Finite Group Databasebeta

← #29571519

Subgroups — #29571519

Order 15616.

802 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840317C211yesmaximal, characteristic
2#21445796C211yesmaximal, characteristic
3#21445796C211yesmaximal, characteristic
4C2×#16839509C211yesmaximal, characteristic, complemented
5C2×#16839508C211yesmaximal, characteristic, complemented
6C2×#16839507C211yesmaximal, characteristic, complemented
7C2×C61×#332C211yesmaximal, characteristic, complemented
8#16840317—22no—
9#16840317—22no—
10#16840317—22no—
11#16840317—22no—
12C2×#14519777C2211yescharacteristic
13C2×#14519768C412yes—
14C2×#14519757—21no—
15C2×#14519753—21no—
16C2×Q8×Dic61—21no—
17C2×#14519742—21no—
18C2×#14519735C412yes—
19C2×C42×D61C2211yescharacteristic
20C2×C4⋊#92418C2211yescharacteristic
21C2×C4⋊#92418C2211yescharacteristic
22C2×#14519689—21no—
23C2×#14519689—21no—
24#16839516—21no—
25#16839516—21no—
26#16839509—22no—
27#16839508—22no—
28#16839507—22no—
29C2×C4⋊Q8×C61C2211yescharacteristic
30C2×C4⋊C8×C61C2211yescharacteristic
31C2×C4⋊C8×C61C2211yescharacteristic
32C61×#332—22no—
33C22×Dic122—21no—
34C22×C4×D61C2×C411yescharacteristic
35C22×C4×D61D411yescharacteristic
36C22×C4×D61D411yescharacteristic
37C22×#92418—21no—
38C22×#92418—21no—
39#14519777—21no—
40#14519777—21no—
41#14519777D412yes—
42#14519777D412yes—
43#14519768—24no—
44#14519768—24no—
45#14519757—24no—
46#14519757—24no—
47#14519753—24no—
48#14519753—24no—
49Q8×Dic61—24no—
50Q8×Dic61—24no—
51#14519742—24no—
52#14519742—24no—
53#14519735—24no—
54#14519735—24no—
55C2×C4⋊Dic61—21no—
56C2×C4⋊Dic61—22no—
57C2×C4⋊Dic61C2×C412yes—
58C2×#11758196—22no—
59C2×#11758198—22no—
60C2×C4×Dic61—22no—
61C2×C4×Dic61C2×C411yescharacteristic
62C2×C4×Dic61D411yescharacteristic
63C2×C4×Dic61D411yescharacteristic
64C42×D61—21no—
65C42×D61—21no—
66C42×D61—21no—
67C42×D61—21no—
68C4⋊#92418—21no—
69C4⋊#92418—21no—
70C4⋊#92418—21no—
71C4⋊#92418—21no—
72#14519689—42no—
73#14519689—42no—
74C22×Q8×C61—21no—
75C22×C8×C61—21no—
76C22×C8×C61—21no—
77C4⋊Q8×C61—21no—
78C4⋊Q8×C61—21no—
79C4⋊Q8×C61D412yes—
80C4⋊Q8×C61D412yes—
81C2×C4⋊C4×C61—21no—
82C2×C4⋊C4×C61C2×C412yes—
83C2×C42×C61C2311yescharacteristic
84C4⋊C8×C61—21no—
85C4⋊C8×C61—21no—
86C4⋊C8×C61—21no—
87C4⋊C8×C61—21no—
88C23×D61C22⋊C411yescharacteristic
89C2×Q8×C61—22no—
90C2×Q8×C61—22no—
91C2×Q8×C61—41no—
92C2×Q8×C61—41no—
93C2×Q8×C61—41no—
94C2×Q8×C61—41no—
95C22×C4×C61—22no—
96C22×C4×C61C22×C411yescharacteristic
97C22×C4×C61C2×D411yescharacteristic
98C22×C4×C61C2×D411yescharacteristic
99C22×Dic61—22no—
100C22×Dic61C22⋊C411yescharacteristic
101C22×Dic61C22⋊C411yescharacteristic
102C22×Dic61C22⋊C411yescharacteristic
103C2×C4×D61—22no—
104C2×C4×D61—21no—
105C2×C4×D61—21no—
106C2×C4×D61—22no—
107C2×C4×D61—21no—
108C2×C4×D61—21no—
109C2×C4×D61—21no—
110C2×C4×D61—21no—
111C2×C4×D61—21no—
112C2×C4×D61—21no—
113C2×C4×D61—21no—
114C2×C4×D61—21no—
115C2×C4×D61—21no—
116C2×C4×D61—21no—
117C2×C4×D61—21no—
118C2×C4×D61—21no—
119C2×Dic122—22no—
120C2×Dic122—22no—
121C2×Dic122—41no—
122C2×Dic122—41no—
123C2×Dic122—41no—
124C2×Dic122—41no—
125C2×C8×C61—41no—
126C2×C8×C61—41no—
127C2×C8×C61—41no—
128C2×C8×C61—41no—
129C2×C8×C61—41no—
130C2×C8×C61—41no—
131C4⋊C4×C61—22no—
132C4⋊C4×C61—22no—
133C4⋊C4×C61—22no—
134C4⋊C4×C61C22⋊C414yes—
135C42×C61C2×D411yescharacteristic
136C42×C61C2×D411yescharacteristic
137C42×C61C2×D411yescharacteristic
138C42×C61C2×D411yescharacteristic
139#11758198—28no—
140C4⋊Dic61—28no—
141C4⋊Dic61—22no—
142C4⋊Dic61—22no—
143C4⋊Dic61—22no—
144C4⋊Dic61C22⋊C414yes—
145#11758196—28no—
146C4×Dic61—28no—
147C4×Dic61—21no—
148C4×Dic61—21no—
149C4×Dic61—21no—
150C4×Dic61—21no—
151C4×Dic61—21no—
152C4×Dic61—21no—
153C2×#92418—41no—
154C2×#92418—41no—
155C2×#92418—41no—
156C2×#92418—41no—
157C2×#92418—41no—
158C2×#92418—41no—
159C23×C61C2×C22⋊C411yescharacteristic
160C22×D61—21no—
161C22×D61—21no—
162C22×D61—21no—
163C22×D61—21no—
164C22×D61—21no—
165C22×D61—21no—
166C22×D61#10112yes—
167Q8×C61—42no—
168Q8×C61—42no—
169Q8×C61—42no—
170Q8×C61—42no—
171C2×C4×C61—21no—
172C2×C4×C61—21no—
173C2×C4×C61—24no—
174C2×C4×C61—42no—
175C2×C4×C61—42no—
176C2×C4×C61C2×C22⋊C411yescharacteristic
177C2×C4×C61C2×C22⋊C411yescharacteristic
178C2×C4×C61#12011yescharacteristic
179C2×C4×C61#12011yescharacteristic
180C2×C4×C61#12011yescharacteristic
181C2×C4×C61#12011yescharacteristic
182C2×C4×C61#13511yescharacteristic
183C2×C4×C61#13511yescharacteristic
184C2×C4×C61#13511yescharacteristic
185C2×C4×C61#13511yescharacteristic
186C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
187C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
188C2×C4×C61#13711yescharacteristic
189C2×C4×C61#13711yescharacteristic
190C2×Dic61—21no—
191C2×Dic61—21no—
192C2×Dic61—21no—
193C2×Dic61—21no—
194C2×Dic61—24no—
195C2×Dic61—21no—
196C2×Dic61—21no—
197C2×Dic61—21no—
198C2×Dic61—21no—
199C2×Dic61—42no—
200C2×Dic61—42no—
201C2×Dic61#10112yes—
202C4×D61—24no—
203C4×D61—24no—
204C4×D61—41no—
205C4×D61—41no—
206C4×D61—41no—
207C4×D61—41no—
208C4×D61—41no—
209C4×D61—41no—
210C4×D61—41no—
211C4×D61—41no—
212Dic122—42no—
213Dic122—42no—
214Dic122—42no—
215Dic122—42no—
216C8×C61—81no—
217C8×C61—81no—
218#92418—81no—
219#92418—81no—
220#8345—611nomaximal, Sylow
221C22×C61#37911yescharacteristic
222C22×C61C2×#10111yescharacteristic
223C22×C61C2×#10111yescharacteristic
224C22×C61#41611yescharacteristic
225C22×C61#41611yescharacteristic
226C22×C61#41711yescharacteristic
227C22×C61#41711yescharacteristic
228C2×D61—22no—
229C2×D61—22no—
230C2×D61—22no—
231C2×D61—41no—
232C2×D61—41no—
233C2×D61—41no—
234C2×D61—41no—
235C4×C61—21no—
236C4×C61—21no—
237C4×C61—44no—
238C4×C61#44911yescharacteristic
239C4×C61#44911yescharacteristic
240C4×C61#44911yescharacteristic
241C4×C61#44911yescharacteristic
242C4×C61#45211yescharacteristic
243C4×C61#45211yescharacteristic
244C4×C61#45211yescharacteristic
245C4×C61#45211yescharacteristic
246Dic61—22no—
247Dic61—44no—
248Dic61—41no—
249Dic61—41no—
250C2×#533—611no—
251#1797—611no—
252#1797—611no—
253C2×#332—611no—
254C2×#332—611no—
255C2×#332—611no—
256C2×#332D6111yescharacteristic, complemented
257C2×C61#154411yescharacteristic
258C2×C61#155211yescharacteristic
259C2×C61#155211yescharacteristic
260C2×C61#156111yescharacteristic
261C2×C61#178411yescharacteristic
262C2×C61#178811yescharacteristic
263C2×C61#178811yescharacteristic
264D61—42no—
265#533—1222no—
266#533—1222no—
267#533—1222no—
268#533—1222no—
269C2×C4⋊Q8—611no—
270C2×C4⋊Q8C2×D6111yescharacteristic
271C2×#125—612no—
272C2×C22⋊Q8—1221no—
273C2×C22⋊Q8—1221no—
274C2×C4×Q8—1221no—
275C2×C4×Q8—1221no—
276C2×#117—612no—
277C22×C42—611no—
278C2×C4⋊C8—611no—
279C2×C4⋊C8—611no—
280C2×C4⋊C8C2×D6111yescharacteristic
281C2×C4⋊C8C2×D6111yescharacteristic
282C2×C22⋊C8—1221no—
283C2×C22⋊C8—1221no—
284#336—1221no—
285#336—1221no—
286#332—22no—
287#332—1222no—
288#332—1222no—
289#332—1222no—
290C61#834511yescharacteristic, complemented, Sylow
291C22×Q8—21no—
292C22×Q8—1221no—
293C23×C4—611no—
294C23×C4—611no—
295C23×C4—611no—
296C22×C8—21no—
297C22×C8—21no—
298C22×C8—1221no—
299C22×C8—1221no—
300C4⋊Q8—21no—
301C4⋊Q8—21no—
302C4⋊Q8—612no—
303C4⋊Q8—612no—
304C4⋊Q8—1221no—
305C4⋊Q8—1221no—
306C4⋊Q8D24412yes—
307C4⋊Q8C22⋊D6112yes—
308#125—1224no—
309#125—1224no—
310C22⋊Q8—1224no—
311C22⋊Q8—1224no—
312C22⋊Q8—1224no—
313C22⋊Q8—1224no—
314C4×Q8—1224no—
315C4×Q8—1224no—
316C4×Q8—1224no—
317C4×Q8—1224no—
318#117—1224no—
319#117—1224no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—612no—
322C2×C4⋊C4—1222no—
323C2×C4⋊C4—1222no—
324C2×C4⋊C4—1221no—
325C2×C4⋊C4C4×D6112yes—
326C2×C22⋊C4—1222no—
327C2×C42—611no—
328C2×C42—611no—
329C2×C42—611no—
330C2×C42—1222no—
331C2×C42—1221no—
332C2×C42—1221no—
333C2×C42—1221no—
334C2×C42—1221no—
335C2×C42C22×D6111yescharacteristic
336C4⋊C8—21no—
337C4⋊C8—21no—
338C4⋊C8—21no—
339C4⋊C8—21no—
340C4⋊C8—1221no—
341C4⋊C8—1221no—
342C4⋊C8—1221no—
343C4⋊C8—1221no—
344C22⋊C8—2442no—
345C22⋊C8—2442no—
346C24—611no—
347C2×Q8—22no—
348C2×Q8—22no—
349C2×Q8—41no—
350C2×Q8—41no—
351C2×Q8—41no—
352C2×Q8—41no—
353C2×Q8—1222no—
354C2×Q8—1222no—
355C2×Q8—2441no—
356C2×Q8—2441no—
357C2×Q8—2441no—
358C2×Q8—2441no—
359C22×C4—22no—
360C22×C4—611no—
361C22×C4—611no—
362C22×C4—611no—
363C22×C4—1222no—
364C22×C4—1222no—
365C22×C4—1221no—
366C22×C4—1221no—
367C22×C4—1222no—
368C22×C4—1221no—
369C22×C4—1221no—
370C22×C4—1221no—
371C22×C4—1221no—
372C22×C4—1221no—
373C22×C4—1221no—
374C22×C4—1221no—
375C22×C4—1221no—
376C22×C4—1221no—
377C22×C4—1221no—
378C22×C4—1221no—
379C22×C4—1221no—
380C22×C4C2×C4×D6111yescharacteristic
381C22×C4D4×D6111yescharacteristic
382C22×C4D4×D6111yescharacteristic
383C2×C8—41no—
384C2×C8—41no—
385C2×C8—41no—
386C2×C8—41no—
387C2×C8—41no—
388C2×C8—41no—
389C2×C8—2441no—
390C2×C8—2441no—
391C2×C8—2441no—
392C2×C8—2441no—
393C2×C8—2441no—
394C2×C8—2441no—
395C4⋊C4—22no—
396C4⋊C4—22no—
397C4⋊C4—22no—
398C4⋊C4—614no—
399C4⋊C4—1228no—
400C4⋊C4—1228no—
401C4⋊C4—1222no—
402C4⋊C4—1222no—
403C4⋊C4—1222no—
404C4⋊C4#1175819814yes—
405C22⋊C4—1228no—
406C42—1228no—
407C42—1221no—
408C42—1221no—
409C42—1221no—
410C42—1221no—
411C42—1221no—
412C42—1221no—
413C42C2×D24411yescharacteristic
414C42D4×D6111yescharacteristic
415C42D4×D6111yescharacteristic
416C42C2×C22⋊D6111yescharacteristic
417C23—612no—
418C23—1221no—
419C23—1221no—
420C23—1221no—
421C23—1221no—
422C23—1221no—
423C23—1221no—
424C23C22⋊C4×D6111yescharacteristic
425Q8—42no—
426Q8—42no—
427Q8—42no—
428Q8—42no—
429Q8—2442no—
430Q8—2442no—
431Q8—2442no—
432Q8—2442no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—24no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—612no—
439C2×C4—1224no—
440C2×C4—1224no—
441C2×C4—1221no—
442C2×C4—1221no—
443C2×C4—1221no—
444C2×C4—1221no—
445C2×C4—1221no—
446C2×C4—1221no—
447C2×C4—1221no—
448C2×C4—1221no—
449C2×C4—1224no—
450C2×C4—2442no—
451C2×C4—2442no—
452C2×C4—2441no—
453C2×C4—2441no—
454C2×C4—2441no—
455C2×C4—2441no—
456C2×C4—2441no—
457C2×C4—2441no—
458C2×C4—2441no—
459C2×C4—2441no—
460C2×C4C22⋊C4×D6111yescharacteristic
461C2×C4C2×#1175819811yescharacteristic
462C2×C4#1451974511yescharacteristic
463C2×C4#1451974511yescharacteristic
464C2×C4#1451974711yescharacteristic
465C2×C4#1451974711yescharacteristic
466C2×C4#1451979611yescharacteristic
467C2×C4#1451979811yescharacteristic
468C2×C4#1451979811yescharacteristic
469C2×C4#1451980011yescharacteristic
470C2×C4#1451980111yescharacteristic
471C2×C4#1451980411yescharacteristic
472C2×C4#1451980611yescharacteristic
473C2×C4#1451980911yescharacteristic
474C8—81no—
475C8—81no—
476C8—4881no—
477C8—4881no—
478C22—1222no—
479C22—1222no—
480C22—1222no—
481C22—2441no—
482C22—2441no—
483C22—2441no—
484C22—2441no—
485C22#1683961711yescharacteristic
486C22#101×D6111yescharacteristic
487C22#101×D6111yescharacteristic
488C22#1683975511yescharacteristic
489C22#1683975711yescharacteristic
490C22#1683976011yescharacteristic
491C22#1683976211yescharacteristic
492C4—21no—
493C4—21no—
494C4—44no—
495C4—1222no—
496C4—2441no—
497C4—2441no—
498C4—2444no—
499C4#1683990411yescharacteristic
500C4#1683990611yescharacteristic
501C4#1683990811yescharacteristic
502C4#1683991011yescharacteristic
503C4#1683992111yescharacteristic
504C4#1683992311yescharacteristic
505C4#1683992511yescharacteristic
506C4#1683992711yescharacteristic
507C2—2442no—
508C2#2144448211yescharacteristic
509C2#2144451611yescharacteristic
510C2#2144451811yescharacteristic
511C2#2144455511yescharacteristic
512C2#2144574111yescharacteristic
513C2#2144575611yescharacteristic
514C2#2144575811yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC2×C61×#332C2
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC2×C42×C61C23
hypercenterC2×#332D61
hypocenterC61#8345
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
4. C2×#16839509C2semidirect
5. C2×#16839508C2semidirect
6. C2×#16839507C2semidirect
7. C2×C61×#332C2semidirect
256. C2×#332D61semidirect
290. C61#8345semidirect

Maximal subgroups

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

subgroupindex
C2×#168403172
#214457962
C2×#168395092
C2×#168395082
C2×#168395072
C2×C61×#3322
#834561