Finite Group Databasebeta

← #30600690

Subgroups — #30600690

Order 15616.

566 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 90 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
1#21462328C211yesmaximal, characteristic, complemented
2#21461958C211yesmaximal, characteristic
3#21461723C211yesmaximal, characteristic, complemented
4#21461255C211yesmaximal, characteristic
5#21460682C211yesmaximal, characteristic, complemented
6#21460661C211yesmaximal, characteristic, complemented
7C2×#16840079C211yesmaximal, characteristic
8C2×#14519835—21no—
9C2×#14519835—21no—
10D61⋊(C22⋊C8)C2211yescharacteristic
11#16840713—21no—
12#16840711—22no—
13#16840704—21no—
14#16840704C2211yescharacteristic
15#16840704C2211yescharacteristic
16C4⋊C4×#6923—21no—
17C4×C22⋊#6923—21no—
18C4×C22⋊#6923C2211yescharacteristic
19#16840635—21no—
20#16840635—21no—
21#16840613—22no—
22C2×#14519748C2211yescharacteristic
23C2×C4⋊C4×D61C2211yescharacteristic
24#16840079—21no—
25#16840079—21no—
26#16840079—21no—
27#16840079—21no—
28C2×#14519709C411yescharacteristic, complemented
29C2×#14519708C411yescharacteristic, complemented
30C2×#14519698C411yescharacteristic, complemented
31C2×#14519689C2211yescharacteristic
32C2×#102×C61C411yescharacteristic, complemented
33C2×D61⋊C8—21no—
34C2×C4⋊#6923—21no—
35C2×C4⋊#6923—21no—
36C2×C4⋊#6923—22no—
37C2×C22⋊#6923—21no—
38C2×C22⋊#6923—21no—
39C2×C22⋊#6923D411yescharacteristic
40C2×C22⋊#6923D411yescharacteristic
41C2×C4×#6923—21no—
42C2×C4×#6923—22no—
43#14519835—42no—
44#14519835—42no—
45#14519834—21no—
46C22⋊#92420—21no—
47(C2×#6923)⋊C4—22no—
48(C2×#6923)⋊C4—22no—
49(C2×#6923)⋊C4—21no—
50(C2×#6923)⋊C4—21no—
51(C2×#6923)⋊C4D412yes—
52C22×C22⋊D61—21no—
53C22×C4×D61—21no—
54C22×C4×D61C2311yescharacteristic
55C22×#92418C2×C411yescharacteristic
56#14519748—21no—
57#14519748—21no—
58#14519748—21no—
59#14519748—21no—
60C2×C4⋊Dic61C2×C411yescharacteristic
61C2×C4⋊Dic61C2×C411yescharacteristic
62C2×#11758196—21no—
63C4⋊C4×D61—21no—
64C4⋊C4×D61—21no—
65C4⋊C4×D61D411yescharacteristic
66C4⋊C4×D61D411yescharacteristic
67C4⋊C4×D61D411yescharacteristic
68C4⋊C4×D61D411yescharacteristic
69C2×C22⋊Dic61—21no—
70#14519709—21no—
71#14519709—21no—
72#14519708—21no—
73#14519708—21no—
74#14519698—21no—
75#14519698—21no—
76#14519689—21no—
77#14519689—21no—
78C22×D4×C61C2×C411yescharacteristic
79C22×C8×C61C2×C411yescharacteristic
80C2×C4⋊C4×C61C2×C411yescharacteristic
81#102×C61—21no—
82#102×C61—21no—
83C24×C61—21no—
84C23×D61C2×D411yescharacteristic
85C22×#6923—21no—
86C22×#6923—21no—
87C22×#6923—22no—
88C22×#6923—41no—
89C2×D4×C61—21no—
90C2×D4×C61—21no—
91C2×D4×C61—41no—
92C2×D4×C61—41no—
93C22×C4×C61—21no—
94C22×C4×C61C22×C411yescharacteristic
95C2×C22⋊D61—41no—
96C2×C22⋊D61—41no—
97C2×C22⋊D61—41no—
98C2×C22⋊D61—41no—
99C2×C22⋊D61—41no—
100C2×C22⋊D61—41no—
101C22×Dic61—21no—
102C22×Dic61—21no—
103C22×Dic61#4111yescharacteristic
104C2×C4×D61—21no—
105C2×C4×D61—21no—
106C2×C4×D61—21no—
107C2×C4×D61—21no—
108C2×C4×D61—41no—
109C2×C4×D61—41no—
110C2×C4×D61—82no—
111C2×C4×D61C2×D411yescharacteristic
112C2×C4×D61C2×D411yescharacteristic
113C2×C4×D61C2×D411yescharacteristic
114C2×C4×D61#4111yescharacteristic
115C22⋊#6923—21no—
116C22⋊#6923—21no—
117C22⋊#6923—21no—
118C22⋊#6923—41no—
119C22⋊#6923—41no—
120C22⋊#6923—41no—
121C22⋊#6923—41no—
122C22⋊#6923SD1612yes—
123C2×#92420—41no—
124C4⋊#6923—41no—
125C4⋊#6923—41no—
126C4⋊#6923—41no—
127C4⋊#6923—41no—
128C4⋊#6923—82no—
129C4×#6923—41no—
130C4×#6923—41no—
131C4×#6923—82no—
132D61⋊C8—41no—
133D61⋊C8—41no—
134C2×C8×C61—21no—
135C2×C8×C61—41no—
136C4⋊C4×C61—21no—
137C4⋊C4×C61C22⋊C411yescharacteristic
138C4⋊C4×C61C22⋊C411yescharacteristic
139C22⋊Dic61—41no—
140C22⋊Dic61—41no—
141C4⋊Dic61—21no—
142C4⋊Dic61—21no—
143C4⋊Dic61—21no—
144C4⋊Dic61C22⋊C411yescharacteristic
145C4⋊Dic61C22⋊C411yescharacteristic
146#11758196—21no—
147#11758196—21no—
148#11758196—21no—
149#11758196—21no—
150C2×#92418—21no—
151C2×#92418—41no—
152C23×C61—41no—
153C23×C61—41no—
154C23×C61—41no—
155C23×C61—81no—
156C23×C61—81no—
157C23×C61C4×D411yescharacteristic
158C22×D61—41no—
159C22×D61—41no—
160C22×D61#12011yescharacteristic
161C22×D61#12111yescharacteristic
162C22×D61C2×SD1611yescharacteristic
163C22×D61#13511yescharacteristic
164C22×D61AGL(1,ℤ/8)11yescharacteristic
165C22×D61#13711yescharacteristic
166C2×#6923—22no—
167C2×#6923—41no—
168C2×#6923—41no—
169C2×#6923—41no—
170C2×#6923—42no—
171C2×#6923—42no—
172C2×#6923—41no—
173C2×#6923—41no—
174C2×#6923—42no—
175C2×#6923—81no—
176C2×#6923—81no—
177C2×#6923—81no—
178D4×C61—41no—
179D4×C61—41no—
180D4×C61—81no—
181C2×C4×C61—21no—
182C2×C4×C61—21no—
183C2×C4×C61—21no—
184C2×C4×C61—21no—
185C2×C4×C61—81no—
186C2×C4×C61C2×C22⋊C411yescharacteristic
187C2×C4×C61C4×D411yescharacteristic
188C22⋊D61—81no—
189C22⋊D61—81no—
190C22⋊D61—81no—
191C22⋊D61—81no—
192C2×Dic61—21no—
193C2×Dic61—21no—
194C2×Dic61—41no—
195C2×Dic61—41no—
196C2×Dic61—41no—
197C2×Dic61—41no—
198C2×Dic61—81no—
199C2×Dic61#12111yescharacteristic
200C2×Dic61#12311yescharacteristic
201C4×D61—21no—
202C4×D61—21no—
203C4×D61—21no—
204C4×D61—21no—
205C4×D61—41no—
206C4×D61—41no—
207C4×D61—42no—
208C4×D61—42no—
209C4×D61—81no—
210C4×D61—81no—
211#92420—81no—
212C8×C61—41no—
213#92418—41no—
214#9261—611nomaximal, Sylow
215C22×C61—21no—
216C22×C61—21no—
217C22×C61—81no—
218C22×C61—81no—
219C22×C61—81no—
220C22×C61—161no—
221C22×C61—161no—
222C22×C61#38611yescharacteristic
223C22×C61C4×SD1611yescharacteristic
224C22×C61#44011yescharacteristic
225C2×D61—21no—
226C2×D61—21no—
227C2×D61—21no—
228C2×D61—21no—
229C2×D61—41no—
230C2×D61—41no—
231C2×D61—41no—
232C2×D61—41no—
233C2×D61#44811yescharacteristic
234C2×D61#44911yescharacteristic
235C2×D61#46011yescharacteristic
236C2×D61#46411yescharacteristic
237#6923—42no—
238#6923—81no—
239#6923—82no—
240#6923—161no—
241C4×C61—21no—
242C4×C61—41no—
243C4×C61—41no—
244C4×C61#41011yescharacteristic
245C4×C61#41011yescharacteristic
246Dic61—21no—
247Dic61—21no—
248Dic61—41no—
249Dic61—41no—
250Dic61—81no—
251C2×#481—611no—
252#2345—611no—
253#1964—611no—
254#1824—611no—
255#1519—611no—
256#1289—611no—
257#1282—611no—
258C2×C61—21no—
259C2×C61—21no—
260C2×C61—161no—
261C2×C61#188011yescharacteristic
262C2×C61#189911yescharacteristic
263C2×C61#190411yescharacteristic
264D61—21no—
265D61—21no—
266D61—21no—
267D61—21no—
268C2×#121—611no—
269C22×C4⋊C4—611no—
270#481—1221no—
271#481—1221no—
272#481—1221no—
273#481—1221no—
274C2×#106—611no—
275C2×#106—611no—
276C2×#102—611no—
277C2×#102#692311yescharacteristic, complemented
278C2×#99—1221no—
279C2×#99—1221no—
280C2×C22⋊C8—611no—
281C2×C22⋊C8—611no—
282#389—1221no—
283#387—1222no—
284#380—611no—
285#380—611no—
286#380—1221no—
287C4×C4⋊C4—1221no—
288C4×C22⋊C4—611no—
289C4×C22⋊C4—1221no—
290#340—1221no—
291#340—1221no—
292#327—1222no—
293C61#926111yescharacteristic, complemented, Sylow
294C22×D4—1221no—
295C22×D4C2×#692311yescharacteristic
296C23×C4—611no—
297C23×C4—1221no—
298C22×C8—611no—
299C22×C8—1221no—
300C22×C8C2×#692311yescharacteristic
301#121—1221no—
302#121—1221no—
303#121—1221no—
304#121—1221no—
305C2×C4⋊C4—611no—
306C2×C4⋊C4—611no—
307C2×C4⋊C4—611no—
308C2×C4⋊C4—611no—
309C2×C4⋊C4—611no—
310C2×C4⋊C4—611no—
311C2×C4⋊C4—1221no—
312C2×C4⋊C4—1221no—
313C2×C4⋊C4—1221no—
314C2×C4⋊C4—1222no—
315C2×C4⋊C4—1221no—
316C2×C4⋊C4—1221no—
317C2×C4⋊C4C2×#692311yescharacteristic
318C2×C22⋊C4—611no—
319C2×C22⋊C4—611no—
320C2×C22⋊C4—1221no—
321C2×C22⋊C4—1221no—
322C2×C22⋊C4—1221no—
323C2×C42—1222no—
324C2×C42—1221no—
325#106—1221no—
326#106—1221no—
327#106—1221no—
328#106—1221no—
329#102—21no—
330#102—21no—
331#102—1221no—
332#102—1221no—
333#99—2442no—
334#99—2442no—
335C22⋊C8—1221no—
336C22⋊C8—1221no—
337C22⋊C8—1221no—
338C22⋊C8—1221no—
339#95—612no—
340#95—1221no—
341#95—1221no—
342#95—1222no—
343#95—1222no—
344C24—21no—
345C24—611no—
346C2×D4—21no—
347C2×D4—21no—
348C2×D4—41no—
349C2×D4—41no—
350C2×D4—2441no—
351C2×D4—2441no—
352C2×D4—2441no—
353C2×D4—2441no—
354C2×D4—2441no—
355C2×D4—2441no—
356C22×C4—21no—
357C22×C4—611no—
358C22×C4—611no—
359C22×C4—611no—
360C22×C4—611no—
361C22×C4—611no—
362C22×C4—1221no—
363C22×C4—1221no—
364C22×C4—1221no—
365C22×C4—1221no—
366C22×C4—1221no—
367C22×C4—1221no—
368C22×C4—1222no—
369C22×C4—1221no—
370C22×C4—1221no—
371C22×C4—4882no—
372C22×C4—2441no—
373C22×C4—2441no—
374C22×C4—2441no—
375C22×C4C22×#692311yescharacteristic
376C2×C8—21no—
377C2×C8—41no—
378C2×C8—1221no—
379C2×C8—2441no—
380C2×C8—2441no—
381C2×C8—2441no—
382C2×C8—2441no—
383C4⋊C4—21no—
384C4⋊C4—611no—
385C4⋊C4—611no—
386C4⋊C4—1221no—
387C4⋊C4—1221no—
388C4⋊C4—1221no—
389C4⋊C4—1221no—
390C4⋊C4—1221no—
391C4⋊C4—1221no—
392C4⋊C4—1221no—
393C4⋊C4—4882no—
394C4⋊C4—2441no—
395C4⋊C4—2441no—
396C4⋊C4—2441no—
397C4⋊C4—2441no—
398C4⋊C4C22⋊#692311yescharacteristic
399C4⋊C4C22⋊#692311yescharacteristic
400C22⋊C4—612no—
401C22⋊C4—1221no—
402C22⋊C4—1221no—
403C22⋊C4—1221no—
404C22⋊C4—2441no—
405C22⋊C4—2441no—
406C22⋊C4—2441no—
407C22⋊C4—2441no—
408C22⋊C4—2441no—
409C22⋊C4—2441no—
410C42—4882no—
411C42—2441no—
412C42—2441no—
413C23—41no—
414C23—41no—
415C23—41no—
416C23—81no—
417C23—81no—
418C23—611no—
419C23—611no—
420C23—611no—
421C23—611no—
422C23—611no—
423C23—611no—
424C23—2441no—
425C23—2441no—
426C23D4×#692311yescharacteristic
427D4—41no—
428D4—41no—
429D4—81no—
430D4—4881no—
431D4—4881no—
432D4—4881no—
433D4—4881no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—81no—
439C2×C4—611no—
440C2×C4—611no—
441C2×C4—1221no—
442C2×C4—1221no—
443C2×C4—1221no—
444C2×C4—1221no—
445C2×C4—1222no—
446C2×C4—1221no—
447C2×C4—1221no—
448C2×C4—4881no—
449C2×C4—4881no—
450C2×C4—4881no—
451C2×C4—4881no—
452C2×C4—4881no—
453C2×C4—4881no—
454C2×C4—2441no—
455C2×C4—2441no—
456C2×C4—2442no—
457C2×C4—2442no—
458C2×C4—2441no—
459C2×C4—2441no—
460C2×C4—2442no—
461C2×C4—2442no—
462C2×C4—2441no—
463C2×C4—2441no—
464C2×C4—2442no—
465C2×C4—2441no—
466C2×C4—2441no—
467C2×C4—2441no—
468C2×C4—2441no—
469C2×C4—2441no—
470C2×C4C2×C22⋊#692311yescharacteristic
471C2×C4D4×#692311yescharacteristic
472C8—41no—
473C8—4881no—
474C8—2441no—
475C22—21no—
476C22—21no—
477C22—81no—
478C22—81no—
479C22—81no—
480C22—161no—
481C22—161no—
482C22—611no—
483C22—611no—
484C22—611no—
485C22—611no—
486C22—1221no—
487C22—1221no—
488C22—1221no—
489C22—1221no—
490C22—2441no—
491C22—2441no—
492C22—2441no—
493C22—2441no—
494C22#1684071011yescharacteristic
495C22SD16×#692311yescharacteristic
496C22#1684080111yescharacteristic
497C4—21no—
498C4—41no—
499C4—41no—
500C4—1221no—
501C4—1221no—
502C4—9761no—
503C4—4881no—
504C4—4882no—
505C4—4881no—
506C4—2442no—
507C4—2441no—
508C4—2441no—
509C4#1684074111yescharacteristic
510C4#1684074211yescharacteristic
511C2—21no—
512C2—21no—
513C2—161no—
514C2—1221no—
515C2—1221no—
516C2—1221no—
517C2—1221no—
518C2#2146181511yescharacteristic
519C2#2146184211yescharacteristic
520C2#2146185311yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#102×C61C4
socleC22×C61#386
prime radicalC2×#14519748C22
cosocleC22×C4×D61C23
hypercenterC2×#102#6923
hypocenterC61#9261
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. #21462328C2semidirect
3. #21461723C2semidirect
5. #21460682C2semidirect
6. #21460661C2semidirect
28. C2×#14519709C4semidirect
29. C2×#14519708C4semidirect
30. C2×#14519698C4semidirect
32. C2×#102×C61C4semidirect
277. C2×#102#6923semidirect
293. C61#9261semidirect

Maximal subgroups

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

subgroupindex
#214623282
#214619582
#214617232
#214612552
#214606822
#214606612
C2×#168400792
#926161