Finite Group Databasebeta

← #29572095

Subgroups — #29572095

Order 15616.

1048 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840416C211yesmaximal, characteristic
2#21446780C211yesmaximal, characteristic, complemented
3#21445820C211yesmaximal, characteristic, complemented
4#21445819C211yesmaximal, characteristic, complemented
5C2×#16839507C211yesmaximal, characteristic, complemented
6C2×#16839491C211yesmaximal, characteristic, complemented
7C2×C61×D4⋊C8C211yesmaximal, characteristic, complemented
8C22×#11758224—21no—
9#16840416—22no—
10#16840416—22no—
11#16840416—22no—
12#16840416C414yescomplemented
13C2×#14519777C2211yescharacteristic
14C2×#14519761—22no—
15C2×#14519757—21no—
16C2×#14519751—21no—
17C2×C4×D244C2211yescharacteristic
18C22×C4⋊Dic61—21no—
19C2×C4⋊#92418C2211yescharacteristic
20C2×#14519699—21no—
21C2×#14519698—21no—
22#16839632C2211yescharacteristic
23#16839525—22no—
24#16839525—21no—
25#16839524—21no—
26#16839507—22no—
27#16839491—22no—
28C2×C4×D4×C61C2211yescharacteristic
29C2×C4⋊C8×C61C2211yescharacteristic
30C2×C4×C8×C61C2211yescharacteristic
31C61×D4⋊C8—22no—
32C2×#11758224—24no—
33C2×#11758224—24no—
34C2×#11758224—42no—
35C2×#11758224—42no—
36C2×#11758224—42no—
37C2×#11758224—42no—
38C22×Dic122—21no—
39C22×D244D411yescharacteristic
40C22×C22⋊D61—22no—
41C23×Dic61—22no—
42C22×C4×D61—21no—
43C22×#92418—21no—
44#14519777—21no—
45#14519777—21no—
46#14519777C2×C412yes—
47#14519777D412yes—
48#14519761—28no—
49#14519761—28no—
50#14519757—24no—
51#14519757—24no—
52#14519751—24no—
53#14519751—24no—
54C4×D244—21no—
55C4×D244—21no—
56C4×D244C2×C412yes—
57C4×D244D412yes—
58C2×C4⋊Dic61—22no—
59C2×C4⋊Dic61—24no—
60C2×C4⋊Dic61—21no—
61C2×C4⋊Dic61—24no—
62C2×C4⋊Dic61—21no—
63C2×C4⋊Dic61—21no—
64C2×C4⋊Dic61—21no—
65C2×C4⋊Dic61D411yescharacteristic
66C2×C4⋊Dic61D412yes—
67C2×#11758198—22no—
68C2×#11758198—21no—
69C4⋊#92418—21no—
70C4⋊#92418—21no—
71#14519699—42no—
72#14519698—42no—
73C22×D4×C61D411yescharacteristic
74C23×C4×C61—21no—
75C22×C8×C61—21no—
76C22×C8×C61—21no—
77C4×D4×C61—21no—
78C4×D4×C61—21no—
79C4×D4×C61C2×C412yes—
80C4×D4×C61D412yes—
81C2×C4⋊C4×C61D411yescharacteristic
82C2×C22⋊C4×C61—21no—
83C2×C42×C61C2311yescharacteristic
84C4⋊C8×C61—21no—
85C4⋊C8×C61—21no—
86C4×C8×C61—21no—
87C4×C8×C61—21no—
88C24×C61—21no—
89C23×D61—21no—
90C2×D4×C61—21no—
91C2×D4×C61—21no—
92C2×D4×C61—21no—
93C2×D4×C61C22⋊C412yes—
94C2×D4×C61D812yes—
95C2×D4×C61SD1612yes—
96C22×C4×C61—21no—
97C22×C4×C61—22no—
98C22×C4×C61—22no—
99C22×C4×C61—41no—
100C22×C4×C61—41no—
101C22×C4×C61—41no—
102C22×C4×C61—41no—
103C22×C4×C61C2×D411yescharacteristic
104C22×C4×C61C2×D411yescharacteristic
105C22×C4×C61C2×D411yescharacteristic
106C2×C22⋊D61—28no—
107C2×C22⋊D61—44no—
108C2×C22⋊D61—44no—
109C22×Dic61—28no—
110C22×Dic61—21no—
111C22×Dic61—22no—
112C22×Dic61—44no—
113C22×Dic61—44no—
114C22×Dic61—41no—
115#11758224—48no—
116#11758224—48no—
117#11758224—48no—
118#11758224—48no—
119C2×D244—21no—
120C2×D244—21no—
121C2×D244—21no—
122C2×D244—21no—
123C2×D244—21no—
124C2×D244C22⋊C412yes—
125C2×C4×D61—22no—
126C2×C4×D61—22no—
127C2×C4×D61—41no—
128C2×C4×D61—41no—
129C2×C4×D61—41no—
130C2×C4×D61—41no—
131C2×Dic122—22no—
132C2×Dic122—22no—
133C2×Dic122—41no—
134C2×Dic122—41no—
135C2×Dic122—41no—
136C2×Dic122—41no—
137C2×C8×C61—22no—
138C2×C8×C61—41no—
139C2×C8×C61—41no—
140C2×C8×C61—41no—
141C2×C8×C61—41no—
142C2×C8×C61—41no—
143C4⋊C4×C61—21no—
144C4⋊C4×C61C22⋊C412yes—
145C22⋊C4×C61—22no—
146C22⋊C4×C61—22no—
147C42×C61C22×C411yescharacteristic
148C42×C61C2×D411yescharacteristic
149C42×C61C2×D411yescharacteristic
150C42×C61C2×D411yescharacteristic
151#11758198—28no—
152#11758198—22no—
153#11758198—22no—
154C4⋊Dic61—28no—
155C4⋊Dic61—22no—
156C4⋊Dic61—21no—
157C4⋊Dic61—22no—
158C4⋊Dic61—22no—
159C4⋊Dic61—42no—
160C4⋊Dic61—41no—
161C4⋊Dic61—41no—
162C4⋊Dic61—41no—
163C4⋊Dic61—41no—
164C4⋊Dic61C22⋊C412yes—
165C4⋊Dic61C22⋊C414yes—
166C2×#92418—41no—
167C2×#92418—41no—
168C2×#92418—41no—
169C23×C61—22no—
170C23×C61—22no—
171C23×C61—22no—
172C23×C61—41no—
173C23×C61—41no—
174C23×C61—41no—
175C23×C61—41no—
176C23×C61#12011yescharacteristic
177C22×D61—22no—
178C22×D61—41no—
179C22×D61—41no—
180C22×D61—41no—
181C22×D61—41no—
182C22×D61—41no—
183C22×D61—41no—
184D4×C61—22no—
185D4×C61—22no—
186D4×C61—22no—
187D4×C61#10214yescomplemented
188C2×C4×C61—21no—
189C2×C4×C61—21no—
190C2×C4×C61—22no—
191C2×C4×C61—41no—
192C2×C4×C61—41no—
193C2×C4×C61—42no—
194C2×C4×C61—42no—
195C2×C4×C61—42no—
196C2×C4×C61—42no—
197C2×C4×C61C2×C22⋊C411yescharacteristic
198C2×C4×C61C2×C22⋊C411yescharacteristic
199C2×C4×C61C2×C22⋊C411yescharacteristic
200C2×C4×C61#12011yescharacteristic
201C2×C4×C61#12011yescharacteristic
202C2×C4×C61#12011yescharacteristic
203C2×C4×C61C2×D811yescharacteristic
204C2×C4×C61C2×SD1611yescharacteristic
205C2×C4×C61#13511yescharacteristic
206C2×C4×C61#13511yescharacteristic
207C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
208C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
209C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
210C2×C4×C61#13711yescharacteristic
211C22⋊D61—416no—
212C2×Dic61—24no—
213C2×Dic61—22no—
214C2×Dic61—416no—
215C2×Dic61—42no—
216C2×Dic61—41no—
217C2×Dic61—42no—
218C2×Dic61—41no—
219C2×Dic61—81no—
220C2×Dic61—81no—
221C2×Dic61—81no—
222D244—22no—
223D244—22no—
224D244—41no—
225D244—41no—
226C4×D61—42no—
227C4×D61—42no—
228C4×D61—42no—
229C4×D61—42no—
230Dic122—42no—
231Dic122—42no—
232Dic122—42no—
233Dic122—42no—
234C8×C61—42no—
235C8×C61—81no—
236#92418—81no—
237#8446—611nomaximal, Sylow
238C22×C61—24no—
239C22×C61—42no—
240C22×C61—42no—
241C22×C61—42no—
242C22×C61—42no—
243C22×C61—42no—
244C22×C61—42no—
245C22×C61#37911yescharacteristic
246C22×C61#44711yescharacteristic
247C22×C61#44911yescharacteristic
248C22×C61#45011yescharacteristic
249C22×C61#45211yescharacteristic
250C22×C61#45411yescharacteristic
251C22×C61#45611yescharacteristic
252C2×D61—42no—
253C2×D61—42no—
254C2×D61—42no—
255C2×D61—81no—
256C2×D61—81no—
257C2×D61—81no—
258C2×D61—81no—
259C4×C61—21no—
260C4×C61—21no—
261C4×C61—42no—
262C4×C61C2×#10211yescharacteristic
263C4×C61#41611yescharacteristic
264C4×C61#41711yescharacteristic
265C4×C61#41811yescharacteristic
266C4×C61#44711yescharacteristic
267C4×C61#44911yescharacteristic
268C4×C61#45011yescharacteristic
269C4×C61#45211yescharacteristic
270Dic61—44no—
271Dic61—42no—
272Dic61—161no—
273C2×#547—611no—
274#1990—611no—
275#1802—611no—
276#1802—611no—
277C2×#332—611no—
278C2×D4⋊C8—611no—
279C2×D4⋊C8D6111yescharacteristic, complemented
280C2×C61—44no—
281C2×C61#162511yescharacteristic
282C2×C61#163511yescharacteristic
283C2×C61#164711yescharacteristic
284C2×C61#165411yescharacteristic
285C2×C61#178611yescharacteristic
286C2×C61#178811yescharacteristic
287C2×C61#179311yescharacteristic
288D61—82no—
289C22×#41—1221no—
290#547—614no—
291#547—1222no—
292#547—1222no—
293#547—1222no—
294C2×C4⋊Q8—611no—
295C2×#123—1222no—
296C2×C22⋊Q8—1221no—
297C2×#121—1221no—
298C2×C4×D4—611no—
299C2×C4×D4C2×D6111yescharacteristic
300C22×C4⋊C4—1221no—
301C2×C4⋊C8—611no—
302C2×C4⋊C8C2×D6111yescharacteristic
303C2×#102—1221no—
304C2×#102—1221no—
305C2×C4×C8C2×D6111yescharacteristic
306#384—611no—
307#340—1221no—
308#340—1222no—
309#340—1221no—
310#332—1222no—
311D4⋊C8—22no—
312D4⋊C8—1222no—
313C61#844611yescharacteristic, complemented, Sylow
314C2×#41—1224no—
315C2×#41—1224no—
316C2×#41—2442no—
317C2×#41—2442no—
318C2×#41—2442no—
319C2×#41—2442no—
320C22×Q8—1221no—
321C22×D4—611no—
322C22×D4—1222no—
323C22×D4D24411yescharacteristic
324C23×C4—21no—
325C23×C4—1222no—
326C23×C4—1221no—
327C22×C8—21no—
328C22×C8—21no—
329C22×C8—1221no—
330C4⋊Q8—612no—
331C4⋊Q8—612no—
332C4⋊Q8—1221no—
333C4⋊Q8—1221no—
334#123—1228no—
335#123—1228no—
336C22⋊Q8—1224no—
337C22⋊Q8—1224no—
338#121—1224no—
339#121—1224no—
340C4×D4—21no—
341C4×D4—21no—
342C4×D4—612no—
343C4×D4—612no—
344C4×D4—1221no—
345C4×D4—1221no—
346C4×D4C4×D6112yes—
347C4×D4C22⋊D6112yes—
348C2×C4⋊C4—611no—
349C2×C4⋊C4—612no—
350C2×C4⋊C4—1224no—
351C2×C4⋊C4—1222no—
352C2×C4⋊C4—1224no—
353C2×C4⋊C4—1221no—
354C2×C4⋊C4—1221no—
355C2×C4⋊C4—1221no—
356C2×C4⋊C4—1221no—
357C2×C4⋊C4D24411yescharacteristic
358C2×C22⋊C4—21no—
359C2×C22⋊C4—1222no—
360C2×C22⋊C4—1221no—
361C2×C42C22×D6111yescharacteristic
362C4⋊C8—21no—
363C4⋊C8—21no—
364C4⋊C8—1221no—
365C4⋊C8—1221no—
366#102—2442no—
367#102—2442no—
368C4×C8—21no—
369C4×C8—21no—
370C24—21no—
371C24—1221no—
372#41—2448no—
373#41—2448no—
374#41—2448no—
375#41—2448no—
376C2×Q8—1222no—
377C2×Q8—1222no—
378C2×Q8—2441no—
379C2×Q8—2441no—
380C2×Q8—2441no—
381C2×Q8—2441no—
382C2×D4—21no—
383C2×D4—21no—
384C2×D4—21no—
385C2×D4—612no—
386C2×D4—1228no—
387C2×D4—1221no—
388C2×D4—1221no—
389C2×D4—1221no—
390C2×D4—1221no—
391C2×D4—1221no—
392C2×D4—2444no—
393C2×D4—2444no—
394C2×D4#1175819012yes—
395C2×D4D48812yes—
396C2×D4#1175819812yes—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—41no—
401C22×C4—41no—
402C22×C4—41no—
403C22×C4—41no—
404C22×C4—1228no—
405C22×C4—1221no—
406C22×C4—1222no—
407C22×C4—1222no—
408C22×C4—1222no—
409C22×C4—2441no—
410C22×C4—2444no—
411C22×C4—2444no—
412C22×C4—2441no—
413C22×C4—2441no—
414C22×C4—2441no—
415C22×C4—2441no—
416C22×C4C2×D24411yescharacteristic
417C22×C4D4×D6111yescharacteristic
418C22×C4D4×D6111yescharacteristic
419C2×C8—22no—
420C2×C8—41no—
421C2×C8—41no—
422C2×C8—41no—
423C2×C8—41no—
424C2×C8—41no—
425C2×C8—2441no—
426C2×C8—2441no—
427C2×C8—2441no—
428C4⋊C4—21no—
429C4⋊C4—612no—
430C4⋊C4—614no—
431C4⋊C4—1228no—
432C4⋊C4—1222no—
433C4⋊C4—1221no—
434C4⋊C4—1222no—
435C4⋊C4—1222no—
436C4⋊C4—2442no—
437C4⋊C4—2441no—
438C4⋊C4—2441no—
439C4⋊C4—2441no—
440C4⋊C4—2441no—
441C4⋊C4#1175819812yes—
442C22⋊C4—22no—
443C22⋊C4—22no—
444C22⋊C4—1228no—
445C22⋊C4—1222no—
446C22⋊C4—1222no—
447C42C2×C4×D6111yescharacteristic
448C42D4×D6111yescharacteristic
449C42D4×D6111yescharacteristic
450C42C2×C22⋊D6111yescharacteristic
451C23—22no—
452C23—22no—
453C23—22no—
454C23—41no—
455C23—41no—
456C23—41no—
457C23—41no—
458C23—1222no—
459C23—2441no—
460C23—2441no—
461C23—2441no—
462C23—2441no—
463C23—2441no—
464C23—2441no—
465C23#1451974711yescharacteristic
466Q8—2442no—
467Q8—2442no—
468Q8—2442no—
469Q8—2442no—
470D4—22no—
471D4—22no—
472D4—22no—
473D4—1222no—
474D4—1222no—
475D4—24416no—
476D4—2441no—
477D4—2441no—
478D4#1451969914yescomplemented
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—22no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—1222no—
489C2×C4—1224no—
490C2×C4—4881no—
491C2×C4—4881no—
492C2×C4—4881no—
493C2×C4—24416no—
494C2×C4—2441no—
495C2×C4—2442no—
496C2×C4—2441no—
497C2×C4—2442no—
498C2×C4—2442no—
499C2×C4—2442no—
500C2×C4—2442no—
501C2×C4—2442no—
502C2×C4C22⋊C4×D6111yescharacteristic
503C2×C4C22⋊C4×D6111yescharacteristic
504C2×C4C2×#1175819811yescharacteristic
505C2×C4#1451974511yescharacteristic
506C2×C4#1451974511yescharacteristic
507C2×C4#1451974711yescharacteristic
508C2×C4C2×D48811yescharacteristic
509C2×C4C2×#1175819011yescharacteristic
510C2×C4#1451979611yescharacteristic
511C2×C4#1451979811yescharacteristic
512C2×C4#1451980111yescharacteristic
513C2×C4#1451980511yescharacteristic
514C2×C4#1451980511yescharacteristic
515C2×C4#1451980611yescharacteristic
516C8—42no—
517C8—81no—
518C8—4881no—
519C22—24no—
520C22—42no—
521C22—42no—
522C22—42no—
523C22—42no—
524C22—42no—
525C22—42no—
526C22—4881no—
527C22—4881no—
528C22—4881no—
529C22—4881no—
530C22—2442no—
531C22—2442no—
532C22—2442no—
533C22#1683961711yescharacteristic
534C22#1683989811yescharacteristic
535C22#1683990811yescharacteristic
536C22#1683991511yescharacteristic
537C22#1683992511yescharacteristic
538C22#1683993611yescharacteristic
539C22#1683994611yescharacteristic
540C4—21no—
541C4—21no—
542C4—42no—
543C4—9761no—
544C4—2442no—
545C4—2444no—
546C4C2×#1451969911yescharacteristic
547C4#1683975511yescharacteristic
548C4#1683976011yescharacteristic
549C4#1683976811yescharacteristic
550C4#1683989811yescharacteristic
551C4#1683990411yescharacteristic
552C4#1683991511yescharacteristic
553C4#1683992111yescharacteristic
554C2—44no—
555C2—4882no—
556C2#2144491011yescharacteristic
557C2#2144497211yescharacteristic
558C2#2144505611yescharacteristic
559C2#2144510611yescharacteristic
560C2#2144575111yescharacteristic
561C2#2144575611yescharacteristic
562C2#2144577911yescharacteristic
subgroupG/H
centerC23#14519747
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC2×C61×D4⋊C8C2
socleC23×C61#120
prime radicalC2×#16840416C2
cosocleC2×C42×C61C23
hypercenterC2×D4⋊C8D61
hypocenterC61#8446
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #21446780C2semidirect
3. #21445820C2semidirect
4. #21445819C2semidirect
5. C2×#16839507C2semidirect
6. C2×#16839491C2semidirect
7. C2×C61×D4⋊C8C2semidirect
12. #16840416C4semidirect
187. D4×C61#102semidirect
279. C2×D4⋊C8D61semidirect
313. C61#8446semidirect
478. D4#14519699semidirect

Maximal subgroups

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

subgroupindex
C2×#168404162
#214467802
#214458202
#214458192
C2×#168395072
C2×#168394912
C2×C61×D4⋊C82
#844661