Finite Group Databasebeta

← #29571700

Subgroups — #29571700

Order 15616.

818 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840467C211yesmaximal, characteristic
2#21445909C211yesmaximal, characteristic, complemented
3#21445804C211yesmaximal, characteristic
4#21444392C211yesmaximal, characteristic, complemented
5#21444390C211yesmaximal, characteristic, complemented
6#21444135C211yesmaximal, characteristic
7C61×#1824C211yesmaximal, characteristic, complemented
8#16840467—22no—
9#16840467—22no—
10#16840467—22no—
11#16840467—22no—
12C2×#14519776C411yescharacteristic, complemented
13C2×#14519767—21no—
14C2×#14519757C411yescharacteristic, complemented
15C2×#14519756—21no—
16C2×#14519756C2211yescharacteristic
17C2×#14519755—21no—
18C2×#14519742C411yescharacteristic, complemented
19C2×C4×C22⋊D61—21no—
20C2×C4×C22⋊D61C2211yescharacteristic
21C2×C4⋊C4×D61C411yescharacteristic, complemented
22C2×#14519691—21no—
23C2×C22⋊#92418C2211yescharacteristic
24#16839622C2211yescharacteristic
25#16839528—21no—
26#16839524—22no—
27#16839500—22no—
28#16839498—22no—
29#16839487—21no—
30#16839485—21no—
31C22×C4⋊C4×C61C2211yescharacteristic
32C2×C22⋊C8×C61C2211yescharacteristic
33C61×#380C2211yescharacteristic
34C61×#340—22no—
35C22×Dic122—21no—
36C22×Dic122C2×C411yescharacteristic
37C22×C22⋊D61D411yescharacteristic
38C22×C4×D61—21no—
39C22×C4×D61C2×C411yescharacteristic
40C22×#92418—21no—
41#14519776—22no—
42#14519776—22no—
43#14519767—24no—
44#14519767—24no—
45#14519757—22no—
46#14519757—22no—
47#14519756—24no—
48#14519756—24no—
49#14519756—21no—
50#14519756—21no—
51#14519756D412yes—
52#14519756D412yes—
53#14519755—24no—
54#14519755—24no—
55#14519742—22no—
56#14519742—22no—
57C4×C22⋊D61—24no—
58C4×C22⋊D61—24no—
59C4×C22⋊D61—21no—
60C4×C22⋊D61—21no—
61C4×C22⋊D61—21no—
62C4×C22⋊D61—21no—
63C2×C4⋊Dic61—21no—
64C2×C4⋊Dic61—21no—
65C2×C4⋊Dic61C2×C411yescharacteristic
66C2×#11758196—21no—
67C2×#11758196—21no—
68C2×#11758196—21no—
69C2×#11758196—21no—
70C2×#11758196D411yescharacteristic
71C4⋊C4×D61—22no—
72C4⋊C4×D61—22no—
73C2×C22⋊Dic61—21no—
74C2×C22⋊Dic61—21no—
75C2×C22⋊Dic61D411yescharacteristic
76C2×#11758198—21no—
77C2×#11758198D411yescharacteristic
78C2×C4×Dic61—21no—
79C2×C4×Dic61C2×C411yescharacteristic
80#14519691—42no—
81C22⋊#92418—21no—
82C22⋊#92418—21no—
83#14519684—21no—
84C23×C4×C61—21no—
85C23×C4×C61C2311yescharacteristic
86C22×C8×C61—21no—
87C2×C4⋊C4×C61—21no—
88C2×C4⋊C4×C61—21no—
89C2×C4⋊C4×C61—21no—
90C2×C4⋊C4×C61—21no—
91C2×C4⋊C4×C61C2×C411yescharacteristic
92C2×C4⋊C4×C61C2×C411yescharacteristic
93C2×C4⋊C4×C61D412yes—
94C2×C4⋊C4×C61D412yes—
95C2×C22⋊C4×C61—21no—
96C22⋊C8×C61—21no—
97C22⋊C8×C61—21no—
98#95×C61—21no—
99C24×C61C2×D411yescharacteristic
100C23×D61C22⋊C411yescharacteristic
101C22×C4×C61—21no—
102C22×C4×C61—21no—
103C22×C4×C61—22no—
104C22×C4×C61—22no—
105C22×C4×C61—42no—
106C22×C4×C61—41no—
107C22×C4×C61—82no—
108C22×C4×C61C22×C411yescharacteristic
109C22×C4×C61C2×D411yescharacteristic
110C22×C4×C61C2×D411yescharacteristic
111C22×C4×C61C2×D411yescharacteristic
112C22×C4×C61C2×D411yescharacteristic
113C22×C4×C61C2×D411yescharacteristic
114C2×C22⋊D61—21no—
115C2×C22⋊D61—21no—
116C2×C22⋊D61—21no—
117C2×C22⋊D61—21no—
118C2×C22⋊D61SD1612yes—
119C2×C22⋊D61Q1612yes—
120C22×Dic61—21no—
121C22×Dic61—21no—
122C22×Dic61—41no—
123C22×Dic61C22⋊C411yescharacteristic
124C22×Dic61C22⋊C411yescharacteristic
125C22×Dic61C22⋊C411yescharacteristic
126C2×C4×D61—21no—
127C2×C4×D61—21no—
128C2×C4×D61—24no—
129C2×C4×D61—42no—
130C2×C4×D61—82no—
131C2×Dic122—21no—
132C2×Dic122—24no—
133C2×Dic122—42no—
134C2×Dic122—82no—
135C2×Dic122C22⋊C412yes—
136C2×C8×C61—42no—
137C2×C8×C61—41no—
138C4⋊C4×C61—21no—
139C4⋊C4×C61—21no—
140C4⋊C4×C61—22no—
141C4⋊C4×C61—22no—
142C4⋊C4×C61—42no—
143C4⋊C4×C61C22⋊C412yes—
144C4⋊C4×C61C22⋊C412yes—
145C22⋊C4×C61—41no—
146C22⋊C4×C61—41no—
147C22⋊Dic61—22no—
148C22⋊Dic61—22no—
149C22⋊Dic61—21no—
150C22⋊Dic61—21no—
151C22⋊Dic61—41no—
152C22⋊Dic61—41no—
153#11758198—24no—
154#11758198—21no—
155#11758198—21no—
156C4⋊Dic61—24no—
157C4⋊Dic61—21no—
158C4⋊Dic61—42no—
159C4⋊Dic61C22⋊C412yes—
160#11758196—24no—
161#11758196—24no—
162#11758196—24no—
163#11758196—22no—
164#11758196—22no—
165#11758196—21no—
166#11758196—21no—
167C4×Dic61—24no—
168C4×Dic61—21no—
169C4×Dic61—21no—
170C2×#92418—42no—
171C2×#92418—41no—
172C23×C61—41no—
173C23×C61—41no—
174C23×C61C2×C22⋊C411yescharacteristic
175C23×C61#12011yescharacteristic
176C23×C61#12011yescharacteristic
177C23×C61C2×SD1611yescharacteristic
178C23×C61C2×Q1611yescharacteristic
179C23×C61#13711yescharacteristic
180C23×C61#13711yescharacteristic
181C22×D61—21no—
182C22×D61—21no—
183C22×D61—41no—
184C22×D61—41no—
185C22×D61#10312yes—
186C2×C4×C61—22no—
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—41no—
194C2×C4×C61—42no—
195C2×C4×C61—42no—
196C2×C4×C61—82no—
197C2×C4×C61—82no—
198C2×C4×C61—81no—
199C2×C4×C61—81no—
200C2×C4×C61—81no—
201C2×C4×C61C2×C22⋊C411yescharacteristic
202C2×C4×C61C2×C22⋊C411yescharacteristic
203C2×C4×C61#12011yescharacteristic
204C2×C4×C61#12011yescharacteristic
205C22⋊D61—22no—
206C22⋊D61—22no—
207C22⋊D61—22no—
208C22⋊D61—22no—
209C2×Dic61—21no—
210C2×Dic61—21no—
211C2×Dic61—22no—
212C2×Dic61—21no—
213C2×Dic61—21no—
214C2×Dic61—22no—
215C2×Dic61—42no—
216C2×Dic61—42no—
217C2×Dic61—41no—
218C2×Dic61—41no—
219C2×Dic61—81no—
220C2×Dic61—81no—
221C2×Dic61—81no—
222C2×Dic61#10312yes—
223C4×D61—42no—
224C4×D61—42no—
225C4×D61—84no—
226Dic122—42no—
227Dic122—42no—
228Dic122—84no—
229C8×C61—81no—
230#92418—81no—
231#8380—611nomaximal, Sylow
232C22×C61—21no—
233C22×C61—21no—
234C22×C61—21no—
235C22×C61—21no—
236C22×C61—21no—
237C22×C61—21no—
238C22×C61—41no—
239C22×C61—41no—
240C22×C61—41no—
241C22×C61—41no—
242C22×C61#37911yescharacteristic
243C22×C61C2×#10311yescharacteristic
244C22×C61#41911yescharacteristic
245C22×C61#44811yescharacteristic
246C22×C61#44811yescharacteristic
247C22×C61#45111yescharacteristic
248C22×C61#45111yescharacteristic
249C2×D61—22no—
250C2×D61—42no—
251C2×D61—41no—
252C2×D61—41no—
253C2×D61—42no—
254C4×C61—21no—
255C4×C61—21no—
256C4×C61—21no—
257C4×C61—42no—
258C4×C61—42no—
259C4×C61—161no—
260C4×C61#41012yes—
261Dic61—22no—
262Dic61—41no—
263Dic61—42no—
264Dic61—42no—
265Dic61—41no—
266Dic61—161no—
267C2×#554—611no—
268#1824—611no—
269#1824D6111yescharacteristic, complemented
270#1799—611no—
271#1520—611no—
272#1520—611no—
273#1459—611no—
274C2×C61—21no—
275C2×C61—21no—
276C2×C61—21no—
277C2×C61—21no—
278C2×C61—21no—
279C2×C61—21no—
280C2×C61#178211yescharacteristic
281C2×C61#178711yescharacteristic
282C2×C61#179511yescharacteristic
283D61—42no—
284#554—1222no—
285#554—1222no—
286#554—1222no—
287#554—1222no—
288C2×C4⋊Q8—611no—
289C2×#125—1221no—
290C2×C22⋊Q8—611no—
291C2×C22⋊Q8—611no—
292C2×C22⋊Q8—1221no—
293C2×C22⋊Q8—1221no—
294C2×C4×Q8—611no—
295C2×C4×D4—611no—
296C2×C4×D4—1221no—
297C22×C4⋊C4—611no—
298C22×C4⋊C4C2×D6111yescharacteristic
299C2×#99—1221no—
300C2×C22⋊C8—611no—
301C2×C22⋊C8C2×D6111yescharacteristic
302#380—611no—
303#380C2×D6111yescharacteristic
304#342—1221no—
305#340—22no—
306#340—1222no—
307#328—1222no—
308#328—1222no—
309#324—1221no—
310#323—1221no—
311C61#838011yescharacteristic, complemented, Sylow
312C22×Q8—611no—
313C22×Q8—1221no—
314C22×D4—611no—
315C23×C4—21no—
316C23×C4—611no—
317C23×C4—1221no—
318C23×C4C22×D6111yescharacteristic
319C22×C8—21no—
320C22×C8—1221no—
321C4⋊Q8—1222no—
322C4⋊Q8—1222no—
323#125—1224no—
324#125—1224no—
325C22⋊Q8—612no—
326C22⋊Q8—612no—
327C22⋊Q8—1222no—
328C22⋊Q8—1224no—
329C22⋊Q8—1224no—
330C22⋊Q8—1224no—
331C22⋊Q8—1224no—
332C22⋊Q8—1221no—
333C22⋊Q8—1221no—
334C22⋊Q8—1222no—
335C4×Q8—1222no—
336C4×Q8—1222no—
337C4×D4—1224no—
338C4×D4—1224no—
339C4×D4—1221no—
340C4×D4—1221no—
341C4×D4—1221no—
342C4×D4—1221no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—611no—
348C2×C4⋊C4—611no—
349C2×C4⋊C4—1222no—
350C2×C4⋊C4—1221no—
351C2×C4⋊C4—1221no—
352C2×C4⋊C4—1221no—
353C2×C4⋊C4—1221no—
354C2×C4⋊C4—1221no—
355C2×C4⋊C4—1222no—
356C2×C4⋊C4—1221no—
357C2×C4⋊C4C4×D6111yescharacteristic
358C2×C4⋊C4C4×D6111yescharacteristic
359C2×C4⋊C4D24412yes—
360C2×C4⋊C4C22⋊D6112yes—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—611no—
363C2×C22⋊C4—611no—
364C2×C22⋊C4—1221no—
365C2×C22⋊C4—1221no—
366C2×C22⋊C4—1221no—
367C2×C42—611no—
368C2×C42—1221no—
369#99—2442no—
370C22⋊C8—21no—
371C22⋊C8—21no—
372C22⋊C8—1221no—
373C22⋊C8—1221no—
374#95—21no—
375#95—1221no—
376C24—611no—
377C24D4×D6111yescharacteristic
378C2×Q8—612no—
379C2×Q8—1224no—
380C2×Q8—1221no—
381C2×Q8—4882no—
382C2×Q8—2442no—
383C2×D4—612no—
384C2×D4—612no—
385C2×D4—1221no—
386C2×D4—1221no—
387C2×D4—1221no—
388C2×D4—1221no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—42no—
394C22×C4—41no—
395C22×C4—82no—
396C22×C4—611no—
397C22×C4—611no—
398C22×C4—611no—
399C22×C4—1224no—
400C22×C4—1221no—
401C22×C4—1221no—
402C22×C4—1221no—
403C22×C4—1221no—
404C22×C4—4882no—
405C22×C4—2442no—
406C22×C4—2441no—
407C22×C4C2×C4×D6111yescharacteristic
408C22×C4C2×D24411yescharacteristic
409C22×C4D4×D6111yescharacteristic
410C22×C4D4×D6111yescharacteristic
411C22×C4D4×D6111yescharacteristic
412C22×C4C2×C22⋊D6111yescharacteristic
413C2×C8—42no—
414C2×C8—41no—
415C2×C8—2442no—
416C2×C8—2441no—
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—42no—
422C4⋊C4—612no—
423C4⋊C4—1224no—
424C4⋊C4—1224no—
425C4⋊C4—1224no—
426C4⋊C4—1224no—
427C4⋊C4—1221no—
428C4⋊C4—1221no—
429C4⋊C4—1222no—
430C4⋊C4—1221no—
431C4⋊C4—1222no—
432C4⋊C4—2442no—
433C4⋊C4#1175819812yes—
434C4⋊C4#1175819812yes—
435C22⋊C4—41no—
436C22⋊C4—41no—
437C22⋊C4—1224no—
438C22⋊C4—1221no—
439C22⋊C4—1222no—
440C22⋊C4—1221no—
441C22⋊C4—1222no—
442C22⋊C4—1221no—
443C22⋊C4—1221no—
444C22⋊C4—2441no—
445C22⋊C4—2441no—
446C42—1224no—
447C42—1221no—
448C42—1221no—
449C23—41no—
450C23—41no—
451C23—612no—
452C23—1221no—
453C23—1221no—
454C23—2441no—
455C23—2441no—
456C23C22⋊C4×D6111yescharacteristic
457C23#1451974511yescharacteristic
458C23#1451974711yescharacteristic
459C23SD16×D6111yescharacteristic
460C23Q16×D6111yescharacteristic
461C23#1451980611yescharacteristic
462C23#1451980911yescharacteristic
463Q8—4884no—
464Q8—2442no—
465Q8—2442no—
466D4—1222no—
467D4—1222no—
468D4—1222no—
469D4—1222no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—82no—
481C2×C4—82no—
482C2×C4—81no—
483C2×C4—81no—
484C2×C4—81no—
485C2×C4—612no—
486C2×C4—1221no—
487C2×C4—1221no—
488C2×C4—1222no—
489C2×C4—1221no—
490C2×C4—1222no—
491C2×C4—1221no—
492C2×C4—4884no—
493C2×C4—4881no—
494C2×C4—4881no—
495C2×C4—4881no—
496C2×C4—2442no—
497C2×C4—2442no—
498C2×C4—2442no—
499C2×C4—2442no—
500C2×C4—2441no—
501C2×C4—2441no—
502C2×C4C22⋊C4×D6111yescharacteristic
503C2×C4C2×#1175819811yescharacteristic
504C2×C4#1451974511yescharacteristic
505C2×C4#1451974711yescharacteristic
506C8—81no—
507C8—4881no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—21no—
514C22—41no—
515C22—41no—
516C22—41no—
517C22—41no—
518C22—1222no—
519C22—2442no—
520C22—2442no—
521C22—2441no—
522C22—2441no—
523C22#1683961711yescharacteristic
524C22#103×D6111yescharacteristic
525C22#1683976911yescharacteristic
526C22#1683989911yescharacteristic
527C22#1683990211yescharacteristic
528C22#1683991611yescharacteristic
529C22#1683991911yescharacteristic
530C4—21no—
531C4—21no—
532C4—21no—
533C4—42no—
534C4—42no—
535C4—161no—
536C4—1222no—
537C4—9761no—
538C4—2441no—
539C4—2442no—
540C4—2442no—
541C4—2441no—
542C4#1683973512yes—
543C2—21no—
544C2—21no—
545C2—21no—
546C2—21no—
547C2—21no—
548C2—21no—
549C2—2442no—
550C2#2144573611yescharacteristic
551C2#2144575211yescharacteristic
552C2#2144578611yescharacteristic
subgroupG/H
centerC22#16839617
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1824C2
socleC22×C61#379
prime radicalC22×C22⋊D61D4
cosocleC23×C4×C61C23
hypercenter#1824D61
hypocenterC61#8380
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1824

Complements

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

NH ≅ G/Ntype
2. #21445909C2semidirect
4. #21444392C2semidirect
5. #21444390C2semidirect
7. C61×#1824C2semidirect
12. C2×#14519776C4semidirect
14. C2×#14519757C4semidirect
18. C2×#14519742C4semidirect
21. C2×C4⋊C4×D61C4semidirect
269. #1824D61semidirect
311. C61#8380semidirect

Maximal subgroups

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

subgroupindex
C2×#168404672
#214459092
#214458042
#214443922
#214443902
#214441352
C61×#18242
#838061