Finite Group Databasebeta

← #30620793

Subgroups — #30620793

Order 15616.

838 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462328C211yesmaximal, characteristic
2#21462327C211yesmaximal, characteristic
3#21461925C212yesmaximal, complemented
4#21461882C212yesmaximal, complemented
5#21461881C212yesmaximal, complemented
6#21461723C211yesmaximal, characteristic
7#21461722C211yesmaximal, characteristic
8#21461696C211yesmaximal, characteristic
9#21461635C212yesmaximal, complemented
10#21461555C211yesmaximal, characteristic
11C2×#106×D61C211yesmaximal, characteristic
12C2×#14519856—21no—
13C2×#14519846C2212yes—
14D61⋊(C22⋊C8)C2211yescharacteristic
15C2×#14519831C2212yes—
16#16840713C2212yes—
17#16840713C2212yes—
18#16840711—22no—
19#16840711—22no—
20#16840705—21no—
21#16840704—21no—
22#16840704C2211yescharacteristic
23#16840704C2211yescharacteristic
24C4⋊C4×#6923C2212yes—
25C4⋊C4×#6923C2212yes—
26C4×C22⋊#6923—21no—
27C4×C22⋊#6923C2211yescharacteristic
28#16840636C2212yes—
29#16840635C2212yes—
30#16840635C2212yes—
31#16840635C2212yes—
32#16840635C2212yes—
33(C2×#6923)⋊C8C2212yes—
34C22×C8×D61C2211yescharacteristic
35C2×C4⋊C4×D61C2211yescharacteristic
36C2×C4⋊C4×D61C2211yescharacteristic
37C2×#14519709C411yescharacteristic, complemented
38C2×#14519708C411yescharacteristic, complemented
39C2×#14519708C411yescharacteristic, complemented
40#106×D61C411yescharacteristic, complemented
41#106×D61C411yescharacteristic, complemented
42#106×D61C411yescharacteristic, complemented
43#106×D61C411yescharacteristic, complemented
44#106×D61C2211yescharacteristic
45#106×D61C2211yescharacteristic
46#106×D61C2211yescharacteristic
47#106×D61C2211yescharacteristic
48C2×#106×C61C411yescharacteristic, complemented
49C2×D61⋊C8C2312yes—
50#14519856—44no—
51C2×C4⋊#6923—22no—
52C2×C4⋊#6923—22no—
53C2×C4⋊#6923C2312yes—
54C2×C4⋊#6923C2312yes—
55C2×C22⋊#6923—21no—
56C2×C22⋊#6923—21no—
57C2×C22⋊#6923D411yescharacteristic
58C2×C22⋊#6923D411yescharacteristic
59C2×C4×#6923—22no—
60C2×C4×#6923—22no—
61C2×C4×#6923C2312yes—
62#14519846—24no—
63#14519834—21no—
64C22⋊#92420—21no—
65#14519831—24no—
66(C2×#6923)⋊C4—22no—
67(C2×#6923)⋊C4—22no—
68(C2×#6923)⋊C4—22no—
69(C2×#6923)⋊C4—22no—
70(C2×#6923)⋊C4—21no—
71(C2×#6923)⋊C4—21no—
72(C2×#6923)⋊C4D412yes—
73C22×C4×D61—21no—
74C22×C4×D61—21no—
75C22×C4×D61C2311yescharacteristic
76C22×#92418C2×C411yescharacteristic
77C2×C8×D61—24no—
78C2×C8×D61C2×C411yescharacteristic
79C2×C8×D61C2×C411yescharacteristic
80C2×C8×D61C2311yescharacteristic
81C2×C8×D61C2311yescharacteristic
82C2×C4⋊Dic61C2×C411yescharacteristic
83C2×C4⋊Dic61C2×C411yescharacteristic
84C2×#11758196—21no—
85C2×#11758196—21no—
86C4⋊C4×D61—21no—
87C4⋊C4×D61—21no—
88C4⋊C4×D61—21no—
89C4⋊C4×D61—21no—
90C4⋊C4×D61C2×C411yescharacteristic
91C4⋊C4×D61C2×C411yescharacteristic
92C4⋊C4×D61C2×C411yescharacteristic
93C4⋊C4×D61C2×C411yescharacteristic
94C4⋊C4×D61C2311yescharacteristic
95C4⋊C4×D61C2311yescharacteristic
96C4⋊C4×D61C2311yescharacteristic
97C4⋊C4×D61C2311yescharacteristic
98#14519709C2×C411yescharacteristic
99#14519709C2×C411yescharacteristic
100#14519709C2×C411yescharacteristic
101#14519709C2×C411yescharacteristic
102#14519708C2×C411yescharacteristic
103#14519708C2×C411yescharacteristic
104#14519708C2×C411yescharacteristic
105#14519708C2×C411yescharacteristic
106#14519708C2×C411yescharacteristic
107#14519708C2×C411yescharacteristic
108#14519708C2×C411yescharacteristic
109#14519708C2×C411yescharacteristic
110C22×C8×C61C2×C411yescharacteristic
111C2×C4⋊C4×C61C2×C411yescharacteristic
112C2×C4⋊C4×C61C2×C411yescharacteristic
113#106×C61C2×C411yescharacteristic
114#106×C61C2×C411yescharacteristic
115#106×C61C2×C411yescharacteristic
116#106×C61C2×C411yescharacteristic
117C23×D61C2×D411yescharacteristic
118C22×#6923—22no—
119C22×#6923—22no—
120C22×#6923C2×D412yes—
121C22×#6923C2×D412yes—
122C22×C4×C61—21no—
123C22×C4×C61—21no—
124C22×C4×C61C22×C411yescharacteristic
125C22×Dic61—21no—
126C22×Dic61—21no—
127C22×Dic61#4111yescharacteristic
128C2×C4×D61—22no—
129C2×C4×D61—22no—
130C2×C4×D61—21no—
131C2×C4×D61—21no—
132C2×C4×D61—21no—
133C2×C4×D61—21no—
134C2×C4×D61—21no—
135C2×C4×D61—21no—
136C2×C4×D61—21no—
137C2×C4×D61—21no—
138C2×C4×D61—42no—
139C2×C4×D61—42no—
140C2×C4×D61—82no—
141C2×C4×D61C22×C411yescharacteristic
142C2×C4×D61C2×D411yescharacteristic
143C2×C4×D61#4111yescharacteristic
144C2×C4×D61C2411yescharacteristic
145C22⋊#6923—22no—
146C22⋊#6923—22no—
147C22⋊#6923—42no—
148C22⋊#6923—42no—
149C2×#92420—22no—
150C4⋊#6923—22no—
151C4⋊#6923—22no—
152C4⋊#6923—22no—
153C4⋊#6923—22no—
154C4⋊#6923—44no—
155C4⋊#6923—82no—
156C4×#6923—22no—
157C4×#6923—22no—
158C4×#6923—44no—
159C4×#6923—82no—
160D61⋊C8—22no—
161D61⋊C8—22no—
162C2×C8×C61—22no—
163C2×C8×C61C22×C411yescharacteristic
164C2×C8×C61C22×C411yescharacteristic
165C4⋊C4×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61C22×C411yescharacteristic
168C4⋊C4×C61C22×C411yescharacteristic
169C4⋊C4×C61C22×C411yescharacteristic
170C4⋊C4×C61C22×C411yescharacteristic
171C4⋊Dic61—21no—
172C4⋊Dic61—21no—
173C4⋊Dic61C22×C411yescharacteristic
174C4⋊Dic61C22×C411yescharacteristic
175C4⋊Dic61C22×C411yescharacteristic
176C4⋊Dic61C22×C411yescharacteristic
177#11758196—21no—
178#11758196—21no—
179#11758196—21no—
180#11758196—21no—
181#11758196—21no—
182#11758196—21no—
183#11758196—21no—
184#11758196—21no—
185C2×#92418—22no—
186C2×#92418C22×C411yescharacteristic
187C2×#92418C22×C411yescharacteristic
188C8×D61—22no—
189C8×D61—22no—
190C8×D61—22no—
191C8×D61#4114yes—
192C23×C61C4×D411yescharacteristic
193C22×D61—22no—
194C22×D61—22no—
195C22×D61C4×D411yescharacteristic
196C22×D61AGL(1,ℤ/8)12yes—
197C22×D61#13712yes—
198C22×D61C22×D411yescharacteristic
199C2×#6923—22no—
200C2×#6923—22no—
201C2×#6923—22no—
202C2×#6923—22no—
203C2×#6923—22no—
204C2×#6923—22no—
205C2×#6923—42no—
206C2×#6923—42no—
207C2×#6923—42no—
208C2×#6923—42no—
209C2×#6923—42no—
210C2×#6923—42no—
211C2×C4×C61—21no—
212C2×C4×C61—21no—
213C2×C4×C61—21no—
214C2×C4×C61—21no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—42no—
218C2×C4×C61—81no—
219C2×C4×C61C4×D411yescharacteristic
220C2×C4×C61C23×C411yescharacteristic
221C2×Dic61—22no—
222C2×Dic61—21no—
223C2×Dic61—21no—
224C2×Dic61—21no—
225C2×Dic61—21no—
226C2×Dic61—42no—
227C2×Dic61—81no—
228C2×Dic61C4×D411yescharacteristic
229C2×Dic61C2×#4111yescharacteristic
230C4×D61—22no—
231C4×D61—21no—
232C4×D61—21no—
233C4×D61—22no—
234C4×D61—41no—
235C4×D61—41no—
236C4×D61—41no—
237C4×D61—41no—
238C4×D61—42no—
239C4×D61—42no—
240C4×D61—42no—
241C4×D61—42no—
242C4×D61—81no—
243C4×D61—81no—
244C4×D61C2×#4112yes—
245C4×D612−1+412yes—
246#92420—42no—
247C8×C61—21no—
248C8×C61#11712yescomplemented
249#92418—21no—
250#92418#11712yescomplemented
251#22615—611nomaximal, Sylow
252C22×C61—21no—
253C22×C61—21no—
254C22×C61#44012yes—
255C22×C61C2×C4×D411yescharacteristic
256C2×D61—21no—
257C2×D61—21no—
258C2×D61—24no—
259C2×D61—24no—
260C2×D61#44012yes—
261C2×D61#54712yes—
262C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
263C2×D61C2×#13711yescharacteristic
264C2×D61#57712yes—
265#6923—42no—
266#6923—42no—
267#6923—82no—
268#6923—82no—
269C4×C61—21no—
270C4×C61—41no—
271C4×C61—41no—
272C4×C61—41no—
273C4×C61—41no—
274C4×C61C2×#11711yescharacteristic
275C4×C61#51911yescharacteristic
276Dic61—21no—
277Dic61—41no—
278Dic61—41no—
279Dic61—41no—
280Dic61—41no—
281Dic61#55212yes—
282C22×#106—611no—
283#2345—611no—
284#2344—611no—
285#1944—612no—
286#1920—612no—
287#1919—612no—
288#1824—611no—
289#1823—611no—
290#1808—611no—
291#1776—612no—
292#1752—611no—
293C2×C61—22no—
294C2×C61#234411yescharacteristic
295C2×C61C2×#44011yescharacteristic
296C2×C61#294911yescharacteristic
297D61—22no—
298D61#334412yes—
299D61#334512yes—
300C23×C8—611no—
301C2×#117—1221no—
302C22×C4⋊C4—611no—
303C22×C4⋊C4—611no—
304C2×#107—612no—
305C2×#106—611no—
306C2×#106—611no—
307C2×#106—611no—
308C2×#106—611no—
309C2×#106—611no—
310C2×#106—611no—
311C2×#106—611no—
312C2×#106—611no—
313C2×#106—611no—
314C2×#106—611no—
315C2×#106—611no—
316C2×#106#692311yescharacteristic, complemented
317C2×C22⋊C8—611no—
318C2×#97—612no—
319#389—612no—
320#389—612no—
321#387—1222no—
322#387—1222no—
323#381—1221no—
324#380—611no—
325#380—611no—
326#380—1221no—
327C4×C4⋊C4—612no—
328C4×C4⋊C4—612no—
329C4×C22⋊C4—611no—
330C4×C22⋊C4—1221no—
331#340—612no—
332#340—612no—
333#340—612no—
334#340—612no—
335#340—612no—
336#336—612no—
337C61#2261511yescharacteristic, complemented, Sylow
338C23×C4—611no—
339C23×C4—1221no—
340C23×C4—1221no—
341C22×C8—611no—
342C22×C8—611no—
343C22×C8—611no—
344C22×C8—611no—
345C22×C8—611no—
346C22×C8—612no—
347C22×C8—1224no—
348C22×C8C2×#692311yescharacteristic
349#117—2444no—
350C2×C4⋊C4—611no—
351C2×C4⋊C4—611no—
352C2×C4⋊C4—611no—
353C2×C4⋊C4—611no—
354C2×C4⋊C4—611no—
355C2×C4⋊C4—611no—
356C2×C4⋊C4—611no—
357C2×C4⋊C4—611no—
358C2×C4⋊C4—611no—
359C2×C4⋊C4—611no—
360C2×C4⋊C4—612no—
361C2×C4⋊C4—612no—
362C2×C4⋊C4—1221no—
363C2×C4⋊C4—1221no—
364C2×C4⋊C4—1221no—
365C2×C4⋊C4—1221no—
366C2×C4⋊C4—1221no—
367C2×C4⋊C4—1221no—
368C2×C4⋊C4—1222no—
369C2×C4⋊C4—1222no—
370C2×C4⋊C4C2×#692311yescharacteristic
371C2×C4⋊C4C2×#692311yescharacteristic
372C2×C22⋊C4—611no—
373C2×C22⋊C4—611no—
374C2×C22⋊C4—1221no—
375C2×C22⋊C4—1221no—
376C2×C42—612no—
377C2×C42—1222no—
378C2×C42—1222no—
379#107—1224no—
380#106—611no—
381#106—611no—
382#106—611no—
383#106—611no—
384#106—611no—
385#106—611no—
386#106—611no—
387#106—611no—
388#106—611no—
389#106—611no—
390#106—611no—
391#106—611no—
392#106C2×#692311yescharacteristic
393#106C2×#692311yescharacteristic
394#106C2×#692311yescharacteristic
395#106C2×#692311yescharacteristic
396C22⋊C8—1221no—
397C22⋊C8—1221no—
398#97—1224no—
399#95—612no—
400#95—1222no—
401#95—1222no—
402#95—1222no—
403#95—1221no—
404#95—1221no—
405#95—1222no—
406C24—611no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—611no—
410C22×C4—611no—
411C22×C4—611no—
412C22×C4—611no—
413C22×C4—611no—
414C22×C4—612no—
415C22×C4—612no—
416C22×C4—1222no—
417C22×C4—1222no—
418C22×C4—1221no—
419C22×C4—1221no—
420C22×C4—1221no—
421C22×C4—1221no—
422C22×C4—1221no—
423C22×C4—1221no—
424C22×C4—1221no—
425C22×C4—1221no—
426C22×C4—1221no—
427C22×C4—1221no—
428C22×C4—1222no—
429C22×C4—1222no—
430C22×C4—4882no—
431C22×C4—2442no—
432C22×C4—2442no—
433C22×C4C22×#692311yescharacteristic
434C2×C8—22no—
435C2×C8—611no—
436C2×C8—614no—
437C2×C8—611no—
438C2×C8—1222no—
439C2×C8—1222no—
440C2×C8—1222no—
441C2×C8—1222no—
442C2×C8—1222no—
443C2×C8—1222no—
444C2×C8—1222no—
445C2×C8C22×#692311yescharacteristic
446C2×C8C22×#692311yescharacteristic
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—611no—
450C4⋊C4—611no—
451C4⋊C4—611no—
452C4⋊C4—611no—
453C4⋊C4—1221no—
454C4⋊C4—1221no—
455C4⋊C4—1221no—
456C4⋊C4—1221no—
457C4⋊C4—1221no—
458C4⋊C4—1221no—
459C4⋊C4—1221no—
460C4⋊C4—1221no—
461C4⋊C4—1222no—
462C4⋊C4—1222no—
463C4⋊C4—1222no—
464C4⋊C4—1222no—
465C4⋊C4—1221no—
466C4⋊C4—1221no—
467C4⋊C4—4882no—
468C4⋊C4—2444no—
469C4⋊C4C22×#692311yescharacteristic
470C4⋊C4C22×#692311yescharacteristic
471C4⋊C4C22×#692311yescharacteristic
472C4⋊C4C22×#692311yescharacteristic
473C22⋊C4—1222no—
474C22⋊C4—1222no—
475C22⋊C4—2442no—
476C22⋊C4—2442no—
477C42—1222no—
478C42—1222no—
479C42—4882no—
480C42—2444no—
481C23—611no—
482C23—612no—
483C23—612no—
484C23—611no—
485C23—1222no—
486C23—1222no—
487C23D4×#692311yescharacteristic
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—42no—
495C2×C4—81no—
496C2×C4—611no—
497C2×C4—612no—
498C2×C4—612no—
499C2×C4—611no—
500C2×C4—1222no—
501C2×C4—1222no—
502C2×C4—1222no—
503C2×C4—1221no—
504C2×C4—1221no—
505C2×C4—1222no—
506C2×C4—1222no—
507C2×C4—1222no—
508C2×C4—1222no—
509C2×C4—1222no—
510C2×C4—1222no—
511C2×C4—1221no—
512C2×C4—1221no—
513C2×C4—1221no—
514C2×C4—1221no—
515C2×C4—4881no—
516C2×C4—4881no—
517C2×C4—4881no—
518C2×C4—2442no—
519C2×C4—2441no—
520C2×C4—2442no—
521C2×C4—2441no—
522C2×C4—2441no—
523C2×C4—2441no—
524C2×C4—2442no—
525C2×C4—2442no—
526C2×C4—2442no—
527C2×C4—2442no—
528C2×C4—2442no—
529C2×C4—2442no—
530C2×C4—2442no—
531C2×C4—2442no—
532C2×C4—2442no—
533C2×C4D4×#692311yescharacteristic
534C2×C4C23×#692311yescharacteristic
535C8—21no—
536C8—612no—
537C8—1221no—
538C8—2442no—
539C8#1451985612yescomplemented
540C22—21no—
541C22—21no—
542C22—611no—
543C22—611no—
544C22—612no—
545C22—612no—
546C22—612no—
547C22—1224no—
548C22—1224no—
549C22—1221no—
550C22—1221no—
551C22#1684080112yes—
552C22C2×D4×#692311yescharacteristic
553C4—21no—
554C4—41no—
555C4—41no—
556C4—41no—
557C4—41no—
558C4—612no—
559C4—1221no—
560C4—4882no—
561C4—4882no—
562C4—2442no—
563C4—2442no—
564C4—2441no—
565C4—2441no—
566C4—2441no—
567C4—2441no—
568C4C2×#1451985611yescharacteristic
569C4#1684083011yescharacteristic
570C2—22no—
571C2—612no—
572C2—612no—
573C2—1222no—
574C2#2146232711yescharacteristic
575C2C2×#1684080111yescharacteristic
576C2#2146257911yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×#106×C61C4
socleC22×C61C2×C4×D4
prime radicalC23×D61C2×D4
cosocleC2×C4×D61C24
hypercenterC2×#106#6923
hypocenterC61#22615
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
3. #21461925C2semidirect
4. #21461882C2semidirect
5. #21461881C2semidirect
9. #21461635C2semidirect
37. C2×#14519709C4semidirect
38. C2×#14519708C4semidirect
39. C2×#14519708C4semidirect
40. #106×D61C4semidirect
41. #106×D61C4semidirect
42. #106×D61C4semidirect
43. #106×D61C4semidirect
48. C2×#106×C61C4semidirect
248. C8×C61#117semidirect
250. #92418#117semidirect
316. C2×#106#6923semidirect
337. C61#22615semidirect
539. C8#14519856semidirect

Maximal subgroups

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

subgroupindex
#214623282
#214623272
#214619252
#214618822
#214618812
#214617232
#214617222
#214616962
#214616352
#214615552
C2×#106×D612
#2261561