Finite Group Databasebeta

← #30600192

Subgroups — #30600192

Order 15616.

964 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×D61⋊(C22⋊C8)C211yesmaximal, characteristic
2#21461642C211yesmaximal, characteristic
3C2×#16840608C212yesmaximal, complemented
4#21460657C212yesmaximal, complemented
5C2×#16839633C211yesmaximal, characteristic
6C22×D61⋊C8—21no—
7C2×#14519834—21no—
8C2×#14519834—21no—
9C2×#14519834—21no—
10D61⋊(C22⋊C8)—24no—
11C2×C22⋊#92420C2212yes—
12C2×C22⋊#92420C2212yes—
13#16840608—24no—
14C23×C4×D61C2211yescharacteristic
15C22×#11758196C2211yescharacteristic
16C22×#11758198C411yescharacteristic
17C22×#11758198C411yescharacteristic
18#16839633—21no—
19#16839633—21no—
20#16839633—21no—
21#16839633—21no—
22C2×#14519684C411yescharacteristic
23C2×#14519684C2211yescharacteristic
24C22×C4⋊C4×C61C411yescharacteristic
25C2×D61⋊C8—24no—
26C2×D61⋊C8—42no—
27C2×D61⋊C8—42no—
28C22×#92420—22no—
29C22×#92420—22no—
30#14519834—24no—
31#14519834—42no—
32#14519834—42no—
33C22⋊#92420—22no—
34C22⋊#92420—22no—
35C22⋊#92420—22no—
36C22⋊#92420D414yes—
37C24×D61C2×C411yescharacteristic
38C23×Dic61C2×C411yescharacteristic
39C23×Dic61C2×C411yescharacteristic
40C23×Dic61C2311yescharacteristic
41C22×C4×D61—22no—
42C22×C4×D61—22no—
43C22×C4×D61—42no—
44C22×C4×D61—42no—
45C22×C4×D61D411yescharacteristic
46C22×C4×D61D411yescharacteristic
47C22×C4×D61D411yescharacteristic
48C22×C4×D61D411yescharacteristic
49C2×#11758196—22no—
50C2×#11758196—21no—
51C2×#11758196—21no—
52C2×#11758196—22no—
53C2×#11758198—21no—
54C2×#11758198—21no—
55C2×#11758198—22no—
56C2×#11758198—21no—
57C2×#11758198—21no—
58C2×#11758198—42no—
59C2×#11758198C814yescomplemented
60#14519684—21no—
61#14519684—21no—
62#14519684—21no—
63#14519684—21no—
64C23×C4×C61C2×C411yescharacteristic
65C23×C4×C61C2×C411yescharacteristic
66C23×C4×C61C2×C411yescharacteristic
67C2×C4⋊C4×C61—21no—
68C2×C4⋊C4×C61—21no—
69C2×C4⋊C4×C61—42no—
70C24×C61C22×C411yescharacteristic
71C23×D61—22no—
72C23×D61—22no—
73C23×D61—22no—
74C23×D61—22no—
75C23×D61—41no—
76C23×D61—41no—
77C23×D61C22⋊C411yescharacteristic
78C23×D61C22⋊C411yescharacteristic
79C23×D61C2×C812yes—
80C23×D61M1612yes—
81C22×C4×C61—21no—
82C22×C4×C61—22no—
83C22×C4×C61—21no—
84C22×C4×C61—22no—
85C22×C4×C61—21no—
86C22×C4×C61—22no—
87C22×C4×C61—41no—
88C22×C4×C61—41no—
89C22×C4×C61—41no—
90C22×C4×C61—41no—
91C22×C4×C61—41no—
92C22×C4×C61C22⋊C411yescharacteristic
93C22×C4×C61C22⋊C411yescharacteristic
94C22×C4×C61C2×C812yescomplemented
95C22×Dic61—21no—
96C22×Dic61—22no—
97C22×Dic61—21no—
98C22×Dic61—22no—
99C22×Dic61—21no—
100C22×Dic61—22no—
101C22×Dic61—41no—
102C22×Dic61—41no—
103C22×Dic61—41no—
104C22×Dic61—41no—
105C22×Dic61C2×C812yescomplemented
106C22×Dic61C2×D411yescharacteristic
107C22×Dic61C2×D411yescharacteristic
108C22×Dic61C2×D412yes—
109C22×Dic61#4112yes—
110C2×C4×D61—22no—
111C2×C4×D61—22no—
112C2×C4×D61—21no—
113C2×C4×D61—21no—
114C2×C4×D61—22no—
115C2×C4×D61—22no—
116C2×C4×D61—21no—
117C2×C4×D61—22no—
118C2×C4×D61—22no—
119C2×C4×D61—21no—
120C2×C4×D61—48no—
121C2×C4×D61—48no—
122C2×C4×D61—41no—
123C2×C4×D61—41no—
124C2×C4×D61—41no—
125C2×C4×D61—41no—
126C2×#92420—24no—
127C2×#92420—42no—
128C2×#92420—42no—
129C2×#92420—42no—
130C2×#92420—42no—
131C2×#92420—42no—
132D61⋊C8—48no—
133C4⋊C4×C61—42no—
134C4⋊C4×C61—42no—
135#11758198—24no—
136#11758198—24no—
137#11758198—42no—
138#11758198—42no—
139#11758196—41no—
140#11758196—42no—
141#11758196—41no—
142C23×C61—21no—
143C23×C61—21no—
144C23×C61—21no—
145C23×C61—21no—
146C23×C61C2×C22⋊C411yescharacteristic
147C23×C61C4×D412yes—
148C23×C61C22×C811yescharacteristic
149C23×C61C2×M1611yescharacteristic
150C23×C61#13112yes—
151C22×D61—21no—
152C22×D61—21no—
153C22×D61—21no—
154C22×D61—21no—
155C22×D61—21no—
156C22×D61—21no—
157C22×D61—21no—
158C22×D61—21no—
159C22×D61—21no—
160C22×D61—21no—
161C22×D61—24no—
162C22×D61—24no—
163C22×D61—24no—
164C22×D61—24no—
165C22×D61—42no—
166C22×D61—42no—
167C22×D61—44no—
168C22×D61—44no—
169C22×D61—44no—
170C22×D61—44no—
171C22×D61C22⋊C812yes—
172C22×D61C22⋊C812yes—
173C22×D61#9912yes—
174C22×D61#10112yes—
175C2×C4×C61—21no—
176C2×C4×C61—21no—
177C2×C4×C61—21no—
178C2×C4×C61—22no—
179C2×C4×C61—21no—
180C2×C4×C61—21no—
181C2×C4×C61—44no—
182C2×C4×C61—42no—
183C2×C4×C61—41no—
184C2×C4×C61—41no—
185C2×C4×C61—42no—
186C2×C4×C61—41no—
187C2×C4×C61—41no—
188C2×C4×C61—41no—
189C2×C4×C61—82no—
190C2×C4×C61#9912yes—
191C2×Dic61—21no—
192C2×Dic61—21no—
193C2×Dic61—21no—
194C2×Dic61—21no—
195C2×Dic61—22no—
196C2×Dic61—24no—
197C2×Dic61—42no—
198C2×Dic61—42no—
199C2×Dic61—41no—
200C2×Dic61—41no—
201C2×Dic61—42no—
202C2×Dic61—41no—
203C2×Dic61—41no—
204C2×Dic61—41no—
205C2×Dic61—82no—
206C2×Dic61#12011yescharacteristic
207C2×Dic61#12112yes—
208C2×Dic61#12311yescharacteristic
209C4×D61—24no—
210C4×D61—24no—
211C4×D61—44no—
212C4×D61—44no—
213C4×D61—42no—
214C4×D61—42no—
215#92420—44no—
216#92420—82no—
217#9081—611nomaximal, Sylow
218C22×C61—22no—
219C22×C61—22no—
220C22×C61—21no—
221C22×C61—21no—
222C22×C61—21no—
223C22×C61—21no—
224C22×C61—22no—
225C22×C61—22no—
226C22×C61#38611yescharacteristic
227C22×C61C2×C22⋊C811yescharacteristic
228C22×C61#40811yescharacteristic
229C22×C61C2×#9911yescharacteristic
230C22×C61C2×#9911yescharacteristic
231C22×C61C2×#10111yescharacteristic
232C22×C61#41311yescharacteristic
233C22×C61C8×D412yes—
234C22×C61#43512yes—
235C2×D61—22no—
236C2×D61—22no—
237C2×D61—22no—
238C2×D61—22no—
239C2×D61—22no—
240C2×D61—22no—
241C2×D61—22no—
242C2×D61—22no—
243C2×D61—22no—
244C2×D61—48no—
245C2×D61—48no—
246C2×D61—41no—
247C2×D61—41no—
248C2×D61—41no—
249C2×D61—41no—
250C2×D61#32414yescomplemented
251C4×C61—22no—
252C4×C61—41no—
253C4×C61—42no—
254C4×C61—81no—
255Dic61—21no—
256Dic61—22no—
257Dic61—21no—
258Dic61—42no—
259Dic61—81no—
260C22×C22⋊C8—611no—
261C2×#385—611no—
262#1779—611no—
263C2×#324—612no—
264#1280—612no—
265C2×C61—22no—
266C2×C61—22no—
267C2×C61C2×#32411yescharacteristic
268C2×C61#145911yescharacteristic
269C2×C61#146811yescharacteristic
270C2×C61#147211yescharacteristic
271C2×C61#186911yescharacteristic
272C2×C61#189811yescharacteristic
273C2×C61#190111yescharacteristic
274D61—24no—
275D61—42no—
276C24×C4—611no—
277C23×C8—1221no—
278C22×C4⋊C4—611no—
279C22×C4⋊C4#692311yescharacteristic
280C22×C22⋊C4—611no—
281C22×C22⋊C4—611no—
282C2×C22⋊C8—612no—
283C2×C22⋊C8—612no—
284C2×C22⋊C8—1224no—
285C2×C22⋊C8—1221no—
286C2×C22⋊C8—1221no—
287C2×C22⋊C8—1221no—
288#385—1221no—
289#385—1221no—
290#385—1221no—
291#385—1221no—
292C2×#95—611no—
293C2×#95—611no—
294#324—1224no—
295C61#908111yescharacteristic, complemented, Sylow
296C25—611no—
297C23×C4—611no—
298C23×C4—611no—
299C23×C4—611no—
300C23×C4—611no—
301C23×C4—611no—
302C23×C4—611no—
303C23×C4—611no—
304C23×C4—1222no—
305C23×C4—1222no—
306C23×C4—2442no—
307C23×C4—2442no—
308C23×C4C2×#692311yescharacteristic
309C23×C4C2×#692311yescharacteristic
310C23×C4C2×#692311yescharacteristic
311C22×C8—1222no—
312C22×C8—1224no—
313C22×C8—1222no—
314C22×C8—2442no—
315C22×C8—2442no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—42no—
319C2×C4⋊C4—1222no—
320C2×C4⋊C4—1221no—
321C2×C4⋊C4—1221no—
322C2×C4⋊C4—1222no—
323C2×C22⋊C4—614no—
324C2×C22⋊C4—1221no—
325C2×C22⋊C4—1221no—
326C2×C22⋊C4—1222no—
327C2×C22⋊C4—1221no—
328C2×C22⋊C4—1221no—
329C2×C22⋊C4—2442no—
330C22⋊C8—614no—
331C22⋊C8—1222no—
332C22⋊C8—1224no—
333C22⋊C8—1222no—
334C22⋊C8—1222no—
335C22⋊C8—2442no—
336C22⋊C8—2442no—
337#95—1221no—
338#95—1221no—
339#95—1221no—
340#95—1221no—
341C24—611no—
342C24—611no—
343C24—612no—
344C24—612no—
345C24—1222no—
346C24—1222no—
347C24—1222no—
348C24—1222no—
349C24—2441no—
350C24—2441no—
351C24C22×#692311yescharacteristic
352C22×C4—21no—
353C22×C4—22no—
354C22×C4—21no—
355C22×C4—22no—
356C22×C4—21no—
357C22×C4—22no—
358C22×C4—41no—
359C22×C4—41no—
360C22×C4—41no—
361C22×C4—41no—
362C22×C4—41no—
363C22×C4—611no—
364C22×C4—611no—
365C22×C4—612no—
366C22×C4—612no—
367C22×C4—612no—
368C22×C4—1221no—
369C22×C4—1221no—
370C22×C4—1221no—
371C22×C4—1222no—
372C22×C4—1222no—
373C22×C4—1221no—
374C22×C4—1222no—
375C22×C4—1222no—
376C22×C4—1222no—
377C22×C4—1221no—
378C22×C4—1222no—
379C22×C4—1221no—
380C22×C4—1222no—
381C22×C4—1222no—
382C22×C4—1222no—
383C22×C4—1221no—
384C22×C4—2441no—
385C22×C4—2441no—
386C22×C4—2441no—
387C22×C4—2441no—
388C22×C4—2448no—
389C22×C4—2448no—
390C22×C4—2441no—
391C22×C4—2441no—
392C22×C4—2441no—
393C22×C4—2441no—
394C22×C4D61⋊C812yescomplemented
395C22×C4C22⋊#692311yescharacteristic
396C22×C4C22⋊#692311yescharacteristic
397C2×C8—1224no—
398C2×C8—2442no—
399C2×C8—2442no—
400C2×C8—2442no—
401C2×C8—2448no—
402C2×C8—2442no—
403C2×C8—2442no—
404C4⋊C4—42no—
405C4⋊C4—42no—
406C4⋊C4—2441no—
407C4⋊C4—2442no—
408C4⋊C4—2441no—
409C22⋊C4—1224no—
410C22⋊C4—1224no—
411C22⋊C4—2442no—
412C22⋊C4—2442no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—612no—
418C23—612no—
419C23—612no—
420C23—612no—
421C23—1224no—
422C23—1224no—
423C23—1221no—
424C23—1221no—
425C23—1221no—
426C23—1221no—
427C23—1221no—
428C23—1221no—
429C23—1221no—
430C23—1221no—
431C23—1221no—
432C23—1221no—
433C23—1224no—
434C23—1224no—
435C23—2442no—
436C23—2442no—
437C23—2444no—
438C23—2444no—
439C23—2444no—
440C23—2444no—
441C23C2×C22⋊#692311yescharacteristic
442C23D4×#692312yes—
443C23C2×D61⋊C811yescharacteristic
444C23D61⋊M1611yescharacteristic
445C23#1451986512yes—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—22no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—44no—
453C2×C4—42no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—42no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—82no—
461C2×C4—611no—
462C2×C4—612no—
463C2×C4—611no—
464C2×C4—1224no—
465C2×C4—1224no—
466C2×C4—1221no—
467C2×C4—1221no—
468C2×C4—1221no—
469C2×C4—1221no—
470C2×C4—1222no—
471C2×C4—1224no—
472C2×C4—4882no—
473C2×C4—2444no—
474C2×C4—2444no—
475C2×C4—2442no—
476C2×C4—2442no—
477C2×C4—2442no—
478C2×C4—2442no—
479C2×C4—2441no—
480C2×C4—2441no—
481C2×C4—2441no—
482C2×C4—2441no—
483C2×C4—2441no—
484C2×C4—2442no—
485C2×C4#1451983512yes—
486C8—4882no—
487C8—2444no—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—22no—
493C22—22no—
494C22—22no—
495C22—22no—
496C22—614no—
497C22—1222no—
498C22—1222no—
499C22—1222no—
500C22—1222no—
501C22—1222no—
502C22—1222no—
503C22—1222no—
504C22—1222no—
505C22—1222no—
506C22—2448no—
507C22—2448no—
508C22—2441no—
509C22—2441no—
510C22—2441no—
511C22—2441no—
512C22#1684071011yescharacteristic
513C22D61⋊(C22⋊C8)11yescharacteristic
514C22#1684073711yescharacteristic
515C22C2×#1451983511yescharacteristic
516C22D61⋊#9911yescharacteristic
517C22D61⋊#10111yescharacteristic
518C22#1684074811yescharacteristic
519C22#1684079012yes—
520C22#1684079212yes—
521C4—22no—
522C4—42no—
523C4—41no—
524C4—81no—
525C4—1222no—
526C4—1221no—
527C4—1221no—
528C4—4881no—
529C4—2442no—
530C2—22no—
531C2—22no—
532C2—1224no—
533C2—2442no—
534C2D61⋊#32411yescharacteristic
535C2#2146105411yescharacteristic
536C2#2146108711yescharacteristic
537C2#2146109911yescharacteristic
538C2#2146179511yescharacteristic
539C2#2146184011yescharacteristic
540C2#2146184711yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC23×C61C22×C8
FrattiniC24C22×#6923
FittingC22×C4⋊C4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC24×D61C2×C4
cosocleC23×Dic61C23
hypercenterC22×C4⋊C4#6923
hypocenterC61#9081
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#16840608C2semidirect
4. #21460657C2semidirect
59. C2×#11758198C8semidirect
94. C22×C4×C61C2×C8semidirect
105. C22×Dic61C2×C8semidirect
250. C2×D61#324semidirect
295. C61#9081semidirect
394. C22×C4D61⋊C8semidirect

Maximal subgroups

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

subgroupindex
C2×D61⋊(C22⋊C8)2
#214616422
C2×#168406082
#214606572
C2×#168396332
#908161