Finite Group Databasebeta

← #30602703

Subgroups — #30602703

Order 15616.

906 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840640C211yesmaximal, characteristic
2C2×#16840640C211yesmaximal, characteristic
3C2×#16840639C212yesmaximal
4C2×#16840639C212yesmaximal
5#21448171C211yesmaximal, characteristic
6C22×C22⋊#6923C2212yes—
7C22×C22⋊#6923C2212yes—
8#16840640—21no—
9#16840640—21no—
10#16840640—21no—
11#16840640—21no—
12#16840639—24no—
13#16840639C418yescomplemented
14C22×#11758198C2211yescharacteristic
15C2×C22⋊C4×D61C2211yescharacteristic
16C2×C22⋊C4×D61C2211yescharacteristic
17C22⋊C4×Dic61C411yescharacteristic, complemented
18C22⋊C4×Dic61C411yescharacteristic, complemented
19C4×#11758198—21no—
20C4×#11758198—21no—
21C4×C22⋊Dic61C411yescharacteristic, complemented
22#16839609—21no—
23#16839609—21no—
24C4×C22⋊C4×C61C411yescharacteristic, complemented
25C23×#6923—22no—
26C23×#6923—22no—
27C2×C22⋊#6923—22no—
28C2×C22⋊#6923—22no—
29C2×C22⋊#6923—22no—
30C2×C22⋊#6923—22no—
31C2×C22⋊#6923—22no—
32C2×C22⋊#6923—22no—
33C2×C22⋊#6923—22no—
34C2×C22⋊#6923—22no—
35C2×C22⋊#6923—22no—
36C2×C22⋊#6923—22no—
37C2×C22⋊#6923C2×C414yes—
38C2×C22⋊#6923C2×C414yes—
39C24×D61C2311yescharacteristic
40C23×Dic61C2×C411yescharacteristic
41C22×C4×D61—21no—
42C22×C4×D61—21no—
43C2×C22⋊Dic61C2×C411yescharacteristic
44C2×C22⋊Dic61C2×C411yescharacteristic
45C2×#11758198—21no—
46C2×#11758198—21no—
47C2×#11758198—22no—
48C2×#11758198—22no—
49C2×#11758198D411yescharacteristic
50C2×#11758198D411yescharacteristic
51C2×#11758198D411yescharacteristic
52C2×#11758198D411yescharacteristic
53C22⋊C4×D61—22no—
54C22⋊C4×D61—21no—
55C22⋊C4×D61—21no—
56C22⋊C4×D61C2×C414yes—
57C22⋊C4×D61D412yes—
58C22⋊C4×D61Q812yes—
59C2×C4×Dic61—21no—
60C2×C4×Dic61—21no—
61C2×C4×Dic61—21no—
62#14519684—21no—
63#14519684—21no—
64#14519684—21no—
65C23×C4×C61C2×C411yescharacteristic
66C2×C22⋊C4×C61C2×C411yescharacteristic
67C2×C22⋊C4×C61C2×C411yescharacteristic
68C2×C42×C61—21no—
69#95×C61—21no—
70C24×C61C22×C411yescharacteristic
71C23×D61—81no—
72C23×D61—81no—
73C23×D61C22×C412yes—
74C23×D61C2×D411yescharacteristic
75C23×D61C2×D411yescharacteristic
76C23×D61C2×D411yescharacteristic
77C23×D61C2×Q811yescharacteristic
78C23×D61#4112yes—
79C23×D61#4112yes—
80C23×D61#4111yescharacteristic
81C23×D61#4111yescharacteristic
82C23×D61#4112yes—
83C22×#6923—24no—
84C22×#6923—24no—
85C22×#6923—42no—
86C22×#6923—42no—
87C22×#6923—42no—
88C22×#6923—42no—
89C22×#6923—82no—
90C22×#6923—82no—
91C22×#6923—82no—
92C22×#6923—82no—
93C22×C4×C61—21no—
94C22×C4×C61—21no—
95C22×C4×C61—21no—
96C22×C4×C61—21no—
97C22×C4×C61—81no—
98C22×C4×C61C22⋊C411yescharacteristic
99C22×C4×C61C22⋊C411yescharacteristic
100C22×Dic61—21no—
101C22×Dic61—21no—
102C22×Dic61—21no—
103C22×Dic61—21no—
104C22×Dic61—81no—
105C22×Dic61C22⋊C411yescharacteristic
106C22×Dic61C22⋊C411yescharacteristic
107C2×C4×D61—24no—
108C2×C4×D61—22no—
109C2×C4×D61—22no—
110C2×C4×D61—81no—
111C2×C4×D61—81no—
112C2×C4×D61—81no—
113C2×C4×D61—81no—
114C22⋊#6923—24no—
115C22⋊#6923—24no—
116C22⋊#6923—24no—
117C22⋊#6923—24no—
118C22⋊#6923—42no—
119C22⋊#6923—42no—
120C22⋊#6923—42no—
121C22⋊#6923—42no—
122C22⋊C4×C61—21no—
123C22⋊C4×C61—21no—
124C22⋊C4×C61C4212yes—
125C22⋊C4×C61C4⋊C412yes—
126C42×C61—81no—
127C22⋊Dic61—21no—
128C22⋊Dic61—21no—
129C22⋊Dic61C4212yes—
130C22⋊Dic61C4⋊C412yes—
131#11758198—24no—
132#11758198—22no—
133#11758198—22no—
134#11758198—22no—
135#11758198—22no—
136#11758198—22no—
137#11758198—22no—
138C4×Dic61—81no—
139C4×Dic61—81no—
140C4×Dic61—81no—
141C23×C61—41no—
142C23×C61—41no—
143C23×C61C2×C4211yescharacteristic
144C23×C61C2×C22⋊C411yescharacteristic
145C23×C61C2×C4⋊C411yescharacteristic
146C23×C61#11711yescharacteristic
147C23×C61#11711yescharacteristic
148C23×C61#11711yescharacteristic
149C23×C61#11711yescharacteristic
150C22×D61—41no—
151C22×D61—41no—
152C22×D61—41no—
153C22×D61—41no—
154C22×D61—42no—
155C22×D61—42no—
156C22×D61—42no—
157C22×D61—42no—
158C22×D61—82no—
159C22×D61—81no—
160C22×D61—81no—
161C22×D61—82no—
162C22×D61—81no—
163C22×D61—81no—
164C22×D61#11712yes—
165C22×D61#11712yes—
166C22×D61C4×D412yes—
167C22×D61C4×D412yes—
168C22×D61C4×D412yes—
169C22×D61C4×Q812yes—
170C22×D61#12111yescharacteristic
171C22×D61#12111yescharacteristic
172C22×D61C22⋊Q811yescharacteristic
173C22×D61C22⋊Q811yescharacteristic
174C22×D61#12312yes—
175C22×D61#12312yes—
176C22×D61#12412yes—
177C22×D61#12512yes—
178C22×D61#12612yes—
179C22×D61#12612yes—
180C2×#6923—44no—
181C2×#6923—44no—
182C2×#6923—82no—
183C2×#6923—82no—
184C2×#6923—82no—
185C2×#6923—82no—
186C2×#6923—84no—
187C2×#6923—84no—
188C2×#6923—84no—
189C2×#6923—84no—
190C2×C4×C61—22no—
191C2×C4×C61—22no—
192C2×C4×C61—21no—
193C2×C4×C61—21no—
194C2×C4×C61—41no—
195C2×C4×C61—41no—
196C2×C4×C61—41no—
197C2×C4×C61—41no—
198C2×C4×C61—41no—
199C2×C4×C61—41no—
200C2×C4×C61—81no—
201C2×C4×C61—81no—
202C2×Dic61—22no—
203C2×Dic61—22no—
204C2×Dic61—21no—
205C2×Dic61—21no—
206C2×Dic61—41no—
207C2×Dic61—41no—
208C2×Dic61—41no—
209C2×Dic61—41no—
210C2×Dic61—41no—
211C2×Dic61—41no—
212C2×Dic61—81no—
213C2×Dic61—81no—
214C4×D61—84no—
215C4×D61—82no—
216C4×D61—82no—
217#10829—611nomaximal, Sylow
218C22×C61—21no—
219C22×C61—21no—
220C22×C61—21no—
221C22×C61—21no—
222C22×C61—21no—
223C22×C61—21no—
224C22×C61—41no—
225C22×C61—41no—
226C22×C61—41no—
227C22×C61—41no—
228C22×C61#37611yescharacteristic
229C22×C61C4×C22⋊C411yescharacteristic
230C22×C61C4×C4⋊C411yescharacteristic
231C22×C61#38011yescharacteristic
232C22×C61#38111yescharacteristic
233C22×C61#38211yescharacteristic
234C22×C61#38311yescharacteristic
235C2×D61—22no—
236C2×D61—22no—
237C2×D61—22no—
238C2×D61—22no—
239C2×D61—42no—
240C2×D61—41no—
241C2×D61—41no—
242C2×D61—42no—
243C2×D61—42no—
244C2×D61—42no—
245C2×D61—42no—
246C2×D61—42no—
247C2×D61—42no—
248C2×D61—42no—
249C2×D61—41no—
250C2×D61—41no—
251C2×D61—42no—
252C2×D61—42no—
253C2×D61#38712yes—
254C2×D61#38712yes—
255C2×D61#38812yes—
256C2×D61#38812yes—
257#6923—84no—
258#6923—84no—
259C4×C61—42no—
260C4×C61—42no—
261C4×C61—41no—
262C4×C61—41no—
263Dic61—42no—
264Dic61—42no—
265Dic61—41no—
266Dic61—41no—
267#2273—611no—
268C2×#342—612no—
269C2×#342—612no—
270C2×#342—611no—
271C2×#342—611no—
272C2×C61—21no—
273C2×C61—21no—
274C2×C61—21no—
275C2×C61—21no—
276C2×C61—21no—
277C2×C61—21no—
278C2×C61#143411yescharacteristic
279C2×C61#182811yescharacteristic
280C2×C61#182811yescharacteristic
281D61—22no—
282D61—22no—
283D61—22no—
284D61—22no—
285C22×C22⋊C4—611no—
286C22×C22⋊C4—611no—
287C22×C22⋊C4—611no—
288C22×C22⋊C4—612no—
289C22×C22⋊C4—612no—
290C4×C22⋊C4—611no—
291C4×C22⋊C4—611no—
292C4×C22⋊C4—611no—
293C4×C22⋊C4—1221no—
294C4×C22⋊C4—1221no—
295C4×C22⋊C4—1221no—
296C4×C22⋊C4—1221no—
297C4×C22⋊C4#692311yescharacteristic, complemented
298#342—618no—
299#342—1224no—
300#342—1221no—
301#342—1221no—
302#342—1221no—
303#342—1221no—
304C61#1082911yescharacteristic, complemented, Sylow
305C25—611no—
306C23×C4—611no—
307C23×C4—1221no—
308C23×C4—1221no—
309C23×C4—1222no—
310C23×C4—1222no—
311C23×C4C2×#692311yescharacteristic
312C2×C22⋊C4—611no—
313C2×C22⋊C4—611no—
314C2×C22⋊C4—614no—
315C2×C22⋊C4—612no—
316C2×C22⋊C4—612no—
317C2×C22⋊C4—611no—
318C2×C22⋊C4—611no—
319C2×C22⋊C4—611no—
320C2×C22⋊C4—611no—
321C2×C22⋊C4—614no—
322C2×C22⋊C4—614no—
323C2×C22⋊C4—1221no—
324C2×C22⋊C4—1221no—
325C2×C22⋊C4—1222no—
326C2×C22⋊C4—1221no—
327C2×C22⋊C4—1221no—
328C2×C22⋊C4—1222no—
329C2×C22⋊C4—1222no—
330C2×C22⋊C4—1222no—
331C2×C22⋊C4—1222no—
332C2×C22⋊C4—1222no—
333C2×C22⋊C4—1222no—
334C2×C22⋊C4—1222no—
335C2×C22⋊C4—1222no—
336C2×C22⋊C4—1222no—
337C2×C22⋊C4—1222no—
338C2×C22⋊C4—1222no—
339C2×C22⋊C4—1222no—
340C2×C22⋊C4C2×#692311yescharacteristic
341C2×C22⋊C4C2×#692311yescharacteristic
342C2×C42—21no—
343C2×C42—1221no—
344C2×C42—1221no—
345C2×C42—1221no—
346#95—21no—
347#95—1221no—
348#95—1221no—
349#95—1221no—
350C24—612no—
351C24—611no—
352C24—611no—
353C24—611no—
354C24—611no—
355C24—612no—
356C24—611no—
357C24—611no—
358C24—612no—
359C24—612no—
360C24—4881no—
361C24—4881no—
362C24C22×#692311yescharacteristic
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—81no—
368C22×C4—611no—
369C22×C4—611no—
370C22×C4—1222no—
371C22×C4—1222no—
372C22×C4—1224no—
373C22×C4—1221no—
374C22×C4—1221no—
375C22×C4—1221no—
376C22×C4—1221no—
377C22×C4—1224no—
378C22×C4—1224no—
379C22×C4—4881no—
380C22×C4—4881no—
381C22×C4—4881no—
382C22×C4—4881no—
383C22×C4—4882no—
384C22×C4—4882no—
385C22×C4—4882no—
386C22×C4—4882no—
387C22×C4—4881no—
388C22×C4—2442no—
389C22×C4—2442no—
390C22×C4—2442no—
391C22×C4—2442no—
392C22×C4C22⋊#692311yescharacteristic
393C22×C4C22⋊#692311yescharacteristic
394C22⋊C4—21no—
395C22⋊C4—21no—
396C22⋊C4—612no—
397C22⋊C4—612no—
398C22⋊C4—1222no—
399C22⋊C4—1222no—
400C22⋊C4—1222no—
401C22⋊C4—1222no—
402C22⋊C4—1222no—
403C22⋊C4—1222no—
404C22⋊C4—1224no—
405C22⋊C4—1221no—
406C22⋊C4—1221no—
407C22⋊C4—1224no—
408C22⋊C4—1224no—
409C22⋊C4—1224no—
410C22⋊C4—1224no—
411C22⋊C4—2442no—
412C22⋊C4—2442no—
413C22⋊C4—2442no—
414C22⋊C4—2442no—
415C22⋊C4C4×#692312yes—
416C22⋊C4C4⋊#692312yes—
417C42—81no—
418C42—4881no—
419C42—4881no—
420C42—4881no—
421C23—41no—
422C23—41no—
423C23—612no—
424C23—612no—
425C23—611no—
426C23—611no—
427C23—611no—
428C23—611no—
429C23—612no—
430C23—612no—
431C23—612no—
432C23—612no—
433C23—612no—
434C23—612no—
435C23—612no—
436C23—612no—
437C23—612no—
438C23—612no—
439C23—4882no—
440C23—4881no—
441C23—4881no—
442C23—4881no—
443C23—4881no—
444C23—4882no—
445C23—2441no—
446C23—2441no—
447C23—2442no—
448C23—2442no—
449C23—2441no—
450C23—2441no—
451C23—2442no—
452C23—2442no—
453C23C2×C4×#692311yescharacteristic
454C23C2×C22⋊#692311yescharacteristic
455C23C2×C4⋊#692311yescharacteristic
456C23#1451985611yescharacteristic
457C23#1451985611yescharacteristic
458C23#1451985611yescharacteristic
459C23#1451985611yescharacteristic
460C2×C4—22no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—22no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—81no—
471C2×C4—81no—
472C2×C4—1222no—
473C2×C4—1221no—
474C2×C4—1221no—
475C2×C4—1222no—
476C2×C4—4882no—
477C2×C4—4882no—
478C2×C4—4884no—
479C2×C4—4882no—
480C2×C4—4882no—
481C2×C4—4882no—
482C2×C4—4882no—
483C2×C4—4884no—
484C2×C4—4884no—
485C2×C4—4884no—
486C2×C4—4884no—
487C2×C4—4881no—
488C2×C4—4881no—
489C2×C4—2444no—
490C2×C4—2444no—
491C2×C4—2441no—
492C2×C4—2441no—
493C2×C4—2441no—
494C2×C4—2441no—
495C2×C4—2441no—
496C2×C4—2441no—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—41no—
504C22—41no—
505C22—41no—
506C22—41no—
507C22—612no—
508C22—612no—
509C22—612no—
510C22—612no—
511C22—1222no—
512C22—1222no—
513C22—1222no—
514C22—1222no—
515C22—2441no—
516C22—2441no—
517C22—2442no—
518C22—2442no—
519C22—2442no—
520C22—2442no—
521C22—2442no—
522C22—2441no—
523C22—2441no—
524C22—2442no—
525C22—2442no—
526C22—2442no—
527C22—2442no—
528C22—2442no—
529C22#1684069811yescharacteristic
530C22C4×C22⋊#692311yescharacteristic
531C22C4×C4⋊#692311yescharacteristic
532C22#1684070411yescharacteristic
533C22#1684070511yescharacteristic
534C22#1684070611yescharacteristic
535C22#1684070711yescharacteristic
536C4—42no—
537C4—42no—
538C4—41no—
539C4—41no—
540C4—4884no—
541C4—4884no—
542C4—2442no—
543C4—2442no—
544C4—2441no—
545C4—2441no—
546C2—21no—
547C2—21no—
548C2—21no—
549C2—21no—
550C2—21no—
551C2—21no—
552C2—1222no—
553C2—1222no—
554C2—1222no—
555C2—1222no—
556C2#2146099511yescharacteristic
557C2#2146173011yescharacteristic
558C2#2146173111yescharacteristic
subgroupG/H
centerC22#16840705
commutatorC23×C61C2×C42
FrattiniC24C22×#6923
FittingC4×C22⋊C4×C61C4
socleC22×C61#381
prime radical, cosocleC24×D61C23
hypercenterC4×C22⋊C4#6923
hypocenterC61#10829
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
13. #16840639C4semidirect
17. C22⋊C4×Dic61C4semidirect
18. C22⋊C4×Dic61C4semidirect
21. C4×C22⋊Dic61C4semidirect
24. C4×C22⋊C4×C61C4semidirect
297. C4×C22⋊C4#6923semidirect
304. C61#10829semidirect

Maximal subgroups

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

subgroupindex
C2×#168406402
C2×#168406392
#214481712
#1082961