Finite Group Databasebeta

← #30603244

Subgroups — #30603244

Order 15616.

958 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840755C212yesmaximal
2#21462299C211yesmaximal, characteristic
3#21461522C211yesmaximal, characteristic
4C2×#16840633C212yesmaximal
5#391×D61C211yesmaximal, characteristic
6C2×D61⋊M16C2212yes—
7C2×#14519856C2212yes—
8#16840755—24no—
9#16840755—24no—
10C2×#14519840—24no—
11#16840713—24no—
12#16840704—22no—
13#16840642—22no—
14#16840633—24no—
15C22×Q8×D61C2211yescharacteristic
16C2×C4⋊C4×D61C2211yescharacteristic
17C2×C42×D61C2211yescharacteristic
18#16839669C411yescharacteristic, complemented
19#16839668C411yescharacteristic, complemented
20#16839667C411yescharacteristic, complemented
21#16839666—22no—
22#95×D61—22no—
23C61×#391C411yescharacteristic, complemented
24C2×#11758213—22no—
25D61⋊M16—22no—
26D61⋊M16—22no—
27D61⋊M16—22no—
28D61⋊M16D414yes—
29C2×#11758217—22no—
30C2×D61⋊C8—22no—
31#14519856—22no—
32#14519856—22no—
33#14519856—22no—
34#14519856—22no—
35C2×C4⋊#6923—24no—
36C2×C4⋊#6923D414yes—
37C2×C22⋊#6923—22no—
38C2×C4×#6923—22no—
39#14519840—216no—
40(C2×#6923)⋊C4—24no—
41C22×Dic122—21no—
42C22×Dic122C2×C411yescharacteristic
43C2×Q8×D61—21no—
44C2×Q8×D61—21no—
45C2×Q8×D61—22no—
46C2×Q8×D61—22no—
47C2×Q8×D61—22no—
48C2×Q8×D61—22no—
49C2×Q8×D61D412yes—
50C2×Q8×D61Q812yes—
51C22×C4×D61—21no—
52C22×C4×D61—21no—
53C22×C4×D61D412yes—
54C22×C4×D61C2311yescharacteristic
55C2×C4⋊Dic61C2×C411yescharacteristic
56C2×#11758196D412yes—
57C4⋊C4×D61—22no—
58C4⋊C4×D61—22no—
59C2×C4×Dic61—21no—
60C2×C4×Dic61C2×C411yescharacteristic
61C42×D61—22no—
62C42×D61—22no—
63#14519684—22no—
64#14519684—22no—
65#14519684—22no—
66C22×Q8×C61C2×C411yescharacteristic
67C2×C4⋊C4×C61C2×C411yescharacteristic
68C2×C42×C61C2×C411yescharacteristic
69#95×C61—22no—
70C23×D61C2×D411yescharacteristic
71C22×#6923—24no—
72C2×Q8×C61—21no—
73C2×Q8×C61—22no—
74C2×Q8×C61—22no—
75C2×Q8×C61C4⋊C412yescomplemented
76C22×C4×C61—21no—
77C22×C4×C61—21no—
78C22×C4×C61C22⋊C412yes—
79C22×C4×C61C22×C411yescharacteristic
80C22×Dic61—21no—
81C22×Dic61—21no—
82C22×Dic61C22⋊C412yes—
83C22×Dic61C2×D411yescharacteristic
84Q8×D61—24no—
85Q8×D61—24no—
86Q8×D61—24no—
87Q8×D61—24no—
88Q8×D61—42no—
89Q8×D61—42no—
90Q8×D61—42no—
91Q8×D61—42no—
92C2×C4×D61—24no—
93C2×C4×D61—22no—
94C2×C4×D61—22no—
95C2×C4×D61—22no—
96C2×C4×D61—22no—
97C2×C4×D61—42no—
98C2×C4×D61—41no—
99C2×C4×D61—41no—
100C2×C4×D61—41no—
101C2×C4×D61—41no—
102C2×C4×D61—41no—
103C2×C4×D61—41no—
104C2×C4×D61—44no—
105C2×C4×D61C2×D411yescharacteristic
106C2×C4×D61C2×D412yes—
107C2×C4×D61C2×D412yes—
108C2×C4×D61C2×Q811yescharacteristic
109C2×C4×D61#4111yescharacteristic
110C2×C4×D61#4112yes—
111C2×C4×D61#4112yes—
112C2×C4×D61#4111yescharacteristic
113C2×Dic122—22no—
114C2×Dic122—22no—
115C2×Dic122—21no—
116C2×Dic122—22no—
117C2×Dic122—22no—
118C2×Dic122—42no—
119C2×Dic122—42no—
120C2×Dic122C4⋊C412yescomplemented
121C22⋊#6923—42no—
122C22⋊#6923—42no—
123#11758217—24no—
124#11758217—42no—
125C2×#92420—42no—
126C4⋊#6923—24no—
127C4⋊#6923—24no—
128C4⋊#6923—84no—
129C4×#6923—42no—
130C4×#6923—42no—
131#11758213—24no—
132#11758213—42no—
133D61⋊C8—24no—
134D61⋊C8—42no—
135C4⋊C4×C61—22no—
136C42×C61—22no—
137C4⋊Dic61—22no—
138#11758196—24no—
139C4×Dic61—22no—
140C4×Dic61—42no—
141C23×C61C2×C22⋊C411yescharacteristic
142C22×D61—22no—
143C22×D61—22no—
144C22×D61#12011yescharacteristic
145C22×D61#12111yescharacteristic
146C22×D61C22⋊Q811yescharacteristic
147C22×D61#12311yescharacteristic
148C22×D61#12411yescharacteristic
149C22×D61#12711yescharacteristic
150C2×#6923—44no—
151C2×#6923—44no—
152C2×#6923—44no—
153Q8×C61—24no—
154Q8×C61—42no—
155C2×C4×C61—22no—
156C2×C4×C61—22no—
157C2×C4×C61—22no—
158C2×C4×C61—41no—
159C2×C4×C61—41no—
160C2×C4×C61—41no—
161C2×C4×C61—41no—
162C2×C4×C61—42no—
163C2×C4×C61C2×C4⋊C411yescharacteristic
164C2×C4×C61#11711yescharacteristic
165C2×C4×C61C4×D412yes—
166C2×C4×C61C4×D412yes—
167C2×Dic61—22no—
168C2×Dic61—22no—
169C2×Dic61—22no—
170C2×Dic61—41no—
171C2×Dic61—41no—
172C2×Dic61—41no—
173C2×Dic61—41no—
174C2×Dic61—42no—
175C2×Dic61#12111yescharacteristic
176C2×Dic61#12112yes—
177C2×Dic61#12112yes—
178C2×Dic61C22⋊Q811yescharacteristic
179C4×D61—44no—
180C4×D61—44no—
181C4×D61—42no—
182C4×D61—42no—
183C4×D61—42no—
184C4×D61—42no—
185C4×D61—44no—
186C4×D61—82no—
187C4×D61#12012yes—
188C4×D61#12112yes—
189C4×D61C22⋊Q812yes—
190C4×D61C22⋊Q812yes—
191C4×D61#12312yes—
192C4×D61#12312yes—
193C4×D61#12412yes—
194C4×D61#12612yes—
195Dic122—24no—
196Dic122—42no—
197Dic122—44no—
198Dic122—44no—
199#92420—44no—
200#11055—611nomaximal, Sylow
201C22×C61—21no—
202C22×C61—21no—
203C22×C61#38011yescharacteristic
204C22×C61#38611yescharacteristic
205C22×C61#39011yescharacteristic
206C2×D61—21no—
207C2×D61—21no—
208C2×D61—22no—
209C2×D61—22no—
210C2×D61—22no—
211C2×D61—22no—
212C2×D61#39211yescharacteristic
213C2×D61#39311yescharacteristic
214C2×D61#39711yescharacteristic
215C2×D61#39911yescharacteristic
216C2×D61#45512yes—
217C2×D61#45612yes—
218#6923—84no—
219C4×C61—42no—
220C4×C61—42no—
221C4×C61—42no—
222C4×C61#38512yes—
223C4×C61#38812yes—
224Dic61—42no—
225Dic61—42no—
226Dic61—42no—
227Dic61#39412yes—
228Dic61#39612yes—
229C2×#419—612no—
230#2316—611no—
231C2×#391—611no—
232C2×#343—611no—
233C2×#339—612no—
234C2×C61—21no—
235C2×C61—21no—
236C2×C61#143911yescharacteristic
237C2×C61#188511yescharacteristic
238C2×C61#188611yescharacteristic
239D61—21no—
240D61—21no—
241D61#200712yes—
242D61#202812yes—
243C23×Q8—611no—
244C22×M16—612no—
245C2×#117—612no—
246C22×C4⋊C4—611no—
247C22×C42—611no—
248#419—1224no—
249#419—1224no—
250C2×#103—1224no—
251#391—611no—
252#391—611no—
253#391—611no—
254#391—1222no—
255#391#692311yescharacteristic, complemented
256#389—1224no—
257#380—1222no—
258C2×#95—1222no—
259#343—1222no—
260#339—1224no—
261C61#1105511yescharacteristic, complemented, Sylow
262C22×Q8—612no—
263C22×Q8—612no—
264C22×Q8—611no—
265C22×Q8—1221no—
266C22×Q8—1221no—
267C22×Q8—1221no—
268C22×Q8—1222no—
269C22×Q8—1222no—
270C22×Q8—1222no—
271C22×Q8—1222no—
272C22×Q8C2×#692311yescharacteristic
273C23×C4—611no—
274C23×C4—612no—
275C23×C4—1221no—
276C23×C4—1221no—
277C2×M16—614no—
278C2×M16—1222no—
279C2×M16—1222no—
280C2×M16—1222no—
281C2×M16—1222no—
282C2×M16—1222no—
283C22×C8—1222no—
284#117—1222no—
285#117—1222no—
286#117—1222no—
287#117—1222no—
288C2×C4⋊C4—612no—
289C2×C4⋊C4—611no—
290C2×C4⋊C4—614no—
291C2×C4⋊C4—1222no—
292C2×C4⋊C4—1222no—
293C2×C4⋊C4—1224no—
294C2×C4⋊C4C2×#692311yescharacteristic
295C2×C22⋊C4—1222no—
296C2×C42—611no—
297C2×C42—1222no—
298C2×C42—1222no—
299C2×C42—1221no—
300C2×C42—1222no—
301C2×C42C2×#692311yescharacteristic
302#103—12216no—
303#95—22no—
304#95—1222no—
305#95—1222no—
306#95—1224no—
307#95—1222no—
308C24—611no—
309C2×Q8—21no—
310C2×Q8—22no—
311C2×Q8—22no—
312C2×Q8—612no—
313C2×Q8—1222no—
314C2×Q8—1222no—
315C2×Q8—1224no—
316C2×Q8—1224no—
317C2×Q8—1224no—
318C2×Q8—1224no—
319C2×Q8—1221no—
320C2×Q8—1222no—
321C2×Q8—1222no—
322C2×Q8—2442no—
323C2×Q8—2442no—
324C2×Q8—2442no—
325C2×Q8—2442no—
326C2×Q8—2442no—
327C2×Q8—2442no—
328C2×Q8C4⋊#692312yescomplemented
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—611no—
332C22×C4—611no—
333C22×C4—611no—
334C22×C4—611no—
335C22×C4—611no—
336C22×C4—612no—
337C22×C4—612no—
338C22×C4—612no—
339C22×C4—612no—
340C22×C4—612no—
341C22×C4—1222no—
342C22×C4—1222no—
343C22×C4—1222no—
344C22×C4—1222no—
345C22×C4—1224no—
346C22×C4—1221no—
347C22×C4—1221no—
348C22×C4—1224no—
349C22×C4—2444no—
350C22×C4—2441no—
351C22×C4—2441no—
352C22×C4—2441no—
353C22×C4—2441no—
354C22×C4—2441no—
355C22×C4—2441no—
356C22×C4—2442no—
357C22×C4C22⋊#692312yes—
358C22×C4C22×#692311yescharacteristic
359M16—1224no—
360M16—1224no—
361M16—2442no—
362M16—2442no—
363C2×C8—1224no—
364C2×C8—2442no—
365C2×C8—2442no—
366C4⋊C4—22no—
367C4⋊C4—1224no—
368C4⋊C4—1224no—
369C4⋊C4—1224no—
370C4⋊C4—1222no—
371C4⋊C4—4884no—
372C22⋊C4—2442no—
373C22⋊C4—2442no—
374C42—22no—
375C42—1222no—
376C42—2442no—
377C42—2442no—
378C42—2442no—
379C23—611no—
380C23—611no—
381C23—611no—
382C23—611no—
383C23—611no—
384C23—611no—
385C23—1222no—
386C23—1222no—
387C23C2×C22⋊#692311yescharacteristic
388Q8—24no—
389Q8—42no—
390Q8—1224no—
391Q8—2444no—
392Q8—2444no—
393Q8—2442no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—42no—
402C2×C4—611no—
403C2×C4—611no—
404C2×C4—612no—
405C2×C4—612no—
406C2×C4—612no—
407C2×C4—612no—
408C2×C4—612no—
409C2×C4—612no—
410C2×C4—612no—
411C2×C4—612no—
412C2×C4—612no—
413C2×C4—612no—
414C2×C4—1222no—
415C2×C4—1222no—
416C2×C4—1222no—
417C2×C4—4882no—
418C2×C4—2444no—
419C2×C4—2442no—
420C2×C4—2442no—
421C2×C4—2442no—
422C2×C4—2442no—
423C2×C4—2444no—
424C2×C4—2444no—
425C2×C4—2444no—
426C2×C4—2444no—
427C2×C4—2444no—
428C2×C4—2441no—
429C2×C4—2441no—
430C2×C4—2441no—
431C2×C4—2441no—
432C2×C4—2442no—
433C2×C4C2×C4⋊#692311yescharacteristic
434C2×C4#1451985611yescharacteristic
435C2×C4D4×#692312yes—
436C2×C4D4×#692312yes—
437C8—2444no—
438C22—21no—
439C22—21no—
440C22—611no—
441C22—611no—
442C22—612no—
443C22—612no—
444C22—611no—
445C22—611no—
446C22—1222no—
447C22—1222no—
448C22—1222no—
449C22—1222no—
450C22—1221no—
451C22—1221no—
452C22#1684070411yescharacteristic
453C22#1684071011yescharacteristic
454C22#1684071411yescharacteristic
455C4—42no—
456C4—42no—
457C4—42no—
458C4—612no—
459C4—612no—
460C4—4884no—
461C4—2442no—
462C4—2442no—
463C4—2442no—
464C4#1684070912yes—
465C4#1684071212yes—
466C2—21no—
467C2—21no—
468C2—612no—
469C2—612no—
470C2—1221no—
471C2—1221no—
472C2#2146100211yescharacteristic
473C2#2146182411yescharacteristic
474C2#2146182511yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#391C4
socleC22×C61#386
prime radicalC23×D61C2×D4
cosocleC22×C4×D61C23
hypercenter#391#6923
hypocenterC61#11055
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #391

Complements

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

NH ≅ G/Ntype
18. #16839669C4semidirect
19. #16839668C4semidirect
20. #16839667C4semidirect
23. C61×#391C4semidirect
75. C2×Q8×C61C4⋊C4semidirect
120. C2×Dic122C4⋊C4semidirect
255. #391#6923semidirect
261. C61#11055semidirect
328. C2×Q8C4⋊#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#168407552
#214622992
#214615222
C2×#168406332
#391×D612
#1105561