Finite Group Databasebeta

← #30597240

Subgroups — #30597240

Order 15616.

994 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462263C211yesmaximal, characteristic
2#21462263C211yesmaximal, characteristic
3#21460718C214yesmaximal
4#21448200C211yesmaximal, characteristic
5C2×#14519856—21no—
6C2×#14519856C412yescomplemented
7#16840705—21no—
8#16840705C412yescomplemented
9#16840704—21no—
10#16840704—21no—
11#16840704—21no—
12#16840704C412yescomplemented
13#16840703C2212yes—
14#16840703C2212yes—
15C4×C22⋊#6923—21no—
16C4×C22⋊#6923—21no—
17C4×C22⋊#6923—21no—
18C4×C22⋊#6923C412yescomplemented
19C23×C4×D61C2211yescharacteristic
20C2×#14519734—21no—
21#16839624—21no—
22#16839621—21no—
23#16839620C412yescomplemented
24#16839617C2212yes—
25C4×#11758198—21no—
26C4×C22⋊Dic61C411yescharacteristic, complemented
27C4×C22⋊C4×C61C411yescharacteristic, complemented
28#14519856—44no—
29#14519856—44no—
30C2×C4⋊#6923—22no—
31C2×C4⋊#6923—22no—
32C2×C22⋊#6923—22no—
33C2×C22⋊#6923—22no—
34C2×C22⋊#6923—22no—
35C2×C22⋊#6923—22no—
36C2×C22⋊#6923C2×C414yes—
37C2×C22⋊#6923C2×C414yes—
38C2×C4×#6923—22no—
39C2×C4×#6923—22no—
40(C2×#6923)⋊C4—22no—
41(C2×#6923)⋊C4—22no—
42(C2×#6923)⋊C4—22no—
43(C2×#6923)⋊C4—22no—
44C24×D61C2311yescharacteristic
45C23×Dic61C2×C411yescharacteristic
46C22×C4×D61—44no—
47C22×C4×D61C2×C411yescharacteristic
48C22×C4×D61C2×C411yescharacteristic
49C22×C4×D61C2×C411yescharacteristic
50C22×C4×D61C2×C411yescharacteristic
51C22×C4×D61D411yescharacteristic
52C22×C4×D61D411yescharacteristic
53C22×C4×D61D411yescharacteristic
54C22×C4×D61D411yescharacteristic
55C22×C4×D61D411yescharacteristic
56C22×C4×D61D411yescharacteristic
57C22×C4×D61Q811yescharacteristic
58C22×C4×D61Q811yescharacteristic
59#14519734—44no—
60C2×#11758196—22no—
61C2×C22⋊Dic61C2×C412yes—
62C2×#11758198—22no—
63C2×#11758198—22no—
64C2×C4×Dic61—21no—
65#14519684—21no—
66#14519684—22no—
67C23×C4×C61C2×C411yescharacteristic
68C2×C22⋊C4×C61C2×C412yes—
69C2×C42×C61—21no—
70#95×C61—21no—
71C24×C61C22×C411yescharacteristic
72C23×D61—42no—
73C23×D61—42no—
74C23×D61—42no—
75C23×D61C22×C411yescharacteristic
76C23×D61C22×C411yescharacteristic
77C23×D61C2×D411yescharacteristic
78C23×D61C2×D411yescharacteristic
79C23×D61C2×D411yescharacteristic
80C23×D61C2×Q811yescharacteristic
81C22×#6923—24no—
82C22×#6923—24no—
83C22×C4×C61—22no—
84C22×C4×C61—42no—
85C22×C4×C61C4211yescharacteristic
86C22×C4×C61C4211yescharacteristic
87C22×C4×C61C22⋊C411yescharacteristic
88C22×C4×C61C22⋊C411yescharacteristic
89C22×C4×C61C4⋊C411yescharacteristic
90C22×C4×C61C4⋊C411yescharacteristic
91C22×Dic61—22no—
92C22×Dic61—42no—
93C22×Dic61C4211yescharacteristic
94C22×Dic61C4211yescharacteristic
95C22×Dic61C22⋊C411yescharacteristic
96C22×Dic61C22⋊C411yescharacteristic
97C22×Dic61C4⋊C411yescharacteristic
98C22×Dic61C4⋊C411yescharacteristic
99C2×C4×D61—24no—
100C2×C4×D61—24no—
101C2×C4×D61—24no—
102C2×C4×D61—42no—
103C2×C4×D61—42no—
104C2×C4×D61—42no—
105C2×C4×D61—42no—
106C2×C4×D61—42no—
107C2×C4×D61—42no—
108C2×C4×D61—42no—
109C2×C4×D61—42no—
110C2×C4×D61—42no—
111C2×C4×D61C22⋊C411yescharacteristic
112C2×C4×D61C22⋊C411yescharacteristic
113C2×C4×D61C22⋊C411yescharacteristic
114C2×C4×D61C22⋊C411yescharacteristic
115C2×C4×D61C22⋊C411yescharacteristic
116C2×C4×D61C22⋊C411yescharacteristic
117C2×C4×D61C22⋊C411yescharacteristic
118C2×C4×D61C22⋊C411yescharacteristic
119C2×C4×D61C4⋊C411yescharacteristic
120C2×C4×D61C4⋊C411yescharacteristic
121C2×C4×D61C4⋊C411yescharacteristic
122C2×C4×D61C4⋊C411yescharacteristic
123C2×C4×D61C4⋊C411yescharacteristic
124C2×C4×D61C4⋊C411yescharacteristic
125C2×C4×D61C4⋊C411yescharacteristic
126C2×C4×D61C4⋊C411yescharacteristic
127C22⋊#6923—44no—
128C22⋊#6923—44no—
129C22⋊#6923—44no—
130C22⋊#6923—44no—
131C22⋊#6923—44no—
132C22⋊#6923—44no—
133C4⋊#6923—44no—
134C4⋊#6923—44no—
135C4×#6923—44no—
136C4×#6923—44no—
137C22⋊C4×C61—42no—
138C42×C61—42no—
139C22⋊Dic61—42no—
140#11758198—44no—
141#11758198—44no—
142#11758196—44no—
143C4×Dic61—42no—
144C23×C61—22no—
145C23×C61—41no—
146C23×C61—41no—
147C23×C61C2×C4211yescharacteristic
148C23×C61C2×C22⋊C411yescharacteristic
149C23×C61C2×C4⋊C411yescharacteristic
150C22×D61—22no—
151C22×D61—22no—
152C22×D61—22no—
153C22×D61—22no—
154C22×D61—22no—
155C22×D61—22no—
156C22×D61—22no—
157C22×D61—22no—
158C22×D61—41no—
159C22×D61—41no—
160C22×D61—41no—
161C22×D61—41no—
162C22×D61—41no—
163C22×D61—41no—
164C22×D61—41no—
165C22×D61—41no—
166C22×D61—41no—
167C22×D61—41no—
168C22×D61—416no—
169C22×D61C2×C22⋊C411yescharacteristic
170C22×D61C2×C22⋊C411yescharacteristic
171C22×D61C2×C4⋊C411yescharacteristic
172C22×D61C2×C4⋊C411yescharacteristic
173C2×#6923—44no—
174C2×#6923—44no—
175C2×#6923—44no—
176C2×#6923—44no—
177C2×#6923—44no—
178C2×#6923—44no—
179C2×C4×C61—22no—
180C2×C4×C61—22no—
181C2×C4×C61—22no—
182C2×C4×C61—41no—
183C2×C4×C61—41no—
184C2×C4×C61—41no—
185C2×C4×C61—42no—
186C2×C4×C61—42no—
187C2×C4×C61—42no—
188C2×C4×C61#9511yescharacteristic
189C2×C4×C61#9511yescharacteristic
190C2×C4×C61#9511yescharacteristic
191C2×C4×C61#9511yescharacteristic
192C2×Dic61—22no—
193C2×Dic61—22no—
194C2×Dic61—22no—
195C2×Dic61—41no—
196C2×Dic61—41no—
197C2×Dic61—41no—
198C2×Dic61—42no—
199C2×Dic61—42no—
200C2×Dic61—42no—
201C2×Dic61#9511yescharacteristic
202C2×Dic61#9511yescharacteristic
203C2×Dic61#9511yescharacteristic
204C2×Dic61#9511yescharacteristic
205C4×D61—22no—
206C4×D61—22no—
207C4×D61—22no—
208C4×D61—22no—
209C4×D61—22no—
210C4×D61—22no—
211C4×D61—22no—
212C4×D61—22no—
213C4×D61—22no—
214C4×D61—41no—
215C4×D61—41no—
216C4×D61—41no—
217C4×D61—41no—
218C4×D61—41no—
219C4×D61—41no—
220C4×D61#9914yes—
221#8102—611nomaximal, Sylow
222C22×C61—21no—
223C22×C61—21no—
224C22×C61—21no—
225C22×C61—21no—
226C22×C61—21no—
227C22×C61—21no—
228C22×C61—21no—
229C22×C61—21no—
230C22×C61—44no—
231C22×C61C2×#9511yescharacteristic
232C22×C61#41012yes—
233C2×D61—21no—
234C2×D61—21no—
235C2×D61—21no—
236C2×D61—21no—
237C2×D61—21no—
238C2×D61—21no—
239C2×D61—21no—
240C2×D61—21no—
241C2×D61—21no—
242C2×D61—21no—
243C2×D61—44no—
244C2×D61—44no—
245C2×D61—44no—
246C2×D61—44no—
247C2×D61—44no—
248C2×D61—44no—
249C2×D61C2×#9912yes—
250C2×D61#41012yes—
251#6923—84no—
252#6923—84no—
253C4×C61—21no—
254C4×C61—21no—
255C4×C61—21no—
256C4×C61—82no—
257C4×C61#34212yes—
258Dic61—21no—
259Dic61—21no—
260Dic61—21no—
261Dic61—82no—
262Dic61#34212yes—
263#2280—611no—
264#2280—611no—
265#2280—611no—
266#1304—614no—
267C2×C61—22no—
268C2×C61—41no—
269C2×C61—41no—
270C2×C61C2×#34211yescharacteristic
271C2×C61#174011yescharacteristic
272C2×C61#174011yescharacteristic
273D61—22no—
274D61—22no—
275D61—41no—
276D61—41no—
277C24×C4—611no—
278C2×#117—612no—
279C2×#117—1221no—
280C2×#117—1221no—
281#381—612no—
282#381—1221no—
283#381—1221no—
284#380—612no—
285#380—612no—
286#380—1221no—
287#380—1221no—
288#380—1221no—
289#380—1221no—
290#379—612no—
291#379—612no—
292#379—612no—
293C4×C22⋊C4—612no—
294C4×C22⋊C4—611no—
295C4×C22⋊C4—1221no—
296C4×C22⋊C4—1221no—
297C4×C22⋊C4—1221no—
298C4×C22⋊C4—1221no—
299C4×C22⋊C4#692311yescharacteristic, complemented
300C61#810211yescharacteristic, complemented, Sylow
301C25—611no—
302C23×C4—611no—
303C23×C4—611no—
304C23×C4—611no—
305C23×C4—611no—
306C23×C4—611no—
307C23×C4—611no—
308C23×C4—611no—
309C23×C4—611no—
310C23×C4—611no—
311C23×C4—611no—
312C23×C4—611no—
313C23×C4—611no—
314C23×C4—611no—
315C23×C4—2444no—
316C23×C4C2×#692311yescharacteristic
317#117—2444no—
318#117—2444no—
319#117—2444no—
320C2×C4⋊C4—1222no—
321C2×C4⋊C4—1222no—
322C2×C4⋊C4—1222no—
323C2×C22⋊C4—614no—
324C2×C22⋊C4—614no—
325C2×C22⋊C4—612no—
326C2×C22⋊C4—1222no—
327C2×C22⋊C4—1222no—
328C2×C22⋊C4—1222no—
329C2×C22⋊C4—1222no—
330C2×C22⋊C4—1222no—
331C2×C22⋊C4—1222no—
332C2×C22⋊C4C2×#692312yes—
333C2×C42—21no—
334C2×C42—1222no—
335C2×C42—1222no—
336C2×C42—1221no—
337#95—21no—
338#95—1222no—
339#95—1222no—
340#95—1222no—
341#95—1222no—
342#95—1222no—
343#95—1221no—
344C24—611no—
345C24—611no—
346C24—611no—
347C24—611no—
348C24—611no—
349C24—611no—
350C24—2442no—
351C24—2442no—
352C24—2442no—
353C24C22×#692311yescharacteristic
354C22×C4—22no—
355C22×C4—42no—
356C22×C4—611no—
357C22×C4—611no—
358C22×C4—611no—
359C22×C4—611no—
360C22×C4—611no—
361C22×C4—611no—
362C22×C4—611no—
363C22×C4—611no—
364C22×C4—611no—
365C22×C4—611no—
366C22×C4—611no—
367C22×C4—611no—
368C22×C4—611no—
369C22×C4—611no—
370C22×C4—611no—
371C22×C4—611no—
372C22×C4—611no—
373C22×C4—611no—
374C22×C4—611no—
375C22×C4—611no—
376C22×C4—611no—
377C22×C4—611no—
378C22×C4—1224no—
379C22×C4—1224no—
380C22×C4—1224no—
381C22×C4—1224no—
382C22×C4—1224no—
383C22×C4—1222no—
384C22×C4—2442no—
385C22×C4—2442no—
386C22×C4—2442no—
387C22×C4—2442no—
388C22×C4—2442no—
389C22×C4—2442no—
390C22×C4—2442no—
391C22×C4—2442no—
392C22×C4—2442no—
393C22×C4—2442no—
394C22×C4C4×#692311yescharacteristic
395C22×C4C4×#692311yescharacteristic
396C22×C4C4⋊#692311yescharacteristic
397C22×C4C4⋊#692311yescharacteristic
398C22×C4C22⋊#692311yescharacteristic
399C22×C4C22⋊#692311yescharacteristic
400C4⋊C4—2444no—
401C4⋊C4—2444no—
402C4⋊C4—2444no—
403C22⋊C4—42no—
404C22⋊C4—2444no—
405C22⋊C4—2444no—
406C22⋊C4—2444no—
407C22⋊C4—2444no—
408C22⋊C4—2444no—
409C22⋊C4—2444no—
410C22⋊C4—2442no—
411C22⋊C4—2444no—
412C22⋊C4—2444no—
413C42—42no—
414C42—2442no—
415C42—2444no—
416C42—2444no—
417C23—22no—
418C23—41no—
419C23—41no—
420C23—611no—
421C23—611no—
422C23—611no—
423C23—611no—
424C23—1222no—
425C23—1222no—
426C23—1222no—
427C23—1222no—
428C23—1222no—
429C23—1222no—
430C23—1222no—
431C23—1222no—
432C23—2441no—
433C23—2441no—
434C23—2441no—
435C23—2441no—
436C23—2441no—
437C23—2441no—
438C23—2441no—
439C23—2441no—
440C23—2441no—
441C23—2441no—
442C23—24416no—
443C23C2×C4×#692311yescharacteristic
444C23C2×C22⋊#692311yescharacteristic
445C23C2×C4⋊#692311yescharacteristic
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—611no—
456C2×C4—614no—
457C2×C4—611no—
458C2×C4—611no—
459C2×C4—611no—
460C2×C4—1222no—
461C2×C4—1222no—
462C2×C4—1222no—
463C2×C4—1222no—
464C2×C4—1222no—
465C2×C4—1222no—
466C2×C4—1222no—
467C2×C4—1222no—
468C2×C4—1222no—
469C2×C4—1222no—
470C2×C4—1222no—
471C2×C4—1222no—
472C2×C4—2441no—
473C2×C4—2441no—
474C2×C4—2441no—
475C2×C4—2441no—
476C2×C4—2441no—
477C2×C4—2441no—
478C2×C4—2441no—
479C2×C4—2441no—
480C2×C4—2441no—
481C2×C4—2442no—
482C2×C4—2442no—
483C2×C4—2444no—
484C2×C4—2444no—
485C2×C4—2444no—
486C2×C4—2444no—
487C2×C4—2444no—
488C2×C4—2444no—
489C2×C4—2442no—
490C2×C4(C2×#6923)⋊C411yescharacteristic
491C2×C4(C2×#6923)⋊C411yescharacteristic
492C2×C4(C2×#6923)⋊C411yescharacteristic
493C2×C4(C2×#6923)⋊C411yescharacteristic
494C22—21no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—44no—
503C22—612no—
504C22—612no—
505C22—1221no—
506C22—1221no—
507C22—1221no—
508C22—1221no—
509C22—1221no—
510C22—1221no—
511C22—1221no—
512C22—1221no—
513C22—1221no—
514C22—1221no—
515C22—2444no—
516C22—2444no—
517C22—2444no—
518C22—2444no—
519C22—2444no—
520C22—2444no—
521C22C2×(C2×#6923)⋊C411yescharacteristic
522C22#1684074112yes—
523C4—21no—
524C4—21no—
525C4—21no—
526C4—82no—
527C4—612no—
528C4—1221no—
529C4—1221no—
530C4—1221no—
531C4—4882no—
532C4—4884no—
533C4—4884no—
534C4#1684063912yes—
535C2—22no—
536C2—41no—
537C2—41no—
538C2—1222no—
539C2—1222no—
540C2—2441no—
541C2—2441no—
542C2C2×#1684063911yescharacteristic
543C2#2146151711yescharacteristic
544C2#2146151811yescharacteristic
subgroupG/H
centerC22C2×(C2×#6923)⋊C4
commutatorC23×C61C2×C42
FrattiniC24C22×#6923
FittingC4×C22⋊C4×C61C4
socleC22×C61C2×#95
prime radical, cosocleC24×D61C23
hypercenterC4×C22⋊C4#6923
hypocenterC61#8102
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
6. C2×#14519856C4semidirect
8. #16840705C4semidirect
12. #16840704C4semidirect
18. C4×C22⋊#6923C4semidirect
23. #16839620C4semidirect
26. C4×C22⋊Dic61C4semidirect
27. C4×C22⋊C4×C61C4semidirect
299. C4×C22⋊C4#6923semidirect
300. C61#8102semidirect

Maximal subgroups

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

subgroupindex
#214622632
#214607182
#214482002
#810261