Finite Group Databasebeta

← #29648258

Subgroups — #29648258

Order 15616.

876 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459643C211yesmaximal, characteristic
2#21454830C212yesmaximal
3#21444455C211yesmaximal, characteristic, complemented
4#21444446C211yesmaximal, characteristic, complemented
5#21444444C211yesmaximal, characteristic, complemented
6#21444433C212yesmaximal, complemented
7#21444432C212yesmaximal, complemented
8#21444419C212yesmaximal, complemented
9#21444412C211yesmaximal, characteristic, complemented
10#330×D61C211yesmaximal, characteristic, complemented
11C2×C61×#330C211yesmaximal, characteristic, complemented
12#16840489—22no—
13#16840468—22no—
14#16840467—22no—
15#16840467—22no—
16#16840393C412yes—
17#16840392C412yes—
18#16840392C412yes—
19#16840319C2211yescharacteristic
20#16840318C2211yescharacteristic
21#16840318C2211yescharacteristic
22#125×D61C2211yescharacteristic
23#125×D61C2211yescharacteristic
24#16840243C412yes—
25C4×#11758222C2211yescharacteristic
26#16839890—22no—
27#16839835—22no—
28#16839833—22no—
29C8×C22⋊D61—22no—
30#16839819C2212yes—
31#16839817C2212yes—
32#16839817C2212yes—
33#16839714C2212yes—
34#97×D61C2212yes—
35#16839504C2211yescharacteristic
36#16839504C2211yescharacteristic
37#16839504C2212yes—
38#16839503C2212yes—
39#16839503C2212yes—
40#16839503C2212yes—
41#16839503C2212yes—
42C2×#125×C61C2211yescharacteristic
43C2×#97×C61C2212yes—
44C61×#330C2211yescharacteristic
45C61×#330C2212yes—
46C61×#330C2211yescharacteristic
47C2×#11758222C2×C411yescharacteristic
48C2×#11758189—22no—
49C2×C8×D61—22no—
50#14519777C2×C412yes—
51#14519776—22no—
52#14519776—22no—
53#14519776—22no—
54#14519776C2×C412yes—
55#14519776C2×C412yes—
56#14519769C2311yescharacteristic
57#14519769C2311yescharacteristic
58#14519768—22no—
59#14519768C2×C412yes—
60#14519768C2×C412yes—
61#14519767—22no—
62#14519767—22no—
63#14519767—22no—
64#14519767—22no—
65#14519757—22no—
66#14519757—22no—
67#14519756—22no—
68#14519756—22no—
69#14519756—22no—
70#14519755—22no—
71#14519755—22no—
72#14519755—22no—
73#14519755—22no—
74C4×Dic122—22no—
75C4×Dic122D412yes—
76#14519742—22no—
77#14519742—22no—
78#14519742—22no—
79C4×D244D412yes—
80#14519739—22no—
81C4×C22⋊D61—22no—
82C4×C22⋊D61—22no—
83C4×C22⋊D61D412yes—
84C4×C22⋊D61D412yes—
85#14519736C2×C412yes—
86#14519736C2×C411yescharacteristic
87#14519735C2×C412yes—
88#14519735C2×C412yes—
89#14519734C2×C411yescharacteristic
90#14519734C2×C411yescharacteristic
91C4⋊C4×D61—22no—
92C4⋊C4×D61—22no—
93C4⋊C4×D61C2×C412yes—
94C4⋊C4×D61C2×C412yes—
95C42×D61C2311yescharacteristic
96C42×D61C2311yescharacteristic
97C4⋊#92418—22no—
98#14519706—22no—
99#14519706—22no—
100C22⋊#92418—22no—
101#14519689—22no—
102#14519689—22no—
103#14519688C2312yes—
104#14519688C2312yes—
105#14519687—22no—
106C8×Dic61—22no—
107C22×C8×C61—22no—
108#125×C61—22no—
109#125×C61C2×C412yes—
110#125×C61C2311yescharacteristic
111#125×C61C2311yescharacteristic
112C2×C4⋊C4×C61—22no—
113C2×C4⋊C4×C61C2×C412yes—
114C2×C42×C61C2311yescharacteristic
115#97×C61—22no—
116#97×C61C2312yes—
117#97×C61C2312yes—
118C22×C4×C61—22no—
119C22×C4×C61C22×C411yescharacteristic
120C22×C4×C61C2×D412yes—
121C2×C22⋊D61C22⋊C411yescharacteristic
122C2×C22⋊D61C22⋊C411yescharacteristic
123#11758222—24no—
124C2×D244C22⋊C411yescharacteristic
125C2×C4×D61—22no—
126C2×C4×D61—22no—
127C2×C4×D61C22×C411yescharacteristic
128C2×C4×D61C22×C411yescharacteristic
129C2×C4×D61C2×D412yes—
130C2×C4×D61C2×D412yes—
131C2×Dic122—22no—
132C2×Dic122—22no—
133C2×Dic122—22no—
134C2×Dic122C22⋊C411yescharacteristic
135C2×C8×C61—22no—
136C2×C8×C61—22no—
137C2×C8×C61—44no—
138C4⋊C4×C61—22no—
139C4⋊C4×C61—22no—
140C4⋊C4×C61—22no—
141C4⋊C4×C61—22no—
142C4⋊C4×C61—22no—
143C4⋊C4×C61C22×C412yes—
144C4⋊C4×C61C22×C412yes—
145C42×C61C22×C411yescharacteristic
146C42×C61C2×D412yes—
147C42×C61C2411yescharacteristic
148C22⋊Dic61—22no—
149C22⋊Dic61C22⋊C412yes—
150#11758198—22no—
151#11758198—22no—
152#11758198C22⋊C412yes—
153#11758198C22⋊C412yes—
154C4⋊Dic61—22no—
155C4⋊Dic61—22no—
156C4⋊Dic61—22no—
157C4⋊Dic61C22⋊C412yes—
158C4⋊Dic61C22×C412yes—
159C4⋊Dic61C22×C412yes—
160#11758196—22no—
161#11758196—22no—
162#11758196—22no—
163#11758196—22no—
164#11758196—22no—
165#11758196—22no—
166#11758196—22no—
167#11758196—22no—
168#11758196C22⋊C412yes—
169#11758196C22⋊C412yes—
170C4×Dic61—22no—
171C4×Dic61—22no—
172C4×Dic61—22no—
173C4×Dic61C22×C411yescharacteristic
174C4×Dic61C22×C411yescharacteristic
175C4×Dic61C2×D412yes—
176C4×Dic61C2×D412yes—
177C2×#92418—22no—
178C2×#92418—22no—
179#11758189—44no—
180C8×D61—44no—
181C23×C61C2×C22⋊C411yescharacteristic
182C22×D61C2×C22⋊C411yescharacteristic
183C22×D61C2×C22⋊C411yescharacteristic
184C2×C4×C61—22no—
185C2×C4×C61—22no—
186C2×C4×C61—22no—
187C2×C4×C61—42no—
188C2×C4×C61—82no—
189C2×C4×C61C2×C22⋊C411yescharacteristic
190C2×C4×C61C2×C22⋊C412yes—
191C2×C4×C61C23×C411yescharacteristic
192C2×C4×C61C22×D412yes—
193C22⋊D61—22no—
194C22⋊D61#10114yes—
195C2×Dic61—22no—
196C2×Dic61—22no—
197C2×Dic61C2×C22⋊C411yescharacteristic
198C2×Dic61C2×C22⋊C412yes—
199C2×Dic61C2×C22⋊C412yes—
200C2×Dic61C2×C22⋊C411yescharacteristic
201D244—22no—
202C4×D61—22no—
203C4×D61—22no—
204C4×D61—42no—
205C4×D61—42no—
206C4×D61—82no—
207C4×D61—82no—
208Dic122—22no—
209Dic122—82no—
210Dic122—82no—
211Dic122—82no—
212C8×C61—24no—
213C8×C61—42no—
214#92418—42no—
215#92418—42no—
216#17689—611nomaximal, Sylow
217C22×C61—22no—
218C22×C61C2×#10112yes—
219C22×C61C22×C22⋊C411yescharacteristic
220C2×D61—22no—
221C2×D61—21no—
222C2×D61—22no—
223C2×D61C2×#10112yes—
224C4×C61—21no—
225C4×C61—21no—
226C4×C61—22no—
227C4×C61—22no—
228C4×C61—42no—
229C4×C61—42no—
230Dic61—21no—
231Dic61—22no—
232Dic61—22no—
233Dic61—42no—
234Dic61—42no—
235Dic61C2×#10112yes—
236#3504—611no—
237#2970—612no—
238#1537—611no—
239#1534—611no—
240#1534—611no—
241#1531—612no—
242#1531—612no—
243#1528—612no—
244#1526—611no—
245C2×#330—611no—
246C2×#330D6111yescharacteristic, complemented
247C2×C61—22no—
248C2×C61C22×#10111yescharacteristic
249C2×C61#290112yes—
250D61—22no—
251D61—41no—
252#557—1222no—
253#554—1222no—
254#554—1222no—
255#554—1222no—
256#544—612no—
257#544—612no—
258#544—612no—
259#533—611no—
260#533—611no—
261#533—611no—
262C2×#125—611no—
263C2×#125—611no—
264C2×#125C2×D6111yescharacteristic
265#520—612no—
266C4×#41—611no—
267#446—1222no—
268#435—1222no—
269#435—1222no—
270C8×D4—1222no—
271#432—612no—
272#432—612no—
273#432—612no—
274C4×M16—612no—
275C2×#97—612no—
276C2×#97C2×D6112yes—
277#330—611no—
278#330—611no—
279#330—612no—
280#330—612no—
281#330—612no—
282#330—612no—
283#330—612no—
284#330C2×D6111yescharacteristic
285#330C2×D6111yescharacteristic
286#330C2×D6112yes—
287C61#1768911yescharacteristic, complemented, Sylow
288C2×#41—611no—
289C2×M16—1222no—
290C22×C8—22no—
291C22×C8—1222no—
292C4⋊Q8—612no—
293C4⋊Q8—612no—
294C4⋊Q8—612no—
295C4⋊Q8—1222no—
296C4⋊Q8—1222no—
297C4⋊Q8—1222no—
298#125—22no—
299#125—612no—
300#125—612no—
301#125—611no—
302#125—611no—
303#125—1222no—
304#125—1222no—
305#125—1222no—
306#125—1222no—
307#125—1222no—
308#125C4×D6112yes—
309#125C22×D6111yescharacteristic
310#125C22×D6111yescharacteristic
311C22⋊Q8—1222no—
312C22⋊Q8—1222no—
313C22⋊Q8—1222no—
314C22⋊Q8—1222no—
315C22⋊Q8—1222no—
316C22⋊Q8—1222no—
317C22⋊Q8—1222no—
318C22⋊Q8—1222no—
319C22⋊Q8—1222no—
320C4×Q8—612no—
321C4×Q8—1222no—
322C4×Q8—1222no—
323C4×Q8—1222no—
324C4×Q8—1222no—
325C4×D4—612no—
326C4×D4—612no—
327C4×D4—612no—
328C4×D4—1222no—
329C4×D4—1222no—
330C4×D4—1222no—
331#117—611no—
332#117—611no—
333#117—611no—
334#117—612no—
335#117—612no—
336#117—612no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—612no—
339C2×C4⋊C4—612no—
340C2×C4⋊C4—1222no—
341C2×C4⋊C4—1222no—
342C2×C4⋊C4C4×D6112yes—
343C2×C42—611no—
344C2×C42—611no—
345C2×C42C22×D6111yescharacteristic
346C4⋊C8—1222no—
347C4⋊C8—1222no—
348C4⋊C8—1222no—
349C22⋊C8—1222no—
350C22⋊C8—1222no—
351C22⋊C8—1222no—
352#97—22no—
353#97—612no—
354#97—612no—
355#97—1222no—
356#97C22×D6112yes—
357#97C22×D6112yes—
358C4×C8—1222no—
359#41—1224no—
360C2×Q8—611no—
361C2×Q8—1222no—
362C2×Q8—1222no—
363C2×Q8—1222no—
364C2×D4—611no—
365C2×D4—611no—
366C2×D4—611no—
367C22×C4—22no—
368C22×C4—611no—
369C22×C4—611no—
370C22×C4—612no—
371C22×C4—612no—
372C22×C4—1222no—
373C22×C4—1222no—
374C22×C4C2×C4×D6111yescharacteristic
375C22×C4D4×D6112yes—
376M16—2444no—
377C2×C8—22no—
378C2×C8—22no—
379C2×C8—44no—
380C2×C8—1222no—
381C2×C8—1222no—
382C2×C8—2444no—
383C4⋊C4—22no—
384C4⋊C4—22no—
385C4⋊C4—22no—
386C4⋊C4—22no—
387C4⋊C4—22no—
388C4⋊C4—612no—
389C4⋊C4—612no—
390C4⋊C4—612no—
391C4⋊C4—612no—
392C4⋊C4—612no—
393C4⋊C4—1222no—
394C4⋊C4—1222no—
395C4⋊C4—1222no—
396C4⋊C4—1222no—
397C4⋊C4—1222no—
398C4⋊C4—1222no—
399C4⋊C4—1222no—
400C4⋊C4—1222no—
401C4⋊C4—1222no—
402C4⋊C4—1222no—
403C4⋊C4—1222no—
404C4⋊C4C2×C4×D6112yes—
405C4⋊C4C2×C4×D6112yes—
406C22⋊C4—612no—
407C22⋊C4—612no—
408C22⋊C4—612no—
409C22⋊C4—1222no—
410C22⋊C4—1222no—
411C22⋊C4—1222no—
412C42—611no—
413C42—611no—
414C42—612no—
415C42—612no—
416C42—1222no—
417C42—1222no—
418C42—1222no—
419C42C2×C4×D6111yescharacteristic
420C42D4×D6112yes—
421C42C23×D6111yescharacteristic
422C23—611no—
423C23—611no—
424C23C22⋊C4×D6111yescharacteristic
425Q8—1222no—
426Q8—4882no—
427Q8—4882no—
428Q8—4882no—
429D4—614no—
430D4—1222no—
431D4—1222no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—42no—
436C2×C4—82no—
437C2×C4—611no—
438C2×C4—611no—
439C2×C4—612no—
440C2×C4—612no—
441C2×C4—1222no—
442C2×C4—1222no—
443C2×C4—1222no—
444C2×C4—1222no—
445C2×C4—4882no—
446C2×C4—4882no—
447C2×C4—2442no—
448C2×C4—2442no—
449C2×C4C22⋊C4×D6111yescharacteristic
450C2×C4C22⋊C4×D6112yes—
451C2×C4C22×C4×D6111yescharacteristic
452C2×C4C2×D4×D6112yes—
453C8—24no—
454C8—42no—
455C8—2442no—
456C8—2442no—
457C22—22no—
458C22—612no—
459C22—1222no—
460C22—1222no—
461C22—1221no—
462C22#101×D6112yes—
463C22C2×C22⋊C4×D6111yescharacteristic
464C4—22no—
465C4—22no—
466C4—21no—
467C4—21no—
468C4—42no—
469C4—42no—
470C4—612no—
471C4—1222no—
472C4—1222no—
473C4—1221no—
474C4—2442no—
475C4—2442no—
476C2—22no—
477C2—1222no—
478C2—2441no—
479C2C2×#101×D6111yescharacteristic
480C2#2145436312yes—
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC2×C61×#330C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#11758222C2×C4
cosocleC42×C61C24
hypercenterC2×#330D61
hypocenterC61#17689
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#330

Complements

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

NH ≅ G/Ntype
3. #21444455C2semidirect
4. #21444446C2semidirect
5. #21444444C2semidirect
6. #21444433C2semidirect
7. #21444432C2semidirect
8. #21444419C2semidirect
9. #21444412C2semidirect
10. #330×D61C2semidirect
11. C2×C61×#330C2semidirect
246. C2×#330D61semidirect
287. C61#17689semidirect

Maximal subgroups

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

subgroupindex
#214596432
#214548302
#214444552
#214444462
#214444442
#214444332
#214444322
#214444192
#214444122
#330×D612
C2×C61×#3302
#1768961