Finite Group Databasebeta

← #30617888

Subgroups — #30617888

Order 15616.

1194 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462497C211yesmaximal, characteristic
2#21462497C211yesmaximal, characteristic
3#21462012C214yesmaximal, complemented
4#21462011C214yesmaximal, complemented
5#21461719C214yesmaximal
6C2×C4⋊Q8×D61C211yesmaximal, characteristic
7#16840785—21no—
8#16840785—21no—
9#16840784—21no—
10#16840784—21no—
11#16840781—21no—
12#16840781—21no—
13#16840780—21no—
14#16840780—21no—
15#16840765C2212yes—
16#16840765C2212yes—
17#16840734C2212yes—
18#16840734C2212yes—
19C4×#11758217C2212yes—
20C4×#11758217C2212yes—
21#16840642C22116yes—
22C22×Q8×D61C412yes—
23C2×#14519777C411yescharacteristic
24C2×#14519776C412yes—
25C2×#14519776C2212yes—
26C2×#14519775C2212yes—
27C4⋊Q8×D61—21no—
28C4⋊Q8×D61—21no—
29C4⋊Q8×D61—21no—
30C4⋊Q8×D61—21no—
31C4⋊Q8×D61—21no—
32C4⋊Q8×D61—21no—
33C4⋊Q8×D61—21no—
34C4⋊Q8×D61—21no—
35C2×C4⋊C4×D61C412yes—
36C2×C4⋊C4×D61C2212yes—
37C2×C42×D61C2211yescharacteristic
38C2×C4⋊Q8×C61C411yescharacteristic
39C2×#11758217C2314yes—
40C2×#11758217C2314yes—
41#14519844—22no—
42#14519844—22no—
43C4⋊#92420—22no—
44C4⋊#92420—22no—
45#14519834—22no—
46#14519834—22no—
47#14519834—22no—
48#14519834—22no—
49#14519832—22no—
50#14519832—22no—
51C4×#92420—22no—
52C4×#92420—22no—
53C22×Dic122C2×C412yes—
54C22×Dic122C2×C414yes—
55C2×Q8×D61—22no—
56C2×Q8×D61—22no—
57C2×Q8×D61—22no—
58C2×Q8×D61—22no—
59C2×Q8×D61—48no—
60C22×C4×D61C2×C411yescharacteristic
61C22×C4×D61C2×C411yescharacteristic
62C22×C4×D61C2×C414yes—
63C22×C4×D61C2311yescharacteristic
64#14519777—21no—
65#14519777—21no—
66#14519777—21no—
67#14519777—21no—
68#14519776—22no—
69#14519776—22no—
70#14519776—22no—
71#14519776—22no—
72#14519776—22no—
73#14519776—22no—
74#14519776—22no—
75#14519776—22no—
76#14519775—22no—
77#14519775—22no—
78#14519775—22no—
79#14519775—22no—
80C2×C4⋊Dic61C2×C412yes—
81C2×C4⋊Dic61C2×C412yes—
82C2×#11758196C2×C414yes—
83C2×#11758196C2314yes—
84C4⋊C4×D61—22no—
85C4⋊C4×D61—22no—
86C4⋊C4×D61—22no—
87C4⋊C4×D61—22no—
88C4⋊C4×D61—22no—
89C4⋊C4×D61—22no—
90C4⋊C4×D61—22no—
91C4⋊C4×D61—22no—
92C2×C4×Dic61C2×C411yescharacteristic
93C2×C4×Dic61C2311yescharacteristic
94C2×C4×Dic61C2311yescharacteristic
95C42×D61D411yescharacteristic
96C42×D61D411yescharacteristic
97C42×D61D411yescharacteristic
98C42×D61D411yescharacteristic
99C42×D61D411yescharacteristic
100C42×D61D411yescharacteristic
101C42×D61D411yescharacteristic
102C42×D61D411yescharacteristic
103C22×Q8×C61C2×C412yes—
104C4⋊Q8×C61—21no—
105C4⋊Q8×C61—21no—
106C4⋊Q8×C61—21no—
107C4⋊Q8×C61—21no—
108C2×C4⋊C4×C61C2×C412yes—
109C2×C4⋊C4×C61C2×C412yes—
110C2×C42×C61C2×C411yescharacteristic
111C23×D61C22×C411yescharacteristic
112C2×Q8×C61—22no—
113C2×Q8×C61—22no—
114C2×Q8×C61—44no—
115C22×C4×C61C22×C411yescharacteristic
116C22×C4×C61C22×C411yescharacteristic
117C22×C4×C61C22×C411yescharacteristic
118C22×C4×C61C22×C414yes—
119C22×Dic61C22×C411yescharacteristic
120C22×Dic61C22×C411yescharacteristic
121C22×Dic61C22×C414yes—
122C22×Dic61C2411yescharacteristic
123Q8×D61—48no—
124Q8×D61—48no—
125Q8×D61—48no—
126Q8×D61—48no—
127C2×C4×D61—24no—
128C2×C4×D61—24no—
129C2×C4×D61—24no—
130C2×C4×D61—24no—
131C2×C4×D61—24no—
132C2×C4×D61—48no—
133C2×C4×D61C22⋊C411yescharacteristic
134C2×C4×D61C22⋊C411yescharacteristic
135C2×C4×D61C22⋊C411yescharacteristic
136C2×C4×D61C22⋊C411yescharacteristic
137C2×C4×D61C22⋊C411yescharacteristic
138C2×C4×D61C22⋊C411yescharacteristic
139C2×C4×D61C22⋊C411yescharacteristic
140C2×C4×D61C22⋊C411yescharacteristic
141C2×C4×D61C2×D411yescharacteristic
142C2×C4×D61C2×D411yescharacteristic
143C2×C4×D61C2×D411yescharacteristic
144C2×C4×D61C2×D411yescharacteristic
145C2×Dic122—22no—
146C2×Dic122—22no—
147C2×Dic122—24no—
148C2×Dic122—24no—
149C2×Dic122—48no—
150C2×Dic122—44no—
151#11758217—28no—
152#11758217—28no—
153C2×#92420—24no—
154C2×#92420—24no—
155C4⋊C4×C61—22no—
156C4⋊C4×C61—22no—
157C4⋊C4×C61—22no—
158C4⋊C4×C61—22no—
159C42×C61C22⋊C411yescharacteristic
160C42×C61C22⋊C411yescharacteristic
161C42×C61C22⋊C411yescharacteristic
162C42×C61C22⋊C411yescharacteristic
163C4⋊Dic61—22no—
164C4⋊Dic61—22no—
165C4⋊Dic61—22no—
166C4⋊Dic61—22no—
167#11758196—24no—
168#11758196—24no—
169#11758196—24no—
170#11758196—24no—
171C4×Dic61C22⋊C411yescharacteristic
172C4×Dic61C22⋊C411yescharacteristic
173C4×Dic61C22⋊C411yescharacteristic
174C4×Dic61C22⋊C411yescharacteristic
175C4×Dic61C2×D411yescharacteristic
176C4×Dic61C2×D411yescharacteristic
177C4×Dic61C2×D411yescharacteristic
178C4×Dic61C2×D411yescharacteristic
179C4×Dic61C2×D411yescharacteristic
180C4×Dic61C2×D411yescharacteristic
181C4×Dic61C2×D411yescharacteristic
182C4×Dic61C2×D411yescharacteristic
183C23×C61C23×C411yescharacteristic
184C22×D61—22no—
185C22×D61—22no—
186C22×D61—22no—
187C22×D61C2×C22⋊C411yescharacteristic
188C22×D61C2×C22⋊C411yescharacteristic
189Q8×C61—44no—
190Q8×C61—44no—
191C2×C4×C61—22no—
192C2×C4×C61—22no—
193C2×C4×C61—22no—
194C2×C4×C61—24no—
195C2×C4×C61—44no—
196C2×C4×C61C2×C22⋊C411yescharacteristic
197C2×C4×C61C2×C22⋊C411yescharacteristic
198C2×C4×C61C2×C22⋊C411yescharacteristic
199C2×C4×C61C2×C22⋊C411yescharacteristic
200C2×C4×C61C2×C22⋊C411yescharacteristic
201C2×C4×C61C2×C22⋊C411yescharacteristic
202C2×Dic61—22no—
203C2×Dic61—22no—
204C2×Dic61—24no—
205C2×Dic61—44no—
206C2×Dic61C2×C22⋊C411yescharacteristic
207C2×Dic61C2×C22⋊C411yescharacteristic
208C2×Dic61C2×C22⋊C411yescharacteristic
209C2×Dic61C2×C22⋊C411yescharacteristic
210C2×Dic61C22×D411yescharacteristic
211C2×Dic61C22×D411yescharacteristic
212C2×Dic612−1+414yes—
213C4×D61—22no—
214C4×D61—22no—
215C4×D61—22no—
216C4×D61—22no—
217C4×D61—22no—
218C4×D61—22no—
219C4×D61—22no—
220C4×D61—22no—
221C4×D61—22no—
222C4×D61—22no—
223C4×D61—48no—
224C4×D61—48no—
225C4×D61#10014yes—
226C4×D61#10114yes—
227Dic122—48no—
228Dic122—44no—
229Dic122—44no—
230Dic122—48no—
231#92420—44no—
232#92420—44no—
233#21829—611nomaximal, Sylow
234C22×C61—21no—
235C22×C61—21no—
236C22×C61C22×C22⋊C411yescharacteristic
237C22×C61#51912yes—
238C2×D61—28no—
239C2×D61—21no—
240C2×D61—21no—
241C2×D61—21no—
242C2×D61—21no—
243C2×D61C2×#10012yes—
244C2×D61C2×#10112yes—
245C4×C61—21no—
246C4×C61—21no—
247C4×C61—21no—
248C4×C61—21no—
249C4×C61—44no—
250C4×C61C2×#10012yes—
251C4×C61C2×#10112yes—
252Dic61—21no—
253Dic61—21no—
254Dic61—44no—
255Dic61C2×#10012yes—
256Dic61C2×#10112yes—
257Dic61#53612yes—
258Dic61#53612yes—
259C22×C4⋊Q8—611no—
260#2920—611no—
261#2920—611no—
262#1997—614no—
263#1997—614no—
264#1821—614no—
265C2×C61—22no—
266C2×C61#231011yescharacteristic
267C2×C61C22×#10011yescharacteristic
268C2×C61C22×#10111yescharacteristic
269D61—22no—
270D61—22no—
271C23×Q8—612no—
272C2×C4⋊Q8—612no—
273C2×C4⋊Q8—612no—
274C2×C4⋊Q8—612no—
275C2×C4⋊Q8—611no—
276C2×C4⋊Q8—1221no—
277C2×C4⋊Q8—1221no—
278C2×C4⋊Q8—1221no—
279C2×C4⋊Q8—1221no—
280C2×C4⋊Q8—1221no—
281C2×C4⋊Q8—1221no—
282C2×C4⋊Q8—1221no—
283C2×C4⋊Q8—1221no—
284C2×C4⋊Q8#692311yescharacteristic
285C22×C4⋊C4—612no—
286C22×C4⋊C4—612no—
287C22×C42—611no—
288#432—1221no—
289#432—1221no—
290#432—1221no—
291#432—1221no—
292#431—1221no—
293#431—1221no—
294#431—1221no—
295#431—1221no—
296#423—612no—
297#423—612no—
298#407—612no—
299#407—612no—
300C4×M16—612no—
301C4×M16—612no—
302#343—6116no—
303C61#2182911yescharacteristic, complemented, Sylow
304C22×Q8—614no—
305C22×Q8—612no—
306C22×Q8—1222no—
307C22×Q8—1222no—
308C22×Q8—1222no—
309C22×Q8—1222no—
310C22×Q8—2448no—
311C22×Q8C2×#692312yes—
312C23×C4—611no—
313C23×C4—611no—
314C23×C4—611no—
315C23×C4—614no—
316C2×M16—614no—
317C2×M16—614no—
318C4⋊Q8—21no—
319C4⋊Q8—21no—
320C4⋊Q8—21no—
321C4⋊Q8—21no—
322C4⋊Q8—1222no—
323C4⋊Q8—1222no—
324C4⋊Q8—1222no—
325C4⋊Q8—1222no—
326C4⋊Q8—1222no—
327C4⋊Q8—1222no—
328C4⋊Q8—1222no—
329C4⋊Q8—1222no—
330C4⋊Q8—1222no—
331C4⋊Q8—1222no—
332C4⋊Q8—1222no—
333C4⋊Q8—1222no—
334C4⋊Q8—1221no—
335C4⋊Q8—1221no—
336C4⋊Q8—1221no—
337C4⋊Q8—1221no—
338C2×C4⋊C4—614no—
339C2×C4⋊C4—614no—
340C2×C4⋊C4—612no—
341C2×C4⋊C4—612no—
342C2×C4⋊C4—1222no—
343C2×C4⋊C4—1222no—
344C2×C4⋊C4—1222no—
345C2×C4⋊C4—1222no—
346C2×C4⋊C4—1222no—
347C2×C4⋊C4—1222no—
348C2×C4⋊C4—1222no—
349C2×C4⋊C4—1222no—
350C2×C4⋊C4C2×#692312yes—
351C2×C4⋊C4C2×#692312yes—
352C2×C42—611no—
353C2×C42—611no—
354C2×C42—611no—
355C2×C42—611no—
356C2×C42—611no—
357C2×C42—611no—
358C2×C42—611no—
359C2×C42—611no—
360C2×C42—611no—
361C2×C42—611no—
362C2×C42—611no—
363C2×C42C2×#692311yescharacteristic
364C4⋊C8—1222no—
365C4⋊C8—1222no—
366C4⋊C8—1222no—
367C4⋊C8—1222no—
368C22⋊C8—1222no—
369C22⋊C8—1222no—
370C22⋊C8—1222no—
371C22⋊C8—1222no—
372#97—1222no—
373#97—1222no—
374C4×C8—1222no—
375C4×C8—1222no—
376C24—611no—
377C2×Q8—22no—
378C2×Q8—22no—
379C2×Q8—44no—
380C2×Q8—1224no—
381C2×Q8—1224no—
382C2×Q8—1222no—
383C2×Q8—1222no—
384C2×Q8—2444no—
385C2×Q8—2448no—
386C2×Q8—2448no—
387C2×Q8—2448no—
388C2×Q8—2448no—
389C2×Q8—2448no—
390C22×C4—611no—
391C22×C4—611no—
392C22×C4—611no—
393C22×C4—611no—
394C22×C4—611no—
395C22×C4—611no—
396C22×C4—611no—
397C22×C4—611no—
398C22×C4—611no—
399C22×C4—611no—
400C22×C4—611no—
401C22×C4—611no—
402C22×C4—611no—
403C22×C4—611no—
404C22×C4—611no—
405C22×C4—614no—
406C22×C4—1224no—
407C22×C4—1224no—
408C22×C4—1224no—
409C22×C4—1224no—
410C22×C4—1224no—
411C22×C4—2448no—
412C22×C4C22×#692311yescharacteristic
413C22×C4C22×#692311yescharacteristic
414C22×C4C22×#692311yescharacteristic
415C22×C4C22×#692314yes—
416M16—1228no—
417M16—1228no—
418C2×C8—1224no—
419C2×C8—1224no—
420C4⋊C4—22no—
421C4⋊C4—22no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—1224no—
425C4⋊C4—1224no—
426C4⋊C4—1224no—
427C4⋊C4—1224no—
428C4⋊C4—1222no—
429C4⋊C4—1222no—
430C4⋊C4—1222no—
431C4⋊C4—1222no—
432C42—611no—
433C42—611no—
434C42—611no—
435C42—611no—
436C42—611no—
437C42—611no—
438C42—611no—
439C42—611no—
440C42—611no—
441C42—611no—
442C42—611no—
443C42—611no—
444C42C22⋊#692311yescharacteristic
445C42C22⋊#692311yescharacteristic
446C42C22⋊#692311yescharacteristic
447C42C22⋊#692311yescharacteristic
448C23—611no—
449C23—611no—
450C23—1222no—
451C23—1222no—
452C23—1222no—
453C23C23×#692311yescharacteristic
454Q8—44no—
455Q8—44no—
456Q8—2444no—
457Q8—2448no—
458Q8—2448no—
459Q8—2444no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—24no—
464C2×C4—44no—
465C2×C4—611no—
466C2×C4—611no—
467C2×C4—611no—
468C2×C4—611no—
469C2×C4—614no—
470C2×C4—614no—
471C2×C4—614no—
472C2×C4—611no—
473C2×C4—611no—
474C2×C4—1222no—
475C2×C4—1222no—
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—1222no—
485C2×C4—1222no—
486C2×C4—1224no—
487C2×C4—2448no—
488C2×C4—2448no—
489C2×C4—2444no—
490C2×C4C2×C22⋊#692311yescharacteristic
491C2×C4C2×C22⋊#692311yescharacteristic
492C2×C4C2×C22⋊#692311yescharacteristic
493C2×C4C2×C22⋊#692311yescharacteristic
494C2×C4C2×C22⋊#692311yescharacteristic
495C2×C4C2×C22⋊#692311yescharacteristic
496C8—2444no—
497C8—2444no—
498C22—21no—
499C22—21no—
500C22—612no—
501C22—612no—
502C22—1228no—
503C22—1221no—
504C22—1221no—
505C22—1221no—
506C22—1221no—
507C22C22×C22⋊#692311yescharacteristic
508C22#1684083012yes—
509C4—21no—
510C4—21no—
511C4—21no—
512C4—21no—
513C4—44no—
514C4—612no—
515C4—612no—
516C4—612no—
517C4—612no—
518C4—1221no—
519C4—1221no—
520C4—2444no—
521C4D61⋊#10012yes—
522C4D61⋊#10112yes—
523C2—22no—
524C2—1222no—
525C2—1222no—
526C2#2146229311yescharacteristic
527C2C2×D61⋊#10011yescharacteristic
528C2C2×D61⋊#10111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×C4⋊Q8×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC23×D61C22×C4
cosocleC22×Dic61C24
hypercenterC2×C4⋊Q8#6923
hypocenterC61#21829
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. #21462012C2semidirect
4. #21462011C2semidirect
303. C61#21829semidirect

Maximal subgroups

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

subgroupindex
#214624972
#214620122
#214620112
#214617192
C2×C4⋊Q8×D612
#2182961