescharacteristic
69C22×C4×C61D811yescharacteristic
70C22×C4×C61C2×D411yescharacteristic
71C22×Dic61—41no—
72C22×Dic61—41no—
73C2×D244—22no—
74C2×D244—22no—
75C2×D244—22no—
76C2×D244—22no—
77C2×D244—41no—
78C2×D244—41no—
79C2×D244—41no—
80C2×D244—41no—
81C2×D244—41no—
82C2×D244—41no—
83C2×D244—41no—
84C2×D244—41no—
85C2×C4×D61—44no—
86C2×C4×D61—82no—
87C2×C4×D61—82no—
88C2×C8×C61—21no—
89C2×C8×C61—21no—
90C2×C8×C61—21no—
91C2×C8×C61C22×C411yescharacteristic
92C2×C8×C61C2×D411yescharacteristic
93C2×C8×C61C2×D411yescharacteristic
94C2×C8×C61C2×D411yescharacteristic
95C2×C8×C61#4111yescharacteristic
96C2×C8×C61#4111yescharacteristic
97C42×C61—21no—
98C42×C61—21no—
99#11758198—44no—
100#11758198—82no—
101#11758198—82no—
102C4⋊Dic61—22no—
103C4⋊Dic61—41no—
104C4⋊Dic61—41no—
105C4⋊Dic61—41no—
106D488—22no—
107D488—22no—
108D488—22no—
109D488—22no—
110D488—22no—
111D488—41no—
112D488—41no—
113D488C22⋊C414yescomplemented
114C16×C61—22no—
115C16×C61—41no—
116C23×C61C2×D811yescharacteristic
117C22×D61—42no—
118C22×D61—42no—
119C22×D61—42no—
120C22×D61—42no—
121C22×D61—81no—
122C22×D61—81no—
123C22×D61—81no—
124C22×D61—81no—
125C22×D61—81no—
126C22×D61—81no—
127C22×D61—81no—
128C22×D61—81no—
129C22×D61—81no—
130C22×D61—81no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61D1612yescomplemented
137C2×C4×C61C4×D411yescharacteristic
138C2×C4×C61#12011yescharacteristic
139C2×C4×C61#12111yescharacteristic
140C2×C4×C61#13511yescharacteristic
141C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
143C2×Dic61—42no—
144C2×Dic61—81no—
145C2×Dic61—81no—
146C2×Dic61—81no—
147C2×Dic61—81no—
148C2×Dic61—81no—
149D244—24no—
150D244—42no—
151D244—42no—
152D244—42no—
153D244—42no—
154D244—42no—
155D244—81no—
156D244—81no—
157C4×D61—88no—
158C8×C61—41no—
159C8×C61C2×C22⋊C411yescharacteristic
160C8×C61C4×D411yescharacteristic
161C8×C61#12111yescharacteristic
162C8×C61#12311yescharacteristic
163#13012—611nomaximal, Sylow
164C22×C61C4×D811yescharacteristic
165C22×C61#44711yescharacteristic
166C22×C61#45911yescharacteristic
167C22×C61C2×D1611yescharacteristic
168C22×C61#50811yescharacteristic
169C22×C61#50911yescharacteristic
170C22×C61#50911yescharacteristic
171C2×D61—44no—
172C2×D61—82no—
173C2×D61—82no—
174C2×D61—82no—
175C2×D61—82no—
176C2×D61—82no—
177C2×D61—82no—
178C2×D61—82no—
179C2×D61—82no—
180C2×D61—82no—
181C2×D61—161no—
182C2×D61—161no—
183C2×D61—161no—
184C2×D61—161no—
185C4×C61—22no—
186C4×C61—41no—
187C4×C61#38611yescharacteristic
188C4×C61#44211yescharacteristic
189C4×C61#44911yescharacteristic
190C4×C61#46311yescharacteristic
191Dic61—82no—
192Dic61—161no—
193C22×D16—611no—
194C2×C4×D8—611no—
195C2×#357—611no—
196C2×#357—611no—
197#1970—611no—
198#1380—611no—
199#1374D6111yescharacteristic, complemented
200C2×C61#187911yescharacteristic
201C2×C61C4×D1611yescharacteristic
202C2×C61#217711yescharacteristic
203C2×C61#218411yescharacteristic
204C2×C61#218611yescharacteristic
205C2×C61#220611yescharacteristic
206C2×C61#221011yescharacteristic
207D61—84no—
208D61—162no—
209C22×D8—611no—
210C22×D8—611no—
211C2×C4×D4—1221no—
212C2×D16—614no—
213C2×D16—1222no—
214C2×D16—1222no—
215C22×C16C2×D6111yescharacteristic
216C22×C16C2×D6111yescharacteristic
217C4×D8—1222no—
218C4×D8—1222no—
219C2×#107—611no—
220C2×#107—611no—
221C2×#102—1221no—
222C2×#102—1221no—
223C2×C4×C8C2×D6111yescharacteristic
224#390—1221no—
225#357—1222no—
226#357—1222no—
227C61#1301211yescharacteristic, complemented, Sylow
228C22×D4—1221no—
229C22×D4—1221no—
230C23×C4—2441no—
231C2×D8—612no—
232C2×D8—612no—
233C2×D8—612no—
234C2×D8—612no—
235C2×D8—1221no—
236C2×D8—1221no—
237C2×D8—1221no—
238C2×D8—1221no—
239C2×D8—1221no—
240C2×D8—1221no—
241C2×D8—1221no—
242C2×D8—1221no—
243C22×C8D24411yescharacteristic
244C22×C8C22×D6111yescharacteristic
245C4×D4—1224no—
246C4×D4—2442no—
247C2×C4⋊C4—1221no—
248C2×C4⋊C4—1221no—
249C2×C22⋊C4—2441no—
250C2×C22⋊C4—2441no—
251C2×C22⋊C4—2441no—
252C2×C42D24411yescharacteristic
253D16—1228no—
254C2×C16—21no—
255C2×C16—21no—
256C2×C16—21no—
257C2×C16—21no—
258C2×C16—21no—
259C2×C16C4×D6112yescomplemented
260#107—612no—
261#107—1221no—
262#107—1221no—
263#107—1221no—
264#102—1224no—
265#102—2442no—
266C4×C8—21no—
267C4×C8—21no—
268C24—2441no—
269C24—2441no—
270C2×D4—1222no—
271C2×D4—1222no—
272C2×D4—1222no—
273C2×D4—1222no—
274C2×D4—2441no—
275C2×D4—2441no—
276C2×D4—2441no—
277C2×D4—2441no—
278C2×D4—2441no—
279C2×D4—2441no—
280C2×D4—2441no—
281C2×D4—2441no—
282C22×C4—4882no—
283C22×C4—4882no—
284C22×C4—2444no—
285C22×C4—2441no—
286C22×C4—2441no—
287C22×C4D48811yescharacteristic
288C22×C4D48811yescharacteristic
289C22×C4C2×D24411yescharacteristic
290D8—614no—
291D8—1222no—
292D8—1222no—
293D8—1222no—
294D8—1222no—
295D8—1222no—
296D8—2441no—
297D8—2441no—
298C2×C8—21no—
299C2×C8—21no—
300C2×C8—21no—
301C2×C8C2×C4×D6111yescharacteristic
302C2×C8#1175822211yescharacteristic
303C2×C8D4×D6111yescharacteristic
304C2×C8D4×D6111yescharacteristic
305C2×C8D4×D6111yescharacteristic
306C2×C8#1175822611yescharacteristic
307C4⋊C4—1222no—
308C4⋊C4—2441no—
309C4⋊C4—2441no—
310C4⋊C4—2441no—
311C22⋊C4—4882no—
312C22⋊C4—4882no—
313C22⋊C4—2444no—
314C42—21no—
315C42—21no—
316C16—22no—
317C16—41no—
318C23—4881no—
319C23—4881no—
320C23—4881no—
321C23—4881no—
322C23—4881no—
323C23—4881no—
324C23—4881no—
325C23—4881no—
326C23—4881no—
327C23—4881no—
328C23—2442no—
329C23—2442no—
330C23—2442no—
331C23—2442no—
332C23C2×D48811yescharacteristic
333D4—1224no—
334D4—4881no—
335D4—4881no—
336D4—2442no—
337D4—2442no—
338D4—2442no—
339D4—2442no—
340D4—2442no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—4888no—
347C2×C4—4881no—
348C2×C4—4881no—
349C2×C4—4881no—
350C2×C4—4881no—
351C2×C4—4881no—
352C2×C4—2442no—
353C2×C4D97612yescomplemented
354C2×C4C4×D24411yescharacteristic
355C2×C4#1451974711yescharacteristic
356C2×C4#1451975211yescharacteristic
357C2×C4#1451979911yescharacteristic
358C2×C4#1451980511yescharacteristic
359C2×C4#1451980511yescharacteristic
360C8—41no—
361C8C22⋊C4×D6111yescharacteristic
362C8#1451973911yescharacteristic
363C8#1451975011yescharacteristic
364C8#1451976211yescharacteristic
365C22—9761no—
366C22—9761no—
367C22—9761no—
368C22—9761no—
369C22—4882no—
370C22—4882no—
371C22—4882no—
372C22—4882no—
373C22—4882no—
374C22—4882no—
375C22—4882no—
376C22—4882no—
377C22—4882no—
378C22—2444no—
379C22C4×D48811yescharacteristic
380C22#1683989811yescharacteristic
381C22#1683995811yescharacteristic
382C22C2×D97611yescharacteristic
383C22#1684019411yescharacteristic
384C22#1684020011yescharacteristic
385C22#1684020011yescharacteristic
386C4—22no—
387C4—41no—
388C4—9761no—
389C4—4882no—
390C4#1683964011yescharacteristic
391C4#1683987511yescharacteristic
392C4#1683990911yescharacteristic
393C4#1683997811yescharacteristic
394C2—9762no—
395C2—4884no—
396C2#2144616611yescharacteristic
397C2C4×D97611yescharacteristic
398C2#2144769611yescharacteristic
399C2#2144773311yescharacteristic
400C2#2144774411yescharacteristic
401C2#2144785511yescharacteristic
402C2#2144787511yescharacteristic
subgroupG/H
centerC23C2×D488
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC61×#1374C2
socleC23×C61C2×D8
prime radicalC22×D976C2
cosocleC22×C8×C61C23
hypercenter#1374D61
hypocenterC61#13012
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ #1374

Complements

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

NH ≅ G/Ntype
2. C2×C4×D488C2semidirect
3. C2×#16839564C2semidirect
4. C2×#16839564C2semidirect
5. #21446685C2semidirect
6. #21443911C2semidirect
7. C61×#1374C2semidirect
13. C2×D976C4semidirect
38. C2×D488C2×C4semidirect
63. C2×C16×C61C2×C4semidirect
113. D488C22⋊C4semidirect
136. C2×C4×C61D16semidirect
199. #1374D61semidirect
227. C61#13012semidirect
259. C2×C16C4×D61semidirect
353. C2×C4D976semidirect

Maximal subgroups

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

subgroupindex
C22×D9762
C2×C4×D4882
C2×#168395642
#214466852
#214439112
C61×#13742
#1301261