Finite Group Databasebeta

← #30610236

Subgroups — #30610236

Order 15616.

1012 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462673C211yesmaximal, characteristic, complemented
2#21462672C211yesmaximal, characteristic, complemented
3#21461096C212yesmaximal, complemented
4#21461095C212yesmaximal, complemented
5#21461086C212yesmaximal, complemented
6#21461085C212yesmaximal, complemented
7#21461078C212yesmaximal, complemented
8#21461073C212yesmaximal, complemented
9C2×#16840364C211yesmaximal, characteristic
10#16840794—24no—
11#16840791—24no—
12#16840783C2212yes—
13#16840783C2212yes—
14#16840733C2212yes—
15#16840732C2212yes—
16D61⋊(C22⋊C8)C2212yes—
17C2×C22⋊#92420C2212yes—
18#16840607C2214yes—
19#16840606C2214yes—
20#16840606C2214yes—
21#16840605C2214yes—
22#16840364—24no—
23#16840364—24no—
24C2×#14519773C411yescharacteristic
25C2×#14519767C411yescharacteristic
26C2×#14519762C411yescharacteristic
27C2×#14519761C2211yescharacteristic
28C2×#14519759C2211yescharacteristic
29C2×#14519752C2211yescharacteristic
30C2×#14519751C411yescharacteristic
31C2×#14519750C411yescharacteristic
32C2×#14519750C411yescharacteristic
33C2×#14519750C411yescharacteristic
34C2×#14519749C2211yescharacteristic
35C2×C4×C22⋊D61C2211yescharacteristic
36C2×#14519737C2211yescharacteristic
37C2×#14519735C2211yescharacteristic
38C2×#123×C61C411yescharacteristic
39C2×#11758213—22no—
40C2×#11758217—22no—
41C2×D61⋊C8—22no—
42C22×#92420—22no—
43C4⋊#92420—22no—
44C4⋊#92420—22no—
45#14519834—22no—
46#14519834—22no—
47C22⋊#92420—22no—
48C22⋊#92420—22no—
49C22⋊#92420C2314yes—
50C22⋊#92420C2314yes—
51#14519832—22no—
52#14519832—22no—
53C22×D244C2×C411yescharacteristic
54C22×D244C2×C411yescharacteristic
55C22×D244C2×C411yescharacteristic
56C22×C22⋊D61C2×C411yescharacteristic
57C22×C22⋊D61C2×C411yescharacteristic
58C22×C22⋊D61C2×C411yescharacteristic
59C22×C22⋊D61C2×C411yescharacteristic
60C22×C22⋊D61C2×C411yescharacteristic
61C22×C22⋊D61C2×C411yescharacteristic
62C23×Dic61C2311yescharacteristic
63C22×C4×D61C2×C411yescharacteristic
64C22×C4×D61C2×C411yescharacteristic
65C22×C4×D61C2311yescharacteristic
66#14519773—24no—
67#14519767—24no—
68#14519762—24no—
69#14519761—22no—
70#14519761—22no—
71#14519759—22no—
72#14519759—22no—
73#14519752—22no—
74#14519752—22no—
75#14519751—24no—
76#14519750—24no—
77#14519750—24no—
78#14519750—24no—
79#14519749—22no—
80#14519749—22no—
81C4×C22⋊D61—22no—
82C4×C22⋊D61—22no—
83#14519737D414yes—
84#14519737D414yes—
85#14519735—22no—
86#14519735—22no—
87C2×C4⋊Dic61C2×C411yescharacteristic
88C2×C4⋊Dic61C2311yescharacteristic
89C2×#11758196C2×C411yescharacteristic
90C2×#11758196C2×C411yescharacteristic
91C2×#11758196C2×C411yescharacteristic
92C2×#11758196C2×C411yescharacteristic
93C2×C22⋊Dic61C2311yescharacteristic
94C2×#11758198C2×C411yescharacteristic
95C2×#11758198C2×C411yescharacteristic
96C2×#11758198C2×C411yescharacteristic
97C2×#11758198C2×C411yescharacteristic
98C2×#11758198C2311yescharacteristic
99C2×#11758198C2311yescharacteristic
100C2×C4×Dic61C2×C411yescharacteristic
101C2×C4×Dic61C2311yescharacteristic
102C22×D4×C61C2×C411yescharacteristic
103C23×C4×C61C2×C411yescharacteristic
104#123×C61—24no—
105C2×C4⋊C4×C61C2×C411yescharacteristic
106C2×C4⋊C4×C61C2×C411yescharacteristic
107C2×C22⋊C4×C61C2×C411yescharacteristic
108C2×C22⋊C4×C61C2×C411yescharacteristic
109C2×C22⋊C4×C61C2×C411yescharacteristic
110C24×C61C22×C411yescharacteristic
111C24×C61C22×C411yescharacteristic
112C23×D61C22×C411yescharacteristic
113C23×D61C22×C411yescharacteristic
114C23×D61C22×C411yescharacteristic
115C2×D4×C61—22no—
116C2×D4×C61—81no—
117C22×C4×C61—22no—
118C22×C4×C61—81no—
119C22×C4×C61C22×C411yescharacteristic
120C22×C4×C61C22×C411yescharacteristic
121C22×C4×C61C22×C411yescharacteristic
122C22×C4×C61C22×C411yescharacteristic
123C22×C4×C61C22×C411yescharacteristic
124C2×C22⋊D61—22no—
125C2×C22⋊D61—22no—
126C2×C22⋊D61—22no—
127C2×C22⋊D61—22no—
128C2×C22⋊D61—22no—
129C2×C22⋊D61—42no—
130C2×C22⋊D61—42no—
131C2×C22⋊D61—81no—
132C2×C22⋊D61—81no—
133C2×C22⋊D61—81no—
134C2×C22⋊D61—81no—
135C2×C22⋊D61C22⋊C414yes—
136C22×Dic61—81no—
137C22×Dic61C22×C411yescharacteristic
138C22×Dic61C22×C411yescharacteristic
139C22×Dic61C22×C411yescharacteristic
140C22×Dic61C22×C411yescharacteristic
141C22×Dic61C2×D412yes—
142C22×Dic61C2×D412yes—
143C22×Dic61C2411yescharacteristic
144C2×D244—22no—
145C2×D244—22no—
146C2×D244—22no—
147C2×D244—81no—
148C2×D244—81no—
149C2×D244—81no—
150C2×C4×D61—22no—
151C2×C4×D61—22no—
152C2×C4×D61—42no—
153C2×C4×D61—81no—
154C2×C4×D61—81no—
155C2×C4×D61C2×D412yes—
156C2×C4×D61C2×D412yes—
157#11758217—82no—
158C2×#92420—24no—
159C2×#92420—24no—
160C2×#92420—82no—
161#11758213—82no—
162D61⋊C8—82no—
163C4⋊C4×C61—22no—
164C4⋊C4×C61—22no—
165C22⋊C4×C61—22no—
166C22⋊C4×C61—22no—
167C22⋊C4×C61C22⋊C414yes—
168C22⋊Dic61—21no—
169C22⋊Dic61—21no—
170#11758198—22no—
171#11758198—22no—
172#11758198—22no—
173#11758198—21no—
174#11758198—21no—
175#11758198—21no—
176#11758198—21no—
177#11758198C22⋊C414yes—
178C4⋊Dic61—22no—
179C4⋊Dic61—21no—
180C4⋊Dic61—21no—
181#11758196—22no—
182#11758196—22no—
183#11758196—22no—
184#11758196C22⋊C414yes—
185C4×Dic61—22no—
186C4×Dic61C2×D412yes—
187C4×Dic61C2×D412yes—
188C23×C61—22no—
189C23×C61—21no—
190C23×C61—22no—
191C23×C61—41no—
192C23×C61—41no—
193C23×C61—41no—
194C23×C61—41no—
195C23×C61C2×C22⋊C412yes—
196C23×C61C23×C411yescharacteristic
197C22×D61—22no—
198C22×D61—21no—
199C22×D61—21no—
200C22×D61—22no—
201C22×D61—22no—
202C22×D61—41no—
203C22×D61—41no—
204C22×D61—41no—
205C22×D61—41no—
206C22×D61—41no—
207C22×D61—41no—
208C22×D61C2×C22⋊C412yes—
209D4×C61—82no—
210C2×C4×C61—21no—
211C2×C4×C61—21no—
212C2×C4×C61—21no—
213C2×C4×C61—22no—
214C2×C4×C61—41no—
215C2×C4×C61—41no—
216C2×C4×C61—41no—
217C2×C4×C61—41no—
218C2×C4×C61—82no—
219C2×C4×C61C2×C22⋊C412yes—
220C2×C4×C61C2×C22⋊C412yes—
221C22⋊D61—44no—
222C22⋊D61—44no—
223C22⋊D61—82no—
224C22⋊D61—82no—
225C22⋊D61—82no—
226C22⋊D61—82no—
227C2×Dic61—22no—
228C2×Dic61—21no—
229C2×Dic61—21no—
230C2×Dic61—42no—
231C2×Dic61—42no—
232C2×Dic61—41no—
233C2×Dic61—41no—
234C2×Dic61—41no—
235C2×Dic61—41no—
236C2×Dic61C2×C22⋊C412yes—
237C2×Dic61C2×C22⋊C412yes—
238C2×Dic61C22×D411yescharacteristic
239C2×Dic61C22×D411yescharacteristic
240D244—82no—
241D244—82no—
242D244—82no—
243C4×D61—42no—
244C4×D61—42no—
245C4×D61—44no—
246C4×D61—82no—
247#92420—44no—
248#92420—44no—
249#17408—611nomaximal, Sylow
250C22×C61—21no—
251C22×C61—21no—
252C22×C61—22no—
253C22×C61—22no—
254C22×C61—22no—
255C22×C61—41no—
256C22×C61—41no—
257C22×C61—41no—
258C22×C61—82no—
259C22×C61—82no—
260C22×C61C22×C22⋊C411yescharacteristic
261C22×C61#56812yes—
262C2×D61—22no—
263C2×D61—22no—
264C2×D61—22no—
265C2×D61—41no—
266C2×D61—41no—
267C2×D61—41no—
268C2×D61—41no—
269C2×D61—41no—
270C2×D61—41no—
271C2×D61—82no—
272C2×D61—82no—
273C2×D61—82no—
274C4×C61—22no—
275C4×C61—22no—
276C4×C61—41no—
277C4×C61—41no—
278C4×C61—41no—
279Dic61—22no—
280Dic61—21no—
281Dic61—21no—
282Dic61—22no—
283Dic61—41no—
284Dic61—41no—
285C2×#540—611no—
286#2973—611no—
287#2973—611no—
288#1471—612no—
289#1471—612no—
290#1468—612no—
291#1468—612no—
292#1466—612no—
293#1464—612no—
294C2×C61—22no—
295C2×C61—42no—
296C2×C61—81no—
297C2×C61#287911yescharacteristic
298C2×C61#288311yescharacteristic
299C2×C61#288811yescharacteristic
300D61—42no—
301D61—81no—
302D61—81no—
303#540—1224no—
304#540—1224no—
305C2×#127—611no—
306C2×#125—611no—
307C2×#123—611no—
308C2×#123—611no—
309C2×#123—611no—
310C2×#123#692311yescharacteristic
311C2×#121—611no—
312C2×#121—611no—
313C2×#121—611no—
314C2×#121—611no—
315C2×#121—611no—
316C2×#121—611no—
317C2×C4×D4—611no—
318C2×C4×D4—611no—
319C2×#117—611no—
320#435—1224no—
321#435—1224no—
322#432—612no—
323#432—612no—
324#407—612no—
325#407—612no—
326C2×C22⋊C8—612no—
327C2×C22⋊C8—612no—
328#324—614no—
329#323—614no—
330#323—614no—
331#323—614no—
332C61#1740811yescharacteristic, complemented, Sylow
333C22×D4—611no—
334C22×D4—611no—
335C22×D4—611no—
336C22×D4—611no—
337C22×D4—611no—
338C22×D4—611no—
339C22×D4—611no—
340C22×D4—611no—
341C22×D4—611no—
342C22×D4C2×#692311yescharacteristic
343C23×C4—611no—
344C23×C4—611no—
345C23×C4—611no—
346C23×C4—611no—
347C23×C4C2×#692311yescharacteristic
348C2×M16—1222no—
349C2×M16—1222no—
350C22×C8—1222no—
351C22×C8—1222no—
352#127—1224no—
353#125—1224no—
354#123—24no—
355#123—1222no—
356#123—1222no—
357#123—1222no—
358#123—1222no—
359#123—1224no—
360#121—1224no—
361#121—1224no—
362#121—1224no—
363#121—1222no—
364#121—1222no—
365#121—1222no—
366#121—1222no—
367#121—1224no—
368C4×D4—614no—
369C4×D4—614no—
370C4×D4—1222no—
371C4×D4—1222no—
372#117—1222no—
373#117—1222no—
374C2×C4⋊C4—611no—
375C2×C4⋊C4—611no—
376C2×C4⋊C4—611no—
377C2×C4⋊C4—611no—
378C2×C4⋊C4—611no—
379C2×C4⋊C4—611no—
380C2×C4⋊C4C2×#692311yescharacteristic
381C2×C4⋊C4C2×#692311yescharacteristic
382C2×C22⋊C4—611no—
383C2×C22⋊C4—611no—
384C2×C22⋊C4—611no—
385C2×C22⋊C4—611no—
386C2×C22⋊C4—611no—
387C2×C22⋊C4—611no—
388C2×C22⋊C4—611no—
389C2×C22⋊C4C2×#692311yescharacteristic
390C2×C22⋊C4C2×#692311yescharacteristic
391C2×C22⋊C4C2×#692311yescharacteristic
392C2×C42—611no—
393C2×C42—611no—
394C4⋊C8—1222no—
395C4⋊C8—1222no—
396C22⋊C8—614no—
397C22⋊C8—614no—
398C22⋊C8—1222no—
399C22⋊C8—1222no—
400C22⋊C8—1222no—
401C22⋊C8—1222no—
402#97—1222no—
403#97—1222no—
404C24—611no—
405C24—611no—
406C24—611no—
407C24C22×#692311yescharacteristic
408C24C22×#692311yescharacteristic
409C2×D4—22no—
410C2×D4—81no—
411C2×D4—614no—
412C2×D4—1222no—
413C2×D4—1222no—
414C2×D4—1222no—
415C2×D4—1222no—
416C2×D4—1222no—
417C2×D4—1222no—
418C2×D4—1222no—
419C2×D4—1222no—
420C2×D4—4881no—
421C2×D4—4881no—
422C2×D4—4881no—
423C2×D4—4881no—
424C2×D4—4881no—
425C2×D4—4881no—
426C2×D4—4881no—
427C2×D4—2442no—
428C2×D4—2442no—
429C22×C4—22no—
430C22×C4—81no—
431C22×C4—611no—
432C22×C4—612no—
433C22×C4—612no—
434C22×C4—611no—
435C22×C4—611no—
436C22×C4—612no—
437C22×C4—612no—
438C22×C4—611no—
439C22×C4—611no—
440C22×C4—1222no—
441C22×C4—1222no—
442C22×C4—4881no—
443C22×C4—4881no—
444C22×C4—4881no—
445C22×C4—2442no—
446C22×C4C22×#692311yescharacteristic
447C22×C4C22×#692311yescharacteristic
448C22×C4C22×#692311yescharacteristic
449C22×C4C22×#692311yescharacteristic
450C22×C4C22×#692311yescharacteristic
451M16—4882no—
452M16—4882no—
453C2×C8—1224no—
454C2×C8—1224no—
455C2×C8—4882no—
456C2×C8—4882no—
457C4⋊C4—22no—
458C4⋊C4—22no—
459C4⋊C4—614no—
460C4⋊C4—1222no—
461C4⋊C4—1222no—
462C4⋊C4—1221no—
463C4⋊C4—1221no—
464C4⋊C4—1222no—
465C4⋊C4—1222no—
466C22⋊C4—22no—
467C22⋊C4—22no—
468C22⋊C4—614no—
469C22⋊C4—1221no—
470C22⋊C4—1221no—
471C22⋊C4—1221no—
472C22⋊C4—1221no—
473C22⋊C4—1222no—
474C22⋊C4—1222no—
475C22⋊C4—1221no—
476C22⋊C4—1221no—
477C22⋊C4—1222no—
478C22⋊C4C22⋊#692314yes—
479C42—612no—
480C42—612no—
481C42—1222no—
482C23—22no—
483C23—21no—
484C23—22no—
485C23—41no—
486C23—41no—
487C23—41no—
488C23—41no—
489C23—612no—
490C23—1222no—
491C23—1222no—
492C23—1222no—
493C23—1221no—
494C23—1221no—
495C23—2441no—
496C23—2441no—
497C23—2441no—
498C23—2441no—
499C23—2441no—
500C23—2441no—
501C23C2×C22⋊#692312yes—
502C23C23×#692311yescharacteristic
503D4—82no—
504D4—4882no—
505D4—4882no—
506D4—4882no—
507D4—4882no—
508D4—4882no—
509D4—4882no—
510D4—4882no—
511D4—2444no—
512D4—2444no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—82no—
522C2×C4—612no—
523C2×C4—612no—
524C2×C4—611no—
525C2×C4—611no—
526C2×C4—1222no—
527C2×C4—1221no—
528C2×C4—1221no—
529C2×C4—4882no—
530C2×C4—2442no—
531C2×C4—2442no—
532C2×C4—2444no—
533C2×C4—2442no—
534C2×C4—2442no—
535C2×C4—2441no—
536C2×C4—2441no—
537C2×C4—2441no—
538C2×C4—2441no—
539C2×C4C2×C22⋊#692312yes—
540C2×C4C2×C22⋊#692312yes—
541C8—2444no—
542C8—2444no—
543C22—21no—
544C22—21no—
545C22—22no—
546C22—22no—
547C22—22no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—82no—
552C22—82no—
553C22—1222no—
554C22—1222no—
555C22—1222no—
556C22—4882no—
557C22—4882no—
558C22—4882no—
559C22—2441no—
560C22—2441no—
561C22—2441no—
562C22—2441no—
563C22—2441no—
564C22—2441no—
565C22C22×C22⋊#692311yescharacteristic
566C22#1684084112yes—
567C4—22no—
568C4—22no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—1222no—
573C4—1221no—
574C4—1221no—
575C4—1222no—
576C4—2441no—
577C4—2441no—
578C2—22no—
579C2—42no—
580C2—81no—
581C2—4881no—
582C2—4881no—
583C2—2442no—
584C2#2146240411yescharacteristic
585C2#2146241911yescharacteristic
586C2#2146242911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×#123×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840364C2
cosocleC22×Dic61C24
hypercenterC2×#123#6923
hypocenterC61#17408
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C22⋊C4 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. #21462673C2semidirect
2. #21462672C2semidirect
3. #21461096C2semidirect
4. #21461095C2semidirect
5. #21461086C2semidirect
6. #21461085C2semidirect
7. #21461078C2semidirect
8. #21461073C2semidirect
332. C61#17408semidirect

Maximal subgroups

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

subgroupindex
#214626732
#214626722
#214610962
#214610952
#214610862
#214610852
#214610782
#214610732
C2×#168403642
#1740861