Finite Group Databasebeta

← #29571433

Subgroups — #29571433

Order 15616.

930 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840238C211yesmaximal, characteristic
2#21444215C211yesmaximal, characteristic, complemented
3#21444214C211yesmaximal, characteristic, complemented
4#21444213C211yesmaximal, characteristic, complemented
5#21444131C211yesmaximal, characteristic
6#21444131C211yesmaximal, characteristic
7C61×#1479C211yesmaximal, characteristic, complemented
8C22×Q8×D61C411yescharacteristic
9#16840238—22no—
10#16840238—22no—
11#16840238—22no—
12#16840238—22no—
13C2×Q8×Dic61C411yescharacteristic
14C2×C4×Dic122—21no—
15C2×C4×Dic122C2211yescharacteristic
16C2×#14519742—21no—
17C2×#14519742C411yescharacteristic
18C2×#14519735—21no—
19C2×#14519735C411yescharacteristic
20C2×#14519734—21no—
21C2×#14519734C2211yescharacteristic
22#16839815C2211yescharacteristic
23#16839815C2211yescharacteristic
24#16839494—22no—
25Q8⋊#92418—22no—
26#16839492—22no—
27#16839487—21no—
28#16839487—21no—
29#16839485—21no—
30#16839485—21no—
31C2×C4×Q8×C61C2211yescharacteristic
32C61×#431C2211yescharacteristic
33C61×#431C2211yescharacteristic
34C61×Q8⋊C8—22no—
35C22×Dic122—21no—
36C22×Dic122C2×C411yescharacteristic
37C2×Q8×D61—22no—
38C2×Q8×D61—22no—
39C2×Q8×D61—22no—
40C2×Q8×D61—22no—
41C2×Q8×D61—22no—
42C2×Q8×D61C814yescomplemented
43C22×C4×D61—21no—
44C22×C4×D61C2×C411yescharacteristic
45Q8×Dic61—22no—
46Q8×Dic61—22no—
47C4×Dic122—24no—
48C4×Dic122—24no—
49C4×Dic122—21no—
50C4×Dic122—21no—
51C4×Dic122D412yes—
52C4×Dic122D412yes—
53#14519742—24no—
54#14519742—24no—
55#14519742—22no—
56#14519742—22no—
57#14519735—24no—
58#14519735—24no—
59#14519735—22no—
60#14519735—22no—
61#14519734—24no—
62#14519734—24no—
63#14519734—21no—
64#14519734—21no—
65#14519734—21no—
66#14519734—21no—
67C2×C4⋊Dic61—21no—
68C2×C4⋊Dic61C2×C411yescharacteristic
69C2×#11758196—21no—
70C2×#11758196—21no—
71C2×#11758196D411yescharacteristic
72C2×#11758196D411yescharacteristic
73C2×#11758198—21no—
74C2×#11758198D411yescharacteristic
75C2×#11758198D411yescharacteristic
76C2×C4×Dic61—21no—
77C2×C4×Dic61—21no—
78C2×C4×Dic61—21no—
79C2×C4×Dic61—21no—
80C2×C4×Dic61C2×C411yescharacteristic
81C4⋊#92418—21no—
82C4⋊#92418—21no—
83C22⋊#92418—21no—
84C22⋊#92418—21no—
85C4×#92418—21no—
86C4×#92418—21no—
87C22×Q8×C61C2×C411yescharacteristic
88C4×Q8×C61—21no—
89C4×Q8×C61—21no—
90C4×Q8×C61D412yes—
91C4×Q8×C61D412yes—
92C2×C4⋊C4×C61—21no—
93C2×C4⋊C4×C61C2×C411yescharacteristic
94C2×C42×C61—21no—
95C2×C42×C61C2311yescharacteristic
96C4⋊C8×C61—21no—
97C4⋊C8×C61—21no—
98C22⋊C8×C61—21no—
99C22⋊C8×C61—21no—
100C4×C8×C61—21no—
101C4×C8×C61—21no—
102C23×D61C22⋊C411yescharacteristic
103C2×Q8×C61—21no—
104C2×Q8×C61—21no—
105C2×Q8×C61—21no—
106C2×Q8×C61C22⋊C412yes—
107C2×Q8×C61C2×C812yes—
108C2×Q8×C61M1612yes—
109C22×C4×C61—21no—
110C22×C4×C61—21no—
111C22×C4×C61C22×C411yescharacteristic
112C22×C4×C61C2×D411yescharacteristic
113C22×C4×C61C2×D411yescharacteristic
114C22×Dic61—21no—
115C22×Dic61—21no—
116C22×Dic61C22⋊C411yescharacteristic
117C22×Dic61C22⋊C411yescharacteristic
118C22×Dic61C22⋊C411yescharacteristic
119Q8×D61—28no—
120Q8×D61—28no—
121Q8×D61—28no—
122Q8×D61—28no—
123C2×C4×D61—24no—
124C2×C4×D61—24no—
125C2×C4×D61—24no—
126C2×C4×D61—21no—
127C2×C4×D61—21no—
128C2×C4×D61—21no—
129C2×C4×D61—21no—
130C2×C4×D61C2×C812yes—
131C2×C4×D61M1612yes—
132C2×Dic122—24no—
133C2×Dic122—24no—
134C2×Dic122—21no—
135C2×Dic122—21no—
136C2×Dic122—21no—
137C2×Dic122—24no—
138C2×Dic122C22⋊C412yes—
139C2×Dic122C2×C812yes—
140C2×Dic122M1612yes—
141C2×C8×C61—41no—
142C2×C8×C61—41no—
143C4⋊C4×C61—21no—
144C4⋊C4×C61—22no—
145C4⋊C4×C61—22no—
146C4⋊C4×C61C22⋊C412yes—
147C42×C61—22no—
148C42×C61—22no—
149C42×C61C2×D411yescharacteristic
150C42×C61C2×D411yescharacteristic
151C42×C61C2×D411yescharacteristic
152C42×C61C2×D411yescharacteristic
153#11758198—24no—
154#11758198—21no—
155#11758198—21no—
156#11758198—21no—
157#11758198—21no—
158C4⋊Dic61—24no—
159C4⋊Dic61—21no—
160C4⋊Dic61C22⋊C412yes—
161#11758196—24no—
162#11758196—22no—
163#11758196—22no—
164#11758196—21no—
165#11758196—21no—
166#11758196—21no—
167#11758196—21no—
168C4×Dic61—24no—
169C4×Dic61—24no—
170C4×Dic61—24no—
171C4×Dic61—21no—
172C4×Dic61—21no—
173C4×Dic61—22no—
174C4×Dic61—22no—
175C2×#92418—41no—
176C2×#92418—41no—
177C23×C61C2×C22⋊C411yescharacteristic
178C22×D61—21no—
179C22×D61—21no—
180C22×D61—41no—
181C22×D61—41no—
182C22×D61C22⋊C812yes—
183Q8×C61—22no—
184Q8×C61—22no—
185Q8×C61—22no—
186Q8×C61C22⋊C814yes—
187C2×C4×C61—22no—
188C2×C4×C61—22no—
189C2×C4×C61—22no—
190C2×C4×C61—22no—
191C2×C4×C61—41no—
192C2×C4×C61—41no—
193C2×C4×C61—42no—
194C2×C4×C61C2×C22⋊C411yescharacteristic
195C2×C4×C61C2×C22⋊C411yescharacteristic
196C2×C4×C61#12011yescharacteristic
197C2×C4×C61#12011yescharacteristic
198C2×C4×C61#12011yescharacteristic
199C2×C4×C61#12011yescharacteristic
200C2×C4×C61C22×C811yescharacteristic
201C2×C4×C61C2×M1611yescharacteristic
202C2×C4×C61C2×M1611yescharacteristic
203C2×C4×C61C2×M1611yescharacteristic
204C2×Dic61—21no—
205C2×Dic61—22no—
206C2×Dic61—22no—
207C2×Dic61—21no—
208C2×Dic61—22no—
209C2×Dic61—21no—
210C2×Dic61—21no—
211C2×Dic61—22no—
212C2×Dic61—42no—
213C2×Dic61—41no—
214C2×Dic61—41no—
215C2×Dic61C22⋊C812yes—
216C4×D61—216no—
217C4×D61—22no—
218C4×D61—22no—
219C4×D61—22no—
220C4×D61—22no—
221Dic122—216no—
222Dic122—22no—
223Dic122—22no—
224Dic122—22no—
225Dic122C22⋊C814yes—
226C8×C61—81no—
227C8×C61—81no—
228#92418—81no—
229#92418—81no—
230#8323—611nomaximal, Sylow
231C22×C61—21no—
232C22×C61—21no—
233C22×C61#37911yescharacteristic
234C22×C61C2×C22⋊C811yescharacteristic
235C22×C61#40711yescharacteristic
236C2×D61—22no—
237C2×D61—42no—
238C2×D61—41no—
239C2×D61—41no—
240C2×D61—42no—
241C4×C61—21no—
242C4×C61—21no—
243C4×C61—21no—
244C4×C61—21no—
245C4×C61—24no—
246C4×C61—42no—
247C4×C61C2×C22⋊C811yescharacteristic
248C4×C61C2×C22⋊C811yescharacteristic
249C4×C61#40711yescharacteristic
250C4×C61#40711yescharacteristic
251Dic61—22no—
252Dic61—24no—
253Dic61—41no—
254Dic61—41no—
255Dic61—42no—
256C2×#519—611no—
257#1479—611no—
258#1479—611no—
259#1479—611no—
260#1479D6111yescharacteristic, complemented
261#1458—611no—
262#1458—611no—
263C2×C61—21no—
264C2×C61—21no—
265C2×C61#177911yescharacteristic
266C2×C61#179611yescharacteristic
267C2×C61#179611yescharacteristic
268D61—42no—
269C23×Q8—611no—
270#519—1222no—
271#519—1222no—
272#519—1222no—
273#519—1222no—
274C2×C4×Q8—611no—
275C2×C4×Q8—611no—
276C2×C4×Q8—611no—
277C2×C4×Q8—1221no—
278C2×C4×Q8—1221no—
279C2×C4×Q8C2×D6111yescharacteristic
280C2×#117—611no—
281C2×#117—611no—
282C2×#117—1221no—
283C2×#117—1221no—
284#431—611no—
285#431—611no—
286#431C2×D6111yescharacteristic
287#431C2×D6111yescharacteristic
288Q8⋊C8—22no—
289Q8⋊C8—1222no—
290Q8⋊C8—1222no—
291Q8⋊C8—1222no—
292#324—1221no—
293#324—1221no—
294#323—1221no—
295#323—1221no—
296C61#832311yescharacteristic, complemented, Sylow
297C22×Q8—614no—
298C22×Q8—611no—
299C22×Q8—1221no—
300C22×Q8—1222no—
301C22×Q8—1222no—
302C22×Q8—1222no—
303C22×Q8—1222no—
304C22×Q8—1222no—
305C22×Q8C4×D6111yescharacteristic
306C23×C4—611no—
307C23×C4—1221no—
308C4×Q8—21no—
309C4×Q8—21no—
310C4×Q8—612no—
311C4×Q8—612no—
312C4×Q8—1224no—
313C4×Q8—1224no—
314C4×Q8—1222no—
315C4×Q8—1224no—
316C4×Q8—1224no—
317C4×Q8—1222no—
318C4×Q8—1222no—
319C4×Q8—1222no—
320C4×Q8—1221no—
321C4×Q8—1221no—
322C4×Q8D24412yes—
323C4×Q8C22⋊D6112yes—
324#117—1224no—
325#117—1224no—
326#117—1222no—
327#117—1224no—
328#117—1224no—
329#117—1222no—
330#117—1221no—
331#117—1221no—
332#117—1221no—
333#117—1221no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—611no—
336C2×C4⋊C4—611no—
337C2×C4⋊C4—611no—
338C2×C4⋊C4—1221no—
339C2×C4⋊C4—1221no—
340C2×C4⋊C4—1221no—
341C2×C4⋊C4C4×D6111yescharacteristic
342C2×C22⋊C4—611no—
343C2×C22⋊C4—611no—
344C2×C22⋊C4—1221no—
345C2×C42—21no—
346C2×C42—611no—
347C2×C42—1221no—
348C2×C42—1221no—
349C2×C42—1221no—
350C2×C42—1221no—
351C2×C42C22×D6111yescharacteristic
352C4⋊C8—21no—
353C4⋊C8—21no—
354C4⋊C8—1221no—
355C4⋊C8—1221no—
356C22⋊C8—21no—
357C22⋊C8—21no—
358C22⋊C8—1221no—
359C22⋊C8—1221no—
360C4×C8—21no—
361C4×C8—21no—
362C4×C8—1221no—
363C4×C8—1221no—
364C24—611no—
365C2×Q8—21no—
366C2×Q8—21no—
367C2×Q8—21no—
368C2×Q8—612no—
369C2×Q8—612no—
370C2×Q8—612no—
371C2×Q8—1224no—
372C2×Q8—1224no—
373C2×Q8—1224no—
374C2×Q8—1228no—
375C2×Q8—1228no—
376C2×Q8—1228no—
377C2×Q8—1228no—
378C2×Q8—1221no—
379C2×Q8—1221no—
380C2×Q8—1221no—
381C2×Q8C8×D6112yes—
382C2×Q8#1175818912yes—
383C2×Q8#1175819812yes—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—611no—
387C22×C4—612no—
388C22×C4—612no—
389C22×C4—611no—
390C22×C4—611no—
391C22×C4—1224no—
392C22×C4—1224no—
393C22×C4—1224no—
394C22×C4—1221no—
395C22×C4—1221no—
396C22×C4—1221no—
397C22×C4—1221no—
398C22×C4—1221no—
399C22×C4—1221no—
400C22×C4C2×C4×D6111yescharacteristic
401C22×C4D4×D6111yescharacteristic
402C22×C4D4×D6111yescharacteristic
403C2×C8—41no—
404C2×C8—41no—
405C2×C8—2441no—
406C2×C8—2441no—
407C4⋊C4—21no—
408C4⋊C4—22no—
409C4⋊C4—22no—
410C4⋊C4—612no—
411C4⋊C4—1224no—
412C4⋊C4—1224no—
413C4⋊C4—1221no—
414C4⋊C4—1221no—
415C4⋊C4—1221no—
416C4⋊C4—1222no—
417C4⋊C4—1221no—
418C4⋊C4—1221no—
419C4⋊C4—1222no—
420C4⋊C4#1175819812yes—
421C22⋊C4—1224no—
422C22⋊C4—1221no—
423C22⋊C4—1221no—
424C22⋊C4—1221no—
425C22⋊C4—1221no—
426C42—22no—
427C42—22no—
428C42—1224no—
429C42—1224no—
430C42—1224no—
431C42—1221no—
432C42—1221no—
433C42—1222no—
434C42—1222no—
435C42C2×D24411yescharacteristic
436C42D4×D6111yescharacteristic
437C42D4×D6111yescharacteristic
438C42C2×C22⋊D6111yescharacteristic
439C23—612no—
440C23—1221no—
441C23—1221no—
442C23—2441no—
443C23—2441no—
444C23C22⋊C4×D6111yescharacteristic
445Q8—22no—
446Q8—22no—
447Q8—22no—
448Q8—614no—
449Q8—12216no—
450Q8—1222no—
451Q8—1222no—
452Q8—1222no—
453Q8#1451968914yes—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—42no—
461C2×C4—612no—
462C2×C4—12216no—
463C2×C4—1222no—
464C2×C4—1221no—
465C2×C4—1222no—
466C2×C4—1221no—
467C2×C4—1222no—
468C2×C4—1222no—
469C2×C4—1222no—
470C2×C4—1222no—
471C2×C4—1222no—
472C2×C4—1222no—
473C2×C4—1221no—
474C2×C4—1221no—
475C2×C4—2442no—
476C2×C4—2441no—
477C2×C4—2441no—
478C2×C4C22⋊C4×D6111yescharacteristic
479C2×C4C2×#1175819811yescharacteristic
480C2×C4#1451974511yescharacteristic
481C2×C4#1451974511yescharacteristic
482C2×C4#1451974711yescharacteristic
483C2×C4#1451974711yescharacteristic
484C2×C4C2×C8×D6111yescharacteristic
485C2×C4M16×D6111yescharacteristic
486C2×C4M16×D6111yescharacteristic
487C2×C4C2×#1175818911yescharacteristic
488C8—81no—
489C8—81no—
490C8—4881no—
491C8—4881no—
492C22—21no—
493C22—21no—
494C22—1222no—
495C22—2442no—
496C22—2442no—
497C22—2441no—
498C22—2441no—
499C22#1683961711yescharacteristic
500C22C22⋊C8×D6111yescharacteristic
501C22#1683972411yescharacteristic
502C4—24no—
503C4—21no—
504C4—21no—
505C4—21no—
506C4—21no—
507C4—42no—
508C4—1222no—
509C4—1224no—
510C4—2441no—
511C4—2442no—
512C4—2441no—
513C4C22⋊C8×D6111yescharacteristic
514C4C2×#1451968911yescharacteristic
515C4#1683972411yescharacteristic
516C4#1683972511yescharacteristic
517C2—21no—
518C2—21no—
519C2—2442no—
520C2#2144572811yescharacteristic
521C2#2144579111yescharacteristic
522C2#2144579311yescharacteristic
subgroupG/H
centerC22#16839617
commutatorC2×C4×C61C22×C8
FrattiniC2×C42C22×D61
FittingC61×#1479C2
socleC22×C61#379
prime radicalC23×D61C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1479D61
hypocenterC61#8323
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1479

Complements

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

NH ≅ G/Ntype
2. #21444215C2semidirect
3. #21444214C2semidirect
4. #21444213C2semidirect
7. C61×#1479C2semidirect
42. C2×Q8×D61C8semidirect
260. #1479D61semidirect
296. C61#8323semidirect

Maximal subgroups

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

subgroupindex
C2×#168402382
#214442152
#214442142
#214442132
#214441312
C61×#14792
#832361