Finite Group Databasebeta

← #29572705

Subgroups — #29572705

Order 15616.

688 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14519739C211yesmaximal, characteristic
2#21445935C211yesmaximal, characteristic, complemented
3C4×#14519706C211yesmaximal, characteristic, complemented
4C2×#16839491C211yesmaximal, characteristic
5C2×#16839489C211yesmaximal, characteristic
6#21443660C211yesmaximal, characteristic, complemented
7C61×#1279C211yesmaximal, characteristic, complemented
8C2×C4×D244C2211yescharacteristic
9C2×#14519739C411yescharacteristic
10C2×#14519739C411yescharacteristic
11C2×C42×D61—21no—
12C2×C4⋊#92418C2211yescharacteristic
13C2×#14519706—21no—
14C2×C4×#92418C2211yescharacteristic
15C4⋊C4×Dic61C411yescharacteristic
16C4⋊C4×Dic61C411yescharacteristic
17C4×#11758198—21no—
18#16839609—21no—
19#16839609—21no—
20C42×Dic61C2211yescharacteristic
21#16839516—21no—
22#16839516—21no—
23#16839516—21no—
24#16839491—22no—
25#16839489—22no—
26C2×C4⋊C8×C61C2211yescharacteristic
27C2×C4×C8×C61C2211yescharacteristic
28C4×C4⋊C4×C61C2211yescharacteristic
29C22×D244C2×C411yescharacteristic
30C22×C4×D61—21no—
31C22×C4×D61—21no—
32C22×C4×D61—21no—
33C22×#92418—21no—
34C22×#92418—21no—
35C4×D244—21no—
36C4×D244—21no—
37C4×D244D412yes—
38C4×D244Q812yes—
39#14519739—22no—
40#14519739—22no—
41#14519739—22no—
42#14519739C814yescomplemented
43C2×C4⋊Dic61C2×C411yescharacteristic
44C2×#11758198—21no—
45C2×#11758198—21no—
46C2×#11758198—21no—
47C2×C4×Dic61—21no—
48C2×C4×Dic61—21no—
49C2×C4×Dic61C2×C411yescharacteristic
50C2×C4×Dic61C2×C411yescharacteristic
51C2×C4×Dic61D411yescharacteristic
52C2×C4×Dic61D411yescharacteristic
53C2×C4×Dic61D411yescharacteristic
54C2×C4×Dic61D411yescharacteristic
55C42×D61—42no—
56C42×D61—42no—
57C4⋊#92418—21no—
58C4⋊#92418—21no—
59#14519706—24no—
60C4×#92418—21no—
61C4×#92418—21no—
62#14519684—21no—
63#14519684—21no—
64C22×C8×C61—21no—
65C22×C8×C61—21no—
66C2×C4⋊C4×C61C2×C411yescharacteristic
67C2×C4⋊C4×C61C2×C411yescharacteristic
68C2×C42×C61—21no—
69C2×C42×C61C2311yescharacteristic
70C4⋊C8×C61—21no—
71C4⋊C8×C61—21no—
72C4×C8×C61—21no—
73C4×C8×C61—21no—
74#95×C61—21no—
75C23×D61—21no—
76C22×C4×C61—21no—
77C22×C4×C61—21no—
78C22×C4×C61C22×C411yescharacteristic
79C22×C4×C61C2×D411yescharacteristic
80C22×C4×C61C2×D411yescharacteristic
81C22×Dic61—21no—
82C22×Dic61C22⋊C411yescharacteristic
83C22×Dic61C22⋊C411yescharacteristic
84C22×Dic61C22⋊C411yescharacteristic
85C22×Dic61C22⋊C411yescharacteristic
86C2×D244—21no—
87C2×D244—21no—
88C2×D244—21no—
89C2×D244C4⋊C412yes—
90C2×D244C2×C812yes—
91C2×D244M1612yes—
92C2×C4×D61—24no—
93C2×C4×D61—22no—
94C2×C4×D61—22no—
95C2×C4×D61—24no—
96C2×C4×D61—42no—
97C2×C4×D61—42no—
98C2×C4×D61—42no—
99C2×C4×D61—41no—
100C2×C4×D61—41no—
101C2×C4×D61—41no—
102C2×C4×D61—41no—
103C2×C4×D61—42no—
104C2×C8×C61—22no—
105C2×C8×C61—41no—
106C2×C8×C61—41no—
107C2×C8×C61—41no—
108C2×C8×C61—41no—
109C2×C8×C61—41no—
110C4⋊C4×C61—21no—
111C4⋊C4×C61—21no—
112C4⋊C4×C61C2×C812yes—
113C4⋊C4×C61M1612yes—
114C42×C61—41no—
115C42×C61—41no—
116C42×C61C2×D411yescharacteristic
117C42×C61C2×Q811yescharacteristic
118C42×C61#4111yescharacteristic
119C42×C61#4111yescharacteristic
120#11758198—24no—
121#11758198—22no—
122#11758198—22no—
123#11758198—24no—
124C4⋊Dic61—21no—
125C4⋊Dic61C4⋊C412yes—
126C4×Dic61—21no—
127C4×Dic61—21no—
128C4×Dic61—21no—
129C4×Dic61—21no—
130C4×Dic61—21no—
131C4×Dic61—21no—
132C4×Dic61—22no—
133C4×Dic61—41no—
134C4×Dic61—42no—
135C4×Dic61—42no—
136C4×Dic61C2×C812yes—
137C4×Dic61M1612yes—
138C2×#92418—22no—
139C2×#92418—41no—
140C2×#92418—41no—
141C2×#92418—41no—
142C2×#92418—41no—
143C2×#92418—41no—
144C23×C61C2×C22⋊C411yescharacteristic
145C22×D61—22no—
146C22×D61—22no—
147C22×D61—22no—
148C22×D61—41no—
149C22×D61—41no—
150C22×D61—41no—
151C22×D61—41no—
152C2×C4×C61—21no—
153C2×C4×C61—21no—
154C2×C4×C61—22no—
155C2×C4×C61—22no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61—41no—
159C2×C4×C61—41no—
160C2×C4×C61C2×C4⋊C411yescharacteristic
161C2×C4×C61#11711yescharacteristic
162C2×C4×C61#12111yescharacteristic
163C2×C4×C61#12111yescharacteristic
164C2×C4×C61C22⋊Q811yescharacteristic
165C2×C4×C61C22⋊Q811yescharacteristic
166C2×C4×C61C22×C811yescharacteristic
167C2×C4×C61C2×M1611yescharacteristic
168C2×C4×C61C2×M1611yescharacteristic
169C2×C4×C61C2×M1611yescharacteristic
170C2×C4×C61#13511yescharacteristic
171C2×C4×C61#13511yescharacteristic
172C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
173C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
174C2×Dic61—21no—
175C2×Dic61—21no—
176C2×Dic61—21no—
177C2×Dic61—21no—
178C2×Dic61—21no—
179C2×Dic61—21no—
180C2×Dic61—22no—
181C2×Dic61—21no—
182C2×Dic61—21no—
183C2×Dic61—21no—
184C2×Dic61—41no—
185C2×Dic61—41no—
186C2×Dic61C22⋊C812yes—
187C2×Dic61C22⋊C812yes—
188C2×Dic61#10412yes—
189D244—22no—
190D244—22no—
191D244—22no—
192D244C4⋊C814yescomplemented
193C4×D61—48no—
194C4×D61—48no—
195C4×D61—42no—
196C4×D61—42no—
197C4×D61—42no—
198C4×D61—42no—
199C8×C61—42no—
200C8×C61—81no—
201#92418—42no—
202#92418—81no—
203#8565—611nomaximal, Sylow
204C22×C61#38011yescharacteristic
205C22×C61C2×C22⋊C811yescharacteristic
206C22×C61#40711yescharacteristic
207C22×C61#41611yescharacteristic
208C22×C61#41811yescharacteristic
209C22×C61C2×#10411yescharacteristic
210C22×C61#42111yescharacteristic
211C2×D61—24no—
212C2×D61—42no—
213C2×D61—42no—
214C2×D61—42no—
215C2×D61—42no—
216C2×D61—42no—
217C2×D61—42no—
218C4×C61—21no—
219C4×C61—21no—
220C4×C61—42no—
221C4×C61—42no—
222C4×C61C2×C4⋊C811yescharacteristic
223C4×C61#42311yescharacteristic
224C4×C61#43111yescharacteristic
225C4×C61#43211yescharacteristic
226C4×C61#46311yescharacteristic
227C4×C61#46311yescharacteristic
228C4×C61#47811yescharacteristic
229C4×C61#47811yescharacteristic
230Dic61—22no—
231Dic61—22no—
232Dic61—22no—
233Dic61—42no—
234Dic61—41no—
235C42×D4—611no—
236#1831—611no—
237C4×C4⋊C8—611no—
238C2×D4⋊C8—611no—
239C2×D4⋊C8—611no—
240#1279—611no—
241#1279D6111yescharacteristic, complemented
242C2×C61#147611yescharacteristic
243C2×C61#147811yescharacteristic
244C2×C61#148811yescharacteristic
245C2×C61#149011yescharacteristic
246C2×C61#179711yescharacteristic
247C2×C61#180411yescharacteristic
248C2×C61#180611yescharacteristic
249D61—44no—
250C2×C4×D4—611no—
251C2×C4×D4—611no—
252C2×C4×D4—611no—
253C22×C42—1221no—
254C2×C4⋊C8—611no—
255C2×C4⋊C8—1221no—
256C2×C4⋊C8C2×D6111yescharacteristic
257C2×C4×C8—611no—
258C2×C4×C8C2×D6111yescharacteristic
259C4×C4⋊C4—611no—
260C4×C4⋊C4—611no—
261C4×C4⋊C4C2×D6111yescharacteristic
262C4×C22⋊C4—1221no—
263C4×C22⋊C4—1221no—
264C4×C22⋊C4—1221no—
265C43—611no—
266#336—1221no—
267#336—1221no—
268#336—1221no—
269D4⋊C8—1222no—
270D4⋊C8—1222no—
271C61#856511yescharacteristic, complemented, Sylow
272C22×D4—611no—
273C23×C4—1221no—
274C23×C4—1221no—
275C23×C4—1221no—
276C22×C8—21no—
277C22×C8—21no—
278C22×C8—1221no—
279C22×C8—1221no—
280C4×D4—614no—
281C4×D4—612no—
282C4×D4—612no—
283C4×D4—1222no—
284C4×D4—1222no—
285C4×D4—1222no—
286C4×D4—1221no—
287C4×D4—1221no—
288C2×C4⋊C4—611no—
289C2×C4⋊C4C4×D6111yescharacteristic
290C2×C4⋊C4C4×D6111yescharacteristic
291C2×C22⋊C4—1221no—
292C2×C22⋊C4—1221no—
293C2×C22⋊C4—1221no—
294C2×C42—21no—
295C2×C42—611no—
296C2×C42—611no—
297C2×C42—611no—
298C2×C42—611no—
299C2×C42—611no—
300C2×C42—611no—
301C2×C42—1221no—
302C2×C42—1221no—
303C2×C42—2442no—
304C2×C42—2442no—
305C2×C42C22×D6111yescharacteristic
306C4⋊C8—21no—
307C4⋊C8—21no—
308C4⋊C8—1224no—
309C4⋊C8—1221no—
310C4⋊C8—1221no—
311C4×C8—21no—
312C4×C8—21no—
313C4×C8—1221no—
314C4×C8—1221no—
315#95—21no—
316#95—1221no—
317#95—1221no—
318C24—1221no—
319C2×D4—612no—
320C2×D4—612no—
321C2×D4—612no—
322C2×D4—1221no—
323C2×D4—1221no—
324C2×D4—1221no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—611no—
328C22×C4—611no—
329C22×C4—611no—
330C22×C4—611no—
331C22×C4—1224no—
332C22×C4—1224no—
333C22×C4—1221no—
334C22×C4—1222no—
335C22×C4—1222no—
336C22×C4—2442no—
337C22×C4—2442no—
338C22×C4—2442no—
339C22×C4—2442no—
340C22×C4—2441no—
341C22×C4—2441no—
342C22×C4—2441no—
343C22×C4—2441no—
344C22×C4C2×C4×D6111yescharacteristic
345C22×C4D4×D6111yescharacteristic
346C22×C4D4×D6111yescharacteristic
347C2×C8—22no—
348C2×C8—41no—
349C2×C8—41no—
350C2×C8—41no—
351C2×C8—41no—
352C2×C8—41no—
353C2×C8—1222no—
354C2×C8—2441no—
355C2×C8—2441no—
356C2×C8—2441no—
357C2×C8—2441no—
358C2×C8—2441no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—612no—
362C4⋊C4—1221no—
363C4⋊C4C8×D6112yes—
364C4⋊C4#1175818912yes—
365C22⋊C4—1224no—
366C22⋊C4—1224no—
367C22⋊C4—1222no—
368C22⋊C4—1222no—
369C42—41no—
370C42—41no—
371C42—612no—
372C42—612no—
373C42—1222no—
374C42—1221no—
375C42—1221no—
376C42—1221no—
377C42—1221no—
378C42—1221no—
379C42—1221no—
380C42—2441no—
381C42—2442no—
382C42—2442no—
383C42#1175822211yescharacteristic
384C42#1175822211yescharacteristic
385C42D4×D6111yescharacteristic
386C42Q8×D6111yescharacteristic
387C23—1222no—
388C23—1222no—
389C23—1222no—
390C23—2441no—
391C23—2441no—
392C23—2441no—
393C23—2441no—
394C23C22⋊C4×D6111yescharacteristic
395D4—614no—
396D4—1222no—
397D4—1222no—
398D4—1222no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—612no—
408C2×C4—612no—
409C2×C4—612no—
410C2×C4—1221no—
411C2×C4—1221no—
412C2×C4—1221no—
413C2×C4—1221no—
414C2×C4—1221no—
415C2×C4—1221no—
416C2×C4—1221no—
417C2×C4—1221no—
418C2×C4—1221no—
419C2×C4—1222no—
420C2×C4—2448no—
421C2×C4—2448no—
422C2×C4—2441no—
423C2×C4—2441no—
424C2×C4—2442no—
425C2×C4—2442no—
426C2×C4—2442no—
427C2×C4—2442no—
428C2×C4C4⋊C4×D6111yescharacteristic
429C2×C4#1451973411yescharacteristic
430C2×C4#1451975011yescharacteristic
431C2×C4#1451975011yescharacteristic
432C2×C4#1451975511yescharacteristic
433C2×C4#1451975511yescharacteristic
434C2×C4C2×C8×D6111yescharacteristic
435C2×C4M16×D6111yescharacteristic
436C2×C4M16×D6111yescharacteristic
437C2×C4C2×#1175818911yescharacteristic
438C2×C4#1451979811yescharacteristic
439C2×C4#1451980011yescharacteristic
440C2×C4#1451980111yescharacteristic
441C2×C4#1451980411yescharacteristic
442C8—42no—
443C8—81no—
444C8—4881no—
445C8—2442no—
446C22—1224no—
447C22—2442no—
448C22—2442no—
449C22—2442no—
450C22—2442no—
451C22—2442no—
452C22—2442no—
453C22#1683962111yescharacteristic
454C22C22⋊C8×D6111yescharacteristic
455C22#1683972411yescharacteristic
456C22#1683975711yescharacteristic
457C22#1683976511yescharacteristic
458C22#104×D6111yescharacteristic
459C22#1683977711yescharacteristic
460C4—21no—
461C4—21no—
462C4—42no—
463C4—42no—
464C4—1222no—
465C4—1222no—
466C4—1222no—
467C4—2441no—
468C4—2442no—
469C4C4⋊C8×D6111yescharacteristic
470C4#1683978411yescharacteristic
471C4#1683981311yescharacteristic
472C4#1683981711yescharacteristic
473C4#1683997611yescharacteristic
474C4#1683998011yescharacteristic
475C4#1684006111yescharacteristic
476C4#1684006511yescharacteristic
477C2—2444no—
478C2#2144420011yescharacteristic
479C2#2144420811yescharacteristic
480C2#2144425211yescharacteristic
481C2#2144426011yescharacteristic
482C2#2144579811yescharacteristic
483C2#2144582811yescharacteristic
484C2#2144583811yescharacteristic
subgroupG/H
centerC22×C4D4×D61
commutatorC2×C4×C61C22×C8
FrattiniC2×C42C22×D61
FittingC61×#1279C2
socleC23×C61C2×C22⋊C4
prime radicalC22×D244C2×C4
cosocleC2×C42×C61C23
hypercenter#1279D61
hypocenterC61#8565
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
2. #21445935C2semidirect
3. C4×#14519706C2semidirect
6. #21443660C2semidirect
7. C61×#1279C2semidirect
42. #14519739C8semidirect
192. D244C4⋊C8semidirect
241. #1279D61semidirect
271. C61#8565semidirect

Maximal subgroups

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

subgroupindex
C4×#145197392
#214459352
C4×#145197062
C2×#168394912
C2×#168394892
#214436602
C61×#12792
#856561