Finite Group Databasebeta

← #29684407

Subgroups — #29684407

Order 15616.

746 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454587C211yesmaximal, characteristic
2#21454462C211yesmaximal, characteristic, complemented
3#21454459C211yesmaximal, characteristic, complemented
4#21446711C211yesmaximal, characteristic
5#21446709C211yesmaximal, characteristic
6#21446571C211yesmaximal, characteristic, complemented
7#21446569C211yesmaximal, characteristic, complemented
8#21446532C211yesmaximal, characteristic, complemented
9#21446530C211yesmaximal, characteristic, complemented
10#21446528C211yesmaximal, characteristic, complemented
11#21445720C211yesmaximal, characteristic, complemented
12#104×Dic61C211yesmaximal, characteristic, complemented
13#21445623C211yesmaximal, characteristic, complemented
14#97×Dic61C211yesmaximal, characteristic, complemented
15C61×#1938C211yesmaximal, characteristic, complemented
16C2×#14519797C2211yescharacteristic
17#41×Dic61C2211yescharacteristic
18#16840230C2211yescharacteristic
19#16839854C412yescomplemented
20#16839853C412yescomplemented
21#16839847C412yescomplemented
22#16839842C412yescomplemented
23#16839822—22no—
24#16839820—22no—
25#16839814—22no—
26#16839812—22no—
27C2×#14519712C2211yescharacteristic
28C2×#14519712C2211yescharacteristic
29#16839798C2211yescharacteristic
30#16839790C2211yescharacteristic
31#16839789C2211yescharacteristic
32#16839788C2211yescharacteristic
33C2×#14519705C2211yescharacteristic
34C2×#14519704C2211yescharacteristic
35C2×#14519703C2211yescharacteristic
36#16839759C2211yescharacteristic
37#16839730C2211yescharacteristic
38#16839729C2211yescharacteristic
39#16839728C2211yescharacteristic
40M16×Dic61C2211yescharacteristic
41M16×Dic61C2211yescharacteristic
42C2×#14519688C2211yescharacteristic
43C2×#14519687C2211yescharacteristic
44C2×#14519687C2211yescharacteristic
45C2×C8×Dic61C2211yescharacteristic
46C2×C8×Dic61C2211yescharacteristic
47C42×Dic61C2211yescharacteristic
48#16839527C2211yescharacteristic
49#16839523C2211yescharacteristic
50#16839522C2211yescharacteristic
51#16839521C2211yescharacteristic
52C61×#424C2211yescharacteristic
53C2×#104×C61C2211yescharacteristic
54C61×#416C2211yescharacteristic
55C61×#408C2211yescharacteristic
56C2×#97×C61C2211yescharacteristic
57C61×#341C2211yescharacteristic
58C61×#339C2211yescharacteristic
59C2×#11758222C2311yescharacteristic
60#14519797—22no—
61#14519797—22no—
62C2×#11758202C2×C411yescharacteristic
63C2×#11758200C2×C411yescharacteristic
64C2×#11758201C2×C411yescharacteristic
65C2×#11758199C2×C411yescharacteristic
66C2×#11758194C2311yescharacteristic
67C2×#11758194C2311yescharacteristic
68C22×#92418C2311yescharacteristic
69C22×#92418C2311yescharacteristic
70Q8×Dic61C2×C412yes—
71#14519742C2×C412yes—
72D4×Dic61—22no—
73D4×Dic61C2×C412yes—
74#14519739C2×C412yes—
75#14519737—22no—
76#14519736—21no—
77#14519736C2311yescharacteristic
78#14519734—21no—
79C2×C4×Dic61—21no—
80C2×C4×Dic61—22no—
81C2×C4×Dic61C2311yescharacteristic
82C2×C4×Dic61C2311yescharacteristic
83C42×D61—21no—
84#14519712—22no—
85#14519712—22no—
86#14519710C2×C412yes—
87#14519708C2×C412yes—
88C4⋊#92418—22no—
89#14519706—22no—
90#14519706—22no—
91#14519705—22no—
92#14519704—22no—
93#14519703—22no—
94#14519702C2×C412yes—
95#14519699C2×C412yes—
96C22⋊#92418—22no—
97#14519689—22no—
98#14519689—22no—
99#14519688—22no—
100#14519687—21no—
101#14519687—21no—
102#14519687—22no—
103#14519687—22no—
104C8×Dic61—21no—
105C8×Dic61—21no—
106C8×Dic61C2×C412yes—
107C8×Dic61C2×C412yes—
108C8×Dic61D412yes—
109C8×Dic61D412yes—
110C2×#41×C61C2311yescharacteristic
111C2×M16×C61C2311yescharacteristic
112C2×M16×C61C2311yescharacteristic
113C22×C8×C61C2311yescharacteristic
114C22×C8×C61C2311yescharacteristic
115#117×C61C2311yescharacteristic
116C2×C42×C61C2311yescharacteristic
117C4⋊C8×C61—22no—
118#104×C61—22no—
119#103×C61C2×C412yes—
120#102×C61C2×C412yes—
121C22⋊C8×C61—22no—
122#97×C61—22no—
123#41×C61—21no—
124#41×C61—21no—
125#41×C61—21no—
126#41×C61—21no—
127C2×Q8×C61C22×C411yescharacteristic
128C2×D4×C61—21no—
129C2×D4×C61C22×C411yescharacteristic
130C22×C4×C61—21no—
131C22×C4×C61—21no—
132C22×C4×C61C2411yescharacteristic
133C2×C22⋊D61—21no—
134C22×Dic61—21no—
135C22×Dic61—22no—
136C22×Dic61#4112yes—
137#11758222—21no—
138#11758222—21no—
139#11758222—21no—
140#11758222—21no—
141C2×D244C22×C411yescharacteristic
142C2×C4×D61—21no—
143C2×C4×D61—22no—
144C2×Dic122C22×C411yescharacteristic
145M16×C61—21no—
146M16×C61—21no—
147M16×C61—21no—
148M16×C61—21no—
149C2×C8×C61—21no—
150C2×C8×C61—21no—
151C2×C8×C61—21no—
152C2×C8×C61—21no—
153C2×C8×C61—21no—
154C2×C8×C61—21no—
155C2×C8×C61C22×C412yes—
156C2×C8×C61C2×D412yes—
157C4⋊C4×C61C22×C412yes—
158C22⋊C4×C61—21no—
159C42×C61—21no—
160C42×C61—21no—
161C42×C61#4112yes—
162C22⋊Dic61—21no—
163C22⋊Dic61—22no—
164#11758202—22no—
165#11758201—22no—
166#11758200—22no—
167#11758199—22no—
168#11758198—22no—
169C4⋊Dic61—22no—
170C4⋊Dic61C22×C412yes—
171#11758196—22no—
172C4×Dic61—21no—
173C4×Dic61—21no—
174C4×Dic61—22no—
175C4×Dic61—22no—
176C4×Dic61—44no—
177C4×Dic61C22×C412yes—
178C4×Dic61C2×D411yescharacteristic
179C4×Dic61C2×D411yescharacteristic
180C4×Dic61#4112yes—
181#11758194—21no—
182#11758194—21no—
183#11758194—21no—
184#11758194—21no—
185C2×#92418—21no—
186C2×#92418—21no—
187C2×#92418—21no—
188C2×#92418—21no—
189C2×#92418C22×C411yescharacteristic
190C2×#92418C22×C411yescharacteristic
191C2×#92418C2×D412yes—
192C2×#92418#4112yes—
193C2×#92418#4112yes—
194C23×C61—21no—
195C23×C61C2×#4111yescharacteristic
196C22×D61—21no—
197Q8×C61—21no—
198Q8×C61—21no—
199D4×C61—21no—
200D4×C61—21no—
201D4×C61—41no—
202D4×C61—41no—
203C2×C4×C61—21no—
204C2×C4×C61—22no—
205C2×C4×C61—22no—
206C2×C4×C61—42no—
207C2×C4×C61—41no—
208C2×C4×C61—41no—
209C2×C4×C61C23×C411yescharacteristic
210C2×C4×C61C22×D411yescharacteristic
211C2×C4×C61C2×#4111yescharacteristic
212C2×C4×C61C2×#4111yescharacteristic
213C2×C4×C61C2×#4111yescharacteristic
214C2×C4×C61C2×#4111yescharacteristic
215C22⋊D61—41no—
216C22⋊D61—41no—
217C2×Dic61—24no—
218C2×Dic61—21no—
219C2×Dic61—22no—
220C2×Dic61—22no—
221C2×Dic61—42no—
222C2×Dic61—44no—
223C2×Dic61C4×D412yes—
224C2×Dic61C4×D412yes—
225D244—21no—
226D244—21no—
227C4×D61—41no—
228C4×D61—41no—
229C4×D61—44no—
230Dic122—21no—
231Dic122—21no—
232C8×C61—22no—
233C8×C61—22no—
234C8×C61—41no—
235C8×C61—41no—
236#92418—22no—
237#92418—41no—
238#92418—41no—
239#92418#11712yes—
240#92418#11712yes—
241#21293—611nomaximal, Sylow
242C22×C61—22no—
243C22×C61—42no—
244C22×C61—41no—
245C22×C61C2×C4×D411yescharacteristic
246C22×C61#52911yescharacteristic
247C22×C61#52911yescharacteristic
248C2×D61—42no—
249C2×D61—41no—
250C4×C61—42no—
251C4×C61—42no—
252C4×C61—41no—
253C4×C61C2×#11711yescharacteristic
254C4×C61C4×#4111yescharacteristic
255C4×C61#53211yescharacteristic
256C4×C61#53211yescharacteristic
257Dic61—22no—
258Dic61—42no—
259Dic61—42no—
260Dic61—41no—
261Dic61#44414yes—
262C4×#135—611no—
263#2922—611no—
264#2922—611no—
265#1975—611no—
266#1975—611no—
267#1946—611no—
268#1946—611no—
269#1938—611no—
270#1938—611no—
271#1938—611no—
272#1938D6111yescharacteristic, complemented
273C4×#108—611no—
274C4×#104—611no—
275C4×#104—611no—
276C4×#97—611no—
277C2×C61—21no—
278C2×C61—21no—
279C2×C61—81no—
280C2×C61#229311yescharacteristic
281C2×C61C2×#44412yes—
282D61—81no—
283C2×#135—611no—
284C4×#41—611no—
285C4×#41—611no—
286C4×Q16—612no—
287C4×SD16—612no—
288C4×SD16—612no—
289C4×D8—612no—
290#433—1222no—
291#433—1222no—
292#431—1222no—
293#431—1222no—
294C2×#108—611no—
295C2×#108—611no—
296#427—611no—
297#424—611no—
298#424—611no—
299#424—611no—
300#424C2×D6111yescharacteristic
301C2×#104—611no—
302C2×#104—611no—
303C2×#104—611no—
304C2×#104C2×D6111yescharacteristic
305#416—611no—
306#416C2×D6111yescharacteristic
307#408—611no—
308#408—611no—
309#408—611no—
310#408C2×D6111yescharacteristic
311C4×M16—611no—
312C4×M16—611no—
313C2×#97—611no—
314C2×#97—611no—
315C2×#97—611no—
316C2×#97C2×D6111yescharacteristic
317C2×C4×C8—611no—
318C2×C4×C8—611no—
319C43—611no—
320#341—611no—
321#341C2×D6111yescharacteristic
322#339—611no—
323#339—611no—
324#339—611no—
325#339C2×D6111yescharacteristic
326C61#2129311yescharacteristic, complemented, Sylow
327C2×#41—611no—
328C2×#41C22×D6111yescharacteristic
329#135—1222no—
330#135—1222no—
331C2×Q16—611no—
332C2×SD16—611no—
333C2×SD16—611no—
334C2×D8—611no—
335C2×M16—611no—
336C2×M16—611no—
337C2×M16C22×D6111yescharacteristic
338C2×M16C22×D6111yescharacteristic
339C22×C8—611no—
340C22×C8—611no—
341C22×C8C22×D6111yescharacteristic
342C22×C8C22×D6111yescharacteristic
343C4×Q8—612no—
344C4×Q8—612no—
345C4×D4—612no—
346C4×D4—612no—
347C4×D4—1222no—
348C4×D4—1222no—
349#117—611no—
350#117—1221no—
351#117—1221no—
352#117C22×D6111yescharacteristic
353C2×C42—611no—
354C2×C42—611no—
355C2×C42—1221no—
356C2×C42—1221no—
357C2×C42—1222no—
358C2×C42C22×D6111yescharacteristic
359#108—1222no—
360#108—1222no—
361#107—612no—
362#106—612no—
363C4⋊C8—22no—
364C4⋊C8—1222no—
365C4⋊C8—1222no—
366C4⋊C8—1222no—
367#104—22no—
368#104—1222no—
369#104—1222no—
370#104—1222no—
371#103—612no—
372#103C4×D6112yes—
373#102—612no—
374#102C4×D6112yes—
375C22⋊C8—22no—
376C22⋊C8—1222no—
377C22⋊C8—1222no—
378C22⋊C8—1222no—
379#97—22no—
380#97—1222no—
381#97—1222no—
382#97—1221no—
383#97—1221no—
384#97—1222no—
385C4×C8—612no—
386C4×C8—612no—
387C4×C8—612no—
388C4×C8—612no—
389C4×C8—1221no—
390C4×C8—1221no—
391#41—21no—
392#41—21no—
393#41—21no—
394#41—21no—
395#41—1221no—
396#41—1221no—
397#41—1221no—
398#41—1221no—
399C2×Q8—611no—
400C2×Q8C2×C4×D6111yescharacteristic
401C2×D4—21no—
402C2×D4—611no—
403C2×D4—1221no—
404C2×D4C2×C4×D6111yescharacteristic
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—612no—
408C22×C4—1222no—
409C22×C4—1222no—
410C22×C4—1221no—
411C22×C4—1221no—
412C22×C4C23×D6111yescharacteristic
413Q16—1222no—
414SD16—1222no—
415SD16—1222no—
416D8—1222no—
417M16—21no—
418M16—21no—
419M16—21no—
420M16—21no—
421M16—1221no—
422M16—1221no—
423M16—1221no—
424M16—1221no—
425C2×C8—21no—
426C2×C8—21no—
427C2×C8—21no—
428C2×C8—21no—
429C2×C8—21no—
430C2×C8—21no—
431C2×C8—611no—
432C2×C8—611no—
433C2×C8—612no—
434C2×C8—612no—
435C2×C8—612no—
436C2×C8—1221no—
437C2×C8—1221no—
438C2×C8—1221no—
439C2×C8—1221no—
440C2×C8C2×C4×D6112yes—
441C2×C8D4×D6112yes—
442C4⋊C4—612no—
443C4⋊C4—1222no—
444C4⋊C4—1222no—
445C4⋊C4C2×C4×D6112yes—
446C22⋊C4—21no—
447C22⋊C4—1222no—
448C22⋊C4—1222no—
449C22⋊C4—1221no—
450C42—21no—
451C42—21no—
452C42—612no—
453C42—611no—
454C42—611no—
455C42—612no—
456C42—1222no—
457C42—1222no—
458C42—1221no—
459C42—1221no—
460C42—2444no—
461C42#1175822412yes—
462C23—21no—
463C23—1221no—
464C23#41×D6111yescharacteristic
465Q8—21no—
466Q8—21no—
467Q8—1221no—
468Q8—1221no—
469D4—21no—
470D4—21no—
471D4—41no—
472D4—41no—
473D4—1221no—
474D4—1221no—
475D4—2441no—
476D4—2441no—
477C2×C4—22no—
478C2×C4—21no—
479C2×C4—22no—
480C2×C4—42no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—612no—
484C2×C4—612no—
485C2×C4—1224no—
486C2×C4—1222no—
487C2×C4—1221no—
488C2×C4—1222no—
489C2×C4—2444no—
490C2×C4—2444no—
491C2×C4—2442no—
492C2×C4—2441no—
493C2×C4—2441no—
494C2×C4C22×C4×D6111yescharacteristic
495C2×C4C2×D4×D6111yescharacteristic
496C2×C4#41×D6111yescharacteristic
497C2×C4#41×D6111yescharacteristic
498C2×C4#41×D6111yescharacteristic
499C2×C4C2×#1175822411yescharacteristic
500C8—22no—
501C8—22no—
502C8—41no—
503C8—41no—
504C8—612no—
505C8—612no—
506C8—1222no—
507C8—2441no—
508C8—2441no—
509C22—22no—
510C22—41no—
511C22—42no—
512C22—2441no—
513C22—2442no—
514C22C4×D4×D6111yescharacteristic
515C22#1684028911yescharacteristic
516C22#1684029511yescharacteristic
517C4—42no—
518C4—41no—
519C4—42no—
520C4—614no—
521C4—1222no—
522C4—2442no—
523C4—2441no—
524C4—2442no—
525C4#117×D6111yescharacteristic
526C4C4×#1175822411yescharacteristic
527C4#1684030711yescharacteristic
528C4#1684031111yescharacteristic
529C2—21no—
530C2—21no—
531C2—81no—
532C2—4881no—
533C2#2144827911yescharacteristic
534C2#444×D6112yes—
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1938C2
socleC22×C61C2×C4×D4
prime radicalC2×#14519797C22
cosocleC22×C4×C61C24
hypercenter#1938D61
hypocenterC61#21293
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1938

Complements

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

NH ≅ G/Ntype
2. #21454462C2semidirect
3. #21454459C2semidirect
6. #21446571C2semidirect
7. #21446569C2semidirect
8. #21446532C2semidirect
9. #21446530C2semidirect
10. #21446528C2semidirect
11. #21445720C2semidirect
12. #104×Dic61C2semidirect
13. #21445623C2semidirect
14. #97×Dic61C2semidirect
15. C61×#1938C2semidirect
19. #16839854C4semidirect
20. #16839853C4semidirect
21. #16839847C4semidirect
22. #16839842C4semidirect
272. #1938D61semidirect
326. C61#21293semidirect

Maximal subgroups

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

subgroupindex
#214545872
#214544622
#214544592
#214467112
#214467092
#214465712
#214465692
#214465322
#214465302
#214465282
#214457202
#104×Dic612
#214456232
#97×Dic612
C61×#19382
#2129361