Finite Group Databasebeta

← #29574698

Subgroups — #29574698

Order 15616.

934 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14519745C211yesmaximal, characteristic
2#21445728C212yesmaximal, complemented
3#21444137C211yesmaximal, characteristic, complemented
4#21443666C212yesmaximal, complemented
5C61×#2972C211yesmaximal, characteristic, complemented
6C23×C4×D61C2211yescharacteristic
7C2×#14519745C411yescharacteristic
8C2×C4×C22⋊D61—21no—
9C2×C22⋊#92418C2212yes—
10C2×#14519689—24no—
11#16839642C411yescharacteristic
12#16839638—21no—
13#16839634C411yescharacteristic
14#16839633—21no—
15#16839617C411yescharacteristic
16C4×#11758198—21no—
17C4×C22⋊Dic61C2211yescharacteristic
18#16839488—21no—
19#16839486—21no—
20C2×C4×D4×C61C2211yescharacteristic
21C8×D4×C61—24no—
22C61×#431—21no—
23C2×C22⋊C8×C61—21no—
24C2×C22⋊C8×C61C2212yes—
25C24×D61C2×C411yescharacteristic
26C22×C22⋊D61—21no—
27C23×Dic61C2×C411yescharacteristic
28C22×C4×D61—21no—
29C22×C4×D61—22no—
30C22×C4×D61—21no—
31C22×C4×D61—22no—
32C22×C4×D61—44no—
33C22×#92418—22no—
34#14519745—22no—
35#14519745C814yescomplemented
36C4×C22⋊D61—44no—
37C2×#11758196—21no—
38C2×C22⋊Dic61—21no—
39C2×C22⋊Dic61C2×C411yescharacteristic
40C2×C22⋊Dic61C2×C411yescharacteristic
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×C4×Dic61—21no—
45C22⋊#92418—22no—
46C22⋊#92418—22no—
47#14519689—48no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51C22×D4×C61C2×C411yescharacteristic
52C23×C4×C61D411yescharacteristic
53C23×C4×C61C2311yescharacteristic
54C22×C8×C61—22no—
55C22×C8×C61D414yescomplemented
56C4×D4×C61—22no—
57C4×D4×C61—22no—
58C2×C4⋊C4×C61D411yescharacteristic
59C2×C22⋊C4×C61C2×C411yescharacteristic
60C2×C22⋊C4×C61D411yescharacteristic
61C2×C42×C61D411yescharacteristic
62C4⋊C8×C61—22no—
63C22⋊C8×C61—22no—
64C22⋊C8×C61—22no—
65C22⋊C8×C61—22no—
66C4×C8×C61—22no—
67C24×C61C22⋊C411yescharacteristic
68C24×C61C22×C411yescharacteristic
69C23×D61—21no—
70C23×D61—22no—
71C23×D61—21no—
72C23×D61—22no—
73C23×D61—42no—
74C23×D61—42no—
75C23×D61C2×C812yescomplemented
76C2×D4×C61—22no—
77C2×D4×C61—22no—
78C2×D4×C61C2×C812yes—
79C2×D4×C61M1612yes—
80C22×C4×C61—21no—
81C22×C4×C61—21no—
82C22×C4×C61—42no—
83C22×C4×C61—42no—
84C22×C4×C61C22⋊C411yescharacteristic
85C22×C4×C61C22⋊C411yescharacteristic
86C22×C4×C61C22⋊C411yescharacteristic
87C22×C4×C61C2×D412yes—
88C22×C4×C61C2×D411yescharacteristic
89C22×C4×C61C2×D411yescharacteristic
90C22×C4×C61#4112yes—
91C2×C22⋊D61—24no—
92C2×C22⋊D61—42no—
93C2×C22⋊D61—42no—
94C22×Dic61—21no—
95C22×Dic61—21no—
96C22×Dic61—22no—
97C22×Dic61—21no—
98C22×Dic61—42no—
99C2×C4×D61—28no—
100C2×C4×D61—24no—
101C2×C4×D61—42no—
102C2×C4×D61—44no—
103C2×C4×D61—44no—
104C2×C4×D61—42no—
105C2×C4×D61—42no—
106C2×C4×D61—44no—
107C2×C4×D61—41no—
108C2×C4×D61—42no—
109C2×C4×D61—41no—
110C2×C8×C61—24no—
111C2×C8×C61—44no—
112C2×C8×C61—82no—
113C4⋊C4×C61—22no—
114C22⋊C4×C61—22no—
115C22⋊C4×C61—22no—
116C42×C61—21no—
117C42×C61—21no—
118C22⋊Dic61—21no—
119C22⋊Dic61—22no—
120C22⋊Dic61—42no—
121C22⋊Dic61C2×C812yescomplemented
122#11758198—24no—
123#11758198—42no—
124#11758198—42no—
125#11758196—42no—
126C4×Dic61—42no—
127C2×#92418—44no—
128C2×#92418—42no—
129C23×C61—21no—
130C23×C61—21no—
131C23×C61—41no—
132C23×C61—41no—
133C23×C61—41no—
134C23×C61—41no—
135C23×C61C22⋊C812yescomplemented
136C23×C61C2×C22⋊C411yescharacteristic
137C23×C61C4×D412yes—
138C23×C61C22×C811yescharacteristic
139C23×C61C2×M1611yescharacteristic
140C23×C61#13112yes—
141C22×D61—22no—
142C22×D61—22no—
143C22×D61—24no—
144C22×D61—24no—
145C22×D61—22no—
146C22×D61—24no—
147C22×D61—44no—
148C22×D61—44no—
149C22×D61—48no—
150C22×D61—41no—
151C22×D61—42no—
152C22×D61—41no—
153C22×D61—42no—
154C22×D61—41no—
155C22×D61—41no—
156C22×D61—42no—
157D4×C61—24no—
158D4×C61—24no—
159C2×C4×C61—21no—
160C2×C4×C61—21no—
161C2×C4×C61—24no—
162C2×C4×C61—22no—
163C2×C4×C61—21no—
164C2×C4×C61—21no—
165C2×C4×C61—41no—
166C2×C4×C61—42no—
167C2×C4×C61—42no—
168C2×C4×C61—41no—
169C2×C4×C61—41no—
170C2×C4×C61—81no—
171C2×C4×C61C22⋊C812yescomplemented
172C2×C4×C61#12011yescharacteristic
173C2×C4×C61#12112yes—
174C2×C4×C61#12311yescharacteristic
175C22⋊D61—48no—
176C2×Dic61—22no—
177C2×Dic61—24no—
178C2×Dic61—22no—
179C2×Dic61—41no—
180C2×Dic61—41no—
181C2×Dic61—42no—
182C2×Dic61—41no—
183C2×Dic61—41no—
184C2×Dic61—41no—
185C2×Dic61—41no—
186C2×Dic61—41no—
187C4×D61—48no—
188C4×D61—44no—
189C4×D61—44no—
190C8×C61—44no—
191#92418—82no—
192#8965—611nomaximal, Sylow
193C22×C61—21no—
194C22×C61—22no—
195C22×C61—21no—
196C22×C61—22no—
197C22×C61—22no—
198C22×C61—41no—
199C22×C61—41no—
200C22×C61—42no—
201C22×C61—42no—
202C22×C61—41no—
203C22×C61—41no—
204C22×C61—81no—
205C22×C61#38611yescharacteristic
206C22×C61C2×C22⋊C811yescharacteristic
207C22×C61#40811yescharacteristic
208C22×C61C8×D412yes—
209C22×C61#43512yes—
210C2×D61—24no—
211C2×D61—28no—
212C2×D61—42no—
213C2×D61—42no—
214C2×D61—42no—
215C2×D61—44no—
216C2×D61—44no—
217C2×D61—44no—
218C2×D61—42no—
219C2×D61—42no—
220C2×D61—42no—
221C4×C61—22no—
222C4×C61—22no—
223C4×C61—21no—
224C4×C61—41no—
225C4×C61—41no—
226C4×C61B(4,𝔽2)12yes—
227Dic61—42no—
228Dic61—42no—
229Dic61—81no—
230#2972D6111yescharacteristic, complemented
231C4×#120—611no—
232#1779—612no—
233#1459—611no—
234#1282—612no—
235C2×C61—21no—
236C2×C61—21no—
237C2×C61—22no—
238C2×C61—22no—
239C2×C61—42no—
240C2×C61#186911yescharacteristic
241C2×C61#188911yescharacteristic
242C2×C61#189111yescharacteristic
243D61—44no—
244C24×C4—611no—
245C2×#120—611no—
246C2×C4×D4—1221no—
247C2×C4×D4C2×D6111yescharacteristic
248C8×D4—24no—
249#431—21no—
250C2×C22⋊C8—21no—
251C2×C22⋊C8—612no—
252C2×C22⋊C8—1224no—
253C2×C22⋊C8C2×D6112yes—
254#386—611no—
255#386—1221no—
256#385—611no—
257#385—1221no—
258#379—611no—
259C4×C22⋊C4—611no—
260C4×C22⋊C4—1221no—
261#324—1221no—
262#323—1221no—
263C61#896511yescharacteristic, complemented, Sylow
264C25—611no—
265C22×D4—1221no—
266C22×D4C4×D6111yescharacteristic
267C23×C4—611no—
268C23×C4—1221no—
269C23×C4—1222no—
270C23×C4—1221no—
271C23×C4—1222no—
272C23×C4—2444no—
273C23×C4C22⋊D6111yescharacteristic
274C23×C4C22×D6111yescharacteristic
275C22×C8—22no—
276C22×C8—1222no—
277C22×C8C22⋊D6114yescomplemented
278#120—614no—
279#120—1222no—
280C4×D4—22no—
281C4×D4—22no—
282C4×D4—2444no—
283C2×C4⋊C4—1221no—
284C2×C4⋊C4D24411yescharacteristic
285C2×C22⋊C4—611no—
286C2×C22⋊C4—611no—
287C2×C22⋊C4—1221no—
288C2×C22⋊C4—1221no—
289C2×C22⋊C4—1221no—
290C2×C22⋊C4—1221no—
291C2×C22⋊C4C4×D6111yescharacteristic
292C2×C22⋊C4D24411yescharacteristic
293C2×C42—1221no—
294C2×C42C22⋊D6111yescharacteristic
295C4⋊C8—22no—
296C22⋊C8—22no—
297C22⋊C8—22no—
298C22⋊C8—22no—
299C22⋊C8—1222no—
300C22⋊C8—1222no—
301C22⋊C8—2448no—
302C4×C8—22no—
303#95—1221no—
304#95—1221no—
305#95—1221no—
306C24—612no—
307C24—1221no—
308C24—1222no—
309C24—1221no—
310C24—1222no—
311C24—2442no—
312C24—2442no—
313C24#1175819811yescharacteristic
314C24C2×C4×D6111yescharacteristic
315C2×D4—22no—
316C2×D4—22no—
317C2×D4—1224no—
318C2×D4—2442no—
319C2×D4—2442no—
320C2×D4C8×D6112yes—
321C2×D4#1175818912yes—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—42no—
325C22×C4—42no—
326C22×C4—1228no—
327C22×C4—1224no—
328C22×C4—1221no—
329C22×C4—1221no—
330C22×C4—1222no—
331C22×C4—1221no—
332C22×C4—2442no—
333C22×C4—2444no—
334C22×C4—2442no—
335C22×C4—2444no—
336C22×C4—2442no—
337C22×C4—2444no—
338C22×C4—2442no—
339C22×C4—2441no—
340C22×C4—2442no—
341C22×C4—2441no—
342C22×C4#1175819811yescharacteristic
343C22×C4#1175819811yescharacteristic
344C22×C4#1175819811yescharacteristic
345C22×C4C2×D24411yescharacteristic
346C22×C4#1175822212yes—
347C22×C4C2×C22⋊D6112yes—
348C22×C4C2×C22⋊D6111yescharacteristic
349C2×C8—24no—
350C2×C8—44no—
351C2×C8—82no—
352C2×C8—2444no—
353C2×C8—2442no—
354C4⋊C4—22no—
355C4⋊C4—2442no—
356C22⋊C4—22no—
357C22⋊C4—22no—
358C22⋊C4—612no—
359C22⋊C4—1221no—
360C22⋊C4—1224no—
361C22⋊C4—1222no—
362C22⋊C4—2442no—
363C22⋊C4—2442no—
364C22⋊C4—2442no—
365C42—21no—
366C42—21no—
367C42—2442no—
368C23—21no—
369C23—21no—
370C23—41no—
371C23—41no—
372C23—41no—
373C23—41no—
374C23—1222no—
375C23—1222no—
376C23—1224no—
377C23—1224no—
378C23—1222no—
379C23—1224no—
380C23—2441no—
381C23—2442no—
382C23—2441no—
383C23—2442no—
384C23—2444no—
385C23—2444no—
386C23—2448no—
387C23—2441no—
388C23—2442no—
389C23—2441no—
390C23#1451968912yescomplemented
391C23C2×#1175819811yescharacteristic
392C23C4×C22⋊D6112yes—
393C23C2×C8×D6111yescharacteristic
394C23C2×#1175818911yescharacteristic
395C23#1451978312yes—
396D4—24no—
397D4—24no—
398D4—2448no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—22no—
402C2×C4—24no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—41no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—81no—
411C2×C4—1222no—
412C2×C4—1224no—
413C2×C4—1222no—
414C2×C4—2448no—
415C2×C4—2444no—
416C2×C4—2441no—
417C2×C4—2441no—
418C2×C4—2441no—
419C2×C4—2441no—
420C2×C4—2441no—
421C2×C4—2442no—
422C2×C4—2441no—
423C2×C4—2441no—
424C2×C4—2444no—
425C2×C4#1451968912yescomplemented
426C2×C4#1451974611yescharacteristic
427C2×C4#1451975112yes—
428C2×C4#1451976011yescharacteristic
429C8—44no—
430C8—4882no—
431C22—21no—
432C22—22no—
433C22—21no—
434C22—22no—
435C22—22no—
436C22—41no—
437C22—41no—
438C22—42no—
439C22—42no—
440C22—41no—
441C22—41no—
442C22—81no—
443C22—1224no—
444C22—1228no—
445C22—2442no—
446C22—2442no—
447C22—2442no—
448C22—2444no—
449C22—2444no—
450C22—2444no—
451C22—2442no—
452C22—2442no—
453C22—2442no—
454C22#1683964111yescharacteristic
455C22C2×#1451968911yescharacteristic
456C22#1683972811yescharacteristic
457C22C8×C22⋊D6112yes—
458C22#1683983312yes—
459C4—22no—
460C4—21no—
461C4—22no—
462C4—41no—
463C4—41no—
464C4—4881no—
465C4—2442no—
466C4—2442no—
467C4#1683994912yes—
468C2—21no—
469C2—21no—
470C2—22no—
471C2—22no—
472C2—42no—
473C2—2444no—
474C2#2144611111yescharacteristic
475C2#2144622711yescharacteristic
476C2#2144623711yescharacteristic
subgroupG/H
centerC2×C4#14519746
commutatorC23×C61C22×C8
FrattiniC23×C4C22×D61
FittingC61×#2972C2
socleC22×C61#386
prime radicalC2×#14519745C4
cosocleC23×C4×C61C23
hypercenter#2972D61
hypocenterC61#8965
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #2972

Complements

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

NH ≅ G/Ntype
2. #21445728C2semidirect
3. #21444137C2semidirect
4. #21443666C2semidirect
5. C61×#2972C2semidirect
35. #14519745C8semidirect
55. C22×C8×C61D4semidirect
75. C23×D61C2×C8semidirect
121. C22⋊Dic61C2×C8semidirect
135. C23×C61C22⋊C8semidirect
171. C2×C4×C61C22⋊C8semidirect
230. #2972D61semidirect
263. C61#8965semidirect
277. C22×C8C22⋊D61semidirect
390. C23#14519689semidirect
425. C2×C4#14519689semidirect

Maximal subgroups

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

subgroupindex
C4×#145197452
#214457282
#214441372
#214436662
C61×#29722
#896561