Finite Group Databasebeta

← #29586204

Subgroups — #29586204

Order 15616.

1266 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C22⋊Dic61C211yesmaximal, characteristic
2C2×#16839529C212yesmaximal
3C2×#16839529C212yesmaximal
4#21444042C211yesmaximal, characteristic
5C2×C61×#385C211yesmaximal, characteristic
6C22×C22⋊Dic61C2212yes—
7C22×C22⋊Dic61C2212yes—
8C22×C4×Dic61—21no—
9C4×C22⋊Dic61—24no—
10C2×#14519684—21no—
11C2×#14519684—22no—
12#16839529—24no—
13#16839529C418yescomplemented
14C24×C4×C61C2211yescharacteristic
15C22×C4⋊C4×C61C412yescomplemented
16C22×C22⋊C4×C61C2211yescharacteristic
17C22×C22⋊C4×C61C2211yescharacteristic
18C61×#385—21no—
19C61×#385—22no—
20C61×#385—21no—
21C2×#95×C61C412yescomplemented
22C23×Dic61—22no—
23C23×Dic61—22no—
24C2×C22⋊Dic61—22no—
25C2×C22⋊Dic61—22no—
26C2×C22⋊Dic61—22no—
27C2×C22⋊Dic61—22no—
28C2×C22⋊Dic61—22no—
29C2×C22⋊Dic61—22no—
30C2×C22⋊Dic61—22no—
31C2×C22⋊Dic61—22no—
32C2×C22⋊Dic61C2×C414yes—
33C2×C22⋊Dic61C2×C414yes—
34C2×C22⋊Dic61D414yes—
35C2×C22⋊Dic61Q814yes—
36C2×C4×Dic61—24no—
37C2×C4×Dic61—44no—
38#14519684—24no—
39#14519684—44no—
40C25×C61C2311yescharacteristic
41C23×C4×C61—22no—
42C23×C4×C61—22no—
43C23×C4×C61—44no—
44C23×C4×C61C2×C412yes—
45C23×C4×C61C2×C411yescharacteristic
46C23×C4×C61C2×C411yescharacteristic
47C23×C4×C61C2×C412yes—
48C23×C4×C61D411yescharacteristic
49C23×C4×C61D412yes—
50C23×C4×C61D411yescharacteristic
51C2×C4⋊C4×C61—22no—
52C2×C4⋊C4×C61—22no—
53C2×C4⋊C4×C61—44no—
54C2×C22⋊C4×C61—21no—
55C2×C22⋊C4×C61—21no—
56C2×C22⋊C4×C61—22no—
57C2×C22⋊C4×C61—22no—
58C2×C22⋊C4×C61—21no—
59C2×C22⋊C4×C61—21no—
60C2×C22⋊C4×C61—22no—
61C2×C22⋊C4×C61C2×C414yes—
62#95×C61—22no—
63#95×C61—22no—
64C24×C61—42no—
65C24×C61—42no—
66C24×C61C22×C411yescharacteristic
67C24×C61C22×C412yes—
68C24×C61C2×D411yescharacteristic
69C24×C61C2×D411yescharacteristic
70C24×C61C2×D412yes—
71C24×C61C2×Q812yes—
72C24×C61#4112yes—
73C24×C61#4112yes—
74C24×C61#4112yes—
75C22×C4×C61—21no—
76C22×C4×C61—21no—
77C22×C4×C61—24no—
78C22×C4×C61—22no—
79C22×C4×C61—22no—
80C22×C4×C61—24no—
81C22×C4×C61—21no—
82C22×C4×C61—24no—
83C22×C4×C61—21no—
84C22×C4×C61—24no—
85C22×C4×C61—24no—
86C22×C4×C61—21no—
87C22×C4×C61—21no—
88C22×C4×C61—22no—
89C22×C4×C61—22no—
90C22×C4×C61—42no—
91C22×C4×C61—42no—
92C22×C4×C61—42no—
93C22×C4×C61—48no—
94C22×C4×C61—48no—
95C22×C4×C61—42no—
96C22×C4×C61—42no—
97C22×C4×C61—42no—
98C22×C4×C61—42no—
99C22×C4×C61C4214yescomplemented
100C22×C4×C61C22⋊C412yes—
101C22×C4×C61C22⋊C412yes—
102C22×Dic61—24no—
103C22×Dic61—24no—
104C22×Dic61—24no—
105C22×Dic61—24no—
106C22×Dic61—44no—
107C22×Dic61—44no—
108C22×Dic61—44no—
109C22×Dic61—44no—
110C22×Dic61—42no—
111C22×Dic61—42no—
112C4⋊C4×C61—44no—
113C4⋊C4×C61—44no—
114C22⋊C4×C61—24no—
115C22⋊C4×C61—24no—
116C22⋊C4×C61—41no—
117C22⋊C4×C61—42no—
118C22⋊C4×C61—41no—
119C22⋊Dic61—24no—
120C22⋊Dic61—24no—
121C22⋊Dic61—24no—
122C22⋊Dic61—24no—
123C22⋊Dic61—24no—
124C22⋊Dic61—42no—
125C22⋊Dic61—42no—
126C22⋊Dic61C4⋊C418yescomplemented
127C4×Dic61—48no—
128C23×C61—22no—
129C23×C61—22no—
130C23×C61—22no—
131C23×C61—22no—
132C23×C61—22no—
133C23×C61—22no—
134C23×C61—42no—
135C23×C61—42no—
136C23×C61—44no—
137C23×C61—42no—
138C23×C61—44no—
139C23×C61—42no—
140C23×C61—44no—
141C23×C61—44no—
142C23×C61C2×C4211yescharacteristic
143C23×C61C2×C22⋊C411yescharacteristic
144C23×C61C2×C4⋊C412yes—
145C23×C61#11711yescharacteristic
146C23×C61#11712yes—
147C23×C61C4×D412yes—
148C23×C61C4×D412yes—
149C23×C61C4×D412yes—
150C23×C61C4×D412yes—
151C23×C61C4×Q812yes—
152C23×C61C4×Q812yes—
153C23×C61#12011yescharacteristic
154C23×C61#12112yes—
155C23×C61C22⋊Q812yes—
156C23×C61C22⋊Q812yes—
157C23×C61#12311yescharacteristic
158C23×C61#12312yes—
159C23×C61#12411yescharacteristic
160C23×C61#12512yes—
161C23×C61#12612yes—
162C23×C61C4⋊Q811yescharacteristic
163C2×C4×C61—24no—
164C2×C4×C61—24no—
165C2×C4×C61—22no—
166C2×C4×C61—22no—
167C2×C4×C61—24no—
168C2×C4×C61—22no—
169C2×C4×C61—22no—
170C2×C4×C61—22no—
171C2×C4×C61—48no—
172C2×C4×C61—48no—
173C2×C4×C61—44no—
174C2×C4×C61—42no—
175C2×C4×C61—42no—
176C2×C4×C61—42no—
177C2×C4×C61—42no—
178C2×C4×C61—44no—
179C2×C4×C61—41no—
180C2×C4×C61—41no—
181C2×C4×C61—42no—
182C2×C4×C61—42no—
183C2×C4×C61—82no—
184C2×C4×C61—82no—
185C2×C4×C61#9914yes—
186C2×Dic61—28no—
187C2×Dic61—44no—
188C2×Dic61—44no—
189C2×Dic61—48no—
190C2×Dic61—48no—
191C2×Dic61—48no—
192C2×Dic61—44no—
193C2×Dic61—82no—
194C2×Dic61—82no—
195C2×Dic61—84no—
196#10912—611nomaximal, Sylow
197C22×C61—21no—
198C22×C61—22no—
199C22×C61—21no—
200C22×C61—22no—
201C22×C61—21no—
202C22×C61—22no—
203C22×C61—22no—
204C22×C61—21no—
205C22×C61—24no—
206C22×C61—22no—
207C22×C61—24no—
208C22×C61—22no—
209C22×C61—24no—
210C22×C61—24no—
211C22×C61—22no—
212C22×C61—22no—
213C22×C61—42no—
214C22×C61—42no—
215C22×C61—42no—
216C22×C61—42no—
217C22×C61—42no—
218C22×C61—42no—
219C22×C61—42no—
220C22×C61—42no—
221C22×C61C4×C22⋊C411yescharacteristic
222C22×C61C4×C4⋊C412yes—
223C22×C61#38512yes—
224C22×C61#38611yescharacteristic
225C22×C61#38712yes—
226C22×C61#38712yes—
227C22×C61#38812yes—
228C22×C61#38912yes—
229C22×C61#39111yescharacteristic
230C22×C61C2×#9912yes—
231C22×C61#41012yes—
232C4×C61—24no—
233C4×C61—42no—
234C4×C61—44no—
235C4×C61—81no—
236C4×C61—81no—
237Dic61—48no—
238Dic61—84no—
239C2×#385D6111yescharacteristic
240C2×C4×C22⋊C4—611no—
241C2×#342—612no—
242C2×#342—612no—
243C22⋊#95—611no—
244C2×C61—22no—
245C2×C61—22no—
246C2×C61—22no—
247C2×C61—22no—
248C2×C61—22no—
249C2×C61—22no—
250C2×C61#143611yescharacteristic
251C2×C61C4×#9912yes—
252C2×C61#189811yescharacteristic
253C2×C61#189911yescharacteristic
254C2×C61#199612yes—
255C24×C4C2×D6111yescharacteristic
256C22×C4⋊C4Dic6112yescomplemented
257C22×C22⋊C4—612no—
258C22×C22⋊C4—612no—
259C22×C22⋊C4C2×D6111yescharacteristic
260C22×C22⋊C4C2×D6111yescharacteristic
261C22×C42—1221no—
262#385—21no—
263#385—22no—
264#385—21no—
265C4×C22⋊C4—1224no—
266C2×#95—1221no—
267C2×#95—1222no—
268C2×#95Dic6112yescomplemented
269#342—618no—
270#342—1224no—
271C61#1091211yescharacteristic, complemented, Sylow
272C25C22×D6111yescharacteristic
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—44no—
276C23×C4—1222no—
277C23×C4—1222no—
278C23×C4C2×Dic6112yes—
279C23×C4C2×Dic6111yescharacteristic
280C23×C4C2×Dic6111yescharacteristic
281C23×C4C2×Dic6112yes—
282C23×C4C22⋊D6111yescharacteristic
283C23×C4C22⋊D6112yes—
284C23×C4C22⋊D6111yescharacteristic
285C2×C4⋊C4—22no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—44no—
288C2×C22⋊C4—22no—
289C2×C22⋊C4—21no—
290C2×C22⋊C4—21no—
291C2×C22⋊C4—22no—
292C2×C22⋊C4—22no—
293C2×C22⋊C4—21no—
294C2×C22⋊C4—21no—
295C2×C22⋊C4—614no—
296C2×C22⋊C4—614no—
297C2×C22⋊C4—614no—
298C2×C22⋊C4—614no—
299C2×C22⋊C4—1222no—
300C2×C22⋊C4—1222no—
301C2×C22⋊C4—1222no—
302C2×C22⋊C4—1222no—
303C2×C22⋊C4—1222no—
304C2×C22⋊C4—1222no—
305C2×C22⋊C4—1222no—
306C2×C22⋊C4—1222no—
307C2×C22⋊C4C4×D6114yes—
308C2×C42—1224no—
309C2×C42—2444no—
310#95—22no—
311#95—22no—
312#95—1224no—
313#95—2444no—
314C24—42no—
315C24—42no—
316C24C2×C4×D6112yes—
317C24#1175822212yes—
318C24D4×D6112yes—
319C24#1175822412yes—
320C24Q8×D6112yes—
321C24#1175822612yes—
322C24C22×Dic6111yescharacteristic
323C24C2×C22⋊D6111yescharacteristic
324C24C2×C22⋊D6111yescharacteristic
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—24no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—24no—
331C22×C4—21no—
332C22×C4—24no—
333C22×C4—21no—
334C22×C4—24no—
335C22×C4—24no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—42no—
341C22×C4—42no—
342C22×C4—42no—
343C22×C4—48no—
344C22×C4—48no—
345C22×C4—42no—
346C22×C4—42no—
347C22×C4—42no—
348C22×C4—42no—
349C22×C4—1224no—
350C22×C4—1224no—
351C22×C4—1224no—
352C22×C4—1224no—
353C22×C4—2444no—
354C22×C4—2444no—
355C22×C4—2442no—
356C22×C4—2442no—
357C22×C4—2444no—
358C22×C4—2444no—
359C22×C4C4×Dic6114yescomplemented
360C22×C4C22⋊Dic6112yes—
361C22×C4C22⋊Dic6112yes—
362C4⋊C4—44no—
363C4⋊C4—44no—
364C22⋊C4—24no—
365C22⋊C4—24no—
366C22⋊C4—41no—
367C22⋊C4—42no—
368C22⋊C4—41no—
369C22⋊C4—618no—
370C22⋊C4—1224no—
371C22⋊C4—1224no—
372C22⋊C4—1224no—
373C22⋊C4—1224no—
374C22⋊C4—1224no—
375C22⋊C4—2442no—
376C22⋊C4—2442no—
377C42—2448no—
378C23—22no—
379C23—22no—
380C23—22no—
381C23—22no—
382C23—22no—
383C23—22no—
384C23—42no—
385C23—42no—
386C23—44no—
387C23—44no—
388C23—42no—
389C23—42no—
390C23—44no—
391C23—44no—
392C23C2×C4×Dic6111yescharacteristic
393C23C2×C22⋊Dic6111yescharacteristic
394C23C4⋊C4×D6112yes—
395C23#1451973512yes—
396C23#1451973611yescharacteristic
397C23C4×C22⋊D6112yes—
398C23C4×C22⋊D6112yes—
399C23#1451973912yes—
400C23D4×Dic6112yes—
401C23#1451974212yes—
402C23Q8×Dic6112yes—
403C23#1451974511yescharacteristic
404C23#1451974912yes—
405C23#1451975312yes—
406C23#1451975512yes—
407C23#1451975811yescharacteristic
408C23#1451976212yes—
409C23#1451976611yescharacteristic
410C23#1451976712yes—
411C23#1451977212yes—
412C23#1451977511yescharacteristic
413C2×C4—24no—
414C2×C4—24no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—24no—
420C2×C4—22no—
421C2×C4—48no—
422C2×C4—48no—
423C2×C4—44no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—44no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—82no—
434C2×C4—82no—
435C2×C4—1228no—
436C2×C4—4882no—
437C2×C4—4882no—
438C2×C4—4884no—
439C2×C4—2448no—
440C2×C4—2444no—
441C2×C4—2444no—
442C2×C4—2444no—
443C2×C4—2448no—
444C2×C4—2448no—
445C2×C4#1451969214yes—
446C22—21no—
447C22—21no—
448C22—22no—
449C22—22no—
450C22—22no—
451C22—22no—
452C22—21no—
453C22—21no—
454C22—22no—
455C22—24no—
456C22—24no—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—24no—
461C22—24no—
462C22—42no—
463C22—42no—
464C22—42no—
465C22—42no—
466C22—42no—
467C22—42no—
468C22—42no—
469C22—42no—
470C22C4×C22⋊Dic6111yescharacteristic
471C22C4⋊C4×Dic6112yes—
472C22#1683963312yes—
473C22#1683964211yescharacteristic
474C22#1683964312yes—
475C22#1683964812yes—
476C22#1683965212yes—
477C22#1683965712yes—
478C22#1683966911yescharacteristic
479C22C2×#1451969212yes—
480C22#1683973612yes—
481C4—24no—
482C4—42no—
483C4—44no—
484C4—81no—
485C4—81no—
486C4—4884no—
487C4—2448no—
488C2—22no—
489C2—22no—
490C2—22no—
491C2—22no—
492C2—22no—
493C2—22no—
494C2#2144405111yescharacteristic
495C2C4×#1451969212yes—
496C2#2144627311yescharacteristic
497C2#2144627811yescharacteristic
498C2#2144680512yes—
subgroupG/H
centerC23C2×C22⋊Dic61
commutatorC23×C61C2×C42
FrattiniC25C22×D61
FittingC2×C61×#385C2
socleC23×C61C2×C22⋊C4
prime radical, cosocleC25×C61C23
hypercenterC2×#385D61
hypocenterC61#10912
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
13. #16839529C4semidirect
15. C22×C4⋊C4×C61C4semidirect
21. C2×#95×C61C4semidirect
99. C22×C4×C61C42semidirect
126. C22⋊Dic61C4⋊C4semidirect
256. C22×C4⋊C4Dic61semidirect
268. C2×#95Dic61semidirect
271. C61#10912semidirect
359. C22×C4C4×Dic61semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊Dic612
C2×#168395292
#214440422
C2×C61×#3852
#1091261