Finite Group Databasebeta

← #29596950

Subgroups — #29596950

Order 15616.

626 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839999C211yesmaximal, characteristic
2C2×#107×D61C211yesmaximal, characteristic, complemented
3C2×#16839564C211yesmaximal, characteristic, complemented
4C2×#16839562C211yesmaximal, characteristic, complemented
5C2×#16839541C211yesmaximal, characteristic, complemented
6#21443910C211yesmaximal, characteristic, complemented
7C61×#1380C211yesmaximal, characteristic, complemented
8C22×D488C2211yescharacteristic
9C22×C8×D61C2211yescharacteristic
10C2×#14519752—21no—
11C2×C4⋊C4×D61—21no—
12C22×#11758185C2211yescharacteristic
13#16839999—22no—
14#16839999C414yescomplemented
15C2×#14519711C2211yescharacteristic
16C2×#14519710—21no—
17#107×D61—22no—
18#107×D61—22no—
19C2×#14519697—21no—
20#16839564—22no—
21#16839562—22no—
22#16839541—22no—
23C22×C16×C61C2211yescharacteristic
24C2×#107×C61C2211yescharacteristic
25C2×#107×C61C2211yescharacteristic
26C22×D244—21no—
27C22×D244—41no—
28C22×C4×D61—41no—
29C22×C4×D61D411yescharacteristic
30C2×D488—21no—
31C2×D488—21no—
32C2×D488—21no—
33C2×D488—21no—
34C2×D488—21no—
35C2×D488C2×C412yescomplemented
36C22×#92418D411yescharacteristic
37C2×C8×D61—21no—
38C2×C8×D61—21no—
39C2×C8×D61—21no—
40C2×C8×D61—21no—
41C2×C8×D61C2×C412yes—
42C2×C8×D61D412yes—
43#14519752—24no—
44#14519752—42no—
45C2×C4⋊Dic61—21no—
46C2×#11758196—41no—
47C4⋊C4×D61—24no—
48C4⋊C4×D61—42no—
49C2×#11758198—41no—
50C2×#11758185—21no—
51C2×#11758185—21no—
52C2×#11758185—21no—
53#14519711—21no—
54#14519711D412yescomplemented
55#14519710—24no—
56#14519697—24no—
57C22×C8×C61C2311yescharacteristic
58C2×C4⋊C4×C61—21no—
59C2×C4⋊C4×C61—21no—
60C2×C16×C61—21no—
61C2×C16×C61—21no—
62C2×C16×C61—21no—
63#107×C61—21no—
64#107×C61—21no—
65#107×C61C2×C412yescomplemented
66#107×C61D412yescomplemented
67C23×D61—41no—
68C23×D61D811yescharacteristic
69C22×C4×C61—41no—
70C22×C4×C61—41no—
71C22×C4×C61C2×D411yescharacteristic
72C22×Dic61—41no—
73C22×Dic61D811yescharacteristic
74C2×D244—22no—
75C2×D244—41no—
76C2×D244—41no—
77C2×D244—41no—
78C2×D244—41no—
79C2×D244—44no—
80C2×D244—41no—
81C2×D244—82no—
82C2×D244—82no—
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×C4×D61—21no—
86C2×C4×D61—21no—
87C2×C4×D61—44no—
88C2×C4×D61—82no—
89C2×C4×D61—82no—
90C2×C4×D61C22⋊C412yes—
91C2×C4×D61SD1612yes—
92C2×C8×C61C22×C411yescharacteristic
93C2×C8×C61C2×D411yescharacteristic
94C2×C8×C61C2×D411yescharacteristic
95C2×C8×C61C2×D411yescharacteristic
96C2×C8×C61#4111yescharacteristic
97C2×C8×C61#4111yescharacteristic
98C4⋊C4×C61—22no—
99C4⋊C4×C61—22no—
100C4⋊C4×C61—41no—
101C4⋊C4×C61—41no—
102#11758198—44no—
103C4⋊Dic61—22no—
104C4⋊Dic61—41no—
105#11758196—44no—
106C2×#92418—21no—
107C2×#92418—21no—
108C2×#92418C22⋊C412yes—
109D488—22no—
110D488—22no—
111D488—41no—
112D488—41no—
113C8×D61—22no—
114C8×D61—22no—
115C8×D61—22no—
116C8×D61—22no—
117C16×C61—41no—
118#11758185—41no—
119C23×C61C2×D811yescharacteristic
120C22×D61—21no—
121C22×D61—21no—
122C22×D61—21no—
123C22×D61—21no—
124C22×D61—42no—
125C22×D61—81no—
126C22×D61—81no—
127C22×D61—81no—
128C22×D61—81no—
129C22×D61—81no—
130C22×D61—81no—
131C22×D61#10212yes—
132C22×D61D1612yes—
133C22×D61SD3212yes—
134C2×C4×C61—42no—
135C2×C4×C61—42no—
136C2×C4×C61—81no—
137C2×C4×C61—81no—
138C2×C4×C61—81no—
139C2×C4×C61—81no—
140C2×C4×C61C2×C22⋊C411yescharacteristic
141C2×C4×C61#12011yescharacteristic
142C2×C4×C61#12311yescharacteristic
143C2×C4×C61C2×SD1611yescharacteristic
144C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C61#13711yescharacteristic
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—42no—
149C2×Dic61—81no—
150C2×Dic61—81no—
151C2×Dic61#10212yes—
152D244—42no—
153D244—42no—
154D244—88no—
155D244—81no—
156D244—81no—
157C4×D61—22no—
158C4×D61—22no—
159C4×D61—22no—
160C4×D61—22no—
161C4×D61—88no—
162C8×C61C4×D411yescharacteristic
163C8×C61C4×D411yescharacteristic
164C8×C61#12111yescharacteristic
165C8×C61#12111yescharacteristic
166#92418—22no—
167#12991—611nomaximal, Sylow
168C22×C61C2×#10211yescharacteristic
169C22×C61#44711yescharacteristic
170C22×C61#48011yescharacteristic
171C22×C61C2×D1611yescharacteristic
172C22×C61C2×SD3211yescharacteristic
173C22×C61#50911yescharacteristic
174C22×C61#51011yescharacteristic
175C2×D61—22no—
176C2×D61—22no—
177C2×D61—22no—
178C2×D61—22no—
179C2×D61—22no—
180C2×D61—22no—
181C2×D61—82no—
182C2×D61—82no—
183C2×D61—82no—
184C2×D61—161no—
185C2×D61—161no—
186C2×D61—161no—
187C2×D61—161no—
188C2×D61#35714yescomplemented
189C4×C61—82no—
190C4×C61—82no—
191C4×C61#38611yescharacteristic
192C4×C61#41711yescharacteristic
193C4×C61#44811yescharacteristic
194C4×C61#48111yescharacteristic
195Dic61—22no—
196Dic61—82no—
197C2×#466—611no—
198C22×#107—611no—
199C2×#357—611no—
200C2×#357—611no—
201C2×C22⋊C16—611no—
202#1380—611no—
203#1380D6111yescharacteristic, complemented
204C2×C61#187411yescharacteristic
205C2×C61C2×#35711yescharacteristic
206C2×C61#213911yescharacteristic
207C2×C61#218411yescharacteristic
208C2×C61#218511yescharacteristic
209C2×C61#223211yescharacteristic
210C2×C61#223311yescharacteristic
211D61—24no—
212D61—162no—
213C22×D8—611no—
214C23×C8—611no—
215C2×#121—1221no—
216C22×C4⋊C4—1221no—
217C22×C16—611no—
218C22×C16C2×D6111yescharacteristic
219#466—614no—
220#466—1222no—
221C2×#107—611no—
222C2×#107—1222no—
223C2×#107—1221no—
224C2×#107—1222no—
225C2×#107C2×D6111yescharacteristic
226C2×#107C2×D6111yescharacteristic
227C2×#102—1221no—
228#357—1222no—
229#357—1222no—
230C22⋊C16—1222no—
231C61#1299111yescharacteristic, complemented, Sylow
232C22×D4—1221no—
233C22×D4—2441no—
234C23×C4—611no—
235C23×C4—2441no—
236C2×D8—612no—
237C2×D8—1221no—
238C2×D8—1221no—
239C2×D8—1221no—
240C2×D8—1221no—
241C2×D8—1221no—
242C22×C8—611no—
243C22×C8—612no—
244C22×C8—612no—
245C22×C8—1221no—
246C22×C8—1221no—
247C22×C8—1221no—
248C22×C8—1221no—
249C22×C8C22×D6111yescharacteristic
250#121—1224no—
251#121—2442no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—1224no—
255C2×C4⋊C4—1221no—
256C2×C4⋊C4—2442no—
257C2×C4⋊C4—2441no—
258C2×C22⋊C4—2441no—
259C2×C16—21no—
260C2×C16—21no—
261C2×C16—21no—
262C2×C16—1221no—
263C2×C16—1221no—
264C2×C16—1221no—
265#107—21no—
266#107—21no—
267#107—612no—
268#107—1224no—
269#107—1221no—
270#107C4×D6112yescomplemented
271#107D24412yescomplemented
272#102—1224no—
273C24—611no—
274C24—2441no—
275C2×D4—1222no—
276C2×D4—4882no—
277C2×D4—4882no—
278C2×D4—2444no—
279C2×D4—2441no—
280C2×D4—2441no—
281C2×D4—2441no—
282C2×D4—2441no—
283C2×D4—2441no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—611no—
287C22×C4—612no—
288C22×C4—612no—
289C22×C4—1221no—
290C22×C4—1221no—
291C22×C4—1221no—
292C22×C4—1221no—
293C22×C4—4882no—
294C22×C4—4882no—
295C22×C4—2444no—
296C22×C4—2441no—
297C22×C4D4×D6111yescharacteristic
298D8—1222no—
299D8—1222no—
300D8—2441no—
301D8—2441no—
302C2×C8—612no—
303C2×C8—1221no—
304C2×C8—1221no—
305C2×C8—1222no—
306C2×C8—1222no—
307C2×C8—1222no—
308C2×C8—1222no—
309C2×C8C2×C4×D6111yescharacteristic
310C2×C8C2×D24411yescharacteristic
311C2×C8#1175822211yescharacteristic
312C2×C8D4×D6111yescharacteristic
313C2×C8D4×D6111yescharacteristic
314C2×C8#1175822611yescharacteristic
315C4⋊C4—22no—
316C4⋊C4—22no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—1222no—
320C4⋊C4—2444no—
321C4⋊C4—2441no—
322C22⋊C4—2444no—
323C16—41no—
324C16—2441no—
325C23—612no—
326C23—612no—
327C23—612no—
328C23—1221no—
329C23—1221no—
330C23—1221no—
331C23—1221no—
332C23—4881no—
333C23—4881no—
334C23—4881no—
335C23—4881no—
336C23—4881no—
337C23—4881no—
338C23—2442no—
339C23D8×D6111yescharacteristic
340D4—4888no—
341D4—4881no—
342D4—4881no—
343D4—2442no—
344D4—2442no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—81no—
348C2×C4—81no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4—612no—
352C2×C4—1221no—
353C2×C4—1221no—
354C2×C4—1222no—
355C2×C4—1222no—
356C2×C4—1222no—
357C2×C4—1222no—
358C2×C4—4888no—
359C2×C4—4881no—
360C2×C4—4881no—
361C2×C4—2442no—
362C2×C4C22⋊C4×D6111yescharacteristic
363C2×C4#1451974711yescharacteristic
364C2×C4#1451976211yescharacteristic
365C2×C4SD16×D6111yescharacteristic
366C2×C4#1451980411yescharacteristic
367C2×C4#1451980911yescharacteristic
368C8—1222no—
369C8#1451973911yescharacteristic
370C8C4×D24411yescharacteristic
371C8#1451975011yescharacteristic
372C8#1451975211yescharacteristic
373C22—614no—
374C22—1222no—
375C22—1222no—
376C22—1222no—
377C22—1222no—
378C22—1222no—
379C22—1222no—
380C22—9761no—
381C22—9761no—
382C22—9761no—
383C22—9761no—
384C22—4882no—
385C22—4882no—
386C22—4882no—
387C22#102×D6111yescharacteristic
388C22#1683989711yescharacteristic
389C22#1684007711yescharacteristic
390C22D16×D6111yescharacteristic
391C22SD32×D6111yescharacteristic
392C22#1684019911yescharacteristic
393C22#1684020411yescharacteristic
394C4—82no—
395C4—82no—
396C4—1222no—
397C4—4882no—
398C4#1683964011yescharacteristic
399C4#1683976211yescharacteristic
400C4#1683990211yescharacteristic
401C4#1684008211yescharacteristic
402C2—1224no—
403C2—9762no—
404C2#2144613511yescharacteristic
405C2#357×D6111yescharacteristic
406C2#2144753011yescharacteristic
407C2#2144773211yescharacteristic
408C2#2144773711yescharacteristic
409C2#2144800111yescharacteristic
410C2#2144800611yescharacteristic
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#12991
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
2. C2×#107×D61C2semidirect
3. C2×#16839564C2semidirect
4. C2×#16839562C2semidirect
5. C2×#16839541C2semidirect
6. #21443910C2semidirect
7. C61×#1380C2semidirect
14. #16839999C4semidirect
35. C2×D488C2×C4semidirect
54. #14519711D4semidirect
65. #107×C61C2×C4semidirect
66. #107×C61D4semidirect
188. C2×D61#357semidirect
203. #1380D61semidirect
231. C61#12991semidirect
270. #107C4×D61semidirect
271. #107D244semidirect

Maximal subgroups

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

subgroupindex
C2×#168399992
C2×#107×D612
C2×#168395642
C2×#168395622
C2×#168395412
#214439102
C61×#13802
#1299161