Finite Group Databasebeta

← #29572083

Subgroups — #29572083

Order 15616.

1116 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840434C211yesmaximal, characteristic
2#21446625C211yesmaximal, characteristic, complemented
3#21445824C211yesmaximal, characteristic, complemented
4#21445820C211yesmaximal, characteristic, complemented
5C2×#16839505C211yesmaximal, characteristic, complemented
6C2×#16839491C211yesmaximal, characteristic, complemented
7C2×C61×Q8⋊C8C211yesmaximal, characteristic, complemented
8C22×#11758226—21no—
9#16840434—22no—
10#16840434—22no—
11#16840434—22no—
12#16840434C414yescomplemented
13C2×#14519774—21no—
14C2×#14519774C2211yescharacteristic
15C2×#14519752—21no—
16C2×#14519752—22no—
17C2×C4×D244—21no—
18C2×C4×D244C2211yescharacteristic
19C2×C4⋊#92418C2211yescharacteristic
20C2×#14519701—21no—
21C2×#14519699—21no—
22C2×#14519699—22no—
23#16839632C2211yescharacteristic
24#16839525—21no—
25#16839524—21no—
26#16839505—22no—
27#16839491—22no—
28C2×C4×Q8×C61C2211yescharacteristic
29C2×C4⋊C8×C61C2211yescharacteristic
30C2×C4×C8×C61C2211yescharacteristic
31C61×Q8⋊C8—22no—
32C2×#11758226—24no—
33C2×#11758226—24no—
34C2×#11758226—42no—
35C2×#11758226—42no—
36C2×#11758226—42no—
37C2×#11758226—42no—
38C22×D244—22no—
39C22×D244—21no—
40C22×D244—21no—
41C22×D244—22no—
42C22×D244D411yescharacteristic
43C22×D244D412yes—
44C22×C4×D61—22no—
45C22×C4×D61—21no—
46C22×#92418—21no—
47#14519774—24no—
48#14519774—24no—
49#14519774—21no—
50#14519774—21no—
51#14519774C2×C412yes—
52#14519774D412yes—
53#14519752—24no—
54#14519752—28no—
55#14519752—28no—
56#14519752—24no—
57C4×D244—24no—
58C4×D244—21no—
59C4×D244—21no—
60C4×D244—24no—
61C4×D244C2×C412yes—
62C4×D244D412yes—
63C2×C4⋊Dic61—21no—
64C2×C4⋊Dic61—21no—
65C2×C4⋊Dic61—21no—
66C2×C4⋊Dic61D411yescharacteristic
67C2×#11758198—22no—
68C2×#11758198—21no—
69C4⋊#92418—21no—
70C4⋊#92418—21no—
71#14519701—42no—
72#14519699—44no—
73#14519699—42no—
74C22×Q8×C61D411yescharacteristic
75C22×C8×C61—21no—
76C22×C8×C61—21no—
77C4×Q8×C61—21no—
78C4×Q8×C61—21no—
79C4×Q8×C61C2×C412yes—
80C4×Q8×C61D412yes—
81C2×C4⋊C4×C61—21no—
82C2×C4⋊C4×C61D411yescharacteristic
83C2×C42×C61—21no—
84C2×C42×C61C2311yescharacteristic
85C4⋊C8×C61—21no—
86C4⋊C8×C61—21no—
87C4×C8×C61—21no—
88C4×C8×C61—21no—
89C23×D61—21no—
90C23×D61—22no—
91C2×Q8×C61—21no—
92C2×Q8×C61—21no—
93C2×Q8×C61—21no—
94C2×Q8×C61C22⋊C412yes—
95C2×Q8×C61D812yes—
96C2×Q8×C61SD1612yes—
97C22×C4×C61—21no—
98C22×C4×C61—21no—
99C22×C4×C61C2×D411yescharacteristic
100C22×C4×C61C2×D411yescharacteristic
101C22×C4×C61C2×D411yescharacteristic
102C22×Dic61—21no—
103C22×Dic61—41no—
104#11758226—48no—
105#11758226—48no—
106#11758226—48no—
107#11758226—48no—
108C2×D244—21no—
109C2×D244—21no—
110C2×D244—21no—
111C2×D244—21no—
112C2×D244—28no—
113C2×D244—22no—
114C2×D244—22no—
115C2×D244—22no—
116C2×D244—22no—
117C2×D244—21no—
118C2×D244—28no—
119C2×D244—22no—
120C2×D244—44no—
121C2×D244—44no—
122C2×D244—41no—
123C2×D244—41no—
124C2×D244—41no—
125C2×D244—41no—
126C2×D244—41no—
127C2×D244—41no—
128C2×D244—41no—
129C2×D244—41no—
130C2×D244—42no—
131C2×D244—42no—
132C2×D244—82no—
133C2×D244—82no—
134C2×D244C22⋊C412yes—
135C2×D244C22⋊C414yes—
136C2×C4×D61—28no—
137C2×C4×D61—22no—
138C2×C4×D61—22no—
139C2×C4×D61—44no—
140C2×C4×D61—44no—
141C2×C4×D61—41no—
142C2×C4×D61—41no—
143C2×C4×D61—41no—
144C2×C4×D61—41no—
145C2×C8×C61—22no—
146C2×C8×C61—41no—
147C2×C8×C61—41no—
148C2×C8×C61—41no—
149C2×C8×C61—41no—
150C2×C8×C61—41no—
151C4⋊C4×C61—22no—
152C4⋊C4×C61—22no—
153C4⋊C4×C61—21no—
154C4⋊C4×C61C22⋊C412yes—
155C42×C61—22no—
156C42×C61—22no—
157C42×C61C22×C411yescharacteristic
158C42×C61C2×D411yescharacteristic
159C42×C61C2×D411yescharacteristic
160C42×C61C2×D411yescharacteristic
161#11758198—28no—
162#11758198—22no—
163#11758198—22no—
164C4⋊Dic61—21no—
165C4⋊Dic61—42no—
166C4⋊Dic61—41no—
167C4⋊Dic61—41no—
168C4⋊Dic61—41no—
169C4⋊Dic61—41no—
170C4⋊Dic61C22⋊C412yes—
171C2×#92418—41no—
172C2×#92418—41no—
173C2×#92418—41no—
174C23×C61#12011yescharacteristic
175C22×D61—24no—
176C22×D61—22no—
177C22×D61—42no—
178C22×D61—41no—
179C22×D61—41no—
180C22×D61—42no—
181C22×D61—42no—
182C22×D61—41no—
183C22×D61—41no—
184C22×D61—42no—
185C22×D61—42no—
186C22×D61—41no—
187C22×D61—42no—
188C22×D61—41no—
189Q8×C61—22no—
190Q8×C61—22no—
191Q8×C61—22no—
192Q8×C61#10214yescomplemented
193C2×C4×C61—22no—
194C2×C4×C61—22no—
195C2×C4×C61—22no—
196C2×C4×C61—21no—
197C2×C4×C61—21no—
198C2×C4×C61—22no—
199C2×C4×C61—41no—
200C2×C4×C61—41no—
201C2×C4×C61C2×C22⋊C411yescharacteristic
202C2×C4×C61C2×C22⋊C411yescharacteristic
203C2×C4×C61C2×C22⋊C411yescharacteristic
204C2×C4×C61#12011yescharacteristic
205C2×C4×C61#12011yescharacteristic
206C2×C4×C61#12011yescharacteristic
207C2×C4×C61C2×D811yescharacteristic
208C2×C4×C61C2×SD1611yescharacteristic
209C2×C4×C61#13511yescharacteristic
210C2×C4×C61#13511yescharacteristic
211C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
212C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
213C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
214C2×C4×C61#13711yescharacteristic
215C2×Dic61—22no—
216C2×Dic61—41no—
217C2×Dic61—41no—
218C2×Dic61—81no—
219C2×Dic61—81no—
220C2×Dic61—81no—
221D244—22no—
222D244—22no—
223D244—44no—
224D244—416no—
225D244—42no—
226D244—42no—
227D244—42no—
228D244—42no—
229D244—42no—
230D244—41no—
231D244—42no—
232D244—42no—
233D244—41no—
234D244—42no—
235D244—82no—
236D244—88no—
237C4×D61—416no—
238C4×D61—42no—
239C4×D61—42no—
240C4×D61—42no—
241C4×D61—42no—
242C8×C61—42no—
243C8×C61—81no—
244#92418—81no—
245#8444—611nomaximal, Sylow
246C22×C61#37911yescharacteristic
247C22×C61#44711yescharacteristic
248C22×C61#44911yescharacteristic
249C22×C61#45011yescharacteristic
250C22×C61#45211yescharacteristic
251C22×C61#45311yescharacteristic
252C22×C61#45511yescharacteristic
253C2×D61—44no—
254C2×D61—42no—
255C2×D61—44no—
256C2×D61—42no—
257C2×D61—42no—
258C2×D61—44no—
259C2×D61—81no—
260C2×D61—82no—
261C2×D61—81no—
262C2×D61—82no—
263C2×D61—81no—
264C2×D61—82no—
265C2×D61—81no—
266C2×D61—82no—
267C4×C61—21no—
268C4×C61—21no—
269C4×C61—24no—
270C4×C61—42no—
271C4×C61C2×#10211yescharacteristic
272C4×C61#41611yescharacteristic
273C4×C61#41711yescharacteristic
274C4×C61#41811yescharacteristic
275C4×C61#44711yescharacteristic
276C4×C61#44911yescharacteristic
277C4×C61#45011yescharacteristic
278C4×C61#45211yescharacteristic
279Dic61—42no—
280Dic61—161no—
281C2×#550—611no—
282#1957—611no—
283#1803—611no—
284#1802—611no—
285C2×#331—611no—
286C2×Q8⋊C8D6111yescharacteristic, complemented
287C2×D4⋊C8—611no—
288C2×C61#162111yescharacteristic
289C2×C61#163111yescharacteristic
290C2×C61#164111yescharacteristic
291C2×C61#164211yescharacteristic
292C2×C61#178611yescharacteristic
293C2×C61#178811yescharacteristic
294C2×C61#179211yescharacteristic
295D61—84no—
296D61—82no—
297C22×#41—1221no—
298#550—614no—
299#550—1222no—
300#550—1222no—
301#550—1222no—
302C2×#127—611no—
303C2×#127—1221no—
304C2×#121—1222no—
305C2×#121—1221no—
306C2×C4×Q8C2×D6111yescharacteristic
307C2×C4×D4—611no—
308C2×C4×D4—1221no—
309C2×C4⋊C8—611no—
310C2×C4⋊C8C2×D6111yescharacteristic
311C2×#103—1221no—
312C2×#102—1221no—
313C2×#102—1222no—
314C2×C4×C8C2×D6111yescharacteristic
315#384—611no—
316#340—1221no—
317#340—1221no—
318#331—1222no—
319Q8⋊C8—22no—
320D4⋊C8—1222no—
321C61#844411yescharacteristic, complemented, Sylow
322C2×#41—1224no—
323C2×#41—1224no—
324C2×#41—2442no—
325C2×#41—2442no—
326C2×#41—2442no—
327C2×#41—2442no—
328C22×Q8D24411yescharacteristic
329C22×D4—611no—
330C22×D4—612no—
331C22×D4—1222no—
332C22×D4—1222no—
333C22×D4—1221no—
334C22×D4—1221no—
335C23×C4—1222no—
336C23×C4—1221no—
337C22×C8—21no—
338C22×C8—21no—
339C22×C8—1221no—
340#127—612no—
341#127—612no—
342#127—1224no—
343#127—1224no—
344#127—1221no—
345#127—1221no—
346#121—1228no—
347#121—1224no—
348#121—1228no—
349#121—1224no—
350C4×Q8—21no—
351C4×Q8—21no—
352C4×Q8C4×D6112yes—
353C4×Q8C22⋊D6112yes—
354C4×D4—612no—
355C4×D4—612no—
356C4×D4—1224no—
357C4×D4—1224no—
358C4×D4—1221no—
359C4×D4—1221no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—611no—
362C2×C4⋊C4—1221no—
363C2×C4⋊C4—1221no—
364C2×C4⋊C4—1221no—
365C2×C4⋊C4D24411yescharacteristic
366C2×C22⋊C4—1222no—
367C2×C22⋊C4—1221no—
368C2×C42—21no—
369C2×C42C22×D6111yescharacteristic
370C4⋊C8—21no—
371C4⋊C8—21no—
372C4⋊C8—1221no—
373C4⋊C8—1221no—
374#103—2442no—
375#102—2444no—
376#102—2442no—
377C4×C8—21no—
378C4×C8—21no—
379C24—1221no—
380C24—1222no—
381#41—2448no—
382#41—2448no—
383#41—2448no—
384#41—2448no—
385C2×Q8—21no—
386C2×Q8—21no—
387C2×Q8—21no—
388C2×Q8#1175819012yes—
389C2×Q8D48812yes—
390C2×Q8#1175819812yes—
391C2×D4—612no—
392C2×D4—614no—
393C2×D4—1228no—
394C2×D4—1228no—
395C2×D4—1221no—
396C2×D4—1222no—
397C2×D4—1222no—
398C2×D4—1222no—
399C2×D4—1222no—
400C2×D4—1221no—
401C2×D4—1222no—
402C2×D4—1221no—
403C2×D4—1221no—
404C2×D4—1221no—
405C2×D4—4882no—
406C2×D4—4882no—
407C2×D4—2442no—
408C2×D4—2442no—
409C2×D4—2444no—
410C2×D4—2444no—
411C2×D4—2441no—
412C2×D4—2441no—
413C2×D4—2441no—
414C2×D4—2441no—
415C2×D4—2441no—
416C2×D4—2441no—
417C2×D4—2441no—
418C2×D4—2441no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—1228no—
422C22×C4—1221no—
423C22×C4—1222no—
424C22×C4—1222no—
425C22×C4—2444no—
426C22×C4—2444no—
427C22×C4—2441no—
428C22×C4—2441no—
429C22×C4—2441no—
430C22×C4—2441no—
431C22×C4—2441no—
432C22×C4C2×D24411yescharacteristic
433C22×C4D4×D6111yescharacteristic
434C22×C4D4×D6111yescharacteristic
435C2×C8—22no—
436C2×C8—41no—
437C2×C8—41no—
438C2×C8—41no—
439C2×C8—41no—
440C2×C8—41no—
441C2×C8—2441no—
442C2×C8—2441no—
443C2×C8—2441no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—21no—
447C4⋊C4—612no—
448C4⋊C4—1221no—
449C4⋊C4—2442no—
450C4⋊C4—2441no—
451C4⋊C4—2441no—
452C4⋊C4—2441no—
453C4⋊C4—2441no—
454C4⋊C4#1175819812yes—
455C22⋊C4—1228no—
456C22⋊C4—1222no—
457C22⋊C4—1222no—
458C42—22no—
459C42—22no—
460C42C2×C4×D6111yescharacteristic
461C42D4×D6111yescharacteristic
462C42D4×D6111yescharacteristic
463C42C2×C22⋊D6111yescharacteristic
464C23—1222no—
465C23—1224no—
466C23—2441no—
467C23—2442no—
468C23—2442no—
469C23—2441no—
470C23—2441no—
471C23—2442no—
472C23—2442no—
473C23—2441no—
474C23—2441no—
475C23—2442no—
476C23—2441no—
477C23—2442no—
478C23#1451974711yescharacteristic
479Q8—22no—
480Q8—22no—
481Q8—22no—
482Q8#1451969914yescomplemented
483D4—1222no—
484D4—1222no—
485D4—4882no—
486D4—4888no—
487D4—2444no—
488D4—24416no—
489D4—2442no—
490D4—2442no—
491D4—2442no—
492D4—2442no—
493D4—2442no—
494D4—2441no—
495D4—2442no—
496D4—2442no—
497D4—2441no—
498D4—2442no—
499C2×C4—21no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—22no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—1222no—
508C2×C4—4881no—
509C2×C4—4881no—
510C2×C4—4881no—
511C2×C4—24416no—
512C2×C4—2441no—
513C2×C4—2441no—
514C2×C4—2442no—
515C2×C4—2442no—
516C2×C4—2442no—
517C2×C4—2442no—
518C2×C4C22⋊C4×D6111yescharacteristic
519C2×C4C22⋊C4×D6111yescharacteristic
520C2×C4C2×#1175819811yescharacteristic
521C2×C4#1451974511yescharacteristic
522C2×C4#1451974511yescharacteristic
523C2×C4#1451974711yescharacteristic
524C2×C4C2×D48811yescharacteristic
525C2×C4C2×#1175819011yescharacteristic
526C2×C4#1451979811yescharacteristic
527C2×C4#1451980011yescharacteristic
528C2×C4#1451980411yescharacteristic
529C2×C4#1451980511yescharacteristic
530C2×C4#1451980511yescharacteristic
531C2×C4#1451980911yescharacteristic
532C8—42no—
533C8—81no—
534C8—4881no—
535C22—4881no—
536C22—4882no—
537C22—4881no—
538C22—4882no—
539C22—4881no—
540C22—4882no—
541C22—4881no—
542C22—4882no—
543C22—2444no—
544C22—2442no—
545C22—2442no—
546C22—2444no—
547C22—2442no—
548C22—2444no—
549C22#1683961711yescharacteristic
550C22#1683989811yescharacteristic
551C22#1683991011yescharacteristic
552C22#1683991511yescharacteristic
553C22#1683992711yescharacteristic
554C22#1683993111yescharacteristic
555C22#1683994111yescharacteristic
556C4—24no—
557C4—21no—
558C4—21no—
559C4—42no—
560C4—9761no—
561C4—2442no—
562C4C2×#1451969911yescharacteristic
563C4#1683975711yescharacteristic
564C4#1683976211yescharacteristic
565C4#1683976811yescharacteristic
566C4#1683989811yescharacteristic
567C4#1683990611yescharacteristic
568C4#1683991511yescharacteristic
569C4#1683992311yescharacteristic
570C2—4882no—
571C2—4884no—
572C2#2144488611yescharacteristic
573C2#2144494811yescharacteristic
574C2#2144501411yescharacteristic
575C2#2144502211yescharacteristic
576C2#2144575111yescharacteristic
577C2#2144575811yescharacteristic
578C2#2144577411yescharacteristic
subgroupG/H
centerC23#14519747
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC2×C61×Q8⋊C8C2
socleC23×C61#120
prime radicalC2×#16840434C2
cosocleC2×C42×C61C23
hypercenterC2×Q8⋊C8D61
hypocenterC61#8444
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. #21446625C2semidirect
3. #21445824C2semidirect
4. #21445820C2semidirect
5. C2×#16839505C2semidirect
6. C2×#16839491C2semidirect
7. C2×C61×Q8⋊C8C2semidirect
12. #16840434C4semidirect
192. Q8×C61#102semidirect
286. C2×Q8⋊C8D61semidirect
321. C61#8444semidirect
482. Q8#14519699semidirect

Maximal subgroups

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

subgroupindex
C2×#168404342
#214466252
#214458242
#214458202
C2×#168395052
C2×#168394912
C2×C61×Q8⋊C82
#844461