Finite Group Databasebeta

← #30596656

Subgroups — #30596656

Order 15616.

1026 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462263C211yesmaximal, characteristic
2C2×#16840704C211yesmaximal, characteristic
3#21460682C214yesmaximal, complemented
4C2×#16839724C211yesmaximal, characteristic
5C2×#14519856—21no—
6C22×C4⋊#6923—21no—
7C22×C22⋊#6923—21no—
8#16840705C412yescomplemented
9#16840704—21no—
10#16840704—21no—
11#16840704—21no—
12#16840704C412yescomplemented
13#16840704C2212yes—
14#16840704C2212yes—
15#16840703—21no—
16C4×C22⋊#6923—21no—
17C4×C22⋊#6923C412yescomplemented
18C2×(C2×#6923)⋊C4C412yescomplemented
19C23×C4×D61C2211yescharacteristic
20C22×#11758189C412yescomplemented
21#16839724—21no—
22#16839724—21no—
23#16839724—21no—
24#16839724—21no—
25C2×C22⋊#92418C411yescharacteristic, complemented
26C2×#14519689C2212yes—
27C2×C22⋊C8×C61C411yescharacteristic, complemented
28C23×#6923—22no—
29#14519856—44no—
30C2×C4⋊#6923—22no—
31C2×C4⋊#6923—22no—
32C2×C4⋊#6923—22no—
33C2×C4⋊#6923—44no—
34C2×C22⋊#6923—22no—
35C2×C22⋊#6923—22no—
36C2×C22⋊#6923—22no—
37C2×C22⋊#6923—22no—
38C2×C22⋊#6923—22no—
39C2×C22⋊#6923—44no—
40C2×C4×#6923—22no—
41(C2×#6923)⋊C4—22no—
42(C2×#6923)⋊C4—22no—
43(C2×#6923)⋊C4C2×C414yes—
44(C2×#6923)⋊C4C2×C414yescomplemented
45C24×D61D411yescharacteristic
46C23×Dic61Q811yescharacteristic
47C22×C4×D61—44no—
48C22×C4×D61C2×C411yescharacteristic
49C22×C4×D61C2×C411yescharacteristic
50C22×C4×D61C2×C411yescharacteristic
51C22×C4×D61C2×C411yescharacteristic
52C22×C4×D61C2×C411yescharacteristic
53C22×C4×D61D411yescharacteristic
54C22×C4×D61D411yescharacteristic
55C22×C4×D61D411yescharacteristic
56C22×C4×D61D411yescharacteristic
57C22×C4×D61D411yescharacteristic
58C22×C4×D61Q811yescharacteristic
59C22×C4×D61C2311yescharacteristic
60C2×#11758189—22no—
61C2×#11758189—22no—
62C2×#11758189—44no—
63C22×#92418C2×C412yescomplemented
64C22⋊#92418—21no—
65C22⋊#92418—21no—
66#14519689—22no—
67#14519689—22no—
68C23×C4×C61C2×C411yescharacteristic
69C22×C8×C61C2×C412yescomplemented
70C22⋊C8×C61—21no—
71C22⋊C8×C61—21no—
72C24×C61C4⋊C411yescharacteristic
73C23×D61—22no—
74C23×D61—22no—
75C23×D61—42no—
76C23×D61—42no—
77C23×D61C22⋊C411yescharacteristic
78C23×D61C22⋊C411yescharacteristic
79C23×D61C22⋊C411yescharacteristic
80C23×D61C22⋊C411yescharacteristic
81C23×D61C4⋊C411yescharacteristic
82C23×D61C2×D411yescharacteristic
83C22×#6923—24no—
84C22×#6923—24no—
85C22×#6923—44no—
86C22×#6923—44no—
87C22×#6923—44no—
88C22×C4×C61—42no—
89C22×C4×C61C4211yescharacteristic
90C22×C4×C61C4211yescharacteristic
91C22×C4×C61C22⋊C411yescharacteristic
92C22×C4×C61C22⋊C411yescharacteristic
93C22×C4×C61C4⋊C411yescharacteristic
94C22×C4×C61C22×C411yescharacteristic
95C22×Dic61—42no—
96C22×Dic61C4⋊C411yescharacteristic
97C22×Dic61C4⋊C411yescharacteristic
98C22×Dic61C4⋊C411yescharacteristic
99C22×Dic61C4⋊C411yescharacteristic
100C22×Dic61C4⋊C411yescharacteristic
101C22×Dic61C2×Q811yescharacteristic
102C2×C4×D61—24no—
103C2×C4×D61—24no—
104C2×C4×D61—24no—
105C2×C4×D61—42no—
106C2×C4×D61—42no—
107C2×C4×D61—42no—
108C2×C4×D61—42no—
109C2×C4×D61—42no—
110C2×C4×D61—42no—
111C2×C4×D61—42no—
112C2×C4×D61—42no—
113C2×C4×D61—42no—
114C2×C4×D61C4211yescharacteristic
115C2×C4×D61C4211yescharacteristic
116C2×C4×D61C22⋊C411yescharacteristic
117C2×C4×D61C22⋊C411yescharacteristic
118C2×C4×D61C22⋊C411yescharacteristic
119C2×C4×D61C22⋊C411yescharacteristic
120C2×C4×D61C22⋊C411yescharacteristic
121C2×C4×D61C22⋊C411yescharacteristic
122C2×C4×D61C4⋊C411yescharacteristic
123C2×C4×D61C4⋊C411yescharacteristic
124C2×C4×D61C4⋊C411yescharacteristic
125C2×C4×D61C4⋊C411yescharacteristic
126C2×C4×D61C22×C411yescharacteristic
127C2×C4×D61C22×C411yescharacteristic
128C2×C4×D61C2×D411yescharacteristic
129C2×C4×D61C2×D411yescharacteristic
130C22⋊#6923—44no—
131C22⋊#6923—44no—
132C22⋊#6923—44no—
133C22⋊#6923—42no—
134C22⋊#6923—44no—
135C22⋊#6923—42no—
136C4⋊#6923—44no—
137C4⋊#6923—44no—
138C4⋊#6923—44no—
139C4×#6923—44no—
140C2×C8×C61—22no—
141C2×C8×C61—42no—
142C2×#92418—22no—
143C2×#92418—42no—
144#11758189—44no—
145#11758189—44no—
146C23×C61—22no—
147C23×C61—22no—
148C23×C61—41no—
149C23×C61#9511yescharacteristic
150C23×C61#9511yescharacteristic
151C23×C61C2×C4⋊C411yescharacteristic
152C22×D61—22no—
153C22×D61—22no—
154C22×D61—21no—
155C22×D61—21no—
156C22×D61—22no—
157C22×D61—22no—
158C22×D61—22no—
159C22×D61—22no—
160C22×D61—22no—
161C22×D61—22no—
162C22×D61—21no—
163C22×D61—21no—
164C22×D61—41no—
165C22×D61—41no—
166C22×D61—41no—
167C22×D61—41no—
168C22×D61—41no—
169C22×D61—41no—
170C22×D61—41no—
171C22×D61—48no—
172C22×D61—48no—
173C22×D61#9511yescharacteristic
174C22×D61#9511yescharacteristic
175C22×D61C2×C22⋊C411yescharacteristic
176C22×D61C2×C22⋊C411yescharacteristic
177C22×D61AGL(1,ℤ/8)12yes—
178C22×D61#13712yes—
179C2×#6923—44no—
180C2×#6923—44no—
181C2×#6923—44no—
182C2×#6923—44no—
183C2×#6923—44no—
184C2×#6923—44no—
185C2×#6923—88no—
186C2×C4×C61—22no—
187C2×C4×C61—22no—
188C2×C4×C61—22no—
189C2×C4×C61—41no—
190C2×C4×C61—41no—
191C2×C4×C61—41no—
192C2×C4×C61#9511yescharacteristic
193C2×C4×C61#9511yescharacteristic
194C2×C4×C61C2×C4211yescharacteristic
195C2×C4×C61C2×C22⋊C411yescharacteristic
196C2×Dic61—22no—
197C2×Dic61—22no—
198C2×Dic61—22no—
199C2×Dic61—41no—
200C2×Dic61—41no—
201C2×Dic61—41no—
202C2×Dic61#9511yescharacteristic
203C2×Dic61#9511yescharacteristic
204C2×Dic61C2×C4⋊C411yescharacteristic
205C2×Dic61C2×C4⋊C411yescharacteristic
206C4×D61—22no—
207C4×D61—22no—
208C4×D61—22no—
209C4×D61—22no—
210C4×D61—22no—
211C4×D61—22no—
212C4×D61—22no—
213C4×D61—22no—
214C4×D61—22no—
215C4×D61—41no—
216C4×D61—41no—
217C4×D61—41no—
218C4×D61—41no—
219C4×D61—41no—
220C4×D61—41no—
221C4×D61#9914yes—
222C8×C61—42no—
223#92418—42no—
224#7983—611nomaximal, Sylow
225C22×C61—21no—
226C22×C61—21no—
227C22×C61—21no—
228C22×C61—21no—
229C22×C61—21no—
230C22×C61—21no—
231C22×C61—21no—
232C22×C61—44no—
233C22×C61H(3,ℤ/4)12yes—
234C22×C61C2×#9511yescharacteristic
235C22×C61#42812yes—
236C2×D61—24no—
237C2×D61—24no—
238C2×D61—21no—
239C2×D61—21no—
240C2×D61—21no—
241C2×D61—21no—
242C2×D61—21no—
243C2×D61—21no—
244C2×D61—21no—
245C2×D61—21no—
246C2×D61—21no—
247C2×D61—42no—
248C2×D61—42no—
249C2×D61—44no—
250C2×D61—44no—
251C2×D61—44no—
252C2×D61—42no—
253C2×D61—42no—
254C2×D61#34212yes—
255C2×D61#41712yes—
256C2×D61#41811yescharacteristic
257C2×D61#41911yescharacteristic
258#6923—84no—
259#6923—84no—
260C4×C61—21no—
261C4×C61—21no—
262C4×C61—21no—
263C4×C61C2×#9912yes—
264Dic61—21no—
265Dic61—21no—
266Dic61—21no—
267Dic61#34212yes—
268C2×#407—611no—
269#2280—611no—
270C2×#380—611no—
271#1289—614no—
272C2×C61—22no—
273C2×C61—22no—
274C2×C61—41no—
275C2×C61C2×H(3,ℤ/4)11yescharacteristic
276C2×C61#173611yescharacteristic
277C2×C61C2×#34211yescharacteristic
278D61—21no—
279D61—22no—
280D61—22no—
281D61—21no—
282D61—41no—
283C24×C4—611no—
284C22×M16—612no—
285C2×#117—1221no—
286C22×C4⋊C4—1221no—
287C22×C22⋊C4—1221no—
288#407—1221no—
289#407—1221no—
290#407—1221no—
291#407—1221no—
292C2×C22⋊C8—611no—
293C2×C22⋊C8—612no—
294C2×C22⋊C8#692311yescharacteristic, complemented
295#381—612no—
296#380—612no—
297#380—612no—
298#380—612no—
299#380—1221no—
300#380—1221no—
301#380—1221no—
302#379—1221no—
303C4×C22⋊C4—612no—
304C4×C22⋊C4—1221no—
305C2×#95—612no—
306C61#798311yescharacteristic, complemented, Sylow
307C25—611no—
308C23×C4—611no—
309C23×C4—611no—
310C23×C4—611no—
311C23×C4—611no—
312C23×C4—611no—
313C23×C4—611no—
314C23×C4—611no—
315C23×C4—611no—
316C23×C4—611no—
317C23×C4—611no—
318C23×C4—611no—
319C23×C4—611no—
320C23×C4—611no—
321C23×C4—1222no—
322C23×C4—2444no—
323C23×C4C2×#692311yescharacteristic
324C2×M16—1222no—
325C2×M16—1222no—
326C2×M16—2444no—
327C22×C8—612no—
328C22×C8C2×#692312yescomplemented
329#117—2444no—
330C2×C4⋊C4—1222no—
331C2×C4⋊C4—1222no—
332C2×C4⋊C4—1222no—
333C2×C4⋊C4—2444no—
334C2×C22⋊C4—1222no—
335C2×C22⋊C4—1222no—
336C2×C22⋊C4—1222no—
337C2×C22⋊C4—1222no—
338C2×C22⋊C4—1222no—
339C2×C22⋊C4—2444no—
340C2×C42—1222no—
341C22⋊C8—21no—
342C22⋊C8—21no—
343C22⋊C8—1222no—
344C22⋊C8—1222no—
345C22⋊C8—1221no—
346C22⋊C8—1221no—
347#95—614no—
348#95—614no—
349#95—1222no—
350#95—1222no—
351C24—611no—
352C24—611no—
353C24—611no—
354C24—611no—
355C24—611no—
356C24—611no—
357C24—1222no—
358C24—1222no—
359C24—2442no—
360C24—2442no—
361C24C4⋊#692311yescharacteristic
362C22×C4—42no—
363C22×C4—611no—
364C22×C4—611no—
365C22×C4—611no—
366C22×C4—611no—
367C22×C4—611no—
368C22×C4—611no—
369C22×C4—611no—
370C22×C4—611no—
371C22×C4—611no—
372C22×C4—611no—
373C22×C4—611no—
374C22×C4—611no—
375C22×C4—611no—
376C22×C4—611no—
377C22×C4—611no—
378C22×C4—611no—
379C22×C4—611no—
380C22×C4—611no—
381C22×C4—611no—
382C22×C4—611no—
383C22×C4—611no—
384C22×C4—611no—
385C22×C4—1224no—
386C22×C4—1224no—
387C22×C4—1224no—
388C22×C4—1224no—
389C22×C4—1224no—
390C22×C4—2442no—
391C22×C4—2442no—
392C22×C4—2442no—
393C22×C4—2442no—
394C22×C4—2442no—
395C22×C4—2442no—
396C22×C4—2442no—
397C22×C4—2442no—
398C22×C4—2442no—
399C22×C4—2442no—
400C22×C4—2444no—
401C22×C4—2444no—
402C22×C4—2444no—
403C22×C4C4×#692311yescharacteristic
404C22×C4C4×#692311yescharacteristic
405C22×C4C4⋊#692311yescharacteristic
406C22×C4C22⋊#692311yescharacteristic
407C22×C4C22⋊#692311yescharacteristic
408C22×C4C22×#692311yescharacteristic
409M16—2444no—
410M16—2444no—
411C2×C8—22no—
412C2×C8—42no—
413C2×C8—1222no—
414C2×C8—2442no—
415C4⋊C4—2444no—
416C4⋊C4—2444no—
417C4⋊C4—2444no—
418C22⋊C4—2444no—
419C22⋊C4—2442no—
420C22⋊C4—2442no—
421C22⋊C4—2444no—
422C22⋊C4—2444no—
423C22⋊C4—2444no—
424C42—2444no—
425C23—22no—
426C23—22no—
427C23—41no—
428C23—611no—
429C23—611no—
430C23—611no—
431C23—612no—
432C23—612no—
433C23—611no—
434C23—1222no—
435C23—1221no—
436C23—1221no—
437C23—1221no—
438C23—1222no—
439C23—1222no—
440C23—1222no—
441C23—1222no—
442C23—1221no—
443C23—1222no—
444C23—1222no—
445C23—1222no—
446C23—2441no—
447C23—2441no—
448C23—2441no—
449C23—2441no—
450C23—2441no—
451C23—2441no—
452C23—2441no—
453C23—2448no—
454C23—2448no—
455C23(C2×#6923)⋊C411yescharacteristic
456C23(C2×#6923)⋊C411yescharacteristic
457C23C2×C4⋊#692311yescharacteristic
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—611no—
465C2×C4—614no—
466C2×C4—611no—
467C2×C4—611no—
468C2×C4—611no—
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—1222no—
481C2×C4—4888no—
482C2×C4—2441no—
483C2×C4—2441no—
484C2×C4—2441no—
485C2×C4—2441no—
486C2×C4—2441no—
487C2×C4—2441no—
488C2×C4—2441no—
489C2×C4—2441no—
490C2×C4—2441no—
491C2×C4—2444no—
492C2×C4—2444no—
493C2×C4—2444no—
494C2×C4—2444no—
495C2×C4—2444no—
496C2×C4—2444no—
497C2×C4(C2×#6923)⋊C411yescharacteristic
498C2×C4(C2×#6923)⋊C411yescharacteristic
499C2×C4C2×C4×#692311yescharacteristic
500C2×C4C2×C22⋊#692311yescharacteristic
501C8—42no—
502C8—2442no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—44no—
511C22—611no—
512C22—612no—
513C22—611no—
514C22—612no—
515C22—1224no—
516C22—1224no—
517C22—1221no—
518C22—1221no—
519C22—1221no—
520C22—1221no—
521C22—1221no—
522C22—1221no—
523C22—1221no—
524C22—1221no—
525C22—1221no—
526C22—2442no—
527C22—2442no—
528C22—2444no—
529C22—2444no—
530C22—2444no—
531C22—2442no—
532C22—2442no—
533C22#1684063012yes—
534C22C2×(C2×#6923)⋊C411yescharacteristic
535C22#1684077312yes—
536C4—21no—
537C4—21no—
538C4—21no—
539C4—612no—
540C4—1221no—
541C4—1221no—
542C4—1221no—
543C4—4884no—
544C4—4884no—
545C4D61⋊#9912yes—
546C2—22no—
547C2—22no—
548C2—41no—
549C2—1221no—
550C2—1222no—
551C2—1221no—
552C2—1222no—
553C2—2441no—
554C2C2×#1684063011yescharacteristic
555C2#2146150711yescharacteristic
556C2#2146151611yescharacteristic
subgroupG/H
centerC22C2×(C2×#6923)⋊C4
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC2×C22⋊C8×C61C4
socleC22×C61C2×#95
prime radicalC24×D61D4
cosocleC22×C4×D61C23
hypercenterC2×C22⋊C8#6923
hypocenterC61#7983
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
3. #21460682C2semidirect
8. #16840705C4semidirect
12. #16840704C4semidirect
17. C4×C22⋊#6923C4semidirect
18. C2×(C2×#6923)⋊C4C4semidirect
20. C22×#11758189C4semidirect
25. C2×C22⋊#92418C4semidirect
27. C2×C22⋊C8×C61C4semidirect
44. (C2×#6923)⋊C4C2×C4semidirect
63. C22×#92418C2×C4semidirect
69. C22×C8×C61C2×C4semidirect
294. C2×C22⋊C8#6923semidirect
306. C61#7983semidirect
328. C22×C8C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214622632
C2×#168407042
#214606822
C2×#168397242
#798361