Finite Group Databasebeta

← #30606271

Subgroups — #30606271

Order 15616.

810 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840748C211yesmaximal, characteristic
2C2×#16840741C211yesmaximal, characteristic
3#21460904C214yesmaximal, complemented
4#21448407C211yesmaximal, characteristic
5C2×D61⋊M16—21no—
6C2×#14519856—21no—
7#16840748—22no—
8#16840748C414yescomplemented
9C2×#14519838—21no—
10C2×#14519837C2212yes—
11#16840741—22no—
12#16840741C414yescomplemented
13C2×#14519836—21no—
14C2×#14519835C2212yes—
15C22×#11758222C2211yescharacteristic
16C22×C4⋊Dic61C411yescharacteristic, complemented
17#16839668—21no—
18#16839664—21no—
19#16839639C412yescomplemented
20#16839639C2212yes—
21#16839619—21no—
22#16839619—21no—
23C2×#117×C61C411yescharacteristic, complemented
24C2×#11758213—41no—
25D61⋊M16—24no—
26D61⋊M16—42no—
27C2×#11758217—22no—
28C2×D61⋊C8—41no—
29#14519856—24no—
30#14519856—42no—
31C2×C4⋊#6923—41no—
32C2×C22⋊#6923—22no—
33C2×C4×#6923—41no—
34#14519838—24no—
35#14519837—22no—
36#14519837C2×C414yes—
37#14519836—24no—
38#14519835—22no—
39#14519835C2×C414yes—
40C2×#11758222—41no—
41C2×#11758222—41no—
42C2×#11758222—42no—
43C2×#11758222C2×C412yes—
44C2×#11758222C2×C412yes—
45C2×#11758222D412yes—
46C2×#11758222Q812yes—
47C22×Dic122D411yescharacteristic
48C22×D244D411yescharacteristic
49C22×C22⋊D61C2×C411yescharacteristic
50C22×C22⋊D61C2311yescharacteristic
51C23×Dic61C2×C412yes—
52C22×C4×D61D411yescharacteristic
53C22×C4×D61D411yescharacteristic
54C2×C4⋊Dic61—21no—
55C2×C4⋊Dic61—21no—
56C2×C4⋊Dic61—41no—
57C2×C4⋊Dic61—41no—
58C2×#11758198—22no—
59C2×#11758198—22no—
60#14519684—22no—
61#14519684—22no—
62C23×C4×C61C2×C411yescharacteristic
63#117×C61—42no—
64C2×C4⋊C4×C61—21no—
65C2×C22⋊C4×C61C2×C412yes—
66C2×C42×C61—21no—
67C24×C61C22×C411yescharacteristic
68C23×D61C22⋊C411yescharacteristic
69C23×D61C2×D411yescharacteristic
70C22×#6923—42no—
71C22×C4×C61—22no—
72C22×C4×C61—21no—
73C22×C4×C61—21no—
74C22×C4×C61—22no—
75C22×C4×C61C4212yes—
76C22×C4×C61C22⋊C411yescharacteristic
77C22×C4×C61C22⋊C411yescharacteristic
78C22×C4×C61C4⋊C412yes—
79C2×C22⋊D61—41no—
80C2×C22⋊D61—41no—
81C2×C22⋊D61—41no—
82C2×C22⋊D61—41no—
83C2×C22⋊D61C4212yes—
84C2×C22⋊D61C4⋊C412yes—
85C2×C22⋊D61C22×C411yescharacteristic
86C2×C22⋊D61C22×C411yescharacteristic
87C2×C22⋊D61C2×D411yescharacteristic
88C2×C22⋊D61C2×Q811yescharacteristic
89C22×Dic61—22no—
90C22×Dic61—42no—
91C22×Dic61—82no—
92C22×Dic61C22⋊C411yescharacteristic
93C22×Dic61C2×D411yescharacteristic
94#11758222—42no—
95#11758222—42no—
96#11758222—42no—
97#11758222—42no—
98#11758222—42no—
99#11758222—42no—
100#11758222—42no—
101#11758222—42no—
102C2×D244—41no—
103C2×D244—41no—
104C2×D244C22⋊C412yes—
105C2×D244C4⋊C412yes—
106C2×C4×D61—21no—
107C2×C4×D61—21no—
108C2×C4×D61—22no—
109C2×C4×D61—21no—
110C2×C4×D61—22no—
111C2×C4×D61—21no—
112C2×C4×D61C22⋊C412yes—
113C2×C4×D61C22⋊C412yes—
114C2×C4×D61C4⋊C412yes—
115C2×C4×D61C4⋊C412yes—
116C2×Dic122—41no—
117C2×Dic122—41no—
118C2×Dic122C22⋊C412yes—
119C2×Dic122C4⋊C412yes—
120C22⋊#6923—24no—
121C22⋊#6923—42no—
122#11758217—24no—
123#11758217—42no—
124C2×#92420—42no—
125C4⋊#6923—44no—
126C4×#6923—44no—
127#11758213—44no—
128D61⋊C8—44no—
129C4⋊C4×C61—42no—
130C22⋊C4×C61—42no—
131C42×C61—42no—
132#11758198—82no—
133#11758198—82no—
134C4⋊Dic61—42no—
135C4⋊Dic61—41no—
136C4⋊Dic61—41no—
137C23×C61—21no—
138C23×C61—21no—
139C23×C61—41no—
140C23×C61—41no—
141C23×C61C2×C4211yescharacteristic
142C23×C61C2×C22⋊C411yescharacteristic
143C23×C61C2×C4⋊C411yescharacteristic
144C22×D61—21no—
145C22×D61—21no—
146C22×D61—21no—
147C22×D61—21no—
148C22×D61—41no—
149C22×D61—41no—
150C22×D61—41no—
151C22×D61—41no—
152C22×D61#9512yes—
153C22×D61C2×C22⋊C411yescharacteristic
154C22×D61C2×C4⋊C411yescharacteristic
155C2×#6923—44no—
156C2×#6923—82no—
157C2×#6923—82no—
158C2×C4×C61—21no—
159C2×C4×C61—21no—
160C2×C4×C61—22no—
161C2×C4×C61—22no—
162C2×C4×C61—22no—
163C2×C4×C61—22no—
164C2×C4×C61—42no—
165C2×C4×C61—42no—
166C2×C4×C61—42no—
167C2×C4×C61#9512yes—
168C2×C4×C61#9512yes—
169C2×C4×C61#9912yes—
170C2×C4×C61#9911yescharacteristic
171C2×C4×C61#9911yescharacteristic
172C22⋊D61—42no—
173C22⋊D61—42no—
174C22⋊D61—41no—
175C22⋊D61—41no—
176C22⋊D61—41no—
177C22⋊D61—41no—
178C2×Dic61—21no—
179C2×Dic61—21no—
180C2×Dic61—21no—
181C2×Dic61—21no—
182C2×Dic61—42no—
183C2×Dic61—42no—
184C2×Dic61—42no—
185C2×Dic61—84no—
186C2×Dic61#9512yes—
187C2×Dic61C2×C22⋊C411yescharacteristic
188C2×Dic61C2×C4⋊C411yescharacteristic
189D244—42no—
190D244—42no—
191C4×D61—22no—
192C4×D61—22no—
193C4×D61—22no—
194C4×D61—22no—
195C4×D61—22no—
196C4×D61—22no—
197C4×D61—22no—
198C4×D61—22no—
199Dic122—42no—
200Dic122—42no—
201#92420—44no—
202#12575—611nomaximal, Sylow
203C22×C61—21no—
204C22×C61—21no—
205C22×C61—21no—
206C22×C61—21no—
207C22×C61—41no—
208C22×C61—41no—
209C22×C61—42no—
210C22×C61—41no—
211C22×C61—41no—
212C22×C61C2×#9511yescharacteristic
213C22×C61C2×#9911yescharacteristic
214C22×C61C2×#9911yescharacteristic
215C2×D61—21no—
216C2×D61—22no—
217C2×D61—21no—
218C2×D61—41no—
219C2×D61—41no—
220C2×D61—41no—
221C2×D61—41no—
222C2×D61—42no—
223C2×D61—41no—
224C2×D61—41no—
225C2×D61—81no—
226C2×D61—81no—
227#6923—84no—
228C4×C61—22no—
229C4×C61—82no—
230C4×C61#34212yes—
231C4×C61#34212yes—
232Dic61—21no—
233Dic61—22no—
234Dic61—21no—
235Dic61—82no—
236C2×#413—611no—
237C2×#410—611no—
238#2311—611no—
239#1390—614no—
240C2×C61—21no—
241C2×C61—21no—
242C2×C61—41no—
243C2×C61—41no—
244C2×C61C2×#34211yescharacteristic
245C2×C61#212211yescharacteristic
246C2×C61#212311yescharacteristic
247D61—41no—
248D61—42no—
249D61—41no—
250C22×#41—611no—
251C22×M16—1221no—
252C2×#117—1221no—
253C2×#117#692311yescharacteristic, complemented
254C22×C4⋊C4—611no—
255#413—614no—
256#413—1222no—
257C2×#101—1221no—
258C2×#100—612no—
259#410—614no—
260#410—1222no—
261C2×#99—612no—
262C2×#99—1221no—
263#391—1221no—
264#390—1221no—
265#386—612no—
266#386—612no—
267#380—1221no—
268#380—1221no—
269C61#1257511yescharacteristic, complemented, Sylow
270C2×#41—612no—
271C2×#41—612no—
272C2×#41—612no—
273C2×#41—612no—
274C2×#41—2442no—
275C2×#41—2441no—
276C2×#41—2441no—
277C22×Q8—611no—
278C22×D4—611no—
279C22×D4—611no—
280C22×D4—611no—
281C23×C4—611no—
282C23×C4—611no—
283C23×C4—612no—
284C23×C4C2×#692311yescharacteristic
285C2×M16—1222no—
286C2×M16—1224no—
287C2×M16—2442no—
288C2×M16—2441no—
289C22×C8—2441no—
290#117—42no—
291#117—1224no—
292#117—2442no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—1221no—
295C2×C4⋊C4—1221no—
296C2×C4⋊C4—2441no—
297C2×C4⋊C4—2441no—
298C2×C4⋊C4—2441no—
299C2×C22⋊C4—1222no—
300C2×C22⋊C4—1222no—
301C2×C22⋊C4—1222no—
302C2×C22⋊C4C2×#692312yes—
303C2×C42—21no—
304C2×C42—2441no—
305#101—1224no—
306#100—614no—
307#100—1222no—
308#99—614no—
309#99—1222no—
310#99—1224no—
311#95—1222no—
312#95—1222no—
313C24—611no—
314C24—611no—
315C24C22×#692311yescharacteristic
316#41—2442no—
317#41—2442no—
318#41—2442no—
319#41—2442no—
320#41—2442no—
321#41—2442no—
322#41—2442no—
323#41—2442no—
324C2×Q8—612no—
325C2×Q8—612no—
326C2×Q8—2441no—
327C2×Q8—2441no—
328C2×D4—611no—
329C2×D4—611no—
330C2×D4—612no—
331C2×D4—611no—
332C2×D4—612no—
333C2×D4—611no—
334C2×D4—612no—
335C2×D4—612no—
336C2×D4—2441no—
337C2×D4—2441no—
338C2×D4—2441no—
339C2×D4—2441no—
340C2×D4—2441no—
341C2×D4—2441no—
342C22×C4—22no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—22no—
346C22×C4—611no—
347C22×C4—611no—
348C22×C4—612no—
349C22×C4—612no—
350C22×C4—612no—
351C22×C4—612no—
352C22×C4—1222no—
353C22×C4—1222no—
354C22×C4—1221no—
355C22×C4—1221no—
356C22×C4—1221no—
357C22×C4—1221no—
358C22×C4—1222no—
359C22×C4—4882no—
360C22×C4—2442no—
361C22×C4—2442no—
362C22×C4C4×#692312yes—
363C22×C4C4⋊#692312yes—
364C22×C4C22⋊#692311yescharacteristic
365C22×C4C22⋊#692311yescharacteristic
366M16—1224no—
367M16—2444no—
368M16—2442no—
369C2×C8—2444no—
370C2×C8—2442no—
371C4⋊C4—42no—
372C4⋊C4—2442no—
373C4⋊C4—2444no—
374C4⋊C4—2441no—
375C4⋊C4—2441no—
376C22⋊C4—42no—
377C22⋊C4—1224no—
378C22⋊C4—4882no—
379C22⋊C4—4882no—
380C22⋊C4—2442no—
381C42—42no—
382C42—2444no—
383C23—21no—
384C23—21no—
385C23—41no—
386C23—41no—
387C23—612no—
388C23—611no—
389C23—611no—
390C23—1221no—
391C23—1221no—
392C23—1221no—
393C23—1221no—
394C23—2441no—
395C23—2441no—
396C23—2441no—
397C23—2441no—
398C23C2×C4×#692311yescharacteristic
399C23C2×C22⋊#692311yescharacteristic
400C23C2×C4⋊#692311yescharacteristic
401Q8—2442no—
402Q8—2442no—
403D4—2442no—
404D4—2442no—
405D4—2441no—
406D4—2441no—
407D4—2441no—
408D4—2442no—
409D4—2442no—
410D4—2441no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—612no—
421C2×C4—611no—
422C2×C4—611no—
423C2×C4—1221no—
424C2×C4—1221no—
425C2×C4—1221no—
426C2×C4—1221no—
427C2×C4—1222no—
428C2×C4—1222no—
429C2×C4—1222no—
430C2×C4—1222no—
431C2×C4—1222no—
432C2×C4—1222no—
433C2×C4—1222no—
434C2×C4—1222no—
435C2×C4—4882no—
436C2×C4—4882no—
437C2×C4—4884no—
438C2×C4—2442no—
439C2×C4—2442no—
440C2×C4—2444no—
441C2×C4—2442no—
442C2×C4(C2×#6923)⋊C412yes—
443C2×C4(C2×#6923)⋊C412yes—
444C2×C4#1451983512yes—
445C2×C4#1451983611yescharacteristic
446C2×C4#1451983611yescharacteristic
447C8—2444no—
448C22—21no—
449C22—21no—
450C22—21no—
451C22—21no—
452C22—41no—
453C22—41no—
454C22—42no—
455C22—41no—
456C22—41no—
457C22—1221no—
458C22—1222no—
459C22—1221no—
460C22—4881no—
461C22—4881no—
462C22—2441no—
463C22—2442no—
464C22—2441no—
465C22—2441no—
466C22—2441no—
467C22—2441no—
468C22—2441no—
469C22C2×(C2×#6923)⋊C411yescharacteristic
470C22C2×#1451983511yescharacteristic
471C22C2×#1451983611yescharacteristic
472C4—22no—
473C4—82no—
474C4—1221no—
475C4—1222no—
476C4—1221no—
477C4—4884no—
478C4—4882no—
479C4#1684064012yes—
480C4#1684064012yes—
481C2—21no—
482C2—21no—
483C2—41no—
484C2—41no—
485C2—2441no—
486C2—2441no—
487C2—2442no—
488C2C2×#1684064011yescharacteristic
489C2#2146208011yescharacteristic
490C2#2146208311yescharacteristic
subgroupG/H
centerC22C2×#14519836
commutatorC23×C61C2×C42
FrattiniC24C22×#6923
FittingC2×#117×C61C4
socleC22×C61C2×#99
prime radicalC22×#11758222C22
cosocleC22×C22⋊D61C23
hypercenterC2×#117#6923
hypocenterC61#12575
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
3. #21460904C2semidirect
8. #16840748C4semidirect
12. #16840741C4semidirect
16. C22×C4⋊Dic61C4semidirect
19. #16839639C4semidirect
23. C2×#117×C61C4semidirect
253. C2×#117#6923semidirect
269. C61#12575semidirect

Maximal subgroups

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

subgroupindex
C2×#168407482
C2×#168407412
#214609042
#214484072
#1257561