Finite Group Databasebeta

← #30599805

Subgroups — #30599805

Order 15616.

684 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊#92420C211yesmaximal, characteristic
2C4×C22⋊#92420C211yesmaximal, characteristic
3C2×Q8⋊#92420C212yesmaximal, complemented
4#21460655C212yesmaximal, complemented
5C22⋊Q8×Dic61C211yesmaximal, characteristic
6C23×#92420—21no—
7C2×C4⋊#92420—21no—
8C2×C4⋊#92420—24no—
9C2×C4⋊#92420C2212yes—
10C2×C22⋊#92420—21no—
11C2×C4×#92420C2212yes—
12#16840628—21no—
13Q8⋊#92420—24no—
14C2×Q8×Dic61C2211yescharacteristic
15C22×C4×Dic61C2211yescharacteristic
16#16839669C411yescharacteristic
17#16839661C411yescharacteristic
18#16839648—21no—
19#16839637—21no—
20#16839622C411yescharacteristic
21C4⋊C4×Dic61—21no—
22C4⋊C4×Dic61C2211yescharacteristic
23C22⋊C4×Dic61—21no—
24C2×C22⋊Q8×C61C411yescharacteristic
25C22×#92420—24no—
26C22×#92420—22no—
27C22×#92420—22no—
28C22×#92420—42no—
29C22×#92420—42no—
30C4⋊#92420—24no—
31C4⋊#92420—22no—
32C4⋊#92420D414yes—
33C22⋊#92420—24no—
34C4×#92420—22no—
35C4×#92420—22no—
36C23×Dic61D411yescharacteristic
37C23×Dic61D411yescharacteristic
38Q8×Dic61—22no—
39Q8×Dic61—22no—
40C2×C4⋊Dic61—21no—
41C2×C4⋊Dic61—21no—
42C2×C4⋊Dic61C2×C411yescharacteristic
43C2×C4⋊Dic61C2×C411yescharacteristic
44C2×C22⋊Dic61—21no—
45C2×C4×Dic61—22no—
46C2×C4×Dic61—22no—
47C2×C4×Dic61—21no—
48C2×C4×Dic61—21no—
49C2×C4×Dic61C2×C411yescharacteristic
50C2×C4×Dic61D411yescharacteristic
51C2×C4×Dic61D411yescharacteristic
52C2×C4×Dic61C2311yescharacteristic
53#14519684—21no—
54#14519684—21no—
55#14519684—21no—
56#14519684—21no—
57#14519684—21no—
58C22×Q8×C61C2×C411yescharacteristic
59C23×C4×C61C2×C411yescharacteristic
60C22⋊Q8×C61—22no—
61C22⋊Q8×C61C814yescomplemented
62C2×C4⋊C4×C61—21no—
63C2×C4⋊C4×C61C2×C411yescharacteristic
64C2×C22⋊C4×C61—21no—
65C24×C61C22⋊C411yescharacteristic
66C2×Q8×C61—21no—
67C2×Q8×C61—22no—
68C2×Q8×C61—22no—
69C2×Q8×C61C2×C812yescomplemented
70C22×C4×C61—22no—
71C22×C4×C61—22no—
72C22×C4×C61—21no—
73C22×C4×C61—21no—
74C22×C4×C61C22⋊C411yescharacteristic
75C22×C4×C61C2×C812yes—
76C22×C4×C61M1612yes—
77C22×C4×C61C22×C411yescharacteristic
78C22×Dic61—21no—
79C22×Dic61—21no—
80C22×Dic61—21no—
81C22×Dic61—21no—
82C22×Dic61—22no—
83C22×Dic61—22no—
84C22×Dic61—21no—
85C22×Dic61—21no—
86C22×Dic61—41no—
87C22×Dic61C22⋊C411yescharacteristic
88C22×Dic61C22⋊C411yescharacteristic
89C22×Dic61SD1612yes—
90C22×Dic61Q1612yes—
91C22×Dic61C2×D411yescharacteristic
92C22×Dic61C2×D411yescharacteristic
93C2×#92420—24no—
94C2×#92420—24no—
95C2×#92420—42no—
96C2×#92420—48no—
97C2×#92420—42no—
98C2×#92420—42no—
99C2×#92420—42no—
100C4⋊C4×C61—24no—
101C4⋊C4×C61—21no—
102C4⋊C4×C61C2×C812yescomplemented
103C22⋊C4×C61—24no—
104C22⋊Dic61—42no—
105C4⋊Dic61—22no—
106C4⋊Dic61—22no—
107C4⋊Dic61—42no—
108C4⋊Dic61—42no—
109C4×Dic61—22no—
110C4×Dic61—21no—
111C4×Dic61—22no—
112C4×Dic61—21no—
113C4×Dic61—41no—
114C4×Dic61—41no—
115C4×Dic61—41no—
116C4×Dic61—41no—
117C4×Dic61C2×D412yes—
118C4×Dic61#4112yes—
119C23×C61—21no—
120C23×C61—21no—
121C23×C61—21no—
122C23×C61—21no—
123C23×C61C22⋊C812yes—
124C23×C61#10312yes—
125C23×C61#10412yes—
126C23×C61C2×C22⋊C411yescharacteristic
127Q8×C61—24no—
128Q8×C61—42no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—24no—
132C2×C4×C61—24no—
133C2×C4×C61—22no—
134C2×C4×C61—22no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61C22⋊C812yes—
140C2×C4×C61C4×D412yes—
141C2×C4×C61C22×C811yescharacteristic
142C2×C4×C61C2×M1611yescharacteristic
143C2×C4×C61#13112yes—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—22no—
149C2×Dic61—22no—
150C2×Dic61—22no—
151C2×Dic61—22no—
152C2×Dic61—21no—
153C2×Dic61—21no—
154C2×Dic61—21no—
155C2×Dic61—44no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61#10312yes—
163C2×Dic61#12011yescharacteristic
164C2×Dic61#12112yes—
165C2×Dic61#12311yescharacteristic
166C2×Dic61C2×SD1611yescharacteristic
167C2×Dic61C2×Q1611yescharacteristic
168C2×Dic61AGL(1,ℤ/8)11yescharacteristic
169C2×Dic61#13711yescharacteristic
170#92420—44no—
171#92420—44no—
172#8937—611nomaximal, Sylow
173C22×C61—22no—
174C22×C61—22no—
175C22×C61—22no—
176C22×C61—22no—
177C22×C61—22no—
178C22×C61—22no—
179C22×C61Q8⋊C814yescomplemented
180C22×C61#38611yescharacteristic
181C22×C61C2×C22⋊C811yescharacteristic
182C22×C61#40811yescharacteristic
183C22×C61C2×#10311yescharacteristic
184C22×C61#41711yescharacteristic
185C22×C61C2×#10411yescharacteristic
186C22×C61#42111yescharacteristic
187C4×C61—22no—
188C4×C61—42no—
189C4×C61—42no—
190C4×C61C8×D412yes—
191C4×C61#43512yes—
192Dic61—22no—
193Dic61—22no—
194Dic61—41no—
195Dic61—81no—
196Dic61—81no—
197Dic61#45011yescharacteristic
198Dic61#45111yescharacteristic
199Dic61#48311yescharacteristic
200Dic61#48411yescharacteristic
201C22×C4⋊C8—611no—
202C4×C22⋊Q8—611no—
203C4×C22⋊C8—611no—
204C2×Q8⋊C8—612no—
205#1279—612no—
206C2×C61—24no—
207C2×C61C2×Q8⋊C811yescharacteristic
208C2×C61#147711yescharacteristic
209C2×C61#148111yescharacteristic
210C2×C61#148311yescharacteristic
211C2×C61#186911yescharacteristic
212C2×C61#187111yescharacteristic
213C2×C61#187211yescharacteristic
214C23×C8—1221no—
215C2×C22⋊Q8#692311yescharacteristic
216C2×C4×Q8—611no—
217C22×C42—611no—
218C2×C4⋊C8—612no—
219C2×C4⋊C8—1224no—
220C2×C4⋊C8—1221no—
221C2×C22⋊C8—1221no—
222C2×C4×C8—612no—
223#391—611no—
224#389—611no—
225#387—1221no—
226#385—1221no—
227#380—611no—
228C4×C4⋊C4—611no—
229C4×C4⋊C4—1221no—
230C4×C22⋊C4—1221no—
231#336—1221no—
232Q8⋊C8—1224no—
233C61#893711yescharacteristic, complemented, Sylow
234C22×Q8C2×#692311yescharacteristic
235C23×C4—611no—
236C23×C4—611no—
237C23×C4C2×#692311yescharacteristic
238C22×C8—1222no—
239C22×C8—1222no—
240C22×C8—1224no—
241C22×C8—2442no—
242C22×C8—2442no—
243C22⋊Q8—22no—
244C22⋊Q8#9242014yescomplemented
245C4×Q8—1222no—
246C4×Q8—1222no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—611no—
249C2×C4⋊C4—611no—
250C2×C4⋊C4—1221no—
251C2×C4⋊C4—1221no—
252C2×C4⋊C4C2×#692311yescharacteristic
253C2×C22⋊C4—21no—
254C2×C22⋊C4—1221no—
255C2×C42—611no—
256C2×C42—611no—
257C2×C42—611no—
258C2×C42—611no—
259C2×C42—1222no—
260C2×C42—1222no—
261C2×C42—1221no—
262C2×C42—1221no—
263C4⋊C8—614no—
264C4⋊C8—1222no—
265C4⋊C8—1224no—
266C22⋊C8—1224no—
267C4×C8—1222no—
268C4×C8—1222no—
269#95—1221no—
270#95—1221no—
271#95—1221no—
272#95—1221no—
273#95—1221no—
274C24C22⋊#692311yescharacteristic
275C2×Q8—21no—
276C2×Q8—22no—
277C2×Q8—22no—
278C2×Q8C2×#9242012yescomplemented
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—611no—
284C22×C4—612no—
285C22×C4—612no—
286C22×C4—611no—
287C22×C4—611no—
288C22×C4—611no—
289C22×C4—1221no—
290C22×C4—1221no—
291C22×C4—1221no—
292C22×C4—1221no—
293C22×C4—1222no—
294C22×C4—1222no—
295C22×C4—1221no—
296C22×C4—1221no—
297C22×C4—2441no—
298C22×C4C2×#9242012yes—
299C22×C4#1175821712yes—
300C22×C4C22⋊#692311yescharacteristic
301C22×C4C22×#692311yescharacteristic
302C2×C8—1224no—
303C2×C8—1224no—
304C2×C8—2442no—
305C2×C8—2442no—
306C2×C8—2442no—
307C2×C8—2448no—
308C2×C8—2442no—
309C4⋊C4—24no—
310C4⋊C4—21no—
311C4⋊C4—1222no—
312C4⋊C4—1222no—
313C4⋊C4—2442no—
314C4⋊C4—2442no—
315C4⋊C4C2×#9242012yescomplemented
316C22⋊C4—24no—
317C22⋊C4—2442no—
318C42—612no—
319C42—612no—
320C42—1221no—
321C42—1221no—
322C42—1222no—
323C42—1222no—
324C42—2441no—
325C42—2441no—
326C42—2441no—
327C42—2441no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23C22⋊#9242012yes—
333C23#1451984012yes—
334C23#1451984212yes—
335C23C2×C22⋊#692311yescharacteristic
336Q8—24no—
337Q8—42no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—24no—
341C2×C4—24no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—611no—
349C2×C4—611no—
350C2×C4—611no—
351C2×C4—611no—
352C2×C4—611no—
353C2×C4—611no—
354C2×C4—612no—
355C2×C4—612no—
356C2×C4—1222no—
357C2×C4—1222no—
358C2×C4—1222no—
359C2×C4—1222no—
360C2×C4—1221no—
361C2×C4—1221no—
362C2×C4—1221no—
363C2×C4—1221no—
364C2×C4—1221no—
365C2×C4—1221no—
366C2×C4—1221no—
367C2×C4—2444no—
368C2×C4—2441no—
369C2×C4—2441no—
370C2×C4—2441no—
371C2×C4—2441no—
372C2×C4—2441no—
373C2×C4—2441no—
374C2×C4C22⋊#9242012yes—
375C2×C4D4×#692312yes—
376C2×C4C22×#9242011yescharacteristic
377C2×C4C2×#1175821711yescharacteristic
378C2×C4#1451986412yes—
379C8—2444no—
380C8—2444no—
381C22—22no—
382C22—22no—
383C22—22no—
384C22—22no—
385C22—22no—
386C22—22no—
387C22Q8⋊#9242014yescomplemented
388C22#1684071011yescharacteristic
389C22C2×C22⋊#9242011yescharacteristic
390C22#1684073511yescharacteristic
391C22C2×#1451984011yescharacteristic
392C22#1684075311yescharacteristic
393C22C2×#1451984211yescharacteristic
394C22#1684075911yescharacteristic
395C4—22no—
396C4—42no—
397C4—42no—
398C4—611no—
399C4—611no—
400C4—611no—
401C4—611no—
402C4—1222no—
403C4—1222no—
404C4—4881no—
405C4—4881no—
406C4—2441no—
407C4D4×#9242012yes—
408C4#1684079312yes—
409C2—24no—
410C2C2×Q8⋊#9242011yescharacteristic
411C2#2146111411yescharacteristic
412C2#2146112711yescharacteristic
413C2#2146113611yescharacteristic
414C2#2146179211yescharacteristic
415C2#2146180011yescharacteristic
416C2#2146180411yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC2×C22⋊Q8×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC2×C22⋊Q8#6923
hypocenterC61#8937
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. C2×Q8⋊#92420C2semidirect
4. #21460655C2semidirect
61. C22⋊Q8×C61C8semidirect
69. C2×Q8×C61C2×C8semidirect
102. C4⋊C4×C61C2×C8semidirect
179. C22×C61Q8⋊C8semidirect
233. C61#8937semidirect
244. C22⋊Q8#92420semidirect
278. C2×Q8C2×#92420semidirect
315. C4⋊C4C2×#92420semidirect
387. C22Q8⋊#92420semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊#924202
C4×C22⋊#924202
C2×Q8⋊#924202
#214606552
C22⋊Q8×Dic612
#893761