Finite Group Databasebeta

← #30596445

Subgroups — #30596445

Order 15616.

954 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462263C211yesmaximal, characteristic
2#21462263C211yesmaximal, characteristic
3#21460668C214yesmaximal, complemented
4#407×D61C211yesmaximal, characteristic
5C2×#14519856—21no—
6C2×#14519856C412yescomplemented
7#16840705—21no—
8#16840705C2212yes—
9#16840704—21no—
10#16840704—21no—
11#16840704—21no—
12#16840704C412yescomplemented
13#16840703—21no—
14#16840703—21no—
15C4×C22⋊#6923—21no—
16C4×C22⋊#6923C412yescomplemented
17C4×C22⋊#6923C412yescomplemented
18C4×C22⋊#6923C2212yes—
19C23×C4×D61C2211yescharacteristic
20C2×M16×D61—21no—
21#16839726C411yescharacteristic, complemented
22#16839725—21no—
23#16839724—21no—
24#16839724C2212yes—
25C22⋊C8×D61—21no—
26C22⋊C8×D61C412yescomplemented
27C61×#407C411yescharacteristic, 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⋊#6923—22no—
37C2×C22⋊#6923—22no—
38C2×C4×#6923—22no—
39C2×C4×#6923C2×C414yes—
40(C2×#6923)⋊C4—22no—
41(C2×#6923)⋊C4—22no—
42(C2×#6923)⋊C4—22no—
43(C2×#6923)⋊C4C2×C414yes—
44C24×D61D411yescharacteristic
45C23×Dic61Q811yescharacteristic
46C22×C4×D61—44no—
47C22×C4×D61C2×C411yescharacteristic
48C22×C4×D61C2×C411yescharacteristic
49C22×C4×D61C2×C411yescharacteristic
50C22×C4×D61C2×C411yescharacteristic
51C22×C4×D61C2×C411yescharacteristic
52C22×C4×D61D411yescharacteristic
53C22×C4×D61D411yescharacteristic
54C22×C4×D61D411yescharacteristic
55C22×C4×D61D411yescharacteristic
56C22×C4×D61D411yescharacteristic
57C22×C4×D61Q811yescharacteristic
58C22×C4×D61C2311yescharacteristic
59C2×#11758194—21no—
60C2×#11758189—22no—
61M16×D61—44no—
62C2×C8×D61—22no—
63C22⋊#92418—21no—
64C22⋊#92418C2×C412yes—
65#14519689—22no—
66#14519689—22no—
67C23×C4×C61C2×C411yescharacteristic
68C2×M16×C61—21no—
69C22⋊C8×C61—21no—
70C22⋊C8×C61C2×C412yes—
71C24×C61C4⋊C411yescharacteristic
72C23×D61—42no—
73C23×D61—42no—
74C23×D61—42no—
75C23×D61C22⋊C411yescharacteristic
76C23×D61C22⋊C411yescharacteristic
77C23×D61C22⋊C411yescharacteristic
78C23×D61C22⋊C411yescharacteristic
79C23×D61C4⋊C411yescharacteristic
80C23×D61C2×D411yescharacteristic
81C22×#6923—24no—
82C22×#6923—24no—
83C22×C4×C61—42no—
84C22×C4×C61C4211yescharacteristic
85C22×C4×C61C4211yescharacteristic
86C22×C4×C61C22⋊C411yescharacteristic
87C22×C4×C61C22⋊C411yescharacteristic
88C22×C4×C61C4⋊C411yescharacteristic
89C22×C4×C61C22×C411yescharacteristic
90C22×Dic61—42no—
91C22×Dic61C4⋊C411yescharacteristic
92C22×Dic61C4⋊C411yescharacteristic
93C22×Dic61C4⋊C411yescharacteristic
94C22×Dic61C4⋊C411yescharacteristic
95C22×Dic61C4⋊C411yescharacteristic
96C22×Dic61C2×Q811yescharacteristic
97C2×C4×D61—24no—
98C2×C4×D61—24no—
99C2×C4×D61—24no—
100C2×C4×D61—42no—
101C2×C4×D61—42no—
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×D61C4211yescharacteristic
110C2×C4×D61C4211yescharacteristic
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×D61C4⋊C411yescharacteristic
118C2×C4×D61C4⋊C411yescharacteristic
119C2×C4×D61C4⋊C411yescharacteristic
120C2×C4×D61C4⋊C411yescharacteristic
121C2×C4×D61C22×C411yescharacteristic
122C2×C4×D61C22×C411yescharacteristic
123C2×C4×D61C2×D411yescharacteristic
124C2×C4×D61C2×D411yescharacteristic
125C22⋊#6923—44no—
126C22⋊#6923—44no—
127C22⋊#6923—44no—
128C22⋊#6923—44no—
129C22⋊#6923—44no—
130C22⋊#6923—44no—
131C4⋊#6923—44no—
132C4⋊#6923—44no—
133C4×#6923—44no—
134C4×#6923—44no—
135M16×C61—42no—
136C2×C8×C61—22no—
137#11758194—42no—
138C2×#92418—22no—
139#11758189—44no—
140C8×D61—44no—
141C23×C61—41no—
142C23×C61—41no—
143C23×C61—41no—
144C23×C61#9511yescharacteristic
145C23×C61#9511yescharacteristic
146C23×C61C2×C4⋊C411yescharacteristic
147C22×D61—22no—
148C22×D61—22no—
149C22×D61—22no—
150C22×D61—22no—
151C22×D61—22no—
152C22×D61—22no—
153C22×D61—22no—
154C22×D61—22no—
155C22×D61—22no—
156C22×D61—41no—
157C22×D61—41no—
158C22×D61—41no—
159C22×D61—41no—
160C22×D61—41no—
161C22×D61—41no—
162C22×D61—41no—
163C22×D61—41no—
164C22×D61—41no—
165C22×D61—416no—
166C22×D61#9511yescharacteristic
167C22×D61#9511yescharacteristic
168C22×D61C2×C22⋊C411yescharacteristic
169C22×D61C2×C22⋊C411yescharacteristic
170C2×#6923—44no—
171C2×#6923—44no—
172C2×#6923—44no—
173C2×#6923—44no—
174C2×#6923—44no—
175C2×#6923—44no—
176C2×C4×C61—22no—
177C2×C4×C61—22no—
178C2×C4×C61—22no—
179C2×C4×C61—41no—
180C2×C4×C61—41no—
181C2×C4×C61—41no—
182C2×C4×C61#9511yescharacteristic
183C2×C4×C61#9511yescharacteristic
184C2×C4×C61C2×C4211yescharacteristic
185C2×C4×C61C2×C22⋊C411yescharacteristic
186C2×Dic61—22no—
187C2×Dic61—22no—
188C2×Dic61—22no—
189C2×Dic61—41no—
190C2×Dic61—41no—
191C2×Dic61—41no—
192C2×Dic61#9511yescharacteristic
193C2×Dic61#9511yescharacteristic
194C2×Dic61C2×C4⋊C411yescharacteristic
195C2×Dic61C2×C4⋊C411yescharacteristic
196C4×D61—22no—
197C4×D61—22no—
198C4×D61—22no—
199C4×D61—22no—
200C4×D61—22no—
201C4×D61—22no—
202C4×D61—22no—
203C4×D61—22no—
204C4×D61—22no—
205C4×D61—41no—
206C4×D61—41no—
207C4×D61—41no—
208C4×D61—41no—
209C4×D61—41no—
210C4×D61—41no—
211C4×D61#9914yes—
212C8×C61—42no—
213#92418—42no—
214#7946—611nomaximal, Sylow
215C22×C61—21no—
216C22×C61—21no—
217C22×C61—21no—
218C22×C61—21no—
219C22×C61—21no—
220C22×C61—21no—
221C22×C61—21no—
222C22×C61—21no—
223C22×C61—21no—
224C22×C61—44no—
225C22×C61C2×#9511yescharacteristic
226C2×D61—21no—
227C2×D61—21no—
228C2×D61—21no—
229C2×D61—21no—
230C2×D61—21no—
231C2×D61—21no—
232C2×D61—21no—
233C2×D61—21no—
234C2×D61—21no—
235C2×D61—44no—
236C2×D61—44no—
237C2×D61—44no—
238C2×D61—44no—
239C2×D61—44no—
240C2×D61—44no—
241C2×D61H(3,ℤ/4)12yes—
242C2×D61C2×#9912yes—
243C2×D61#42112yes—
244#6923—84no—
245#6923—84no—
246C4×C61—21no—
247C4×C61—21no—
248C4×C61—21no—
249C4×C61#34212yes—
250Dic61—21no—
251Dic61—21no—
252Dic61—21no—
253Dic61#34212yes—
254C2×#407—611no—
255#2280—611no—
256#2280—611no—
257#1284—614no—
258C2×C61—41no—
259C2×C61—41no—
260C2×C61—41no—
261C2×C61C2×H(3,ℤ/4)11yescharacteristic
262C2×C61#173311yescharacteristic
263C2×C61C2×#34211yescharacteristic
264D61—22no—
265D61—22no—
266D61—22no—
267D61—41no—
268C24×C4—611no—
269C22×M16—1221no—
270C2×#117—612no—
271C2×#117—1221no—
272#407—611no—
273#407—612no—
274#407—1221no—
275#407—1221no—
276#407#692311yescharacteristic, complemented
277C2×C22⋊C8—612no—
278C2×C22⋊C8—1221no—
279#381—612no—
280#381—1221no—
281#380—612no—
282#380—1221no—
283#380—1221no—
284#380—1221no—
285#379—1221no—
286#379—1221no—
287C4×C22⋊C4—612no—
288C4×C22⋊C4—612no—
289C4×C22⋊C4—612no—
290C4×C22⋊C4—1221no—
291C61#794611yescharacteristic, complemented, Sylow
292C25—611no—
293C23×C4—611no—
294C23×C4—611no—
295C23×C4—611no—
296C23×C4—611no—
297C23×C4—611no—
298C23×C4—611no—
299C23×C4—611no—
300C23×C4—611no—
301C23×C4—611no—
302C23×C4—611no—
303C23×C4—611no—
304C23×C4—611no—
305C23×C4—611no—
306C23×C4—2444no—
307C23×C4C2×#692311yescharacteristic
308C2×M16—21no—
309C2×M16—1222no—
310C2×M16—1221no—
311C2×M16—2444no—
312C22×C8—1222no—
313#117—2444no—
314#117—2444no—
315C2×C4⋊C4—1222no—
316C2×C4⋊C4—1222no—
317C2×C22⋊C4—1222no—
318C2×C22⋊C4—1222no—
319C2×C22⋊C4—1222no—
320C2×C22⋊C4—1222no—
321C2×C22⋊C4—1222no—
322C2×C22⋊C4—1222no—
323C2×C42—614no—
324C2×C42—1222no—
325C22⋊C8—21no—
326C22⋊C8—612no—
327C22⋊C8—1222no—
328C22⋊C8—1222no—
329C22⋊C8—1221no—
330C22⋊C8C2×#692312yes—
331#95—614no—
332#95—1222no—
333#95—1222no—
334#95—1222no—
335C24—611no—
336C24—611no—
337C24—611no—
338C24—611no—
339C24—611no—
340C24—611no—
341C24—2442no—
342C24—2442no—
343C24—2442no—
344C24C4⋊#692311yescharacteristic
345C22×C4—42no—
346C22×C4—611no—
347C22×C4—611no—
348C22×C4—611no—
349C22×C4—611no—
350C22×C4—611no—
351C22×C4—611no—
352C22×C4—611no—
353C22×C4—611no—
354C22×C4—611no—
355C22×C4—611no—
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—1224no—
369C22×C4—1224no—
370C22×C4—1224no—
371C22×C4—1224no—
372C22×C4—1224no—
373C22×C4—2442no—
374C22×C4—2442no—
375C22×C4—2442no—
376C22×C4—2442no—
377C22×C4—2442no—
378C22×C4—2442no—
379C22×C4—2442no—
380C22×C4—2442no—
381C22×C4—2442no—
382C22×C4—2442no—
383C22×C4C4×#692311yescharacteristic
384C22×C4C4×#692311yescharacteristic
385C22×C4C4⋊#692311yescharacteristic
386C22×C4C22⋊#692311yescharacteristic
387C22×C4C22⋊#692311yescharacteristic
388C22×C4C22×#692311yescharacteristic
389M16—42no—
390M16—2444no—
391M16—2442no—
392C2×C8—22no—
393C2×C8—1222no—
394C2×C8—2444no—
395C4⋊C4—2444no—
396C4⋊C4—2444no—
397C22⋊C4—2444no—
398C22⋊C4—2444no—
399C22⋊C4—2444no—
400C22⋊C4—2444no—
401C22⋊C4—2444no—
402C22⋊C4—2444no—
403C42—2444no—
404C42—2444no—
405C23—41no—
406C23—41no—
407C23—41no—
408C23—611no—
409C23—611no—
410C23—611no—
411C23—611no—
412C23—1222no—
413C23—1222no—
414C23—1222no—
415C23—1222no—
416C23—1222no—
417C23—1222no—
418C23—1222no—
419C23—1222no—
420C23—1222no—
421C23—2441no—
422C23—2441no—
423C23—2441no—
424C23—2441no—
425C23—2441no—
426C23—2441no—
427C23—2441no—
428C23—2441no—
429C23—2441no—
430C23—24416no—
431C23(C2×#6923)⋊C411yescharacteristic
432C23(C2×#6923)⋊C411yescharacteristic
433C23C2×C4⋊#692311yescharacteristic
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—611no—
441C2×C4—614no—
442C2×C4—611no—
443C2×C4—611no—
444C2×C4—611no—
445C2×C4—1222no—
446C2×C4—1222no—
447C2×C4—1222no—
448C2×C4—1222no—
449C2×C4—1222no—
450C2×C4—1222no—
451C2×C4—1222no—
452C2×C4—1222no—
453C2×C4—1222no—
454C2×C4—1222no—
455C2×C4—1222no—
456C2×C4—1222no—
457C2×C4—2441no—
458C2×C4—2441no—
459C2×C4—2441no—
460C2×C4—2441no—
461C2×C4—2441no—
462C2×C4—2441no—
463C2×C4—2441no—
464C2×C4—2441no—
465C2×C4—2441no—
466C2×C4—2444no—
467C2×C4—2444no—
468C2×C4—2444no—
469C2×C4—2444no—
470C2×C4—2444no—
471C2×C4—2444no—
472C2×C4(C2×#6923)⋊C411yescharacteristic
473C2×C4(C2×#6923)⋊C411yescharacteristic
474C2×C4C2×C4×#692311yescharacteristic
475C2×C4C2×C22⋊#692311yescharacteristic
476C8—42no—
477C8—2442no—
478C22—21no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—21no—
483C22—21no—
484C22—21no—
485C22—21no—
486C22—21no—
487C22—44no—
488C22—612no—
489C22—612no—
490C22—612no—
491C22—1221no—
492C22—1221no—
493C22—1221no—
494C22—1221no—
495C22—1221no—
496C22—1221no—
497C22—1221no—
498C22—1221no—
499C22—1221no—
500C22—2444no—
501C22—2444no—
502C22—2444no—
503C22—2444no—
504C22—2444no—
505C22—2444no—
506C22C2×(C2×#6923)⋊C411yescharacteristic
507C4—21no—
508C4—21no—
509C4—21no—
510C4—612no—
511C4—1221no—
512C4—1221no—
513C4—1221no—
514C4—4884no—
515C4—4884no—
516C4#1684063912yes—
517C2—41no—
518C2—41no—
519C2—41no—
520C2—1222no—
521C2—1222no—
522C2—1222no—
523C2—2441no—
524C2#2146149111yescharacteristic
525C2#2146150111yescharacteristic
526C2C2×#1684063911yescharacteristic
subgroupG/H
centerC22C2×(C2×#6923)⋊C4
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC61×#407C4
socleC22×C61C2×#95
prime radicalC24×D61D4
cosocleC22×C4×D61C23
hypercenter#407#6923
hypocenterC61#7946
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
3. #21460668C2semidirect
6. C2×#14519856C4semidirect
12. #16840704C4semidirect
16. C4×C22⋊#6923C4semidirect
17. C4×C22⋊#6923C4semidirect
21. #16839726C4semidirect
26. C22⋊C8×D61C4semidirect
27. C61×#407C4semidirect
276. #407#6923semidirect
291. C61#7946semidirect

Maximal subgroups

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

subgroupindex
#214622632
#214606682
#407×D612
#794661