Finite Group Databasebeta

← #29580229

Subgroups — #29580229

Order 15616.

872 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 872 conjugacy classes of subgroups — too many to draw. Only its 113 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×#16839900C211yesmaximal, characteristic
2#21451563C211yesmaximal, characteristic
3C2×#16839683C211yesmaximal, characteristic, complemented
4#21445755C211yesmaximal, characteristic, complemented
5C2×#16839487C211yesmaximal, characteristic, complemented
6#21443698C211yesmaximal, characteristic, complemented
7C2×C61×#327C211yesmaximal, characteristic
8C23×Dic122C2211yescharacteristic
9C22×#11758200—21no—
10C2×#14519758—21no—
11C22×C4⋊Dic61—21no—
12C22×#11758196C2211yescharacteristic
13#16839900—22no—
14#16839900—22no—
15C2×#14519702—22no—
16C2×#14519700—21no—
17C2×C22⋊#92418C2211yescharacteristic
18#16839693—21no—
19#16839685—22no—
20#16839683—22no—
21#16839683—22no—
22#16839676—21no—
23#16839642—21no—
24#16839622C2211yescharacteristic
25C2×#14519684—21no—
26#16839487—22no—
27C2×#121×C61C2211yescharacteristic
28C2×C22⋊C8×C61C2211yescharacteristic
29C2×#95×C61C2211yescharacteristic
30C61×#327—22no—
31C22×Dic122—21no—
32C22×Dic122—21no—
33C22×Dic122—21no—
34C22×Dic122—21no—
35C22×Dic122—21no—
36C22×Dic122—44no—
37C22×Dic122D412yes—
38C23×Dic61—21no—
39C23×Dic61D411yescharacteristic
40C23×Dic61D411yescharacteristic
41C2×#11758200—24no—
42C2×#11758200—44no—
43C22×#92418—21no—
44#14519758—42no—
45#14519758—42no—
46C2×C4⋊Dic61—24no—
47C2×C4⋊Dic61—44no—
48C2×C4⋊Dic61D412yes—
49C2×#11758196—22no—
50C2×#11758196—21no—
51C2×#11758196—21no—
52C2×#11758196—21no—
53C2×#11758196—21no—
54C2×#11758196—21no—
55C2×#11758196—21no—
56C2×C22⋊Dic61—22no—
57C2×C22⋊Dic61—21no—
58C2×C22⋊Dic61—22no—
59#14519702—44no—
60#14519700—24no—
61C22⋊#92418—21no—
62C22⋊#92418D412yes—
63#14519684—24no—
64#14519684—22no—
65#14519684—21no—
66C22×D4×C61—21no—
67C22×D4×C61D411yescharacteristic
68C23×C4×C61—21no—
69C23×C4×C61C2311yescharacteristic
70C22×C8×C61—21no—
71#121×C61—21no—
72#121×C61—21no—
73#121×C61—21no—
74#121×C61—21no—
75C2×C4⋊C4×C61D411yescharacteristic
76C2×C22⋊C4×C61—21no—
77C22⋊C8×C61—21no—
78C22⋊C8×C61—21no—
79#95×C61—21no—
80#95×C61D412yes—
81C24×C61—21no—
82C24×C61C2×D411yescharacteristic
83C2×D4×C61—21no—
84C2×D4×C61—21no—
85C2×D4×C61—42no—
86C2×D4×C61—41no—
87C2×D4×C61—41no—
88C2×D4×C61—41no—
89C2×D4×C61—41no—
90C2×D4×C61—41no—
91C2×D4×C61—41no—
92C22×C4×C61—24no—
93C22×C4×C61—22no—
94C22×C4×C61—21no—
95C22×C4×C61—42no—
96C22×C4×C61—42no—
97C22×C4×C61—41no—
98C22×C4×C61—41no—
99C22×C4×C61C2×D411yescharacteristic
100C22×C4×C61C2×D411yescharacteristic
101C22×C4×C61C2×D411yescharacteristic
102C22×C4×C61C2×D411yescharacteristic
103C22×C4×C61C2×D411yescharacteristic
104C22×C4×C61#4111yescharacteristic
105C22×Dic61—24no—
106C22×Dic61—22no—
107C22×Dic61—21no—
108C22×Dic61—21no—
109C22×Dic61—21no—
110C22×Dic61—21no—
111C22×Dic61—21no—
112C22×Dic61—21no—
113C22×Dic61—21no—
114C22×Dic61—21no—
115C22×Dic61—22no—
116C22×Dic61—21no—
117C22×Dic61—42no—
118C22×Dic61—41no—
119C22×Dic61—41no—
120C22×Dic61—42no—
121C22×Dic61SD1612yescomplemented
122C2×Dic122—24no—
123C2×Dic122—24no—
124C2×Dic122—22no—
125C2×Dic122—22no—
126C2×Dic122—44no—
127C2×Dic122—44no—
128C2×Dic122—44no—
129C2×Dic122—44no—
130C2×Dic122—42no—
131C2×Dic122—42no—
132C2×Dic122—41no—
133C2×Dic122—41no—
134C2×C8×C61—42no—
135C2×C8×C61—41no—
136C4⋊C4×C61—21no—
137C4⋊C4×C61—21no—
138C22⋊C4×C61—41no—
139C22⋊C4×C61—41no—
140C22⋊Dic61—44no—
141C22⋊Dic61—41no—
142C22⋊Dic61—41no—
143C22⋊Dic61—82no—
144#11758200—48no—
145C4⋊Dic61—48no—
146C4⋊Dic61—42no—
147#11758196—44no—
148#11758196—41no—
149#11758196—41no—
150#11758196—41no—
151#11758196—41no—
152C2×#92418—22no—
153C2×#92418—42no—
154C23×C61—22no—
155C23×C61—22no—
156C23×C61—41no—
157C23×C61—41no—
158C23×C61—41no—
159C23×C61—42no—
160C23×C61—42no—
161C23×C61#12011yescharacteristic
162C23×C61#12011yescharacteristic
163C23×C61#12111yescharacteristic
164C23×C61C2×SD1611yescharacteristic
165C23×C61#13511yescharacteristic
166C23×C61AGL(1,ℤ/8)11yescharacteristic
167C23×C61#13711yescharacteristic
168D4×C61—42no—
169D4×C61—81no—
170D4×C61—81no—
171D4×C61—81no—
172D4×C61—81no—
173D4×C61—81no—
174C2×C4×C61—22no—
175C2×C4×C61—22no—
176C2×C4×C61—24no—
177C2×C4×C61—41no—
178C2×C4×C61—41no—
179C2×C4×C61—41no—
180C2×C4×C61—41no—
181C2×C4×C61—42no—
182C2×C4×C61—44no—
183C2×C4×C61—44no—
184C2×C4×C61—42no—
185C2×C4×C61—41no—
186C2×C4×C61—41no—
187C2×C4×C61—41no—
188C2×C4×C61#12011yescharacteristic
189C2×C4×C61#12111yescharacteristic
190C2×C4×C61#12111yescharacteristic
191C2×C4×C61#12711yescharacteristic
192C2×Dic61—24no—
193C2×Dic61—22no—
194C2×Dic61—22no—
195C2×Dic61—22no—
196C2×Dic61—42no—
197C2×Dic61—44no—
198C2×Dic61—41no—
199C2×Dic61—42no—
200C2×Dic61—41no—
201C2×Dic61—41no—
202C2×Dic61—44no—
203C2×Dic61—41no—
204C2×Dic61—42no—
205C2×Dic61—41no—
206C2×Dic61—42no—
207C2×Dic61—42no—
208C2×Dic61—42no—
209C2×Dic61—42no—
210C2×Dic61—81no—
211Dic122—24no—
212Dic122—24no—
213Dic122—42no—
214Dic122—44no—
215Dic122—42no—
216Dic122—44no—
217C8×C61—81no—
218#92418—42no—
219#9917—611nomaximal, Sylow
220C22×C61—22no—
221C22×C61—22no—
222C22×C61—22no—
223C22×C61—22no—
224C22×C61—21no—
225C22×C61—21no—
226C22×C61—21no—
227C22×C61—21no—
228C22×C61—82no—
229C22×C61—82no—
230C22×C61—81no—
231C22×C61—81no—
232C22×C61—81no—
233C22×C61#39211yescharacteristic
234C22×C61#44811yescharacteristic
235C22×C61#44911yescharacteristic
236C22×C61#45011yescharacteristic
237C22×C61#45211yescharacteristic
238C22×C61#45612yes—
239C22×C61B(4,𝔽2)12yes—
240C22×C61#46511yescharacteristic
241C22×C61#46811yescharacteristic
242C4×C61—21no—
243C4×C61—21no—
244C4×C61—21no—
245C4×C61—21no—
246C4×C61—44no—
247C4×C61—81no—
248Dic61—42no—
249Dic61—44no—
250Dic61—82no—
251Dic61—81no—
252C2×#448—611no—
253#2618—611no—
254C2×#395—611no—
255#1787—611no—
256C2×#327D6111yescharacteristic
257C2×#324—611no—
258#1294—611no—
259C2×C61—21no—
260C2×C61—21no—
261C2×C61—21no—
262C2×C61—21no—
263C2×C61—161no—
264C2×C61#160312yes—
265C2×C61#160412yes—
266C2×C61#200011yescharacteristic
267C2×C61#200511yescharacteristic
268C2×C61#202111yescharacteristic
269C23×Q8—611no—
270C22×SD16—1221no—
271C2×#123—1221no—
272C2×#121C2×D6111yescharacteristic
273C22×C4⋊C4—611no—
274C22×C4⋊C4—1221no—
275#448—1222no—
276#448—1222no—
277C2×#103—1221no—
278C2×#103—1222no—
279C2×C22⋊C8—611no—
280C2×C22⋊C8C2×D6111yescharacteristic
281#398—1221no—
282#396—1222no—
283#395—1222no—
284#395—1222no—
285#394—1221no—
286#386—1221no—
287#380—611no—
288C2×#95—1221no—
289C2×#95C2×D6111yescharacteristic
290#327—22no—
291#324—1222no—
292C61#991711yescharacteristic, complemented, Sylow
293C22×Q8—612no—
294C22×Q8—1221no—
295C22×Q8—1221no—
296C22×Q8—1221no—
297C22×Q8—1221no—
298C22×Q8—1221no—
299C22×Q8—2444no—
300C22×D4—21no—
301C22×D4D24411yescharacteristic
302C23×C4—21no—
303C23×C4—611no—
304C23×C4—611no—
305C23×C4—1221no—
306C23×C4C22×D6111yescharacteristic
307C2×SD16—1224no—
308C2×SD16—2444no—
309C22×C8—21no—
310C22×C8—1221no—
311#123—2442no—
312#123—2442no—
313#121—21no—
314#121—21no—
315#121—21no—
316#121—21no—
317C2×C4⋊C4—612no—
318C2×C4⋊C4—1224no—
319C2×C4⋊C4—1222no—
320C2×C4⋊C4—1221no—
321C2×C4⋊C4—1221no—
322C2×C4⋊C4—1221no—
323C2×C4⋊C4—1221no—
324C2×C4⋊C4—1221no—
325C2×C4⋊C4—1221no—
326C2×C4⋊C4—2444no—
327C2×C4⋊C4D24411yescharacteristic
328C2×C22⋊C4—21no—
329C2×C22⋊C4—1222no—
330C2×C22⋊C4—1222no—
331C2×C22⋊C4—1221no—
332#103—1224no—
333#103—2444no—
334C22⋊C8—21no—
335C22⋊C8—21no—
336C22⋊C8—612no—
337C22⋊C8—1221no—
338#95—21no—
339#95—1224no—
340#95—1222no—
341#95—1221no—
342#95C22⋊D6112yes—
343C24—21no—
344C24D4×D6111yescharacteristic
345C2×Q8—1224no—
346C2×Q8—1224no—
347C2×Q8—1222no—
348C2×Q8—1222no—
349C2×Q8—2442no—
350C2×Q8—2442no—
351C2×Q8—2444no—
352C2×Q8—2444no—
353C2×Q8—2444no—
354C2×Q8—2444no—
355C2×Q8—2441no—
356C2×Q8—2441no—
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—42no—
360C2×D4—41no—
361C2×D4—41no—
362C2×D4—41no—
363C2×D4—41no—
364C2×D4—41no—
365C2×D4—41no—
366C22×C4—24no—
367C22×C4—22no—
368C22×C4—21no—
369C22×C4—42no—
370C22×C4—42no—
371C22×C4—41no—
372C22×C4—41no—
373C22×C4—612no—
374C22×C4—1224no—
375C22×C4—1221no—
376C22×C4—1222no—
377C22×C4—1221no—
378C22×C4—1221no—
379C22×C4—1221no—
380C22×C4—1221no—
381C22×C4—1221no—
382C22×C4—1221no—
383C22×C4—1221no—
384C22×C4—1222no—
385C22×C4—1221no—
386C22×C4—2442no—
387C22×C4—2442no—
388C22×C4—2441no—
389C22×C4—2441no—
390C22×C4C2×D24411yescharacteristic
391C22×C4#1175822211yescharacteristic
392C22×C4D4×D6111yescharacteristic
393C22×C4D4×D6111yescharacteristic
394C22×C4D4×D6111yescharacteristic
395C22×C4C2×C22⋊D6111yescharacteristic
396SD16—2448no—
397C2×C8—42no—
398C2×C8—41no—
399C2×C8—1222no—
400C2×C8—2442no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—2442no—
404C4⋊C4—2448no—
405C4⋊C4—2444no—
406C4⋊C4—2441no—
407C4⋊C4—2441no—
408C4⋊C4—2441no—
409C4⋊C4—2441no—
410C22⋊C4—41no—
411C22⋊C4—41no—
412C22⋊C4—4882no—
413C22⋊C4—2444no—
414C22⋊C4—2441no—
415C22⋊C4—2441no—
416C23—22no—
417C23—22no—
418C23—42no—
419C23—42no—
420C23—41no—
421C23—41no—
422C23—41no—
423C23#1451974511yescharacteristic
424C23#1451974711yescharacteristic
425C23#1451975011yescharacteristic
426C23SD16×D6111yescharacteristic
427C23#1451979611yescharacteristic
428C23#1451980111yescharacteristic
429C23#1451980611yescharacteristic
430Q8—1224no—
431Q8—1224no—
432Q8—2444no—
433Q8—2442no—
434Q8—2442no—
435Q8—2444no—
436D4—42no—
437D4—81no—
438D4—81no—
439D4—81no—
440D4—81no—
441D4—81no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—24no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—42no—
450C2×C4—44no—
451C2×C4—44no—
452C2×C4—42no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—1224no—
457C2×C4—1222no—
458C2×C4—1222no—
459C2×C4—1222no—
460C2×C4—4881no—
461C2×C4—2442no—
462C2×C4—2442no—
463C2×C4—2442no—
464C2×C4—2442no—
465C2×C4—2442no—
466C2×C4—2441no—
467C2×C4—2442no—
468C2×C4—2444no—
469C2×C4—2444no—
470C2×C4—2441no—
471C2×C4—2441no—
472C2×C4—2441no—
473C2×C4—2441no—
474C2×C4—2442no—
475C2×C4#1451974711yescharacteristic
476C2×C4#1451975011yescharacteristic
477C2×C4#1451975111yescharacteristic
478C2×C4#1451977311yescharacteristic
479C8—81no—
480C8—2442no—
481C22—21no—
482C22—21no—
483C22—22no—
484C22—22no—
485C22—22no—
486C22—22no—
487C22—21no—
488C22—21no—
489C22—81no—
490C22—81no—
491C22—82no—
492C22—82no—
493C22—81no—
494C22#1683967111yescharacteristic
495C22#1683989911yescharacteristic
496C22#1683990411yescharacteristic
497C22#1683991411yescharacteristic
498C22#1683992511yescharacteristic
499C22#1683994612yes—
500C22#1683995012yes—
501C22#1683999011yescharacteristic
502C22#1684000711yescharacteristic
503C4—21no—
504C4—21no—
505C4—21no—
506C4—21no—
507C4—44no—
508C4—81no—
509C4—4881no—
510C4—4882no—
511C4—2444no—
512C4—2442no—
513C2—21no—
514C2—21no—
515C2—21no—
516C2—21no—
517C2—161no—
518C2#2144478312yes—
519C2#2144478912yes—
520C2#2144682311yescharacteristic
521C2#2144685411yescharacteristic
522C2#2144694411yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC2×C61×#327C2
socleC23×C61#120
prime radicalC2×#121×C61C22
hypercenterC2×#327D61
hypocenterC61#9917
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#327

Complements

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

NH ≅ G/Ntype
3. C2×#16839683C2semidirect
4. #21445755C2semidirect
5. C2×#16839487C2semidirect
6. #21443698C2semidirect
121. C22×Dic61SD16semidirect
292. C61#9917semidirect

Maximal subgroups

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

subgroupindex
C2×#168399002
#214515632
C2×#168396832
#214457552
C2×#168394872
#214436982
C2×C61×#3272
#991761