Finite Group Databasebeta

← #30596307

Subgroups — #30596307

Order 15616.

1130 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D61⋊(C22⋊C8)C211yesmaximal, characteristic
2C2×D61⋊(C22⋊C8)C211yesmaximal, characteristic
3#21460662C214yesmaximal, complemented
4C4×C22⋊C4×D61C211yesmaximal, characteristic
5C22×D61⋊C8—21no—
6C22×D61⋊C8C412yescomplemented
7C2×#14519834—21no—
8C2×#14519834C412yescomplemented
9D61⋊(C22⋊C8)—21no—
10D61⋊(C22⋊C8)—21no—
11D61⋊(C22⋊C8)—21no—
12D61⋊(C22⋊C8)—21no—
13D61⋊(C22⋊C8)—21no—
14D61⋊(C22⋊C8)—21no—
15D61⋊(C22⋊C8)C412yescomplemented
16D61⋊(C22⋊C8)C412yescomplemented
17C2×C22⋊#92420C2212yes—
18C2×C22⋊#92420C2212yes—
19C23×C4×D61C2211yescharacteristic
20C2×C22⋊C4×D61C412yes—
21C2×C42×D61—21no—
22C22⋊C4×Dic61C2212yes—
23C4×#11758198—21no—
24C4×C22⋊Dic61C411yescharacteristic
25#16839609—21no—
26#95×D61—21no—
27C4×C22⋊C4×C61C411yescharacteristic
28C2×D61⋊C8—22no—
29C2×D61⋊C8—22no—
30C2×D61⋊C8—22no—
31C2×D61⋊C8—22no—
32C2×D61⋊C8—44no—
33C2×D61⋊C8—44no—
34C22×#92420—22no—
35C22×#92420C2×C414yescomplemented
36#14519834—22no—
37#14519834—22no—
38#14519834—22no—
39#14519834—22no—
40C22⋊#92420—22no—
41C22⋊#92420—22no—
42C22⋊#92420—22no—
43C22⋊#92420C2×C414yescomplemented
44C24×D61C2×C411yescharacteristic
45C23×Dic61C2311yescharacteristic
46C22×C4×D61—22no—
47C22×C4×D61—44no—
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×D61D411yescharacteristic
58C22×C4×D61Q811yescharacteristic
59C22×C4×D61Q811yescharacteristic
60C2×C22⋊Dic61C2×C412yes—
61C2×#11758198—22no—
62C22⋊C4×D61—24no—
63C22⋊C4×D61C818yescomplemented
64C2×C4×Dic61—21no—
65C2×C4×Dic61—22no—
66C42×D61—44no—
67#14519684—21no—
68#14519684—22no—
69C23×C4×C61C2×C411yescharacteristic
70C2×C22⋊C4×C61C2×C412yes—
71C2×C42×C61—21no—
72#95×C61—21no—
73C24×C61C22×C411yescharacteristic
74C23×D61—42no—
75C23×D61—42no—
76C23×D61C4211yescharacteristic
77C23×D61C4211yescharacteristic
78C23×D61C22⋊C411yescharacteristic
79C23×D61C22⋊C411yescharacteristic
80C23×D61C4⋊C411yescharacteristic
81C23×D61C4⋊C411yescharacteristic
82C23×D61C2×C814yes—
83C23×D61M1614yes—
84C22×C4×C61—22no—
85C22×C4×C61—42no—
86C22×C4×C61C4211yescharacteristic
87C22×C4×C61C4211yescharacteristic
88C22×C4×C61C22⋊C411yescharacteristic
89C22×C4×C61C22⋊C411yescharacteristic
90C22×C4×C61C4⋊C411yescharacteristic
91C22×C4×C61C4⋊C411yescharacteristic
92C22×Dic61—22no—
93C22×Dic61—42no—
94C22×Dic61C22×C411yescharacteristic
95C22×Dic61C22×C411yescharacteristic
96C22×Dic61C2×D411yescharacteristic
97C22×Dic61C2×D411yescharacteristic
98C22×Dic61C2×D411yescharacteristic
99C22×Dic61C2×Q811yescharacteristic
100C2×C4×D61—24no—
101C2×C4×D61—24no—
102C2×C4×D61—24no—
103C2×C4×D61—28no—
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×D61—42no—
112C2×C4×D61—42no—
113C2×C4×D61—44no—
114C2×C4×D61—44no—
115C2×C4×D61C22⋊C411yescharacteristic
116C2×C4×D61C22⋊C411yescharacteristic
117C2×C4×D61C22⋊C411yescharacteristic
118C2×C4×D61C22⋊C411yescharacteristic
119C2×C4×D61C22⋊C411yescharacteristic
120C2×C4×D61C22⋊C411yescharacteristic
121C2×C4×D61C22⋊C411yescharacteristic
122C2×C4×D61C22⋊C411yescharacteristic
123C2×C4×D61C4⋊C411yescharacteristic
124C2×C4×D61C4⋊C411yescharacteristic
125C2×C4×D61C4⋊C411yescharacteristic
126C2×C4×D61C4⋊C411yescharacteristic
127C2×C4×D61C4⋊C411yescharacteristic
128C2×C4×D61C4⋊C411yescharacteristic
129C2×C4×D61C4⋊C411yescharacteristic
130C2×C4×D61C4⋊C411yescharacteristic
131C2×#92420—24no—
132C2×#92420—24no—
133C2×#92420—44no—
134C2×#92420—44no—
135D61⋊C8—44no—
136D61⋊C8—44no—
137D61⋊C8—44no—
138D61⋊C8—44no—
139C22⋊C4×C61—22no—
140C22⋊C4×C61C2×C814yescomplemented
141C42×C61—42no—
142C22⋊Dic61—22no—
143C22⋊Dic61C2×C814yescomplemented
144#11758198—28no—
145C4×Dic61—44no—
146C4×Dic61—42no—
147C23×C61—41no—
148C23×C61—41no—
149C23×C61C2×C4211yescharacteristic
150C23×C61C2×C22⋊C411yescharacteristic
151C23×C61C2×C4⋊C411yescharacteristic
152C23×C61C22×C812yes—
153C23×C61C2×M1612yes—
154C22×D61—22no—
155C22×D61—22no—
156C22×D61—22no—
157C22×D61—22no—
158C22×D61—22no—
159C22×D61—22no—
160C22×D61—48no—
161C22×D61—48no—
162C22×D61—41no—
163C22×D61—41no—
164C22×D61—41no—
165C22×D61—41no—
166C22×D61—41no—
167C22×D61—41no—
168C22×D61#9511yescharacteristic
169C22×D61#9511yescharacteristic
170C22×D61#9511yescharacteristic
171C22×D61#9511yescharacteristic
172C22×D61C4×C812yes—
173C22×D61C4×C812yes—
174C22×D61#9712yes—
175C22×D61#9712yes—
176C22×D61C22⋊C814yes—
177C22×D61C22⋊C814yes—
178C22×D61C4⋊C814yes—
179C22×D61C4⋊C814yes—
180C2×C4×C61—22no—
181C2×C4×C61—22no—
182C2×C4×C61—22no—
183C2×C4×C61—24no—
184C2×C4×C61—41no—
185C2×C4×C61—41no—
186C2×C4×C61—41no—
187C2×C4×C61—42no—
188C2×C4×C61—42no—
189C2×C4×C61#9511yescharacteristic
190C2×C4×C61#9511yescharacteristic
191C2×C4×C61#9511yescharacteristic
192C2×C4×C61#9511yescharacteristic
193C2×Dic61—22no—
194C2×Dic61—22no—
195C2×Dic61—22no—
196C2×Dic61—24no—
197C2×Dic61—41no—
198C2×Dic61—41no—
199C2×Dic61—41no—
200C2×Dic61—42no—
201C2×Dic61—42no—
202C2×Dic61C2×C22⋊C411yescharacteristic
203C2×Dic61C2×C22⋊C411yescharacteristic
204C2×Dic61C2×C4⋊C411yescharacteristic
205C2×Dic61C2×C4⋊C411yescharacteristic
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—22no—
215C4×D61—41no—
216C4×D61—41no—
217C4×D61—41no—
218C4×D61—41no—
219C4×D61—41no—
220C4×D61—41no—
221C4×D61—416no—
222C4×D61#9914yes—
223#92420—44no—
224#92420—44no—
225C2×#1282—611nomaximal, Sylow
226C22×C61—21no—
227C22×C61—21no—
228C22×C61—21no—
229C22×C61—21no—
230C22×C61—21no—
231C22×C61—21no—
232C22×C61—42no—
233C22×C61—42no—
234C22×C61C2×#9511yescharacteristic
235C22×C61C2×C4×C811yescharacteristic
236C22×C61C2×#9711yescharacteristic
237C22×C61C2×C22⋊C812yes—
238C22×C61C2×C4⋊C812yes—
239C2×D61—21no—
240C2×D61—21no—
241C2×D61—21no—
242C2×D61—21no—
243C2×D61—21no—
244C2×D61—21no—
245C2×D61—28no—
246C2×D61—24no—
247C2×D61—24no—
248C2×D61—28no—
249C2×D61—42no—
250C2×D61—42no—
251C2×D61—44no—
252C2×D61—44no—
253C2×D61#33612yes—
254C2×D61#33612yes—
255C2×D61#33612yes—
256C2×D61#33612yes—
257C2×D61#34212yes—
258C2×D61#34412yes—
259C4×C61—21no—
260C4×C61—21no—
261C4×C61—21no—
262C4×C61—44no—
263C4×C61#34212yes—
264Dic61—21no—
265Dic61—21no—
266Dic61—21no—
267Dic61—44no—
268Dic61C2×#9912yes—
269C22×C22⋊C8—611no—
270C22×C22⋊C8—611no—
271C2×C4×C22⋊C4—611no—
272#1282—614no—
273C2×C61—22no—
274C2×C61—21no—
275C2×C61—21no—
276C2×C61—22no—
277C2×C61C2×#33611yescharacteristic
278C2×C61C2×#34211yescharacteristic
279C2×C61C2×#34411yescharacteristic
280D61—22no—
281D61—22no—
282D61—22no—
283D61#128214yescomplemented
284C24×C4—611no—
285C23×C8—612no—
286C23×C8—1221no—
287C22×C22⋊C4—612no—
288C22×C42—1221no—
289C2×C22⋊C8—612no—
290C2×C22⋊C8—612no—
291C2×C22⋊C8—612no—
292C2×C22⋊C8—612no—
293C2×C22⋊C8—612no—
294C2×C22⋊C8—1221no—
295C2×C22⋊C8—1221no—
296C2×C22⋊C8—1221no—
297C2×C22⋊C8—1221no—
298C2×C22⋊C8—1221no—
299C2×C22⋊C8—1221no—
300C2×C22⋊C8—1221no—
301C4×C22⋊C4—611no—
302C4×C22⋊C4—612no—
303C4×C22⋊C4—1221no—
304C4×C22⋊C4—1221no—
305C4×C22⋊C4#692311yescharacteristic
306C2×#95—1221no—
307C61C2×#128211yescharacteristic, complemented, Sylow
308C25—611no—
309C23×C4—611no—
310C23×C4—611no—
311C23×C4—611no—
312C23×C4—611no—
313C23×C4—611no—
314C23×C4—611no—
315C23×C4—611no—
316C23×C4—611no—
317C23×C4—611no—
318C23×C4—611no—
319C23×C4—611no—
320C23×C4—611no—
321C23×C4—611no—
322C23×C4—1222no—
323C23×C4—2444no—
324C23×C4C2×#692311yescharacteristic
325C22×C8—614no—
326C22×C8—1222no—
327C22×C8—1222no—
328C22×C8—1222no—
329C22×C8—1222no—
330C22×C8—1222no—
331C22×C8—2444no—
332C22×C8—2444no—
333C2×C22⋊C4—612no—
334C2×C22⋊C4—618no—
335C2×C22⋊C4—1224no—
336C2×C22⋊C4—1222no—
337C2×C22⋊C4C2×#692312yes—
338C2×C42—21no—
339C2×C42—1222no—
340C2×C42—1221no—
341C2×C42—2444no—
342C22⋊C8—614no—
343C22⋊C8—1222no—
344C22⋊C8—1222no—
345C22⋊C8—1222no—
346C22⋊C8—1222no—
347C22⋊C8—1222no—
348C22⋊C8—1222no—
349C22⋊C8—1222no—
350#95—21no—
351#95—1222no—
352#95—1221no—
353C24—611no—
354C24—611no—
355C24—611no—
356C24—611no—
357C24—611no—
358C24—611no—
359C24—614no—
360C24—614no—
361C24—2442no—
362C24—2442no—
363C24C22×#692311yescharacteristic
364C22×C4—22no—
365C22×C4—42no—
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—611no—
379C22×C4—611no—
380C22×C4—611no—
381C22×C4—611no—
382C22×C4—611no—
383C22×C4—611no—
384C22×C4—611no—
385C22×C4—611no—
386C22×C4—611no—
387C22×C4—611no—
388C22×C4—1224no—
389C22×C4—1224no—
390C22×C4—1224no—
391C22×C4—1228no—
392C22×C4—1222no—
393C22×C4—2442no—
394C22×C4—2442no—
395C22×C4—2442no—
396C22×C4—2442no—
397C22×C4—2442no—
398C22×C4—2442no—
399C22×C4—2442no—
400C22×C4—2442no—
401C22×C4—2442no—
402C22×C4—2444no—
403C22×C4—2444no—
404C22×C4—2442no—
405C22×C4C4×#692311yescharacteristic
406C22×C4C4×#692311yescharacteristic
407C22×C4C4⋊#692311yescharacteristic
408C22×C4C4⋊#692311yescharacteristic
409C22×C4C22⋊#692311yescharacteristic
410C22×C4C22⋊#692311yescharacteristic
411C2×C8—1224no—
412C2×C8—1224no—
413C2×C8—2444no—
414C2×C8—2444no—
415C2×C8—2444no—
416C2×C8—2444no—
417C2×C8—2444no—
418C2×C8—2444no—
419C22⋊C4—22no—
420C22⋊C4—614no—
421C22⋊C4—1228no—
422C22⋊C4—1222no—
423C22⋊C4D61⋊C814yescomplemented
424C42—42no—
425C42—2442no—
426C42—2444no—
427C23—41no—
428C23—41no—
429C23—611no—
430C23—612no—
431C23—612no—
432C23—614no—
433C23—614no—
434C23—611no—
435C23—611no—
436C23—611no—
437C23—612no—
438C23—612no—
439C23—614no—
440C23—614no—
441C23—1222no—
442C23—1222no—
443C23—1222no—
444C23—1222no—
445C23—1222no—
446C23—1222no—
447C23—2441no—
448C23—2441no—
449C23—2441no—
450C23—2441no—
451C23—2441no—
452C23—2441no—
453C23—2448no—
454C23—2448no—
455C23C2×C4×#692311yescharacteristic
456C23C2×C22⋊#692311yescharacteristic
457C23C2×C4⋊#692311yescharacteristic
458C23C2×D61⋊C812yes—
459C23D61⋊M1612yes—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—24no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—611no—
470C2×C4—614no—
471C2×C4—611no—
472C2×C4—611no—
473C2×C4—611no—
474C2×C4—1222no—
475C2×C4—1222no—
476C2×C4—1222no—
477C2×C4—1222no—
478C2×C4—1222no—
479C2×C4—1222no—
480C2×C4—1222no—
481C2×C4—1222no—
482C2×C4—1222no—
483C2×C4—1222no—
484C2×C4—1222no—
485C2×C4—1222no—
486C2×C4—1224no—
487C2×C4—2441no—
488C2×C4—2441no—
489C2×C4—2441no—
490C2×C4—2441no—
491C2×C4—2441no—
492C2×C4—2441no—
493C2×C4—24416no—
494C2×C4—2441no—
495C2×C4—2441no—
496C2×C4—2441no—
497C2×C4—2442no—
498C2×C4—2442no—
499C2×C4(C2×#6923)⋊C411yescharacteristic
500C2×C4(C2×#6923)⋊C411yescharacteristic
501C2×C4(C2×#6923)⋊C411yescharacteristic
502C2×C4(C2×#6923)⋊C411yescharacteristic
503C8—2444no—
504C8—2444no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—42no—
512C22—42no—
513C22—612no—
514C22—612no—
515C22—612no—
516C22—612no—
517C22—612no—
518C22—612no—
519C22—1228no—
520C22—1224no—
521C22—1224no—
522C22—1228no—
523C22—1221no—
524C22—1221no—
525C22—1221no—
526C22—1221no—
527C22—1221no—
528C22—1221no—
529C22—2444no—
530C22—2442no—
531C22—2442no—
532C22—2444no—
533C22C2×(C2×#6923)⋊C411yescharacteristic
534C22C4×D61⋊C811yescharacteristic
535C22#1684072111yescharacteristic
536C22D61⋊(C22⋊C8)12yes—
537C22D61⋊(C4⋊C8)12yes—
538C4—21no—
539C4—21no—
540C4—21no—
541C4—44no—
542C4—612no—
543C4—1221no—
544C4—1221no—
545C4—1221no—
546C4—2444no—
547C4#1684063912yes—
548C2—22no—
549C2—21no—
550C2—21no—
551C2—22no—
552C2—614no—
553C2—1222no—
554C2—1222no—
555C2—1222no—
556C2#2146148011yescharacteristic
557C2C2×#1684063911yescharacteristic
558C2#2146152711yescharacteristic
subgroupG/H
centerC2×C4(C2×#6923)⋊C4
commutatorC22×C61C2×C4×C8
FrattiniC24C22×#6923
FittingC4×C22⋊C4×C61C4
socleC22×C61C2×#95
prime radicalC24×D61C2×C4
cosocleC23×Dic61C23
hypercenterC4×C22⋊C4#6923
hypocenterC61C2×#1282
LCSG ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #21460662C2semidirect
6. C22×D61⋊C8C4semidirect
8. C2×#14519834C4semidirect
15. D61⋊(C22⋊C8)C4semidirect
16. D61⋊(C22⋊C8)C4semidirect
35. C22×#92420C2×C4semidirect
43. C22⋊#92420C2×C4semidirect
63. C22⋊C4×D61C8semidirect
140. C22⋊C4×C61C2×C8semidirect
143. C22⋊Dic61C2×C8semidirect
283. D61#1282semidirect
307. C61C2×#1282semidirect
423. C22⋊C4D61⋊C8semidirect

Maximal subgroups

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

subgroupindex
C2×D61⋊(C22⋊C8)2
#214606622
C4×C22⋊C4×D612
C2×#128261