Finite Group Databasebeta

← #30598220

Subgroups — #30598220

Order 15616.

908 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 908 conjugacy classes of subgroups — too many to draw. Only its 118 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#21461711C211yesmaximal, characteristic, complemented
2C2×#16840615C212yesmaximal, complemented
3C2×#16840614C212yesmaximal
4#21460995C211yesmaximal, characteristic, complemented
5C2×#16840297C211yesmaximal, characteristic
6C2×#14519834C2212yes—
7C2×(C2×#6923)⋊C4—21no—
8C2×(C2×#6923)⋊C4—21no—
9C2×(C2×#6923)⋊C4C2212yes—
10#16840628—21no—
11#16840628—21no—
12#16840615—24no—
13#16840614—24no—
14#16840297—24no—
15#16840297—24no—
16C2×#14519772—21no—
17C2×#14519765C411yescharacteristic, complemented
18C2×#14519762—21no—
19C2×#14519757C2211yescharacteristic
20C2×#14519752C2211yescharacteristic
21C2×#14519742C411yescharacteristic, complemented
22C2×#14519739—21no—
23C2×#14519739C411yescharacteristic, complemented
24C2×#14519735—21no—
25C2×C42×D61C2211yescharacteristic
26C2×#125×C61C411yescharacteristic, complemented
27C23×#6923—22no—
28C22×#92420—22no—
29#14519834—22no—
30#14519834—22no—
31(C2×#6923)⋊C4—24no—
32(C2×#6923)⋊C4—22no—
33(C2×#6923)⋊C4—22no—
34(C2×#6923)⋊C4—42no—
35C22×Dic122C2×C411yescharacteristic
36C22×D244—21no—
37C22×D244C2×C411yescharacteristic
38C22×C4×D61—21no—
39C22×C4×D61D411yescharacteristic
40C22×C4×D61D411yescharacteristic
41C22×C4×D61C2311yescharacteristic
42#14519772—28no—
43#14519765—22no—
44#14519765—22no—
45#14519762—28no—
46#14519757—22no—
47#14519757D414yes—
48#14519752—22no—
49#14519752D414yes—
50#14519742—22no—
51#14519742—22no—
52#14519739—28no—
53#14519739—22no—
54#14519739—22no—
55#14519735—28no—
56C2×C4⋊Dic61—21no—
57C2×#11758196—21no—
58C2×#11758198—21no—
59C2×#11758198—21no—
60C2×#11758198—21no—
61C2×#11758198—21no—
62C2×#11758198—21no—
63C2×C4×Dic61—21no—
64C2×C4×Dic61C2×C411yescharacteristic
65C2×C4×Dic61D411yescharacteristic
66C2×C4×Dic61D411yescharacteristic
67C42×D61—22no—
68C42×D61—22no—
69#125×C61—22no—
70#125×C61—22no—
71C2×C4⋊C4×C61—21no—
72C2×C4⋊C4×C61—21no—
73C2×C4⋊C4×C61C2×C411yescharacteristic
74C2×C4⋊C4×C61C2×C411yescharacteristic
75C2×C42×C61C2×C411yescharacteristic
76C23×D61—21no—
77C23×D61C2×D411yescharacteristic
78C22×#6923—24no—
79C22×#6923—42no—
80C22×#6923—42no—
81C22×#6923—42no—
82C22×#6923—42no—
83C22×#6923—42no—
84C22×#6923—42no—
85C22×C4×C61—21no—
86C22×C4×C61—21no—
87C22×C4×C61C22⋊C411yescharacteristic
88C22×C4×C61C22⋊C411yescharacteristic
89C22×C4×C61C22×C411yescharacteristic
90C22×Dic61—21no—
91C22×Dic61C22⋊C411yescharacteristic
92C22×Dic61C22⋊C411yescharacteristic
93C22×Dic61C2×D411yescharacteristic
94C2×D244—24no—
95C2×D244—21no—
96C2×D244—41no—
97C2×D244—41no—
98C2×D244—42no—
99C2×D244—41no—
100C2×D244—41no—
101C2×D244C22⋊C412yes—
102C2×C4×D61—24no—
103C2×C4×D61—22no—
104C2×C4×D61—22no—
105C2×C4×D61—22no—
106C2×C4×D61—21no—
107C2×C4×D61—21no—
108C2×C4×D61—22no—
109C2×C4×D61—41no—
110C2×C4×D61—41no—
111C2×C4×D61—41no—
112C2×C4×D61—42no—
113C2×C4×D61—42no—
114C2×C4×D61C2×D412yes—
115C2×C4×D61C2×D412yes—
116C2×Dic122—21no—
117C2×Dic122—41no—
118C2×Dic122—41no—
119C2×Dic122C22⋊C412yes—
120C2×#92420—42no—
121C2×#92420—42no—
122C2×#92420—42no—
123C4⋊C4×C61—24no—
124C4⋊C4×C61—24no—
125C4⋊C4×C61—21no—
126C4⋊C4×C61—21no—
127C4⋊C4×C61C22⋊C412yes—
128C4⋊C4×C61C22⋊C412yes—
129C42×C61—21no—
130C42×C61—21no—
131#11758198—24no—
132#11758198—24no—
133#11758198—24no—
134#11758198—24no—
135#11758198—24no—
136C4⋊Dic61—24no—
137#11758196—24no—
138C4×Dic61—24no—
139C4×Dic61—21no—
140C4×Dic61—21no—
141C4×Dic61—22no—
142C4×Dic61—22no—
143C23×C61C2×C22⋊C411yescharacteristic
144C22×D61—21no—
145C22×D61—21no—
146C22×D61—21no—
147C22×D61—21no—
148C22×D61—22no—
149C22×D61—41no—
150C22×D61—41no—
151C22×D61—41no—
152C22×D61—41no—
153C22×D61—41no—
154C22×D61—41no—
155C22×D61#12012yes—
156C22×D61#13512yes—
157C22×D61AGL(1,ℤ/8)11yescharacteristic
158C22×D61#13711yescharacteristic
159C2×#6923—44no—
160C2×#6923—44no—
161C2×#6923—44no—
162C2×#6923—82no—
163C2×#6923—82no—
164C2×#6923—82no—
165C2×#6923—82no—
166C2×C4×C61—21no—
167C2×C4×C61—21no—
168C2×C4×C61—22no—
169C2×C4×C61—21no—
170C2×C4×C61—21no—
171C2×C4×C61—22no—
172C2×C4×C61—21no—
173C2×C4×C61—21no—
174C2×C4×C61—21no—
175C2×C4×C61—21no—
176C2×C4×C61—41no—
177C2×C4×C61—41no—
178C2×C4×C61—41no—
179C2×C4×C61—41no—
180C2×C4×C61C2×C22⋊C411yescharacteristic
181C2×C4×C61C2×C22⋊C411yescharacteristic
182C2×Dic61—21no—
183C2×Dic61—21no—
184C2×Dic61—21no—
185C2×Dic61—21no—
186C2×Dic61—21no—
187C2×Dic61—22no—
188C2×Dic61—21no—
189C2×Dic61—21no—
190C2×Dic61—41no—
191C2×Dic61—41no—
192C2×Dic61#10412yes—
193C2×Dic61#12012yes—
194D244—42no—
195D244—42no—
196D244—44no—
197D244—44no—
198C4×D61—42no—
199C4×D61—42no—
200C4×D61—44no—
201C4×D61—48no—
202C4×D61—42no—
203C4×D61—42no—
204Dic122—42no—
205Dic122—42no—
206#92420—82no—
207#8330—611nomaximal, Sylow
208C22×C61#37911yescharacteristic
209C22×C61#41011yescharacteristic
210C22×C61#41011yescharacteristic
211C22×C61#41611yescharacteristic
212C22×C61#41711yescharacteristic
213C22×C61C2×#10411yescharacteristic
214C22×C61#42111yescharacteristic
215C2×D61—22no—
216C2×D61—21no—
217C2×D61—21no—
218C2×D61—21no—
219C2×D61—21no—
220C2×D61—22no—
221C2×D61—22no—
222C2×D61—22no—
223C2×D61—42no—
224C2×D61—42no—
225C2×D61—42no—
226C2×D61—81no—
227C2×D61—81no—
228C2×D61—81no—
229C2×D61—81no—
230C2×D61#44912yes—
231C2×D61#45212yes—
232#6923—84no—
233C4×C61—21no—
234C4×C61—21no—
235C4×C61—41no—
236C4×C61—42no—
237C4×C61—41no—
238C4×C61—42no—
239Dic61—22no—
240Dic61—22no—
241Dic61—42no—
242Dic61—41no—
243C2×#529—611no—
244#1817—611no—
245C2×#328—612no—
246C2×#327—612no—
247#1434—611no—
248C2×C61#150011yescharacteristic
249C2×C61#150911yescharacteristic
250C2×C61#151211yescharacteristic
251C2×C61#152111yescharacteristic
252C2×C61#178211yescharacteristic
253C2×C61#178811yescharacteristic
254C2×C61#178911yescharacteristic
255D61—22no—
256D61—22no—
257D61—82no—
258#529—1224no—
259#529—1224no—
260C2×#126—1221no—
261C2×#125#692311yescharacteristic, complemented
262C2×#124—611no—
263C2×#123—1221no—
264C2×C22⋊Q8—611no—
265C2×#121—611no—
266C2×C4×Q8—611no—
267C2×C4×D4—611no—
268C2×C4×D4—1221no—
269C2×#117—1221no—
270C22×C42—611no—
271C2×C22⋊C8—612no—
272C2×#95—612no—
273C2×#95—1221no—
274C2×#95—1221no—
275#336—1221no—
276#336—1221no—
277#328—1224no—
278#327—1224no—
279C61#833011yescharacteristic, complemented, Sylow
280C22×Q8—611no—
281C22×D4—611no—
282C22×D4—1221no—
283C23×C4—611no—
284C23×C4—611no—
285C23×C4—611no—
286C23×C4—1221no—
287C23×C4—1222no—
288C22×C8—1222no—
289#126—1228no—
290#125—22no—
291#125—22no—
292#124—1222no—
293#124—1222no—
294#123—1228no—
295C22⋊Q8—614no—
296C22⋊Q8—1222no—
297#121—614no—
298#121—1222no—
299C4×Q8—1222no—
300C4×Q8—1222no—
301C4×D4—1222no—
302C4×D4—1228no—
303C4×D4—1222no—
304#117—1228no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—1221no—
308C2×C4⋊C4—1221no—
309C2×C4⋊C4C2×#692311yescharacteristic
310C2×C4⋊C4C2×#692311yescharacteristic
311C2×C22⋊C4—1221no—
312C2×C22⋊C4—1221no—
313C2×C22⋊C4—1221no—
314C2×C22⋊C4—1221no—
315C2×C22⋊C4—1221no—
316C2×C42—611no—
317C2×C42—611no—
318C2×C42—611no—
319C2×C42—1222no—
320C2×C42—1222no—
321C2×C42—1221no—
322C2×C42C2×#692311yescharacteristic
323C22⋊C8—1222no—
324C22⋊C8—1222no—
325#95—1222no—
326#95—1222no—
327#95—1224no—
328#95—2442no—
329C24—611no—
330C24—1221no—
331C2×Q8—612no—
332C2×Q8—1221no—
333C2×Q8—2441no—
334C2×Q8—2441no—
335C2×D4—612no—
336C2×D4—1224no—
337C2×D4—1221no—
338C2×D4—2441no—
339C2×D4—2441no—
340C2×D4—2442no—
341C2×D4—2441no—
342C2×D4—2441no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—611no—
346C22×C4—611no—
347C22×C4—612no—
348C22×C4—612no—
349C22×C4—611no—
350C22×C4—1222no—
351C22×C4—1221no—
352C22×C4—1222no—
353C22×C4—1222no—
354C22×C4—1222no—
355C22×C4—1221no—
356C22×C4—1224no—
357C22×C4—1221no—
358C22×C4—1224no—
359C22×C4—2441no—
360C22×C4—2441no—
361C22×C4—2441no—
362C22×C4—2442no—
363C22×C4—2442no—
364C22×C4—2442no—
365C22×C4—2442no—
366C22×C4—2442no—
367C22×C4—2442no—
368C22×C4—2442no—
369C22×C4—2442no—
370C22×C4C22⋊#692311yescharacteristic
371C22×C4C22⋊#692311yescharacteristic
372C22×C4C22×#692311yescharacteristic
373C2×C8—2442no—
374C2×C8—2442no—
375C2×C8—2442no—
376C4⋊C4—24no—
377C4⋊C4—24no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—1224no—
381C4⋊C4—1224no—
382C4⋊C4C22⋊#692312yes—
383C4⋊C4C22⋊#692312yes—
384C22⋊C4—1224no—
385C22⋊C4—1224no—
386C22⋊C4—1224no—
387C22⋊C4—1224no—
388C22⋊C4—1224no—
389C42—21no—
390C42—21no—
391C42—1222no—
392C42—1222no—
393C42—1224no—
394C42—1221no—
395C42—1221no—
396C23—612no—
397C23—611no—
398C23—611no—
399C23—612no—
400C23—1221no—
401C23—1221no—
402C23—1221no—
403C23—1221no—
404C23—1222no—
405C23—2441no—
406C23—2441no—
407C23—2441no—
408C23—2441no—
409C23—2441no—
410C23—2441no—
411C23C2×C22⋊#692311yescharacteristic
412Q8—2442no—
413Q8—2442no—
414D4—2442no—
415D4—2442no—
416D4—2444no—
417D4—2444no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—612no—
433C2×C4—612no—
434C2×C4—1221no—
435C2×C4—1221no—
436C2×C4—1221no—
437C2×C4—1221no—
438C2×C4—1221no—
439C2×C4—1221no—
440C2×C4—1221no—
441C2×C4—1222no—
442C2×C4—4882no—
443C2×C4—4882no—
444C2×C4—4882no—
445C2×C4—4882no—
446C2×C4—2442no—
447C2×C4—2442no—
448C2×C4—2444no—
449C2×C4—2448no—
450C2×C4—2442no—
451C2×C4—2442no—
452C2×C4—2444no—
453C2×C4—2444no—
454C2×C4—2444no—
455C2×C4—2441no—
456C2×C4—2441no—
457C2×C4C2×C22⋊#692311yescharacteristic
458C2×C4C2×C22⋊#692311yescharacteristic
459C8—4882no—
460C22—612no—
461C22—612no—
462C22—1222no—
463C22—1222no—
464C22—1222no—
465C22—1222no—
466C22—1221no—
467C22—1221no—
468C22—1221no—
469C22—1221no—
470C22—4881no—
471C22—4881no—
472C22—4881no—
473C22—4881no—
474C22—2442no—
475C22—2442no—
476C22—2442no—
477C22#1684070311yescharacteristic
478C22#1684074311yescharacteristic
479C22#1684074311yescharacteristic
480C22#1684075211yescharacteristic
481C22#1684075311yescharacteristic
482C22D61⋊#10411yescharacteristic
483C22#1684075911yescharacteristic
484C4—21no—
485C4—21no—
486C4—41no—
487C4—42no—
488C4—41no—
489C4—42no—
490C4—1222no—
491C4—1222no—
492C4—4884no—
493C4—2442no—
494C4—2441no—
495C2—1222no—
496C2—1222no—
497C2—4882no—
498C2#2146119311yescharacteristic
499C2#2146122211yescharacteristic
500C2#2146123311yescharacteristic
501C2#2146126211yescharacteristic
502C2#2146165011yescharacteristic
503C2#2146165911yescharacteristic
504C2#2146166111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#125×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519752C22
cosocleC22×C4×D61C23
hypercenterC2×#125#6923
hypocenterC61#8330
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
1. #21461711C2semidirect
2. C2×#16840615C2semidirect
4. #21460995C2semidirect
17. C2×#14519765C4semidirect
21. C2×#14519742C4semidirect
23. C2×#14519739C4semidirect
26. C2×#125×C61C4semidirect
261. C2×#125#6923semidirect
279. C61#8330semidirect

Maximal subgroups

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

subgroupindex
#214617112
C2×#168406152
C2×#168406142
#214609952
C2×#168402972
#833061