Finite Group Databasebeta

← #29580239

Subgroups — #29580239

Order 15616.

812 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840076C211yesmaximal, characteristic, complemented
2#21451553C211yesmaximal, characteristic
3C2×#16839687C211yesmaximal, characteristic, complemented
4#21445906C211yesmaximal, characteristic, complemented
5C2×#16839497C211yesmaximal, characteristic, complemented
6#21443699C211yesmaximal, characteristic, complemented
7C2×C61×#323C211yesmaximal, characteristic, complemented
8C2×#14519751C2211yescharacteristic
9C2×#14519746—21no—
10C22×C4⋊Dic61C2211yescharacteristic
11C22×C22⋊Dic61—21no—
12#16840076—22no—
13#16840076—22no—
14C2×#14519711—21no—
15C2×#14519699—21no—
16#16839687—21no—
17#16839687—22no—
18#16839687—22no—
19#16839678—22no—
20#16839671—21no—
21#16839641—21no—
22#16839622C2211yescharacteristic
23C2×#14519684—21no—
24C2×#14519684C2211yescharacteristic
25#16839525—22no—
26#16839497—22no—
27C22×C22⋊C4×C61C2211yescharacteristic
28C2×C22⋊C8×C61C2211yescharacteristic
29C2×C22⋊C8×C61C2211yescharacteristic
30C61×#323—22no—
31C22×D244D411yescharacteristic
32C22×C22⋊D61—21no—
33C22×C22⋊D61—22no—
34C23×Dic61—21no—
35C23×Dic61—21no—
36#14519751—21no—
37#14519751—21no—
38#14519751—21no—
39#14519751—21no—
40#14519746—42no—
41#14519746—42no—
42C2×C4⋊Dic61—21no—
43C2×C4⋊Dic61—21no—
44C2×C4⋊Dic61—21no—
45C2×C4⋊Dic61—21no—
46C2×C4⋊Dic61—21no—
47C2×C4⋊Dic61D411yescharacteristic
48C2×C4⋊Dic61D412yes—
49C2×C4⋊Dic61D412yescomplemented
50C2×C22⋊Dic61—24no—
51C2×C22⋊Dic61—22no—
52C2×C22⋊Dic61—21no—
53C2×C22⋊Dic61—42no—
54C2×C22⋊Dic61—42no—
55C2×#11758198—21no—
56C2×#11758198—22no—
57#14519711—24no—
58#14519699—24no—
59#14519684—24no—
60#14519684—22no—
61#14519684—21no—
62#14519684—21no—
63#14519684D412yescomplemented
64C25×C61D411yescharacteristic
65C23×C4×C61D411yescharacteristic
66C23×C4×C61C2311yescharacteristic
67C22×C8×C61—21no—
68C22×C8×C61—21no—
69C2×C22⋊C4×C61—21no—
70C2×C22⋊C4×C61—21no—
71C2×C22⋊C4×C61—21no—
72C2×C22⋊C4×C61—21no—
73C2×C22⋊C4×C61—21no—
74C2×C22⋊C4×C61—21no—
75C22⋊C8×C61—21no—
76C22⋊C8×C61—21no—
77C22⋊C8×C61—21no—
78C22⋊C8×C61D412yescomplemented
79C24×C61—21no—
80C24×C61—21no—
81C24×C61—21no—
82C24×C61—21no—
83C24×C61—21no—
84C24×C61—21no—
85C24×C61—42no—
86C24×C61—42no—
87C24×C61D812yes—
88C24×C61C2×D411yescharacteristic
89C23×D61—21no—
90C22×C4×C61—21no—
91C22×C4×C61—21no—
92C22×C4×C61—21no—
93C22×C4×C61—42no—
94C22×C4×C61—42no—
95C22×C4×C61C2×D411yescharacteristic
96C22×C4×C61C2×D411yescharacteristic
97C22×C4×C61C2×D411yescharacteristic
98C22×C4×C61C2×D411yescharacteristic
99C22×C4×C61C2×D411yescharacteristic
100C22×C4×C61#4111yescharacteristic
101C2×C22⋊D61—44no—
102C2×C22⋊D61—41no—
103C2×C22⋊D61—41no—
104C2×C22⋊D61—41no—
105C2×C22⋊D61—41no—
106C2×C22⋊D61—41no—
107C2×C22⋊D61—41no—
108C2×C22⋊D61—82no—
109C2×C22⋊D61—82no—
110C22×Dic61—22no—
111C22×Dic61—22no—
112C22×Dic61—21no—
113C22×Dic61—22no—
114C22×Dic61—42no—
115C22×Dic61—42no—
116C22×Dic61—41no—
117C22×Dic61—41no—
118C22×Dic61—41no—
119C22×Dic61—41no—
120C22×Dic61—41no—
121C22×Dic61—41no—
122C22×Dic61—41no—
123C22×Dic61—41no—
124C2×D244—21no—
125C2×D244—21no—
126C2×D244—42no—
127C2×C8×C61—22no—
128C2×C8×C61—42no—
129C2×C8×C61—42no—
130C2×C8×C61—41no—
131C22⋊C4×C61—41no—
132C22⋊C4×C61—41no—
133C22⋊C4×C61—41no—
134C22⋊C4×C61—41no—
135C22⋊Dic61—48no—
136C22⋊Dic61—44no—
137C22⋊Dic61—41no—
138C22⋊Dic61—41no—
139#11758198—41no—
140#11758198—41no—
141#11758198—82no—
142C4⋊Dic61—22no—
143C4⋊Dic61—21no—
144C4⋊Dic61—22no—
145C4⋊Dic61—21no—
146C4⋊Dic61—41no—
147C4⋊Dic61—41no—
148C4⋊Dic61—42no—
149C23×C61—22no—
150C23×C61—22no—
151C23×C61—22no—
152C23×C61—22no—
153C23×C61—22no—
154C23×C61—44no—
155C23×C61—44no—
156C23×C61—42no—
157C23×C61—42no—
158C23×C61—41no—
159C23×C61—41no—
160C23×C61—41no—
161C23×C61—42no—
162C23×C61—42no—
163C23×C61—41no—
164C23×C61—82no—
165C23×C61—82no—
166C23×C61—81no—
167C23×C61—81no—
168C23×C61#12011yescharacteristic
169C23×C61#12011yescharacteristic
170C23×C61#12111yescharacteristic
171C23×C61C2×D811yescharacteristic
172C23×C61#13511yescharacteristic
173C23×C61AGL(1,ℤ/8)11yescharacteristic
174C23×C61AGL(1,ℤ/8)11yescharacteristic
175C22×D61—41no—
176C22×D61—41no—
177C22×D61—41no—
178C22×D61—42no—
179C22×D61—42no—
180C2×C4×C61—22no—
181C2×C4×C61—22no—
182C2×C4×C61—41no—
183C2×C4×C61—41no—
184C2×C4×C61—41no—
185C2×C4×C61—41no—
186C2×C4×C61—42no—
187C2×C4×C61—41no—
188C2×C4×C61—42no—
189C2×C4×C61—81no—
190C2×C4×C61#12011yescharacteristic
191C2×C4×C61#12111yescharacteristic
192C2×C4×C61#12111yescharacteristic
193C2×C4×C61#12711yescharacteristic
194C22⋊D61—88no—
195C22⋊D61—81no—
196C22⋊D61—81no—
197C22⋊D61—81no—
198C22⋊D61—81no—
199C2×Dic61—42no—
200C2×Dic61—42no—
201C2×Dic61—42no—
202C2×Dic61—41no—
203C2×Dic61—42no—
204C2×Dic61—42no—
205C2×Dic61—42no—
206C2×Dic61—41no—
207C2×Dic61—42no—
208C2×Dic61—41no—
209C2×Dic61—42no—
210C2×Dic61—42no—
211C2×Dic61—82no—
212C2×Dic61—82no—
213C2×Dic61—81no—
214C2×Dic61—81no—
215C2×Dic61—81no—
216C2×Dic61—81no—
217D244—42no—
218D244—81no—
219C8×C61—42no—
220C8×C61—81no—
221#9918—611nomaximal, Sylow
222C22×C61—22no—
223C22×C61—22no—
224C22×C61—22no—
225C22×C61—22no—
226C22×C61—21no—
227C22×C61—21no—
228C22×C61—21no—
229C22×C61—21no—
230C22×C61—44no—
231C22×C61—44no—
232C22×C61—42no—
233C22×C61—82no—
234C22×C61—82no—
235C22×C61—82no—
236C22×C61—82no—
237C22×C61—81no—
238C22×C61—81no—
239C22×C61#39211yescharacteristic
240C22×C61#44711yescharacteristic
241C22×C61#44711yescharacteristic
242C22×C61#44911yescharacteristic
243C22×C61#44911yescharacteristic
244C22×C61#45512yes—
245C22×C61#45812yes—
246C22×C61#46611yescharacteristic
247C22×C61#46911yescharacteristic
248C2×D61—82no—
249C2×D61—82no—
250C2×D61—81no—
251C2×D61—81no—
252C2×D61—81no—
253C4×C61—21no—
254C4×C61—21no—
255C4×C61—21no—
256C4×C61—21no—
257C4×C61—81no—
258Dic61—82no—
259Dic61—82no—
260Dic61—82no—
261Dic61—81no—
262C2×#480—611no—
263#2617—611no—
264C2×#397—611no—
265#1823—611no—
266C2×#327—611no—
267C2×#323D6111yescharacteristic, complemented
268#1294—611no—
269C2×C61—21no—
270C2×C61—21no—
271C2×C61—21no—
272C2×C61—21no—
273C2×C61—82no—
274C2×C61#160712yes—
275C2×C61#161212yes—
276C2×C61#199911yescharacteristic
277C2×C61#200411yescharacteristic
278C2×C61#202211yescharacteristic
279D61—161no—
280C2×#121—611no—
281C2×#120—1221no—
282C22×C4⋊C4—611no—
283C22×C22⋊C4—1221no—
284C22×C22⋊C4C2×D6111yescharacteristic
285#480—1222no—
286#480—1222no—
287C2×#107—1221no—
288C2×#102—1221no—
289C2×C22⋊C8C2×D6111yescharacteristic
290C2×C22⋊C8C2×D6111yescharacteristic
291#397—1222no—
292#397—1221no—
293#397—1222no—
294#394—1222no—
295#392—1221no—
296#386—1221no—
297#380—611no—
298C2×#95—611no—
299C2×#95—1221no—
300#340—1222no—
301#327—1222no—
302#323—22no—
303C61#991811yescharacteristic, complemented, Sylow
304C25D24411yescharacteristic
305C22×D4—611no—
306C22×D4—1222no—
307C22×D4—1221no—
308C23×C4—1221no—
309C23×C4—1221no—
310C23×C4D24411yescharacteristic
311C23×C4C22×D6111yescharacteristic
312C22×C8—21no—
313C22×C8—21no—
314#121—1221no—
315#121—1221no—
316#121—1221no—
317#121—1221no—
318#120—2442no—
319#120—2442no—
320C2×C4⋊C4—612no—
321C2×C4⋊C4—611no—
322C2×C4⋊C4—612no—
323C2×C4⋊C4—1221no—
324C2×C4⋊C4—1221no—
325C2×C4⋊C4—1221no—
326C2×C4⋊C4—1221no—
327C2×C4⋊C4—1221no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—21no—
334C2×C22⋊C4—1222no—
335C2×C22⋊C4—1224no—
336C2×C22⋊C4—1222no—
337C2×C22⋊C4—1221no—
338C2×C22⋊C4—1221no—
339C2×C22⋊C4—2442no—
340C2×C22⋊C4—2442no—
341#107—1224no—
342#102—1224no—
343C22⋊C8—21no—
344C22⋊C8—21no—
345C22⋊C8—21no—
346C22⋊C8C22⋊D6112yescomplemented
347#95—612no—
348#95—1224no—
349#95—1222no—
350#95—1221no—
351#95—1221no—
352C24—21no—
353C24—21no—
354C24—21no—
355C24—21no—
356C24—21no—
357C24—21no—
358C24—42no—
359C24—42no—
360C24—1221no—
361C24D48812yes—
362C24C2×D24411yescharacteristic
363C2×D4—1221no—
364C2×D4—1221no—
365C2×D4—4882no—
366C2×D4—4882no—
367C2×D4—2442no—
368C2×D4—2444no—
369C2×D4—2441no—
370C2×D4—2441no—
371C2×D4—2441no—
372C2×D4—2441no—
373C2×D4—2441no—
374C2×D4—2441no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—42no—
379C22×C4—42no—
380C22×C4—1222no—
381C22×C4—1222no—
382C22×C4—1222no—
383C22×C4—1221no—
384C22×C4—2442no—
385C22×C4—2442no—
386C22×C4—2441no—
387C22×C4—2441no—
388C22×C4—2441no—
389C22×C4—2441no—
390C22×C4—2441no—
391C22×C4—2441no—
392C22×C4—2441no—
393C22×C4—2441no—
394C22×C4#1175822211yescharacteristic
395C22×C4D4×D6111yescharacteristic
396C22×C4D4×D6111yescharacteristic
397C22×C4D4×D6111yescharacteristic
398C22×C4D4×D6111yescharacteristic
399C22×C4C2×C22⋊D6111yescharacteristic
400C2×C8—22no—
401C2×C8—42no—
402C2×C8—42no—
403C2×C8—41no—
404C4⋊C4—1222no—
405C4⋊C4—1221no—
406C4⋊C4—1222no—
407C4⋊C4—1221no—
408C4⋊C4—2442no—
409C4⋊C4—2441no—
410C4⋊C4—2441no—
411C22⋊C4—41no—
412C22⋊C4—41no—
413C22⋊C4—41no—
414C22⋊C4—41no—
415C22⋊C4—4882no—
416C22⋊C4—2448no—
417C22⋊C4—2444no—
418C22⋊C4—2441no—
419C22⋊C4—2441no—
420C22⋊C4—2441no—
421C22⋊C4—2441no—
422C23—22no—
423C23—22no—
424C23—22no—
425C23—22no—
426C23—22no—
427C23—44no—
428C23—42no—
429C23—42no—
430C23—44no—
431C23—42no—
432C23—42no—
433C23—41no—
434C23—41no—
435C23—41no—
436C23—41no—
437C23—82no—
438C23—81no—
439C23—81no—
440C23—82no—
441C23—2442no—
442C23—2442no—
443C23—2441no—
444C23—2441no—
445C23—2441no—
446C23#1451974711yescharacteristic
447C23#1451974711yescharacteristic
448C23#1451975111yescharacteristic
449C23C2×D48811yescharacteristic
450C23#1451979911yescharacteristic
451C23#1451980511yescharacteristic
452C23#1451980511yescharacteristic
453D4—4881no—
454D4—4888no—
455D4—4881no—
456D4—4881no—
457D4—4881no—
458D4—4881no—
459D4—2442no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—41no—
469C2×C4—81no—
470C2×C4—4882no—
471C2×C4—4882no—
472C2×C4—4881no—
473C2×C4—4881no—
474C2×C4—4881no—
475C2×C4—4881no—
476C2×C4—2442no—
477C2×C4—2442no—
478C2×C4—2442no—
479C2×C4—2442no—
480C2×C4—2442no—
481C2×C4—2442no—
482C2×C4—2441no—
483C2×C4—2442no—
484C2×C4—2442no—
485C2×C4—2441no—
486C2×C4—2441no—
487C2×C4—2442no—
488C2×C4#1451974511yescharacteristic
489C2×C4#1451975011yescharacteristic
490C2×C4#1451975011yescharacteristic
491C2×C4#1451977311yescharacteristic
492C8—42no—
493C8—81no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—22no—
499C22—22no—
500C22—22no—
501C22—22no—
502C22—44no—
503C22—42no—
504C22—44no—
505C22—82no—
506C22—82no—
507C22—82no—
508C22—81no—
509C22—81no—
510C22—82no—
511C22—4881no—
512C22—4881no—
513C22—4881no—
514C22—4882no—
515C22—4882no—
516C22#1683967111yescharacteristic
517C22#1683989811yescharacteristic
518C22#1683989811yescharacteristic
519C22#1683990911yescharacteristic
520C22#1683990911yescharacteristic
521C22#1683994212yes—
522C22#1683995312yes—
523C22#1683999811yescharacteristic
524C22#1684001511yescharacteristic
525C4—21no—
526C4—21no—
527C4—21no—
528C4—21no—
529C4—81no—
530C4—4882no—
531C4—4882no—
532C4—4881no—
533C4—4882no—
534C2—21no—
535C2—21no—
536C2—21no—
537C2—21no—
538C2—82no—
539C2—9761no—
540C2#2144480712yes—
541C2#2144483512yes—
542C2#2144681711yescharacteristic
543C2#2144685011yescharacteristic
544C2#2144694911yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC2×C61×#323C2
socleC23×C61#120
prime radical#21451553C2
hypercenterC2×#323D61
hypocenterC61#9918
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#323

Complements

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

NH ≅ G/Ntype
1. C2×#16840076C2semidirect
3. C2×#16839687C2semidirect
4. #21445906C2semidirect
5. C2×#16839497C2semidirect
6. #21443699C2semidirect
7. C2×C61×#323C2semidirect
49. C2×C4⋊Dic61D4semidirect
63. #14519684D4semidirect
78. C22⋊C8×C61D4semidirect
267. C2×#323D61semidirect
303. C61#9918semidirect
346. C22⋊C8C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168400762
#214515532
C2×#168396872
#214459062
C2×#168394972
#214436992
C2×C61×#3232
#991861