Finite Group Databasebeta

← #29573341

Subgroups — #29573341

Order 15616.

898 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
1C2×#16839609C211yesmaximal, characteristic
2#21445728C212yesmaximal
3#21443662C211yesmaximal, characteristic, complemented
4#21443661C212yesmaximal, complemented
5C61×#1280C211yesmaximal, characteristic, complemented
6C23×C4×D61C2211yescharacteristic
7C22×#11758198C411yescharacteristic
8C22×#11758198C411yescharacteristic
9C22×C4×Dic61C411yescharacteristic
10C22×C4×Dic61C411yescharacteristic
11C2×C22⋊#92418C2212yes—
12C2×#14519689—22no—
13C2×#14519689—22no—
14#16839609—22no—
15#16839609—22no—
16C2×#14519684C2211yescharacteristic
17C2×C22⋊C8×C61C2212yes—
18C2×#95×C61C2211yescharacteristic
19C24×D61C2×C411yescharacteristic
20C23×Dic61C2×C411yescharacteristic
21C23×Dic61C2×C411yescharacteristic
22C23×Dic61C2×C411yescharacteristic
23C22×C4×D61—22no—
24C22×C4×D61—21no—
25C22×C4×D61—21no—
26C22×C4×D61—42no—
27C22×C4×D61—42no—
28C22×C4×D61D412yes—
29C22×C4×D61D412yes—
30C22×#92418—22no—
31C2×#11758198—22no—
32C2×#11758198—22no—
33C2×#11758198—22no—
34C2×#11758198—22no—
35C2×#11758198—22no—
36C2×#11758198C814yescomplemented
37C2×C4×Dic61—21no—
38C2×C4×Dic61—21no—
39C2×C4×Dic61—21no—
40C2×C4×Dic61—21no—
41C2×C4×Dic61—42no—
42C2×C4×Dic61—42no—
43C22⋊#92418—22no—
44C22⋊#92418—22no—
45#14519689—44no—
46#14519689—44no—
47#14519684—22no—
48C23×C4×C61C2×C411yescharacteristic
49C23×C4×C61C2×C411yescharacteristic
50C23×C4×C61C2311yescharacteristic
51C22×C8×C61—22no—
52C22⋊C8×C61—22no—
53C22⋊C8×C61—22no—
54#95×C61—22no—
55C24×C61C22×C411yescharacteristic
56C23×D61—21no—
57C23×D61—21no—
58C23×D61—21no—
59C23×D61—21no—
60C23×D61—41no—
61C23×D61—41no—
62C23×D61—41no—
63C23×D61—41no—
64C23×D61C22⋊C412yes—
65C23×D61C2×C812yes—
66C23×D61M1612yes—
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61—41no—
72C22×C4×C61—41no—
73C22×C4×C61—41no—
74C22×C4×C61—41no—
75C22×C4×C61—41no—
76C22×C4×C61—41no—
77C22×C4×C61C2×C812yes—
78C22×C4×C61M1612yes—
79C22×C4×C61C2×D412yes—
80C22×C4×C61#4112yes—
81C22×C4×C61#4111yescharacteristic
82C22×C4×C61#4111yescharacteristic
83C22×Dic61—21no—
84C22×Dic61—21no—
85C22×Dic61—22no—
86C22×Dic61—22no—
87C22×Dic61—21no—
88C22×Dic61—21no—
89C22×Dic61—21no—
90C22×Dic61—21no—
91C22×Dic61—41no—
92C22×Dic61—41no—
93C22×Dic61—41no—
94C22×Dic61—41no—
95C22×Dic61C22⋊C411yescharacteristic
96C22×Dic61C22⋊C411yescharacteristic
97C22×Dic61C2×C812yes—
98C22×Dic61M1612yes—
99C2×C4×D61—22no—
100C2×C4×D61—22no—
101C2×C4×D61—22no—
102C2×C4×D61—22no—
103C2×C4×D61—24no—
104C2×C4×D61—24no—
105C2×C4×D61—42no—
106C2×C4×D61—42no—
107C2×C4×D61—44no—
108C2×C4×D61—48no—
109C2×C4×D61—44no—
110C2×C8×C61—42no—
111C2×C8×C61—42no—
112C2×C8×C61—42no—
113#11758198—28no—
114#11758198—28no—
115C4×Dic61—42no—
116C4×Dic61—42no—
117C4×Dic61—42no—
118C4×Dic61—42no—
119C2×#92418—42no—
120C2×#92418—42no—
121C2×#92418—42no—
122C23×C61—21no—
123C23×C61—21no—
124C23×C61—21no—
125C23×C61—21no—
126C23×C61C2×C22⋊C411yescharacteristic
127C23×C61#11711yescharacteristic
128C23×C61#11711yescharacteristic
129C23×C61C22×C811yescharacteristic
130C23×C61C2×M1611yescharacteristic
131C23×C61C2×M1611yescharacteristic
132C23×C61C2×M1611yescharacteristic
133C22×D61—22no—
134C22×D61—22no—
135C22×D61—22no—
136C22×D61—22no—
137C22×D61—22no—
138C22×D61—22no—
139C22×D61—22no—
140C22×D61—22no—
141C22×D61—22no—
142C22×D61—22no—
143C22×D61—42no—
144C22×D61—42no—
145C22×D61—42no—
146C22×D61—42no—
147C22×D61—42no—
148C22×D61—42no—
149C22×D61—42no—
150C22×D61—42no—
151C22×D61—42no—
152C22×D61—42no—
153C22×D61—42no—
154C22×D61—42no—
155C22×D61C22⋊C814yes—
156C2×C4×C61—22no—
157C2×C4×C61—22no—
158C2×C4×C61—22no—
159C2×C4×C61—22no—
160C2×C4×C61—41no—
161C2×C4×C61—42no—
162C2×C4×C61—41no—
163C2×C4×C61—42no—
164C2×C4×C61—42no—
165C2×C4×C61—41no—
166C2×C4×C61—41no—
167C2×C4×C61—41no—
168C2×C4×C61—41no—
169C2×C4×C61—42no—
170C2×C4×C61—42no—
171C2×C4×C61#12312yes—
172C2×C4×C61#12312yes—
173C2×Dic61—24no—
174C2×Dic61—24no—
175C2×Dic61—21no—
176C2×Dic61—21no—
177C2×Dic61—21no—
178C2×Dic61—21no—
179C2×Dic61—22no—
180C2×Dic61—22no—
181C2×Dic61—42no—
182C2×Dic61—42no—
183C2×Dic61—41no—
184C2×Dic61—41no—
185C2×Dic61—41no—
186C2×Dic61—41no—
187C2×Dic61—42no—
188C2×Dic61—42no—
189C2×Dic61#9912yes—
190C2×Dic61#9912yes—
191C4×D61—44no—
192C4×D61—44no—
193C4×D61—44no—
194C4×D61—44no—
195C8×C61—82no—
196#92418—82no—
197#8700—611nomaximal, Sylow
198C22×C61—21no—
199C22×C61—21no—
200C22×C61—21no—
201C22×C61—21no—
202C22×C61—21no—
203C22×C61—21no—
204C22×C61—21no—
205C22×C61—21no—
206C22×C61—21no—
207C22×C61—21no—
208C22×C61—21no—
209C22×C61—21no—
210C22×C61#38111yescharacteristic
211C22×C61C2×C22⋊C811yescharacteristic
212C22×C61#40711yescharacteristic
213C22×C61C2×#9911yescharacteristic
214C22×C61C2×#9911yescharacteristic
215C22×C61#41311yescharacteristic
216C22×C61#41311yescharacteristic
217C22×C61#43111yescharacteristic
218C22×C61#43111yescharacteristic
219C22×C61#43211yescharacteristic
220C22×C61#43211yescharacteristic
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—22no—
233C4×C61—22no—
234C4×C61—42no—
235C4×C61—42no—
236Dic61—22no—
237Dic61—22no—
238Dic61—42no—
239Dic61—42no—
240C2×C4×C22⋊C4—611no—
241#1779—612no—
242#1280—612no—
243#1280—611no—
244#1280D6111yescharacteristic, complemented
245C2×C61—21no—
246C2×C61—21no—
247C2×C61—21no—
248C2×C61—21no—
249C2×C61#145911yescharacteristic
250C2×C61#145911yescharacteristic
251C2×C61#146511yescharacteristic
252C2×C61#146511yescharacteristic
253C2×C61#181711yescharacteristic
254C2×C61#181911yescharacteristic
255C2×C61#182211yescharacteristic
256D61—44no—
257C24×C4—611no—
258C22×C22⋊C4—611no—
259C22×C22⋊C4—611no—
260C22×C42—611no—
261C22×C42—611no—
262C2×C22⋊C8—612no—
263C2×C22⋊C8—1222no—
264C2×C22⋊C8—1222no—
265C2×C22⋊C8C2×D6112yes—
266C4×C22⋊C4—1222no—
267C4×C22⋊C4—1222no—
268C2×#95—611no—
269C2×#95C2×D6111yescharacteristic
270C61#870011yescharacteristic, complemented, Sylow
271C25—611no—
272C23×C4—611no—
273C23×C4—611no—
274C23×C4—611no—
275C23×C4—612no—
276C23×C4—612no—
277C23×C4—1222no—
278C23×C4—1221no—
279C23×C4—1221no—
280C23×C4—2442no—
281C23×C4—2442no—
282C23×C4C4×D6111yescharacteristic
283C23×C4C4×D6111yescharacteristic
284C23×C4C22×D6111yescharacteristic
285C22×C8—22no—
286C22×C8—1222no—
287C2×C22⋊C4—614no—
288C2×C22⋊C4—1222no—
289C2×C22⋊C4—1222no—
290C2×C22⋊C4—1222no—
291C2×C22⋊C4—1222no—
292C2×C22⋊C4—1222no—
293C2×C42—1221no—
294C2×C42—1221no—
295C2×C42—1221no—
296C2×C42—1221no—
297C2×C42—2442no—
298C2×C42—2442no—
299C22⋊C8—22no—
300C22⋊C8—22no—
301C22⋊C8—1222no—
302C22⋊C8—1222no—
303C22⋊C8—2444no—
304C22⋊C8—2444no—
305#95—22no—
306#95—1222no—
307C24—612no—
308C24—612no—
309C24—612no—
310C24—1221no—
311C24—1221no—
312C24—1221no—
313C24—1221no—
314C24—2441no—
315C24—2441no—
316C24—2441no—
317C24—2441no—
318C24C2×C4×D6111yescharacteristic
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—611no—
330C22×C4—611no—
331C22×C4—612no—
332C22×C4—612no—
333C22×C4—1224no—
334C22×C4—1224no—
335C22×C4—1222no—
336C22×C4—1222no—
337C22×C4—1221no—
338C22×C4—1221no—
339C22×C4—1221no—
340C22×C4—1221no—
341C22×C4—1221no—
342C22×C4—1221no—
343C22×C4—1222no—
344C22×C4—1222no—
345C22×C4—1222no—
346C22×C4—1222no—
347C22×C4—2442no—
348C22×C4—2442no—
349C22×C4—2448no—
350C22×C4—2444no—
351C22×C4—2444no—
352C22×C4—2441no—
353C22×C4—2441no—
354C22×C4—2441no—
355C22×C4—2441no—
356C22×C4C8×D6112yes—
357C22×C4#1175818912yes—
358C22×C4#1175822212yes—
359C22×C4D4×D6112yes—
360C22×C4#1175822411yescharacteristic
361C22×C4#1175822611yescharacteristic
362C2×C8—42no—
363C2×C8—42no—
364C2×C8—42no—
365C2×C8—2442no—
366C2×C8—2442no—
367C2×C8—2442no—
368C22⋊C4—1228no—
369C22⋊C4—1228no—
370C42—2442no—
371C42—2442no—
372C42—2442no—
373C42—2442no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—21no—
378C23—614no—
379C23—1222no—
380C23—1222no—
381C23—1222no—
382C23—1222no—
383C23—1222no—
384C23—1222no—
385C23—1222no—
386C23—1222no—
387C23—1222no—
388C23—1222no—
389C23—2442no—
390C23—2442no—
391C23—2442no—
392C23—2442no—
393C23—2442no—
394C23—2442no—
395C23—2442no—
396C23—2442no—
397C23—2442no—
398C23—2442no—
399C23—2442no—
400C23—2442no—
401C23C22⋊C4×D6111yescharacteristic
402C23#1451973411yescharacteristic
403C23#1451973511yescharacteristic
404C23C2×C8×D6111yescharacteristic
405C23M16×D6111yescharacteristic
406C23M16×D6111yescharacteristic
407C23C2×#1175818911yescharacteristic
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—42no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—612no—
424C2×C4—612no—
425C2×C4—1224no—
426C2×C4—1224no—
427C2×C4—1221no—
428C2×C4—1221no—
429C2×C4—1221no—
430C2×C4—1221no—
431C2×C4—1222no—
432C2×C4—1222no—
433C2×C4—2444no—
434C2×C4—2444no—
435C2×C4—2444no—
436C2×C4—2444no—
437C2×C4—2442no—
438C2×C4—2442no—
439C2×C4—2441no—
440C2×C4—2441no—
441C2×C4—2441no—
442C2×C4—2441no—
443C2×C4—2442no—
444C2×C4—2442no—
445C2×C4#1451975912yes—
446C2×C4#1451976212yes—
447C8—82no—
448C8—4882no—
449C22—21no—
450C22—21no—
451C22—21no—
452C22—21no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—1224no—
462C22—1224no—
463C22—1224no—
464C22—2444no—
465C22—2444no—
466C22—2444no—
467C22—2444no—
468C22—2442no—
469C22—2442no—
470C22—2442no—
471C22—2442no—
472C22#1683962411yescharacteristic
473C22C22⋊C8×D6111yescharacteristic
474C22#1683972411yescharacteristic
475C22#99×D6111yescharacteristic
476C22#99×D6111yescharacteristic
477C22#1683974311yescharacteristic
478C22#1683974511yescharacteristic
479C22#1683981311yescharacteristic
480C22#1683981411yescharacteristic
481C22#1683981711yescharacteristic
482C22#1683981811yescharacteristic
483C4—22no—
484C4—22no—
485C4—42no—
486C4—42no—
487C4—1222no—
488C4—1222no—
489C4—2442no—
490C4—2442no—
491C2—21no—
492C2—21no—
493C2—21no—
494C2—21no—
495C2—2444no—
496C2#2144413411yescharacteristic
497C2#2144413611yescharacteristic
498C2#2144415411yescharacteristic
499C2#2144415611yescharacteristic
500C2#2144588611yescharacteristic
501C2#2144589211yescharacteristic
502C2#2144590111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC23×C61C22×C8
FrattiniC23×C4C22×D61
FittingC61×#1280C2
socleC23×C61C2×C22⋊C4
prime radicalC24×D61C2×C4
cosocleC23×C4×C61C23
hypercenter#1280D61
hypocenterC61#8700
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

Complements

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

NH ≅ G/Ntype
3. #21443662C2semidirect
4. #21443661C2semidirect
5. C61×#1280C2semidirect
36. C2×#11758198C8semidirect
244. #1280D61semidirect
270. C61#8700semidirect

Maximal subgroups

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

subgroupindex
C2×#168396092
#214457282
#214436622
#214436612
C61×#12802
#870061