Finite Group Databasebeta

← #29583338

Subgroups — #29583338

Order 15616.

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

normal subgroups only

This group has 760 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
1#21451921C211yesmaximal, characteristic
2#21446134C212yesmaximal, complemented
3C2×#16839497C212yesmaximal, complemented
4#21444083C211yesmaximal, characteristic, complemented
5C61×#1280C211yesmaximal, characteristic, complemented
6C2×#14519751—21no—
7C2×#14519751—21no—
8C2×#14519751C2212yes—
9C22×C4⋊Dic61C2211yescharacteristic
10C22×#11758196—21no—
11C2×#14519699—22no—
12#16839699—22no—
13#16839672—22no—
14C2×#14519684—21no—
15C2×#14519684C2211yescharacteristic
16#16839525—22no—
17#16839497—24no—
18C2×C22⋊C8×C61C2212yes—
19C2×#95×C61C2211yescharacteristic
20C22×D244—21no—
21C22×D244—21no—
22C22×D244D412yes—
23C22×C22⋊D61—22no—
24C23×Dic61—21no—
25C23×Dic61—21no—
26#14519751—22no—
27#14519751—22no—
28#14519751—22no—
29#14519751—22no—
30#14519751—42no—
31#14519751—42no—
32#14519751—42no—
33#14519751—42no—
34C2×C4⋊Dic61—22no—
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61—42no—
38C2×C4⋊Dic61D412yes—
39C2×#11758196—42no—
40C2×#11758196—42no—
41C2×#11758196—42no—
42C2×#11758198—22no—
43C2×#11758198—22no—
44C2×#11758198—22no—
45#14519699—44no—
46#14519684—21no—
47#14519684—42no—
48#14519684D412yescomplemented
49C23×C4×C61D411yescharacteristic
50C23×C4×C61D411yescharacteristic
51C23×C4×C61C2311yescharacteristic
52C22×C8×C61—22no—
53C22⋊C8×C61—22no—
54C22⋊C8×C61—22no—
55#95×C61—22no—
56C24×C61C2×D411yescharacteristic
57C23×D61—22no—
58C22×C4×C61—21no—
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61—41no—
63C22×C4×C61—41no—
64C22×C4×C61—41no—
65C22×C4×C61—41no—
66C22×C4×C61—41no—
67C22×C4×C61—41no—
68C22×C4×C61D812yes—
69C22×C4×C61SD1612yes—
70C22×C4×C61C2×D412yes—
71C22×C4×C61C2×D411yescharacteristic
72C22×C4×C61#4112yes—
73C22×C4×C61#4111yescharacteristic
74C2×C22⋊D61—42no—
75C2×C22⋊D61—42no—
76C2×C22⋊D61—42no—
77C2×C22⋊D61—42no—
78C2×C22⋊D61—42no—
79C2×C22⋊D61—42no—
80C22×Dic61—22no—
81C22×Dic61—22no—
82C22×Dic61—22no—
83C22×Dic61—22no—
84C22×Dic61—22no—
85C22×Dic61—41no—
86C22×Dic61—41no—
87C22×Dic61—41no—
88C22×Dic61—41no—
89C22×Dic61—41no—
90C22×Dic61—41no—
91C22×Dic61—41no—
92C22×Dic61—41no—
93C22×Dic61—41no—
94C22×Dic61—41no—
95C2×D244—22no—
96C2×D244—22no—
97C2×D244—42no—
98C2×D244—42no—
99C2×D244—42no—
100C2×D244—42no—
101C2×D244—81no—
102C2×D244—81no—
103C2×D244—81no—
104C2×D244—81no—
105C2×C8×C61—42no—
106C2×C8×C61—42no—
107C2×C8×C61—42no—
108#11758198—44no—
109#11758198—44no—
110#11758198—42no—
111#11758198—42no—
112C4⋊Dic61—24no—
113C4⋊Dic61—22no—
114C4⋊Dic61—22no—
115C4⋊Dic61—42no—
116C4⋊Dic61—42no—
117C4⋊Dic61—42no—
118#11758196—48no—
119C23×C61—21no—
120C23×C61—21no—
121C23×C61—21no—
122C23×C61—21no—
123C23×C61#12011yescharacteristic
124C23×C61#12111yescharacteristic
125C23×C61#12411yescharacteristic
126C23×C61C2×D811yescharacteristic
127C23×C61C2×SD1611yescharacteristic
128C23×C61AGL(1,ℤ/8)11yescharacteristic
129C23×C61AGL(1,ℤ/8)11yescharacteristic
130C22×D61—42no—
131C22×D61—42no—
132C22×D61—42no—
133C22×D61—42no—
134C22×D61—42no—
135C22×D61—42no—
136C22×D61—42no—
137C2×C4×C61—22no—
138C2×C4×C61—22no—
139C2×C4×C61—22no—
140C2×C4×C61—22no—
141C2×C4×C61—41no—
142C2×C4×C61—42no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—42no—
149C2×C4×C61—42no—
150C2×C4×C61—81no—
151C2×C4×C61—81no—
152C2×C4×C61#12112yes—
153C2×C4×C61#12312yes—
154C22⋊D61—82no—
155C22⋊D61—82no—
156C22⋊D61—82no—
157C22⋊D61—82no—
158C2×Dic61—24no—
159C2×Dic61—42no—
160C2×Dic61—42no—
161C2×Dic61—42no—
162C2×Dic61—42no—
163C2×Dic61—42no—
164C2×Dic61—42no—
165C2×Dic61—42no—
166C2×Dic61—42no—
167C2×Dic61—42no—
168C2×Dic61—42no—
169C2×Dic61—42no—
170C2×Dic61—42no—
171C2×Dic61—81no—
172C2×Dic61—81no—
173C2×Dic61—81no—
174C2×Dic61—81no—
175D244—44no—
176D244—82no—
177D244—84no—
178D244—84no—
179C8×C61—82no—
180#10402—611nomaximal, Sylow
181C22×C61—21no—
182C22×C61—21no—
183C22×C61—21no—
184C22×C61—21no—
185C22×C61—21no—
186C22×C61—21no—
187C22×C61—21no—
188C22×C61—21no—
189C22×C61—21no—
190C22×C61—21no—
191C22×C61—21no—
192C22×C61—21no—
193C22×C61#39411yescharacteristic
194C22×C61#44711yescharacteristic
195C22×C61#45011yescharacteristic
196C22×C61#45311yescharacteristic
197C22×C61#45611yescharacteristic
198C22×C61B(4,𝔽2)11yescharacteristic
199C22×C61#45811yescharacteristic
200C22×C61#45911yescharacteristic
201C22×C61#46011yescharacteristic
202C22×C61#48611yescharacteristic
203C22×C61#49011yescharacteristic
204C2×D61—82no—
205C2×D61—82no—
206C2×D61—82no—
207C2×D61—82no—
208C2×D61—82no—
209C2×D61—82no—
210C2×D61—82no—
211C4×C61—22no—
212C4×C61—22no—
213C4×C61—42no—
214C4×C61—42no—
215Dic61—44no—
216Dic61—82no—
217Dic61—82no—
218#2656—611no—
219#1874—612no—
220C2×#327—612no—
221#1444—611no—
222#1280D6111yescharacteristic, complemented
223C2×C61—21no—
224C2×C61—21no—
225C2×C61—21no—
226C2×C61—21no—
227C2×C61#159511yescharacteristic
228C2×C61#160411yescharacteristic
229C2×C61#161011yescharacteristic
230C2×C61#161311yescharacteristic
231C2×C61#203911yescharacteristic
232C2×C61#204111yescharacteristic
233C2×C61#204411yescharacteristic
234D61—162no—
235C2×#121—612no—
236C2×#121—1221no—
237C2×#121—1221no—
238C22×C4⋊C4—611no—
239C22×C4⋊C4—1221no—
240C2×#102—1222no—
241C2×C22⋊C8C2×D6112yes—
242#399—1222no—
243#392—1222no—
244C2×#95—611no—
245C2×#95—1221no—
246C2×#95C2×D6111yescharacteristic
247#340—1222no—
248#327—1224no—
249C61#1040211yescharacteristic, complemented, Sylow
250C22×D4—612no—
251C22×D4—1221no—
252C22×D4—1221no—
253C22×D4—1222no—
254C23×C4—1221no—
255C23×C4—1221no—
256C23×C4D24411yescharacteristic
257C23×C4D24411yescharacteristic
258C23×C4C22×D6111yescharacteristic
259C22×C8—22no—
260#121—1222no—
261#121—1222no—
262#121—1222no—
263#121—1222no—
264#121—2442no—
265#121—2442no—
266#121—2442no—
267#121—2442no—
268C2×C4⋊C4—612no—
269C2×C4⋊C4—1222no—
270C2×C4⋊C4—1221no—
271C2×C4⋊C4—1221no—
272C2×C4⋊C4—2442no—
273C2×C4⋊C4—2442no—
274C2×C4⋊C4—2442no—
275C2×C4⋊C4—2442no—
276C2×C22⋊C4—1222no—
277C2×C22⋊C4—1222no—
278C2×C22⋊C4—1222no—
279#102—2444no—
280C22⋊C8—22no—
281C22⋊C8—22no—
282#95—22no—
283#95—612no—
284#95—1221no—
285#95—2442no—
286C24—1222no—
287C24C2×D24411yescharacteristic
288C2×D4—1222no—
289C2×D4—1222no—
290C2×D4—4881no—
291C2×D4—4881no—
292C2×D4—4881no—
293C2×D4—4881no—
294C2×D4—2442no—
295C2×D4—2442no—
296C2×D4—2442no—
297C2×D4—2442no—
298C2×D4—2442no—
299C2×D4—2442no—
300C2×D4—2442no—
301C2×D4—2442no—
302C2×D4—2442no—
303C2×D4—2442no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—1222no—
315C22×C4—1222no—
316C22×C4—1222no—
317C22×C4—1222no—
318C22×C4—1222no—
319C22×C4—2441no—
320C22×C4—2441no—
321C22×C4—2441no—
322C22×C4—2441no—
323C22×C4—2441no—
324C22×C4—2441no—
325C22×C4—2441no—
326C22×C4—2441no—
327C22×C4—2441no—
328C22×C4—2441no—
329C22×C4#1175819012yes—
330C22×C4D48812yes—
331C22×C4#1175822212yes—
332C22×C4D4×D6112yes—
333C22×C4D4×D6111yescharacteristic
334C22×C4#1175822611yescharacteristic
335C2×C8—42no—
336C2×C8—42no—
337C2×C8—42no—
338C4⋊C4—1224no—
339C4⋊C4—1222no—
340C4⋊C4—1222no—
341C4⋊C4—2442no—
342C4⋊C4—2442no—
343C4⋊C4—2442no—
344C4⋊C4—2448no—
345C22⋊C4—2444no—
346C22⋊C4—2444no—
347C22⋊C4—2442no—
348C22⋊C4—2442no—
349C23—21no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—2442no—
354C23—2442no—
355C23—2442no—
356C23—2442no—
357C23—2442no—
358C23—2442no—
359C23—2442no—
360C23#1451974711yescharacteristic
361C23#1451975211yescharacteristic
362C23#1451976511yescharacteristic
363C23C2×D48811yescharacteristic
364C23C2×#1175819011yescharacteristic
365C23#1451980511yescharacteristic
366C23#1451980511yescharacteristic
367D4—4882no—
368D4—4884no—
369D4—4884no—
370D4—4882no—
371D4—4882no—
372D4—4882no—
373D4—4882no—
374D4—2444no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—42no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—81no—
389C2×C4—81no—
390C2×C4—1224no—
391C2×C4—4881no—
392C2×C4—4881no—
393C2×C4—4881no—
394C2×C4—4881no—
395C2×C4—2442no—
396C2×C4—2442no—
397C2×C4—2442no—
398C2×C4—2442no—
399C2×C4—2442no—
400C2×C4—2442no—
401C2×C4—2442no—
402C2×C4—2442no—
403C2×C4—2442no—
404C2×C4—2442no—
405C2×C4—2442no—
406C2×C4—2442no—
407C2×C4#1451975012yes—
408C2×C4#1451976212yes—
409C8—82no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—4882no—
423C22—4882no—
424C22—4882no—
425C22—4882no—
426C22—4882no—
427C22—4882no—
428C22—4882no—
429C22#1683968011yescharacteristic
430C22#1683989811yescharacteristic
431C22#1683991511yescharacteristic
432C22#1683993211yescharacteristic
433C22#1683994711yescharacteristic
434C22#1683995011yescharacteristic
435C22#1683995311yescharacteristic
436C22#1683995811yescharacteristic
437C22#1683996311yescharacteristic
438C22#1684010911yescharacteristic
439C22#1684012711yescharacteristic
440C4—22no—
441C4—22no—
442C4—42no—
443C4—42no—
444C4—4882no—
445C4—4882no—
446C4—2444no—
447C2—21no—
448C2—21no—
449C2—21no—
450C2—21no—
451C2—9762no—
452C2#2144473911yescharacteristic
453C2#2144479011yescharacteristic
454C2#2144482411yescharacteristic
455C2#2144484111yescharacteristic
456C2#2144704411yescharacteristic
457C2#2144705411yescharacteristic
458C2#2144707111yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#1280C2
socleC23×C61#120
prime radical#21451921C2
hypercenter#1280D61
hypocenterC61#10402
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

Complements

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

NH ≅ G/Ntype
2. #21446134C2semidirect
3. C2×#16839497C2semidirect
4. #21444083C2semidirect
5. C61×#1280C2semidirect
48. #14519684D4semidirect
222. #1280D61semidirect
249. C61#10402semidirect

Maximal subgroups

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

subgroupindex
#214519212
#214461342
C2×#168394972
#214440832
C61×#12802
#1040261