Finite Group Databasebeta

← #30602187

Subgroups — #30602187

Order 15616.

654 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14519834C211yesmaximal, characteristic
2#21460997C211yesmaximal, characteristic
3#21460692C212yesmaximal
4#21460692C212yesmaximal
5#21454170C211yesmaximal, characteristic
6C22×C4⋊#6923—21no—
7C2×#14519834C2212yes—
8C2×C4×#92420—21no—
9C2×(C2×#6923)⋊C4—21no—
10C2×(C2×#6923)⋊C4C2212yes—
11#16840628—21no—
12C2×#14519776C411yescharacteristic, complemented
13C2×#14519755—21no—
14C2×C42×D61C2211yescharacteristic
15#16839666—21no—
16#16839660C411yescharacteristic, complemented
17#16839657—21no—
18#16839631C411yescharacteristic, complemented
19#16839621—21no—
20#16839619C2211yescharacteristic
21#16839619C2211yescharacteristic
22C61×#389C411yescharacteristic, complemented
23C23×#6923—22no—
24C22×#92420—22no—
25C2×C4⋊#6923—24no—
26C2×C4⋊#6923—42no—
27C2×C4⋊#6923—42no—
28#14519834—22no—
29#14519834Q814yescomplemented
30C4×#92420—42no—
31(C2×#6923)⋊C4—24no—
32(C2×#6923)⋊C4—42no—
33C22×Dic122—21no—
34C22×C4×D61D411yescharacteristic
35C22×C4×D61D411yescharacteristic
36C22×C4×D61C2311yescharacteristic
37#14519776—42no—
38#14519755—42no—
39#14519755—42no—
40C2×C4⋊Dic61C2×C411yescharacteristic
41C2×C4⋊Dic61C2×C411yescharacteristic
42C2×#11758196—21no—
43C2×#11758196—21no—
44C2×#11758196—21no—
45C2×#11758196—21no—
46C2×#11758198—21no—
47C2×#11758198—21no—
48C2×C4×Dic61C2×C411yescharacteristic
49C2×C4×Dic61D411yescharacteristic
50C2×C4×Dic61D411yescharacteristic
51C42×D61—42no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55C2×C4⋊C4×C61—21no—
56C2×C4⋊C4×C61C2×C411yescharacteristic
57C2×C4⋊C4×C61C2×C411yescharacteristic
58C2×C42×C61C2×C411yescharacteristic
59#95×C61—21no—
60C23×D61C2×D411yescharacteristic
61C22×#6923—24no—
62C22×#6923—42no—
63C22×#6923—42no—
64C22×#6923—42no—
65C22×#6923—42no—
66C22×#6923—42no—
67C22×#6923—42no—
68C22×C4×C61—21no—
69C22×C4×C61—21no—
70C22×C4×C61C22⋊C411yescharacteristic
71C22×C4×C61C22⋊C411yescharacteristic
72C22×C4×C61C22×C411yescharacteristic
73C22×Dic61—21no—
74C22×Dic61—21no—
75C22×Dic61C22⋊C411yescharacteristic
76C22×Dic61C22⋊C411yescharacteristic
77C22×Dic61C2×D411yescharacteristic
78C2×C4×D61—22no—
79C2×C4×D61—22no—
80C2×C4×D61—41no—
81C2×C4×D61—41no—
82C2×C4×D61—41no—
83C2×C4×D61—41no—
84C2×C4×D61D812yes—
85C2×C4×D61SD1612yes—
86C2×C4×D61SD1612yes—
87C2×C4×D61Q1612yes—
88C2×C4×D61C2×Q812yes—
89C2×C4×D61#4112yes—
90C2×Dic122—42no—
91C2×Dic122—42no—
92C2×Dic122—42no—
93C2×#92420—24no—
94C2×#92420—42no—
95C2×#92420—42no—
96C4⋊#6923—48no—
97C4⋊C4×C61—41no—
98C4⋊C4×C61—41no—
99C4⋊C4×C61—42no—
100C42×C61—41no—
101#11758198—41no—
102#11758198—41no—
103#11758198—41no—
104#11758198—41no—
105C4⋊Dic61—41no—
106C4⋊Dic61—41no—
107#11758196—42no—
108#11758196—42no—
109#11758196—42no—
110#11758196—42no—
111C4×Dic61—22no—
112C4×Dic61—22no—
113C4×Dic61—41no—
114C23×C61C2×C22⋊C411yescharacteristic
115C22×D61—21no—
116C22×D61—21no—
117C22×D61—21no—
118C22×D61—21no—
119C22×D61#12411yescharacteristic
120C22×D61C4⋊Q811yescharacteristic
121C22×D61C2×D811yescharacteristic
122C22×D61C2×SD1611yescharacteristic
123C22×D61C2×SD1611yescharacteristic
124C22×D61C2×Q1611yescharacteristic
125C2×#6923—44no—
126C2×#6923—44no—
127C2×#6923—44no—
128C2×#6923—82no—
129C2×#6923—82no—
130C2×#6923—82no—
131C2×#6923—82no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61#10212yes—
145C2×C4×C61#10312yes—
146C2×C4×C61C4×Q812yes—
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61#9912yes—
158C2×Dic61#10212yes—
159C2×Dic61#10312yes—
160C2×Dic61#10412yes—
161C2×Dic61C22⋊Q812yes—
162C4×D61—24no—
163C4×D61—24no—
164C4×D61—42no—
165C4×D61—42no—
166C4×D61—42no—
167C4×D61—42no—
168Dic122—84no—
169#92420—44no—
170#9884—611nomaximal, Sylow
171C22×C61#39111yescharacteristic
172C22×C61C2×#9911yescharacteristic
173C22×C61#41011yescharacteristic
174C22×C61C2×#10211yescharacteristic
175C22×C61C2×#10311yescharacteristic
176C22×C61C2×#10411yescharacteristic
177C22×C61#42111yescharacteristic
178C2×D61—21no—
179C2×D61—21no—
180C2×D61—21no—
181C2×D61—21no—
182C2×D61—21no—
183C2×D61—21no—
184C2×D61—21no—
185C2×D61—21no—
186C2×D61—21no—
187C2×D61—21no—
188C2×D61—21no—
189C2×D61—21no—
190C2×D61#48611yescharacteristic
191C2×D61#48711yescharacteristic
192C2×D61#49811yescharacteristic
193C2×D61#50011yescharacteristic
194#6923—84no—
195C4×C61—22no—
196C4×C61—22no—
197C4×C61—22no—
198C4×C61—81no—
199C4×C61—81no—
200Dic61—22no—
201Dic61—22no—
202Dic61—81no—
203Dic61—81no—
204Dic61#32814yes—
205#2857—611no—
206C4×C22⋊C8—611no—
207C4⋊#95—611no—
208#1294—612no—
209#1294—612no—
210C2×C61C2×#32811yescharacteristic
211C2×C61#150211yescharacteristic
212C2×C61#151811yescharacteristic
213C2×C61#151911yescharacteristic
214C2×C61#198611yescharacteristic
215C2×C61#199011yescharacteristic
216C2×C61#199611yescharacteristic
217D61—21no—
218D61—21no—
219D61—21no—
220D61—21no—
221C2×C4⋊Q8—611no—
222C2×C22⋊Q8—1221no—
223C22×C4⋊C4—1221no—
224C22×C42—611no—
225C2×C22⋊C8—612no—
226C2×C4×C8—1221no—
227#391—1221no—
228#389—611no—
229#389—1221no—
230#389#692311yescharacteristic, complemented
231#384—611no—
232#380—611no—
233#380—611no—
234#380—1221no—
235C2×#95—612no—
236C2×#95—1221no—
237#336—1221no—
238C61#988411yescharacteristic, complemented, Sylow
239C22×Q8—1221no—
240C23×C4—611no—
241C23×C4—611no—
242C23×C4—611no—
243C23×C4—1222no—
244C22×C8—1222no—
245C4⋊Q8—2442no—
246C22⋊Q8—2442no—
247C22⋊Q8—2442no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—611no—
250C2×C4⋊C4—611no—
251C2×C4⋊C4—1221no—
252C2×C4⋊C4—1221no—
253C2×C4⋊C4—1221no—
254C2×C4⋊C4—1224no—
255C2×C4⋊C4—1221no—
256C2×C4⋊C4—2442no—
257C2×C4⋊C4—2442no—
258C2×C4⋊C4C2×#692311yescharacteristic
259C2×C4⋊C4C2×#692311yescharacteristic
260C2×C22⋊C4—1221no—
261C2×C22⋊C4—1221no—
262C2×C42—611no—
263C2×C42—611no—
264C2×C42—611no—
265C2×C42—2442no—
266C2×C42C2×#692311yescharacteristic
267C22⋊C8—614no—
268C22⋊C8—1222no—
269C4×C8—2442no—
270#95—21no—
271#95—1221no—
272#95—1221no—
273#95—1224no—
274#95—1221no—
275#95—2442no—
276C24—611no—
277C2×Q8—2442no—
278C2×Q8—2442no—
279C2×Q8—2442no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—611no—
283C22×C4—611no—
284C22×C4—611no—
285C22×C4—612no—
286C22×C4—612no—
287C22×C4—612no—
288C22×C4—612no—
289C22×C4—612no—
290C22×C4—612no—
291C22×C4—1222no—
292C22×C4—1222no—
293C22×C4—1224no—
294C22×C4—1221no—
295C22×C4—1221no—
296C22×C4—2441no—
297C22×C4—2441no—
298C22×C4—2441no—
299C22×C4—2441no—
300C22×C4—2442no—
301C22×C4—2442no—
302C22×C4—2442no—
303C22×C4—2442no—
304C22×C4—2442no—
305C22×C4—2442no—
306C22×C4C22⋊#692311yescharacteristic
307C22×C4C22⋊#692311yescharacteristic
308C22×C4C22×#692311yescharacteristic
309C2×C8—1224no—
310C2×C8—2442no—
311C2×C8—2442no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—42no—
315C4⋊C4—2441no—
316C4⋊C4—2441no—
317C4⋊C4—2442no—
318C4⋊C4—2442no—
319C4⋊C4—2442no—
320C4⋊C4—2448no—
321C4⋊C4—2442no—
322C22⋊C4—2441no—
323C22⋊C4—2441no—
324C22⋊C4—2441no—
325C22⋊C4—2441no—
326C42—41no—
327C42—1222no—
328C42—1222no—
329C42—2441no—
330C23—611no—
331C23—611no—
332C23—611no—
333C23—611no—
334C23—611no—
335C23—611no—
336C23—1221no—
337C23—1221no—
338C23—1221no—
339C23—1221no—
340C23C2×C22⋊#692311yescharacteristic
341Q8—4884no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—612no—
355C2×C4—612no—
356C2×C4—612no—
357C2×C4—612no—
358C2×C4—612no—
359C2×C4—1224no—
360C2×C4—1224no—
361C2×C4—1221no—
362C2×C4—1221no—
363C2×C4—1221no—
364C2×C4—1221no—
365C2×C4—4882no—
366C2×C4—4882no—
367C2×C4—4882no—
368C2×C4—4882no—
369C2×C4—2442no—
370C2×C4—2442no—
371C2×C4—2442no—
372C2×C4—2442no—
373C2×C4—2444no—
374C2×C4—2444no—
375C2×C4—2444no—
376C2×C4—2441no—
377C2×C4—2441no—
378C2×C4—2441no—
379C2×C4—2441no—
380C2×C4—2441no—
381C2×C4—2441no—
382C2×C4#1451983912yes—
383C2×C4#1451984012yes—
384C2×C4Q8×#692312yes—
385C8—2444no—
386C22—611no—
387C22—611no—
388C22—611no—
389C22—611no—
390C22—1221no—
391C22—1221no—
392C22—1221no—
393C22—1221no—
394C22—1221no—
395C22—1221no—
396C22—1221no—
397C22—1221no—
398C22—1221no—
399C22—1221no—
400C22—1221no—
401C22—1221no—
402C22(C2×#6923)⋊Q811yescharacteristic
403C22D61⋊#9911yescharacteristic
404C22#1684074111yescharacteristic
405C22C2×#1451983911yescharacteristic
406C22C2×#1451984011yescharacteristic
407C22D61⋊#10411yescharacteristic
408C22#1684075911yescharacteristic
409C4—22no—
410C4—22no—
411C4—22no—
412C4—81no—
413C4—81no—
414C4—614no—
415C4—1222no—
416C4—1222no—
417C4—4884no—
418C4—4881no—
419C4—4881no—
420C2—1221no—
421C2—1221no—
422C2—1221no—
423C2—1221no—
424C2D61⋊#32811yescharacteristic
425C2#2146119811yescharacteristic
426C2#2146125211yescharacteristic
427C2#2146125411yescharacteristic
428C2#2146199611yescharacteristic
429C2#2146200011yescharacteristic
430C2#2146201011yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#389C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C2×D4
cosocleC22×C4×D61C23
hypercenter#389#6923
hypocenterC61#9884
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
12. C2×#14519776C4semidirect
16. #16839660C4semidirect
18. #16839631C4semidirect
22. C61×#389C4semidirect
29. #14519834Q8semidirect
230. #389#6923semidirect
238. C61#9884semidirect

Maximal subgroups

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

subgroupindex
C4×#145198342
#214609972
#214606922
#214541702
#988461