Finite Group Databasebeta

← #30610299

Subgroups — #30610299

Order 15616.

1002 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462510C212yesmaximal, complemented
2#21461096C212yesmaximal, complemented
3#21461090C214yesmaximal, complemented
4#21461076C211yesmaximal, characteristic, complemented
5#21461073C212yesmaximal, complemented
6#21461056C211yesmaximal, characteristic, complemented
7#21461053C212yesmaximal, complemented
8C2×#16840478C211yesmaximal, characteristic
9#16840787—24no—
10#16840783C2214yes—
11#16840779C2214yes—
12#16840769—22no—
13#16840733C2212yes—
14D61⋊(C22⋊C8)C2212yes—
15#16840727—22no—
16#16840607C2211yescharacteristic
17#16840607C2212yes—
18#16840607C2211yescharacteristic
19#16840606C2214yes—
20#16840606C2212yes—
21#16840606C2214yes—
22#16840606C2212yes—
23#16840478—22no—
24#16840478—22no—
25#16840478—24no—
26C2×#14519766C412yes—
27C2×#14519766C2212yes—
28C2×#14519752C412yes—
29C2×#14519752C411yescharacteristic
30C2×#14519752C2211yescharacteristic
31C2×C4×D244C411yescharacteristic
32C2×C4×D244C2211yescharacteristic
33C2×#14519735C411yescharacteristic
34C2×#14519735C2212yes—
35C2×#14519735C2211yescharacteristic
36C2×C4⋊Q8×C61C411yescharacteristic
37C2×#11758213—22no—
38C2×D61⋊C8—22no—
39#14519844—24no—
40C4⋊#92420—24no—
41#14519834—22no—
42#14519834—22no—
43C22⋊#92420C2312yes—
44C22⋊#92420C2312yes—
45C22⋊#92420C2314yes—
46#14519832—24no—
47C4×#92420—24no—
48C22×D244C2×C411yescharacteristic
49C22×D244C2×C411yescharacteristic
50C22×D244C2×C412yes—
51C22×D244C2×C412yes—
52C22×C4×D61C2×C412yes—
53C22×C4×D61C2×C411yescharacteristic
54C22×C4×D61C2311yescharacteristic
55#14519766—24no—
56#14519766—24no—
57#14519766—24no—
58#14519766—24no—
59#14519752—22no—
60#14519752—22no—
61#14519752—22no—
62#14519752—22no—
63#14519752—24no—
64#14519752—24no—
65C4×D244—22no—
66C4×D244—22no—
67C4×D244—22no—
68C4×D244—21no—
69C4×D244—21no—
70#14519735—22no—
71#14519735—21no—
72#14519735—21no—
73#14519735—24no—
74#14519735—24no—
75#14519735D412yes—
76#14519735D412yes—
77#14519735D414yes—
78C2×C4⋊Dic61C2×C411yescharacteristic
79C2×C4⋊Dic61C2311yescharacteristic
80C2×#11758198C2×C412yes—
81C2×#11758198C2×C412yes—
82C2×#11758198C2×C412yes—
83C2×#11758198C2×C411yescharacteristic
84C2×#11758198C2×C412yes—
85C2×#11758198C2312yes—
86C2×#11758198C2311yescharacteristic
87C2×C4×Dic61C2×C412yes—
88C2×C4×Dic61C2312yes—
89C22×Q8×C61C2×C412yes—
90C4⋊Q8×C61—22no—
91C4⋊Q8×C61—22no—
92C2×C4⋊C4×C61C2×C411yescharacteristic
93C2×C4⋊C4×C61C2×C412yes—
94C2×C4⋊C4×C61C2×C411yescharacteristic
95C2×C42×C61C2×C411yescharacteristic
96C23×D61C22×C412yes—
97C23×D61C22×C411yescharacteristic
98C23×D61C22×C411yescharacteristic
99C2×Q8×C61—24no—
100C2×Q8×C61—82no—
101C22×C4×C61C22×C411yescharacteristic
102C22×C4×C61C22×C411yescharacteristic
103C22×C4×C61C22×C412yes—
104C22×C4×C61C22×C411yescharacteristic
105C22×C4×C61C22×C412yes—
106C22×Dic61C22×C412yes—
107C22×Dic61C22×C411yescharacteristic
108C22×Dic61C2411yescharacteristic
109C2×D244—22no—
110C2×D244—21no—
111C2×D244—21no—
112C2×D244—22no—
113C2×D244—24no—
114C2×D244—24no—
115C2×D244—41no—
116C2×D244—42no—
117C2×D244—82no—
118C2×D244—82no—
119C2×C4×D61—21no—
120C2×C4×D61—21no—
121C2×C4×D61—24no—
122C2×C4×D61—22no—
123C2×C4×D61—22no—
124C2×C4×D61—42no—
125C2×C4×D61—42no—
126C2×C4×D61—42no—
127C2×C4×D61C2×D412yes—
128C2×C4×D61C2×D412yes—
129C2×#92420—22no—
130C2×#92420—24no—
131C2×#92420—22no—
132#11758213—44no—
133D61⋊C8—44no—
134C4⋊C4×C61—24no—
135C4⋊C4×C61—21no—
136C4⋊C4×C61—21no—
137C4⋊C4×C61C22⋊C412yes—
138C4⋊C4×C61C22⋊C412yes—
139C42×C61—21no—
140C42×C61—21no—
141#11758198—22no—
142#11758198—24no—
143#11758198—22no—
144#11758198—22no—
145#11758198—22no—
146#11758198—22no—
147#11758198—24no—
148#11758198—22no—
149#11758198C22⋊C414yes—
150#11758198C22⋊C414yes—
151C4⋊Dic61—22no—
152C4⋊Dic61C22⋊C412yes—
153C4⋊Dic61C22⋊C411yescharacteristic
154C4⋊Dic61C22⋊C411yescharacteristic
155C4×Dic61—22no—
156C4×Dic61—22no—
157C4×Dic61C2×D414yes—
158C4×Dic61C2×D414yes—
159C23×C61C23×C411yescharacteristic
160C22×D61—21no—
161C22×D61—21no—
162C22×D61—22no—
163C22×D61—21no—
164C22×D61—22no—
165C22×D61—21no—
166C22×D61—22no—
167C22×D61—21no—
168C22×D61—41no—
169C22×D61—41no—
170C22×D61—41no—
171C22×D61—42no—
172C22×D61—41no—
173C22×D61—42no—
174C22×D61C2×C22⋊C412yes—
175Q8×C61—84no—
176C2×C4×C61—21no—
177C2×C4×C61—21no—
178C2×C4×C61—22no—
179C2×C4×C61—22no—
180C2×C4×C61—21no—
181C2×C4×C61—42no—
182C2×C4×C61—42no—
183C2×C4×C61—41no—
184C2×C4×C61C2×C22⋊C414yes—
185C2×C4×C61C2×C22⋊C411yescharacteristic
186C2×C4×C61C2×C22⋊C411yescharacteristic
187C2×C4×C61#13112yes—
188C2×Dic61—22no—
189C2×Dic61—22no—
190C2×Dic61—21no—
191C2×Dic61—41no—
192C2×Dic61—41no—
193C2×Dic61C2×C22⋊C412yes—
194C2×Dic61C2×C22⋊C412yes—
195C2×Dic61C22×D412yes—
196D244—44no—
197D244—42no—
198D244—42no—
199D244—84no—
200D244—84no—
201C4×D61—24no—
202C4×D61—42no—
203C4×D61—44no—
204C4×D61—44no—
205C4×D61—42no—
206C4×D61—42no—
207#92420—42no—
208#92420—42no—
209#92420—44no—
210#17418—611nomaximal, Sylow
211C22×C61—21no—
212C22×C61—21no—
213C22×C61C22×C22⋊C411yescharacteristic
214C22×C61C2×#13111yescharacteristic
215C22×C61#56811yescharacteristic
216C2×D61—22no—
217C2×D61—22no—
218C2×D61—22no—
219C2×D61—42no—
220C2×D61—41no—
221C2×D61—41no—
222C2×D61—42no—
223C2×D61—41no—
224C2×D61—42no—
225C2×D61—81no—
226C2×D61—81no—
227C2×D61—82no—
228C2×D61—81no—
229C2×D61—82no—
230C2×D61—81no—
231C4×C61—22no—
232C4×C61—21no—
233C4×C61—24no—
234C4×C61—42no—
235C4×C61—41no—
236C4×C61#41012yes—
237Dic61—22no—
238Dic61—22no—
239Dic61—22no—
240Dic61—41no—
241C2×#555—611no—
242#2924—612no—
243#1471—612no—
244#1469—614no—
245#1465—611no—
246#1464—612no—
247#1459—611no—
248#1458—612no—
249C2×C61—21no—
250C2×C61—21no—
251C2×C61#288011yescharacteristic
252C2×C61C2×#41011yescharacteristic
253C2×C61#288811yescharacteristic
254D61—42no—
255D61—82no—
256D61—81no—
257#555—1222no—
258#555—1222no—
259#555—1224no—
260C2×C4⋊Q8#692311yescharacteristic
261C2×#124—612no—
262C2×#124—612no—
263C2×#121—612no—
264C2×#121—611no—
265C2×#121—611no—
266C2×C4×D4—611no—
267C2×C4×D4—611no—
268C2×#117—611no—
269C2×#117—612no—
270C2×#117—611no—
271#433—1224no—
272#432—614no—
273#431—614no—
274#424—1222no—
275#407—612no—
276C2×C22⋊C8—612no—
277#405—1222no—
278#324—611no—
279#324—612no—
280#324—611no—
281#323—614no—
282#323—612no—
283#323—614no—
284#323—612no—
285C61#1741811yescharacteristic, complemented, Sylow
286C22×Q8C2×#692312yes—
287C22×D4—611no—
288C22×D4—612no—
289C22×D4—612no—
290C22×D4—611no—
291C23×C4—611no—
292C23×C4—612no—
293C23×C4—611no—
294C2×M16—1222no—
295C22×C8—1222no—
296C4⋊Q8—22no—
297C4⋊Q8—22no—
298#124—1224no—
299#124—1224no—
300#124—1224no—
301#124—1224no—
302#121—1224no—
303#121—1224no—
304#121—1222no—
305#121—1222no—
306#121—1222no—
307#121—1222no—
308C4×D4—1222no—
309C4×D4—1221no—
310C4×D4—1221no—
311C4×D4—1222no—
312C4×D4—1222no—
313#117—612no—
314#117—612no—
315#117—614no—
316#117—1224no—
317#117—1224no—
318#117—1222no—
319#117—1221no—
320#117—1221no—
321C2×C4⋊C4—611no—
322C2×C4⋊C4—611no—
323C2×C4⋊C4C2×#692311yescharacteristic
324C2×C4⋊C4C2×#692312yes—
325C2×C4⋊C4C2×#692311yescharacteristic
326C2×C22⋊C4—612no—
327C2×C22⋊C4—612no—
328C2×C22⋊C4—612no—
329C2×C22⋊C4—612no—
330C2×C22⋊C4—611no—
331C2×C22⋊C4—612no—
332C2×C22⋊C4—611no—
333C2×C42—612no—
334C2×C42—612no—
335C2×C42C2×#692311yescharacteristic
336C4⋊C8—1224no—
337C4⋊C8—1224no—
338C22⋊C8—612no—
339C22⋊C8—612no—
340C22⋊C8—614no—
341C22⋊C8—1222no—
342C22⋊C8—1222no—
343#97—1224no—
344C4×C8—1224no—
345C24—611no—
346C24—612no—
347C24—611no—
348C2×Q8—24no—
349C2×Q8—82no—
350C2×D4—1224no—
351C2×D4—1222no—
352C2×D4—1224no—
353C2×D4—1221no—
354C2×D4—1221no—
355C2×D4—1222no—
356C2×D4—4882no—
357C2×D4—4882no—
358C2×D4—2441no—
359C2×D4—2442no—
360C22×C4—612no—
361C22×C4—611no—
362C22×C4—612no—
363C22×C4—612no—
364C22×C4—611no—
365C22×C4—1222no—
366C22×C4—1222no—
367C22×C4—1221no—
368C22×C4—1221no—
369C22×C4—1224no—
370C22×C4—2442no—
371C22×C4—2442no—
372C22×C4—2442no—
373C22×C4C22×#692311yescharacteristic
374C22×C4C22×#692311yescharacteristic
375C22×C4C22×#692312yes—
376C22×C4C22×#692311yescharacteristic
377C22×C4C22×#692312yes—
378M16—2444no—
379C2×C8—1222no—
380C2×C8—1224no—
381C2×C8—1222no—
382C2×C8—2444no—
383C4⋊C4—24no—
384C4⋊C4—21no—
385C4⋊C4—21no—
386C4⋊C4—612no—
387C4⋊C4—611no—
388C4⋊C4—611no—
389C4⋊C4—1222no—
390C4⋊C4C22⋊#692312yes—
391C4⋊C4C22⋊#692312yes—
392C22⋊C4—614no—
393C22⋊C4—614no—
394C22⋊C4—1222no—
395C22⋊C4—1222no—
396C22⋊C4—1224no—
397C22⋊C4—1222no—
398C22⋊C4—1222no—
399C22⋊C4—1222no—
400C22⋊C4—1222no—
401C22⋊C4—1224no—
402C42—21no—
403C42—21no—
404C42—614no—
405C42—614no—
406C42—1222no—
407C42—1222no—
408C23—612no—
409C23—1221no—
410C23—1221no—
411C23—1222no—
412C23—1221no—
413C23—1222no—
414C23—1221no—
415C23—1222no—
416C23—1221no—
417C23—2441no—
418C23—2441no—
419C23—2441no—
420C23—2442no—
421C23—2441no—
422C23—2442no—
423C23C23×#692311yescharacteristic
424Q8—84no—
425D4—4884no—
426D4—4884no—
427D4—2444no—
428D4—2442no—
429D4—2442no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—22no—
433C2×C4—21no—
434C2×C4—22no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—41no—
438C2×C4—612no—
439C2×C4—612no—
440C2×C4—612no—
441C2×C4—1222no—
442C2×C4—1222no—
443C2×C4—1224no—
444C2×C4—1221no—
445C2×C4—2442no—
446C2×C4—2444no—
447C2×C4—2444no—
448C2×C4—2442no—
449C2×C4—2441no—
450C2×C4—2442no—
451C2×C4—2441no—
452C2×C4C2×C22⋊#692311yescharacteristic
453C2×C4C2×C22⋊#692314yes—
454C2×C4C2×C22⋊#692311yescharacteristic
455C2×C4#1451986512yes—
456C8—2442no—
457C8—2442no—
458C8—2444no—
459C22—21no—
460C22—21no—
461C22—1222no—
462C22—1222no—
463C22—1222no—
464C22—4882no—
465C22—4881no—
466C22—4882no—
467C22—4881no—
468C22—4881no—
469C22—4881no—
470C22—2442no—
471C22—2441no—
472C22—2441no—
473C22—2442no—
474C22—2441no—
475C22—2442no—
476C22C22×C22⋊#692311yescharacteristic
477C22C2×#1451986511yescharacteristic
478C22#1684084211yescharacteristic
479C4—22no—
480C4—21no—
481C4—24no—
482C4—42no—
483C4—41no—
484C4—1222no—
485C4—1222no—
486C4—1222no—
487C4—2441no—
488C4#1684074312yes—
489C2—21no—
490C2—21no—
491C2—4882no—
492C2—4881no—
493C2—2442no—
494C2#2146240811yescharacteristic
495C2C2×#1684074311yescharacteristic
496C2#2146242911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×C4⋊Q8×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840478C2
cosocleC22×Dic61C24
hypercenterC2×C4⋊Q8#6923
hypocenterC61#17418
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4⋊C4 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #21462510C2semidirect
2. #21461096C2semidirect
3. #21461090C2semidirect
4. #21461076C2semidirect
5. #21461073C2semidirect
6. #21461056C2semidirect
7. #21461053C2semidirect
285. C61#17418semidirect

Maximal subgroups

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

subgroupindex
#214625102
#214610962
#214610902
#214610762
#214610732
#214610562
#214610532
C2×#168404782
#1741861