Finite Group Databasebeta

← #29575765

Subgroups — #29575765

Order 15616.

946 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454103C211yesmaximal, characteristic
2C2×#16839621C211yesmaximal, characteristic
3#21445728C211yesmaximal, characteristic
4C2×#16839499C211yesmaximal, characteristic, complemented
5#21443699C211yesmaximal, characteristic, complemented
6#21443698C211yesmaximal, characteristic, complemented
7C2×C61×#328C211yesmaximal, characteristic, complemented
8C23×C4×D61C2211yescharacteristic
9C2×#14519753C412yescomplemented
10C22×#11758196—21no—
11C22×#11758198—21no—
12C2×C22⋊#92418C2211yescharacteristic
13C2×#14519689—22no—
14#16839634—21no—
15#16839633—22no—
16#16839622C2211yescharacteristic
17#16839621—22no—
18#16839621—22no—
19#16839619C412yescomplemented
20#16839617—21no—
21C2×#14519684C2211yescharacteristic
22#16839499—22no—
23C2×C22⋊Q8×C61C2211yescharacteristic
24C2×C22⋊C8×C61C2211yescharacteristic
25C2×#95×C61C2211yescharacteristic
26C61×#328—22no—
27C24×D61D411yescharacteristic
28C23×Dic61—21no—
29C23×Dic61D411yescharacteristic
30C22×C4×D61—21no—
31C22×C4×D61—21no—
32C22×C4×D61—21no—
33C22×C4×D61—21no—
34C22×C4×D61—44no—
35C22×C4×D61C2×C412yes—
36C22×C4×D61D412yes—
37C22×#92418—21no—
38#14519753—44no—
39C2×C4⋊Dic61C2×C412yes—
40C2×#11758196—24no—
41C2×#11758196—22no—
42C2×#11758196—44no—
43C2×C22⋊Dic61—21no—
44C2×#11758198—24no—
45C2×#11758198—22no—
46C2×#11758198—22no—
47C2×#11758198—42no—
48C2×#11758198—42no—
49C22⋊#92418—21no—
50C22⋊#92418—21no—
51#14519689—44no—
52#14519684—21no—
53#14519684—21no—
54#14519684—22no—
55#14519684D412yes—
56C22×Q8×C61C2×C411yescharacteristic
57C23×C4×C61—21no—
58C23×C4×C61C2311yescharacteristic
59C22×C8×C61—21no—
60C22⋊Q8×C61—21no—
61C22⋊Q8×C61—21no—
62C22⋊Q8×C61—21no—
63C22⋊Q8×C61—21no—
64C2×C4⋊C4×C61—21no—
65C2×C4⋊C4×C61C2×C411yescharacteristic
66C2×C22⋊C4×C61—21no—
67C22⋊C8×C61—21no—
68C22⋊C8×C61—21no—
69#95×C61—21no—
70#95×C61D412yes—
71C24×C61C2×D411yescharacteristic
72C23×D61—21no—
73C23×D61—21no—
74C23×D61—21no—
75C23×D61—21no—
76C23×D61—42no—
77C23×D61—42no—
78C23×D61C22⋊C412yes—
79C23×D61SD1612yes—
80C23×D61Q1612yes—
81C2×Q8×C61—21no—
82C2×Q8×C61—21no—
83C2×Q8×C61—42no—
84C22×C4×C61—21no—
85C22×C4×C61—21no—
86C22×C4×C61—22no—
87C22×C4×C61—42no—
88C22×C4×C61—42no—
89C22×C4×C61—42no—
90C22×C4×C61—41no—
91C22×C4×C61—41no—
92C22×C4×C61C22×C411yescharacteristic
93C22×C4×C61C2×D411yescharacteristic
94C22×C4×C61C2×D411yescharacteristic
95C22×C4×C61C2×D411yescharacteristic
96C22×C4×C61#4111yescharacteristic
97C22×C4×C61#4111yescharacteristic
98C22×Dic61—21no—
99C22×Dic61—21no—
100C22×Dic61—24no—
101C22×Dic61—22no—
102C22×Dic61—22no—
103C22×Dic61—42no—
104C22×Dic61—42no—
105C22×Dic61—41no—
106C22×Dic61—41no—
107C22×Dic61C22⋊C412yes—
108C2×C4×D61—22no—
109C2×C4×D61—22no—
110C2×C4×D61—22no—
111C2×C4×D61—22no—
112C2×C4×D61—24no—
113C2×C4×D61—24no—
114C2×C4×D61—42no—
115C2×C4×D61—42no—
116C2×C4×D61—44no—
117C2×C4×D61—44no—
118C2×C4×D61—44no—
119C2×C4×D61—44no—
120C2×C8×C61—42no—
121C2×C8×C61—41no—
122C4⋊C4×C61—21no—
123C4⋊C4×C61—21no—
124C4⋊C4×C61—41no—
125C4⋊C4×C61—41no—
126C22⋊C4×C61—41no—
127C22⋊C4×C61—41no—
128C22⋊Dic61—41no—
129C22⋊Dic61—41no—
130#11758198—44no—
131#11758198—48no—
132#11758198—44no—
133C4⋊Dic61—42no—
134#11758196—48no—
135#11758196—44no—
136C2×#92418—42no—
137C2×#92418—41no—
138C23×C61—22no—
139C23×C61—22no—
140C23×C61C2×C22⋊C411yescharacteristic
141C23×C61#12011yescharacteristic
142C23×C61#12311yescharacteristic
143C23×C61C2×SD1611yescharacteristic
144C23×C61C2×Q1611yescharacteristic
145C23×C61AGL(1,ℤ/8)11yescharacteristic
146C23×C61#13711yescharacteristic
147C22×D61—22no—
148C22×D61—22no—
149C22×D61—22no—
150C22×D61—22no—
151C22×D61—22no—
152C22×D61—22no—
153C22×D61—22no—
154C22×D61—22no—
155C22×D61—22no—
156C22×D61—22no—
157C22×D61—44no—
158C22×D61—44no—
159C22×D61—42no—
160C22×D61—42no—
161C22×D61—42no—
162C22×D61—42no—
163C22×D61—44no—
164C22×D61—44no—
165C22×D61#10314yes—
166Q8×C61—81no—
167Q8×C61—81no—
168C2×C4×C61—22no—
169C2×C4×C61—22no—
170C2×C4×C61—41no—
171C2×C4×C61—41no—
172C2×C4×C61—41no—
173C2×C4×C61—41no—
174C2×C4×C61—42no—
175C2×C4×C61—42no—
176C2×C4×C61—41no—
177C2×C4×C61—41no—
178C2×C4×C61—42no—
179C2×C4×C61—42no—
180C2×C4×C61—42no—
181C2×C4×C61—82no—
182C2×C4×C61—82no—
183C2×C4×C61C4×D411yescharacteristic
184C2×C4×C61C4×D411yescharacteristic
185C2×C4×C61#12111yescharacteristic
186C2×C4×C61#12111yescharacteristic
187C2×Dic61—24no—
188C2×Dic61—24no—
189C2×Dic61—22no—
190C2×Dic61—22no—
191C2×Dic61—42no—
192C2×Dic61—42no—
193C2×Dic61—42no—
194C2×Dic61—42no—
195C2×Dic61—42no—
196C2×Dic61—42no—
197C2×Dic61—82no—
198C2×Dic61—82no—
199C2×Dic61#9914yes—
200C4×D61—44no—
201C4×D61—44no—
202C4×D61—44no—
203C4×D61—44no—
204C8×C61—81no—
205#92418—81no—
206#9151—611nomaximal, Sylow
207C22×C61—21no—
208C22×C61—21no—
209C22×C61—21no—
210C22×C61—21no—
211C22×C61—22no—
212C22×C61—22no—
213C22×C61—22no—
214C22×C61—22no—
215C22×C61#38611yescharacteristic
216C22×C61C2×#9912yes—
217C22×C61C2×#10311yescharacteristic
218C22×C61#41711yescharacteristic
219C22×C61#42112yes—
220C22×C61#45011yescharacteristic
221C22×C61#45111yescharacteristic
222C22×C61#48311yescharacteristic
223C22×C61#48411yescharacteristic
224C2×D61—24no—
225C2×D61—24no—
226C2×D61—24no—
227C2×D61—44no—
228C2×D61—44no—
229C2×D61—44no—
230C2×D61—44no—
231C2×D61—42no—
232C2×D61—42no—
233C2×D61—42no—
234C2×D61—42no—
235C4×C61—21no—
236C4×C61—21no—
237C4×C61—21no—
238C4×C61—21no—
239C4×C61—82no—
240C4×C61—81no—
241C4×C61—81no—
242Dic61—24no—
243Dic61—82no—
244Dic61—82no—
245#2848—611no—
246C2×#380—611no—
247#1779—611no—
248C2×#328—611no—
249C2×#328D6111yescharacteristic, complemented
250#1294—611no—
251#1294—611no—
252C2×C61—21no—
253C2×C61—21no—
254C2×C61—21no—
255C2×C61—21no—
256C2×C61#151312yes—
257C2×C61#152012yes—
258C2×C61#187211yescharacteristic
259C2×C61#189711yescharacteristic
260C2×C61#189811yescharacteristic
261D61—44no—
262C24×C4—611no—
263C2×C22⋊Q8—612no—
264C2×C22⋊Q8C2×D6111yescharacteristic
265C22×C4⋊C4—1221no—
266C22×C22⋊C4—1221no—
267C2×C22⋊C8—611no—
268C2×C22⋊C8—1222no—
269C2×C22⋊C8C2×D6111yescharacteristic
270#385—1221no—
271#385—1222no—
272#380—611no—
273#380—612no—
274#380—1222no—
275#380—1222no—
276#379—1221no—
277C2×#95—611no—
278C2×#95C2×D6111yescharacteristic
279#328—22no—
280#328—1222no—
281C61#915111yescharacteristic, complemented, Sylow
282C25—611no—
283C22×Q8C4×D6111yescharacteristic
284C23×C4—21no—
285C23×C4—611no—
286C23×C4—612no—
287C23×C4—612no—
288C23×C4—1221no—
289C23×C4—1221no—
290C23×C4—1221no—
291C23×C4—1221no—
292C23×C4—1221no—
293C23×C4—2444no—
294C23×C4C22×D6111yescharacteristic
295C22×C8—21no—
296C22×C8—1221no—
297C22⋊Q8—21no—
298C22⋊Q8—21no—
299C22⋊Q8—21no—
300C22⋊Q8—21no—
301C22⋊Q8—2444no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—612no—
304C2×C4⋊C4—1222no—
305C2×C4⋊C4—1224no—
306C2×C4⋊C4—2444no—
307C2×C4⋊C4C4×D6111yescharacteristic
308C2×C22⋊C4—21no—
309C2×C22⋊C4—1222no—
310C2×C22⋊C4—1222no—
311C2×C22⋊C4—1224no—
312C2×C22⋊C4—1221no—
313C2×C22⋊C4—2442no—
314C2×C22⋊C4—2442no—
315C22⋊C8—21no—
316C22⋊C8—21no—
317C22⋊C8—1221no—
318C22⋊C8—1221no—
319C22⋊C8—2444no—
320#95—21no—
321#95—612no—
322#95—1222no—
323#95—1221no—
324#95—1221no—
325#95C22⋊D6112yes—
326C24—612no—
327C24—612no—
328C24—612no—
329C24—1221no—
330C24—1221no—
331C24—1221no—
332C24—1221no—
333C24—2442no—
334C24—2442no—
335C24D4×D6111yescharacteristic
336C2×Q8—21no—
337C2×Q8—21no—
338C2×Q8—42no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—22no—
342C22×C4—42no—
343C22×C4—42no—
344C22×C4—42no—
345C22×C4—41no—
346C22×C4—41no—
347C22×C4—612no—
348C22×C4—1224no—
349C22×C4—1224no—
350C22×C4—1224no—
351C22×C4—1221no—
352C22×C4—1221no—
353C22×C4—1222no—
354C22×C4—1222no—
355C22×C4—1222no—
356C22×C4—1222no—
357C22×C4—1222no—
358C22×C4—1222no—
359C22×C4—2442no—
360C22×C4—2442no—
361C22×C4—2444no—
362C22×C4—2444no—
363C22×C4—2444no—
364C22×C4—2444no—
365C22×C4—2442no—
366C22×C4—2442no—
367C22×C4—2441no—
368C22×C4—2441no—
369C22×C4C2×C4×D6111yescharacteristic
370C22×C4#1175822211yescharacteristic
371C22×C4D4×D6111yescharacteristic
372C22×C4D4×D6111yescharacteristic
373C22×C4#1175822411yescharacteristic
374C22×C4C2×C22⋊D6111yescharacteristic
375C2×C8—42no—
376C2×C8—41no—
377C2×C8—2442no—
378C2×C8—2441no—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—41no—
382C4⋊C4—41no—
383C4⋊C4—2442no—
384C4⋊C4—2444no—
385C4⋊C4—2448no—
386C22⋊C4—41no—
387C22⋊C4—41no—
388C22⋊C4—2448no—
389C22⋊C4—2444no—
390C22⋊C4—2444no—
391C22⋊C4—2441no—
392C22⋊C4—2441no—
393C23—22no—
394C23—22no—
395C23—614no—
396C23—1222no—
397C23—1222no—
398C23—1222no—
399C23—1222no—
400C23—1222no—
401C23—1222no—
402C23—1222no—
403C23—1222no—
404C23—1222no—
405C23—1222no—
406C23—2444no—
407C23—2444no—
408C23—2442no—
409C23—2442no—
410C23—2444no—
411C23—2444no—
412C23—2442no—
413C23—2442no—
414C23C22⋊C4×D6111yescharacteristic
415C23#1451974511yescharacteristic
416C23#1451975911yescharacteristic
417C23SD16×D6111yescharacteristic
418C23Q16×D6111yescharacteristic
419C23#1451980411yescharacteristic
420C23#1451980911yescharacteristic
421Q8—81no—
422Q8—81no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—42no—
436C2×C4—82no—
437C2×C4—82no—
438C2×C4—614no—
439C2×C4—1224no—
440C2×C4—1224no—
441C2×C4—1222no—
442C2×C4—1222no—
443C2×C4—4882no—
444C2×C4—4882no—
445C2×C4—2444no—
446C2×C4—2444no—
447C2×C4—2444no—
448C2×C4—2444no—
449C2×C4—2442no—
450C2×C4—2442no—
451C2×C4—2442no—
452C2×C4—2442no—
453C2×C4—2442no—
454C2×C4—2442no—
455C2×C4#1451973711yescharacteristic
456C2×C4C4×C22⋊D6111yescharacteristic
457C2×C4#1451974811yescharacteristic
458C2×C4#1451975011yescharacteristic
459C8—81no—
460C8—4881no—
461C22—22no—
462C22—22no—
463C22—22no—
464C22—22no—
465C22—21no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—1224no—
470C22—1224no—
471C22—1224no—
472C22—2444no—
473C22—2444no—
474C22—2444no—
475C22—2444no—
476C22—2442no—
477C22—2442no—
478C22—2442no—
479C22—2442no—
480C22#1683963811yescharacteristic
481C22#99×D6112yes—
482C22#103×D6111yescharacteristic
483C22#1683976211yescharacteristic
484C22#1683977712yes—
485C22#1683991111yescharacteristic
486C22#1683991611yescharacteristic
487C22#1684009111yescharacteristic
488C22#1684009611yescharacteristic
489C4—21no—
490C4—21no—
491C4—21no—
492C4—21no—
493C4—82no—
494C4—81no—
495C4—81no—
496C4—1224no—
497C4—4882no—
498C4—4882no—
499C2—21no—
500C2—21no—
501C2—21no—
502C2—21no—
503C2—2444no—
504C2#2144436112yes—
505C2#2144438912yes—
506C2#2144612311yescharacteristic
507C2#2144626411yescharacteristic
508C2#2144626911yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC2×C61×#328C2
socleC23×C61C2×C22⋊C4
prime radicalC24×D61D4
cosocleC23×C4×C61C23
hypercenterC2×#328D61
hypocenterC61#9151
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
4. C2×#16839499C2semidirect
5. #21443699C2semidirect
6. #21443698C2semidirect
7. C2×C61×#328C2semidirect
9. C2×#14519753C4semidirect
19. #16839619C4semidirect
249. C2×#328D61semidirect
281. C61#9151semidirect

Maximal subgroups

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

subgroupindex
#214541032
C2×#168396212
#214457282
C2×#168394992
#214436992
#214436982
C2×C61×#3282
#915161