Finite Group Databasebeta

← #30600436

Subgroups — #30600436

Order 15616.

980 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 980 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840705C211yesmaximal, characteristic, complemented
2#21461642C211yesmaximal, characteristic, complemented
3C2×#16840613C212yesmaximal, complemented
4#21460692C212yesmaximal, complemented
5#21454098C211yesmaximal, characteristic
6C22×C22⋊#6923—21no—
7C2×#14519834—21no—
8C2×#14519834C2212yes—
9C2×C22⋊#92420—21no—
10#16840705—24no—
11C2×(C2×#6923)⋊C4—21no—
12C2×(C2×#6923)⋊C4C2212yes—
13#16840613—24no—
14C23×C4×D61C2211yescharacteristic
15C2×#14519748C411yescharacteristic, complemented
16C2×#14519748C2211yescharacteristic
17C2×#14519745—21no—
18#16839642—21no—
19#16839638—21no—
20#16839638—21no—
21#16839622C411yescharacteristic, complemented
22#16839619C411yescharacteristic, complemented
23#16839619C2211yescharacteristic
24C2×#121×C61C411yescharacteristic, complemented
25C23×#6923—22no—
26C22×#92420—22no—
27C2×C22⋊#6923—24no—
28C2×C22⋊#6923—42no—
29C2×C22⋊#6923—42no—
30#14519834—22no—
31#14519834—22no—
32#14519834—42no—
33C22⋊#92420—42no—
34(C2×#6923)⋊C4—24no—
35(C2×#6923)⋊C4—22no—
36(C2×#6923)⋊C4D414yescomplemented
37C24×D61D411yescharacteristic
38C22×C22⋊D61—21no—
39C22×C22⋊D61—21no—
40C23×Dic61D411yescharacteristic
41C22×C4×D61—22no—
42C22×C4×D61—22no—
43C22×C4×D61—42no—
44C22×C4×D61—42no—
45C22×C4×D61C2×C411yescharacteristic
46C22×C4×D61D411yescharacteristic
47C22×C4×D61D411yescharacteristic
48C22×C4×D61C2311yescharacteristic
49#14519748—22no—
50#14519748—22no—
51#14519748—42no—
52#14519745—44no—
53C2×C4⋊Dic61C2×C411yescharacteristic
54C2×C4⋊Dic61C2×C411yescharacteristic
55C2×C22⋊Dic61—21no—
56C2×C22⋊Dic61—21no—
57C2×C22⋊Dic61—21no—
58C2×#11758198—21no—
59C2×#11758198—21no—
60#14519684—21no—
61#14519684—21no—
62#14519684—21no—
63C22×D4×C61—21no—
64C22×D4×C61C2×C411yescharacteristic
65C23×C4×C61C2×C411yescharacteristic
66#121×C61—42no—
67C2×C4⋊C4×C61C2×C411yescharacteristic
68C2×C22⋊C4×C61—21no—
69C24×C61—21no—
70C24×C61C22⋊C411yescharacteristic
71C23×D61—22no—
72C23×D61—22no—
73C23×D61—21no—
74C23×D61—21no—
75C23×D61—22no—
76C23×D61—22no—
77C23×D61—41no—
78C23×D61—41no—
79C23×D61C22⋊C411yescharacteristic
80C23×D61C2×D411yescharacteristic
81C22×#6923—24no—
82C22×#6923—42no—
83C22×#6923—42no—
84C22×#6923—42no—
85C22×#6923—42no—
86C22×#6923—42no—
87C22×#6923—42no—
88C2×D4×C61—22no—
89C2×D4×C61—41no—
90C2×D4×C61—41no—
91C2×D4×C61—42no—
92C2×D4×C61—42no—
93C2×D4×C61—42no—
94C22×C4×C61—22no—
95C22×C4×C61—22no—
96C22×C4×C61—21no—
97C22×C4×C61—41no—
98C22×C4×C61C22⋊C411yescharacteristic
99C22×C4×C61C22×C411yescharacteristic
100C2×C22⋊D61—42no—
101C2×C22⋊D61—42no—
102C2×C22⋊D61—42no—
103C2×C22⋊D61—41no—
104C2×C22⋊D61—41no—
105C2×C22⋊D61—42no—
106C2×C22⋊D61—42no—
107C22×Dic61—22no—
108C22×Dic61—22no—
109C22×Dic61—21no—
110C22×Dic61—21no—
111C22×Dic61—41no—
112C22×Dic61C22⋊C411yescharacteristic
113C22×Dic61C2×D411yescharacteristic
114C2×C4×D61—22no—
115C2×C4×D61—22no—
116C2×C4×D61—21no—
117C2×C4×D61—21no—
118C2×C4×D61—22no—
119C2×C4×D61—22no—
120C2×C4×D61—41no—
121C2×C4×D61—41no—
122C2×C4×D61—41no—
123C2×C4×D61—41no—
124C2×C4×D61—41no—
125C2×C4×D61—41no—
126C2×C4×D61—48no—
127C2×C4×D61—48no—
128C2×C4×D61C2×D412yes—
129C2×C4×D61#4112yes—
130C22⋊#6923—48no—
131C2×#92420—42no—
132C2×#92420—42no—
133C2×#92420—42no—
134C4⋊C4×C61—41no—
135C22⋊C4×C61—42no—
136C22⋊Dic61—42no—
137C22⋊Dic61—42no—
138C22⋊Dic61—42no—
139#11758198—42no—
140#11758198—42no—
141C4⋊Dic61—22no—
142C4⋊Dic61—41no—
143C23×C61—21no—
144C23×C61—21no—
145C23×C61—21no—
146C23×C61—21no—
147C23×C61—21no—
148C23×C61—21no—
149C23×C61—41no—
150C23×C61—41no—
151C23×C61—41no—
152C23×C61—41no—
153C23×C61—41no—
154C23×C61—41no—
155C23×C61—41no—
156C23×C61#9912yes—
157C23×C61C2×C22⋊C411yescharacteristic
158C22×D61—21no—
159C22×D61—21no—
160C22×D61—21no—
161C22×D61—21no—
162C22×D61—24no—
163C22×D61—24no—
164C22×D61—21no—
165C22×D61—21no—
166C22×D61—21no—
167C22×D61—21no—
168C22×D61—21no—
169C22×D61—21no—
170C22×D61—44no—
171C22×D61—44no—
172C22×D61—44no—
173C22×D61—44no—
174C22×D61—42no—
175C22×D61—42no—
176C22×D61—42no—
177C22×D61—42no—
178C22×D61#9912yes—
179C22×D61#12011yescharacteristic
180C22×D61#12311yescharacteristic
181C22×D61#13512yes—
182C22×D61AGL(1,ℤ/8)12yes—
183C2×#6923—44no—
184C2×#6923—44no—
185C2×#6923—44no—
186C2×#6923—82no—
187C2×#6923—82no—
188C2×#6923—82no—
189C2×#6923—82no—
190D4×C61—82no—
191D4×C61—84no—
192C2×C4×C61—21no—
193C2×C4×C61—21no—
194C2×C4×C61—21no—
195C2×C4×C61—21no—
196C2×C4×C61—21no—
197C2×C4×C61—44no—
198C2×C4×C61—41no—
199C2×C4×C61—41no—
200C2×C4×C61—41no—
201C2×C4×C61C4×D412yes—
202C22⋊D61—84no—
203C22⋊D61—82no—
204C22⋊D61—82no—
205C2×Dic61—21no—
206C2×Dic61—21no—
207C2×Dic61—21no—
208C2×Dic61—21no—
209C2×Dic61—21no—
210C2×Dic61—44no—
211C2×Dic61—41no—
212C2×Dic61—41no—
213C2×Dic61—41no—
214C2×Dic61—41no—
215C2×Dic61—41no—
216C2×Dic61—41no—
217C2×Dic61#12112yes—
218C4×D61—42no—
219C4×D61—42no—
220C4×D61—44no—
221C4×D61—44no—
222C4×D61—42no—
223C4×D61—42no—
224#92420—82no—
225#9158—611nomaximal, Sylow
226C22×C61—22no—
227C22×C61—22no—
228C22×C61—22no—
229C22×C61—41no—
230C22×C61—41no—
231C22×C61—41no—
232C22×C61—41no—
233C22×C61—81no—
234C22×C61—81no—
235C22×C61—81no—
236C22×C61—81no—
237C22×C61—81no—
238C22×C61—81no—
239C22×C61—81no—
240C22×C61#38611yescharacteristic
241C22×C61C2×#9911yescharacteristic
242C22×C61C2×#9911yescharacteristic
243C22×C61#41611yescharacteristic
244C22×C61#41811yescharacteristic
245C22×C61#42111yescharacteristic
246C22×C61#42111yescharacteristic
247C2×D61—21no—
248C2×D61—21no—
249C2×D61—21no—
250C2×D61—21no—
251C2×D61—22no—
252C2×D61—22no—
253C2×D61—22no—
254C2×D61—22no—
255C2×D61—22no—
256C2×D61—22no—
257C2×D61—22no—
258C2×D61—48no—
259C2×D61—48no—
260C2×D61—41no—
261C2×D61—41no—
262C2×D61—41no—
263C2×D61—41no—
264C2×D61#44912yes—
265C2×D61#48212yes—
266#6923—84no—
267C4×C61—22no—
268C4×C61—41no—
269C4×C61—81no—
270Dic61—22no—
271Dic61—41no—
272Dic61—81no—
273Dic61—81no—
274#2847—611no—
275C2×#381—611no—
276#1779—611no—
277C2×#327—612no—
278#1294—612no—
279C2×C61—42no—
280C2×C61—161no—
281C2×C61#151011yescharacteristic
282C2×C61#151011yescharacteristic
283C2×C61#151611yescharacteristic
284C2×C61#151611yescharacteristic
285C2×C61#187511yescharacteristic
286C2×C61#189711yescharacteristic
287C2×C61#189811yescharacteristic
288D61—22no—
289D61—22no—
290D61—42no—
291C24×C4—611no—
292C2×#121—611no—
293C2×#121—611no—
294C2×#121#692311yescharacteristic, complemented
295C2×#120—1221no—
296C22×C22⋊C4—1221no—
297C2×C22⋊C8—612no—
298C2×C22⋊C8—1221no—
299C2×C22⋊C8—1221no—
300#386—1221no—
301#386—1221no—
302#386—1221no—
303#381—1224no—
304#380—611no—
305#380—611no—
306#380—611no—
307C2×#95—612no—
308C2×#95—1221no—
309#327—1224no—
310C61#915811yescharacteristic, complemented, Sylow
311C25—611no—
312C22×D4—21no—
313C22×D4—1221no—
314C22×D4—1221no—
315C22×D4C2×#692311yescharacteristic
316C23×C4—611no—
317C23×C4—611no—
318C23×C4—611no—
319C23×C4—611no—
320C23×C4—611no—
321C23×C4—1222no—
322C23×C4—1222no—
323C23×C4—1222no—
324C23×C4—2442no—
325C23×C4—2442no—
326C23×C4C2×#692311yescharacteristic
327C22×C8—1222no—
328#121—42no—
329#121—1222no—
330#121—1222no—
331#121—2442no—
332#120—2444no—
333C2×C4⋊C4—611no—
334C2×C4⋊C4—611no—
335C2×C4⋊C4C2×#692311yescharacteristic
336C2×C22⋊C4—21no—
337C2×C22⋊C4—1221no—
338C2×C22⋊C4—1221no—
339C2×C22⋊C4—1221no—
340C2×C22⋊C4—1221no—
341C2×C22⋊C4—1224no—
342C2×C22⋊C4—1221no—
343C2×C22⋊C4—2442no—
344C2×C22⋊C4—2442no—
345C22⋊C8—1222no—
346C22⋊C8—1222no—
347C22⋊C8—2442no—
348C22⋊C8—2442no—
349#95—614no—
350#95—1221no—
351#95—1221no—
352#95—1222no—
353#95—1224no—
354#95—1221no—
355C24—21no—
356C24—611no—
357C24—611no—
358C24—1221no—
359C24—1222no—
360C24—1221no—
361C24—1222no—
362C24—1222no—
363C24—1222no—
364C24—2441no—
365C24—2441no—
366C24C22⋊#692311yescharacteristic
367C2×D4—22no—
368C2×D4—41no—
369C2×D4—41no—
370C2×D4—42no—
371C2×D4—42no—
372C2×D4—42no—
373C2×D4—2442no—
374C2×D4—2441no—
375C2×D4—2441no—
376C2×D4—2442no—
377C2×D4—2442no—
378C2×D4—2442no—
379C2×D4—2442no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—21no—
383C22×C4—41no—
384C22×C4—611no—
385C22×C4—612no—
386C22×C4—612no—
387C22×C4—611no—
388C22×C4—1222no—
389C22×C4—1221no—
390C22×C4—1222no—
391C22×C4—1222no—
392C22×C4—1221no—
393C22×C4—1222no—
394C22×C4—1222no—
395C22×C4—1222no—
396C22×C4—1224no—
397C22×C4—1221no—
398C22×C4—1221no—
399C22×C4—2441no—
400C22×C4—2441no—
401C22×C4—2441no—
402C22×C4—2441no—
403C22×C4—2441no—
404C22×C4—2441no—
405C22×C4—2448no—
406C22×C4—2448no—
407C22×C4—2441no—
408C22×C4—2442no—
409C22×C4—2442no—
410C22×C4—2442no—
411C22×C4—2442no—
412C22×C4—2442no—
413C22×C4—2442no—
414C22×C4C22⋊#692311yescharacteristic
415C22×C4C22×#692311yescharacteristic
416C2×C8—2442no—
417C2×C8—2442no—
418C2×C8—2442no—
419C4⋊C4—41no—
420C4⋊C4—1222no—
421C4⋊C4—2441no—
422C22⋊C4—42no—
423C22⋊C4—2442no—
424C22⋊C4—2442no—
425C22⋊C4—2442no—
426C22⋊C4—2442no—
427C22⋊C4—2442no—
428C22⋊C4—2448no—
429C23—21no—
430C23—21no—
431C23—21no—
432C23—21no—
433C23—21no—
434C23—21no—
435C23—41no—
436C23—41no—
437C23—41no—
438C23—41no—
439C23—41no—
440C23—41no—
441C23—41no—
442C23—611no—
443C23—611no—
444C23—612no—
445C23—612no—
446C23—612no—
447C23—1224no—
448C23—1224no—
449C23—1221no—
450C23—1221no—
451C23—1221no—
452C23—1221no—
453C23—1221no—
454C23—1221no—
455C23—1221no—
456C23—1221no—
457C23—1221no—
458C23—1221no—
459C23—2444no—
460C23—2444no—
461C23—2442no—
462C23—2442no—
463C23—2444no—
464C23—2444no—
465C23—2442no—
466C23—2442no—
467C23#1451983512yes—
468C23C2×C22⋊#692311yescharacteristic
469D4—82no—
470D4—84no—
471D4—4882no—
472D4—4882no—
473D4—4884no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—44no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—612no—
484C2×C4—1221no—
485C2×C4—1221no—
486C2×C4—1221no—
487C2×C4—1221no—
488C2×C4—1221no—
489C2×C4—4882no—
490C2×C4—4882no—
491C2×C4—4882no—
492C2×C4—4882no—
493C2×C4—2442no—
494C2×C4—2442no—
495C2×C4—2444no—
496C2×C4—2444no—
497C2×C4—2442no—
498C2×C4—2442no—
499C2×C4—2444no—
500C2×C4—2444no—
501C2×C4—2444no—
502C2×C4—2444no—
503C2×C4—2441no—
504C2×C4—2441no—
505C2×C4—2441no—
506C2×C4—2441no—
507C2×C4—2441no—
508C2×C4—2441no—
509C2×C4D4×#692312yes—
510C8—4882no—
511C22—22no—
512C22—22no—
513C22—22no—
514C22—41no—
515C22—41no—
516C22—41no—
517C22—41no—
518C22—81no—
519C22—81no—
520C22—81no—
521C22—81no—
522C22—81no—
523C22—81no—
524C22—81no—
525C22—612no—
526C22—612no—
527C22—1221no—
528C22—1221no—
529C22—1221no—
530C22—1221no—
531C22—1222no—
532C22—1222no—
533C22—1222no—
534C22—1222no—
535C22—1222no—
536C22—1222no—
537C22—1222no—
538C22—2448no—
539C22—2448no—
540C22—2441no—
541C22—2441no—
542C22—2441no—
543C22—2441no—
544C22#1684071011yescharacteristic
545C22C2×#1451983511yescharacteristic
546C22D61⋊#9911yescharacteristic
547C22#1684075211yescharacteristic
548C22#1684075411yescharacteristic
549C22#1684075911yescharacteristic
550C22#1684076011yescharacteristic
551C4—22no—
552C4—41no—
553C4—81no—
554C4—1222no—
555C4—4884no—
556C4—4881no—
557C4—4881no—
558C4—2441no—
559C2—42no—
560C2—161no—
561C2—1222no—
562C2—1222no—
563C2—2442no—
564C2#2146122411yescharacteristic
565C2#2146122511yescharacteristic
566C2#2146124411yescharacteristic
567C2#2146124511yescharacteristic
568C2#2146180711yescharacteristic
569C2#2146183911yescharacteristic
570C2#2146184011yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#121×C61C4
socleC23×C61C2×C22⋊C4
prime radical#21454098C2
cosocleC22×C4×D61C23
hypercenterC2×#121#6923
hypocenterC61#9158
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#16840705C2semidirect
2. #21461642C2semidirect
3. C2×#16840613C2semidirect
4. #21460692C2semidirect
15. C2×#14519748C4semidirect
21. #16839622C4semidirect
22. #16839619C4semidirect
24. C2×#121×C61C4semidirect
36. (C2×#6923)⋊C4D4semidirect
294. C2×#121#6923semidirect
310. C61#9158semidirect

Maximal subgroups

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

subgroupindex
C2×#168407052
#214616422
C2×#168406132
#214606922
#214540982
#915861