Finite Group Databasebeta

← #30610172

Subgroups — #30610172

Order 15616.

1386 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
1C2×#16840732C212yesmaximal
2#21461098C218yesmaximal, complemented
3#21461069C212yesmaximal, complemented
4#21461067C212yesmaximal, complemented
5C22×#14519754C211yesmaximal, characteristic
6C22×#11758217—22no—
7#16840732—22no—
8#16840732—22no—
9#16840732C2214yes—
10#16840732C2214yes—
11C2×C22⋊#92420—22no—
12C2×C22⋊#92420C2214yes—
13#16840608C2218yescomplemented
14#16840607C2218yescomplemented
15C23×Dic122C411yescharacteristic
16C24×Dic61C2211yescharacteristic
17C2×#14519754—22no—
18C2×#14519754—22no—
19C2×#14519754—22no—
20C2×#14519754—22no—
21C2×#14519754C414yes—
22C2×#14519754C2214yes—
23C22×C4⋊Dic61C2211yescharacteristic
24C22×#11758196C411yescharacteristic
25C22×#11758196C2211yescharacteristic
26C22×C22⋊Dic61C411yescharacteristic
27C22×C22⋊C4×C61C411yescharacteristic
28C2×#11758217—24no—
29C2×#11758217—24no—
30C2×#11758217—48no—
31C22×#92420—24no—
32C22⋊#92420—24no—
33C22⋊#92420—24no—
34C22⋊#92420—24no—
35C22⋊#92420C2318yes—
36C22×Dic122—21no—
37C22×Dic122—22no—
38C22×Dic122—21no—
39C22×Dic122—44no—
40C22×Dic122C2×C414yes—
41C23×Dic61—44no—
42C23×Dic61C2×C411yescharacteristic
43C23×Dic61C2×C411yescharacteristic
44C23×Dic61C2×C411yescharacteristic
45C23×Dic61C2×C412yes—
46C23×Dic61D412yes—
47C23×Dic61D412yes—
48C23×Dic61D412yes—
49C23×Dic61D412yes—
50C23×Dic61C2311yescharacteristic
51C23×Dic61C2312yes—
52#14519754—24no—
53#14519754—24no—
54#14519754—24no—
55#14519754—24no—
56#14519754—24no—
57#14519754—24no—
58#14519754—24no—
59#14519754—24no—
60C2×C4⋊Dic61—22no—
61C2×C4⋊Dic61—22no—
62C2×C4⋊Dic61C2×C412yes—
63C2×C4⋊Dic61C2312yes—
64C2×#11758196—21no—
65C2×#11758196—22no—
66C2×#11758196—21no—
67C2×#11758196—22no—
68C2×#11758196—22no—
69C2×#11758196C2×C414yes—
70C2×#11758196C2×C412yes—
71C2×#11758196C2312yes—
72C2×C22⋊Dic61—22no—
73C2×C22⋊Dic61—21no—
74C2×C22⋊Dic61—21no—
75C2×C22⋊Dic61C2×C414yes—
76C25×C61C2×C411yescharacteristic
77C23×C4×C61C2×C411yescharacteristic
78C23×C4×C61C2×C411yescharacteristic
79C2×C22⋊C4×C61—22no—
80C2×C22⋊C4×C61—21no—
81C2×C22⋊C4×C61—21no—
82C2×C22⋊C4×C61C2×C414yes—
83C24×C61—24no—
84C24×C61—42no—
85C24×C61—42no—
86C24×C61C22⋊C412yes—
87C24×C61C22⋊C411yescharacteristic
88C24×C61C22⋊C411yescharacteristic
89C24×C61C22×C411yescharacteristic
90C24×C61C22×C412yes—
91C22×C4×C61—21no—
92C22×C4×C61—21no—
93C22×C4×C61—21no—
94C22×C4×C61—21no—
95C22×C4×C61—42no—
96C22×C4×C61—42no—
97C22×C4×C61C22×C412yes—
98C22×C4×C61C22×C412yes—
99C22×Dic61—24no—
100C22×Dic61—28no—
101C22×Dic61—21no—
102C22×Dic61—21no—
103C22×Dic61—21no—
104C22×Dic61—21no—
105C22×Dic61—44no—
106C22×Dic61—44no—
107C22×Dic61—44no—
108C22×Dic61—44no—
109C22×Dic61—44no—
110C22×Dic61—42no—
111C22×Dic61—42no—
112C22×Dic61—42no—
113C22×Dic61C22⋊C411yescharacteristic
114C22×Dic61C22⋊C412yes—
115C22×Dic61C22⋊C412yes—
116C22×Dic61C22⋊C412yes—
117C22×Dic61C22⋊C412yes—
118C22×Dic61C22⋊C412yes—
119C22×Dic61C22⋊C411yescharacteristic
120C22×Dic61C22×C412yes—
121C22×Dic61C22×C412yes—
122C22×Dic61C22×C412yes—
123C22×Dic61C22×C411yescharacteristic
124C22×Dic61C2×D412yes—
125C22×Dic61C2×D412yes—
126C22×Dic61C2×D412yes—
127C22×Dic61C2×D412yes—
128C22×Dic61C2×D412yes—
129C22×Dic61C2×D412yes—
130C22×Dic61C2411yescharacteristic
131C2×Dic122—24no—
132C2×Dic122—24no—
133C2×Dic122—44no—
134C2×Dic122—48no—
135C2×Dic122—44no—
136C2×Dic122—48no—
137#11758217—48no—
138#11758217—48no—
139C2×#92420—28no—
140C2×#92420—48no—
141C22⋊C4×C61—24no—
142C22⋊C4×C61—24no—
143C22⋊Dic61—24no—
144C22⋊Dic61—24no—
145C4⋊Dic61—24no—
146C4⋊Dic61—24no—
147#11758196—24no—
148#11758196—24no—
149#11758196—24no—
150#11758196—24no—
151C23×C61—22no—
152C23×C61—22no—
153C23×C61—22no—
154C23×C61—24no—
155C23×C61—24no—
156C23×C61—24no—
157C23×C61—22no—
158C23×C61—24no—
159C23×C61—41no—
160C23×C61—41no—
161C23×C61—42no—
162C23×C61—41no—
163C23×C61—42no—
164C23×C61—41no—
165C23×C61—416no—
166C23×C61#10114yes—
167C23×C61C2×C22⋊C412yes—
168C23×C61C2×C22⋊C411yescharacteristic
169C23×C61C2×C22⋊C412yes—
170C23×C61C2×C22⋊C411yescharacteristic
171C23×C61C23×C411yescharacteristic
172C2×C4×C61—22no—
173C2×C4×C61—22no—
174C2×C4×C61—24no—
175C2×C4×C61—42no—
176C2×C4×C61—42no—
177C2×C4×C61—42no—
178C2×C4×C61—42no—
179C2×C4×C61—42no—
180C2×Dic61—24no—
181C2×Dic61—22no—
182C2×Dic61—24no—
183C2×Dic61—24no—
184C2×Dic61—24no—
185C2×Dic61—24no—
186C2×Dic61—24no—
187C2×Dic61—24no—
188C2×Dic61—22no—
189C2×Dic61—22no—
190C2×Dic61—24no—
191C2×Dic61—42no—
192C2×Dic61—42no—
193C2×Dic61—41no—
194C2×Dic61—42no—
195C2×Dic61—42no—
196C2×Dic61—42no—
197C2×Dic61—41no—
198C2×Dic61—42no—
199C2×Dic61—42no—
200C2×Dic61—42no—
201C2×Dic61—42no—
202C2×Dic61—42no—
203C2×Dic61#9914yes—
204C2×Dic61C2×C22⋊C412yes—
205C2×Dic61C2×C22⋊C412yes—
206C2×Dic61C2×C22⋊C412yes—
207C2×Dic61C22×D412yes—
208Dic122—48no—
209Dic122—48no—
210#92420—48no—
211#17397—611nomaximal, Sylow
212C22×C61—28no—
213C22×C61—21no—
214C22×C61—21no—
215C22×C61—22no—
216C22×C61—21no—
217C22×C61—21no—
218C22×C61—22no—
219C22×C61—21no—
220C22×C61—21no—
221C22×C61—22no—
222C22×C61—22no—
223C22×C61—22no—
224C22×C61—44no—
225C22×C61—48no—
226C22×C61—48no—
227C22×C61—44no—
228C22×C61C2×#9912yes—
229C22×C61C2×#10112yes—
230C22×C61C2×#10114yes—
231C22×C61C22×C22⋊C411yescharacteristic
232C22×C61#56812yes—
233C4×C61—42no—
234C4×C61—42no—
235Dic61—22no—
236Dic61—22no—
237Dic61—22no—
238Dic61—42no—
239Dic61—42no—
240Dic61C2×#9914yes—
241C22×C22⋊Q8—611no—
242C2×#407—612no—
243#1472—618no—
244#1463—612no—
245#1463—612no—
246C2×C61—22no—
247C2×C61—22no—
248C2×C61—22no—
249C2×C61—24no—
250C2×C61—42no—
251C2×C61#287911yescharacteristic
252C2×C61C22×#9911yescharacteristic
253C2×C61C22×#10111yescharacteristic
254C23×Q8—611no—
255C24×C4—611no—
256C22×M16—1222no—
257C2×C22⋊Q8—614no—
258C2×C22⋊Q8—614no—
259C2×C22⋊Q8—1222no—
260C2×C22⋊Q8—1222no—
261C2×C22⋊Q8—1222no—
262C2×C22⋊Q8—1222no—
263C22×C4⋊C4—611no—
264C22×C4⋊C4—611no—
265C22×C4⋊C4—611no—
266C22×C22⋊C4—611no—
267C22×C22⋊C4#692311yescharacteristic
268#407—614no—
269#407—614no—
270#407—1222no—
271#407—1222no—
272C2×C22⋊C8—614no—
273C2×C22⋊C8—1222no—
274#324—618no—
275#324—618no—
276C61#1739711yescharacteristic, complemented, Sylow
277C25C2×#692311yescharacteristic
278C22×Q8—614no—
279C22×Q8—1221no—
280C22×Q8—1222no—
281C22×Q8—1221no—
282C22×Q8—2444no—
283C23×C4—612no—
284C23×C4—611no—
285C23×C4—612no—
286C23×C4—612no—
287C23×C4—612no—
288C23×C4—611no—
289C23×C4—612no—
290C23×C4—612no—
291C23×C4—611no—
292C23×C4—611no—
293C23×C4—2444no—
294C23×C4C2×#692311yescharacteristic
295C23×C4C2×#692311yescharacteristic
296C2×M16—1224no—
297C2×M16—1224no—
298C2×M16—2448no—
299C22×C8—1224no—
300C22⋊Q8—1224no—
301C22⋊Q8—1224no—
302C22⋊Q8—1224no—
303C22⋊Q8—1224no—
304C22⋊Q8—1224no—
305C22⋊Q8—1224no—
306C22⋊Q8—1224no—
307C22⋊Q8—1224no—
308C2×C4⋊C4—612no—
309C2×C4⋊C4—612no—
310C2×C4⋊C4—614no—
311C2×C4⋊C4—612no—
312C2×C4⋊C4—612no—
313C2×C4⋊C4—1221no—
314C2×C4⋊C4—1222no—
315C2×C4⋊C4—1221no—
316C2×C4⋊C4—1222no—
317C2×C4⋊C4—1222no—
318C2×C4⋊C4—1222no—
319C2×C4⋊C4—1222no—
320C2×C22⋊C4—22no—
321C2×C22⋊C4—21no—
322C2×C22⋊C4—21no—
323C2×C22⋊C4—614no—
324C2×C22⋊C4—1222no—
325C2×C22⋊C4—1221no—
326C2×C22⋊C4—1221no—
327C2×C22⋊C4C2×#692314yes—
328C22⋊C8—618no—
329C22⋊C8—1224no—
330C22⋊C8—1224no—
331C22⋊C8—1224no—
332C24—24no—
333C24—42no—
334C24—42no—
335C24C22⋊#692312yes—
336C24C22⋊#692311yescharacteristic
337C24C22⋊#692311yescharacteristic
338C24C22×#692311yescharacteristic
339C24C22×#692312yes—
340C2×Q8—1224no—
341C2×Q8—1224no—
342C2×Q8—2444no—
343C2×Q8—2448no—
344C2×Q8—2448no—
345C2×Q8—2444no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—42no—
351C22×C4—42no—
352C22×C4—611no—
353C22×C4—612no—
354C22×C4—612no—
355C22×C4—611no—
356C22×C4—612no—
357C22×C4—612no—
358C22×C4—612no—
359C22×C4—612no—
360C22×C4—612no—
361C22×C4—612no—
362C22×C4—612no—
363C22×C4—612no—
364C22×C4—612no—
365C22×C4—612no—
366C22×C4—611no—
367C22×C4—611no—
368C22×C4—612no—
369C22×C4—612no—
370C22×C4—1228no—
371C22×C4—1224no—
372C22×C4—1221no—
373C22×C4—1221no—
374C22×C4—1221no—
375C22×C4—1221no—
376C22×C4—2444no—
377C22×C4—2444no—
378C22×C4—2444no—
379C22×C4—2444no—
380C22×C4—2442no—
381C22×C4—2444no—
382C22×C4—2442no—
383C22×C4—2442no—
384C22×C4C22×#692312yes—
385C22×C4C22×#692312yes—
386M16—2448no—
387M16—2448no—
388C2×C8—1228no—
389C2×C8—2448no—
390C4⋊C4—1224no—
391C4⋊C4—1224no—
392C4⋊C4—1224no—
393C4⋊C4—1224no—
394C4⋊C4—1224no—
395C4⋊C4—1224no—
396C22⋊C4—24no—
397C22⋊C4—24no—
398C22⋊C4—1224no—
399C22⋊C4—1224no—
400C23—22no—
401C23—22no—
402C23—22no—
403C23—24no—
404C23—24no—
405C23—22no—
406C23—24no—
407C23—24no—
408C23—41no—
409C23—41no—
410C23—42no—
411C23—41no—
412C23—42no—
413C23—41no—
414C23—416no—
415C23#1451983814yes—
416C23C2×C22⋊#692312yes—
417C23C2×C22⋊#692311yescharacteristic
418C23C2×C22⋊#692312yes—
419C23C2×C22⋊#692311yescharacteristic
420C23C23×#692311yescharacteristic
421Q8—2448no—
422Q8—2448no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—24no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—614no—
432C2×C4—612no—
433C2×C4—612no—
434C2×C4—612no—
435C2×C4—612no—
436C2×C4—1224no—
437C2×C4—1224no—
438C2×C4—1224no—
439C2×C4—1224no—
440C2×C4—1224no—
441C2×C4—1224no—
442C2×C4—1224no—
443C2×C4—1222no—
444C2×C4—1222no—
445C2×C4—1222no—
446C2×C4—1224no—
447C2×C4—2441no—
448C2×C4—2442no—
449C2×C4—2442no—
450C2×C4—2442no—
451C2×C4—2441no—
452C2×C4—2442no—
453C2×C4—2442no—
454C2×C4—2442no—
455C2×C4—2442no—
456C2×C4—2442no—
457C2×C4—2442no—
458C2×C4—2442no—
459C8—2448no—
460C22—28no—
461C22—21no—
462C22—21no—
463C22—22no—
464C22—21no—
465C22—21no—
466C22—22no—
467C22—21no—
468C22—21no—
469C22—22no—
470C22—22no—
471C22—22no—
472C22—44no—
473C22—48no—
474C22—48no—
475C22—44no—
476C22D61⋊#9912yes—
477C22C2×#1451983812yes—
478C22C2×#1451983814yes—
479C22C22×C22⋊#692311yescharacteristic
480C22#1684084012yes—
481C4—42no—
482C4—42no—
483C4—614no—
484C4—1222no—
485C4—1222no—
486C4—1222no—
487C4—2442no—
488C4—2442no—
489C2—22no—
490C2—22no—
491C2—22no—
492C2—24no—
493C2—42no—
494C2#2146240311yescharacteristic
495C2C2×D61⋊#9911yescharacteristic
496C2C22×#1451983811yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC22×C22⋊C4×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC25×C61C2×C4
cosocleC22×Dic61C24
hypercenterC22×C22⋊C4#6923
hypocenterC61#17397
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C25 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #21461098C2semidirect
3. #21461069C2semidirect
4. #21461067C2semidirect
13. #16840608C22semidirect
14. #16840607C22semidirect
276. C61#17397semidirect

Maximal subgroups

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

subgroupindex
C2×#168407322
#214610982
#214610692
#214610672
C22×#145197542
#1739761