Finite Group Databasebeta

← #29597374

Subgroups — #29597374

Order 15616.

578 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C16×D61C211yesmaximal, characteristic, complemented
2C2×#16839999C211yesmaximal, characteristic
3C2×#16839564C211yesmaximal, characteristic, complemented
4C2×#16839562C211yesmaximal, characteristic, complemented
5#21445845C211yesmaximal, characteristic, complemented
6#21443910C211yesmaximal, characteristic, complemented
7C61×#1380C211yesmaximal, characteristic, complemented
8C22×D488C2211yescharacteristic
9C22×C8×D61C2211yescharacteristic
10C2×#14519752—21no—
11C22×#11758185C2211yescharacteristic
12C2×C16×D61—22no—
13C2×C16×D61—22no—
14C2×C16×D61—22no—
15#16839999—22no—
16#16839999C414yescomplemented
17C2×#14519711C2211yescharacteristic
18C2×#14519697—21no—
19#16839619—21no—
20#16839564—22no—
21#16839562—22no—
22#16839524—21no—
23C22×C16×C61C2211yescharacteristic
24C2×#107×C61C2211yescharacteristic
25C2×#107×C61C2211yescharacteristic
26C22×D244—21no—
27C22×D244—41no—
28C22×C4×D61D411yescharacteristic
29C2×D488—21no—
30C2×D488—21no—
31C2×D488—21no—
32C2×D488—21no—
33C2×D488—21no—
34C2×D488C2×C412yes—
35C22×#92418D411yescharacteristic
36C2×C8×D61—21no—
37C2×C8×D61—21no—
38C2×C8×D61—21no—
39C2×C8×D61—21no—
40C2×C8×D61C2×C412yes—
41C2×C8×D61D412yes—
42#14519752—24no—
43#14519752—42no—
44C2×C4⋊Dic61—21no—
45C2×#11758198—41no—
46C2×#11758198—41no—
47C2×#11758185—21no—
48C2×#11758185—21no—
49C2×#11758185D412yescomplemented
50C16×D61—28no—
51#14519711—21no—
52#14519711—21no—
53#14519697—24no—
54#14519684—41no—
55C22×C8×C61C2311yescharacteristic
56C2×C4⋊C4×C61—21no—
57C2×C4⋊C4×C61—21no—
58C2×C16×C61—21no—
59C2×C16×C61—21no—
60C2×C16×C61D412yescomplemented
61#107×C61—21no—
62#107×C61—21no—
63#107×C61—21no—
64#107×C61C2×C412yes—
65C23×D61—41no—
66C23×D61D811yescharacteristic
67C22×C4×C61—41no—
68C22×C4×C61—41no—
69C22×C4×C61C2×D411yescharacteristic
70C22×Dic61—41no—
71C22×Dic61D811yescharacteristic
72C2×D244—22no—
73C2×D244—41no—
74C2×D244—41no—
75C2×D244—41no—
76C2×D244—41no—
77C2×D244—44no—
78C2×D244—41no—
79C2×D244—82no—
80C2×D244—82no—
81C2×C4×D61—21no—
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×C4×D61C22⋊C412yes—
86C2×C4×D61SD1612yes—
87C2×C8×C61C22×C411yescharacteristic
88C2×C8×C61C2×D411yescharacteristic
89C2×C8×C61C2×D411yescharacteristic
90C2×C8×C61C2×D411yescharacteristic
91C2×C8×C61#4111yescharacteristic
92C2×C8×C61#4111yescharacteristic
93C4⋊C4×C61—22no—
94C4⋊C4×C61—41no—
95C4⋊C4×C61—41no—
96C4⋊C4×C61—41no—
97#11758198—44no—
98#11758198—82no—
99C4⋊Dic61—41no—
100C4⋊Dic61—41no—
101C2×#92418—21no—
102C2×#92418—21no—
103C2×#92418C22⋊C412yes—
104D488—22no—
105D488—22no—
106D488—41no—
107D488—41no—
108C8×D61—22no—
109C8×D61—22no—
110C8×D61—22no—
111C8×D61—22no—
112C16×C61—22no—
113#11758185—22no—
114C23×C61C2×D811yescharacteristic
115C22×D61—21no—
116C22×D61—21no—
117C22×D61—21no—
118C22×D61—21no—
119C22×D61—42no—
120C22×D61—81no—
121C22×D61—81no—
122C22×D61—81no—
123C22×D61—81no—
124C22×D61—81no—
125C22×D61—81no—
126C22×D61#10212yes—
127C22×D61D1612yes—
128C22×D61SD3212yes—
129C2×C4×C61—42no—
130C2×C4×C61—81no—
131C2×C4×C61—81no—
132C2×C4×C61—81no—
133C2×C4×C61—81no—
134C2×C4×C61—81no—
135C2×C4×C61C2×C22⋊C411yescharacteristic
136C2×C4×C61#12111yescharacteristic
137C2×C4×C61#12111yescharacteristic
138C2×C4×C61C2×SD1611yescharacteristic
139C2×C4×C61#13511yescharacteristic
140C2×C4×C61#13511yescharacteristic
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—81no—
144C2×Dic61—81no—
145C2×Dic61—81no—
146C2×Dic61#10212yes—
147D244—42no—
148D244—42no—
149D244—88no—
150D244—81no—
151D244—81no—
152C4×D61—22no—
153C4×D61—22no—
154C4×D61—22no—
155C4×D61—22no—
156C8×C61C4×D411yescharacteristic
157C8×C61C4×D411yescharacteristic
158C8×C61#12011yescharacteristic
159C8×C61#12311yescharacteristic
160#92418—22no—
161#13059—611nomaximal, Sylow
162C22×C61C2×#10211yescharacteristic
163C22×C61#46611yescharacteristic
164C22×C61#46611yescharacteristic
165C22×C61C2×D1611yescharacteristic
166C22×C61C2×SD3211yescharacteristic
167C22×C61#50811yescharacteristic
168C22×C61#50811yescharacteristic
169C2×D61—22no—
170C2×D61—22no—
171C2×D61—22no—
172C2×D61—22no—
173C2×D61—22no—
174C2×D61—22no—
175C2×D61—82no—
176C2×D61—82no—
177C2×D61—82no—
178C2×D61—161no—
179C2×D61—161no—
180C2×D61—161no—
181C2×D61—161no—
182C2×D61#35714yescomplemented
183C4×C61—82no—
184C4×C61—161no—
185C4×C61#38611yescharacteristic
186C4×C61#41611yescharacteristic
187C4×C61#46511yescharacteristic
188C4×C61#46511yescharacteristic
189Dic61—22no—
190Dic61—161no—
191C23×C16—611no—
192C2×#466—611no—
193C2×#357—611no—
194C2×#357—611no—
195#1808—611no—
196#1380—611no—
197#1380D6111yescharacteristic, complemented
198C2×C61#189311yescharacteristic
199C2×C61C2×#35711yescharacteristic
200C2×C61#213811yescharacteristic
201C2×C61#221511yescharacteristic
202C2×C61#221511yescharacteristic
203C2×C61#221711yescharacteristic
204C2×C61#221711yescharacteristic
205D61—24no—
206D61—162no—
207C22×D8—611no—
208C23×C8—611no—
209C2×#121—1221no—
210C22×C16—611no—
211C22×C16—1222no—
212C22×C16—1222no—
213C22×C16—1222no—
214C22×C16C2×D6111yescharacteristic
215#466—614no—
216#466—1222no—
217C2×#107—611no—
218C2×#107C2×D6111yescharacteristic
219C2×#107C2×D6111yescharacteristic
220C2×#102—1221no—
221#380—1221no—
222#357—1222no—
223#357—1222no—
224#340—1221no—
225C61#1305911yescharacteristic, complemented, Sylow
226C22×D4—1221no—
227C22×D4—2441no—
228C23×C4—611no—
229C2×D8—612no—
230C2×D8—1221no—
231C2×D8—1221no—
232C2×D8—1221no—
233C2×D8—1221no—
234C2×D8—1221no—
235C22×C8—611no—
236C22×C8—612no—
237C22×C8—612no—
238C22×C8—1221no—
239C22×C8—1221no—
240C22×C8—1221no—
241C22×C8—1221no—
242C22×C8C22×D6111yescharacteristic
243#121—1224no—
244#121—2442no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—1221no—
248C2×C22⋊C4—2441no—
249C2×C22⋊C4—2441no—
250C2×C16—21no—
251C2×C16—21no—
252C2×C16—612no—
253C2×C16—1228no—
254C2×C16—1221no—
255C2×C16—1221no—
256C2×C16D24412yescomplemented
257#107—21no—
258#107—21no—
259#107—21no—
260#107—1221no—
261#107—1221no—
262#107C4×D6112yes—
263#102—1224no—
264#95—2441no—
265C24—611no—
266C24—2441no—
267C2×D4—1222no—
268C2×D4—4882no—
269C2×D4—4882no—
270C2×D4—2444no—
271C2×D4—2441no—
272C2×D4—2441no—
273C2×D4—2441no—
274C2×D4—2441no—
275C2×D4—2441no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—611no—
279C22×C4—612no—
280C22×C4—612no—
281C22×C4—1221no—
282C22×C4—1221no—
283C22×C4—1221no—
284C22×C4—1221no—
285C22×C4—2441no—
286C22×C4D4×D6111yescharacteristic
287D8—1222no—
288D8—1222no—
289D8—2441no—
290D8—2441no—
291C2×C8—612no—
292C2×C8—1221no—
293C2×C8—1221no—
294C2×C8—1222no—
295C2×C8—1222no—
296C2×C8—1222no—
297C2×C8—1222no—
298C2×C8C2×C4×D6111yescharacteristic
299C2×C8C2×D24411yescharacteristic
300C2×C8#1175822211yescharacteristic
301C2×C8D4×D6111yescharacteristic
302C2×C8D4×D6111yescharacteristic
303C2×C8#1175822611yescharacteristic
304C4⋊C4—22no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—2441no—
309C4⋊C4—2441no—
310C22⋊C4—4882no—
311C22⋊C4—2444no—
312C16—22no—
313C16—1222no—
314C23—612no—
315C23—612no—
316C23—612no—
317C23—1221no—
318C23—1221no—
319C23—1221no—
320C23—1221no—
321C23—4881no—
322C23—4881no—
323C23—4881no—
324C23—4881no—
325C23—4881no—
326C23—4881no—
327C23—2442no—
328C23D8×D6111yescharacteristic
329D4—4888no—
330D4—4881no—
331D4—4881no—
332D4—2442no—
333D4—2442no—
334C2×C4—42no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—612no—
341C2×C4—1221no—
342C2×C4—1221no—
343C2×C4—1222no—
344C2×C4—1222no—
345C2×C4—1222no—
346C2×C4—1222no—
347C2×C4—4881no—
348C2×C4—4881no—
349C2×C4—4881no—
350C2×C4C22⋊C4×D6111yescharacteristic
351C2×C4#1451975011yescharacteristic
352C2×C4#1451975211yescharacteristic
353C2×C4SD16×D6111yescharacteristic
354C2×C4#1451979811yescharacteristic
355C2×C4#1451980011yescharacteristic
356C8—1222no—
357C8#1451973911yescharacteristic
358C8C4×D24411yescharacteristic
359C8#1451974711yescharacteristic
360C8#1451976211yescharacteristic
361C22—614no—
362C22—1222no—
363C22—1222no—
364C22—1222no—
365C22—1222no—
366C22—1222no—
367C22—1222no—
368C22—9761no—
369C22—9761no—
370C22—9761no—
371C22—9761no—
372C22—4882no—
373C22—4882no—
374C22—4882no—
375C22#102×D6111yescharacteristic
376C22#1683999711yescharacteristic
377C22#1683999911yescharacteristic
378C22D16×D6111yescharacteristic
379C22SD32×D6111yescharacteristic
380C22#1684019311yescharacteristic
381C22#1684019511yescharacteristic
382C4—82no—
383C4—161no—
384C4—1222no—
385C4—9761no—
386C4#1683964011yescharacteristic
387C4#1683975711yescharacteristic
388C4#1683999211yescharacteristic
389C4#1683999411yescharacteristic
390C2—1224no—
391C2—9762no—
392C2#2144624611yescharacteristic
393C2#357×D6111yescharacteristic
394C2#2144752511yescharacteristic
395C2#2144790411yescharacteristic
396C2#2144790611yescharacteristic
397C2#2144791611yescharacteristic
398C2#2144791811yescharacteristic
subgroupG/H
centerC23D8×D61
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC61×#1380C2
socleC23×C61C2×D8
prime radicalC2×#16839999C2
cosocleC22×C8×C61C23
hypercenter#1380D61
hypocenterC61#13059
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ #1380

Complements

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

NH ≅ G/Ntype
1. C22×C16×D61C2semidirect
3. C2×#16839564C2semidirect
4. C2×#16839562C2semidirect
5. #21445845C2semidirect
6. #21443910C2semidirect
7. C61×#1380C2semidirect
16. #16839999C4semidirect
49. C2×#11758185D4semidirect
60. C2×C16×C61D4semidirect
182. C2×D61#357semidirect
197. #1380D61semidirect
225. C61#13059semidirect
256. C2×C16D244semidirect

Maximal subgroups

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

subgroupindex
C22×C16×D612
C2×#168399992
C2×#168395642
C2×#168395622
#214458452
#214439102
C61×#13802
#1305961