Finite Group Databasebeta

← #30600402

Subgroups — #30600402

Order 15616.

752 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 752 conjugacy classes of subgroups — too many to draw. Only its 120 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×#16840767C211yesmaximal, characteristic, complemented
2#21461676C211yesmaximal, characteristic, complemented
3C2×#16840620C212yesmaximal, complemented
4#21460697C212yesmaximal, complemented
5#21454163C211yesmaximal, characteristic
6C22×#11758213—21no—
7#16840767—24no—
8C2×#14519844—21no—
9C2×#14519844C2212yes—
10C2×#14519844C2212yes—
11C2×#14519834—21no—
12#16840628—21no—
13#16840620—24no—
14C2×#14519773C2211yescharacteristic
15C2×#14519752C411yescharacteristic
16C2×#14519750—21no—
17C2×#14519750—21no—
18C2×#14519748C411yescharacteristic
19C2×C42×D61C2211yescharacteristic
20#16839664C411yescharacteristic
21#16839662—21no—
22#16839662—21no—
23#16839631C2211yescharacteristic
24C61×#390C411yescharacteristic
25C2×#11758213—24no—
26C2×#11758213—42no—
27C2×#11758213—42no—
28C22×#92420—22no—
29C22×#92420—22no—
30#14519844—24no—
31#14519844—22no—
32#14519844—22no—
33#14519844—22no—
34#14519844D414yescomplemented
35#14519834—42no—
36C22×D244—21no—
37C22×D244C2×C411yescharacteristic
38C22×C22⋊D61—21no—
39C22×C22⋊D61—21no—
40C22×C22⋊D61—21no—
41C22×C4×D61C2×C411yescharacteristic
42C22×C4×D61D411yescharacteristic
43C22×C4×D61D411yescharacteristic
44#14519773—22no—
45#14519773—22no—
46#14519752—42no—
47#14519750—44no—
48#14519750—42no—
49#14519750—42no—
50#14519748—42no—
51C2×C4⋊Dic61C2×C411yescharacteristic
52C2×#11758196—21no—
53C2×#11758196—21no—
54C2×C22⋊Dic61—21no—
55C2×#11758198—21no—
56C2×#11758198—21no—
57C2×#11758198—21no—
58C2×C4×Dic61D411yescharacteristic
59C2×C4×Dic61D411yescharacteristic
60C2×C4×Dic61C2311yescharacteristic
61C42×D61—22no—
62C42×D61—22no—
63C22×D4×C61C2×C411yescharacteristic
64C2×C4⋊C4×C61C2×C411yescharacteristic
65C2×C22⋊C4×C61—21no—
66C2×C22⋊C4×C61—21no—
67C2×C42×C61C2×C411yescharacteristic
68C24×C61—21no—
69C23×D61—21no—
70C23×D61C22⋊C411yescharacteristic
71C2×D4×C61—22no—
72C2×D4×C61—41no—
73C2×D4×C61—41no—
74C22×C4×C61—21no—
75C22×C4×C61C22⋊C411yescharacteristic
76C22×C4×C61C22⋊C411yescharacteristic
77C22×C4×C61C22×C411yescharacteristic
78C2×C22⋊D61—42no—
79C2×C22⋊D61—42no—
80C2×C22⋊D61—42no—
81C2×C22⋊D61—41no—
82C2×C22⋊D61—42no—
83C2×C22⋊D61—41no—
84C2×C22⋊D61—41no—
85C2×C22⋊D61—41no—
86C2×C22⋊D61—41no—
87C2×C22⋊D61—41no—
88C2×C22⋊D61—42no—
89C2×C22⋊D61—41no—
90C2×C22⋊D61—41no—
91C22×Dic61—21no—
92C22×Dic61C22⋊C411yescharacteristic
93C22×Dic61C2×D411yescharacteristic
94C22×Dic61C2×D411yescharacteristic
95C2×D244—22no—
96C2×D244—41no—
97C2×D244—41no—
98C2×D244—42no—
99C2×D244—42no—
100C2×D244—42no—
101C2×C4×D61—21no—
102C2×C4×D61—21no—
103C2×C4×D61—21no—
104C2×C4×D61—21no—
105C2×C4×D61—22no—
106C2×C4×D61—22no—
107C2×C4×D61—22no—
108C2×C4×D61—21no—
109C2×C4×D61—22no—
110C2×C4×D61—21no—
111C2×C4×D61—41no—
112C2×C4×D61D812yes—
113C2×C4×D61SD1612yes—
114C2×#92420—24no—
115C2×#92420—42no—
116C2×#92420—42no—
117C2×#92420—42no—
118C2×#92420—42no—
119C2×#92420—42no—
120#11758213—48no—
121C4⋊C4×C61—41no—
122C22⋊C4×C61—42no—
123C22⋊C4×C61—42no—
124C42×C61—22no—
125C22⋊Dic61—42no—
126#11758198—42no—
127#11758198—42no—
128#11758198—42no—
129C4⋊Dic61—41no—
130#11758196—41no—
131#11758196—41no—
132#11758196—42no—
133C4×Dic61—21no—
134C4×Dic61—22no—
135C4×Dic61—21no—
136C4×Dic61C2×D412yes—
137C4×Dic61#4112yes—
138C23×C61—41no—
139C23×C61—41no—
140C23×C61—41no—
141C23×C61—41no—
142C23×C61—41no—
143C23×C61—41no—
144C23×C61—41no—
145C23×C61C2×C22⋊C411yescharacteristic
146C22×D61—21no—
147C22×D61—21no—
148C22×D61—21no—
149C22×D61—21no—
150C22×D61—21no—
151C22×D61—21no—
152C22×D61—41no—
153C22×D61—41no—
154C22×D61—41no—
155C22×D61—41no—
156C22×D61—41no—
157C22×D61—41no—
158C22×D61—41no—
159C22×D61#10212yes—
160D4×C61—82no—
161C2×C4×C61—21no—
162C2×C4×C61—21no—
163C2×C4×C61—21no—
164C2×C4×C61—21no—
165C2×C4×C61—21no—
166C2×C4×C61—21no—
167C2×C4×C61—21no—
168C2×C4×C61—41no—
169C2×C4×C61—41no—
170C2×C4×C61—41no—
171C2×C4×C61#10212yes—
172C2×C4×C61C4×D412yes—
173C22⋊D61—84no—
174C22⋊D61—81no—
175C22⋊D61—81no—
176C22⋊D61—82no—
177C22⋊D61—82no—
178C22⋊D61—81no—
179C22⋊D61—81no—
180C2×Dic61—21no—
181C2×Dic61—21no—
182C2×Dic61—41no—
183C2×Dic61—41no—
184C2×Dic61—41no—
185C2×Dic61#10012yes—
186C2×Dic61#12011yescharacteristic
187C2×Dic61#12112yes—
188C2×Dic61#12311yescharacteristic
189C2×Dic61C2×D811yescharacteristic
190C2×Dic61C2×SD1611yescharacteristic
191C2×Dic61AGL(1,ℤ/8)11yescharacteristic
192C2×Dic61AGL(1,ℤ/8)12yes—
193C2×Dic61AGL(1,ℤ/8)11yescharacteristic
194C2×Dic61#13711yescharacteristic
195C2×Dic61#13711yescharacteristic
196D244—82no—
197D244—84no—
198C4×D61—22no—
199C4×D61—22no—
200C4×D61—22no—
201C4×D61—22no—
202C4×D61—44no—
203C4×D61—42no—
204C4×D61—42no—
205#92420—44no—
206#92420—82no—
207#9141—611nomaximal, Sylow
208C22×C61—81no—
209C22×C61—81no—
210C22×C61—81no—
211C22×C61—81no—
212C22×C61—81no—
213C22×C61—81no—
214C22×C61—81no—
215C22×C61#38611yescharacteristic
216C22×C61C2×#10011yescharacteristic
217C22×C61#41311yescharacteristic
218C22×C61C2×#10211yescharacteristic
219C22×C61#41711yescharacteristic
220C22×C61#41711yescharacteristic
221C22×C61#41811yescharacteristic
222C2×D61—22no—
223C2×D61—22no—
224C2×D61—22no—
225C2×D61—41no—
226C2×D61—41no—
227C2×D61—41no—
228C2×D61—41no—
229C2×D61—81no—
230C2×D61—81no—
231C2×D61—81no—
232C2×D61—81no—
233C2×D61—81no—
234C2×D61—81no—
235C2×D61—81no—
236C4×C61—22no—
237C4×C61—22no—
238C4×C61—41no—
239C4×C61—81no—
240Dic61—22no—
241Dic61—81no—
242Dic61#44711yescharacteristic
243Dic61#44811yescharacteristic
244Dic61#46812yes—
245Dic61#46912yes—
246Dic61#48011yescharacteristic
247Dic61#48111yescharacteristic
248C2×#423—611no—
249#2856—611no—
250#1797—611no—
251C2×#331—612no—
252#1296—612no—
253C2×C61—161no—
254C2×C61#154511yescharacteristic
255C2×C61#154711yescharacteristic
256C2×C61#155711yescharacteristic
257C2×C61#156011yescharacteristic
258C2×C61#187411yescharacteristic
259C2×C61#189511yescharacteristic
260C2×C61#190011yescharacteristic
261D61—42no—
262D61—161no—
263C22×M16—1221no—
264C2×#127—611no—
265C2×#121—611no—
266C2×#121—611no—
267C2×#121—1221no—
268C2×#121—1221no—
269C22×C42—611no—
270#423—1224no—
271C2×C4⋊C8—612no—
272C2×C4⋊C8—612no—
273C2×C4⋊C8—1221no—
274C2×C22⋊C8—1221no—
275#390—611no—
276#390—1221no—
277#390—1221no—
278#390#692311yescharacteristic
279#384—611no—
280#336—1221no—
281#331—1224no—
282C61#914111yescharacteristic, complemented, Sylow
283C22×D4—611no—
284C22×D4—1221no—
285C22×D4—1221no—
286C22×D4—1221no—
287C22×D4—1221no—
288C22×D4C2×#692311yescharacteristic
289C23×C4—611no—
290C23×C4—611no—
291C23×C4—611no—
292C2×M16—1224no—
293C2×M16—2442no—
294C2×M16—2442no—
295C22×C8—1222no—
296C22×C8—1222no—
297#127—1222no—
298#127—1222no—
299#121—2442no—
300#121—2442no—
301#121—2444no—
302#121—2442no—
303#121—2442no—
304C2×C4⋊C4—611no—
305C2×C4⋊C4—1221no—
306C2×C4⋊C4—1221no—
307C2×C4⋊C4C2×#692311yescharacteristic
308C2×C22⋊C4—21no—
309C2×C22⋊C4—21no—
310C2×C22⋊C4—1221no—
311C2×C22⋊C4—1221no—
312C2×C22⋊C4—1221no—
313C2×C22⋊C4—1221no—
314C2×C42—611no—
315C2×C42—611no—
316C2×C42—611no—
317C2×C42—1222no—
318C2×C42—1222no—
319C2×C42C2×#692311yescharacteristic
320C4⋊C8—614no—
321C4⋊C8—1222no—
322C4⋊C8—1222no—
323C4⋊C8—1222no—
324C4⋊C8—1224no—
325C22⋊C8—2442no—
326C24—21no—
327C24—611no—
328C24—1221no—
329C2×D4—22no—
330C2×D4—41no—
331C2×D4—41no—
332C2×D4—1222no—
333C2×D4—2441no—
334C2×D4—2441no—
335C2×D4—2442no—
336C2×D4—2442no—
337C2×D4—2442no—
338C2×D4—2441no—
339C2×D4—2441no—
340C2×D4—2442no—
341C2×D4—2441no—
342C2×D4—2442no—
343C2×D4—2441no—
344C2×D4—2441no—
345C2×D4—2441no—
346C2×D4—2441no—
347C2×D4—2441no—
348C2×D4—2442no—
349C2×D4—2442no—
350C2×D4—2442no—
351C22×C4—21no—
352C22×C4—611no—
353C22×C4—611no—
354C22×C4—611no—
355C22×C4—612no—
356C22×C4—612no—
357C22×C4—1221no—
358C22×C4—1221no—
359C22×C4—1221no—
360C22×C4—1221no—
361C22×C4—1221no—
362C22×C4—1222no—
363C22×C4—1222no—
364C22×C4—1222no—
365C22×C4—1221no—
366C22×C4—1222no—
367C22×C4—1221no—
368C22×C4—2441no—
369C22×C4C22⋊#692311yescharacteristic
370C22×C4C22⋊#692311yescharacteristic
371C22×C4C22×#692311yescharacteristic
372M16—2448no—
373C2×C8—1224no—
374C2×C8—2442no—
375C2×C8—2442no—
376C2×C8—2442no—
377C2×C8—2442no—
378C2×C8—2442no—
379C4⋊C4—41no—
380C4⋊C4—2441no—
381C4⋊C4—2441no—
382C4⋊C4—2441no—
383C4⋊C4—2442no—
384C22⋊C4—42no—
385C22⋊C4—42no—
386C22⋊C4—2442no—
387C22⋊C4—2442no—
388C22⋊C4—2442no—
389C22⋊C4—2442no—
390C42—22no—
391C42—612no—
392C42—612no—
393C42—1221no—
394C42—1222no—
395C42—1221no—
396C23—41no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23—41no—
402C23—41no—
403C23—612no—
404C23—1221no—
405C23—1221no—
406C23—1221no—
407C23—1221no—
408C23—1221no—
409C23—1221no—
410C23—2441no—
411C23—2441no—
412C23—2441no—
413C23—2441no—
414C23—2441no—
415C23—2441no—
416C23—2441no—
417C23C2×C22⋊#692311yescharacteristic
418D4—82no—
419D4—4882no—
420D4—4884no—
421D4—4881no—
422D4—4881no—
423D4—4881no—
424D4—4881no—
425D4—4882no—
426D4—4882no—
427D4—4884no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—611no—
439C2×C4—612no—
440C2×C4—611no—
441C2×C4—611no—
442C2×C4—611no—
443C2×C4—611no—
444C2×C4—611no—
445C2×C4—611no—
446C2×C4—611no—
447C2×C4—612no—
448C2×C4—612no—
449C2×C4—1222no—
450C2×C4—1222no—
451C2×C4—1222no—
452C2×C4—1222no—
453C2×C4—1221no—
454C2×C4—1221no—
455C2×C4—2444no—
456C2×C4—2442no—
457C2×C4—2442no—
458C2×C4—2441no—
459C2×C4—2441no—
460C2×C4—2441no—
461C2×C4#1451983912yes—
462C2×C4D4×#692312yes—
463C8—4882no—
464C8—2444no—
465C22—81no—
466C22—81no—
467C22—81no—
468C22—81no—
469C22—81no—
470C22—81no—
471C22—81no—
472C22—1222no—
473C22—1222no—
474C22—1222no—
475C22—4881no—
476C22—4881no—
477C22—4881no—
478C22—4881no—
479C22—4881no—
480C22—4881no—
481C22—4881no—
482C22—2441no—
483C22—2441no—
484C22—2441no—
485C22—2441no—
486C22#1684071011yescharacteristic
487C22D61⋊#10011yescharacteristic
488C22#1684074811yescharacteristic
489C22C2×#1451983911yescharacteristic
490C22#1684075311yescharacteristic
491C22#1684075311yescharacteristic
492C22#1684075411yescharacteristic
493C4—22no—
494C4—22no—
495C4—41no—
496C4—81no—
497C4—611no—
498C4—611no—
499C4—611no—
500C4—611no—
501C4—612no—
502C4—612no—
503C4—1222no—
504C4—4881no—
505C2—161no—
506C2—9761no—
507C2—2442no—
508C2#2146132711yescharacteristic
509C2#2146133011yescharacteristic
510C2#2146135011yescharacteristic
511C2#2146135711yescharacteristic
512C2#2146180611yescharacteristic
513C2#2146183511yescharacteristic
514C2#2146184511yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#390C4
socleC23×C61C2×C22⋊C4
prime radical#21454163C2
cosocleC2×C4×Dic61C23
hypercenter#390#6923
hypocenterC61#9141
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#16840767C2semidirect
2. #21461676C2semidirect
3. C2×#16840620C2semidirect
4. #21460697C2semidirect
34. #14519844D4semidirect
282. C61#9141semidirect

Maximal subgroups

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

subgroupindex
C2×#168407672
#214616762
C2×#168406202
#214606972
#214541632
#914161