Finite Group Databasebeta

← #29599611

Subgroups — #29599611

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×#16839580C211yesmaximal, characteristic, complemented
3C2×#16839564C211yesmaximal, characteristic
4#21446683C211yesmaximal, characteristic
5#21446681C211yesmaximal, characteristic, complemented
6#21443910C211yesmaximal, characteristic, complemented
7C2×C61×#358C211yesmaximal, characteristic, complemented
8C22×D488C2211yescharacteristic
9C2×#14519720—22no—
10C2×#14519720—22no—
11C2×#14519720—22no—
12C22×#11758185C2211yescharacteristic
13C2×#14519711C2211yescharacteristic
14C2×#14519701—21no—
15C2×#14519697—21no—
16C2×C8×Dic61C2211yescharacteristic
17#16839669—21no—
18#16839663—21no—
19#16839580—22no—
20#16839564—22no—
21C22×Q16×C61C2211yescharacteristic
22C22×C16×C61C2211yescharacteristic
23C2×#107×C61C2211yescharacteristic
24C61×#358—22no—
25C22×D244—21no—
26C2×D488—21no—
27C2×D488—21no—
28C2×D488—21no—
29C2×D488—21no—
30C2×D488—21no—
31C2×D488D412yes—
32C22×#92418D411yescharacteristic
33C2×C4⋊Dic61—21no—
34C2×#11758198—41no—
35C2×#11758198—41no—
36C2×C4×Dic61D411yescharacteristic
37#14519720—28no—
38C2×#11758185—21no—
39C2×#11758185—21no—
40C2×#11758185D412yes—
41#14519711—21no—
42#14519711—21no—
43#14519701—42no—
44#14519697—42no—
45C8×Dic61—21no—
46C8×Dic61—21no—
47#14519684—41no—
48#14519684—41no—
49C22×Q8×C61—21no—
50C2×Q16×C61—21no—
51C2×Q16×C61—21no—
52C2×Q16×C61—21no—
53C2×Q16×C61—21no—
54C2×Q16×C61—21no—
55C2×Q16×C61D412yes—
56C22×C8×C61C2311yescharacteristic
57C2×C4⋊C4×C61—21no—
58C2×C16×C61—21no—
59C2×C16×C61—21no—
60C2×C16×C61—21no—
61#107×C61—21no—
62#107×C61—21no—
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×C61C2×D411yescharacteristic
73C22×Dic61—41no—
74C22×Dic61D811yescharacteristic
75C22×Dic61D811yescharacteristic
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×C61C2×D411yescharacteristic
87C2×C8×C61C2×D411yescharacteristic
88C2×C8×C61C2×D411yescharacteristic
89C2×C8×C61#4111yescharacteristic
90C2×C8×C61#4111yescharacteristic
91C2×C8×C61#4111yescharacteristic
92C4⋊C4×C61—41no—
93C4⋊C4×C61—41no—
94#11758198—82no—
95#11758198—82no—
96C4⋊Dic61—41no—
97C4⋊Dic61—41no—
98C4×Dic61—21no—
99C4×Dic61—21no—
100C2×#92418—21no—
101C2×#92418—21no—
102C2×#92418—21no—
103D488—22no—
104D488—22no—
105D488—41no—
106D488—41no—
107C16×C61—41no—
108#11758185—22no—
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—42no—
122C2×C4×C61—81no—
123C2×C4×C61—81no—
124C2×C4×C61—81no—
125C2×C4×C61—81no—
126C2×C4×C61—81no—
127C2×C4×C61#12111yescharacteristic
128C2×C4×C61#12111yescharacteristic
129C2×C4×C61#12111yescharacteristic
130C2×C4×C61#13511yescharacteristic
131C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
132C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—81no—
139C2×Dic61—81no—
140C2×Dic61—81no—
141C2×Dic61SD3212yescomplemented
142D244—42no—
143D244—42no—
144D244—81no—
145D244—81no—
146C8×C61#12011yescharacteristic
147C8×C61#12311yescharacteristic
148C8×C61#12311yescharacteristic
149C8×C61#12411yescharacteristic
150#92418—41no—
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—82no—
167C4×C61—161no—
168C4×C61#39411yescharacteristic
169C4×C61#46311yescharacteristic
170C4×C61#46311yescharacteristic
171C4×C61#46911yescharacteristic
172Dic61—22no—
173Dic61—41no—
174Dic61—161no—
175C22×SD32—611no—
176C2×C4⋊C16—611no—
177C2×#358D6111yescharacteristic, complemented
178C2×#357—611no—
179#1970—611no—
180#1969—611no—
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×C16C2×D6111yescharacteristic
197C2×#107—611no—
198C2×#107C2×D6111yescharacteristic
199C2×#103—1221no—
200C2×#102—1221no—
201C2×C4×C8—611no—
202#391—1221no—
203#390—1221no—
204C4⋊C16—1222no—
205#358—22no—
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×Q16C22⋊D6112yes—
216C2×D8—612no—
217C2×D8—1221no—
218C2×D8—1221no—
219C2×D8—1221no—
220C2×D8—1221no—
221C2×D8—1221no—
222C22×C8—611no—
223C22×C8C22×D6111yescharacteristic
224C2×C4⋊C4—21no—
225C2×C4⋊C4—1221no—
226C2×C22⋊C4—2441no—
227C2×C22⋊C4—2441no—
228C2×C42—611no—
229SD32—1228no—
230C2×C16—21no—
231C2×C16—21no—
232C2×C16—21no—
233C2×C16—612no—
234C2×C16—1221no—
235C2×C16—1221no—
236#107—21no—
237#107—21no—
238#107—1221no—
239#107—1221no—
240#103—2442no—
241#102—2442no—
242C4×C8—1221no—
243C4×C8—1221no—
244#95—2441no—
245#95—2441no—
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—611no—
262C22×C4—611no—
263C22×C4—2441no—
264C22×C4D4×D6111yescharacteristic
265Q16—22no—
266Q16—22no—
267Q16—41no—
268Q16—41no—
269D8—1222no—
270D8—1222no—
271D8—2441no—
272D8—2441no—
273C2×C8—1221no—
274C2×C8—1221no—
275C2×C8—1221no—
276C2×C8#1175822211yescharacteristic
277C2×C8#1175822211yescharacteristic
278C2×C8D4×D6111yescharacteristic
279C2×C8D4×D6111yescharacteristic
280C2×C8#1175822411yescharacteristic
281C2×C8C2×C22⋊D6111yescharacteristic
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—2441no—
285C4⋊C4—2441no—
286C22⋊C4—4882no—
287C22⋊C4—4882no—
288C42—1221no—
289C42—1221no—
290C16—41no—
291C16—1222no—
292C23—4881no—
293C23—4881no—
294C23—4881no—
295C23—4881no—
296C23—4881no—
297C23—4881no—
298C23—2442no—
299C23D8×D6111yescharacteristic
300Q8—42no—
301Q8—42no—
302Q8—81no—
303Q8—81no—
304D4—4881no—
305D4—4881no—
306D4—2442no—
307D4—2442no—
308C2×C4—42no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—612no—
315C2×C4—1221no—
316C2×C4—1221no—
317C2×C4—1221no—
318C2×C4—1221no—
319C2×C4—1221no—
320C2×C4—4881no—
321C2×C4—4881no—
322C2×C4—4881no—
323C2×C4#1451974911yescharacteristic
324C2×C4#1451975011yescharacteristic
325C2×C4#1451975011yescharacteristic
326C2×C4#1451979811yescharacteristic
327C2×C4#1451980111yescharacteristic
328C2×C4#1451980411yescharacteristic
329C8—2441no—
330C8#1451974511yescharacteristic
331C8#1451975911yescharacteristic
332C8#1451976011yescharacteristic
333C8#1451976311yescharacteristic
334C22—9761no—
335C22—9761no—
336C22—9761no—
337C22—9761no—
338C22—4882no—
339C22—4882no—
340C22—4882no—
341C22#1683995511yescharacteristic
342C22#1683995611yescharacteristic
343C22#1683999711yescharacteristic
344C22SD32×D6111yescharacteristic
345C22#1684019511yescharacteristic
346C22#1684019911yescharacteristic
347C22#1684020411yescharacteristic
348C4—82no—
349C4—161no—
350C4—1222no—
351C4—9761no—
352C4—2441no—
353C4#1683967711yescharacteristic
354C4#1683997611yescharacteristic
355C4#1683997911yescharacteristic
356C4#1684001411yescharacteristic
357C2—9762no—
358C2#2144712811yescharacteristic
359C2#2144785711yescharacteristic
360C2#2144786311yescharacteristic
361C2#2144787711yescharacteristic
362C2#2144788311yescharacteristic
363C2#2144791811yescharacteristic
364C2#2144793511yescharacteristic
subgroupG/H
centerC23D8×D61
commutator, cosocleC22×C8×C61C23
FrattiniC22×C8C22×D61
FittingC2×C61×#358C2
socleC23×C61C2×D8
prime radicalC22×D488C22
hypercenterC2×#358D61
hypocenterC61#13449
LCSG ▷ C22×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#358

Complements

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

NH ≅ G/Ntype
2. C2×#16839580C2semidirect
5. #21446681C2semidirect
6. #21443910C2semidirect
7. C2×C61×#358C2semidirect
141. C2×Dic61SD32semidirect
177. C2×#358D61semidirect
207. C61#13449semidirect

Maximal subgroups

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

subgroupindex
C22×#145197202
C2×#168395802
C2×#168395642
#214466832
#214466812
#214439102
C2×C61×#3582
#1344961