Finite Group Databasebeta

← #29595480

Subgroups — #29595480

Order 15616.

1160 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 1160 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840269C211yesmaximal, characteristic
2C2×#16839551C212yesmaximal, complemented
3C2×#16839548C212yesmaximal, complemented
4#21445747C211yesmaximal, characteristic, complemented
5C61×#1782C211yesmaximal, characteristic, complemented
6C23×C4×D61C411yescharacteristic, complemented
7#16840269—24no—
8#16840269—24no—
9C2×#14519758C411yescharacteristic, complemented
10C2×#14519758C2211yescharacteristic
11C2×#14519753—21no—
12C2×#14519748—21no—
13C2×#14519745C411yescharacteristic, complemented
14C2×#14519745C2211yescharacteristic
15C2×C4×C22⋊D61—21no—
16C2×C4×C22⋊D61—21no—
17C2×#14519736C411yescharacteristic, complemented
18C2×#14519696—21no—
19C2×#14519694C2212yes—
20#16839726—21no—
21#16839551—24no—
22#16839548—24no—
23C22×#41×C61C2211yescharacteristic
24C2×#99×C61—21no—
25C2×#99×C61C2212yes—
26C61×#381—21no—
27C24×D61C2×C411yescharacteristic
28C22×C22⋊D61—21no—
29C22×C22⋊D61—21no—
30C23×Dic61C2×C411yescharacteristic
31C22×C4×D61—22no—
32C22×C4×D61—21no—
33C22×C4×D61—21no—
34C22×C4×D61—22no—
35C22×C4×D61—42no—
36C22×C4×D61—42no—
37C2×#11758194—22no—
38#14519758—22no—
39#14519758—22no—
40#14519758—22no—
41#14519758D414yes—
42#14519753—28no—
43#14519748—28no—
44#14519745—22no—
45#14519745—22no—
46#14519745—22no—
47#14519745D414yes—
48C4×C22⋊D61—28no—
49C4×C22⋊D61—28no—
50#14519736—22no—
51#14519736—22no—
52C2×C4⋊Dic61—21no—
53C2×#11758196—21no—
54C2×#11758196—21no—
55C2×C22⋊Dic61—21no—
56C2×C22⋊Dic61—21no—
57C2×C22⋊Dic61C2×C411yescharacteristic
58C2×C22⋊Dic61C2×C411yescharacteristic
59C2×#11758198—21no—
60C2×#11758198—21no—
61C2×C4×Dic61—21no—
62#14519696—42no—
63#14519694—22no—
64#14519694—22no—
65C22⋊#92418—42no—
66C2×#41×C61—22no—
67C2×#41×C61—22no—
68C2×#41×C61—42no—
69C2×#41×C61—42no—
70C22×Q8×C61D411yescharacteristic
71C22×D4×C61C2×C411yescharacteristic
72C22×D4×C61D411yescharacteristic
73C22×D4×C61C2311yescharacteristic
74C23×C4×C61C2×C411yescharacteristic
75C23×C4×C61D411yescharacteristic
76C23×C4×C61D411yescharacteristic
77C2×C22⋊C4×C61—22no—
78#99×C61—22no—
79#99×C61—22no—
80#99×C61—42no—
81#95×C61—42no—
82C24×C61C22⋊C411yescharacteristic
83C24×C61C22×C411yescharacteristic
84C24×C61C2×D411yescharacteristic
85C23×D61—21no—
86C23×D61—21no—
87C23×D61—44no—
88C23×D61—41no—
89C23×D61—41no—
90C23×D61C22⋊C412yes—
91#41×C61—48no—
92#41×C61—48no—
93C2×Q8×C61—22no—
94C2×Q8×C61—22no—
95C2×Q8×C61—41no—
96C2×D4×C61—21no—
97C2×D4×C61—21no—
98C2×D4×C61—22no—
99C2×D4×C61—22no—
100C2×D4×C61—41no—
101C2×D4×C61—41no—
102C2×D4×C61—41no—
103C2×D4×C61—41no—
104C2×D4×C61—41no—
105C2×D4×C61C2×D412yes—
106C2×D4×C61C2×D412yes—
107C22×C4×C61—21no—
108C22×C4×C61—21no—
109C22×C4×C61—22no—
110C22×C4×C61—22no—
111C22×C4×C61—22no—
112C22×C4×C61—22no—
113C22×C4×C61—22no—
114C22×C4×C61—22no—
115C22×C4×C61—41no—
116C22×C4×C61—41no—
117C22×C4×C61—42no—
118C22×C4×C61C22⋊C411yescharacteristic
119C22×C4×C61C22⋊C411yescharacteristic
120C22×C4×C61C22⋊C411yescharacteristic
121C22×C4×C61C2×D411yescharacteristic
122C2×C22⋊D61—24no—
123C2×C22⋊D61—24no—
124C2×C22⋊D61—44no—
125C2×C22⋊D61—44no—
126C22×Dic61—21no—
127C22×Dic61—21no—
128C22×Dic61—21no—
129C22×Dic61—21no—
130C22×Dic61—41no—
131C22×Dic61—41no—
132C22×Dic61C22⋊C412yes—
133C2×C4×D61—24no—
134C2×C4×D61—24no—
135C2×C4×D61—48no—
136C2×C4×D61—42no—
137C2×C4×D61—42no—
138C2×C4×D61—48no—
139C2×C4×D61—42no—
140C2×C4×D61—42no—
141C22⋊C4×C61—42no—
142C22⋊C4×C61—42no—
143C22⋊Dic61—24no—
144C22⋊Dic61—21no—
145C22⋊Dic61—21no—
146C22⋊Dic61—24no—
147C22⋊Dic61C22⋊C412yes—
148C22⋊Dic61C22⋊C412yes—
149#11758198—24no—
150#11758198—24no—
151C4⋊Dic61—24no—
152#11758196—24no—
153#11758196—24no—
154C4×Dic61—24no—
155#11758194—42no—
156#11758194—42no—
157C2×#92418—42no—
158C23×C61—21no—
159C23×C61—21no—
160C23×C61—21no—
161C23×C61—21no—
162C23×C61—21no—
163C23×C61—21no—
164C23×C61—21no—
165C23×C61—42no—
166C23×C61—42no—
167C23×C61—42no—
168C23×C61C2×C22⋊C411yescharacteristic
169C23×C61C2×C22⋊C411yescharacteristic
170C23×C61C2×C22⋊C411yescharacteristic
171C23×C61#12012yes—
172C22×D61—24no—
173C22×D61—22no—
174C22×D61—44no—
175C22×D61—44no—
176C22×D61—42no—
177C22×D61—42no—
178C22×D61—48no—
179C22×D61—44no—
180C22×D61—41no—
181C22×D61—41no—
182C22×D61—42no—
183C22×D61—44no—
184Q8×C61—44no—
185D4×C61—42no—
186D4×C61—42no—
187D4×C61—44no—
188D4×C61—42no—
189D4×C61—42no—
190C2×C4×C61—24no—
191C2×C4×C61—24no—
192C2×C4×C61—21no—
193C2×C4×C61—21no—
194C2×C4×C61—21no—
195C2×C4×C61—21no—
196C2×C4×C61—21no—
197C2×C4×C61—21no—
198C2×C4×C61—21no—
199C2×C4×C61—21no—
200C2×C4×C61—21no—
201C2×C4×C61—44no—
202C2×C4×C61—44no—
203C2×C4×C61—82no—
204C2×C4×C61—84no—
205C2×C4×C61#9912yes—
206C2×C4×C61#9912yes—
207C2×C4×C61#12012yes—
208C22⋊D61—48no—
209C22⋊D61—48no—
210C2×Dic61—22no—
211C2×Dic61—22no—
212C2×Dic61—22no—
213C2×Dic61—42no—
214C2×Dic61—42no—
215C2×Dic61—42no—
216C2×Dic61—41no—
217C2×Dic61—41no—
218C2×Dic61—42no—
219C4×D61—48no—
220C4×D61—48no—
221#92418—82no—
222#12689—611nomaximal, Sylow
223C22×C61—22no—
224C22×C61—21no—
225C22×C61—21no—
226C22×C61—22no—
227C22×C61—42no—
228C22×C61—41no—
229C22×C61—41no—
230C22×C61—42no—
231C22×C61—42no—
232C22×C61—42no—
233C22×C61—42no—
234C22×C61—42no—
235C22×C61—41no—
236C22×C61—81no—
237C22×C61—81no—
238C22×C61#37911yescharacteristic
239C22×C61C2×#9911yescharacteristic
240C22×C61C2×#9911yescharacteristic
241C2×D61—24no—
242C2×D61—42no—
243C2×D61—44no—
244C2×D61—48no—
245C2×D61—44no—
246C2×D61—44no—
247C2×D61—42no—
248C2×D61—44no—
249C4×C61—22no—
250C4×C61—22no—
251C4×C61—22no—
252C4×C61—41no—
253C4×C61—162no—
254Dic61—42no—
255Dic61—42no—
256Dic61—42no—
257C2×#525—611no—
258C2×#352—612no—
259C2×AΣL(1,𝔽16)—612no—
260#1785—611no—
261#1782D6111yescharacteristic, complemented
262C2×C61—21no—
263C2×C61—21no—
264C2×C61—42no—
265C2×C61—41no—
266C2×C61—41no—
267C2×C61—81no—
268C2×C61#178111yescharacteristic
269C2×C61#212012yes—
270D61—44no—
271C22×#41C2×D6111yescharacteristic
272C24×C4—611no—
273#525—1224no—
274#525—1224no—
275C2×#123—611no—
276C2×#123—611no—
277C2×C22⋊Q8—1221no—
278C2×#121—1221no—
279C2×#120—611no—
280C2×#120—611no—
281C2×C4×D4—1221no—
282C2×C4×D4—1221no—
283C2×#117—611no—
284C2×#101—1221no—
285C2×#100—612no—
286C2×#99—21no—
287C2×#99C2×D6112yes—
288#407—1221no—
289#381—21no—
290#352—1224no—
291AΣL(1,𝔽16)—1224no—
292C61#1268911yescharacteristic, complemented, Sylow
293C25—611no—
294C2×#41—22no—
295C2×#41—22no—
296C2×#41—42no—
297C2×#41—42no—
298C22×Q8D24411yescharacteristic
299C22×D4—1221no—
300C22×D4—1221no—
301C22×D4C4×D6111yescharacteristic
302C22×D4C22⋊D6111yescharacteristic
303C22×D4C22×D6111yescharacteristic
304C23×C4—611no—
305C23×C4—1222no—
306C23×C4—1222no—
307C23×C4—1221no—
308C23×C4—1221no—
309C23×C4—2442no—
310C23×C4—2442no—
311C23×C4C4×D6111yescharacteristic
312C23×C4D24411yescharacteristic
313C23×C4C22⋊D6111yescharacteristic
314C2×M16—1222no—
315#123—614no—
316#123—1222no—
317#123—1222no—
318#123—1222no—
319C22⋊Q8—1228no—
320#121—1228no—
321#120—614no—
322#120—1222no—
323#120—1222no—
324#120—1222no—
325C4×D4—1228no—
326C4×D4—1228no—
327#117—1222no—
328#117—1222no—
329C2×C4⋊C4—1221no—
330C2×C4⋊C4—1221no—
331C2×C4⋊C4—1221no—
332C2×C22⋊C4—22no—
333C2×C22⋊C4—611no—
334C2×C22⋊C4—611no—
335C2×C22⋊C4—1221no—
336C2×C22⋊C4—1221no—
337C2×C22⋊C4—1221no—
338C2×C22⋊C4—1221no—
339C2×C42—1221no—
340#101—2442no—
341#100—1222no—
342#100—1222no—
343#99—22no—
344#99—22no—
345#99—42no—
346C22⋊C8—2442no—
347#95—42no—
348C24—612no—
349C24—1221no—
350C24—1221no—
351C24—2441no—
352C24—2441no—
353C24—2444no—
354C24#1175819811yescharacteristic
355C24C2×C4×D6111yescharacteristic
356C24C2×C22⋊D6111yescharacteristic
357#41—48no—
358#41—48no—
359C2×Q8—22no—
360C2×Q8—22no—
361C2×Q8—41no—
362C2×D4—21no—
363C2×D4—21no—
364C2×D4—22no—
365C2×D4—22no—
366C2×D4—41no—
367C2×D4—41no—
368C2×D4—41no—
369C2×D4—41no—
370C2×D4—41no—
371C2×D4—1224no—
372C2×D4—1224no—
373C2×D4—2444no—
374C2×D4—2444no—
375C2×D4D4×D6112yes—
376C2×D4D4×D6112yes—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—41no—
386C22×C4—41no—
387C22×C4—42no—
388C22×C4—612no—
389C22×C4—1224no—
390C22×C4—1224no—
391C22×C4—1221no—
392C22×C4—1221no—
393C22×C4—1221no—
394C22×C4—1221no—
395C22×C4—2448no—
396C22×C4—2448no—
397C22×C4—2442no—
398C22×C4—2442no—
399C22×C4—2442no—
400C22×C4—2442no—
401C22×C4—2441no—
402C22×C4—2441no—
403C22×C4#1175819811yescharacteristic
404C22×C4#1175819811yescharacteristic
405C22×C4#1175819811yescharacteristic
406C22×C4C2×D24411yescharacteristic
407M16—2442no—
408M16—2442no—
409C2×C8—2442no—
410C4⋊C4—1224no—
411C4⋊C4—1224no—
412C4⋊C4—1224no—
413C22⋊C4—42no—
414C22⋊C4—42no—
415C22⋊C4—612no—
416C22⋊C4—612no—
417C22⋊C4—1224no—
418C22⋊C4—1224no—
419C22⋊C4—1221no—
420C22⋊C4—1221no—
421C22⋊C4—1224no—
422C22⋊C4—1224no—
423C42—1224no—
424C23—21no—
425C23—21no—
426C23—21no—
427C23—21no—
428C23—21no—
429C23—21no—
430C23—21no—
431C23—42no—
432C23—42no—
433C23—42no—
434C23—1224no—
435C23—1222no—
436C23—2442no—
437C23—2442no—
438C23—2442no—
439C23—2444no—
440C23—2444no—
441C23—2444no—
442C23—2448no—
443C23—2444no—
444C23—2441no—
445C23—2441no—
446C23C22⋊C4×D6111yescharacteristic
447C23C22⋊C4×D6111yescharacteristic
448C23C2×#1175819811yescharacteristic
449C23#1451974512yes—
450Q8—44no—
451D4—42no—
452D4—42no—
453D4—44no—
454D4—42no—
455D4—42no—
456D4—2448no—
457D4—2448no—
458C2×C4—24no—
459C2×C4—24no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—44no—
470C2×C4—44no—
471C2×C4—82no—
472C2×C4—84no—
473C2×C4—1222no—
474C2×C4—1222no—
475C2×C4—1222no—
476C2×C4—2448no—
477C2×C4—2448no—
478C2×C4—2442no—
479C2×C4—2442no—
480C2×C4—2442no—
481C2×C4—2441no—
482C2×C4—2441no—
483C2×C4—2442no—
484C2×C4#1451969112yes—
485C2×C4#1451969112yes—
486C2×C4#1451974712yes—
487C8—4882no—
488C22—22no—
489C22—21no—
490C22—21no—
491C22—22no—
492C22—42no—
493C22—41no—
494C22—41no—
495C22—42no—
496C22—42no—
497C22—42no—
498C22—42no—
499C22—42no—
500C22—41no—
501C22—81no—
502C22—81no—
503C22—1224no—
504C22—2442no—
505C22—2444no—
506C22—2444no—
507C22—2444no—
508C22—2448no—
509C22—2444no—
510C22—2442no—
511C22#1683961711yescharacteristic
512C22C2×#1451969111yescharacteristic
513C22C2×#1451969111yescharacteristic
514C4—22no—
515C4—22no—
516C4—22no—
517C4—41no—
518C4—162no—
519C4—2442no—
520C4—2442no—
521C4—2442no—
522C2—21no—
523C2—21no—
524C2—42no—
525C2—41no—
526C2—41no—
527C2—81no—
528C2—2444no—
529C2#2144573311yescharacteristic
530C2#2144745812yes—
subgroupG/H
centerC22C2×#14519691
commutatorC24×C61C22×C4
FrattiniC22×D4C22×D61
FittingC61×#1782C2
socleC22×C61C2×#99
prime radicalC2×#16840269C2
cosocleC22×D4×C61C23
hypercenter#1782D61
hypocenterC61#12689
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×#41 ◁ #1782

Complements

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

NH ≅ G/Ntype
2. C2×#16839551C2semidirect
3. C2×#16839548C2semidirect
4. #21445747C2semidirect
5. C61×#1782C2semidirect
6. C23×C4×D61C4semidirect
9. C2×#14519758C4semidirect
13. C2×#14519745C4semidirect
17. C2×#14519736C4semidirect
261. #1782D61semidirect
292. C61#12689semidirect

Maximal subgroups

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

subgroupindex
C2×#168402692
C2×#168395512
C2×#168395482
#214457472
C61×#17822
#1268961