Finite Group Databasebeta

← #29571498

Subgroups — #29571498

Order 15616.

1030 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊Q8×D61C211yesmaximal, characteristic
2#21445796C211yesmaximal, characteristic
3#21445796C211yesmaximal, characteristic
4C2×#16839509C211yesmaximal, characteristic, complemented
5C2×#16839508C211yesmaximal, characteristic, complemented
6C2×#16839507C211yesmaximal, characteristic, complemented
7C2×C61×#332C211yesmaximal, characteristic, complemented
8C22×Q8×D61—21no—
9C2×#14519777C2211yescharacteristic
10C2×#14519776—21no—
11C2×#14519776C412yes—
12C2×#14519775—21no—
13C4⋊Q8×D61—22no—
14C4⋊Q8×D61—22no—
15C4⋊Q8×D61—22no—
16C4⋊Q8×D61—22no—
17C2×C4⋊C4×D61—21no—
18C2×C4⋊C4×D61C412yes—
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×Dic122—22no—
35C2×Q8×D61—24no—
36C2×Q8×D61—24no—
37C2×Q8×D61—42no—
38C2×Q8×D61—42no—
39C2×Q8×D61—42no—
40C2×Q8×D61—42no—
41C22×C4×D61—22no—
42C22×C4×D61C2×C411yescharacteristic
43C22×C4×D61D411yescharacteristic
44C22×C4×D61D411yescharacteristic
45C22×#92418—21no—
46C22×#92418—21no—
47#14519777—21no—
48#14519777—21no—
49#14519777D412yes—
50#14519777D412yes—
51#14519776—24no—
52#14519776—24no—
53#14519776—24no—
54#14519776—24no—
55#14519775—24no—
56#14519775—24no—
57C2×C4⋊Dic61—21no—
58C2×C4⋊Dic61C2×C412yes—
59C2×#11758196—22no—
60C2×#11758196—22no—
61C4⋊C4×D61—24no—
62C4⋊C4×D61—24no—
63C4⋊C4×D61—24no—
64C4⋊C4×D61—24no—
65C2×C4×Dic61C2×C411yescharacteristic
66C2×C4×Dic61D411yescharacteristic
67C2×C4×Dic61D411yescharacteristic
68C42×D61—21no—
69C42×D61—21no—
70C42×D61—21no—
71C42×D61—21no—
72C4⋊#92418—21no—
73C4⋊#92418—21no—
74C4⋊#92418—21no—
75C4⋊#92418—21no—
76#14519689—42no—
77#14519689—42no—
78C22×Q8×C61—21no—
79C22×C8×C61—21no—
80C22×C8×C61—21no—
81C4⋊Q8×C61—21no—
82C4⋊Q8×C61—21no—
83C4⋊Q8×C61D412yes—
84C4⋊Q8×C61D412yes—
85C2×C4⋊C4×C61—21no—
86C2×C4⋊C4×C61C2×C412yes—
87C2×C42×C61C2311yescharacteristic
88C4⋊C8×C61—21no—
89C4⋊C8×C61—21no—
90C4⋊C8×C61—21no—
91C4⋊C8×C61—21no—
92C23×D61C22⋊C411yescharacteristic
93C2×Q8×C61—22no—
94C2×Q8×C61—22no—
95C2×Q8×C61—41no—
96C2×Q8×C61—41no—
97C2×Q8×C61—41no—
98C2×Q8×C61—41no—
99C22×C4×C61—22no—
100C22×C4×C61C22×C411yescharacteristic
101C22×C4×C61C2×D411yescharacteristic
102C22×C4×C61C2×D411yescharacteristic
103C22×Dic61—22no—
104C22×Dic61C22⋊C411yescharacteristic
105C22×Dic61C22⋊C411yescharacteristic
106C22×Dic61C22⋊C411yescharacteristic
107Q8×D61—48no—
108Q8×D61—48no—
109Q8×D61—48no—
110Q8×D61—48no—
111C2×C4×D61—22no—
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×C4×D61—21no—
120C2×C4×D61—21no—
121C2×C4×D61—21no—
122C2×C4×D61—22no—
123C2×C4×D61—28no—
124C2×C4×D61—44no—
125C2×C4×D61—44no—
126C2×C4×D61D812yes—
127C2×C4×D61SD1612yes—
128C2×C4×D61SD1612yes—
129C2×C4×D61Q1612yes—
130C2×Dic122—28no—
131C2×Dic122—22no—
132C2×Dic122—22no—
133C2×Dic122—44no—
134C2×Dic122—41no—
135C2×Dic122—41no—
136C2×Dic122—41no—
137C2×Dic122—41no—
138C2×Dic122—44no—
139C2×C8×C61—41no—
140C2×C8×C61—41no—
141C2×C8×C61—41no—
142C2×C8×C61—41no—
143C2×C8×C61—41no—
144C2×C8×C61—41no—
145C4⋊C4×C61—22no—
146C4⋊C4×C61—22no—
147C4⋊C4×C61—22no—
148C4⋊C4×C61C22⋊C414yes—
149C42×C61C2×D411yescharacteristic
150C42×C61C2×D411yescharacteristic
151C42×C61C2×D411yescharacteristic
152C42×C61C2×D411yescharacteristic
153C4⋊Dic61—22no—
154C4⋊Dic61—22no—
155C4⋊Dic61—22no—
156C4⋊Dic61C22⋊C414yes—
157#11758196—28no—
158#11758196—28no—
159C4×Dic61—21no—
160C4×Dic61—21no—
161C4×Dic61—21no—
162C4×Dic61—21no—
163C4×Dic61—21no—
164C4×Dic61—21no—
165C2×#92418—41no—
166C2×#92418—41no—
167C2×#92418—41no—
168C2×#92418—41no—
169C2×#92418—41no—
170C2×#92418—41no—
171C23×C61C2×C22⋊C411yescharacteristic
172C22×D61—21no—
173C22×D61—21no—
174C22×D61—21no—
175C22×D61—21no—
176C22×D61#10112yes—
177C22×D61#10212yes—
178C22×D61#10312yes—
179Q8×C61—42no—
180Q8×C61—42no—
181Q8×C61—42no—
182Q8×C61—42no—
183C2×C4×C61—21no—
184C2×C4×C61—21no—
185C2×C4×C61—24no—
186C2×C4×C61—42no—
187C2×C4×C61—42no—
188C2×C4×C61C2×C22⋊C411yescharacteristic
189C2×C4×C61C2×C22⋊C411yescharacteristic
190C2×C4×C61#12011yescharacteristic
191C2×C4×C61#12011yescharacteristic
192C2×C4×C61#12011yescharacteristic
193C2×C4×C61#12011yescharacteristic
194C2×C4×C61C2×D811yescharacteristic
195C2×C4×C61C2×SD1611yescharacteristic
196C2×C4×C61C2×SD1611yescharacteristic
197C2×C4×C61C2×Q1611yescharacteristic
198C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
199C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
200C2×C4×C61#13711yescharacteristic
201C2×C4×C61#13711yescharacteristic
202C2×Dic61—21no—
203C2×Dic61—21no—
204C2×Dic61—21no—
205C2×Dic61—21no—
206C2×Dic61—21no—
207C2×Dic61—21no—
208C2×Dic61—24no—
209C2×Dic61—42no—
210C2×Dic61—42no—
211C2×Dic61#10112yes—
212C2×Dic61#10212yes—
213C2×Dic61#10312yes—
214C4×D61—24no—
215C4×D61—24no—
216C4×D61—22no—
217C4×D61—22no—
218C4×D61—22no—
219C4×D61—22no—
220C4×D61—22no—
221C4×D61—22no—
222C4×D61—22no—
223C4×D61—22no—
224C4×D61—416no—
225Dic122—416no—
226Dic122—42no—
227Dic122—42no—
228Dic122—42no—
229Dic122—42no—
230C8×C61—81no—
231C8×C61—81no—
232#92418—81no—
233#92418—81no—
234#8340—611nomaximal, Sylow
235C22×C61#37911yescharacteristic
236C22×C61C2×#10111yescharacteristic
237C22×C61C2×#10111yescharacteristic
238C22×C61C2×#10211yescharacteristic
239C22×C61C2×#10311yescharacteristic
240C22×C61#41811yescharacteristic
241C22×C61#41911yescharacteristic
242C2×D61—22no—
243C2×D61—22no—
244C2×D61—22no—
245C2×D61—22no—
246C2×D61—22no—
247C2×D61—22no—
248C2×D61#33214yescomplemented
249C4×C61—21no—
250C4×C61—21no—
251C4×C61—44no—
252C4×C61#44711yescharacteristic
253C4×C61#44711yescharacteristic
254C4×C61#44811yescharacteristic
255C4×C61#44811yescharacteristic
256C4×C61#45011yescharacteristic
257C4×C61#45011yescharacteristic
258C4×C61#45111yescharacteristic
259C4×C61#45111yescharacteristic
260Dic61—22no—
261Dic61—22no—
262Dic61—22no—
263Dic61—44no—
264C22×C4⋊Q8—611no—
265#1797—611no—
266#1797—611no—
267C2×#332—611no—
268C2×#332—611no—
269C2×#332—611no—
270C2×#332D6111yescharacteristic, complemented
271C2×C61C2×#33211yescharacteristic
272C2×C61#154611yescharacteristic
273C2×C61#154911yescharacteristic
274C2×C61#155611yescharacteristic
275C2×C61#178411yescharacteristic
276C2×C61#178611yescharacteristic
277C2×C61#178711yescharacteristic
278D61—24no—
279C23×Q8—1221no—
280C2×C4⋊Q8—612no—
281C2×C4⋊Q8—611no—
282C2×C4⋊Q8—1221no—
283C2×C4⋊Q8—1221no—
284C2×C4⋊Q8—1222no—
285C2×C4⋊Q8—1222no—
286C2×C4⋊Q8—1222no—
287C2×C4⋊Q8—1222no—
288C2×C4⋊Q8C2×D6111yescharacteristic
289C22×C4⋊C4—612no—
290C22×C4⋊C4—1221no—
291C22×C42—611no—
292C2×C4⋊C8—611no—
293C2×C4⋊C8—611no—
294C2×C4⋊C8C2×D6111yescharacteristic
295C2×C4⋊C8C2×D6111yescharacteristic
296C2×C22⋊C8—1221no—
297C2×C22⋊C8—1221no—
298#336—1221no—
299#336—1221no—
300#332—22no—
301#332—1222no—
302#332—1222no—
303#332—1222no—
304C61#834011yescharacteristic, complemented, Sylow
305C22×Q8—21no—
306C22×Q8—1222no—
307C22×Q8—1224no—
308C22×Q8—1224no—
309C22×Q8—1221no—
310C22×Q8—2442no—
311C22×Q8—2442no—
312C22×Q8—2442no—
313C22×Q8—2442no—
314C23×C4—611no—
315C23×C4—611no—
316C23×C4—611no—
317C23×C4—1222no—
318C22×C8—21no—
319C22×C8—21no—
320C22×C8—1221no—
321C22×C8—1221no—
322C4⋊Q8—21no—
323C4⋊Q8—21no—
324C4⋊Q8—612no—
325C4⋊Q8—612no—
326C4⋊Q8—1224no—
327C4⋊Q8—1224no—
328C4⋊Q8—1224no—
329C4⋊Q8—1224no—
330C4⋊Q8—1224no—
331C4⋊Q8—1224no—
332C4⋊Q8—1221no—
333C4⋊Q8—1221no—
334C4⋊Q8D24412yes—
335C4⋊Q8C22⋊D6112yes—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—612no—
338C2×C4⋊C4—1224no—
339C2×C4⋊C4—1224no—
340C2×C4⋊C4—1224no—
341C2×C4⋊C4—1222no—
342C2×C4⋊C4—1222no—
343C2×C4⋊C4—1221no—
344C2×C4⋊C4—1224no—
345C2×C4⋊C4C4×D6112yes—
346C2×C42—611no—
347C2×C42—611no—
348C2×C42—611no—
349C2×C42—1221no—
350C2×C42—1221no—
351C2×C42—1221no—
352C2×C42—1221no—
353C2×C42C22×D6111yescharacteristic
354C4⋊C8—21no—
355C4⋊C8—21no—
356C4⋊C8—21no—
357C4⋊C8—21no—
358C4⋊C8—1221no—
359C4⋊C8—1221no—
360C4⋊C8—1221no—
361C4⋊C8—1221no—
362C22⋊C8—2442no—
363C22⋊C8—2442no—
364C24—611no—
365C2×Q8—22no—
366C2×Q8—22no—
367C2×Q8—41no—
368C2×Q8—41no—
369C2×Q8—41no—
370C2×Q8—41no—
371C2×Q8—1228no—
372C2×Q8—1222no—
373C2×Q8—1222no—
374C2×Q8—2444no—
375C2×Q8—2444no—
376C2×Q8—2448no—
377C2×Q8—2448no—
378C2×Q8—2448no—
379C2×Q8—2448no—
380C2×Q8—2441no—
381C2×Q8—2441no—
382C2×Q8—2441no—
383C2×Q8—2441no—
384C22×C4—22no—
385C22×C4—611no—
386C22×C4—611no—
387C22×C4—611no—
388C22×C4—612no—
389C22×C4—612no—
390C22×C4—612no—
391C22×C4—612no—
392C22×C4—1222no—
393C22×C4—1222no—
394C22×C4—1228no—
395C22×C4—1221no—
396C22×C4—1221no—
397C22×C4—1221no—
398C22×C4—1221no—
399C22×C4—1221no—
400C22×C4—1221no—
401C22×C4—1221no—
402C22×C4—1221no—
403C22×C4—1221no—
404C22×C4—1221no—
405C22×C4—1222no—
406C22×C4—2444no—
407C22×C4—2444no—
408C22×C4C2×C4×D6111yescharacteristic
409C22×C4D4×D6111yescharacteristic
410C22×C4D4×D6111yescharacteristic
411C2×C8—41no—
412C2×C8—41no—
413C2×C8—41no—
414C2×C8—41no—
415C2×C8—41no—
416C2×C8—41no—
417C2×C8—2441no—
418C2×C8—2441no—
419C2×C8—2441no—
420C2×C8—2441no—
421C2×C8—2441no—
422C2×C8—2441no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—614no—
427C4⋊C4—1228no—
428C4⋊C4—1228no—
429C4⋊C4—1222no—
430C4⋊C4—1222no—
431C4⋊C4—1222no—
432C4⋊C4#1175819814yes—
433C42—1221no—
434C42—1221no—
435C42—1221no—
436C42—1221no—
437C42—1221no—
438C42—1221no—
439C42C2×D24411yescharacteristic
440C42D4×D6111yescharacteristic
441C42D4×D6111yescharacteristic
442C42C2×C22⋊D6111yescharacteristic
443C23—612no—
444C23—612no—
445C23—612no—
446C23—1221no—
447C23—1221no—
448C23—1221no—
449C23—1221no—
450C23C22⋊C4×D6111yescharacteristic
451Q8—42no—
452Q8—42no—
453Q8—42no—
454Q8—42no—
455Q8—24416no—
456Q8—2442no—
457Q8—2442no—
458Q8—2442no—
459Q8—2442no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—24no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—612no—
466C2×C4—612no—
467C2×C4—612no—
468C2×C4—1224no—
469C2×C4—1224no—
470C2×C4—1221no—
471C2×C4—1221no—
472C2×C4—1221no—
473C2×C4—1221no—
474C2×C4—1221no—
475C2×C4—1221no—
476C2×C4—1222no—
477C2×C4—1222no—
478C2×C4—1222no—
479C2×C4—1222no—
480C2×C4—1222no—
481C2×C4—1222no—
482C2×C4—1222no—
483C2×C4—1222no—
484C2×C4—1224no—
485C2×C4—24416no—
486C2×C4—2442no—
487C2×C4—2442no—
488C2×C4C22⋊C4×D6111yescharacteristic
489C2×C4C2×#1175819811yescharacteristic
490C2×C4#1451974511yescharacteristic
491C2×C4#1451974511yescharacteristic
492C2×C4#1451974711yescharacteristic
493C2×C4#1451974711yescharacteristic
494C2×C4D8×D6111yescharacteristic
495C2×C4SD16×D6111yescharacteristic
496C2×C4SD16×D6111yescharacteristic
497C2×C4Q16×D6111yescharacteristic
498C2×C4#1451980111yescharacteristic
499C2×C4#1451980411yescharacteristic
500C2×C4#1451980611yescharacteristic
501C2×C4#1451980911yescharacteristic
502C8—81no—
503C8—81no—
504C8—4881no—
505C8—4881no—
506C22—614no—
507C22—1222no—
508C22—1222no—
509C22—1222no—
510C22—1222no—
511C22—1222no—
512C22—1222no—
513C22#1683961711yescharacteristic
514C22#101×D6111yescharacteristic
515C22#101×D6111yescharacteristic
516C22#102×D6111yescharacteristic
517C22#103×D6111yescharacteristic
518C22#1683976511yescharacteristic
519C22#1683976911yescharacteristic
520C4—21no—
521C4—21no—
522C4—44no—
523C4—1222no—
524C4—1222no—
525C4—1222no—
526C4—2444no—
527C4#1683989411yescharacteristic
528C4#1683989711yescharacteristic
529C4#1683989911yescharacteristic
530C4#1683990211yescharacteristic
531C4#1683991111yescharacteristic
532C4#1683991411yescharacteristic
533C4#1683991611yescharacteristic
534C4#1683991911yescharacteristic
535C2—1224no—
536C2#332×D6111yescharacteristic
537C2#2144448911yescharacteristic
538C2#2144450211yescharacteristic
539C2#2144453411yescharacteristic
540C2#2144574111yescharacteristic
541C2#2144574811yescharacteristic
542C2#2144575211yescharacteristic
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#8340
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
248. C2×D61#332semidirect
270. C2×#332D61semidirect
304. C61#8340semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊Q8×D612
#214457962
C2×#168395092
C2×#168395082
C2×#168395072
C2×C61×#3322
#834061