Finite Group Databasebeta

← #29575780

Subgroups — #29575780

Order 15616.

902 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454103C211yesmaximal, characteristic
2C2×#16839624C211yesmaximal, 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×#11758198—21no—
11C2×C22⋊#92418C2211yescharacteristic
12C2×#14519689—22no—
13#16839634—21no—
14#16839633—22no—
15#16839624—22no—
16#16839624—22no—
17#16839622C2211yescharacteristic
18#16839619C412yescomplemented
19#16839617—21no—
20C2×#14519684—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—22no—
41C2×C22⋊Dic61—21no—
42C2×#11758198—24no—
43C2×#11758198—22no—
44C2×#11758198—22no—
45C2×#11758198—44no—
46C22⋊#92418—21no—
47C22⋊#92418—21no—
48#14519689—44no—
49#14519684—24no—
50#14519684—21no—
51#14519684—21no—
52#14519684—22no—
53#14519684D412yes—
54C22×Q8×C61C2×C411yescharacteristic
55C23×C4×C61—21no—
56C23×C4×C61C2311yescharacteristic
57C22×C8×C61—21no—
58C22⋊Q8×C61—21no—
59C22⋊Q8×C61—21no—
60C22⋊Q8×C61—21no—
61C22⋊Q8×C61—21no—
62C2×C4⋊C4×C61—21no—
63C2×C4⋊C4×C61C2×C411yescharacteristic
64C2×C22⋊C4×C61—21no—
65C22⋊C8×C61—21no—
66C22⋊C8×C61—21no—
67#95×C61—21no—
68#95×C61D412yes—
69C24×C61C2×D411yescharacteristic
70C23×D61—21no—
71C23×D61—21no—
72C23×D61—24no—
73C23×D61—21no—
74C23×D61—21no—
75C23×D61—21no—
76C23×D61—21no—
77C23×D61—42no—
78C23×D61C22⋊C412yes—
79C2×Q8×C61—21no—
80C2×Q8×C61—21no—
81C2×Q8×C61—42no—
82C22×C4×C61—21no—
83C22×C4×C61—21no—
84C22×C4×C61—22no—
85C22×C4×C61—42no—
86C22×C4×C61—42no—
87C22×C4×C61—42no—
88C22×C4×C61—41no—
89C22×C4×C61—41no—
90C22×C4×C61C22×C411yescharacteristic
91C22×C4×C61C2×D411yescharacteristic
92C22×C4×C61C2×D411yescharacteristic
93C22×C4×C61C2×D411yescharacteristic
94C22×C4×C61#4111yescharacteristic
95C22×C4×C61#4111yescharacteristic
96C22×Dic61—21no—
97C22×Dic61—21no—
98C22×Dic61—22no—
99C22×Dic61—22no—
100C22×Dic61—42no—
101C22×Dic61—42no—
102C22×Dic61—42no—
103C22×Dic61—41no—
104C22×Dic61—41no—
105C22×Dic61C22⋊C412yes—
106C2×C4×D61—24no—
107C2×C4×D61—24no—
108C2×C4×D61—22no—
109C2×C4×D61—22no—
110C2×C4×D61—22no—
111C2×C4×D61—22no—
112C2×C4×D61—42no—
113C2×C4×D61—42no—
114C2×C4×D61—44no—
115C2×C4×D61—44no—
116C2×C4×D61—44no—
117C2×C4×D61—44no—
118C2×C8×C61—42no—
119C2×C8×C61—41no—
120C4⋊C4×C61—21no—
121C4⋊C4×C61—21no—
122C4⋊C4×C61—41no—
123C4⋊C4×C61—41no—
124C22⋊C4×C61—41no—
125C22⋊C4×C61—41no—
126C22⋊Dic61—41no—
127C22⋊Dic61—41no—
128#11758198—44no—
129#11758198—48no—
130#11758198—44no—
131C4⋊Dic61—42no—
132#11758196—44no—
133C2×#92418—42no—
134C2×#92418—41no—
135C23×C61—22no—
136C23×C61—22no—
137C23×C61C2×C22⋊C411yescharacteristic
138C23×C61#12011yescharacteristic
139C23×C61#12311yescharacteristic
140C23×C61#13511yescharacteristic
141C23×C61#13511yescharacteristic
142C23×C61#13711yescharacteristic
143C23×C61#13711yescharacteristic
144C22×D61—24no—
145C22×D61—24no—
146C22×D61—22no—
147C22×D61—22no—
148C22×D61—22no—
149C22×D61—22no—
150C22×D61—22no—
151C22×D61—22no—
152C22×D61—44no—
153C22×D61—44no—
154C22×D61—44no—
155C22×D61—44no—
156C22×D61—42no—
157C22×D61—42no—
158C22×D61—41no—
159C22×D61—41no—
160C22×D61—41no—
161C22×D61—41no—
162C22×D61#9914yes—
163Q8×C61—81no—
164Q8×C61—81no—
165C2×C4×C61—22no—
166C2×C4×C61—22no—
167C2×C4×C61—41no—
168C2×C4×C61—41no—
169C2×C4×C61—41no—
170C2×C4×C61—41no—
171C2×C4×C61—42no—
172C2×C4×C61—42no—
173C2×C4×C61—41no—
174C2×C4×C61—41no—
175C2×C4×C61—42no—
176C2×C4×C61—42no—
177C2×C4×C61—42no—
178C2×C4×C61—82no—
179C2×C4×C61—82no—
180C2×C4×C61C4×D411yescharacteristic
181C2×C4×C61C4×D411yescharacteristic
182C2×C4×C61#12111yescharacteristic
183C2×C4×C61#12111yescharacteristic
184C2×Dic61—22no—
185C2×Dic61—22no—
186C2×Dic61—22no—
187C2×Dic61—42no—
188C2×Dic61—42no—
189C2×Dic61—42no—
190C2×Dic61—42no—
191C2×Dic61—42no—
192C2×Dic61—42no—
193C2×Dic61—42no—
194C2×Dic61—42no—
195C2×Dic61—82no—
196C2×Dic61—82no—
197C4×D61—44no—
198C4×D61—44no—
199C4×D61—44no—
200C4×D61—44no—
201C8×C61—81no—
202#92418—81no—
203#9154—611nomaximal, Sylow
204C22×C61—21no—
205C22×C61—21no—
206C22×C61—21no—
207C22×C61—21no—
208C22×C61—22no—
209C22×C61—22no—
210C22×C61—22no—
211C22×C61—22no—
212C22×C61#38611yescharacteristic
213C22×C61C2×#9912yes—
214C22×C61#41611yescharacteristic
215C22×C61#41911yescharacteristic
216C22×C61#42112yes—
217C22×C61#45211yescharacteristic
218C22×C61#45211yescharacteristic
219C22×C61#48511yescharacteristic
220C22×C61#48511yescharacteristic
221C2×D61—24no—
222C2×D61—24no—
223C2×D61—24no—
224C2×D61—44no—
225C2×D61—44no—
226C2×D61—44no—
227C2×D61—44no—
228C2×D61—42no—
229C2×D61—42no—
230C2×D61—42no—
231C2×D61—42no—
232C4×C61—21no—
233C4×C61—21no—
234C4×C61—21no—
235C4×C61—21no—
236C4×C61—82no—
237C4×C61—81no—
238C4×C61—81no—
239Dic61—42no—
240Dic61—82no—
241Dic61—82no—
242#2848—611no—
243C2×#381—611no—
244#1779—611no—
245C2×#328—611no—
246C2×#328D6111yescharacteristic, complemented
247#1294—611no—
248#1294—611no—
249C2×C61—21no—
250C2×C61—21no—
251C2×C61—21no—
252C2×C61—21no—
253C2×C61#151112yes—
254C2×C61#151612yes—
255C2×C61#187311yescharacteristic
256C2×C61#189711yescharacteristic
257C2×C61#189811yescharacteristic
258D61—44no—
259C24×C4—611no—
260C2×C22⋊Q8—612no—
261C2×C22⋊Q8C2×D6111yescharacteristic
262C22×C22⋊C4—1221no—
263C2×C22⋊C8—611no—
264C2×C22⋊C8—1222no—
265C2×C22⋊C8C2×D6111yescharacteristic
266#385—1221no—
267#385—1222no—
268#381—1222no—
269#381—1222no—
270#380—611no—
271#380—612no—
272#379—1221no—
273C2×#95—611no—
274C2×#95—1221no—
275C2×#95C2×D6111yescharacteristic
276#328—22no—
277#328—1222no—
278C61#915411yescharacteristic, complemented, Sylow
279C25—611no—
280C22×Q8C4×D6111yescharacteristic
281C23×C4—21no—
282C23×C4—611no—
283C23×C4—612no—
284C23×C4—612no—
285C23×C4—1221no—
286C23×C4—1221no—
287C23×C4—1221no—
288C23×C4—1221no—
289C23×C4—1221no—
290C23×C4—2444no—
291C23×C4C22×D6111yescharacteristic
292C22×C8—21no—
293C22×C8—1221no—
294C22⋊Q8—21no—
295C22⋊Q8—21no—
296C22⋊Q8—21no—
297C22⋊Q8—21no—
298C22⋊Q8—2444no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—612no—
301C2×C4⋊C4—1222no—
302C2×C4⋊C4C4×D6111yescharacteristic
303C2×C22⋊C4—21no—
304C2×C22⋊C4—1222no—
305C2×C22⋊C4—1222no—
306C2×C22⋊C4—1224no—
307C2×C22⋊C4—1221no—
308C2×C22⋊C4—2444no—
309C22⋊C8—21no—
310C22⋊C8—21no—
311C22⋊C8—1221no—
312C22⋊C8—1221no—
313C22⋊C8—2444no—
314#95—21no—
315#95—612no—
316#95—1222no—
317#95—1224no—
318#95—1221no—
319#95—1221no—
320#95C22⋊D6112yes—
321C24—612no—
322C24—1224no—
323C24—1221no—
324C24—1221no—
325C24—1221no—
326C24—1221no—
327C24—1221no—
328C24—1221no—
329C24—2442no—
330C24D4×D6111yescharacteristic
331C2×Q8—21no—
332C2×Q8—21no—
333C2×Q8—42no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—22no—
337C22×C4—42no—
338C22×C4—42no—
339C22×C4—42no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4—612no—
343C22×C4—1224no—
344C22×C4—1224no—
345C22×C4—1221no—
346C22×C4—1221no—
347C22×C4—1222no—
348C22×C4—1222no—
349C22×C4—1222no—
350C22×C4—1222no—
351C22×C4—1222no—
352C22×C4—1222no—
353C22×C4—2442no—
354C22×C4—2442no—
355C22×C4—2444no—
356C22×C4—2444no—
357C22×C4—2444no—
358C22×C4—2444no—
359C22×C4—2442no—
360C22×C4—2442no—
361C22×C4—2442no—
362C22×C4—2441no—
363C22×C4—2441no—
364C22×C4C2×C4×D6111yescharacteristic
365C22×C4#1175822211yescharacteristic
366C22×C4D4×D6111yescharacteristic
367C22×C4D4×D6111yescharacteristic
368C22×C4#1175822411yescharacteristic
369C22×C4C2×C22⋊D6111yescharacteristic
370C2×C8—42no—
371C2×C8—41no—
372C2×C8—2442no—
373C2×C8—2441no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—41no—
377C4⋊C4—41no—
378C4⋊C4—2442no—
379C4⋊C4—2444no—
380C22⋊C4—41no—
381C22⋊C4—41no—
382C22⋊C4—2444no—
383C22⋊C4—2448no—
384C22⋊C4—2444no—
385C22⋊C4—2441no—
386C22⋊C4—2441no—
387C23—22no—
388C23—22no—
389C23—614no—
390C23—1224no—
391C23—1224no—
392C23—1222no—
393C23—1222no—
394C23—1222no—
395C23—1222no—
396C23—1222no—
397C23—1222no—
398C23—2444no—
399C23—2444no—
400C23—2444no—
401C23—2444no—
402C23—2442no—
403C23—2442no—
404C23—2441no—
405C23—2441no—
406C23—2441no—
407C23—2441no—
408C23C22⋊C4×D6111yescharacteristic
409C23#1451974511yescharacteristic
410C23#1451975911yescharacteristic
411C23#1451979811yescharacteristic
412C23#1451980011yescharacteristic
413C23#1451980611yescharacteristic
414C23#1451980911yescharacteristic
415Q8—81no—
416Q8—81no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—42no—
430C2×C4—82no—
431C2×C4—82no—
432C2×C4—1222no—
433C2×C4—1222no—
434C2×C4—1222no—
435C2×C4—4882no—
436C2×C4—4882no—
437C2×C4—2444no—
438C2×C4—2444no—
439C2×C4—2444no—
440C2×C4—2444no—
441C2×C4—2442no—
442C2×C4—2442no—
443C2×C4—2442no—
444C2×C4—2442no—
445C2×C4—2442no—
446C2×C4—2442no—
447C2×C4—2442no—
448C2×C4—2442no—
449C2×C4#1451973711yescharacteristic
450C2×C4C4×C22⋊D6111yescharacteristic
451C2×C4#1451974811yescharacteristic
452C2×C4#1451975011yescharacteristic
453C8—81no—
454C8—4881no—
455C22—22no—
456C22—22no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—22no—
462C22—22no—
463C22—1224no—
464C22—1224no—
465C22—1224no—
466C22—2444no—
467C22—2444no—
468C22—2444no—
469C22—2444no—
470C22—2442no—
471C22—2442no—
472C22—2442no—
473C22—2442no—
474C22#1683963811yescharacteristic
475C22#99×D6112yes—
476C22#1683975711yescharacteristic
477C22#1683976911yescharacteristic
478C22#1683977712yes—
479C22#1683992111yescharacteristic
480C22#1683992311yescharacteristic
481C22#1684010111yescharacteristic
482C22#1684010211yescharacteristic
483C4—21no—
484C4—21no—
485C4—21no—
486C4—21no—
487C4—82no—
488C4—81no—
489C4—81no—
490C4—4882no—
491C4—4882no—
492C4—2442no—
493C2—21no—
494C2—21no—
495C2—21no—
496C2—21no—
497C2—2444no—
498C2#2144435012yes—
499C2#2144437412yes—
500C2#2144612811yescharacteristic
501C2#2144626411yescharacteristic
502C2#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#9154
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
18. #16839619C4semidirect
246. C2×#328D61semidirect
278. C61#9154semidirect

Maximal subgroups

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

subgroupindex
#214541032
C2×#168396242
#214457282
C2×#168394992
#214436992
#214436982
C2×C61×#3282
#915461