Finite Group Databasebeta

← #30620333

Subgroups — #30620333

Order 15616.

1322 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462559C212yesmaximal, complemented
2#21462011C212yesmaximal, complemented
3#21461845C214yesmaximal, complemented
4#21461719C212yesmaximal, complemented
5#21461683C211yesmaximal, characteristic, complemented
6C4×#14519837C211yesmaximal, characteristic, complemented
7#21461522C212yesmaximal, complemented
8C2×#16840414C211yesmaximal, characteristic
9C2×D61⋊M16C2214yes—
10#16840796—22no—
11#16840792—24no—
12#16840790—22no—
13#16840765C2212yes—
14C2×#14519837C2212yes—
15C2×#14519837C2212yes—
16#16840734C2214yes—
17C4×#11758217C2212yes—
18#16840642C2211yescharacteristic
19#16840642C2214yes—
20#16840642C2212yes—
21#16840642C2211yescharacteristic
22#16840642C2214yes—
23C22×#11758226C411yescharacteristic
24C22×#11758222C411yescharacteristic
25#16840414—22no—
26#16840414—24no—
27#16840414—22no—
28C2×#14519775C2211yescharacteristic
29C2×#14519762C412yes—
30C2×#14519759C412yes—
31C2×#14519757C411yescharacteristic
32C2×#14519750C2212yes—
33C2×#14519739C2211yescharacteristic
34C2×C4×C22⋊D61C2211yescharacteristic
35C2×C4⋊C4×D61C2212yes—
36C2×C22⋊Q8×C61C411yescharacteristic
37C2×#11758213—24no—
38D61⋊M16—28no—
39D61⋊M16—44no—
40C2×#11758217C2312yes—
41C2×#11758217C2314yes—
42C2×#11758217C2312yes—
43C2×D61⋊C8—24no—
44#14519844—22no—
45C4⋊#92420—22no—
46#14519837—24no—
47#14519837—42no—
48#14519834—24no—
49#14519834—24no—
50#14519832—22no—
51C4×#92420—22no—
52C2×#11758226—21no—
53C2×#11758226—22no—
54C2×#11758226—21no—
55C2×#11758226—44no—
56C2×#11758222—22no—
57C2×#11758222—21no—
58C2×#11758222—21no—
59C2×#11758222—44no—
60C22×Dic122C2×C411yescharacteristic
61C22×D244C2×C411yescharacteristic
62C22×D244C2×C412yes—
63C22×C22⋊D61C2×C412yes—
64C22×C22⋊D61C2311yescharacteristic
65C22×C4×D61C2×C412yes—
66C22×C4×D61C2×C412yes—
67C22×C4×D61C2×C411yescharacteristic
68C22×C4×D61C2312yes—
69#14519775—22no—
70#14519775—22no—
71#14519762—24no—
72#14519762—24no—
73#14519759—24no—
74#14519759—24no—
75#14519757—22no—
76#14519757—22no—
77#14519750—24no—
78#14519750—24no—
79#14519739D412yes—
80#14519739D414yes—
81#14519739D412yes—
82C4×C22⋊D61—22no—
83C4×C22⋊D61—22no—
84C2×C4⋊Dic61C2×C412yes—
85C2×#11758196C2×C412yes—
86C2×#11758196C2311yescharacteristic
87C2×#11758196C2312yes—
88C4⋊C4×D61—24no—
89C4⋊C4×D61—24no—
90C2×C22⋊Dic61C2×C411yescharacteristic
91C2×#11758198C2×C411yescharacteristic
92C2×#11758198C2×C412yes—
93C2×#11758198C2×C412yes—
94C2×C4×Dic61C2311yescharacteristic
95C22×Q8×C61C2×C411yescharacteristic
96C23×C4×C61C2×C411yescharacteristic
97C22⋊Q8×C61—22no—
98C22⋊Q8×C61—22no—
99C2×C4⋊C4×C61C2×C412yes—
100C2×C4⋊C4×C61C2×C411yescharacteristic
101C2×C22⋊C4×C61C2×C412yes—
102C24×C61C22×C411yescharacteristic
103C23×D61C22×C412yes—
104C23×D61C22×C411yescharacteristic
105C2×Q8×C61—21no—
106C2×Q8×C61—21no—
107C2×Q8×C61—42no—
108C22×C4×C61—21no—
109C22×C4×C61—21no—
110C22×C4×C61—42no—
111C22×C4×C61C22×C411yescharacteristic
112C22×C4×C61C22×C412yes—
113C22×C4×C61C22×C411yescharacteristic
114C22×C4×C61C22×C412yes—
115C2×C22⋊D61—22no—
116C2×C22⋊D61—22no—
117C2×C22⋊D61—22no—
118C2×C22⋊D61—22no—
119C2×C22⋊D61—21no—
120C2×C22⋊D61—21no—
121C2×C22⋊D61—44no—
122C22×Dic61C22×C411yescharacteristic
123C22×Dic61C22×C412yes—
124C22×Dic61C22×C411yescharacteristic
125C22×Dic61C2411yescharacteristic
126#11758226—48no—
127#11758226—44no—
128#11758226—44no—
129#11758222—48no—
130#11758222—44no—
131#11758222—44no—
132C2×D244—24no—
133C2×D244—22no—
134C2×D244—22no—
135C2×D244—44no—
136C2×D244C22⋊C412yes—
137C2×D244C22⋊C411yescharacteristic
138C2×D244C22⋊C411yescharacteristic
139C2×C4×D61—24no—
140C2×C4×D61—22no—
141C2×C4×D61—22no—
142C2×C4×D61—22no—
143C2×C4×D61—22no—
144C2×C4×D61—22no—
145C2×C4×D61—22no—
146C2×C4×D61—21no—
147C2×C4×D61—21no—
148C2×C4×D61—42no—
149C2×C4×D61—44no—
150C2×C4×D61—44no—
151C2×C4×D61C2×D414yes—
152C2×C4×D61C2×D414yes—
153C2×Dic122—21no—
154C2×Dic122—21no—
155C2×Dic122—42no—
156#11758217—22no—
157#11758217—22no—
158#11758217—24no—
159#11758217—24no—
160#11758217—22no—
161#11758217#4114yescomplemented
162C2×#92420—22no—
163C2×#92420—22no—
164C2×#92420—24no—
165#11758213—48no—
166D61⋊C8—48no—
167C4⋊C4×C61—24no—
168C4⋊C4×C61C22⋊C412yes—
169C4⋊C4×C61C22⋊C412yes—
170C22⋊C4×C61—24no—
171C22⋊Dic61—22no—
172#11758198—24no—
173#11758198—22no—
174#11758198C22⋊C414yes—
175#11758198C22⋊C414yes—
176C4⋊Dic61—24no—
177#11758196—24no—
178#11758196—22no—
179#11758196—24no—
180C4×Dic61C2×D412yes—
181C4×Dic61C2×D412yes—
182C23×C61—21no—
183C23×C61—21no—
184C23×C61—21no—
185C23×C61—41no—
186C23×C61—41no—
187C23×C61C23×C411yescharacteristic
188C22×D61—22no—
189C22×D61—22no—
190C22×D61—24no—
191C22×D61—21no—
192C22×D61—21no—
193C22×D61—21no—
194C22×D61—42no—
195C22×D61—41no—
196C22×D61—41no—
197C22×D61C2×C22⋊C412yes—
198C22×D61C2×C22⋊C412yes—
199Q8×C61—42no—
200Q8×C61—42no—
201C2×C4×C61—22no—
202C2×C4×C61—22no—
203C2×C4×C61—22no—
204C2×C4×C61—22no—
205C2×C4×C61—21no—
206C2×C4×C61—42no—
207C2×C4×C61—42no—
208C2×C4×C61—41no—
209C2×C4×C61—42no—
210C2×C4×C61C2×C22⋊C411yescharacteristic
211C2×C4×C61C2×C22⋊C414yes—
212C2×C4×C61C2×C22⋊C411yescharacteristic
213C22⋊D61—44no—
214C22⋊D61—44no—
215C22⋊D61—42no—
216C22⋊D61—42no—
217C2×Dic61—22no—
218C2×Dic61—21no—
219C2×Dic61—41no—
220C2×Dic61—42no—
221C2×Dic61—41no—
222C2×Dic61C2×C22⋊C412yes—
223C2×Dic61C22×D412yes—
224C2×Dic61C2×#4112yes—
225C2×Dic61H(5,𝔽2)11yescharacteristic
226C2×Dic612−1+411yescharacteristic
227D244—24no—
228D244—22no—
229D244—44no—
230D244—44no—
231D244#10014yescomplemented
232C4×D61—24no—
233C4×D61—24no—
234C4×D61—24no—
235C4×D61—24no—
236C4×D61—42no—
237C4×D61—44no—
238C4×D61—44no—
239C4×D61—44no—
240C4×D61—44no—
241C4×D61—42no—
242Dic122—42no—
243Dic122—42no—
244#92420—24no—
245#92420—44no—
246#92420—42no—
247#22479—611nomaximal, Sylow
248C22×C61—21no—
249C22×C61—21no—
250C22×C61—41no—
251C22×C61—41no—
252C22×C61—41no—
253C22×C61—81no—
254C22×C61—81no—
255C22×C61C22×C22⋊C411yescharacteristic
256C22×C61C4×#4111yescharacteristic
257C22×C61#52011yescharacteristic
258C2×D61—22no—
259C2×D61—22no—
260C2×D61—22no—
261C2×D61—22no—
262C2×D61—22no—
263C2×D61—44no—
264C2×D61—44no—
265C2×D61—41no—
266C2×D61—41no—
267C2×D61—41no—
268C2×D61—81no—
269C2×D61—81no—
270C2×D61C2×#10014yes—
271C4×C61—24no—
272C4×C61—21no—
273C4×C61—41no—
274C4×C61—42no—
275C4×C61C2×#10012yes—
276Dic61—22no—
277Dic61—42no—
278Dic61—41no—
279Dic61#54612yes—
280Dic61#54712yes—
281C2×#547—611no—
282D4×M16—612no—
283#1997—612no—
284#1900—614no—
285#1821—612no—
286#1800—611no—
287C4×#100—611no—
288C2×#343—612no—
289C2×C61—21no—
290C2×C61—21no—
291C2×C61—81no—
292C2×C61#233911yescharacteristic
293C2×C61C22×#10011yescharacteristic
294C2×C61#288911yescharacteristic
295D61—24no—
296D61—42no—
297D61—81no—
298C22×#41—611no—
299C22×#41—611no—
300C22×M16—614no—
301#547—1222no—
302#547—1224no—
303#547—1222no—
304C2×C4⋊Q8—611no—
305C2×#123—612no—
306C2×#123—612no—
307C2×C22⋊Q8—611no—
308C2×C22⋊Q8#692311yescharacteristic
309C2×#121—612no—
310C2×C4×D4—611no—
311C2×C4×D4—611no—
312C22×C4⋊C4—612no—
313#436—1222no—
314#435—1224no—
315C8×D4—1222no—
316#423—612no—
317C2×#100—612no—
318C2×#100—612no—
319#407—614no—
320C4×M16—612no—
321#343—612no—
322#343—611no—
323#343—614no—
324#343—614no—
325#343—611no—
326C61#2247911yescharacteristic, complemented, Sylow
327C2×#41—1221no—
328C2×#41—1222no—
329C2×#41—1221no—
330C2×#41—1221no—
331C2×#41—1222no—
332C2×#41—1221no—
333C2×#41—2444no—
334C2×#41—2444no—
335C22×Q8—611no—
336C22×Q8C2×#692311yescharacteristic
337C22×D4—611no—
338C22×D4—612no—
339C22×D4—611no—
340C22×D4—612no—
341C23×C4—612no—
342C23×C4—612no—
343C23×C4—612no—
344C23×C4—611no—
345C23×C4C2×#692311yescharacteristic
346C2×M16—612no—
347C2×M16—614no—
348C2×M16—612no—
349C2×M16—1224no—
350C2×M16—1228no—
351C2×M16—2444no—
352C22×C8—1224no—
353C4⋊Q8—1222no—
354C4⋊Q8—1222no—
355#123—1224no—
356#123—1224no—
357#123—1224no—
358#123—1224no—
359C22⋊Q8—22no—
360C22⋊Q8—22no—
361C22⋊Q8—1222no—
362C22⋊Q8—1222no—
363#121—1224no—
364#121—1224no—
365C4×D4—612no—
366C4×D4—614no—
367C4×D4—612no—
368C4×D4—1222no—
369C4×D4—1222no—
370C2×C4⋊C4—611no—
371C2×C4⋊C4—612no—
372C2×C4⋊C4—612no—
373C2×C4⋊C4—612no—
374C2×C4⋊C4—1224no—
375C2×C4⋊C4—1224no—
376C2×C4⋊C4C2×#692312yes—
377C2×C4⋊C4C2×#692311yescharacteristic
378C2×C22⋊C4—612no—
379C2×C22⋊C4—611no—
380C2×C22⋊C4—611no—
381C2×C22⋊C4—612no—
382C2×C22⋊C4C2×#692312yes—
383C2×C42—611no—
384C4⋊C8—1222no—
385C4⋊C8—1222no—
386#100—1224no—
387#100—2442no—
388C22⋊C8—1224no—
389C22⋊C8—1224no—
390#97—1222no—
391C4×C8—1222no—
392C24—612no—
393C24—611no—
394C24C22×#692311yescharacteristic
395#41—2444no—
396#41—2448no—
397#41—2444no—
398#41—2444no—
399#41—2448no—
400#41—2444no—
401C2×Q8—21no—
402C2×Q8—21no—
403C2×Q8—42no—
404C2×Q8—1221no—
405C2×Q8—1221no—
406C2×Q8—2442no—
407C2×D4—611no—
408C2×D4—612no—
409C2×D4—611no—
410C2×D4—1224no—
411C2×D4—1222no—
412C2×D4—1222no—
413C2×D4—1222no—
414C2×D4—1221no—
415C2×D4—1222no—
416C2×D4—1221no—
417C2×D4—1222no—
418C2×D4—1222no—
419C2×D4—2444no—
420C2×D4—2444no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—42no—
424C22×C4—611no—
425C22×C4—611no—
426C22×C4—614no—
427C22×C4—614no—
428C22×C4—611no—
429C22×C4—612no—
430C22×C4—1224no—
431C22×C4—1222no—
432C22×C4—1222no—
433C22×C4—1222no—
434C22×C4—1222no—
435C22×C4—1222no—
436C22×C4—1222no—
437C22×C4—1221no—
438C22×C4—1221no—
439C22×C4—2442no—
440C22×C4—2444no—
441C22×C4—2444no—
442C22×C4C22×#692311yescharacteristic
443C22×C4C22×#692312yes—
444C22×C4C22×#692311yescharacteristic
445C22×C4C22×#692312yes—
446M16—614no—
447M16—1222no—
448M16—1222no—
449M16—1224no—
450M16—1224no—
451M16—1222no—
452M16—2448no—
453C2×C8—1222no—
454C2×C8—1222no—
455C2×C8—1224no—
456C2×C8—2448no—
457C4⋊C4—24no—
458C4⋊C4—1222no—
459C4⋊C4—1224no—
460C4⋊C4—1224no—
461C4⋊C4—1224no—
462C4⋊C4C22⋊#692312yes—
463C4⋊C4C22⋊#692312yes—
464C22⋊C4—24no—
465C22⋊C4—614no—
466C22⋊C4—614no—
467C22⋊C4—1222no—
468C22⋊C4—1222no—
469C22⋊C4—1224no—
470C42—612no—
471C42—612no—
472C23—21no—
473C23—21no—
474C23—21no—
475C23—41no—
476C23—41no—
477C23—612no—
478C23—612no—
479C23—1224no—
480C23—1222no—
481C23—1222no—
482C23—1221no—
483C23—1221no—
484C23—1221no—
485C23—2442no—
486C23—2441no—
487C23—2441no—
488C23C23×#692311yescharacteristic
489Q8—42no—
490Q8—42no—
491Q8—2442no—
492Q8—2442no—
493D4—614no—
494D4—1224no—
495D4—1222no—
496D4—2444no—
497D4—2444no—
498D4—2442no—
499D4—2442no—
500D4—2444no—
501D4—2444no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—21no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—41no—
510C2×C4—42no—
511C2×C4—612no—
512C2×C4—612no—
513C2×C4—611no—
514C2×C4—611no—
515C2×C4—612no—
516C2×C4—1224no—
517C2×C4—1224no—
518C2×C4—1224no—
519C2×C4—1224no—
520C2×C4—1221no—
521C2×C4—1222no—
522C2×C4—2442no—
523C2×C4—2444no—
524C2×C4—2444no—
525C2×C4—2444no—
526C2×C4—2444no—
527C2×C4—2441no—
528C2×C4—2442no—
529C2×C4—2441no—
530C2×C4—2442no—
531C2×C4C2×C22⋊#692311yescharacteristic
532C2×C4C2×C22⋊#692314yes—
533C2×C4C2×C22⋊#692311yescharacteristic
534C8—1224no—
535C8—2444no—
536C8—2442no—
537C22—21no—
538C22—21no—
539C22—41no—
540C22—41no—
541C22—41no—
542C22—81no—
543C22—81no—
544C22—614no—
545C22—1222no—
546C22—1222no—
547C22—1222no—
548C22—1222no—
549C22—1222no—
550C22—4881no—
551C22—4881no—
552C22—2444no—
553C22—2444no—
554C22—2441no—
555C22—2441no—
556C22—2441no—
557C22C22×C22⋊#692311yescharacteristic
558C22#41×#692311yescharacteristic
559C22#1684083111yescharacteristic
560C4—24no—
561C4—21no—
562C4—41no—
563C4—42no—
564C4—612no—
565C4—612no—
566C4—1222no—
567C4—2441no—
568C4—2442no—
569C4D61⋊#10012yes—
570C2—21no—
571C2—21no—
572C2—81no—
573C2—1224no—
574C2—4881no—
575C2—2442no—
576C2#2146232211yescharacteristic
577C2C2×D61⋊#10011yescharacteristic
578C2#2146243211yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×C22⋊Q8×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840414C2
cosocleC22×Dic61C24
hypercenterC2×C22⋊Q8#6923
hypocenterC61#22479
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4⋊C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #21462559C2semidirect
2. #21462011C2semidirect
3. #21461845C2semidirect
4. #21461719C2semidirect
5. #21461683C2semidirect
6. C4×#14519837C2semidirect
7. #21461522C2semidirect
161. #11758217#41semidirect
231. D244#100semidirect
326. C61#22479semidirect

Maximal subgroups

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

subgroupindex
#214625592
#214620112
#214618452
#214617192
#214616832
C4×#145198372
#214615222
C2×#168404142
#2247961