Finite Group Databasebeta

← #30595349

Subgroups — #30595349

Order 15616.

680 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14519834C211yesmaximal, characteristic, complemented
2#21461480C211yesmaximal, characteristic, complemented
3#21460638C212yesmaximal, complemented
4#21460635C212yesmaximal, complemented
5C4×#14519748C211yesmaximal, characteristic
6C22×D61⋊C8—21no—
7C2×#14519834—21no—
8C2×C4×#92420—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×#14519748C411yescharacteristic
13C2×C4×C22⋊D61—21no—
14C2×C42×D61C2211yescharacteristic
15#16839665C2211yescharacteristic
16#16839658C2211yescharacteristic
17#16839650—21no—
18#16839638—21no—
19#16839619C411yescharacteristic
20C4×C4⋊Dic61C411yescharacteristic
21C4×C22⋊Dic61—21no—
22C2×C4×D4×C61C411yescharacteristic
23C2×D61⋊C8—24no—
24C2×D61⋊C8—42no—
25C2×D61⋊C8—42no—
26C22×#92420—22no—
27C22×#92420—22no—
28#14519834—24no—
29C4×#92420—42no—
30C22×C22⋊D61—21no—
31C22×C4×D61C2×C411yescharacteristic
32C22×C4×D61D411yescharacteristic
33C22×C4×D61D411yescharacteristic
34#14519748—22no—
35#14519748C814yescomplemented
36C4×C22⋊D61—42no—
37C4×C22⋊D61—42no—
38C2×C4⋊Dic61C2×C411yescharacteristic
39C2×C4⋊Dic61C2×C411yescharacteristic
40C2×#11758196—21no—
41C2×C22⋊Dic61—21no—
42C2×C22⋊Dic61—21no—
43C2×C22⋊Dic61—21no—
44C2×#11758198—21no—
45C2×C4×Dic61—21no—
46C2×C4×Dic61D411yescharacteristic
47C2×C4×Dic61D411yescharacteristic
48C2×C4×Dic61C2311yescharacteristic
49C42×D61—42no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53C22×D4×C61C2×C411yescharacteristic
54C23×C4×C61—21no—
55C4×D4×C61—42no—
56C2×C4⋊C4×C61C2×C411yescharacteristic
57C2×C22⋊C4×C61—21no—
58C2×C42×C61C2×C411yescharacteristic
59C24×C61—21no—
60C23×D61C22⋊C411yescharacteristic
61C2×D4×C61—21no—
62C2×D4×C61—41no—
63C2×D4×C61—41no—
64C2×D4×C61C2×C812yescomplemented
65C22×C4×C61—21no—
66C22×C4×C61—42no—
67C22×C4×C61—42no—
68C22×C4×C61—42no—
69C22×C4×C61C22⋊C411yescharacteristic
70C22×C4×C61C22⋊C411yescharacteristic
71C22×C4×C61C22×C411yescharacteristic
72C2×C22⋊D61—24no—
73C2×C22⋊D61—42no—
74C2×C22⋊D61—42no—
75C22×Dic61—21no—
76C22×Dic61—21no—
77C22×Dic61C22⋊C411yescharacteristic
78C22×Dic61C2×D411yescharacteristic
79C22×Dic61C2×D411yescharacteristic
80C2×C4×D61—22no—
81C2×C4×D61—22no—
82C2×C4×D61—22no—
83C2×C4×D61—22no—
84C2×C4×D61—41no—
85C2×C4×D61—41no—
86C2×C4×D61—41no—
87C2×C4×D61C2×C812yes—
88C2×C4×D61M1612yes—
89C2×C4×D61D812yes—
90C2×C4×D61SD1612yes—
91C2×#92420—24no—
92C2×#92420—24no—
93C2×#92420—42no—
94C2×#92420—42no—
95C2×#92420—42no—
96C2×#92420—42no—
97D61⋊C8—48no—
98C4⋊C4×C61—41no—
99C22⋊C4×C61—42no—
100C42×C61—22no—
101C22⋊Dic61—24no—
102C22⋊Dic61—41no—
103C22⋊Dic61—41no—
104C22⋊Dic61—42no—
105#11758198—42no—
106C4⋊Dic61—21no—
107C4⋊Dic61—41no—
108C4⋊Dic61C2×C812yescomplemented
109#11758196—41no—
110#11758196—41no—
111C4×Dic61—22no—
112C4×Dic61—41no—
113C4×Dic61—41no—
114C4×Dic61—42no—
115C23×C61—22no—
116C23×C61—41no—
117C23×C61—41no—
118C23×C61—41no—
119C23×C61—41no—
120C23×C61—41no—
121C23×C61—41no—
122C23×C61C2×C22⋊C411yescharacteristic
123C22×D61—21no—
124C22×D61—21no—
125C22×D61—21no—
126C22×D61—21no—
127C22×D61C22⋊C812yes—
128C22×D61#10212yes—
129C22×D61#10412yes—
130D4×C61—42no—
131D4×C61—42no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61—84no—
141C2×C4×C61#9912yes—
142C2×C4×C61#10212yes—
143C2×C4×C61#10412yes—
144C2×C4×C61C22×C811yescharacteristic
145C2×C4×C61C2×M1611yescharacteristic
146C22⋊D61—48no—
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—21no—
152C2×Dic61—21no—
153C2×Dic61—22no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61C22⋊C812yes—
160C2×Dic61C2×D811yescharacteristic
161C2×Dic61C2×SD1611yescharacteristic
162C2×Dic61#13512yes—
163C4×D61—24no—
164C4×D61—24no—
165C4×D61—42no—
166C4×D61—42no—
167C4×D61—44no—
168#92420—44no—
169#92420—44no—
170#7565—611nomaximal, Sylow
171C22×C61—42no—
172C22×C61—42no—
173C22×C61—42no—
174C22×C61—81no—
175C22×C61—81no—
176C22×C61—81no—
177C22×C61—81no—
178C22×C61C2×C22⋊C811yescharacteristic
179C22×C61C2×#9911yescharacteristic
180C22×C61#41311yescharacteristic
181C22×C61C2×#10211yescharacteristic
182C22×C61#41611yescharacteristic
183C22×C61C2×#10411yescharacteristic
184C22×C61C2×#10411yescharacteristic
185C2×D61—22no—
186C2×D61—22no—
187C2×D61—22no—
188C2×D61—22no—
189C2×D61—22no—
190C2×D61—22no—
191C2×D61D4⋊C814yes—
192C4×C61—21no—
193C4×C61—21no—
194C4×C61—41no—
195C4×C61—81no—
196C4×C61#32714yes—
197Dic61—22no—
198Dic61—21no—
199Dic61—21no—
200Dic61—22no—
201Dic61—42no—
202Dic61—81no—
203C4×#121—611no—
204C4×C22⋊C8—611no—
205C2×#336—611no—
206#1271—612no—
207#1270—612no—
208C2×C61—82no—
209C2×C61#145911yescharacteristic
210C2×C61C2×D4⋊C811yescharacteristic
211C2×C61#147611yescharacteristic
212C2×C61C2×#32711yescharacteristic
213C2×C61#150111yescharacteristic
214C2×C61#152411yescharacteristic
215C2×C61#154011yescharacteristic
216D61—24no—
217C23×C8—1221no—
218C2×#121—611no—
219C2×C4×D4—1221no—
220C2×C4×D4#692311yescharacteristic
221C22×C42—611no—
222C2×C22⋊C8—1221no—
223C2×C4×C8—1221no—
224#390—611no—
225#389—611no—
226#388—1221no—
227#386—1221no—
228#380—611no—
229C4×C4⋊C4—611no—
230C4×C22⋊C4—1221no—
231#336—612no—
232#336—612no—
233#336—1221no—
234C61#756511yescharacteristic, complemented, Sylow
235C22×D4—1221no—
236C22×D4C2×#692311yescharacteristic
237C23×C4—21no—
238C23×C4—611no—
239C23×C4—611no—
240C23×C4—611no—
241C22×C8—1222no—
242C22×C8—1222no—
243C22×C8—1224no—
244C22×C8—2442no—
245C22×C8—2442no—
246#121—614no—
247#121—1222no—
248C4×D4—42no—
249C4×D4—2442no—
250C4×D4—2442no—
251C2×C4⋊C4—611no—
252C2×C4⋊C4—611no—
253C2×C4⋊C4—1221no—
254C2×C4⋊C4C2×#692311yescharacteristic
255C2×C22⋊C4—21no—
256C2×C22⋊C4—1221no—
257C2×C22⋊C4—1221no—
258C2×C22⋊C4—1221no—
259C2×C22⋊C4—1221no—
260C2×C42—611no—
261C2×C42—611no—
262C2×C42—611no—
263C2×C42—1221no—
264C2×C42—2442no—
265C2×C42C2×#692311yescharacteristic
266C22⋊C8—1224no—
267C4×C8—2442no—
268#95—1221no—
269#95—1221no—
270#95—1221no—
271C24—21no—
272C24—611no—
273C2×D4—21no—
274C2×D4—41no—
275C2×D4—41no—
276C2×D4—1224no—
277C2×D4—2442no—
278C2×D4—2442no—
279C2×D4D61⋊C812yescomplemented
280C22×C4—21no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4—611no—
285C22×C4—611no—
286C22×C4—611no—
287C22×C4—612no—
288C22×C4—612no—
289C22×C4—612no—
290C22×C4—612no—
291C22×C4—1222no—
292C22×C4—1222no—
293C22×C4—1222no—
294C22×C4—1222no—
295C22×C4—1221no—
296C22×C4—1221no—
297C22×C4—2441no—
298C22×C4—2441no—
299C22×C4—2441no—
300C22×C4C22⋊#692311yescharacteristic
301C22×C4C22⋊#692311yescharacteristic
302C22×C4C22×#692311yescharacteristic
303C2×C8—1224no—
304C2×C8—1224no—
305C2×C8—2442no—
306C2×C8—2442no—
307C2×C8—2442no—
308C2×C8—2448no—
309C2×C8—2442no—
310C4⋊C4—41no—
311C4⋊C4—612no—
312C4⋊C4—1221no—
313C4⋊C4—2441no—
314C4⋊C4—2441no—
315C4⋊C4—2441no—
316C22⋊C4—42no—
317C22⋊C4—1224no—
318C22⋊C4—2442no—
319C22⋊C4—2441no—
320C22⋊C4—2441no—
321C22⋊C4—2442no—
322C42—22no—
323C42—1222no—
324C42—2441no—
325C42—2441no—
326C42—2442no—
327C23—22no—
328C23—41no—
329C23—41no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23—612no—
335C23—612no—
336C23—612no—
337C23—1221no—
338C23—1221no—
339C23—1221no—
340C23—1221no—
341C23C2×C22⋊#692311yescharacteristic
342D4—42no—
343D4—42no—
344D4—2448no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—84no—
354C2×C4—612no—
355C2×C4—611no—
356C2×C4—611no—
357C2×C4—612no—
358C2×C4—1221no—
359C2×C4—1221no—
360C2×C4—1221no—
361C2×C4—1221no—
362C2×C4—1221no—
363C2×C4—1221no—
364C2×C4—1224no—
365C2×C4—1224no—
366C2×C4—1222no—
367C2×C4—2442no—
368C2×C4—2442no—
369C2×C4—2444no—
370C2×C4—2441no—
371C2×C4—2441no—
372C2×C4—2441no—
373C2×C4—2441no—
374C2×C4—2441no—
375C2×C4#1451983512yes—
376C2×C4#1451983912yes—
377C2×C4#1451984112yes—
378C2×C4C2×D61⋊C811yescharacteristic
379C2×C4D61⋊M1611yescharacteristic
380C8—2444no—
381C8—2444no—
382C22—42no—
383C22—42no—
384C22—42no—
385C22—81no—
386C22—81no—
387C22—81no—
388C22—81no—
389C22—614no—
390C22—1222no—
391C22—1222no—
392C22—1222no—
393C22—1222no—
394C22—1222no—
395C22—1222no—
396C22D61⋊(C22⋊C8)11yescharacteristic
397C22C2×#1451983511yescharacteristic
398C22#1684074811yescharacteristic
399C22C2×#1451983911yescharacteristic
400C22#1684075211yescharacteristic
401C22C2×#1451984111yescharacteristic
402C22D61⋊#10411yescharacteristic
403C4—21no—
404C4—21no—
405C4—41no—
406C4—81no—
407C4—1222no—
408C4—1221no—
409C4—1221no—
410C4—1222no—
411C4—4881no—
412C4—2442no—
413C4#1684061314yes—
414C2—82no—
415C2—1224no—
416C2#2146105411yescharacteristic
417C2D61⋊(D4⋊C8)11yescharacteristic
418C2#2146111111yescharacteristic
419C2C2×#1684061311yescharacteristic
420C2#2146119411yescharacteristic
421C2#2146126911yescharacteristic
422C2#2146131611yescharacteristic
subgroupG/H
centerC22×C4C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC2×C4×D4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519748C4
cosocleC2×C4×Dic61C23
hypercenterC2×C4×D4#6923
hypocenterC61#7565
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C4×#14519834C2semidirect
2. #21461480C2semidirect
3. #21460638C2semidirect
4. #21460635C2semidirect
35. #14519748C8semidirect
64. C2×D4×C61C2×C8semidirect
108. C4⋊Dic61C2×C8semidirect
234. C61#7565semidirect
279. C2×D4D61⋊C8semidirect

Maximal subgroups

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

subgroupindex
C4×#145198342
#214614802
#214606382
#214606352
C4×#145197482
#756561