Finite Group Databasebeta

← #30610366

Subgroups — #30610366

Order 15616.

1016 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462680C212yesmaximal, complemented
2#21461089C212yesmaximal, complemented
3#21461085C214yesmaximal, complemented
4#21461081C211yesmaximal, characteristic, complemented
5#21461074C212yesmaximal, complemented
6#21461061C211yesmaximal, characteristic, complemented
7#21461054C212yesmaximal, complemented
8C2×#16840495C211yesmaximal, characteristic
9#16840796—22no—
10#16840792—24no—
11#16840790—22no—
12#16840783C2212yes—
13#16840779C2212yes—
14#16840733C2214yes—
15D61⋊(C22⋊C8)C2214yes—
16#16840608C2211yescharacteristic
17#16840608C2212yes—
18#16840608C2211yescharacteristic
19#16840607C2212yes—
20#16840607C2212yes—
21#16840605C2214yes—
22#16840605C2214yes—
23#16840495—22no—
24#16840495—24no—
25#16840495—22no—
26C2×#14519773C411yescharacteristic
27C2×#14519765C411yescharacteristic
28C2×#14519764C2211yescharacteristic
29C2×#14519763C412yes—
30C2×#14519760C412yes—
31C2×#14519759C2212yes—
32C2×C4×Dic122C2211yescharacteristic
33C2×#14519742C411yescharacteristic
34C2×#14519739C2211yescharacteristic
35C2×C4×C22⋊D61C2212yes—
36C2×C4×D4×C61C411yescharacteristic
37C2×#11758213—24no—
38C2×D61⋊C8—24no—
39#14519844—22no—
40C4⋊#92420—22no—
41#14519834—24no—
42#14519834—24no—
43C22⋊#92420C2312yes—
44C22⋊#92420C2314yes—
45C22⋊#92420C2312yes—
46#14519832—22no—
47C4×#92420—22no—
48C22×Dic122C2×C411yescharacteristic
49C22×Dic122C2×C411yescharacteristic
50C22×D244C2×C411yescharacteristic
51C22×C22⋊D61C2×C412yes—
52C22×C22⋊D61C2×C412yes—
53C22×C4×D61C2312yes—
54#14519773—22no—
55#14519773—22no—
56#14519765—22no—
57#14519765—22no—
58#14519764—22no—
59#14519764—22no—
60#14519763—24no—
61#14519763—24no—
62#14519760—24no—
63#14519760—24no—
64#14519759—24no—
65#14519759—24no—
66C4×Dic122—22no—
67C4×Dic122—22no—
68#14519742—22no—
69#14519742—21no—
70#14519742—21no—
71#14519739D412yes—
72#14519739D414yes—
73#14519739D412yes—
74C4×C22⋊D61—24no—
75C4×C22⋊D61—24no—
76C2×C4⋊Dic61C2311yescharacteristic
77C2×#11758196C2×C412yes—
78C2×#11758196C2×C411yescharacteristic
79C2×#11758196C2311yescharacteristic
80C2×C22⋊Dic61C2×C412yes—
81C2×C22⋊Dic61C2312yes—
82C2×#11758198C2×C412yes—
83C2×#11758198C2×C412yes—
84C2×#11758198C2×C412yes—
85C2×C4×Dic61C2×C412yes—
86C2×C4×Dic61C2×C411yescharacteristic
87C2×C4×Dic61C2311yescharacteristic
88C22×D4×C61C2×C411yescharacteristic
89C23×C4×C61C2×C412yes—
90C4×D4×C61—22no—
91C4×D4×C61—21no—
92C4×D4×C61—21no—
93C2×C4⋊C4×C61C2×C411yescharacteristic
94C2×C22⋊C4×C61C2×C412yes—
95C2×C42×C61C2×C411yescharacteristic
96C24×C61C22×C412yes—
97C23×D61C22×C412yes—
98C2×D4×C61—21no—
99C2×D4×C61—21no—
100C2×D4×C61—42no—
101C22×C4×C61—22no—
102C22×C4×C61—22no—
103C22×C4×C61—82no—
104C22×C4×C61C22×C411yescharacteristic
105C22×C4×C61C22×C411yescharacteristic
106C22×C4×C61C22×C411yescharacteristic
107C22×C4×C61C22×C412yes—
108C2×C22⋊D61—24no—
109C2×C22⋊D61—24no—
110C2×C22⋊D61—24no—
111C2×C22⋊D61—42no—
112C2×C22⋊D61—82no—
113C22×Dic61C22×C411yescharacteristic
114C22×Dic61C22×C411yescharacteristic
115C22×Dic61C22×C411yescharacteristic
116C22×Dic61C22×C412yes—
117C22×Dic61C2411yescharacteristic
118C2×D244—42no—
119C2×D244C22⋊C412yes—
120C2×D244C22⋊C412yes—
121C2×C4×D61—82no—
122C2×C4×D61C2×D414yes—
123C2×C4×D61C2×D414yes—
124C2×Dic122—21no—
125C2×Dic122—21no—
126C2×Dic122—22no—
127C2×Dic122—22no—
128C2×Dic122—41no—
129C2×Dic122—42no—
130C2×#92420—22no—
131C2×#92420—22no—
132C2×#92420—24no—
133#11758213—84no—
134D61⋊C8—84no—
135C4⋊C4×C61C22⋊C412yes—
136C4⋊C4×C61C22⋊C411yescharacteristic
137C4⋊C4×C61C22⋊C411yescharacteristic
138C22⋊C4×C61—22no—
139C22⋊C4×C61—22no—
140C42×C61—21no—
141C42×C61—21no—
142C22⋊Dic61—24no—
143C22⋊Dic61—24no—
144#11758198—24no—
145#11758198—24no—
146#11758198C22⋊C414yes—
147#11758198C22⋊C414yes—
148C4⋊Dic61—22no—
149#11758196—22no—
150#11758196—22no—
151#11758196—22no—
152#11758196—22no—
153C4×Dic61—22no—
154C4×Dic61—22no—
155C4×Dic61—21no—
156C4×Dic61—21no—
157C4×Dic61C2×D412yes—
158C4×Dic61C2×D412yes—
159C23×C61—22no—
160C23×C61—22no—
161C23×C61—22no—
162C23×C61—42no—
163C23×C61—42no—
164C23×C61C23×C411yescharacteristic
165C22×D61—22no—
166C22×D61—22no—
167C22×D61—42no—
168C22×D61—42no—
169C22×D61C2×C22⋊C414yes—
170D4×C61—42no—
171D4×C61—42no—
172C2×C4×C61—22no—
173C2×C4×C61—21no—
174C2×C4×C61—21no—
175C2×C4×C61—21no—
176C2×C4×C61—21no—
177C2×C4×C61—42no—
178C2×C4×C61—41no—
179C2×C4×C61—82no—
180C2×C4×C61—82no—
181C2×C4×C61C2×C22⋊C411yescharacteristic
182C2×C4×C61C2×C22⋊C412yes—
183C2×C4×C61C2×C22⋊C412yes—
184C2×C4×C61C2×C22⋊C411yescharacteristic
185C22⋊D61—48no—
186C22⋊D61—84no—
187C2×Dic61—21no—
188C2×Dic61—21no—
189C2×Dic61—21no—
190C2×Dic61—21no—
191C2×Dic61—21no—
192C2×Dic61—22no—
193C2×Dic61—41no—
194C2×Dic61—42no—
195C2×Dic61—41no—
196C2×Dic61C2×C22⋊C412yes—
197C2×Dic61#13112yes—
198C2×Dic61C22×D412yes—
199D244—24no—
200D244—42no—
201C4×D61—44no—
202C4×D61—44no—
203Dic122—44no—
204Dic122—42no—
205Dic122—42no—
206#92420—42no—
207#92420—44no—
208#92420—42no—
209#17429—611nomaximal, Sylow
210C22×C61—21no—
211C22×C61—21no—
212C22×C61—42no—
213C22×C61—42no—
214C22×C61—42no—
215C22×C61—82no—
216C22×C61—82no—
217C22×C61C22×C22⋊C411yescharacteristic
218C22×C61C2×#13111yescharacteristic
219C22×C61#56811yescharacteristic
220C2×D61—24no—
221C2×D61—24no—
222C2×D61—24no—
223C2×D61—82no—
224C2×D61—82no—
225C4×C61—22no—
226C4×C61—22no—
227C4×C61—21no—
228C4×C61—41no—
229C4×C61—41no—
230C4×C61#41312yes—
231Dic61—22no—
232Dic61—22no—
233Dic61—22no—
234Dic61—41no—
235Dic61—42no—
236C2×#559—611no—
237#2974—612no—
238#1469—612no—
239#1468—614no—
240#1467—611no—
241#1465—612no—
242#1461—611no—
243#1459—612no—
244C2×C61—21no—
245C2×C61—21no—
246C2×C61—82no—
247C2×C61#288011yescharacteristic
248C2×C61#288311yescharacteristic
249C2×C61C2×#41311yescharacteristic
250D61—44no—
251#559—1222no—
252#559—1224no—
253#559—1222no—
254C2×#127—611no—
255C2×#124—611no—
256C2×#124—612no—
257C2×#124—611no—
258C2×#123—612no—
259C2×#123—612no—
260C2×C4×Q8—611no—
261C2×C4×Q8—611no—
262C2×C4×D4—612no—
263C2×C4×D4—611no—
264C2×C4×D4#692311yescharacteristic
265#436—1222no—
266#435—1224no—
267C8×D4—1222no—
268#432—612no—
269#431—612no—
270#407—614no—
271C2×C22⋊C8—614no—
272#324—612no—
273#324—612no—
274#324—611no—
275#324—612no—
276#324—611no—
277#323—614no—
278#323—614no—
279C61#1742911yescharacteristic, complemented, Sylow
280C22×Q8—611no—
281C22×Q8—611no—
282C22×D4—612no—
283C22×D4—612no—
284C22×D4—611no—
285C22×D4C2×#692311yescharacteristic
286C23×C4—612no—
287C23×C4C2×#692312yes—
288C2×M16—1224no—
289C22×C8—1224no—
290#127—1222no—
291#127—1222no—
292#124—1222no—
293#124—1222no—
294#124—1222no—
295#124—1222no—
296#124—1224no—
297#124—1224no—
298#123—1224no—
299#123—1224no—
300#123—1224no—
301#123—1224no—
302C4×Q8—1222no—
303C4×Q8—1222no—
304C4×Q8—1222no—
305C4×Q8—1221no—
306C4×Q8—1221no—
307C4×D4—22no—
308C4×D4—21no—
309C4×D4—21no—
310C4×D4—612no—
311C4×D4—614no—
312C4×D4—612no—
313C4×D4—1224no—
314C4×D4—1224no—
315C2×C4⋊C4—611no—
316C2×C4⋊C4—611no—
317C2×C4⋊C4—611no—
318C2×C4⋊C4—612no—
319C2×C4⋊C4C2×#692311yescharacteristic
320C2×C22⋊C4—612no—
321C2×C22⋊C4—612no—
322C2×C22⋊C4—612no—
323C2×C22⋊C4—612no—
324C2×C22⋊C4—612no—
325C2×C22⋊C4C2×#692312yes—
326C2×C42—611no—
327C2×C42—612no—
328C2×C42—611no—
329C2×C42C2×#692311yescharacteristic
330C4⋊C8—1222no—
331C4⋊C8—1222no—
332C22⋊C8—612no—
333C22⋊C8—614no—
334C22⋊C8—612no—
335C22⋊C8—1224no—
336C22⋊C8—1224no—
337#97—1222no—
338C4×C8—1222no—
339C24—612no—
340C24C22×#692312yes—
341C2×Q8—1222no—
342C2×Q8—1222no—
343C2×Q8—1221no—
344C2×Q8—1221no—
345C2×Q8—2441no—
346C2×Q8—2442no—
347C2×D4—21no—
348C2×D4—21no—
349C2×D4—42no—
350C2×D4—612no—
351C2×D4—612no—
352C2×D4—1224no—
353C2×D4—1224no—
354C2×D4—1224no—
355C2×D4—4882no—
356C2×D4—2442no—
357C2×D4—2442no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—82no—
361C22×C4—611no—
362C22×C4—611no—
363C22×C4—611no—
364C22×C4—614no—
365C22×C4—614no—
366C22×C4—612no—
367C22×C4—611no—
368C22×C4—4882no—
369C22×C4C22×#692311yescharacteristic
370C22×C4C22×#692311yescharacteristic
371C22×C4C22×#692311yescharacteristic
372C22×C4C22×#692312yes—
373M16—4884no—
374C2×C8—1222no—
375C2×C8—1222no—
376C2×C8—1224no—
377C2×C8—4884no—
378C4⋊C4—1222no—
379C4⋊C4—1222no—
380C4⋊C4—1222no—
381C4⋊C4—1222no—
382C4⋊C4—1222no—
383C4⋊C4C22⋊#692312yes—
384C4⋊C4C22⋊#692311yescharacteristic
385C4⋊C4C22⋊#692311yescharacteristic
386C22⋊C4—22no—
387C22⋊C4—22no—
388C22⋊C4—614no—
389C22⋊C4—614no—
390C22⋊C4—1224no—
391C22⋊C4—1224no—
392C22⋊C4—1224no—
393C22⋊C4—1224no—
394C42—21no—
395C42—21no—
396C42—612no—
397C42—612no—
398C42—1222no—
399C42—1222no—
400C42—1221no—
401C42—1221no—
402C23—22no—
403C23—22no—
404C23—22no—
405C23—42no—
406C23—42no—
407C23—614no—
408C23—1222no—
409C23—1222no—
410C23—2442no—
411C23—2442no—
412C23C23×#692311yescharacteristic
413Q8—2442no—
414Q8—2444no—
415Q8—2442no—
416D4—42no—
417D4—42no—
418D4—1224no—
419D4—4884no—
420D4—2442no—
421D4—2448no—
422C2×C4—22no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—42no—
428C2×C4—41no—
429C2×C4—82no—
430C2×C4—82no—
431C2×C4—612no—
432C2×C4—612no—
433C2×C4—612no—
434C2×C4—1221no—
435C2×C4—1221no—
436C2×C4—1221no—
437C2×C4—1221no—
438C2×C4—1222no—
439C2×C4—1221no—
440C2×C4—2444no—
441C2×C4—2444no—
442C2×C4—2441no—
443C2×C4—2441no—
444C2×C4—2442no—
445C2×C4C2×C22⋊#692311yescharacteristic
446C2×C4C2×C22⋊#692312yes—
447C2×C4C2×C22⋊#692312yes—
448C2×C4C2×C22⋊#692311yescharacteristic
449C8—2442no—
450C8—2444no—
451C8—2442no—
452C22—21no—
453C22—21no—
454C22—42no—
455C22—42no—
456C22—42no—
457C22—82no—
458C22—82no—
459C22—1224no—
460C22—1224no—
461C22—1224no—
462C22—4882no—
463C22—4882no—
464C22C22×C22⋊#692311yescharacteristic
465C22D61⋊#13111yescharacteristic
466C22#1684084111yescharacteristic
467C4—22no—
468C4—22no—
469C4—21no—
470C4—41no—
471C4—41no—
472C4—1222no—
473C4—1222no—
474C4—1222no—
475C4—2441no—
476C4—2442no—
477C4#1684074812yes—
478C2—21no—
479C2—21no—
480C2—82no—
481C2—2444no—
482C2#2146241011yescharacteristic
483C2#2146241811yescharacteristic
484C2C2×#1684074811yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×C4×D4×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519773C4
cosocleC22×Dic61C24
hypercenterC2×C4×D4#6923
hypocenterC61#17429
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4⋊C4 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #21462680C2semidirect
2. #21461089C2semidirect
3. #21461085C2semidirect
4. #21461081C2semidirect
5. #21461074C2semidirect
6. #21461061C2semidirect
7. #21461054C2semidirect
279. C61#17429semidirect

Maximal subgroups

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

subgroupindex
#214626802
#214610892
#214610852
#214610812
#214610742
#214610612
#214610542
C2×#168404952
#1742961