Finite Group Databasebeta

← #29599612

Subgroups — #29599612

Order 15616.

446 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519720C211yesmaximal, characteristic
2C2×C4⋊#11758185C211yesmaximal, characteristic, complemented
3C2×#16839566C211yesmaximal, characteristic, complemented
4C2×#16839562C211yesmaximal, characteristic
5#21446685C211yesmaximal, characteristic
6#21443910C211yesmaximal, characteristic, complemented
7C61×#1969C211yesmaximal, characteristic, complemented
8C22×D488C2211yescharacteristic
9C2×#14519720—22no—
10C2×#14519720—22no—
11C2×#14519720—22no—
12C22×#11758185C2211yescharacteristic
13C22×#11758185C2211yescharacteristic
14C2×#14519711C2211yescharacteristic
15C2×#14519699—21no—
16#16839664—21no—
17C4⋊#11758185—22no—
18#16839566—22no—
19#16839562—22no—
20C22×Q16×C61C2211yescharacteristic
21C2×#107×C61C2211yescharacteristic
22C2×#103×C61—21no—
23C2×C4×C8×C61C2211yescharacteristic
24C61×#391—21no—
25C22×D244—21no—
26C2×D488—21no—
27C2×D488—21no—
28C2×D488—21no—
29C2×D488—21no—
30C2×D488—21no—
31C2×D488D412yes—
32C2×C4⋊Dic61—21no—
33C2×#11758198—41no—
34C2×#11758198—41no—
35#14519720—28no—
36C2×#11758185—21no—
37C2×#11758185—21no—
38C2×#11758185—21no—
39C2×#11758185—21no—
40C2×#11758185—21no—
41C2×#11758185D412yes—
42#14519711—21no—
43#14519711—21no—
44#14519699—42no—
45C22×Q8×C61—21no—
46C2×Q16×C61—21no—
47C2×Q16×C61—21no—
48C2×Q16×C61—21no—
49C2×Q16×C61—21no—
50C2×Q16×C61—21no—
51C2×Q16×C61D412yes—
52C22×C8×C61D411yescharacteristic
53C22×C8×C61C2311yescharacteristic
54C2×C4⋊C4×C61—21no—
55C2×C42×C61D411yescharacteristic
56#107×C61—21no—
57#107×C61—21no—
58#103×C61—42no—
59C4×C8×C61—21no—
60C4×C8×C61—21no—
61#95×C61—41no—
62#95×C61—41no—
63C23×D61—41no—
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—41no—
71C22×C4×C61—41no—
72C22×C4×C61D811yescharacteristic
73C22×C4×C61D811yescharacteristic
74C22×C4×C61C2×D411yescharacteristic
75C22×Dic61—41no—
76C2×D244—22no—
77C2×D244—41no—
78C2×D244—41no—
79C2×D244—41no—
80C2×D244—41no—
81C2×D244—41no—
82Q16×C61—22no—
83Q16×C61—22no—
84Q16×C61—41no—
85Q16×C61—41no—
86C2×C8×C61—21no—
87C2×C8×C61—21no—
88C2×C8×C61—21no—
89C2×C8×C61C2×D411yescharacteristic
90C2×C8×C61C2×D411yescharacteristic
91C2×C8×C61C2×D411yescharacteristic
92C2×C8×C61#4111yescharacteristic
93C2×C8×C61#4111yescharacteristic
94C2×C8×C61#4111yescharacteristic
95C4⋊C4×C61—41no—
96C4⋊C4×C61—41no—
97C42×C61—21no—
98C42×C61—21no—
99#11758198—82no—
100#11758198—82no—
101C4⋊Dic61—41no—
102C4⋊Dic61—41no—
103D488—22no—
104D488—22no—
105D488—41no—
106D488—41no—
107#11758185—22no—
108#11758185—41no—
109C23×C61C2×D811yescharacteristic
110C22×D61—42no—
111C22×D61—81no—
112C22×D61—81no—
113C22×D61—81no—
114C22×D61—81no—
115C22×D61—81no—
116C22×D61—81no—
117Q8×C61—42no—
118Q8×C61—42no—
119Q8×C61—81no—
120Q8×C61—81no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—42no—
127C2×C4×C61—81no—
128C2×C4×C61—81no—
129C2×C4×C61—81no—
130C2×C4×C61—81no—
131C2×C4×C61—81no—
132C2×C4×C61SD3212yescomplemented
133C2×C4×C61#12111yescharacteristic
134C2×C4×C61#12111yescharacteristic
135C2×C4×C61#12111yescharacteristic
136C2×C4×C61#13511yescharacteristic
137C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
139C2×Dic61—81no—
140C2×Dic61—81no—
141C2×Dic61—81no—
142D244—42no—
143D244—42no—
144D244—81no—
145D244—81no—
146C8×C61—41no—
147C8×C61#12011yescharacteristic
148C8×C61#12311yescharacteristic
149C8×C61#12311yescharacteristic
150C8×C61#12411yescharacteristic
151#13449—611nomaximal, Sylow
152C22×C61#45911yescharacteristic
153C22×C61#45911yescharacteristic
154C22×C61#46611yescharacteristic
155C22×C61C2×SD3211yescharacteristic
156C22×C61#50811yescharacteristic
157C22×C61#50911yescharacteristic
158C22×C61#51011yescharacteristic
159C2×D61—82no—
160C2×D61—82no—
161C2×D61—82no—
162C2×D61—161no—
163C2×D61—161no—
164C2×D61—161no—
165C2×D61—161no—
166C4×C61—22no—
167C4×C61—41no—
168C4×C61—82no—
169C4×C61—161no—
170C4×C61#39411yescharacteristic
171C4×C61#46311yescharacteristic
172C4×C61#46311yescharacteristic
173C4×C61#46911yescharacteristic
174Dic61—161no—
175C22×SD32—611no—
176C2×C4⋊C16—611no—
177C2×#358—611no—
178C2×#357—611no—
179#1970—611no—
180#1969D6111yescharacteristic, complemented
181#1380—611no—
182C2×C61#205411yescharacteristic
183C2×C61#220711yescharacteristic
184C2×C61#220811yescharacteristic
185C2×C61#221011yescharacteristic
186C2×C61#221111yescharacteristic
187C2×C61#221711yescharacteristic
188C2×C61#222011yescharacteristic
189D61—162no—
190C22×Q16C2×D6111yescharacteristic
191C22×D8—611no—
192C2×SD32—1222no—
193C2×SD32—1222no—
194C2×SD32—1222no—
195C22×C16—611no—
196C22×C16—611no—
197C2×#107—611no—
198C2×#107C2×D6111yescharacteristic
199C2×#103—21no—
200C2×#102—1221no—
201C2×C4×C8C2×D6111yescharacteristic
202#391—21no—
203#390—1221no—
204C4⋊C16—1222no—
205#358—1222no—
206#357—1222no—
207C61#1344911yescharacteristic, complemented, Sylow
208C22×Q8—21no—
209C22×D4—1221no—
210C2×Q16—21no—
211C2×Q16—21no—
212C2×Q16—21no—
213C2×Q16—21no—
214C2×Q16—21no—
215C2×Q16D24412yes—
216C2×D8—612no—
217C2×D8—1221no—
218C2×D8—1221no—
219C2×D8—1221no—
220C2×D8—1221no—
221C2×D8—1221no—
222C22×C8C22⋊D6111yescharacteristic
223C22×C8C22×D6111yescharacteristic
224C2×C4⋊C4—21no—
225C2×C4⋊C4—1221no—
226C2×C22⋊C4—2441no—
227C2×C22⋊C4—2441no—
228C2×C42C22⋊D6111yescharacteristic
229SD32—1228no—
230C2×C16—612no—
231C2×C16—1221no—
232C2×C16—1221no—
233C2×C16—1221no—
234C2×C16—1221no—
235C2×C16—1221no—
236#107—21no—
237#107—21no—
238#107—1221no—
239#107—1221no—
240#103—42no—
241#102—2442no—
242C4×C8—21no—
243C4×C8—21no—
244#95—41no—
245#95—41no—
246C24—2441no—
247C2×Q8—22no—
248C2×Q8—41no—
249C2×Q8—41no—
250C2×Q8—41no—
251C2×Q8—41no—
252C2×Q8—41no—
253C2×D4—1222no—
254C2×D4—2441no—
255C2×D4—2441no—
256C2×D4—2441no—
257C2×D4—2441no—
258C2×D4—2441no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—2441no—
262C22×C4#1175819911yescharacteristic
263C22×C4#1175819911yescharacteristic
264C22×C4C2×C22⋊D6111yescharacteristic
265Q16—22no—
266Q16—22no—
267Q16—41no—
268Q16—41no—
269D8—1222no—
270D8—1222no—
271D8—2441no—
272D8—2441no—
273C2×C8—21no—
274C2×C8—21no—
275C2×C8—21no—
276C2×C8C2×D24411yescharacteristic
277C2×C8#1175822211yescharacteristic
278C2×C8D4×D6111yescharacteristic
279C2×C8D4×D6111yescharacteristic
280C2×C8#1175822411yescharacteristic
281C2×C8#1175822411yescharacteristic
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—2441no—
285C4⋊C4—2441no—
286C22⋊C4—4882no—
287C22⋊C4—4882no—
288C42—21no—
289C42—21no—
290C16—1222no—
291C16—2441no—
292C23—4881no—
293C23—4881no—
294C23—4881no—
295C23—4881no—
296C23—4881no—
297C23—4881no—
298C23—2442no—
299C23C2×#1175819911yescharacteristic
300Q8—42no—
301Q8—42no—
302Q8—81no—
303Q8—81no—
304D4—4881no—
305D4—4881no—
306D4—2442no—
307D4—2442no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—4881no—
320C2×C4—4881no—
321C2×C4—4881no—
322C2×C4#1451972012yescomplemented
323C2×C4#1451974811yescharacteristic
324C2×C4#1451974911yescharacteristic
325C2×C4#1451975111yescharacteristic
326C2×C4#1451979711yescharacteristic
327C2×C4#1451980211yescharacteristic
328C2×C4#1451980311yescharacteristic
329C8—41no—
330C8#1451974711yescharacteristic
331C8#1451975911yescharacteristic
332C8#1451976111yescharacteristic
333C8#1451976311yescharacteristic
334C22—9761no—
335C22—9761no—
336C22—9761no—
337C22—9761no—
338C22—4882no—
339C22—4882no—
340C22—4882no—
341C22#1683995411yescharacteristic
342C22#1683995711yescharacteristic
343C22#1683999611yescharacteristic
344C22C2×#1451972011yescharacteristic
345C22#1684019211yescharacteristic
346C22#1684019711yescharacteristic
347C22#1684020311yescharacteristic
348C4—22no—
349C4—41no—
350C4—82no—
351C4—161no—
352C4—9761no—
353C4#1683967811yescharacteristic
354C4#1683997411yescharacteristic
355C4#1683997711yescharacteristic
356C4#1684001311yescharacteristic
357C2—9762no—
358C2#2144712911yescharacteristic
359C2#2144785911yescharacteristic
360C2#2144786111yescharacteristic
361C2#2144787111yescharacteristic
362C2#2144788111yescharacteristic
363C2#2144791711yescharacteristic
364C2#2144793411yescharacteristic
subgroupG/H
centerC23C2×#11758199
commutator, cosocleC22×C8×C61C23
FrattiniC22×C8C22×D61
FittingC61×#1969C2
socleC23×C61C2×D8
prime radicalC22×D488C22
hypercenter#1969D61
hypocenterC61#13449
LCSG ▷ C22×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ #1969

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊#11758185C2semidirect
3. C2×#16839566C2semidirect
6. #21443910C2semidirect
7. C61×#1969C2semidirect
132. C2×C4×C61SD32semidirect
180. #1969D61semidirect
207. C61#13449semidirect
322. C2×C4#14519720semidirect

Maximal subgroups

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

subgroupindex
C22×#145197202
C2×C4⋊#117581852
C2×#168395662
C2×#168395622
#214466852
#214439102
C61×#19692
#1344961