Finite Group Databasebeta

← #30603295

Subgroups — #30603295

Order 15616.

1006 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519847C211yesmaximal, characteristic, complemented
2C2×#16840733C212yesmaximal
3C2×#16840638C212yesmaximal, complemented
4C2×#16840638C211yesmaximal, characteristic, complemented
5C2×C22⋊C8×D61C211yesmaximal, characteristic
6C22×#11758213C2212yes—
7C22×#11758213C2212yes—
8C2×#14519847—22no—
9C2×#14519847—24no—
10#16840733—24no—
11#16840733—24no—
12C2×#14519834—22no—
13C2×C22⋊#92420—22no—
14#16840638—22no—
15#16840638—24no—
16C23×C4×D61C2211yescharacteristic
17C22×C8×D61C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19C2×C22⋊#92418C411yescharacteristic
20C2×#14519689C411yescharacteristic
21C2×#14519689C411yescharacteristic
22C22⋊C8×D61—22no—
23C22⋊C8×D61—22no—
24C2×C22⋊C8×C61C411yescharacteristic
25C2×#11758213—22no—
26C2×#11758213—22no—
27C2×#11758213—22no—
28C2×#11758213—22no—
29C2×#11758213—22no—
30C2×#11758213—22no—
31C2×#11758213—22no—
32C2×#11758213—22no—
33C2×#11758213—22no—
34C2×#11758213—22no—
35C2×#11758213D414yes—
36C2×#11758213D414yes—
37C22×#92420—22no—
38C22×#92420—22no—
39#14519847—28no—
40#14519834—28no—
41C22⋊#92420—28no—
42C24×D61Q811yescharacteristic
43C23×Dic61D411yescharacteristic
44C22×C4×D61—22no—
45C22×C4×D61—22no—
46C22×C4×D61—21no—
47C22×C4×D61—21no—
48C22×C4×D61—21no—
49C22×C4×D61—21no—
50C22×C4×D61—22no—
51C22×C4×D61—22no—
52C22×C4×D61C2×C411yescharacteristic
53C22×C4×D61D411yescharacteristic
54C22×C4×D61Q811yescharacteristic
55C22×C4×D61C2311yescharacteristic
56C22×#92418C2×C411yescharacteristic
57C22×#92418C2×C411yescharacteristic
58C2×C8×D61—22no—
59C2×C8×D61—22no—
60C2×C8×D61—21no—
61C2×C8×D61—21no—
62C2×C8×D61—22no—
63C2×C8×D61—22no—
64C2×C8×D61D412yes—
65C2×C8×D61D412yes—
66C22⋊#92418—22no—
67#14519689—22no—
68#14519689—22no—
69C23×C4×C61C2×C411yescharacteristic
70C22×C8×C61C2×C411yescharacteristic
71C22×C8×C61C2×C411yescharacteristic
72C22⋊C8×C61—22no—
73C24×C61C4⋊C411yescharacteristic
74C23×D61—22no—
75C23×D61—22no—
76C23×D61—21no—
77C23×D61—21no—
78C23×D61—22no—
79C23×D61—22no—
80C23×D61—42no—
81C23×D61C4⋊C411yescharacteristic
82C23×D61C2×Q811yescharacteristic
83C22×C4×C61—21no—
84C22×C4×C61—21no—
85C22×C4×C61—22no—
86C22×C4×C61—22no—
87C22×C4×C61C4⋊C411yescharacteristic
88C22×C4×C61C22×C411yescharacteristic
89C22×Dic61—22no—
90C22×Dic61—21no—
91C22×Dic61—21no—
92C22×Dic61—22no—
93C22×Dic61C4⋊C411yescharacteristic
94C22×Dic61C2×D411yescharacteristic
95C2×C4×D61—22no—
96C2×C4×D61—21no—
97C2×C4×D61—21no—
98C2×C4×D61—22no—
99C2×C4×D61—21no—
100C2×C4×D61—21no—
101C2×C4×D61—22no—
102C2×C4×D61—22no—
103C2×C4×D61—22no—
104C2×C4×D61—21no—
105C2×C4×D61—21no—
106C2×C4×D61—22no—
107C2×C4×D61—41no—
108C2×C4×D61—42no—
109C2×C4×D61—42no—
110C2×C4×D61—42no—
111C2×C4×D61—41no—
112C2×C4×D61—42no—
113C2×C4×D61—42no—
114C2×C4×D61—41no—
115C2×C4×D61—42no—
116C2×C4×D61—41no—
117C2×C4×D61C2×D412yes—
118C2×C4×D61C2×D411yescharacteristic
119C2×C4×D61C2×D411yescharacteristic
120C2×C4×D61C2×D412yes—
121C2×C4×D61#4111yescharacteristic
122C2×C4×D61#4112yes—
123C2×C4×D61#4112yes—
124C2×C4×D61#4111yescharacteristic
125C2×#92420—24no—
126C2×#92420—24no—
127C2×#92420—42no—
128C2×#92420—42no—
129C2×#92420—42no—
130C2×#92420—42no—
131#11758213—24no—
132#11758213—24no—
133#11758213—24no—
134#11758213—24no—
135#11758213—42no—
136#11758213—42no—
137#11758213—42no—
138#11758213—42no—
139C2×C8×C61—22no—
140C2×C8×C61—21no—
141C2×C8×C61—22no—
142C2×C8×C61C22⋊C412yes—
143C2×#92418—22no—
144C2×#92418—21no—
145C2×#92418—22no—
146C2×#92418C22⋊C412yes—
147C8×D61—22no—
148C8×D61—24no—
149C8×D61—22no—
150C8×D61—42no—
151C8×D61—41no—
152C8×D61—41no—
153C23×C61—21no—
154C23×C61—22no—
155C23×C61—21no—
156C23×C61—22no—
157C23×C61#10812yescomplemented
158C23×C61C2×C4⋊C411yescharacteristic
159C22×D61—21no—
160C22×D61—21no—
161C22×D61—22no—
162C22×D61—24no—
163C22×D61—24no—
164C22×D61—21no—
165C22×D61—22no—
166C22×D61—21no—
167C22×D61—22no—
168C22×D61—44no—
169C22×D61—44no—
170C22×D61—44no—
171C22×D61—44no—
172C22×D61—42no—
173C22×D61—42no—
174C22×D61—41no—
175C22×D61—42no—
176C22×D61—41no—
177C22×D61#10812yescomplemented
178C22×D61C22⋊Q812yes—
179C22×D61C22⋊Q811yescharacteristic
180C22×D61C22⋊Q811yescharacteristic
181C22×D61C22⋊Q812yes—
182C2×C4×C61—21no—
183C2×C4×C61—22no—
184C2×C4×C61—41no—
185C2×C4×C61—42no—
186C2×C4×C61—41no—
187C2×C4×C61C2×C22⋊C411yescharacteristic
188C2×C4×C61#11711yescharacteristic
189C2×C4×C61C4×D412yes—
190C2×C4×C61C4×D412yes—
191C2×Dic61—21no—
192C2×Dic61—22no—
193C2×Dic61—41no—
194C2×Dic61—42no—
195C2×Dic61—41no—
196C2×Dic61#12012yes—
197C2×Dic61#12111yescharacteristic
198C2×Dic61#12111yescharacteristic
199C2×Dic61#12312yes—
200C4×D61—41no—
201C4×D61—42no—
202C4×D61—41no—
203C4×D61—41no—
204C4×D61—42no—
205C4×D61—41no—
206C4×D61—41no—
207C4×D61—42no—
208C4×D61—41no—
209C4×D61#12011yescharacteristic
210C4×D61#12112yes—
211C4×D61#12112yes—
212C4×D61#12112yes—
213C4×D61#12312yes—
214C4×D61#12311yescharacteristic
215C4×D61#12412yes—
216C4×D61#12411yescharacteristic
217C4×D61#12612yes—
218C4×D61#12711yescharacteristic
219#92420—44no—
220#92420—44no—
221C8×C61—22no—
222C8×C61—41no—
223#92418—22no—
224#92418—41no—
225#11097—611nomaximal, Sylow
226C22×C61—22no—
227C22×C61—24no—
228C22×C61—41no—
229C22×C61—42no—
230C22×C61—41no—
231C22×C61#38011yescharacteristic
232C22×C61#38512yes—
233C22×C61C2×#10811yescharacteristic
234C22×C61C2×#10811yescharacteristic
235C22×C61#43012yes—
236C2×D61—21no—
237C2×D61—21no—
238C2×D61—21no—
239C2×D61—21no—
240C2×D61—22no—
241C2×D61—22no—
242C2×D61—22no—
243C2×D61—22no—
244C2×D61—22no—
245C2×D61—24no—
246C2×D61—44no—
247C2×D61—48no—
248C2×D61—44no—
249C2×D61—41no—
250C2×D61—42no—
251C2×D61—41no—
252C2×D61#39311yescharacteristic
253C2×D61#39612yes—
254C2×D61#39911yescharacteristic
255C4×C61—41no—
256C4×C61#38611yescharacteristic
257C4×C61#38812yes—
258C4×C61#39011yescharacteristic
259Dic61—41no—
260Dic61#39211yescharacteristic
261Dic61#39412yes—
262Dic61#39711yescharacteristic
263C22×#108—611no—
264C2×#407—612no—
265C22×C22⋊C8—611no—
266C2×#341—611no—
267C2×#341—612no—
268C2×C61—42no—
269C2×C61#143911yescharacteristic
270C2×C61#181011yescharacteristic
271C2×C61#181111yescharacteristic
272C2×C61#185512yes—
273C2×C61#185512yes—
274D61—21no—
275D61—22no—
276D61—21no—
277D61—42no—
278C24×C4—611no—
279C22×M16—612no—
280C22×M16—612no—
281C23×C8—611no—
282C23×C8—611no—
283C2×#108—1222no—
284C2×#108—1224no—
285#407—1224no—
286#407—1224no—
287C2×C22⋊C8—611no—
288C2×C22⋊C8—611no—
289C2×C22⋊C8—611no—
290C2×C22⋊C8—1222no—
291C2×C22⋊C8—1222no—
292C2×C22⋊C8—1222no—
293C2×C22⋊C8—1222no—
294C2×C22⋊C8#692311yescharacteristic
295#341—1222no—
296#341—1224no—
297C61#1109711yescharacteristic, complemented, Sylow
298C25—611no—
299C23×C4—611no—
300C23×C4—611no—
301C23×C4—611no—
302C23×C4—611no—
303C23×C4—611no—
304C23×C4—1221no—
305C23×C4—1221no—
306C23×C4—1222no—
307C23×C4—1222no—
308C23×C4—1221no—
309C23×C4—1221no—
310C23×C4—1222no—
311C23×C4—1222no—
312C23×C4C2×#692311yescharacteristic
313C2×M16—614no—
314C2×M16—614no—
315C2×M16—1222no—
316C2×M16—1222no—
317C2×M16—1222no—
318C2×M16—1222no—
319C2×M16—1222no—
320C2×M16—1222no—
321C2×M16—1222no—
322C2×M16—1222no—
323C2×M16—1222no—
324C2×M16—1222no—
325C22×C8—611no—
326C22×C8—612no—
327C22×C8—612no—
328C22×C8—611no—
329C22×C8—1222no—
330C22×C8—1222no—
331C22×C8—1222no—
332C22×C8—1221no—
333C22×C8—1221no—
334C22×C8—1222no—
335C22×C8—1222no—
336C22×C8—1222no—
337C22×C8C2×#692311yescharacteristic
338C22×C8C2×#692311yescharacteristic
339#108—1228no—
340C22⋊C8—22no—
341C22⋊C8—1222no—
342C22⋊C8—1222no—
343C22⋊C8—1228no—
344C22⋊C8—1228no—
345C22⋊C8—1222no—
346C24—611no—
347C24—611no—
348C24—1221no—
349C24—1221no—
350C24—1222no—
351C24—1222no—
352C24—1222no—
353C24—1222no—
354C24—2442no—
355C24C4⋊#692311yescharacteristic
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—611no—
361C22×C4—611no—
362C22×C4—611no—
363C22×C4—611no—
364C22×C4—611no—
365C22×C4—612no—
366C22×C4—612no—
367C22×C4—612no—
368C22×C4—612no—
369C22×C4—611no—
370C22×C4—1222no—
371C22×C4—1221no—
372C22×C4—1221no—
373C22×C4—1222no—
374C22×C4—1221no—
375C22×C4—1221no—
376C22×C4—1222no—
377C22×C4—1222no—
378C22×C4—1222no—
379C22×C4—1221no—
380C22×C4—1221no—
381C22×C4—1222no—
382C22×C4—1221no—
383C22×C4—1221no—
384C22×C4—1222no—
385C22×C4—1222no—
386C22×C4—2441no—
387C22×C4—2442no—
388C22×C4—2441no—
389C22×C4—2442no—
390C22×C4—2442no—
391C22×C4—2442no—
392C22×C4—2442no—
393C22×C4—2442no—
394C22×C4—2441no—
395C22×C4—2441no—
396C22×C4C4⋊#692311yescharacteristic
397C22×C4C22×#692311yescharacteristic
398M16—1224no—
399M16—1224no—
400M16—1224no—
401M16—1224no—
402M16—2442no—
403M16—2442no—
404M16—2442no—
405M16—2442no—
406C2×C8—22no—
407C2×C8—21no—
408C2×C8—22no—
409C2×C8—612no—
410C2×C8—1222no—
411C2×C8—1224no—
412C2×C8—1222no—
413C2×C8—1222no—
414C2×C8—1224no—
415C2×C8—1224no—
416C2×C8—1221no—
417C2×C8—1222no—
418C2×C8—2442no—
419C2×C8—2441no—
420C2×C8—2441no—
421C2×C8—2442no—
422C2×C8—2442no—
423C2×C8—2442no—
424C2×C8—2442no—
425C2×C8C22⋊#692312yes—
426C23—21no—
427C23—22no—
428C23—21no—
429C23—22no—
430C23—611no—
431C23—611no—
432C23—612no—
433C23—612no—
434C23—612no—
435C23—1224no—
436C23—1224no—
437C23—1221no—
438C23—1221no—
439C23—1222no—
440C23—1221no—
441C23—1222no—
442C23—1221no—
443C23—1222no—
444C23—2444no—
445C23—2444no—
446C23—2441no—
447C23—2442no—
448C23—2441no—
449C23—2444no—
450C23—2444no—
451C23—2442no—
452C23—2442no—
453C23#1451984712yescomplemented
454C23C2×C4⋊#692311yescharacteristic
455C2×C4—21no—
456C2×C4—22no—
457C2×C4—41no—
458C2×C4—42no—
459C2×C4—41no—
460C2×C4—611no—
461C2×C4—611no—
462C2×C4—612no—
463C2×C4—612no—
464C2×C4—611no—
465C2×C4—612no—
466C2×C4—611no—
467C2×C4—612no—
468C2×C4—612no—
469C2×C4—612no—
470C2×C4—612no—
471C2×C4—612no—
472C2×C4—611no—
473C2×C4—611no—
474C2×C4—1221no—
475C2×C4—1222no—
476C2×C4—2441no—
477C2×C4—2442no—
478C2×C4—2441no—
479C2×C4—2441no—
480C2×C4—2442no—
481C2×C4—2441no—
482C2×C4—2441no—
483C2×C4—2442no—
484C2×C4—2441no—
485C2×C4—2441no—
486C2×C4—2442no—
487C2×C4—2441no—
488C2×C4C2×C22⋊#692311yescharacteristic
489C2×C4#1451985611yescharacteristic
490C2×C4D4×#692312yes—
491C2×C4D4×#692312yes—
492C8—22no—
493C8—41no—
494C8—1222no—
495C8—2444no—
496C8—2444no—
497C8—2441no—
498C22—24no—
499C22—22no—
500C22—41no—
501C22—42no—
502C22—41no—
503C22—611no—
504C22—612no—
505C22—611no—
506C22—1222no—
507C22—1222no—
508C22—1222no—
509C22—1222no—
510C22—1221no—
511C22—1221no—
512C22—1221no—
513C22—1221no—
514C22—1224no—
515C22—1222no—
516C22—2444no—
517C22—2448no—
518C22—2444no—
519C22—2441no—
520C22—2442no—
521C22—2441no—
522C22#1684070411yescharacteristic
523C22#1684070912yes—
524C22C2×#1451984711yescharacteristic
525C22D61⋊#10811yescharacteristic
526C22#1684077712yes—
527C4—41no—
528C4—611no—
529C4—612no—
530C4—611no—
531C4—2441no—
532C4#1684071011yescharacteristic
533C4#1684071212yes—
534C4#1684071411yescharacteristic
535C2—42no—
536C2—1221no—
537C2—1222no—
538C2—1221no—
539C2—2442no—
540C2#2146100211yescharacteristic
541C2#2146169811yescharacteristic
542C2#2146170011yescharacteristic
543C2#2146177212yes—
544C2#2146177312yes—
subgroupG/H
centerC23C2×C4⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×C22⋊C8×C61C4
socleC23×C61C2×C4⋊C4
prime radicalC24×D61Q8
cosocleC22×C4×D61C23
hypercenterC2×C22⋊C8#6923
hypocenterC61#11097
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
1. C22×#14519847C2semidirect
3. C2×#16840638C2semidirect
4. C2×#16840638C2semidirect
157. C23×C61#108semidirect
177. C22×D61#108semidirect
297. C61#11097semidirect
453. C23#14519847semidirect

Maximal subgroups

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

subgroupindex
C22×#145198472
C2×#168407332
C2×#168406382
C2×C22⋊C8×D612
#1109761