Finite Group Databasebeta

← #29597081

Subgroups — #29597081

Order 15616.

554 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519720C211yesmaximal, characteristic
2C2×#16839844C211yesmaximal, characteristic
3C2×#16839564C211yesmaximal, characteristic
4#21446681C211yesmaximal, characteristic, complemented
5#21443910C211yesmaximal, characteristic, complemented
6#21443896C211yesmaximal, characteristic, complemented
7C2×C61×#358C211yesmaximal, characteristic, complemented
8C22×D488C2211yescharacteristic
9C2×#14519739—21no—
10C2×#14519720—22no—
11C2×#14519720—22no—
12C2×#14519720C414yescomplemented
13C22×#11758185C2211yescharacteristic
14#16839844—22no—
15#16839844—22no—
16C2×#14519711C2211yescharacteristic
17C2×#14519701—21no—
18C2×#14519697—21no—
19C2×C8×Dic61C2211yescharacteristic
20#16839669—21no—
21#16839564—22no—
22C22×Q16×C61C2211yescharacteristic
23C22×C16×C61C2211yescharacteristic
24C2×#107×C61C2211yescharacteristic
25C61×#358—22no—
26C22×D244—21no—
27C22×C4×D61—41no—
28C2×D488—21no—
29C2×D488—21no—
30C2×D488—21no—
31C2×D488C2×C412yes—
32C2×D488D412yes—
33C2×D488D412yes—
34C22×#92418D411yescharacteristic
35#14519739—24no—
36#14519739—42no—
37C2×C4⋊Dic61—21no—
38C2×#11758198—41no—
39C2×C4×Dic61D411yescharacteristic
40#14519720—28no—
41C2×#11758185—21no—
42C2×#11758185—21no—
43C2×#11758185C2×C412yescomplemented
44#14519711—21no—
45#14519711—21no—
46#14519701—42no—
47#14519697—24no—
48C8×Dic61—21no—
49C8×Dic61—21no—
50#14519684—41no—
51#14519684—41no—
52C22×Q8×C61—21no—
53C2×Q16×C61—21no—
54C2×Q16×C61—21no—
55C2×Q16×C61—21no—
56C2×Q16×C61—21no—
57C2×Q16×C61—21no—
58C2×Q16×C61C2×C412yescomplemented
59C22×C8×C61C2311yescharacteristic
60C2×C4⋊C4×C61—21no—
61C2×C16×C61—21no—
62C2×C16×C61—21no—
63C2×C16×C61—21no—
64#107×C61—21no—
65#107×C61D412yes—
66C23×D61—41no—
67C2×Q8×C61—22no—
68C2×Q8×C61—41no—
69C2×Q8×C61—41no—
70C2×Q8×C61—41no—
71C2×Q8×C61—41no—
72C2×Q8×C61—41no—
73C22×C4×C61—41no—
74C22×C4×C61—41no—
75C22×C4×C61C2×D411yescharacteristic
76C22×Dic61—41no—
77C22×Dic61D811yescharacteristic
78C22×Dic61D811yescharacteristic
79C2×D244—22no—
80C2×D244—22no—
81C2×D244—22no—
82C2×D244—41no—
83C2×D244—41no—
84C2×D244—41no—
85C2×C4×D61—44no—
86C2×C4×D61—82no—
87C2×C4×D61—82no—
88Q16×C61—22no—
89Q16×C61—22no—
90Q16×C61—41no—
91Q16×C61—41no—
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—41no—
100#11758198—44no—
101C4⋊Dic61—41no—
102C4⋊Dic61—41no—
103C4×Dic61—21no—
104C4×Dic61—21no—
105C2×#92418—21no—
106C2×#92418—21no—
107C2×#92418—21no—
108D488—22no—
109D488—22no—
110D488—22no—
111D488C22⋊C414yes—
112C16×C61—41no—
113#11758185—22no—
114C23×C61C2×D811yescharacteristic
115C22×D61—42no—
116C22×D61—42no—
117C22×D61—42no—
118C22×D61—81no—
119C22×D61—81no—
120C22×D61—81no—
121C22×D61—81no—
122Q8×C61—42no—
123Q8×C61—42no—
124Q8×C61—81no—
125Q8×C61—81no—
126C2×C4×C61—42no—
127C2×C4×C61—42no—
128C2×C4×C61—81no—
129C2×C4×C61—81no—
130C2×C4×C61—81no—
131C2×C4×C61—81no—
132C2×C4×C61C4×D411yescharacteristic
133C2×C4×C61#12011yescharacteristic
134C2×C4×C61#12111yescharacteristic
135C2×C4×C61#13511yescharacteristic
136C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—81no—
144C2×Dic61—81no—
145C2×Dic61—81no—
146C2×Dic61SD3212yescomplemented
147D244—24no—
148D244—42no—
149D244—42no—
150D244—42no—
151C4×D61—88no—
152C8×C61C2×C22⋊C411yescharacteristic
153C8×C61C4×D411yescharacteristic
154C8×C61#12111yescharacteristic
155C8×C61#12311yescharacteristic
156#92418—41no—
157#13014—611nomaximal, Sylow
158C22×C61C4×D811yescharacteristic
159C22×C61#44711yescharacteristic
160C22×C61#45911yescharacteristic
161C22×C61C2×SD3211yescharacteristic
162C22×C61#50811yescharacteristic
163C22×C61#50911yescharacteristic
164C22×C61#51011yescharacteristic
165C2×D61—44no—
166C2×D61—82no—
167C2×D61—82no—
168C2×D61—82no—
169C2×D61—82no—
170C2×D61—82no—
171C2×D61—82no—
172C4×C61—82no—
173C4×C61—82no—
174C4×C61#38611yescharacteristic
175C4×C61#44211yescharacteristic
176C4×C61#44911yescharacteristic
177C4×C61#46311yescharacteristic
178Dic61—22no—
179Dic61—41no—
180Dic61—161no—
181C22×SD32—611no—
182C2×C4×D8—611no—
183C2×#358D6111yescharacteristic, complemented
184C2×#357—611no—
185#1969—611no—
186#1380—611no—
187#1374—611no—
188C2×C61#187911yescharacteristic
189C2×C61C4×SD3211yescharacteristic
190C2×C61#217511yescharacteristic
191C2×C61#218711yescharacteristic
192C2×C61#218911yescharacteristic
193C2×C61#220811yescharacteristic
194C2×C61#221011yescharacteristic
195D61—84no—
196C22×Q16C2×D6111yescharacteristic
197C22×D8—611no—
198C2×C4×D4—1221no—
199C2×SD32—614no—
200C2×SD32—1222no—
201C2×SD32—1222no—
202C22×C16—611no—
203C22×C16C2×D6111yescharacteristic
204C4×D8—1222no—
205C4×D8—1222no—
206C2×#107—611no—
207C2×#107C2×D6111yescharacteristic
208C2×#103—1221no—
209C2×#102—1221no—
210C2×C4×C8—611no—
211#391—1221no—
212#358—22no—
213#357—1222no—
214C61#1301411yescharacteristic, complemented, Sylow
215C22×Q8—21no—
216C22×D4—1221no—
217C23×C4—2441no—
218C2×Q16—21no—
219C2×Q16—21no—
220C2×Q16—21no—
221C2×Q16—21no—
222C2×Q16—21no—
223C2×Q16C4×D6112yescomplemented
224C2×D8—612no—
225C2×D8—612no—
226C2×D8—612no—
227C2×D8—1221no—
228C2×D8—1221no—
229C2×D8—1221no—
230C22×C8—611no—
231C22×C8C22×D6111yescharacteristic
232C4×D4—1224no—
233C4×D4—2442no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—1221no—
236C2×C22⋊C4—2441no—
237C2×C42—611no—
238SD32—1228no—
239C2×C16—21no—
240C2×C16—21no—
241C2×C16—21no—
242C2×C16—612no—
243C2×C16—1221no—
244C2×C16—1221no—
245#107—21no—
246#107—1221no—
247#107—1221no—
248#107C22⋊D6112yes—
249#103—2442no—
250#102—1224no—
251C4×C8—1221no—
252C4×C8—1221no—
253#95—2441no—
254#95—2441no—
255C24—2441no—
256C2×Q8—22no—
257C2×Q8—41no—
258C2×Q8—41no—
259C2×Q8—41no—
260C2×Q8—41no—
261C2×Q8—41no—
262C2×D4—1222no—
263C2×D4—1222no—
264C2×D4—1222no—
265C2×D4—2441no—
266C2×D4—2441no—
267C2×D4—2441no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—611no—
271C22×C4—611no—
272C22×C4—4882no—
273C22×C4—4882no—
274C22×C4—2444no—
275C22×C4—2441no—
276C22×C4D4×D6111yescharacteristic
277Q16—22no—
278Q16—22no—
279Q16—41no—
280Q16—41no—
281D8—614no—
282D8—1222no—
283D8—1222no—
284D8—1222no—
285C2×C8—1221no—
286C2×C8—1221no—
287C2×C8—1221no—
288C2×C8C2×C4×D6111yescharacteristic
289C2×C8#1175822211yescharacteristic
290C2×C8D4×D6111yescharacteristic
291C2×C8D4×D6111yescharacteristic
292C2×C8#1175822411yescharacteristic
293C2×C8C2×C22⋊D6111yescharacteristic
294C4⋊C4—22no—
295C4⋊C4—41no—
296C4⋊C4—2441no—
297C4⋊C4—2441no—
298C22⋊C4—2444no—
299C42—1221no—
300C42—1221no—
301C16—41no—
302C16—1222no—
303C23—4881no—
304C23—4881no—
305C23—4881no—
306C23—4881no—
307C23—2442no—
308C23—2442no—
309C23—2442no—
310C23D8×D6111yescharacteristic
311Q8—42no—
312Q8—42no—
313Q8—81no—
314Q8—81no—
315D4—1224no—
316D4—2442no—
317D4—2442no—
318D4—2442no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4—612no—
326C2×C4—1221no—
327C2×C4—1221no—
328C2×C4—1221no—
329C2×C4—1221no—
330C2×C4—1221no—
331C2×C4—4888no—
332C2×C4—4881no—
333C2×C4—4881no—
334C2×C4—4881no—
335C2×C4#1451973711yescharacteristic
336C2×C4#1451974511yescharacteristic
337C2×C4#1451975011yescharacteristic
338C2×C4#1451979811yescharacteristic
339C2×C4#1451980111yescharacteristic
340C2×C4#1451980411yescharacteristic
341C8—2441no—
342C8C22⋊C4×D6111yescharacteristic
343C8C4×C22⋊D6111yescharacteristic
344C8#1451974811yescharacteristic
345C8#1451975911yescharacteristic
346C22—4882no—
347C22—4882no—
348C22—4882no—
349C22—4882no—
350C22—4882no—
351C22—4882no—
352C22—2444no—
353C22#1683984211yescharacteristic
354C22#1683989411yescharacteristic
355C22#1683995611yescharacteristic
356C22SD32×D6111yescharacteristic
357C22#1684019511yescharacteristic
358C22#1684019911yescharacteristic
359C22#1684020411yescharacteristic
360C4—82no—
361C4—82no—
362C4—1222no—
363C4—9761no—
364C4—2441no—
365C4#1683963811yescharacteristic
366C4#1683987111yescharacteristic
367C4#1683990611yescharacteristic
368C4#1683997611yescharacteristic
369C2—4884no—
370C2#2144616411yescharacteristic
371C2#2144766811yescharacteristic
372C2#2144768611yescharacteristic
373C2#2144774611yescharacteristic
374C2#2144775811yescharacteristic
375C2#2144786311yescharacteristic
376C2#2144787711yescharacteristic
subgroupG/H
centerC23D8×D61
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC2×C61×#358C2
socleC23×C61C2×D8
prime radicalC22×D488C22
cosocleC22×C8×C61C23
hypercenterC2×#358D61
hypocenterC61#13014
LCSG ▷ C2×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
4. #21446681C2semidirect
5. #21443910C2semidirect
6. #21443896C2semidirect
7. C2×C61×#358C2semidirect
12. C2×#14519720C4semidirect
43. C2×#11758185C2×C4semidirect
58. C2×Q16×C61C2×C4semidirect
146. C2×Dic61SD32semidirect
183. C2×#358D61semidirect
214. C61#13014semidirect
223. C2×Q16C4×D61semidirect

Maximal subgroups

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

subgroupindex
C22×#145197202
C2×#168398442
C2×#168395642
#214466812
#214439102
#214438962
C2×C61×#3582
#1301461