Finite Group Databasebeta

← #29580244

Subgroups — #29580244

Order 15616.

716 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840075C211yesmaximal, characteristic
2#21451561C211yesmaximal, characteristic
3#21445905C211yesmaximal, characteristic, complemented
4C2×#16839495C211yesmaximal, characteristic
5C2×#16839488C211yesmaximal, characteristic, complemented
6#21443698C211yesmaximal, characteristic, complemented
7C2×C61×#398C211yesmaximal, characteristic, complemented
8C2×#14519760—21no—
9C2×#14519751C2211yescharacteristic
10#16840075—22no—
11#16840075—22no—
12C2×#14519710—21no—
13C2×#14519697—21no—
14C2×C22⋊#92418C2211yescharacteristic
15C2×C22⋊#92418C2211yescharacteristic
16#16839692—21no—
17#16839684—22no—
18#16839679—21no—
19#16839641—21no—
20#16839622C2211yescharacteristic
21#16839524—22no—
22#16839495—22no—
23#16839488—22no—
24C22×C4⋊C4×C61—21no—
25C22×C4⋊C4×C61C2211yescharacteristic
26C22×C4⋊C4×C61C2211yescharacteristic
27C61×#398—22no—
28C61×#398—22no—
29C2×#95×C61—21no—
30C2×#95×C61C2211yescharacteristic
31C22×D244D411yescharacteristic
32C22×C22⋊D61—21no—
33C22×#92418—21no—
34C22×#92418—21no—
35#14519760—42no—
36#14519760—42no—
37#14519751—21no—
38#14519751—21no—
39#14519751—21no—
40#14519751—21no—
41C2×C4⋊Dic61D411yescharacteristic
42C2×C4⋊Dic61D412yes—
43C2×#11758196—22no—
44C2×C22⋊Dic61—21no—
45C2×#11758198—22no—
46C2×#11758198—21no—
47C2×#11758198—22no—
48#14519710—24no—
49#14519697—24no—
50C22⋊#92418—21no—
51C22⋊#92418—21no—
52C22⋊#92418—21no—
53C22⋊#92418D412yes—
54#14519684—22no—
55#14519684—21no—
56C23×C4×C61—21no—
57C23×C4×C61—21no—
58C23×C4×C61D411yescharacteristic
59C23×C4×C61D411yescharacteristic
60C23×C4×C61C2311yescharacteristic
61C2×C4⋊C4×C61—21no—
62C2×C4⋊C4×C61—21no—
63C2×C4⋊C4×C61—21no—
64C2×C4⋊C4×C61—21no—
65C2×C4⋊C4×C61—24no—
66C2×C4⋊C4×C61—21no—
67C2×C4⋊C4×C61—21no—
68C2×C4⋊C4×C61—21no—
69C2×C4⋊C4×C61—21no—
70C2×C4⋊C4×C61—21no—
71C2×C4⋊C4×C61—21no—
72C2×C4⋊C4×C61—21no—
73C2×C4⋊C4×C61—42no—
74C2×C4⋊C4×C61—42no—
75C2×C4⋊C4×C61D412yes—
76#95×C61—24no—
77#95×C61—21no—
78#95×C61D412yes—
79C24×C61C2×D411yescharacteristic
80C23×D61—21no—
81C22×C4×C61—24no—
82C22×C4×C61—22no—
83C22×C4×C61—21no—
84C22×C4×C61—21no—
85C22×C4×C61—21no—
86C22×C4×C61—21no—
87C22×C4×C61—21no—
88C22×C4×C61—21no—
89C22×C4×C61—21no—
90C22×C4×C61—22no—
91C22×C4×C61—21no—
92C22×C4×C61—21no—
93C22×C4×C61—42no—
94C22×C4×C61—42no—
95C22×C4×C61—41no—
96C22×C4×C61—41no—
97C22×C4×C61—42no—
98C22×C4×C61—41no—
99C22×C4×C61—41no—
100C22×C4×C61—41no—
101C22×C4×C61—41no—
102C22×C4×C61—41no—
103C22×C4×C61—41no—
104C22×C4×C61D812yes—
105C22×C4×C61C2×D411yescharacteristic
106C22×C4×C61C2×D411yescharacteristic
107C22×C4×C61C2×D411yescharacteristic
108C22×C4×C61C2×D411yescharacteristic
109C22×C4×C61C2×D411yescharacteristic
110C22×C4×C61#4111yescharacteristic
111C2×C22⋊D61—41no—
112C2×C22⋊D61—41no—
113C2×C22⋊D61—41no—
114C2×C22⋊D61—41no—
115C2×C22⋊D61—41no—
116C2×C22⋊D61—41no—
117C22×Dic61—21no—
118C22×Dic61—22no—
119C2×D244—21no—
120C2×D244—21no—
121C2×D244—42no—
122C4⋊C4×C61—22no—
123C4⋊C4×C61—22no—
124C4⋊C4×C61—48no—
125C4⋊C4×C61—41no—
126C4⋊C4×C61—41no—
127C4⋊C4×C61—41no—
128C4⋊C4×C61—41no—
129C4⋊C4×C61—41no—
130C4⋊C4×C61—41no—
131C22⋊Dic61—41no—
132C22⋊Dic61—41no—
133#11758198—44no—
134#11758198—41no—
135#11758198—41no—
136#11758198—82no—
137C4⋊Dic61—21no—
138C4⋊Dic61—21no—
139C4⋊Dic61—42no—
140#11758196—44no—
141C2×#92418—22no—
142C2×#92418—42no—
143C2×#92418—42no—
144C2×#92418—41no—
145C23×C61—22no—
146C23×C61—22no—
147C23×C61#12011yescharacteristic
148C23×C61#12011yescharacteristic
149C23×C61#12111yescharacteristic
150C23×C61C2×D811yescharacteristic
151C23×C61#13511yescharacteristic
152C23×C61AGL(1,ℤ/8)11yescharacteristic
153C23×C61AGL(1,ℤ/8)11yescharacteristic
154C22×D61—41no—
155C22×D61—41no—
156C22×D61—41no—
157C22×D61—42no—
158C22×D61—42no—
159C2×C4×C61—22no—
160C2×C4×C61—22no—
161C2×C4×C61—24no—
162C2×C4×C61—22no—
163C2×C4×C61—22no—
164C2×C4×C61—22no—
165C2×C4×C61—41no—
166C2×C4×C61—41no—
167C2×C4×C61—41no—
168C2×C4×C61—41no—
169C2×C4×C61—44no—
170C2×C4×C61—44no—
171C2×C4×C61—42no—
172C2×C4×C61—41no—
173C2×C4×C61—42no—
174C2×C4×C61—41no—
175C2×C4×C61—41no—
176C2×C4×C61—41no—
177C2×C4×C61—42no—
178C2×C4×C61—42no—
179C2×C4×C61—41no—
180C2×C4×C61—42no—
181C2×C4×C61—42no—
182C2×C4×C61—42no—
183C2×C4×C61—81no—
184C2×C4×C61—81no—
185C2×C4×C61—81no—
186C2×C4×C61—81no—
187C2×C4×C61—81no—
188C2×C4×C61#12011yescharacteristic
189C2×C4×C61#12111yescharacteristic
190C2×C4×C61#12111yescharacteristic
191C2×C4×C61#12711yescharacteristic
192C22⋊D61—81no—
193C22⋊D61—81no—
194C22⋊D61—81no—
195C22⋊D61—81no—
196C2×Dic61—41no—
197C2×Dic61—41no—
198C2×Dic61—42no—
199C2×Dic61—41no—
200C2×Dic61—42no—
201C2×Dic61—42no—
202D244—42no—
203D244—81no—
204#92418—42no—
205#92418—81no—
206#9919—611nomaximal, Sylow
207C22×C61—22no—
208C22×C61—22no—
209C22×C61—22no—
210C22×C61—22no—
211C22×C61—21no—
212C22×C61—21no—
213C22×C61—21no—
214C22×C61—21no—
215C22×C61#39211yescharacteristic
216C22×C61#44711yescharacteristic
217C22×C61#44711yescharacteristic
218C22×C61#44911yescharacteristic
219C22×C61#44911yescharacteristic
220C22×C61#45612yes—
221C22×C61#45812yes—
222C22×C61#46611yescharacteristic
223C22×C61#46911yescharacteristic
224C2×D61—82no—
225C2×D61—82no—
226C2×D61—81no—
227C2×D61—81no—
228C2×D61—81no—
229C4×C61—21no—
230C4×C61—21no—
231C4×C61—21no—
232C4×C61—21no—
233C4×C61—44no—
234C4×C61—42no—
235C4×C61—82no—
236C4×C61—81no—
237Dic61—82no—
238Dic61—81no—
239C2×#480—611no—
240#2618—611no—
241C2×#398D6111yescharacteristic, complemented
242#1823—611no—
243C2×#327—611no—
244C2×#324—611no—
245#1294—611no—
246C2×C61—21no—
247C2×C61—21no—
248C2×C61—21no—
249C2×C61—21no—
250C2×C61#160912yes—
251C2×C61#161012yes—
252C2×C61#199911yescharacteristic
253C2×C61#200511yescharacteristic
254C2×C61#202211yescharacteristic
255D61—161no—
256C2×#123—1221no—
257C2×#121—611no—
258C22×C4⋊C4—21no—
259C22×C4⋊C4C2×D6111yescharacteristic
260C22×C4⋊C4C2×D6111yescharacteristic
261#480—1222no—
262#480—1222no—
263C2×#107—1221no—
264C2×#102—1221no—
265C2×C22⋊C8—611no—
266C2×C22⋊C8—611no—
267#398—22no—
268#398—22no—
269#398—1221no—
270#396—1222no—
271#394—1221no—
272#386—1221no—
273#380—611no—
274C2×#95—21no—
275C2×#95C2×D6111yescharacteristic
276#340—1222no—
277#327—1222no—
278#324—1222no—
279C61#991911yescharacteristic, complemented, Sylow
280C22×D4—611no—
281C22×D4—1221no—
282C23×C4—21no—
283C23×C4—21no—
284C23×C4C22⋊D6111yescharacteristic
285C23×C4C22⋊D6111yescharacteristic
286C23×C4C22×D6111yescharacteristic
287C22×C8—1221no—
288C22×C8—1221no—
289#123—2442no—
290#123—2442no—
291#121—1221no—
292#121—1221no—
293#121—1221no—
294#121—1221no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4—611no—
310C2×C4⋊C4—612no—
311C2×C4⋊C4—1222no—
312C2×C4⋊C4C22⋊D6112yes—
313C2×C22⋊C4—1222no—
314C2×C22⋊C4—1222no—
315C2×C22⋊C4—1221no—
316C2×C22⋊C4—1221no—
317#107—1224no—
318#102—1224no—
319C22⋊C8—612no—
320C22⋊C8—1221no—
321C22⋊C8—1221no—
322C22⋊C8—1221no—
323#95—24no—
324#95—21no—
325#95—1222no—
326#95—1221no—
327#95C22⋊D6112yes—
328C24—1221no—
329C24C2×C22⋊D6111yescharacteristic
330C2×D4—1221no—
331C2×D4—1221no—
332C2×D4—2442no—
333C2×D4—2441no—
334C2×D4—2441no—
335C2×D4—2441no—
336C2×D4—2441no—
337C2×D4—2441no—
338C2×D4—2441no—
339C22×C4—24no—
340C22×C4—21no—
341C22×C4—22no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—22no—
350C22×C4—21no—
351C22×C4—42no—
352C22×C4—42no—
353C22×C4—41no—
354C22×C4—41no—
355C22×C4—42no—
356C22×C4—41no—
357C22×C4—41no—
358C22×C4—41no—
359C22×C4—41no—
360C22×C4—41no—
361C22×C4—41no—
362C22×C4—1222no—
363C22×C4—1221no—
364C22×C4#1175819912yes—
365C22×C4D4×D6111yescharacteristic
366C22×C4D4×D6111yescharacteristic
367C22×C4D4×D6111yescharacteristic
368C22×C4#1175822411yescharacteristic
369C22×C4C2×C22⋊D6111yescharacteristic
370C22×C4C2×C22⋊D6111yescharacteristic
371C2×C8—1222no—
372C2×C8—2442no—
373C2×C8—2441no—
374C2×C8—2442no—
375C4⋊C4—22no—
376C4⋊C4—22no—
377C4⋊C4—48no—
378C4⋊C4—41no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C4⋊C4—41no—
382C4⋊C4—41no—
383C4⋊C4—41no—
384C4⋊C4—1221no—
385C4⋊C4—1221no—
386C4⋊C4—2442no—
387C4⋊C4—2444no—
388C22⋊C4—4882no—
389C22⋊C4—2444no—
390C22⋊C4—2441no—
391C22⋊C4—2441no—
392C22⋊C4—2441no—
393C22⋊C4—2441no—
394C23—22no—
395C23—22no—
396C23—2442no—
397C23—2442no—
398C23—2441no—
399C23—2441no—
400C23—2441no—
401C23#1451974511yescharacteristic
402C23#1451974611yescharacteristic
403C23#1451974911yescharacteristic
404C23C2×#1175819911yescharacteristic
405C23#1451979711yescharacteristic
406C23#1451980211yescharacteristic
407C23#1451980311yescharacteristic
408D4—4881no—
409D4—4881no—
410D4—4881no—
411D4—4881no—
412D4—4881no—
413D4—2442no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—24no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—42no—
425C2×C4—44no—
426C2×C4—44no—
427C2×C4—41no—
428C2×C4—42no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—41no—
438C2×C4—81no—
439C2×C4—81no—
440C2×C4—81no—
441C2×C4—81no—
442C2×C4—81no—
443C2×C4—2442no—
444C2×C4—2442no—
445C2×C4—2442no—
446C2×C4—2441no—
447C2×C4—2441no—
448C2×C4—2441no—
449C2×C4#1451974511yescharacteristic
450C2×C4#1451974811yescharacteristic
451C2×C4#1451974911yescharacteristic
452C2×C4#1451977311yescharacteristic
453C8—4881no—
454C8—2442no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—22no—
460C22—22no—
461C22—22no—
462C22—22no—
463C22—4881no—
464C22—4881no—
465C22—4881no—
466C22—4882no—
467C22—4882no—
468C22#1683967011yescharacteristic
469C22#1683989511yescharacteristic
470C22#1683989611yescharacteristic
471C22#1683990511yescharacteristic
472C22#1683990711yescharacteristic
473C22#1683994412yes—
474C22#1683995112yes—
475C22#1683999611yescharacteristic
476C22#1684001311yescharacteristic
477C4—21no—
478C4—21no—
479C4—21no—
480C4—21no—
481C4—44no—
482C4—42no—
483C4—81no—
484C4—82no—
485C4—4881no—
486C4—4882no—
487C2—21no—
488C2—21no—
489C2—21no—
490C2—21no—
491C2—9761no—
492C2#2144481412yes—
493C2#2144482112yes—
494C2#2144681511yescharacteristic
495C2#2144685511yescharacteristic
496C2#2144694711yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC2×C61×#398C2
socleC23×C61#120
prime radicalC2×#14519751C22
hypercenterC2×#398D61
hypocenterC61#9919
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
3. #21445905C2semidirect
5. C2×#16839488C2semidirect
6. #21443698C2semidirect
7. C2×C61×#398C2semidirect
241. C2×#398D61semidirect
279. C61#9919semidirect

Maximal subgroups

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

subgroupindex
C2×#168400752
#214515612
#214459052
C2×#168394952
C2×#168394882
#214436982
C2×C61×#3982
#991961