Finite Group Databasebeta

← #29582317

Subgroups — #29582317

Order 15616.

744 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839962C211yesmaximal, characteristic, complemented
2C2×#16839958C211yesmaximal, characteristic
3#21450737C211yesmaximal, characteristic, complemented
4#21446625C211yesmaximal, characteristic, complemented
5C2×#16839491C211yesmaximal, characteristic, complemented
6#21443703C211yesmaximal, characteristic, complemented
7C2×C61×Q8⋊C8C211yesmaximal, characteristic, complemented
8C22×#11758201—21no—
9C22×D488—21no—
10C2×#14519774C2211yescharacteristic
11C2×#14519753—21no—
12C2×C4×D244C2211yescharacteristic
13#16839962—22no—
14#16839962—22no—
15#16839958—22no—
16#16839958—22no—
17C2×C4⋊#92418C2211yescharacteristic
18C2×#14519699—21no—
19C2×#14519699—22no—
20C2×#14519697—21no—
21#16839684—22no—
22#16839664—21no—
23#16839660—21no—
24#16839632C2211yescharacteristic
25#16839619—21no—
26#16839491—22no—
27C2×C4×Q8×C61C2211yescharacteristic
28C2×C4⋊C8×C61C2211yescharacteristic
29C2×C4×C8×C61C2211yescharacteristic
30C61×Q8⋊C8—22no—
31C22×D244—21no—
32C22×D244—21no—
33C22×D244—21no—
34C22×D244D411yescharacteristic
35C22×C4×D61—21no—
36C2×#11758201—24no—
37C2×#11758201—42no—
38C2×#11758201—42no—
39C2×D488—24no—
40C2×D488—42no—
41C2×D488—42no—
42C22×#92418—21no—
43#14519774—21no—
44#14519774—21no—
45#14519774—21no—
46#14519774D412yes—
47#14519753—42no—
48#14519753—42no—
49C4×D244—21no—
50C4×D244—21no—
51C4×D244—21no—
52C4×D244—21no—
53C2×C4⋊Dic61—21no—
54C2×C4⋊Dic61—21no—
55C2×C4⋊Dic61D411yescharacteristic
56C2×C4⋊Dic61D412yes—
57C2×#11758196—22no—
58C2×#11758198—22no—
59C2×#11758198—21no—
60C2×#11758198—22no—
61C4⋊#92418—21no—
62C4⋊#92418D412yes—
63#14519699—24no—
64#14519699—44no—
65#14519697—24no—
66#14519684—22no—
67C22×Q8×C61D411yescharacteristic
68C22×C8×C61—21no—
69C22×C8×C61—21no—
70C4×Q8×C61—21no—
71C4×Q8×C61—21no—
72C4×Q8×C61—21no—
73C4×Q8×C61—21no—
74C2×C4⋊C4×C61—21no—
75C2×C4⋊C4×C61D411yescharacteristic
76C2×C42×C61—21no—
77C2×C42×C61C2311yescharacteristic
78C4⋊C8×C61—21no—
79C4⋊C8×C61D412yes—
80C4×C8×C61—21no—
81C4×C8×C61—21no—
82C23×D61—21no—
83C23×D61—41no—
84C2×Q8×C61—21no—
85C2×Q8×C61—21no—
86C2×Q8×C61—21no—
87C2×Q8×C61—21no—
88C2×Q8×C61—21no—
89C2×Q8×C61D812yescomplemented
90C22×C4×C61—21no—
91C22×C4×C61—21no—
92C22×C4×C61C2×D411yescharacteristic
93C22×C4×C61C2×D411yescharacteristic
94C22×C4×C61C2×D411yescharacteristic
95C22×Dic61—21no—
96C22×Dic61—22no—
97C2×D244—21no—
98C2×D244—21no—
99C2×D244—21no—
100C2×D244—21no—
101C2×D244—22no—
102C2×D244—22no—
103C2×D244—22no—
104C2×D244—21no—
105C2×D244—42no—
106C2×D244—42no—
107C2×D244—41no—
108C2×D244—41no—
109C2×D244—41no—
110C2×D244—41no—
111C2×D244—41no—
112C2×D244—41no—
113C2×D244—41no—
114C2×D244—41no—
115C2×D244—41no—
116C2×D244—41no—
117C2×D244—41no—
118C2×D244SD1612yescomplemented
119C2×C4×D61—41no—
120C2×C4×D61—41no—
121C2×C4×D61—41no—
122C2×C4×D61—41no—
123C2×C4×D61—41no—
124C2×C4×D61—41no—
125C2×C8×C61—22no—
126C2×C8×C61—22no—
127C2×C8×C61—41no—
128C2×C8×C61—41no—
129C2×C8×C61—41no—
130C2×C8×C61—41no—
131C4⋊C4×C61—21no—
132C4⋊C4×C61—21no—
133C4⋊C4×C61—41no—
134C4⋊C4×C61—41no—
135C42×C61—41no—
136C42×C61—41no—
137C42×C61C2×D411yescharacteristic
138C42×C61C2×D411yescharacteristic
139C42×C61C2×D411yescharacteristic
140C42×C61#4111yescharacteristic
141#11758201—48no—
142#11758198—44no—
143#11758198—41no—
144#11758198—41no—
145#11758198—82no—
146C4⋊Dic61—21no—
147C4⋊Dic61—21no—
148C4⋊Dic61—41no—
149C4⋊Dic61—41no—
150C4⋊Dic61—41no—
151C4⋊Dic61—41no—
152C4⋊Dic61—42no—
153#11758196—44no—
154C2×#92418—22no—
155C2×#92418—41no—
156C2×#92418—41no—
157D488—48no—
158C23×C61#12011yescharacteristic
159C22×D61—22no—
160C22×D61—41no—
161C22×D61—41no—
162C22×D61—41no—
163C22×D61—41no—
164C22×D61—41no—
165C22×D61—41no—
166C22×D61—42no—
167C22×D61—81no—
168C22×D61—81no—
169C22×D61—81no—
170C22×D61—81no—
171C22×D61—81no—
172C22×D61—81no—
173Q8×C61—22no—
174Q8×C61—22no—
175Q8×C61—41no—
176Q8×C61—41no—
177C2×C4×C61—21no—
178C2×C4×C61—21no—
179C2×C4×C61—22no—
180C2×C4×C61—41no—
181C2×C4×C61—41no—
182C2×C4×C61—41no—
183C2×C4×C61—41no—
184C2×C4×C61—41no—
185C2×C4×C61#12011yescharacteristic
186C2×C4×C61#12011yescharacteristic
187C2×C4×C61#12111yescharacteristic
188C2×C4×C61#12111yescharacteristic
189C2×C4×C61#12111yescharacteristic
190C2×C4×C61#12711yescharacteristic
191C2×C4×C61C2×D811yescharacteristic
192C2×C4×C61C2×SD1611yescharacteristic
193C2×C4×C61#13511yescharacteristic
194C2×C4×C61#13511yescharacteristic
195C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
196C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
197C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
198C2×C4×C61#13711yescharacteristic
199C2×Dic61—41no—
200C2×Dic61—41no—
201C2×Dic61—42no—
202C2×Dic61—42no—
203C2×Dic61—41no—
204C2×Dic61—42no—
205D244—22no—
206D244—22no—
207D244—44no—
208D244—42no—
209D244—42no—
210D244—42no—
211D244—41no—
212D244—42no—
213D244—41no—
214D244—82no—
215D244—81no—
216D244—81no—
217D244—81no—
218D244—81no—
219C4×D61—81no—
220C4×D61—81no—
221C4×D61—81no—
222C4×D61—81no—
223C8×C61—42no—
224C8×C61—42no—
225#92418—42no—
226#10229—611nomaximal, Sylow
227C22×C61#39211yescharacteristic
228C22×C61#44711yescharacteristic
229C22×C61#44811yescharacteristic
230C22×C61#44911yescharacteristic
231C22×C61#44911yescharacteristic
232C22×C61#45311yescharacteristic
233C22×C61#45411yescharacteristic
234C2×D61—42no—
235C2×D61—42no—
236C2×D61—42no—
237C2×D61—81no—
238C2×D61—81no—
239C2×D61—81no—
240C2×D61—81no—
241C2×D61—82no—
242C2×D61—82no—
243C2×D61—82no—
244C2×D61—161no—
245C2×D61—161no—
246C2×D61—161no—
247C2×D61—161no—
248C4×C61—21no—
249C4×C61—21no—
250C4×C61—42no—
251C4×C61—81no—
252C4×C61#44711yescharacteristic
253C4×C61#44911yescharacteristic
254C4×C61#45011yescharacteristic
255C4×C61#45211yescharacteristic
256C4×C61#46511yescharacteristic
257C4×C61#46611yescharacteristic
258C4×C61#46811yescharacteristic
259C4×C61#46911yescharacteristic
260Dic61—82no—
261Dic61—81no—
262C2×#460—611no—
263C2×#459—611no—
264#2538—611no—
265#1957—611no—
266C2×Q8⋊C8D6111yescharacteristic, complemented
267C2×D4⋊C8—611no—
268#1296—611no—
269C2×C61#162111yescharacteristic
270C2×C61#162211yescharacteristic
271C2×C61#162711yescharacteristic
272C2×C61#162811yescharacteristic
273C2×C61#199911yescharacteristic
274C2×C61#200011yescharacteristic
275C2×C61#200611yescharacteristic
276D61—82no—
277D61—162no—
278C22×SD16—1221no—
279C22×D8—1221no—
280C2×#127—611no—
281C2×C22⋊Q8—1221no—
282C2×C4×Q8C2×D6111yescharacteristic
283C2×C4×D4—611no—
284#460—1222no—
285#460—1222no—
286#459—1222no—
287#459—1222no—
288C2×C4⋊C8—611no—
289C2×C4⋊C8C2×D6111yescharacteristic
290C2×#102—1221no—
291C2×#102—1221no—
292C2×#102—1222no—
293C2×C4×C8C2×D6111yescharacteristic
294#396—1222no—
295#390—1221no—
296#389—1221no—
297#384—611no—
298#380—1221no—
299Q8⋊C8—22no—
300D4⋊C8—1222no—
301C61#1022911yescharacteristic, complemented, Sylow
302C22×Q8D24411yescharacteristic
303C22×D4—611no—
304C22×D4—1221no—
305C22×D4—1221no—
306C22×D4—1221no—
307C23×C4—1221no—
308C2×SD16—1224no—
309C2×SD16—2442no—
310C2×SD16—2442no—
311C2×D8—1224no—
312C2×D8—2442no—
313C2×D8—2442no—
314C22×C8—21no—
315C22×C8—21no—
316C22×C8—1221no—
317#127—612no—
318#127—1221no—
319#127—1221no—
320#127—1221no—
321C22⋊Q8—2442no—
322C22⋊Q8—2442no—
323C4×Q8—21no—
324C4×Q8—21no—
325C4×Q8—21no—
326C4×Q8—21no—
327C4×D4—1221no—
328C4×D4—1221no—
329C4×D4—1221no—
330C4×D4—1221no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—611no—
333C2×C4⋊C4—612no—
334C2×C4⋊C4—1222no—
335C2×C4⋊C4—1221no—
336C2×C4⋊C4—1221no—
337C2×C4⋊C4D24411yescharacteristic
338C2×C22⋊C4—1222no—
339C2×C22⋊C4—1222no—
340C2×C22⋊C4—1221no—
341C2×C42—21no—
342C2×C42C22×D6111yescharacteristic
343C4⋊C8—21no—
344C4⋊C8—612no—
345C4⋊C8—1221no—
346C4⋊C8C22⋊D6112yes—
347#102—1224no—
348#102—1224no—
349#102—2444no—
350C4×C8—21no—
351C4×C8—21no—
352#95—1222no—
353C24—1221no—
354C24—2441no—
355C2×Q8—21no—
356C2×Q8—21no—
357C2×Q8—21no—
358C2×Q8—21no—
359C2×Q8—21no—
360C2×Q8D48812yescomplemented
361C2×D4—612no—
362C2×D4—1221no—
363C2×D4—1221no—
364C2×D4—1222no—
365C2×D4—1222no—
366C2×D4—1221no—
367C2×D4—1222no—
368C2×D4—1221no—
369C2×D4—1221no—
370C2×D4—2442no—
371C2×D4—2442no—
372C2×D4—2441no—
373C2×D4—2441no—
374C2×D4—2441no—
375C2×D4—2441no—
376C2×D4—2441no—
377C2×D4—2441no—
378C2×D4—2441no—
379C2×D4—2441no—
380C2×D4—2441no—
381C2×D4—2441no—
382C2×D4—2441no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—1221no—
386C22×C4—1222no—
387C22×C4—2441no—
388C22×C4—2441no—
389C22×C4—2441no—
390C22×C4—2441no—
391C22×C4—2441no—
392C22×C4—2441no—
393C22×C4C2×D24411yescharacteristic
394C22×C4D4×D6111yescharacteristic
395C22×C4D4×D6111yescharacteristic
396SD16—2448no—
397D8—2448no—
398C2×C8—22no—
399C2×C8—22no—
400C2×C8—41no—
401C2×C8—41no—
402C2×C8—41no—
403C2×C8—41no—
404C2×C8—1222no—
405C2×C8—2441no—
406C2×C8—2441no—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—41no—
410C4⋊C4—41no—
411C4⋊C4—1221no—
412C4⋊C4—1221no—
413C4⋊C4—2442no—
414C4⋊C4—2444no—
415C4⋊C4—2441no—
416C4⋊C4—2441no—
417C4⋊C4—2441no—
418C4⋊C4—2441no—
419C22⋊C4—4882no—
420C22⋊C4—2444no—
421C22⋊C4—2441no—
422C22⋊C4—2441no—
423C42—41no—
424C42—41no—
425C42#1175822211yescharacteristic
426C42D4×D6111yescharacteristic
427C42D4×D6111yescharacteristic
428C42C2×C22⋊D6111yescharacteristic
429C23—1222no—
430C23—4881no—
431C23—4881no—
432C23—4881no—
433C23—4881no—
434C23—4881no—
435C23—4881no—
436C23—2442no—
437C23—2441no—
438C23—2441no—
439C23—2441no—
440C23—2441no—
441C23—2441no—
442C23—2441no—
443C23#1451974711yescharacteristic
444Q8—22no—
445Q8—22no—
446Q8—41no—
447Q8—41no—
448D4—1222no—
449D4—1222no—
450D4—4882no—
451D4—4881no—
452D4—4881no—
453D4—4881no—
454D4—4881no—
455D4—2444no—
456D4—2441no—
457D4—2442no—
458D4—2442no—
459D4—2442no—
460D4—2442no—
461D4—2441no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—22no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—4881no—
471C2×C4—4881no—
472C2×C4—4881no—
473C2×C4—4881no—
474C2×C4—2442no—
475C2×C4—2441no—
476C2×C4—2441no—
477C2×C4—2442no—
478C2×C4—2441no—
479C2×C4—2442no—
480C2×C4#1451974511yescharacteristic
481C2×C4#1451974711yescharacteristic
482C2×C4#1451975011yescharacteristic
483C2×C4#1451975011yescharacteristic
484C2×C4#1451975111yescharacteristic
485C2×C4#1451977311yescharacteristic
486C2×C4C2×D48811yescharacteristic
487C2×C4SD16×D6111yescharacteristic
488C2×C4#1451979911yescharacteristic
489C2×C4#1451980011yescharacteristic
490C2×C4#1451980411yescharacteristic
491C2×C4#1451980511yescharacteristic
492C2×C4#1451980511yescharacteristic
493C2×C4#1451980911yescharacteristic
494C8—42no—
495C8—42no—
496C8—2442no—
497C22—9761no—
498C22—9761no—
499C22—9761no—
500C22—9761no—
501C22—4882no—
502C22—4882no—
503C22—4882no—
504C22—4881no—
505C22—4881no—
506C22—4881no—
507C22—4881no—
508C22—2442no—
509C22—2442no—
510C22—2442no—
511C22#1683967111yescharacteristic
512C22#1683989811yescharacteristic
513C22#1683990211yescharacteristic
514C22#1683990911yescharacteristic
515C22#1683991011yescharacteristic
516C22#1683993111yescharacteristic
517C22#1683993611yescharacteristic
518C4—21no—
519C4—21no—
520C4—42no—
521C4—81no—
522C4—4882no—
523C4—4881no—
524C4#1683989811yescharacteristic
525C4#1683990911yescharacteristic
526C4#1683991111yescharacteristic
527C4#1683992311yescharacteristic
528C4#1683999411yescharacteristic
529C4#1683999811yescharacteristic
530C4#1684001111yescharacteristic
531C4#1684001511yescharacteristic
532C2—9762no—
533C2—4882no—
534C2#2144488611yescharacteristic
535C2#2144489411yescharacteristic
536C2#2144492411yescharacteristic
537C2#2144493211yescharacteristic
538C2#2144681711yescharacteristic
539C2#2144682111yescharacteristic
540C2#2144686211yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC2×C61×Q8⋊C8C2
socleC23×C61#120
prime radicalC2×#16839958C2
hypercenterC2×Q8⋊C8D61
hypocenterC61#10229
LCSG ▷ C2×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
1. C2×#16839962C2semidirect
3. #21450737C2semidirect
4. #21446625C2semidirect
5. C2×#16839491C2semidirect
6. #21443703C2semidirect
7. C2×C61×Q8⋊C8C2semidirect
89. C2×Q8×C61D8semidirect
118. C2×D244SD16semidirect
266. C2×Q8⋊C8D61semidirect
301. C61#10229semidirect
360. C2×Q8D488semidirect

Maximal subgroups

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

subgroupindex
C2×#168399622
C2×#168399582
#214507372
#214466252
C2×#168394912
#214437032
C2×C61×Q8⋊C82
#1022961