Finite Group Databasebeta

← #29597076

Subgroups — #29597076

Order 15616.

526 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519722C211yesmaximal, characteristic
2C2×C4×Dic244C211yesmaximal, characteristic, complemented
3C2×#16839567C211yesmaximal, characteristic, complemented
4C2×#16839564C211yesmaximal, characteristic
5#21446685C211yesmaximal, characteristic
6#21443911C211yesmaximal, characteristic, complemented
7C61×#1374C211yesmaximal, characteristic, complemented
8C22×Dic244C2211yescharacteristic
9C22×D488C2211yescharacteristic
10C2×C4×Dic122—21no—
11C2×#14519722—22no—
12C2×#14519722—22no—
13C2×#14519722C414yescomplemented
14C4×Dic244—22no—
15C4×Dic244—22no—
16C2×#14519711C2211yescharacteristic
17C2×#14519711C2211yescharacteristic
18C2×#14519702—21no—
19C2×#14519699—21no—
20#16839664—21no—
21#16839567—22no—
22#16839564—22no—
23C22×C16×C61C2211yescharacteristic
24C22×C16×C61C2211yescharacteristic
25C2×C4×C8×C61C2211yescharacteristic
26C22×Dic122—21no—
27C22×D244—21no—
28C2×Dic244—21no—
29C2×Dic244—21no—
30C2×Dic244—21no—
31C2×Dic244C2×C412yes—
32C2×Dic244D412yes—
33C2×Dic244D412yes—
34C2×D488—21no—
35C2×D488—21no—
36C2×D488—21no—
37C2×D488—21no—
38C2×D488—21no—
39C2×D488C2×C412yes—
40C4×Dic122—24no—
41C4×Dic122—42no—
42C2×C4⋊Dic61—21no—
43C2×C4⋊Dic61—21no—
44C2×#11758196—41no—
45C2×#11758198—41no—
46C2×#11758198—41no—
47C2×C4×Dic61—41no—
48#14519722—28no—
49#14519711—21no—
50#14519711—21no—
51#14519711—21no—
52#14519711D412yes—
53#14519702—24no—
54#14519699—42no—
55C22×C8×C61D411yescharacteristic
56C22×C8×C61C2311yescharacteristic
57C2×C42×C61D411yescharacteristic
58C2×C16×C61—21no—
59C2×C16×C61—21no—
60C2×C16×C61—21no—
61C2×C16×C61—21no—
62C2×C16×C61—21no—
63C2×C16×C61C2×C412yes—
64C4×C8×C61—21no—
65C4×C8×C61—21no—
66C23×D61—41no—
67C22×C4×C61D811yescharacteristic
68C22×C4×C61D811yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C22×Dic61—41no—
71C22×Dic61—41no—
72C22×Dic61—41no—
73C2×D244—22no—
74C2×D244—41no—
75C2×D244—41no—
76C2×D244—41no—
77C2×D244—41no—
78C2×D244—41no—
79C2×Dic122—22no—
80C2×Dic122—22no—
81C2×Dic122—22no—
82C2×Dic122—41no—
83C2×Dic122—41no—
84C2×Dic122—41no—
85C2×C8×C61—21no—
86C2×C8×C61—21no—
87C2×C8×C61—21no—
88C2×C8×C61C22×C411yescharacteristic
89C2×C8×C61C2×D411yescharacteristic
90C2×C8×C61C2×D411yescharacteristic
91C2×C8×C61C2×D411yescharacteristic
92C2×C8×C61#4111yescharacteristic
93C2×C8×C61#4111yescharacteristic
94C42×C61—21no—
95C42×C61—21no—
96#11758198—82no—
97#11758198—82no—
98C4⋊Dic61—22no—
99C4⋊Dic61—41no—
100C4⋊Dic61—41no—
101C4⋊Dic61—41no—
102#11758196—44no—
103C4×Dic61—44no—
104Dic244—22no—
105Dic244—22no—
106Dic244—22no—
107Dic244C22⋊C414yescomplemented
108D488—22no—
109D488—22no—
110D488—41no—
111D488—41no—
112C16×C61—22no—
113C16×C61—41no—
114C23×C61C2×D811yescharacteristic
115C22×D61—42no—
116C22×D61—81no—
117C22×D61—81no—
118C22×D61—81no—
119C22×D61—81no—
120C22×D61—81no—
121C22×D61—81no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61SD3212yescomplemented
128C2×C4×C61C4×D411yescharacteristic
129C2×C4×C61#12011yescharacteristic
130C2×C4×C61#12111yescharacteristic
131C2×C4×C61#13511yescharacteristic
132C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
134C2×Dic61—42no—
135C2×Dic61—42no—
136C2×Dic61—42no—
137C2×Dic61—42no—
138C2×Dic61—81no—
139C2×Dic61—81no—
140C2×Dic61—81no—
141C2×Dic61—81no—
142C2×Dic61—81no—
143D244—42no—
144D244—42no—
145D244—81no—
146D244—81no—
147Dic122—24no—
148Dic122—42no—
149Dic122—42no—
150Dic122—42no—
151C8×C61—41no—
152C8×C61C2×C22⋊C411yescharacteristic
153C8×C61C4×D411yescharacteristic
154C8×C61#12111yescharacteristic
155C8×C61#12311yescharacteristic
156#13013—611nomaximal, Sylow
157C22×C61C4×D811yescharacteristic
158C22×C61#44711yescharacteristic
159C22×C61#45911yescharacteristic
160C22×C61C2×SD3211yescharacteristic
161C22×C61#50811yescharacteristic
162C22×C61#50911yescharacteristic
163C22×C61#51011yescharacteristic
164C2×D61—82no—
165C2×D61—82no—
166C2×D61—82no—
167C2×D61—161no—
168C2×D61—161no—
169C2×D61—161no—
170C2×D61—161no—
171C4×C61—22no—
172C4×C61—41no—
173C4×C61#38611yescharacteristic
174C4×C61#44211yescharacteristic
175C4×C61#44911yescharacteristic
176C4×C61#46311yescharacteristic
177Dic61—44no—
178Dic61—82no—
179Dic61—161no—
180C22×SD32—611no—
181C2×C4×Q16—611no—
182C2×#358—611no—
183C2×#357—611no—
184#1970—611no—
185#1380—611no—
186#1374D6111yescharacteristic, complemented
187C2×C61#187911yescharacteristic
188C2×C61C4×SD3211yescharacteristic
189C2×C61#217511yescharacteristic
190C2×C61#218511yescharacteristic
191C2×C61#218611yescharacteristic
192C2×C61#220711yescharacteristic
193C2×C61#221111yescharacteristic
194D61—162no—
195C22×Q16—611no—
196C22×D8—611no—
197C2×C4×Q8—1221no—
198C2×SD32—614no—
199C2×SD32—1222no—
200C2×SD32—1222no—
201C22×C16C2×D6111yescharacteristic
202C22×C16C2×D6111yescharacteristic
203C4×Q16—1222no—
204C4×Q16—1222no—
205C2×#107—611no—
206C2×#107—611no—
207C2×#103—1221no—
208C2×#102—1221no—
209C2×C4×C8C2×D6111yescharacteristic
210#390—1221no—
211#358—1222no—
212#357—1222no—
213C61#1301311yescharacteristic, complemented, Sylow
214C22×Q8—1221no—
215C22×D4—1221no—
216C2×Q16—612no—
217C2×Q16—612no—
218C2×Q16—612no—
219C2×Q16—1221no—
220C2×Q16—1221no—
221C2×Q16—1221no—
222C2×D8—612no—
223C2×D8—1221no—
224C2×D8—1221no—
225C2×D8—1221no—
226C2×D8—1221no—
227C2×D8—1221no—
228C22×C8D24411yescharacteristic
229C22×C8C22×D6111yescharacteristic
230C4×Q8—1224no—
231C4×Q8—2442no—
232C2×C4⋊C4—1221no—
233C2×C4⋊C4—1221no—
234C2×C4⋊C4—2441no—
235C2×C22⋊C4—2441no—
236C2×C22⋊C4—2441no—
237C2×C42—2441no—
238C2×C42D24411yescharacteristic
239SD32—1228no—
240C2×C16—21no—
241C2×C16—21no—
242C2×C16—21no—
243C2×C16—21no—
244C2×C16—21no—
245C2×C16C4×D6112yes—
246#107—612no—
247#107—1221no—
248#107—1221no—
249#107—1221no—
250#103—1224no—
251#102—2442no—
252C4×C8—21no—
253C4×C8—21no—
254C24—2441no—
255C2×Q8—1222no—
256C2×Q8—1222no—
257C2×Q8—1222no—
258C2×Q8—2441no—
259C2×Q8—2441no—
260C2×Q8—2441no—
261C2×D4—1222no—
262C2×D4—2441no—
263C2×D4—2441no—
264C2×D4—2441no—
265C2×D4—2441no—
266C2×D4—2441no—
267C22×C4—2441no—
268C22×C4—2441no—
269C22×C4—2441no—
270C22×C4D48811yescharacteristic
271C22×C4D48811yescharacteristic
272C22×C4C2×D24411yescharacteristic
273Q16—614no—
274Q16—1222no—
275Q16—1222no—
276Q16—1222no—
277D8—1222no—
278D8—1222no—
279D8—2441no—
280D8—2441no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8C2×C4×D6111yescharacteristic
285C2×C8#1175822211yescharacteristic
286C2×C8D4×D6111yescharacteristic
287C2×C8D4×D6111yescharacteristic
288C2×C8D4×D6111yescharacteristic
289C2×C8#1175822611yescharacteristic
290C4⋊C4—1222no—
291C4⋊C4—2444no—
292C4⋊C4—2441no—
293C4⋊C4—2441no—
294C4⋊C4—2441no—
295C22⋊C4—4882no—
296C22⋊C4—4882no—
297C42—21no—
298C42—21no—
299C42—2444no—
300C16—22no—
301C16—41no—
302C23—4881no—
303C23—4881no—
304C23—4881no—
305C23—4881no—
306C23—4881no—
307C23—4881no—
308C23—2442no—
309C23C2×D48811yescharacteristic
310Q8—1224no—
311Q8—2442no—
312Q8—2442no—
313Q8—2442no—
314D4—4881no—
315D4—4881no—
316D4—2442no—
317D4—2442no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—4881no—
324C2×C4—4881no—
325C2×C4—4881no—
326C2×C4—4881no—
327C2×C4—4881no—
328C2×C4—2442no—
329C2×C4—2442no—
330C2×C4—2442no—
331C2×C4—2442no—
332C2×C4#1451972212yescomplemented
333C2×C4C4×D24411yescharacteristic
334C2×C4#1451974711yescharacteristic
335C2×C4#1451975211yescharacteristic
336C2×C4#1451979911yescharacteristic
337C2×C4#1451980511yescharacteristic
338C2×C4#1451980511yescharacteristic
339C8—41no—
340C8C22⋊C4×D6111yescharacteristic
341C8#1451973911yescharacteristic
342C8#1451975011yescharacteristic
343C8#1451976211yescharacteristic
344C22—9761no—
345C22—9761no—
346C22—9761no—
347C22—9761no—
348C22—4882no—
349C22—4882no—
350C22—4882no—
351C22C4×D48811yescharacteristic
352C22#1683989811yescharacteristic
353C22#1683995811yescharacteristic
354C22C2×#1451972211yescharacteristic
355C22#1684019411yescharacteristic
356C22#1684020011yescharacteristic
357C22#1684020511yescharacteristic
358C4—22no—
359C4—41no—
360C4—9761no—
361C4—4882no—
362C4—2444no—
363C4#1683964011yescharacteristic
364C4#1683987511yescharacteristic
365C4#1683990911yescharacteristic
366C4#1683997811yescharacteristic
367C2—9762no—
368C2#2144616611yescharacteristic
369C2C4×#1451972211yescharacteristic
370C2#2144768511yescharacteristic
371C2#2144773811yescharacteristic
372C2#2144774411yescharacteristic
373C2#2144786011yescharacteristic
374C2#2144788211yescharacteristic
subgroupG/H
centerC23C2×D488
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC61×#1374C2
socleC23×C61C2×D8
prime radicalC22×D488C22
cosocleC22×C8×C61C23
hypercenter#1374D61
hypocenterC61#13013
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ #1374

Complements

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

NH ≅ G/Ntype
2. C2×C4×Dic244C2semidirect
3. C2×#16839567C2semidirect
6. #21443911C2semidirect
7. C61×#1374C2semidirect
13. C2×#14519722C4semidirect
107. Dic244C22⋊C4semidirect
127. C2×C4×C61SD32semidirect
186. #1374D61semidirect
213. C61#13013semidirect
332. C2×C4#14519722semidirect

Maximal subgroups

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

subgroupindex
C22×#145197222
C2×C4×Dic2442
C2×#168395672
C2×#168395642
#214466852
#214439112
C61×#13742
#1301361