Finite Group Databasebeta

← #29576482

Subgroups — #29576482

Order 15616.

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

normal subgroups only

This group has 750 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×#16839903C211yesmaximal, characteristic
2#21448651C211yesmaximal, characteristic, complemented
3#21446654C211yesmaximal, characteristic
4#21445753C211yesmaximal, characteristic, complemented
5#21444386C211yesmaximal, characteristic
6#21443666C211yesmaximal, characteristic, complemented
7C61×#1289C211yesmaximal, characteristic, complemented
8C23×Dic122C2211yescharacteristic
9C22×#11758190C412yescomplemented
10C2×#14519751C2211yescharacteristic
11C2×#14519742—21no—
12#16839903—21no—
13#16839903—22no—
14#16839903—21no—
15C2×#14519702C412yescomplemented
16C2×#14519700—22no—
17C2×#14519691—21no—
18C2×#14519691—21no—
19C2×C22⋊#92418C2211yescharacteristic
20#16839667—21no—
21#16839666—22no—
22#16839620—21no—
23C22⋊C4×Dic61—21no—
24C4×C22⋊Dic61C2211yescharacteristic
25#16839495—22no—
26C2×C22⋊C8×C61C2211yescharacteristic
27C61×#380C2211yescharacteristic
28C61×#380C2211yescharacteristic
29C22×Dic122—21no—
30C22×Dic122—21no—
31C22×Dic122—21no—
32C22×Dic122—44no—
33C22×Dic122C2×C412yes—
34C22×Dic122D411yescharacteristic
35C22×Dic122D412yes—
36C22×Dic122D411yescharacteristic
37C22×D244C2×C411yescharacteristic
38C22×C22⋊D61—21no—
39C23×Dic61—21no—
40C2×#11758190—22no—
41C2×#11758190—22no—
42C2×#11758190—44no—
43C22×#92418—21no—
44#14519751—21no—
45#14519751—21no—
46#14519751—21no—
47#14519751—21no—
48#14519742—44no—
49C2×C4⋊Dic61C2×C411yescharacteristic
50C2×#11758196—22no—
51C2×C22⋊Dic61D411yescharacteristic
52C2×C22⋊Dic61D411yescharacteristic
53C2×#11758198—21no—
54C2×C4×Dic61—22no—
55C2×C4×Dic61—21no—
56#14519702—22no—
57#14519702—22no—
58#14519700—44no—
59#14519691—42no—
60#14519691—42no—
61C22⋊#92418—21no—
62C22⋊#92418—21no—
63#14519684—22no—
64#14519684—22no—
65#14519684—21no—
66C23×C4×C61C2311yescharacteristic
67C22×C8×C61C2×C412yes—
68C2×C4⋊C4×C61—21no—
69C2×C4⋊C4×C61—21no—
70C2×C22⋊C4×C61—21no—
71C2×C22⋊C4×C61—21no—
72C22⋊C8×C61—21no—
73C22⋊C8×C61—21no—
74#95×C61—21no—
75#95×C61D412yes—
76C24×C61C2×D411yescharacteristic
77C23×D61—21no—
78C22×C4×C61—22no—
79C22×C4×C61—42no—
80C22×C4×C61—41no—
81C22×C4×C61C22×C411yescharacteristic
82C22×C4×C61C2×D411yescharacteristic
83C22×C4×C61C2×D411yescharacteristic
84C22×C4×C61C2×D411yescharacteristic
85C22×C4×C61#4111yescharacteristic
86C22×C4×C61#4111yescharacteristic
87C2×C22⋊D61—41no—
88C2×C22⋊D61—41no—
89C2×C22⋊D61—41no—
90C2×C22⋊D61—41no—
91C2×C22⋊D61—41no—
92C2×C22⋊D61—41no—
93C22×Dic61—21no—
94C22×Dic61—22no—
95C22×Dic61—21no—
96C22×Dic61—21no—
97C22×Dic61—22no—
98C22×Dic61—21no—
99C22×Dic61—21no—
100C22×Dic61—44no—
101C2×D244—21no—
102C2×D244—21no—
103C2×D244—42no—
104C2×Dic122—21no—
105C2×Dic122—24no—
106C2×Dic122—24no—
107C2×Dic122—24no—
108C2×Dic122—22no—
109C2×Dic122—22no—
110C2×Dic122—21no—
111C2×Dic122—42no—
112C2×Dic122—42no—
113C2×Dic122—42no—
114C2×Dic122—44no—
115C2×Dic122—44no—
116C2×Dic122—44no—
117C2×Dic122C22⋊C412yes—
118C2×Dic122C22⋊C412yes—
119C2×C8×C61—22no—
120C2×C8×C61—42no—
121C4⋊C4×C61—42no—
122C4⋊C4×C61—42no—
123C22⋊C4×C61—41no—
124C22⋊C4×C61—41no—
125C22⋊C4×C61—41no—
126C22⋊C4×C61—41no—
127C22⋊Dic61—21no—
128C22⋊Dic61—21no—
129C22⋊Dic61—21no—
130C22⋊Dic61SD1612yescomplemented
131#11758198—41no—
132#11758198—41no—
133C4⋊Dic61—21no—
134C4⋊Dic61—21no—
135#11758196—44no—
136C4×Dic61—44no—
137C4×Dic61—42no—
138C2×#92418—42no—
139C2×#92418—41no—
140#11758190—44no—
141#11758190—44no—
142C23×C61—41no—
143C23×C61—41no—
144C23×C61C4×D411yescharacteristic
145C23×C61#12011yescharacteristic
146C23×C61#12111yescharacteristic
147C23×C61C2×SD1611yescharacteristic
148C23×C61#13511yescharacteristic
149C23×C61AGL(1,ℤ/8)11yescharacteristic
150C23×C61#13711yescharacteristic
151C22×D61—41no—
152C22×D61—41no—
153C22×D61—41no—
154C22×D61—81no—
155C22×D61—81no—
156C2×C4×C61—22no—
157C2×C4×C61—22no—
158C2×C4×C61—22no—
159C2×C4×C61—41no—
160C2×C4×C61—41no—
161C2×C4×C61—41no—
162C2×C4×C61—42no—
163C2×C4×C61—42no—
164C2×C4×C61—42no—
165C2×C4×C61—81no—
166C2×C4×C61—81no—
167C2×C4×C61—81no—
168C2×C4×C61C2×C22⋊C411yescharacteristic
169C2×C4×C61C4×D411yescharacteristic
170C2×C4×C61#12111yescharacteristic
171C2×C4×C61#12311yescharacteristic
172C22⋊D61—81no—
173C22⋊D61—81no—
174C22⋊D61—81no—
175C22⋊D61—81no—
176C2×Dic61—24no—
177C2×Dic61—22no—
178C2×Dic61—22no—
179C2×Dic61—22no—
180C2×Dic61—44no—
181C2×Dic61—44no—
182C2×Dic61—41no—
183C2×Dic61—42no—
184C2×Dic61—41no—
185C2×Dic61—41no—
186C2×Dic61—41no—
187C2×Dic61—41no—
188C2×Dic61—41no—
189C2×Dic61—41no—
190C2×Dic61—41no—
191D244—42no—
192D244—81no—
193Dic122—24no—
194Dic122—22no—
195Dic122—22no—
196Dic122—22no—
197Dic122—44no—
198Dic122—44no—
199Dic122—42no—
200Dic122#9914yescomplemented
201C8×C61—42no—
202#92418—81no—
203#9262—611nomaximal, Sylow
204C22×C61—21no—
205C22×C61—21no—
206C22×C61—21no—
207C22×C61—21no—
208C22×C61—21no—
209C22×C61—21no—
210C22×C61—41no—
211C22×C61—41no—
212C22×C61—41no—
213C22×C61—41no—
214C22×C61#38611yescharacteristic
215C22×C61C4×SD1611yescharacteristic
216C22×C61#44011yescharacteristic
217C22×C61#44811yescharacteristic
218C22×C61#44911yescharacteristic
219C22×C61#46011yescharacteristic
220C22×C61#46411yescharacteristic
221C2×D61—81no—
222C2×D61—81no—
223C2×D61—81no—
224C2×D61—161no—
225C2×D61—161no—
226C4×C61—21no—
227C4×C61—21no—
228C4×C61—21no—
229C4×C61—82no—
230C4×C61—161no—
231C4×C61C2×#9912yes—
232Dic61—24no—
233Dic61—42no—
234Dic61—42no—
235Dic61—81no—
236Dic61—81no—
237C2×#448—611no—
238Q8×C22⋊C4—611no—
239#1964—611no—
240#1787—611no—
241#1519—611no—
242#1289D6111yescharacteristic, complemented
243#1282—611no—
244C2×C61—21no—
245C2×C61—21no—
246C2×C61—21no—
247C2×C61—21no—
248C2×C61—21no—
249C2×C61—21no—
250C2×C61#188011yescharacteristic
251C2×C61#189811yescharacteristic
252C2×C61#190511yescharacteristic
253D61—161no—
254C23×Q8—611no—
255C22×SD16—612no—
256C2×#121—611no—
257C2×C4×Q8—1221no—
258#448—1221no—
259#448—1222no—
260#448—1221no—
261C2×#103—612no—
262C2×#103—1222no—
263C2×#99—1221no—
264C2×#99—1221no—
265C2×C22⋊C8—611no—
266C2×C22⋊C8C2×D6111yescharacteristic
267#391—1221no—
268#391—1222no—
269#380—1221no—
270#380C2×D6111yescharacteristic
271#380C2×D6111yescharacteristic
272C4×C22⋊C4—611no—
273C4×C22⋊C4—1221no—
274#327—1222no—
275C61#926211yescharacteristic, complemented, Sylow
276C22×Q8—612no—
277C22×Q8—611no—
278C22×Q8—612no—
279C22×Q8—611no—
280C22×Q8—1221no—
281C22×Q8—1221no—
282C22×Q8—1221no—
283C22×Q8—2444no—
284C22×D4—611no—
285C22×D4—1221no—
286C23×C4—1221no—
287C23×C4C22×D6111yescharacteristic
288C2×SD16—1222no—
289C2×SD16—1222no—
290C2×SD16—2444no—
291C22×C8—1221no—
292C22×C8C4×D6112yes—
293#121—1221no—
294#121—1221no—
295#121—1221no—
296#121—1221no—
297C4×Q8—2444no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—611no—
301C2×C4⋊C4—1222no—
302C2×C22⋊C4—21no—
303C2×C22⋊C4—21no—
304C2×C22⋊C4—611no—
305C2×C22⋊C4—611no—
306C2×C22⋊C4—1221no—
307C2×C42—1222no—
308C2×C42—1221no—
309#103—1222no—
310#103—1222no—
311#103—2444no—
312#99—2442no—
313#99—2442no—
314C22⋊C8—21no—
315C22⋊C8—21no—
316C22⋊C8—1221no—
317C22⋊C8—1221no—
318#95—21no—
319#95—1222no—
320#95—1222no—
321#95—1221no—
322#95D24412yes—
323C24—1221no—
324C24D4×D6111yescharacteristic
325C2×Q8—612no—
326C2×Q8—612no—
327C2×Q8—1224no—
328C2×Q8—1224no—
329C2×Q8—1224no—
330C2×Q8—1222no—
331C2×Q8—1222no—
332C2×Q8—1221no—
333C2×Q8—1221no—
334C2×Q8—2442no—
335C2×Q8—2442no—
336C2×Q8—2442no—
337C2×Q8—2444no—
338C2×Q8—2444no—
339C2×Q8—2444no—
340C2×D4—1221no—
341C2×D4—1221no—
342C2×D4—2442no—
343C2×D4—2441no—
344C2×D4—2441no—
345C2×D4—2441no—
346C2×D4—2441no—
347C2×D4—2441no—
348C2×D4—2441no—
349C22×C4—22no—
350C22×C4—42no—
351C22×C4—41no—
352C22×C4—1221no—
353C22×C4—1222no—
354C22×C4—1221no—
355C22×C4—1221no—
356C22×C4—1222no—
357C22×C4—1221no—
358C22×C4—1221no—
359C22×C4—2444no—
360C22×C4C2×C4×D6111yescharacteristic
361C22×C4C2×D24411yescharacteristic
362C22×C4#1175822211yescharacteristic
363C22×C4D4×D6111yescharacteristic
364C22×C4D4×D6111yescharacteristic
365C22×C4#1175822611yescharacteristic
366SD16—2444no—
367SD16—2444no—
368C2×C8—22no—
369C2×C8—42no—
370C2×C8—2442no—
371C2×C8—2441no—
372C4⋊C4—42no—
373C4⋊C4—42no—
374C4⋊C4—1221no—
375C4⋊C4—1221no—
376C4⋊C4—2444no—
377C22⋊C4—41no—
378C22⋊C4—41no—
379C22⋊C4—41no—
380C22⋊C4—41no—
381C22⋊C4—612no—
382C22⋊C4—1221no—
383C22⋊C4—1221no—
384C22⋊C4—1221no—
385C22⋊C4—2441no—
386C22⋊C4—2441no—
387C42—2442no—
388C42—2444no—
389C23—41no—
390C23—41no—
391C23—4881no—
392C23—4881no—
393C23—2441no—
394C23—2441no—
395C23—2441no—
396C23#1451973911yescharacteristic
397C23#1451974711yescharacteristic
398C23#1451975011yescharacteristic
399C23SD16×D6111yescharacteristic
400C23#1451979811yescharacteristic
401C23#1451980111yescharacteristic
402C23#1451980911yescharacteristic
403Q8—614no—
404Q8—1224no—
405Q8—1222no—
406Q8—1222no—
407Q8—1222no—
408Q8—2444no—
409Q8—2444no—
410Q8—2442no—
411D4—4881no—
412D4—4881no—
413D4—4881no—
414D4—4881no—
415D4—4881no—
416D4—2442no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—81no—
427C2×C4—81no—
428C2×C4—81no—
429C2×C4—1224no—
430C2×C4—1222no—
431C2×C4—1222no—
432C2×C4—1222no—
433C2×C4—2444no—
434C2×C4—2444no—
435C2×C4—2441no—
436C2×C4—2441no—
437C2×C4—2441no—
438C2×C4—2441no—
439C2×C4—2441no—
440C2×C4—2441no—
441C2×C4—2441no—
442C2×C4—2441no—
443C2×C4—2442no—
444C2×C4C22⋊C4×D6111yescharacteristic
445C2×C4C4×D24411yescharacteristic
446C2×C4#1451975211yescharacteristic
447C2×C4#1451976211yescharacteristic
448C8—42no—
449C8—4881no—
450C22—21no—
451C22—21no—
452C22—21no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—9761no—
461C22—9761no—
462C22—4881no—
463C22—4881no—
464C22—4881no—
465C22#1683964011yescharacteristic
466C22#1683984911yescharacteristic
467C22#1683986111yescharacteristic
468C22#1683990211yescharacteristic
469C22#1683990811yescharacteristic
470C22#1683996111yescharacteristic
471C22#1683998711yescharacteristic
472C4—21no—
473C4—21no—
474C4—21no—
475C4—82no—
476C4—161no—
477C4—1224no—
478C4—4881no—
479C4—4881no—
480C4—2442no—
481C4—2442no—
482C4#99×D6112yes—
483C2—21no—
484C2—21no—
485C2—21no—
486C2—21no—
487C2—21no—
488C2—21no—
489C2—9761no—
490C2#2144617511yescharacteristic
491C2#2144627111yescharacteristic
492C2#2144631411yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1289C2
socleC22×C61#386
prime radicalC2×#14519751C22
cosocleC23×C4×C61C23
hypercenter#1289D61
hypocenterC61#9262
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1289

Complements

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

NH ≅ G/Ntype
2. #21448651C2semidirect
4. #21445753C2semidirect
6. #21443666C2semidirect
7. C61×#1289C2semidirect
9. C22×#11758190C4semidirect
15. C2×#14519702C4semidirect
130. C22⋊Dic61SD16semidirect
200. Dic122#99semidirect
242. #1289D61semidirect
275. C61#9262semidirect

Maximal subgroups

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

subgroupindex
C2×#168399032
#214486512
#214466542
#214457532
#214443862
#214436662
C61×#12892
#926261