Finite Group Databasebeta

← #30606270

Subgroups — #30606270

Order 15616.

810 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840749C211yesmaximal, characteristic
2C2×#16840742C211yesmaximal, characteristic
3#21460904C212yesmaximal, complemented
4#21460903C212yesmaximal, complemented
5#21448406C211yesmaximal, characteristic
6C22×#11758217—21no—
7C2×#14519856—21no—
8#16840749—22no—
9#16840749C414yescomplemented
10C2×#14519838—21no—
11C2×#14519837C2212yes—
12#16840742—22no—
13#16840742C414yescomplemented
14C2×#14519835—21no—
15C2×#14519835C2212yes—
16C22×#11758224C2211yescharacteristic
17C2×#14519733C411yescharacteristic, complemented
18C22×#11758196C411yescharacteristic, complemented
19#16839666—21no—
20#16839662—21no—
21#16839642C411yescharacteristic, complemented
22#16839641C2211yescharacteristic
23#16839639C2211yescharacteristic
24#16839621—21no—
25#16839620—21no—
26C61×#386C411yescharacteristic, complemented
27C2×#11758217—24no—
28C2×#11758217—22no—
29C2×#11758217—41no—
30C2×#11758217—42no—
31C22×#92420—41no—
32#14519856—24no—
33#14519856—42no—
34C2×C4⋊#6923—41no—
35C2×C22⋊#6923—22no—
36C2×C4×#6923—41no—
37#14519838—24no—
38#14519837—22no—
39#14519837C2×C414yes—
40#14519835—24no—
41#14519835—22no—
42#14519835C2×C414yes—
43C2×#11758224—41no—
44C2×#11758224—41no—
45C2×#11758224—42no—
46C2×#11758224C2×C412yes—
47C2×#11758224C2×C412yes—
48C2×#11758224D412yes—
49C2×#11758224Q812yes—
50C22×Dic122D411yescharacteristic
51C22×C22⋊D61D411yescharacteristic
52C22×C22⋊D61C2311yescharacteristic
53C23×Dic61C2×C411yescharacteristic
54C23×Dic61C2×C411yescharacteristic
55C23×Dic61D411yescharacteristic
56C22×C4×D61D411yescharacteristic
57#14519733—42no—
58C2×#11758196—21no—
59C2×#11758196—21no—
60C2×#11758196—21no—
61C2×#11758196—41no—
62C2×#11758196—41no—
63C2×C22⋊Dic61—21no—
64C2×C22⋊Dic61C2×C411yescharacteristic
65C2×#11758198—21no—
66C2×#11758198—21no—
67C2×C4×Dic61—21no—
68#14519684—21no—
69#14519684—21no—
70#14519684—21no—
71C22×D4×C61C2×C411yescharacteristic
72C23×C4×C61C2×C411yescharacteristic
73C2×C22⋊C4×C61—21no—
74C2×C22⋊C4×C61C2×C411yescharacteristic
75#95×C61—21no—
76C24×C61C22⋊C411yescharacteristic
77C24×C61C22×C411yescharacteristic
78C23×D61C2×D411yescharacteristic
79C22×#6923—42no—
80C2×D4×C61—41no—
81C2×D4×C61—41no—
82C2×D4×C61C4212yes—
83C2×D4×C61C4⋊C412yes—
84C22×C4×C61—21no—
85C22×C4×C61—21no—
86C22×C4×C61—41no—
87C22×C4×C61—81no—
88C22×C4×C61C22⋊C411yescharacteristic
89C2×C22⋊D61—41no—
90C2×C22⋊D61—41no—
91C2×C22⋊D61—41no—
92C2×C22⋊D61—41no—
93C2×C22⋊D61C22⋊C412yes—
94C2×C22⋊D61C4⋊C412yes—
95C2×C22⋊D61C22×C411yescharacteristic
96C2×C22⋊D61C22×C411yescharacteristic
97C2×C22⋊D61C2×D411yescharacteristic
98C2×C22⋊D61C2×Q811yescharacteristic
99C22×Dic61—21no—
100C22×Dic61—21no—
101C22×Dic61—22no—
102C22×Dic61—21no—
103C22×Dic61—21no—
104C22×Dic61—22no—
105C22×Dic61—21no—
106C22×Dic61—21no—
107C22×Dic61—41no—
108C22×Dic61—81no—
109C22×Dic61C4212yes—
110C22×Dic61C22⋊C411yescharacteristic
111C22×Dic61C22⋊C412yes—
112C22×Dic61C22⋊C411yescharacteristic
113C22×Dic61C4⋊C412yes—
114C22×Dic61C4⋊C412yes—
115C22×Dic61C2×D411yescharacteristic
116#11758224—42no—
117#11758224—42no—
118#11758224—42no—
119#11758224—42no—
120#11758224—42no—
121#11758224—42no—
122#11758224—42no—
123#11758224—42no—
124C2×C4×D61—21no—
125C2×C4×D61—21no—
126C2×C4×D61—22no—
127C2×C4×D61C22⋊C412yes—
128C2×C4×D61C4⋊C412yes—
129C2×Dic122—41no—
130C2×Dic122—41no—
131C2×Dic122C22⋊C412yes—
132C2×Dic122C4⋊C412yes—
133C22⋊#6923—24no—
134C22⋊#6923—42no—
135#11758217—24no—
136#11758217—42no—
137#11758217—44no—
138C2×#92420—42no—
139C2×#92420—44no—
140C4⋊#6923—44no—
141C4×#6923—44no—
142C22⋊C4×C61—41no—
143C22⋊C4×C61—81no—
144C22⋊Dic61—41no—
145C22⋊Dic61—81no—
146#11758198—81no—
147#11758198—81no—
148#11758196—42no—
149#11758196—41no—
150#11758196—41no—
151#11758196—42no—
152C4×Dic61—42no—
153C23×C61—21no—
154C23×C61—21no—
155C23×C61—21no—
156C23×C61—21no—
157C23×C61—41no—
158C23×C61—41no—
159C23×C61—41no—
160C23×C61—41no—
161C23×C61#9512yes—
162C23×C61C2×C4211yescharacteristic
163C23×C61C2×C22⋊C411yescharacteristic
164C23×C61C2×C4⋊C411yescharacteristic
165C22×D61—21no—
166C22×D61—21no—
167C22×D61—41no—
168C22×D61—41no—
169C22×D61C2×C22⋊C411yescharacteristic
170C22×D61C2×C4⋊C411yescharacteristic
171C2×#6923—44no—
172C2×#6923—82no—
173C2×#6923—82no—
174D4×C61—42no—
175D4×C61—42no—
176C2×C4×C61—21no—
177C2×C4×C61—21no—
178C2×C4×C61—41no—
179C2×C4×C61—41no—
180C2×C4×C61—41no—
181C2×C4×C61—41no—
182C2×C4×C61—41no—
183C2×C4×C61—41no—
184C2×C4×C61—82no—
185C2×C4×C61#9512yes—
186C22⋊D61—42no—
187C22⋊D61—42no—
188C22⋊D61—41no—
189C22⋊D61—41no—
190C22⋊D61—41no—
191C22⋊D61—41no—
192C2×Dic61—21no—
193C2×Dic61—21no—
194C2×Dic61—21no—
195C2×Dic61—21no—
196C2×Dic61—22no—
197C2×Dic61—22no—
198C2×Dic61—22no—
199C2×Dic61—22no—
200C2×Dic61—22no—
201C2×Dic61—22no—
202C2×Dic61—22no—
203C2×Dic61—22no—
204C2×Dic61—41no—
205C2×Dic61—41no—
206C2×Dic61—41no—
207C2×Dic61—41no—
208C2×Dic61—41no—
209C2×Dic61—41no—
210C2×Dic61—82no—
211C2×Dic61#9512yes—
212C2×Dic61#9512yes—
213C2×Dic61#9912yes—
214C2×Dic61#9911yescharacteristic
215C2×Dic61#9911yescharacteristic
216C2×Dic61C2×C22⋊C411yescharacteristic
217C2×Dic61C2×C4⋊C411yescharacteristic
218C4×D61—22no—
219C4×D61—22no—
220C4×D61—22no—
221C4×D61—22no—
222Dic122—42no—
223Dic122—42no—
224#92420—44no—
225#12575—611nomaximal, Sylow
226C22×C61—21no—
227C22×C61—21no—
228C22×C61—22no—
229C22×C61—21no—
230C22×C61—21no—
231C22×C61—42no—
232C22×C61—41no—
233C22×C61—41no—
234C22×C61—42no—
235C22×C61—41no—
236C22×C61—41no—
237C22×C61—41no—
238C22×C61—41no—
239C22×C61—81no—
240C22×C61C2×#9511yescharacteristic
241C22×C61C2×#9911yescharacteristic
242C22×C61C2×#9911yescharacteristic
243C2×D61—21no—
244C2×D61—21no—
245C2×D61—41no—
246C2×D61—41no—
247C2×D61—41no—
248C2×D61—41no—
249C2×D61—81no—
250#6923—84no—
251C4×C61—22no—
252C4×C61—81no—
253C4×C61—81no—
254Dic61—21no—
255Dic61—22no—
256Dic61—21no—
257Dic61—81no—
258Dic61—81no—
259Dic61#34212yes—
260Dic61#34212yes—
261C2×#413—611no—
262C2×#410—611no—
263#2311—611no—
264#1390—612no—
265#1390—612no—
266C2×C61—21no—
267C2×C61—21no—
268C2×C61—41no—
269C2×C61—41no—
270C2×C61—42no—
271C2×C61C2×#34211yescharacteristic
272C2×C61#212211yescharacteristic
273C2×C61#212311yescharacteristic
274D61—41no—
275D61—41no—
276C22×#41—611no—
277C22×M16—1221no—
278C2×#117—611no—
279C2×#117—1221no—
280C22×C4⋊C4—611no—
281#413—614no—
282#413—1222no—
283C2×#101—1221no—
284C2×#100—612no—
285#410—614no—
286#410—1222no—
287C2×#99—612no—
288C2×#99—1221no—
289#391—1221no—
290#390—1221no—
291#386—611no—
292#386—611no—
293#386—611no—
294#386#692311yescharacteristic, complemented
295#380—1221no—
296#380—1221no—
297C61#1257511yescharacteristic, complemented, Sylow
298C2×#41—612no—
299C2×#41—612no—
300C2×#41—612no—
301C2×#41—612no—
302C2×#41—2441no—
303C2×#41—2441no—
304C2×#41—2442no—
305C22×Q8—611no—
306C22×D4—611no—
307C22×D4—611no—
308C22×D4C2×#692311yescharacteristic
309C23×C4—611no—
310C23×C4—611no—
311C23×C4—611no—
312C23×C4—611no—
313C23×C4C2×#692311yescharacteristic
314C2×M16—1222no—
315C2×M16—1224no—
316C2×M16—2442no—
317C2×M16—2441no—
318C22×C8—2441no—
319#117—1224no—
320#117—2442no—
321#117—2442no—
322C2×C4⋊C4—1221no—
323C2×C4⋊C4—1221no—
324C2×C4⋊C4—1221no—
325C2×C4⋊C4—2441no—
326C2×C4⋊C4—2441no—
327C2×C4⋊C4—2441no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—611no—
330C2×C22⋊C4—1222no—
331C2×C22⋊C4—1221no—
332C2×C22⋊C4—1221no—
333C2×C22⋊C4—1221no—
334C2×C22⋊C4C2×#692311yescharacteristic
335C2×C42—1221no—
336C2×C42—2441no—
337#101—1224no—
338#100—614no—
339#100—1222no—
340#99—614no—
341#99—1222no—
342#99—1224no—
343#95—21no—
344#95—1221no—
345#95—1221no—
346#95—1221no—
347C24—611no—
348C24C22⋊#692311yescharacteristic
349C24C22×#692311yescharacteristic
350#41—2442no—
351#41—2442no—
352#41—2442no—
353#41—2442no—
354#41—2442no—
355#41—2442no—
356#41—2442no—
357#41—2442no—
358C2×Q8—612no—
359C2×Q8—612no—
360C2×Q8—2441no—
361C2×Q8—2441no—
362C2×D4—41no—
363C2×D4—41no—
364C2×D4—612no—
365C2×D4—612no—
366C2×D4—611no—
367C2×D4—611no—
368C2×D4—611no—
369C2×D4—611no—
370C2×D4—2441no—
371C2×D4—2441no—
372C2×D4—2441no—
373C2×D4—2441no—
374C2×D4C4×#692312yes—
375C2×D4C4⋊#692312yes—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—41no—
379C22×C4—81no—
380C22×C4—611no—
381C22×C4—612no—
382C22×C4—612no—
383C22×C4—612no—
384C22×C4—611no—
385C22×C4—611no—
386C22×C4—612no—
387C22×C4—612no—
388C22×C4—612no—
389C22×C4—1221no—
390C22×C4—1221no—
391C22×C4—1222no—
392C22×C4—1221no—
393C22×C4—1221no—
394C22×C4—1222no—
395C22×C4—1221no—
396C22×C4—1222no—
397C22×C4—1221no—
398C22×C4—1221no—
399C22×C4—1221no—
400C22×C4—4881no—
401C22×C4—2442no—
402C22×C4—2441no—
403C22×C4C22⋊#692311yescharacteristic
404M16—1224no—
405M16—2444no—
406M16—2442no—
407C2×C8—2444no—
408C2×C8—2442no—
409C4⋊C4—2441no—
410C4⋊C4—2441no—
411C4⋊C4—2442no—
412C4⋊C4—2442no—
413C4⋊C4—2444no—
414C22⋊C4—41no—
415C22⋊C4—81no—
416C22⋊C4—1224no—
417C22⋊C4—4881no—
418C22⋊C4—4881no—
419C22⋊C4—4881no—
420C22⋊C4—2442no—
421C22⋊C4—2441no—
422C42—2442no—
423C42—2444no—
424C23—21no—
425C23—21no—
426C23—21no—
427C23—21no—
428C23—41no—
429C23—41no—
430C23—41no—
431C23—41no—
432C23—611no—
433C23—611no—
434C23—1221no—
435C23—1221no—
436C23—2441no—
437C23—2441no—
438C23(C2×#6923)⋊C412yes—
439C23C2×C4×#692311yescharacteristic
440C23C2×C22⋊#692311yescharacteristic
441C23C2×C4⋊#692311yescharacteristic
442Q8—2442no—
443Q8—2442no—
444D4—42no—
445D4—42no—
446D4—2441no—
447D4—2441no—
448D4—2442no—
449D4—2442no—
450D4—2441no—
451D4—2441no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—82no—
461C2×C4—612no—
462C2×C4—611no—
463C2×C4—611no—
464C2×C4—612no—
465C2×C4—612no—
466C2×C4—611no—
467C2×C4—611no—
468C2×C4—1222no—
469C2×C4—1222no—
470C2×C4—1222no—
471C2×C4—1222no—
472C2×C4—1222no—
473C2×C4—1222no—
474C2×C4—1222no—
475C2×C4—1222no—
476C2×C4—1222no—
477C2×C4—1222no—
478C2×C4—1222no—
479C2×C4—1222no—
480C2×C4—1221no—
481C2×C4—1221no—
482C2×C4—1221no—
483C2×C4—1221no—
484C2×C4—4882no—
485C2×C4—4882no—
486C2×C4—4882no—
487C2×C4—2441no—
488C2×C4—2441no—
489C2×C4—2441no—
490C2×C4—2441no—
491C2×C4—2444no—
492C2×C4—2441no—
493C2×C4—2441no—
494C2×C4(C2×#6923)⋊C412yes—
495C8—2444no—
496C22—21no—
497C22—21no—
498C22—22no—
499C22—21no—
500C22—21no—
501C22—42no—
502C22—41no—
503C22—41no—
504C22—42no—
505C22—41no—
506C22—41no—
507C22—41no—
508C22—41no—
509C22—81no—
510C22—1221no—
511C22—1221no—
512C22—4881no—
513C22—2441no—
514C22—2441no—
515C22—2441no—
516C22—2441no—
517C22C2×(C2×#6923)⋊C411yescharacteristic
518C22D61⋊#9911yescharacteristic
519C22D61⋊#9911yescharacteristic
520C4—22no—
521C4—81no—
522C4—81no—
523C4—612no—
524C4—612no—
525C4—1221no—
526C4—1222no—
527C4—1221no—
528C4—4881no—
529C4—4884no—
530C4—4881no—
531C2—21no—
532C2—21no—
533C2—41no—
534C2—41no—
535C2—42no—
536C2—2441no—
537C2—2441no—
538C2#2146151611yescharacteristic
539C2#2146207911yescharacteristic
540C2#2146208211yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC23×C61C2×C42
FrattiniC24C22×#6923
FittingC61×#386C4
socleC22×C61C2×#99
prime radicalC22×#11758224C22
cosocleC22×C22⋊D61C23
hypercenter#386#6923
hypocenterC61#12575
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #386

Complements

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

NH ≅ G/Ntype
3. #21460904C2semidirect
4. #21460903C2semidirect
9. #16840749C4semidirect
13. #16840742C4semidirect
17. C2×#14519733C4semidirect
18. C22×#11758196C4semidirect
21. #16839642C4semidirect
26. C61×#386C4semidirect
294. #386#6923semidirect
297. C61#12575semidirect

Maximal subgroups

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

subgroupindex
C2×#168407492
C2×#168407422
#214609042
#214609032
#214484062
#1257561