Finite Group Databasebeta

← #29571349

Subgroups — #29571349

Order 15616.

1522 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D61C211yesmaximal, characteristic
2#21445729C211yesmaximal, characteristic, complemented
3C2×#16839487C212yesmaximal, complemented
4C2×#16839485C212yesmaximal, complemented
5C61×#1779C211yesmaximal, characteristic, complemented
6C23×C22⋊D61C411yescharacteristic
7C23×C4×D61C411yescharacteristic
8C2×C4×C22⋊D61—24no—
9C2×C4×C22⋊D61—24no—
10C2×C4×C22⋊D61—22no—
11C2×C4×C22⋊D61—22no—
12C22×#11758196C2211yescharacteristic
13C22×C22⋊Dic61C411yescharacteristic
14C22×#11758198C2211yescharacteristic
15C22×C4×Dic61C411yescharacteristic
16C2×C22⋊#92418—22no—
17C2×C22⋊#92418C2212yes—
18#16839487—24no—
19#16839485—24no—
20C24×C4×C61C2211yescharacteristic
21C2×C22⋊C8×C61—22no—
22C2×C22⋊C8×C61C2212yes—
23C24×D61C2×C411yescharacteristic
24C22×C22⋊D61—22no—
25C22×C22⋊D61—22no—
26C22×C22⋊D61—22no—
27C22×C22⋊D61—22no—
28C22×C22⋊D61—22no—
29C22×C22⋊D61—22no—
30C22×C22⋊D61C814yescomplemented
31C23×Dic61C2×C411yescharacteristic
32C23×Dic61C2×C411yescharacteristic
33C23×Dic61C2×C411yescharacteristic
34C22×C4×D61—22no—
35C22×C4×D61—22no—
36C22×C4×D61—22no—
37C22×C4×D61—44no—
38C22×#92418—22no—
39C4×C22⋊D61—216no—
40C4×C22⋊D61—216no—
41C2×#11758196—21no—
42C2×#11758196—22no—
43C2×#11758196—21no—
44C2×#11758196D414yes—
45C2×C22⋊Dic61—22no—
46C2×C22⋊Dic61—22no—
47C2×C22⋊Dic61—22no—
48C2×#11758198—21no—
49C2×#11758198—22no—
50C2×#11758198—21no—
51C2×#11758198D414yes—
52C2×C4×Dic61—22no—
53C2×C4×Dic61—22no—
54C2×C4×Dic61—22no—
55C22⋊#92418—22no—
56C22⋊#92418—22no—
57C22⋊#92418—44no—
58C25×C61C2×C411yescharacteristic
59C23×C4×C61—22no—
60C23×C4×C61—22no—
61C23×C4×C61—44no—
62C23×C4×C61C2×C411yescharacteristic
63C23×C4×C61D412yes—
64C23×C4×C61D412yes—
65C23×C4×C61C2311yescharacteristic
66C22×C8×C61—22no—
67C22⋊C8×C61—22no—
68C22⋊C8×C61—22no—
69C22⋊C8×C61—44no—
70C24×C61—21no—
71C24×C61—21no—
72C24×C61—21no—
73C24×C61—21no—
74C24×C61—42no—
75C24×C61—42no—
76C24×C61C22⋊C412yes—
77C24×C61C2×C812yes—
78C24×C61M1612yes—
79C24×C61C22×C411yescharacteristic
80C23×D61—21no—
81C23×D61—21no—
82C23×D61—21no—
83C23×D61—21no—
84C23×D61—42no—
85C23×D61—42no—
86C23×D61C22⋊C412yes—
87C23×D61C2×C812yes—
88C23×D61M1612yes—
89C22×C4×C61—21no—
90C22×C4×C61—21no—
91C22×C4×C61—24no—
92C22×C4×C61—24no—
93C22×C4×C61—24no—
94C22×C4×C61—24no—
95C22×C4×C61—24no—
96C22×C4×C61—42no—
97C22×C4×C61—42no—
98C22×C4×C61—42no—
99C22×C4×C61—48no—
100C22×C4×C61—48no—
101C22×C4×C61C22⋊C412yes—
102C22×C4×C61C2×D411yescharacteristic
103C22×C4×C61C2×D411yescharacteristic
104C22×C4×C61C2×D412yes—
105C22×C4×C61C2×D412yes—
106C2×C22⋊D61—28no—
107C2×C22⋊D61—28no—
108C2×C22⋊D61—28no—
109C2×C22⋊D61—28no—
110C2×C22⋊D61—28no—
111C2×C22⋊D61—28no—
112C2×C22⋊D61—28no—
113C22×Dic61—21no—
114C22×Dic61—21no—
115C22×Dic61—21no—
116C22×Dic61—21no—
117C22×Dic61—21no—
118C22×Dic61—21no—
119C22×Dic61—21no—
120C22×Dic61—21no—
121C22×Dic61—42no—
122C22×Dic61—42no—
123C22×Dic61C22⋊C412yes—
124C22×Dic61C22⋊C412yes—
125C22×Dic61C22⋊C412yes—
126C22×Dic61C2×C812yes—
127C22×Dic61M1612yes—
128C2×C4×D61—28no—
129C2×C4×D61—48no—
130C2×C4×D61—44no—
131C2×C4×D61—48no—
132C2×C4×D61—44no—
133C2×C8×C61—44no—
134C2×C8×C61—42no—
135C22⋊Dic61—28no—
136#11758198—24no—
137#11758198—24no—
138#11758196—24no—
139#11758196—24no—
140C4×Dic61—28no—
141C2×#92418—44no—
142C2×#92418—42no—
143C23×C61—22no—
144C23×C61—22no—
145C23×C61—22no—
146C23×C61—22no—
147C23×C61—22no—
148C23×C61—22no—
149C23×C61—22no—
150C23×C61—22no—
151C23×C61—22no—
152C23×C61—22no—
153C23×C61—22no—
154C23×C61—22no—
155C23×C61—44no—
156C23×C61—44no—
157C23×C61—42no—
158C23×C61—42no—
159C23×C61—44no—
160C23×C61—44no—
161C23×C61—42no—
162C23×C61—42no—
163C23×C61C22⋊C814yes—
164C23×C61C2×C22⋊C411yescharacteristic
165C23×C61C2×C22⋊C411yescharacteristic
166C23×C61C2×C22⋊C411yescharacteristic
167C23×C61C22×C811yescharacteristic
168C23×C61C2×M1611yescharacteristic
169C23×C61C2×M1611yescharacteristic
170C23×C61C2×M1611yescharacteristic
171C22×D61—22no—
172C22×D61—22no—
173C22×D61—22no—
174C22×D61—22no—
175C22×D61—22no—
176C22×D61—22no—
177C22×D61—42no—
178C22×D61—44no—
179C22×D61—44no—
180C22×D61—42no—
181C22×D61—42no—
182C22×D61—42no—
183C22×D61—42no—
184C22×D61—42no—
185C22×D61—44no—
186C22×D61—44no—
187C22×D61C22⋊C814yescomplemented
188C2×C4×C61—24no—
189C2×C4×C61—24no—
190C2×C4×C61—22no—
191C2×C4×C61—22no—
192C2×C4×C61—22no—
193C2×C4×C61—22no—
194C2×C4×C61—42no—
195C2×C4×C61—42no—
196C2×C4×C61—48no—
197C2×C4×C61—48no—
198C2×C4×C61#9914yes—
199C2×C4×C61#12012yes—
200C2×C4×C61#12012yes—
201C22⋊D61—232no—
202C2×Dic61—22no—
203C2×Dic61—22no—
204C2×Dic61—22no—
205C2×Dic61—22no—
206C2×Dic61—22no—
207C2×Dic61—22no—
208C2×Dic61—22no—
209C2×Dic61—22no—
210C2×Dic61—42no—
211C2×Dic61—42no—
212C2×Dic61—42no—
213C2×Dic61—42no—
214C2×Dic61—42no—
215C2×Dic61—42no—
216C2×Dic61C22⋊C814yescomplemented
217C4×D61—416no—
218C8×C61—82no—
219#92418—82no—
220#8301—611nomaximal, Sylow
221C22×C61—22no—
222C22×C61—22no—
223C22×C61—22no—
224C22×C61—22no—
225C22×C61—21no—
226C22×C61—21no—
227C22×C61—21no—
228C22×C61—21no—
229C22×C61—24no—
230C22×C61—24no—
231C22×C61—24no—
232C22×C61—44no—
233C22×C61—44no—
234C22×C61—44no—
235C22×C61—44no—
236C22×C61—42no—
237C22×C61—42no—
238C22×C61—42no—
239C22×C61—42no—
240C22×C61#37911yescharacteristic
241C22×C61C2×C22⋊C811yescharacteristic
242C22×C61C2×C22⋊C811yescharacteristic
243C22×C61C2×C22⋊C811yescharacteristic
244C22×C61#40711yescharacteristic
245C22×C61#40711yescharacteristic
246C22×C61#40711yescharacteristic
247C22×C61C2×#9912yes—
248C22×C61#41312yes—
249C2×D61—24no—
250C2×D61—44no—
251C2×D61—44no—
252C2×D61—44no—
253C2×D61—44no—
254C2×D61—44no—
255C2×D61—42no—
256C2×D61—42no—
257C2×D61—44no—
258C4×C61—22no—
259C4×C61—22no—
260C4×C61—24no—
261Dic61—24no—
262Dic61—42no—
263Dic61—42no—
264C22×C4×D4—611no—
265#1779—611no—
266#1779D6111yescharacteristic, complemented
267C2×#324—612no—
268C2×#323—612no—
269C2×C61—21no—
270C2×C61—21no—
271C2×C61—21no—
272C2×C61—21no—
273C2×C61—44no—
274C2×C61#145912yes—
275C2×C61#146512yes—
276C2×C61#177911yescharacteristic
277C2×C61#178111yescharacteristic
278C2×C61#178511yescharacteristic
279D61—44no—
280C23×D4—611no—
281C24×C4—611no—
282C24×C4C2×D6111yescharacteristic
283C2×C4×D4—1224no—
284C2×C4×D4—1224no—
285C2×C4×D4—1222no—
286C2×C4×D4—1222no—
287C22×C4⋊C4—611no—
288C22×C22⋊C4—611no—
289C22×C22⋊C4—611no—
290C22×C42—611no—
291C2×C22⋊C8—22no—
292C2×C22⋊C8—612no—
293C2×C22⋊C8—1222no—
294C2×C22⋊C8C2×D6112yes—
295#324—1224no—
296#323—1224no—
297C61#830111yescharacteristic, complemented, Sylow
298C25—611no—
299C25C4×D6111yescharacteristic
300C22×D4—614no—
301C22×D4—1222no—
302C22×D4—1222no—
303C22×D4—1222no—
304C22×D4—1222no—
305C22×D4—1222no—
306C22×D4—1222no—
307C23×C4—22no—
308C23×C4—22no—
309C23×C4—44no—
310C23×C4—611no—
311C23×C4—611no—
312C23×C4—611no—
313C23×C4—1222no—
314C23×C4—1222no—
315C23×C4—1222no—
316C23×C4—2444no—
317C23×C4C4×D6111yescharacteristic
318C23×C4D24412yes—
319C23×C4C22⋊D6112yes—
320C23×C4C22×D6111yescharacteristic
321C22×C8—22no—
322C22×C8—1222no—
323C4×D4—12216no—
324C4×D4—12216no—
325C2×C4⋊C4—614no—
326C2×C4⋊C4—1221no—
327C2×C4⋊C4—1222no—
328C2×C4⋊C4—1221no—
329C2×C22⋊C4—614no—
330C2×C22⋊C4—1222no—
331C2×C22⋊C4—1222no—
332C2×C22⋊C4—1222no—
333C2×C22⋊C4—1221no—
334C2×C22⋊C4—1222no—
335C2×C22⋊C4—1221no—
336C2×C42—1222no—
337C2×C42—1222no—
338C2×C42—1222no—
339C22⋊C8—22no—
340C22⋊C8—22no—
341C22⋊C8—44no—
342C22⋊C8—1222no—
343C22⋊C8—1222no—
344C22⋊C8—2444no—
345C24—21no—
346C24—21no—
347C24—21no—
348C24—21no—
349C24—42no—
350C24—42no—
351C24—612no—
352C24—612no—
353C24—612no—
354C24—1221no—
355C24—1221no—
356C24—1221no—
357C24—1221no—
358C24—2442no—
359C24—2442no—
360C24C8×D6112yes—
361C24#1175818912yes—
362C24#1175819812yes—
363C24C2×C4×D6111yescharacteristic
364C2×D4—1228no—
365C2×D4—1228no—
366C2×D4—1228no—
367C2×D4—1228no—
368C2×D4—1228no—
369C2×D4—1228no—
370C2×D4—1228no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—24no—
374C22×C4—24no—
375C22×C4—24no—
376C22×C4—24no—
377C22×C4—24no—
378C22×C4—42no—
379C22×C4—42no—
380C22×C4—42no—
381C22×C4—48no—
382C22×C4—48no—
383C22×C4—612no—
384C22×C4—612no—
385C22×C4—612no—
386C22×C4—612no—
387C22×C4—612no—
388C22×C4—1228no—
389C22×C4—1221no—
390C22×C4—1221no—
391C22×C4—1221no—
392C22×C4—1221no—
393C22×C4—1221no—
394C22×C4—1221no—
395C22×C4—1221no—
396C22×C4—1221no—
397C22×C4—2448no—
398C22×C4—2448no—
399C22×C4—2444no—
400C22×C4—2444no—
401C22×C4—2442no—
402C22×C4—2442no—
403C22×C4#1175819812yes—
404C22×C4C2×D24411yescharacteristic
405C22×C4D4×D6112yes—
406C22×C4D4×D6112yes—
407C22×C4C2×C22⋊D6111yescharacteristic
408C2×C8—44no—
409C2×C8—42no—
410C2×C8—2444no—
411C2×C8—2442no—
412C4⋊C4—1224no—
413C4⋊C4—1224no—
414C22⋊C4—1228no—
415C22⋊C4—1224no—
416C22⋊C4—1224no—
417C42—1228no—
418C23—22no—
419C23—22no—
420C23—22no—
421C23—22no—
422C23—22no—
423C23—22no—
424C23—22no—
425C23—22no—
426C23—22no—
427C23—22no—
428C23—22no—
429C23—22no—
430C23—44no—
431C23—44no—
432C23—42no—
433C23—42no—
434C23—44no—
435C23—44no—
436C23—42no—
437C23—42no—
438C23—614no—
439C23—1222no—
440C23—1222no—
441C23—1222no—
442C23—1222no—
443C23—1222no—
444C23—1222no—
445C23—2442no—
446C23—2444no—
447C23—2444no—
448C23—2442no—
449C23—2442no—
450C23—2444no—
451C23—2444no—
452C23—2442no—
453C23—2442no—
454C23—2442no—
455C23#1451968914yes—
456C23C22⋊C4×D6111yescharacteristic
457C23C22⋊C4×D6111yescharacteristic
458C23C2×#1175819811yescharacteristic
459C23C2×C8×D6111yescharacteristic
460C23M16×D6111yescharacteristic
461C23M16×D6111yescharacteristic
462C23C2×#1175818911yescharacteristic
463D4—12232no—
464C2×C4—24no—
465C2×C4—24no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—48no—
473C2×C4—48no—
474C2×C4—614no—
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—24416no—
484C2×C4—2442no—
485C2×C4—2442no—
486C2×C4—2442no—
487C2×C4—2442no—
488C2×C4—2442no—
489C2×C4—2442no—
490C2×C4#1451969114yes—
491C2×C4#1451974512yes—
492C2×C4#1451974712yes—
493C8—82no—
494C8—4882no—
495C22—22no—
496C22—22no—
497C22—22no—
498C22—22no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—24no—
504C22—24no—
505C22—24no—
506C22—44no—
507C22—44no—
508C22—44no—
509C22—44no—
510C22—42no—
511C22—42no—
512C22—42no—
513C22—42no—
514C22—1224no—
515C22—2444no—
516C22—2444no—
517C22—2444no—
518C22—2444no—
519C22—2444no—
520C22—2444no—
521C22—2442no—
522C22—2442no—
523C22#1683961711yescharacteristic
524C22C22⋊C8×D6111yescharacteristic
525C22C22⋊C8×D6111yescharacteristic
526C22C2×#1451968911yescharacteristic
527C22#1683972411yescharacteristic
528C22#1683972411yescharacteristic
529C22#1683972511yescharacteristic
530C22C2×#1451969112yes—
531C22#1683974412yes—
532C4—22no—
533C4—22no—
534C4—24no—
535C4—1224no—
536C4—2442no—
537C4—2442no—
538C2—21no—
539C2—21no—
540C2—21no—
541C2—21no—
542C2—44no—
543C2—2444no—
544C2#2144413512yes—
545C2#2144415512yes—
546C2#2144572811yescharacteristic
547C2#2144573311yescharacteristic
548C2#2144574511yescharacteristic
subgroupG/H
centerC23C2×#11758198
commutatorC23×C61C22×C8
FrattiniC23×C4C22×D61
FittingC61×#1779C2
socleC23×C61C2×C22⋊C4
prime radicalC23×C22⋊D61C4
cosocleC23×C4×C61C23
hypercenter#1779D61
hypocenterC61#8301
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C24×C4 ◁ #1779

Complements

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

NH ≅ G/Ntype
2. #21445729C2semidirect
3. C2×#16839487C2semidirect
4. C2×#16839485C2semidirect
5. C61×#1779C2semidirect
30. C22×C22⋊D61C8semidirect
187. C22×D61C22⋊C8semidirect
216. C2×Dic61C22⋊C8semidirect
266. #1779D61semidirect
297. C61#8301semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D612
#214457292
C2×#168394872
C2×#168394852
C61×#17792
#830161