Finite Group Databasebeta

← #352×Dic61 #29595152

Subgroups — #352×Dic61 #29595152

Order 15616.

576 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#123×Dic61C211yesmaximal, characteristic
2C2×#16839552C211yesmaximal, characteristic
3#100×Dic61C211yesmaximal, characteristic
4#99×Dic61C211yesmaximal, characteristic
5#21443938C211yesmaximal, characteristic
6#21443936C211yesmaximal, characteristic
7C2×C61×#352C211yesmaximal, characteristic
8C2×D4×Dic61C2211yescharacteristic
9C22×C4×Dic61C411yescharacteristic, complemented
10C2×#14519694C2211yescharacteristic
11C2×#14519692C2211yescharacteristic
12M16×Dic61—21no—
13#16839655—21no—
14#16839648—21no—
15#16839642C2211yescharacteristic
16#16839637C411yescharacteristic, complemented
17#16839625C411yescharacteristic, complemented
18C4⋊C4×Dic61—21no—
19C22⋊C4×Dic61—21no—
20C22⋊C4×Dic61—21no—
21C22⋊C4×Dic61C411yescharacteristic, complemented
22#16839552C414yescomplemented
23#16839530—21no—
24#16839528—21no—
25C2×#123×C61C2211yescharacteristic
26C2×#100×C61C2211yescharacteristic
27C2×#99×C61C2211yescharacteristic
28C61×#352C414yescomplemented
29C23×Dic61C2×C411yescharacteristic
30C23×Dic61C2×C411yescharacteristic
31C23×Dic61D411yescharacteristic
32C2×#11758194—21no—
33D4×Dic61—41no—
34D4×Dic61—41no—
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61D411yescharacteristic
37C2×C22⋊Dic61—21no—
38C2×C22⋊Dic61—21no—
39C2×C22⋊Dic61C2×C411yescharacteristic
40C2×C22⋊Dic61C2×C411yescharacteristic
41C2×C22⋊Dic61D411yescharacteristic
42C2×C4×Dic61—21no—
43C2×C4×Dic61—21no—
44C2×C4×Dic61—21no—
45C2×C4×Dic61—41no—
46C2×C4×Dic61—41no—
47C2×C4×Dic61—41no—
48C2×C4×Dic61D411yescharacteristic
49#14519694—21no—
50#14519694C2×C412yes—
51#14519692—21no—
52#14519692C2×C412yes—
53#14519687—41no—
54C8×Dic61—41no—
55#14519684—21no—
56#14519684—21no—
57#14519684—21no—
58#14519684—21no—
59#14519684—21no—
60#14519684—41no—
61C22×D4×C61C2311yescharacteristic
62C23×C4×C61C2×C411yescharacteristic
63C2×M16×C61—21no—
64#123×C61—21no—
65#123×C61—21no—
66#123×C61C2×C412yes—
67#123×C61C2×C412yes—
68C2×C4⋊C4×C61—21no—
69C2×C22⋊C4×C61—21no—
70C2×C22⋊C4×C61—21no—
71C2×C22⋊C4×C61C2×C411yescharacteristic
72#100×C61—21no—
73#100×C61C2×C412yes—
74#99×C61—21no—
75#99×C61C2×C412yes—
76C24×C61C22×C411yescharacteristic
77C24×C61C2×D411yescharacteristic
78C2×D4×C61—41no—
79C2×D4×C61—41no—
80C2×D4×C61C22×C411yescharacteristic
81C2×D4×C61C22×C411yescharacteristic
82C2×D4×C61#4111yescharacteristic
83C2×D4×C61#4111yescharacteristic
84C22×C4×C61—21no—
85C22×C4×C61—21no—
86C22×C4×C61—21no—
87C22×C4×C61—41no—
88C22×C4×C61—41no—
89C22×C4×C61—41no—
90C22×C4×C61C4212yescomplemented
91C22×C4×C61C2×D411yescharacteristic
92C22×Dic61—21no—
93C22×Dic61—21no—
94C22×Dic61—21no—
95C22×Dic61—21no—
96C22×Dic61—21no—
97C22×Dic61—21no—
98C22×Dic61—42no—
99C22×Dic61—42no—
100C22×Dic61—42no—
101C22×Dic61—41no—
102C22×Dic61—41no—
103C22×Dic61C22⋊C411yescharacteristic
104C22×Dic61C22⋊C411yescharacteristic
105C22×Dic61C22⋊C411yescharacteristic
106C22×Dic61C22⋊C411yescharacteristic
107M16×C61—22no—
108M16×C61—41no—
109C2×C8×C61—41no—
110C4⋊C4×C61—22no—
111C4⋊C4×C61—22no—
112C22⋊C4×C61—21no—
113C22⋊C4×C61—22no—
114C22⋊C4×C61—22no—
115C22⋊C4×C61—22no—
116C22⋊C4×C61—41no—
117C22⋊C4×C61C4212yescomplemented
118C22⋊Dic61—22no—
119C22⋊Dic61—41no—
120C22⋊Dic61—41no—
121C22⋊Dic61—42no—
122C22⋊Dic61—41no—
123C22⋊Dic61—41no—
124C4⋊Dic61—41no—
125C4⋊Dic61—42no—
126C4×Dic61—21no—
127C4×Dic61—21no—
128C4×Dic61—42no—
129C4×Dic61—42no—
130C4×Dic61—41no—
131C4×Dic61—41no—
132C4×Dic61—82no—
133#11758194—22no—
134#11758194—41no—
135C2×#92418—41no—
136C23×C61—21no—
137C23×C61—21no—
138C23×C61—21no—
139C23×C61—21no—
140C23×C61—41no—
141C23×C61—41no—
142C23×C61—41no—
143C23×C61—41no—
144C23×C61C2×C4211yescharacteristic
145C23×C61C2×C22⋊C411yescharacteristic
146C23×C61#11711yescharacteristic
147C23×C61C4×D411yescharacteristic
148C23×C61C4×D411yescharacteristic
149D4×C61—41no—
150D4×C61—41no—
151D4×C61—41no—
152D4×C61—41no—
153C2×C4×C61—21no—
154C2×C4×C61—21no—
155C2×C4×C61—22no—
156C2×C4×C61—22no—
157C2×C4×C61—41no—
158C2×C4×C61—41no—
159C2×C4×C61—42no—
160C2×C4×C61—41no—
161C2×C4×C61—41no—
162C2×C4×C61—42no—
163C2×C4×C61—42no—
164C2×C4×C61—81no—
165C2×C4×C61—81no—
166C2×C4×C61C4×D411yescharacteristic
167C2×C4×C61C4×D411yescharacteristic
168C2×Dic61—22no—
169C2×Dic61—22no—
170C2×Dic61—21no—
171C2×Dic61—21no—
172C2×Dic61—21no—
173C2×Dic61—42no—
174C2×Dic61—41no—
175C2×Dic61—42no—
176C2×Dic61—41no—
177C2×Dic61—42no—
178C2×Dic61—42no—
179C2×Dic61—41no—
180C2×Dic61—41no—
181C2×Dic61—41no—
182C2×Dic61—42no—
183C2×Dic61—41no—
184C2×Dic61—42no—
185C2×Dic61—41no—
186C2×Dic61—41no—
187C2×Dic61—81no—
188C2×Dic61—81no—
189C2×Dic61—81no—
190C2×Dic61#9911yescharacteristic
191C2×Dic61#9911yescharacteristic
192C8×C61—42no—
193#92418—42no—
194C4×#352—611nomaximal, Sylow
195C22×C61—21no—
196C22×C61—21no—
197C22×C61—21no—
198C22×C61—21no—
199C22×C61—21no—
200C22×C61—21no—
201C22×C61—41no—
202C22×C61—41no—
203C22×C61—41no—
204C22×C61—41no—
205C22×C61—42no—
206C22×C61—41no—
207C22×C61—41no—
208C22×C61—41no—
209C22×C61—41no—
210C22×C61—81no—
211C22×C61C4×C22⋊C411yescharacteristic
212C22×C61C2×#9911yescharacteristic
213C22×C61#41011yescharacteristic
214C4×C61—21no—
215C4×C61—21no—
216C4×C61—42no—
217C4×C61—42no—
218C4×C61—82no—
219Dic61—21no—
220Dic61—41no—
221Dic61—41no—
222Dic61—41no—
223Dic61—42no—
224Dic61—81no—
225Dic61—82no—
226Dic61#35212yesdirect product factor
227C4×#123—611no—
228C2×#352—611no—
229C2×#352D6111yescharacteristic
230C4×#100—611no—
231C4×#99—611no—
232#1390—611no—
233#1390—611no—
234C2×C61—21no—
235C2×C61—21no—
236C2×C61—41no—
237C2×C61—41no—
238C2×C61—41no—
239C2×C61—41no—
240C2×C61C4×#9911yescharacteristic
241C2×C61C2×#35211yescharacteristic
242C2×C61#212011yescharacteristic
243C2×#123C2×D6111yescharacteristic
244C2×C4×D4—611no—
245C22×C42—611no—
246C2×#100—611no—
247C2×#100C2×D6111yescharacteristic
248C2×#99—611no—
249C2×#99C2×D6111yescharacteristic
250C4×M16—1221no—
251#388—1221no—
252#387—1221no—
253#386—611no—
254#385—611no—
255#381—611no—
256C4×C4⋊C4—1221no—
257C4×C22⋊C4—611no—
258C4×C22⋊C4—1221no—
259C4×C22⋊C4—1221no—
260#352—614no—
261#352Dic6114yesdirect product factor
262#343—1221no—
263#342—1221no—
264C61C4×#35211yescharacteristic, complemented, Sylow
265C22×D4C22×D6111yescharacteristic
266C23×C4—611no—
267C23×C4—611no—
268C23×C4—611no—
269C23×C4C4×D6111yescharacteristic
270C2×M16—21no—
271C2×M16—1221no—
272#123—21no—
273#123—21no—
274#123C4×D6112yes—
275#123C2×Dic6112yes—
276C4×D4—2441no—
277C4×D4—2441no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—611no—
280C2×C4⋊C4—1221no—
281C2×C22⋊C4—21no—
282C2×C22⋊C4—21no—
283C2×C22⋊C4—611no—
284C2×C22⋊C4—611no—
285C2×C22⋊C4—611no—
286C2×C22⋊C4—1221no—
287C2×C22⋊C4—1221no—
288C2×C22⋊C4C4×D6111yescharacteristic
289C2×C42—611no—
290C2×C42—1221no—
291C2×C42—1221no—
292C2×C42—1221no—
293C2×C42—2441no—
294C2×C42—2441no—
295C2×C42—2441no—
296#100—21no—
297#100—612no—
298#100—1221no—
299#100C2×Dic6112yes—
300#99—21no—
301#99—612no—
302#99—1221no—
303#99C2×Dic6112yes—
304#97—2441no—
305C4×C8—2441no—
306#95—1221no—
307#95—1221no—
308#95—1221no—
309#95—1221no—
310#95—1221no—
311#95—2441no—
312C24C2×C4×D6111yescharacteristic
313C24D4×D6111yescharacteristic
314C2×D4—41no—
315C2×D4—41no—
316C2×D4C2×C4×D6111yescharacteristic
317C2×D4#1175822411yescharacteristic
318C2×D4#1175822411yescharacteristic
319C2×D4C22×Dic6111yescharacteristic
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—611no—
327C22×C4—611no—
328C22×C4—611no—
329C22×C4—611no—
330C22×C4—1221no—
331C22×C4—1221no—
332C22×C4—1221no—
333C22×C4—1221no—
334C22×C4—1221no—
335C22×C4—1221no—
336C22×C4—2442no—
337C22×C4—2442no—
338C22×C4—2442no—
339C22×C4—2441no—
340C22×C4—2441no—
341C22×C4C4×Dic6112yescomplemented
342C22×C4D4×D6111yescharacteristic
343M16—22no—
344M16—41no—
345M16—1222no—
346M16—2441no—
347C2×C8—41no—
348C2×C8—2441no—
349C4⋊C4—22no—
350C4⋊C4—22no—
351C4⋊C4—2441no—
352C4⋊C4—2442no—
353C22⋊C4—21no—
354C22⋊C4—22no—
355C22⋊C4—22no—
356C22⋊C4—22no—
357C22⋊C4—41no—
358C22⋊C4—1222no—
359C22⋊C4—2441no—
360C22⋊C4—2441no—
361C22⋊C4—2442no—
362C22⋊C4—2441no—
363C22⋊C4—2441no—
364C22⋊C4C4×Dic6112yescomplemented
365C42—1221no—
366C42—1221no—
367C42—4882no—
368C42—2441no—
369C42—2441no—
370C42—2442no—
371C42—2442no—
372C23—21no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—41no—
377C23—41no—
378C23—41no—
379C23—41no—
380C23C2×C4×Dic6111yescharacteristic
381C23C22⋊C4×D6111yescharacteristic
382C23#1451973311yescharacteristic
383C23#1451973711yescharacteristic
384C23D4×Dic6111yescharacteristic
385D4—41no—
386D4—41no—
387D4—41no—
388D4—41no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—42no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—81no—
401C2×C4—81no—
402C2×C4—611no—
403C2×C4—611no—
404C2×C4—1222no—
405C2×C4—1222no—
406C2×C4—1221no—
407C2×C4—1221no—
408C2×C4—1221no—
409C2×C4—4881no—
410C2×C4—4881no—
411C2×C4—4881no—
412C2×C4—2442no—
413C2×C4—2442no—
414C2×C4—2442no—
415C2×C4—2441no—
416C2×C4—2442no—
417C2×C4—2441no—
418C2×C4—2441no—
419C2×C4—2441no—
420C2×C4—2442no—
421C2×C4—2441no—
422C2×C4—2441no—
423C2×C4—2441no—
424C2×C4—2441no—
425C2×C4—2442no—
426C2×C4#1451973711yescharacteristic
427C2×C4D4×Dic6111yescharacteristic
428C8—42no—
429C8—2442no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—41no—
437C22—41no—
438C22—41no—
439C22—41no—
440C22—42no—
441C22—41no—
442C22—41no—
443C22—41no—
444C22—41no—
445C22—81no—
446C22C22⋊C4×Dic6111yescharacteristic
447C22#99×D6111yescharacteristic
448C22#1683973411yescharacteristic
449C4—21no—
450C4—21no—
451C4—42no—
452C4—42no—
453C4—82no—
454C4—612no—
455C4—1221no—
456C4—4881no—
457C4—4882no—
458C4—2441no—
459C4—2441no—
460C4—2441no—
461C4—2442no—
462C2—21no—
463C2—21no—
464C2—41no—
465C2—41no—
466C2—41no—
467C2—41no—
468C2#99×Dic6111yescharacteristic
469C2#352×D6111yescharacteristic
470C2#2144745911yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC23×C61C2×C42
FrattiniC22×D4C22×D61
FittingC2×C61×#352C2
socleC22×C61C2×#99
prime radical, cosocleC22×D4×C61C23
hypercenterC2×#352D61
hypocenterC61C4×#352
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#352

Complements

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

NH ≅ G/Ntype
9. C22×C4×Dic61C4semidirect
16. #16839637C4semidirect
17. #16839625C4semidirect
21. C22⋊C4×Dic61C4semidirect
22. #16839552C4semidirect
28. C61×#352C4semidirect
90. C22×C4×C61C42semidirect
117. C22⋊C4×C61C42semidirect
226. Dic61#352direct (N × H)
261. #352Dic61direct (N × H)
264. C61C4×#352semidirect
341. C22×C4C4×Dic61semidirect
364. C22⋊C4C4×Dic61semidirect

Maximal subgroups

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

subgroupindex
#123×Dic612
C2×#168395522
#100×Dic612
#99×Dic612
#214439382
#214439362
C2×C61×#3522
C4×#35261