Finite Group Databasebeta

← #30596259

Subgroups — #30596259

Order 15616.

982 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840732C211yesmaximal, characteristic
2C22×C22⋊#92420C211yesmaximal, characteristic
3#21460657C214yesmaximal, complemented
4C2×#16839623C211yesmaximal, characteristic
5C22×#11758217—21no—
6C23×#92420—21no—
7#16840732—22no—
8#16840732C414yescomplemented
9C2×C22⋊#92420—22no—
10C2×C22⋊#92420—21no—
11C2×C22⋊#92420—21no—
12C2×C22⋊#92420C414yescomplemented
13C2×C22⋊#92420C2212yes—
14C2×C22⋊#92420C2212yes—
15C24×Dic61C2211yescharacteristic
16C22×C22⋊Dic61C411yescharacteristic
17#16839623—21no—
18#16839623—21no—
19#16839623—21no—
20#16839623—21no—
21C2×#14519684C412yes—
22C2×#14519684C2212yes—
23C22×C22⋊C4×C61C411yescharacteristic
24C2×#11758217—24no—
25C2×#11758217—42no—
26C2×#11758217—42no—
27C22×#92420—24no—
28C22×#92420—22no—
29C22×#92420—22no—
30C22×#92420—42no—
31C22×#92420—42no—
32C22⋊#92420—24no—
33C22⋊#92420—24no—
34C22⋊#92420—22no—
35C22⋊#92420—22no—
36C22⋊#92420C2×C414yes—
37C22⋊#92420C2×C414yes—
38C23×Dic61—42no—
39C23×Dic61—42no—
40C23×Dic61C2×C412yes—
41C23×Dic61C2×C411yescharacteristic
42C23×Dic61C2×C412yes—
43C23×Dic61C2×C412yes—
44C23×Dic61D411yescharacteristic
45C23×Dic61D411yescharacteristic
46C23×Dic61D412yes—
47C23×Dic61D411yescharacteristic
48C23×Dic61D411yescharacteristic
49C23×Dic61Q812yes—
50C23×Dic61C2311yescharacteristic
51C2×C22⋊Dic61—21no—
52C2×C22⋊Dic61—21no—
53C2×C22⋊Dic61—42no—
54#14519684—22no—
55#14519684—22no—
56#14519684—22no—
57#14519684—22no—
58C25×C61C2×C411yescharacteristic
59C23×C4×C61C2×C412yes—
60C2×C22⋊C4×C61—21no—
61C2×C22⋊C4×C61—21no—
62C2×C22⋊C4×C61—42no—
63C24×C61—22no—
64C24×C61—22no—
65C24×C61—24no—
66C24×C61—42no—
67C24×C61C4212yes—
68C24×C61C22⋊C411yescharacteristic
69C24×C61C22⋊C411yescharacteristic
70C24×C61C4⋊C412yes—
71C24×C61C22×C411yescharacteristic
72C22×C4×C61—22no—
73C22×C4×C61—24no—
74C22×C4×C61—42no—
75C22×C4×C61—42no—
76C22×Dic61—22no—
77C22×Dic61—22no—
78C22×Dic61—22no—
79C22×Dic61—22no—
80C22×Dic61—22no—
81C22×Dic61—24no—
82C22×Dic61—44no—
83C22×Dic61—44no—
84C22×Dic61—41no—
85C22×Dic61—41no—
86C22×Dic61—44no—
87C22×Dic61—41no—
88C22×Dic61—41no—
89C22×Dic61—41no—
90C22×Dic61—41no—
91C22×Dic61—44no—
92C22×Dic61—41no—
93C22×Dic61—41no—
94C22×Dic61—42no—
95C22×Dic61—42no—
96C22×Dic61C4212yes—
97C22×Dic61C22⋊C411yescharacteristic
98C22×Dic61C22⋊C411yescharacteristic
99C22×Dic61C22⋊C412yes—
100C22×Dic61C22⋊C412yes—
101C22×Dic61C22⋊C412yes—
102C22×Dic61C22⋊C412yes—
103C22×Dic61C4⋊C412yes—
104C22×Dic61C4⋊C412yes—
105C22×Dic61C4⋊C412yes—
106C22×Dic61C4⋊C412yes—
107C22×Dic61C4⋊C412yes—
108C22×Dic61C22×C411yescharacteristic
109C22×Dic61C22×C411yescharacteristic
110C22×Dic61C2×D411yescharacteristic
111C22×Dic61C2×D411yescharacteristic
112C22×Dic61C2×D411yescharacteristic
113C22×Dic61C2×Q811yescharacteristic
114#11758217—48no—
115C2×#92420—24no—
116C2×#92420—24no—
117C2×#92420—48no—
118C2×#92420—42no—
119C2×#92420—42no—
120C2×#92420—42no—
121C2×#92420—42no—
122C22⋊C4×C61—42no—
123C22⋊C4×C61—42no—
124C22⋊Dic61—42no—
125C22⋊Dic61—42no—
126C23×C61—22no—
127C23×C61—21no—
128C23×C61—21no—
129C23×C61—22no—
130C23×C61—22no—
131C23×C61—24no—
132C23×C61—24no—
133C23×C61—24no—
134C23×C61—22no—
135C23×C61—21no—
136C23×C61—21no—
137C23×C61—22no—
138C23×C61—24no—
139C23×C61—42no—
140C23×C61—42no—
141C23×C61—48no—
142C23×C61—48no—
143C23×C61#9512yes—
144C23×C61#9512yes—
145C23×C61#9912yes—
146C23×C61#9912yes—
147C23×C61C2×C4211yescharacteristic
148C23×C61C2×C22⋊C411yescharacteristic
149C23×C61C2×C4⋊C411yescharacteristic
150C23×C61#13114yes—
151C2×C4×C61—42no—
152C2×C4×C61—42no—
153C2×C4×C61—42no—
154C2×C4×C61—84no—
155C2×Dic61—24no—
156C2×Dic61—24no—
157C2×Dic61—24no—
158C2×Dic61—24no—
159C2×Dic61—21no—
160C2×Dic61—21no—
161C2×Dic61—21no—
162C2×Dic61—21no—
163C2×Dic61—21no—
164C2×Dic61—21no—
165C2×Dic61—21no—
166C2×Dic61—21no—
167C2×Dic61—42no—
168C2×Dic61—42no—
169C2×Dic61—42no—
170C2×Dic61—42no—
171C2×Dic61—42no—
172C2×Dic61—42no—
173C2×Dic61—41no—
174C2×Dic61—41no—
175C2×Dic61—41no—
176C2×Dic61—41no—
177C2×Dic61—42no—
178C2×Dic61—42no—
179C2×Dic61—42no—
180C2×Dic61—84no—
181C2×Dic61#9512yes—
182C2×Dic61#9512yes—
183C2×Dic61C2×C22⋊C411yescharacteristic
184C2×Dic61C2×C22⋊C411yescharacteristic
185C2×Dic61C2×C4⋊C411yescharacteristic
186C2×Dic61C2×C4⋊C411yescharacteristic
187#92420—44no—
188#92420—44no—
189#7913—611nomaximal, Sylow
190C22×C61—24no—
191C22×C61—24no—
192C22×C61—24no—
193C22×C61—24no—
194C22×C61—22no—
195C22×C61—21no—
196C22×C61—21no—
197C22×C61—22no—
198C22×C61—21no—
199C22×C61—21no—
200C22×C61—22no—
201C22×C61—22no—
202C22×C61—22no—
203C22×C61—48no—
204C22×C61—48no—
205C22×C61—42no—
206C22×C61—42no—
207C22×C61#34214yes—
208C22×C61C2×#9511yescharacteristic
209C22×C61#40512yes—
210C22×C61#40812yes—
211C22×C61C2×#9911yescharacteristic
212C22×C61C2×#9911yescharacteristic
213C22×C61#41312yes—
214C22×C61#42412yes—
215C4×C61—82no—
216Dic61—21no—
217Dic61—21no—
218Dic61—22no—
219Dic61—22no—
220Dic61—21no—
221Dic61—21no—
222Dic61—82no—
223C2×#407—611no—
224C22×C22⋊C8—611no—
225C2×#381—611no—
226#1280—614no—
227C2×C61—24no—
228C2×C61—22no—
229C2×C61—22no—
230C2×C61—42no—
231C2×C61#146812yes—
232C2×C61#146812yes—
233C2×C61#172911yescharacteristic
234C2×C61C2×#34211yescharacteristic
235C2×C61#174211yescharacteristic
236C24×C4—611no—
237C22×M16—1221no—
238C23×C8—1221no—
239C22×C22⋊C4—611no—
240C22×C22⋊C4#692311yescharacteristic
241#407—614no—
242#407—1222no—
243C2×C22⋊C8—612no—
244C2×C22⋊C8—612no—
245C2×C22⋊C8—614no—
246C2×C22⋊C8—1222no—
247C2×C22⋊C8—1221no—
248C2×C22⋊C8—1221no—
249#381—1221no—
250#381—1221no—
251#381—1221no—
252#381—1221no—
253C2×#95—612no—
254C2×#95—612no—
255C61#791311yescharacteristic, complemented, Sylow
256C25C2×#692311yescharacteristic
257C23×C4—611no—
258C23×C4—611no—
259C23×C4—612no—
260C23×C4—612no—
261C23×C4—612no—
262C23×C4—612no—
263C23×C4—611no—
264C23×C4—611no—
265C23×C4—611no—
266C23×C4—611no—
267C23×C4—612no—
268C23×C4—2442no—
269C23×C4—2442no—
270C23×C4C2×#692312yes—
271C2×M16—1224no—
272C2×M16—2442no—
273C2×M16—2442no—
274C22×C8—1224no—
275C22×C8—1222no—
276C22×C8—1222no—
277C22×C8—2442no—
278C22×C8—2442no—
279C2×C22⋊C4—21no—
280C2×C22⋊C4—21no—
281C2×C22⋊C4—42no—
282C2×C22⋊C4—1221no—
283C2×C22⋊C4—1221no—
284C2×C22⋊C4—2442no—
285C22⋊C8—614no—
286C22⋊C8—614no—
287C22⋊C8—1224no—
288C22⋊C8—1222no—
289C22⋊C8—1222no—
290C22⋊C8—1224no—
291#95—1222no—
292#95—1222no—
293#95—1222no—
294#95—1222no—
295C24—22no—
296C24—22no—
297C24—24no—
298C24—42no—
299C24C4×#692312yes—
300C24C4⋊#692312yes—
301C24C22⋊#692311yescharacteristic
302C24C22⋊#692311yescharacteristic
303C24C22×#692311yescharacteristic
304C22×C4—22no—
305C22×C4—24no—
306C22×C4—42no—
307C22×C4—42no—
308C22×C4—612no—
309C22×C4—612no—
310C22×C4—612no—
311C22×C4—612no—
312C22×C4—611no—
313C22×C4—611no—
314C22×C4—611no—
315C22×C4—611no—
316C22×C4—612no—
317C22×C4—612no—
318C22×C4—612no—
319C22×C4—612no—
320C22×C4—611no—
321C22×C4—611no—
322C22×C4—612no—
323C22×C4—611no—
324C22×C4—612no—
325C22×C4—611no—
326C22×C4—1222no—
327C22×C4—1222no—
328C22×C4—1222no—
329C22×C4—1222no—
330C22×C4—1224no—
331C22×C4—1222no—
332C22×C4—2441no—
333C22×C4—2441no—
334C22×C4—2441no—
335C22×C4—2441no—
336C22×C4—2441no—
337C22×C4—2441no—
338C22×C4—2441no—
339C22×C4—2441no—
340C22×C4—2444no—
341C22×C4—2444no—
342C22×C4—2444no—
343C22×C4—2444no—
344C22×C4—2442no—
345C22×C4—2442no—
346M16—2448no—
347C2×C8—1224no—
348C2×C8—1224no—
349C2×C8—2442no—
350C2×C8—2442no—
351C2×C8—2448no—
352C2×C8—2442no—
353C2×C8—2442no—
354C22⋊C4—42no—
355C22⋊C4—42no—
356C22⋊C4—2442no—
357C22⋊C4—2442no—
358C23—22no—
359C23—21no—
360C23—21no—
361C23—22no—
362C23—22no—
363C23—24no—
364C23—22no—
365C23—21no—
366C23—21no—
367C23—22no—
368C23—24no—
369C23—24no—
370C23—24no—
371C23—42no—
372C23—42no—
373C23—48no—
374C23—48no—
375C23(C2×#6923)⋊C412yes—
376C23(C2×#6923)⋊C412yes—
377C23#1451983512yes—
378C23#1451983612yes—
379C23C2×C4×#692311yescharacteristic
380C23C2×C22⋊#692311yescharacteristic
381C23C2×C4⋊#692311yescharacteristic
382C23#1451986414yes—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—84no—
387C2×C4—612no—
388C2×C4—612no—
389C2×C4—611no—
390C2×C4—611no—
391C2×C4—611no—
392C2×C4—611no—
393C2×C4—1221no—
394C2×C4—1221no—
395C2×C4—1221no—
396C2×C4—1221no—
397C2×C4—1221no—
398C2×C4—1221no—
399C2×C4—1221no—
400C2×C4—1221no—
401C2×C4—1224no—
402C2×C4—1224no—
403C2×C4—1224no—
404C2×C4—1224no—
405C2×C4—4884no—
406C2×C4—2441no—
407C2×C4—2441no—
408C2×C4—2441no—
409C2×C4—2442no—
410C2×C4—2442no—
411C2×C4—2442no—
412C2×C4—2442no—
413C2×C4—2441no—
414C2×C4—2442no—
415C2×C4—2442no—
416C2×C4—2442no—
417C2×C4—2442no—
418C2×C4—2442no—
419C8—2444no—
420C8—2444no—
421C22—21no—
422C22—21no—
423C22—22no—
424C22—21no—
425C22—21no—
426C22—24no—
427C22—24no—
428C22—24no—
429C22—24no—
430C22—22no—
431C22—22no—
432C22—22no—
433C22—22no—
434C22—48no—
435C22—48no—
436C22—42no—
437C22—42no—
438C22#1684064014yes—
439C22C2×(C2×#6923)⋊C411yescharacteristic
440C22#1684072612yes—
441C22#1684073512yes—
442C22C2×#1451983511yescharacteristic
443C22C2×#1451983611yescharacteristic
444C22#1684074912yes—
445C22#1684076812yes—
446C4—82no—
447C4—1221no—
448C4—1221no—
449C4—1222no—
450C4—1222no—
451C4—1221no—
452C4—1221no—
453C4—4882no—
454C2—22no—
455C2—22no—
456C2—24no—
457C2—42no—
458C2#2146108412yes—
459C2#2146108612yes—
460C2#2146148511yescharacteristic
461C2C2×#1684064011yescharacteristic
462C2#2146152511yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC23×C61C2×C42
FrattiniC24C22×#6923
FittingC22×C22⋊C4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC25×C61C2×C4
cosocleC23×Dic61C23
hypercenterC22×C22⋊C4#6923
hypocenterC61#7913
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C25 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #21460657C2semidirect
8. #16840732C4semidirect
12. C2×C22⋊#92420C4semidirect
255. C61#7913semidirect

Maximal subgroups

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

subgroupindex
C2×#168407322
C22×C22⋊#924202
#214606572
C2×#168396232
#791361