Finite Group Databasebeta

← #30598165

Subgroups — #30598165

Order 15616.

1116 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
1#21461673C211yesmaximal, characteristic, complemented
2C4×C22⋊#92420C211yesmaximal, characteristic, complemented
3C2×#16840610C212yesmaximal, complemented
4C2×D4⋊#92420C212yesmaximal, complemented
5C2×#16840307C211yesmaximal, characteristic
6C2×C4⋊#92420C2212yes—
7C2×C22⋊#92420—21no—
8C2×C22⋊#92420—21no—
9C2×C4×#92420C2212yes—
10#16840628—21no—
11#16840628—21no—
12#16840610—24no—
13D4⋊#92420—24no—
14C22×#11758224—21no—
15#16840307—24no—
16#16840307—24no—
17C2×#14519776C411yescharacteristic
18C2×#14519773C411yescharacteristic
19C2×#14519763—21no—
20C2×#14519751C411yescharacteristic
21C2×#14519749—21no—
22C2×D4×Dic61C2211yescharacteristic
23C2×#14519739C2211yescharacteristic
24C2×#14519737—21no—
25C22×C4×Dic61C2211yescharacteristic
26C2×#121×C61C411yescharacteristic
27C22×#92420—22no—
28C22×#92420—22no—
29C4⋊#92420—22no—
30C4⋊#92420—22no—
31C22⋊#92420—24no—
32C22⋊#92420—42no—
33C4×#92420—22no—
34C4×#92420—22no—
35C2×#11758224—28no—
36C2×#11758224—44no—
37C2×#11758224—42no—
38C2×#11758224—42no—
39C22×Dic122—21no—
40C22×D244C2×C411yescharacteristic
41C22×C22⋊D61—21no—
42C22×C22⋊D61—21no—
43C22×C22⋊D61—21no—
44C23×Dic61—21no—
45C23×Dic61D411yescharacteristic
46C23×Dic61D411yescharacteristic
47C22×C4×D61—21no—
48#14519776—22no—
49#14519776—22no—
50#14519773—22no—
51#14519773—22no—
52#14519763—28no—
53#14519751—22no—
54#14519751—22no—
55#14519749—28no—
56D4×Dic61—22no—
57D4×Dic61D414yes—
58#14519739—22no—
59#14519739D414yes—
60#14519737—28no—
61C2×C4⋊Dic61C2×C411yescharacteristic
62C2×#11758196—21no—
63C2×C22⋊Dic61—21no—
64C2×#11758198—21no—
65C2×#11758198—21no—
66C2×C4×Dic61—22no—
67C2×C4×Dic61—22no—
68C2×C4×Dic61C2×C411yescharacteristic
69C2×C4×Dic61D411yescharacteristic
70C2×C4×Dic61D411yescharacteristic
71C2×C4×Dic61C2311yescharacteristic
72C22×D4×C61—21no—
73C22×D4×C61C2×C411yescharacteristic
74C23×C4×C61C2×C411yescharacteristic
75#121×C61—22no—
76#121×C61—22no—
77C2×C4⋊C4×C61C2×C411yescharacteristic
78C2×C22⋊C4×C61—21no—
79C24×C61—21no—
80C24×C61C22⋊C411yescharacteristic
81C23×D61—21no—
82C2×D4×C61—24no—
83C2×D4×C61—21no—
84C2×D4×C61—22no—
85C2×D4×C61—22no—
86C2×D4×C61—42no—
87C2×D4×C61—42no—
88C2×D4×C61C22⋊C412yes—
89C22×C4×C61—21no—
90C22×C4×C61—21no—
91C22×C4×C61—21no—
92C22×C4×C61—22no—
93C22×C4×C61—22no—
94C22×C4×C61C22⋊C411yescharacteristic
95C22×C4×C61C22×C411yescharacteristic
96C2×C22⋊D61—24no—
97C2×C22⋊D61—24no—
98C2×C22⋊D61—24no—
99C2×C22⋊D61—42no—
100C2×C22⋊D61—42no—
101C2×C22⋊D61—42no—
102C2×C22⋊D61—42no—
103C2×C22⋊D61—42no—
104C2×C22⋊D61—42no—
105C22×Dic61—22no—
106C22×Dic61—22no—
107C22×Dic61—21no—
108C22×Dic61—22no—
109C22×Dic61—24no—
110C22×Dic61—22no—
111C22×Dic61—41no—
112C22×Dic61—41no—
113C22×Dic61—41no—
114C22×Dic61—42no—
115C22×Dic61C22⋊C411yescharacteristic
116C22×Dic61C22⋊C411yescharacteristic
117C22×Dic61D812yes—
118C22×Dic61SD1612yes—
119C22×Dic61C2×D411yescharacteristic
120C22×Dic61C2×D411yescharacteristic
121#11758224—416no—
122#11758224—416no—
123C2×D244—22no—
124C2×D244—22no—
125C2×D244—21no—
126C2×D244C22⋊C412yes—
127C2×C4×D61—24no—
128C2×C4×D61—41no—
129C2×C4×D61—41no—
130C2×C4×D61—42no—
131C2×Dic122—24no—
132C2×Dic122—42no—
133C2×Dic122—42no—
134C2×#92420—24no—
135C2×#92420—42no—
136C2×#92420—42no—
137C2×#92420—42no—
138C2×#92420—42no—
139C2×#92420—42no—
140C4⋊C4×C61—21no—
141C4⋊C4×C61C22⋊C412yes—
142C22⋊C4×C61—24no—
143C22⋊Dic61—24no—
144#11758198—24no—
145#11758198—24no—
146C4⋊Dic61—21no—
147C4⋊Dic61C22⋊C412yes—
148#11758196—24no—
149C4×Dic61—21no—
150C4×Dic61—21no—
151C4×Dic61—22no—
152C4×Dic61—22no—
153C4×Dic61C2×D412yes—
154C4×Dic61C2×D412yes—
155C23×C61—21no—
156C23×C61—21no—
157C23×C61—21no—
158C23×C61—21no—
159C23×C61—21no—
160C23×C61—21no—
161C23×C61—22no—
162C23×C61—41no—
163C23×C61—41no—
164C23×C61—41no—
165C23×C61—41no—
166C23×C61—41no—
167C23×C61—41no—
168C23×C61#10212yes—
169C23×C61C2×C22⋊C411yescharacteristic
170C22×D61—22no—
171C22×D61—41no—
172C22×D61—41no—
173C22×D61—41no—
174C22×D61—41no—
175C22×D61—41no—
176C22×D61—41no—
177D4×C61—24no—
178D4×C61—48no—
179D4×C61—42no—
180C2×C4×C61—21no—
181C2×C4×C61—22no—
182C2×C4×C61—21no—
183C2×C4×C61—21no—
184C2×C4×C61—41no—
185C2×C4×C61—41no—
186C2×C4×C61—42no—
187C2×C4×C61—42no—
188C2×C4×C61C2×C22⋊C411yescharacteristic
189C2×C4×C61C2×C22⋊C411yescharacteristic
190C2×C4×C61#13112yes—
191C2×C4×C61#13112yes—
192C22⋊D61—48no—
193C22⋊D61—48no—
194C22⋊D61—48no—
195C2×Dic61—21no—
196C2×Dic61—21no—
197C2×Dic61—21no—
198C2×Dic61—21no—
199C2×Dic61—21no—
200C2×Dic61—21no—
201C2×Dic61—24no—
202C2×Dic61—24no—
203C2×Dic61—22no—
204C2×Dic61—44no—
205C2×Dic61—41no—
206C2×Dic61—41no—
207C2×Dic61—44no—
208C2×Dic61—44no—
209C2×Dic61#10212yes—
210C2×Dic61#10412yes—
211C2×Dic61#12012yes—
212C2×Dic61#12012yes—
213C2×Dic61C2×D811yescharacteristic
214C2×Dic61C2×SD1611yescharacteristic
215C2×Dic61AGL(1,ℤ/8)12yes—
216D244—24no—
217D244—42no—
218C4×D61—44no—
219C4×D61—44no—
220Dic122—48no—
221#92420—44no—
222#92420—82no—
223#8313—611nomaximal, Sylow
224C22×C61—22no—
225C22×C61—22no—
226C22×C61—22no—
227C22×C61—41no—
228C22×C61—41no—
229C22×C61—41no—
230C22×C61—41no—
231C22×C61—42no—
232C22×C61—42no—
233C22×C61—42no—
234C22×C61—81no—
235C22×C61—81no—
236C22×C61—81no—
237C22×C61—81no—
238C22×C61#37911yescharacteristic
239C22×C61#40811yescharacteristic
240C22×C61#40811yescharacteristic
241C22×C61C2×#10211yescharacteristic
242C22×C61#41811yescharacteristic
243C22×C61C2×#10411yescharacteristic
244C22×C61#42111yescharacteristic
245C2×D61—42no—
246C2×D61—42no—
247C2×D61—42no—
248C2×D61—81no—
249C2×D61—81no—
250C2×D61—81no—
251C2×D61—81no—
252C4×C61—41no—
253C4×C61—42no—
254C4×C61#40812yes—
255C4×C61#40812yes—
256Dic61—22no—
257Dic61—22no—
258Dic61—22no—
259Dic61—42no—
260Dic61#44712yes—
261Dic61#45012yes—
262C2×#532—611no—
263#1797—611no—
264C4×C22⋊C8—611no—
265C2×D4⋊C8—612no—
266C2×D4⋊C8—612no—
267C2×C61—42no—
268C2×C61—82no—
269C2×C61#148011yescharacteristic
270C2×C61#148411yescharacteristic
271C2×C61#149211yescharacteristic
272C2×C61#149611yescharacteristic
273C2×C61#178011yescharacteristic
274C2×C61#178611yescharacteristic
275C2×C61#178911yescharacteristic
276D61—82no—
277C22×#41—1221no—
278#532—1224no—
279#532—1224no—
280C2×C4⋊Q8—611no—
281C2×#127—611no—
282C2×#124—1221no—
283C2×#121—611no—
284C2×#121—1221no—
285C2×#121#692311yescharacteristic
286C2×C4×D4—611no—
287C2×C4×D4—611no—
288C2×C4×D4—1221no—
289C22×C42—611no—
290C2×C4⋊C8—612no—
291C2×C22⋊C8—1221no—
292C2×C22⋊C8—1221no—
293C2×C4×C8—612no—
294#336—1221no—
295#336—1221no—
296D4⋊C8—1224no—
297D4⋊C8—1224no—
298C61#831311yescharacteristic, complemented, Sylow
299C2×#41—1228no—
300C2×#41—2442no—
301C2×#41—2442no—
302C2×#41—2444no—
303C22×Q8—1221no—
304C22×D4—21no—
305C22×D4—611no—
306C22×D4—1221no—
307C22×D4—1221no—
308C22×D4—1221no—
309C22×D4C2×#692311yescharacteristic
310C23×C4—611no—
311C23×C4—611no—
312C23×C4—1221no—
313C23×C4—1221no—
314C23×C4C2×#692311yescharacteristic
315C22×C8—1222no—
316C22×C8—1222no—
317C4⋊Q8—1222no—
318C4⋊Q8—1222no—
319#127—1222no—
320#127—1222no—
321#124—1228no—
322#121—22no—
323#121—22no—
324#121—1222no—
325#121—1222no—
326#121—1228no—
327C4×D4—614no—
328C4×D4—614no—
329C4×D4—1222no—
330C4×D4—1222no—
331C4×D4—1228no—
332C2×C4⋊C4—611no—
333C2×C4⋊C4—1221no—
334C2×C4⋊C4C2×#692311yescharacteristic
335C2×C22⋊C4—21no—
336C2×C22⋊C4—1221no—
337C2×C22⋊C4—1221no—
338C2×C22⋊C4—1221no—
339C2×C42—611no—
340C2×C42—611no—
341C2×C42—611no—
342C2×C42—611no—
343C2×C42—1222no—
344C2×C42—1222no—
345C4⋊C8—1222no—
346C4⋊C8—1222no—
347C22⋊C8—1224no—
348C22⋊C8—2442no—
349C4×C8—1222no—
350C4×C8—1222no—
351C24—21no—
352C24—1221no—
353C24C22⋊#692311yescharacteristic
354#41—24416no—
355#41—24416no—
356C2×Q8—1224no—
357C2×Q8—2442no—
358C2×Q8—2442no—
359C2×D4—24no—
360C2×D4—21no—
361C2×D4—22no—
362C2×D4—22no—
363C2×D4—42no—
364C2×D4—42no—
365C2×D4—612no—
366C2×D4—1224no—
367C2×D4—1224no—
368C2×D4—1224no—
369C2×D4—1221no—
370C2×D4—1222no—
371C2×D4—1222no—
372C2×D4—2442no—
373C2×D4—2442no—
374C2×D4—2442no—
375C2×D4—2442no—
376C2×D4—2442no—
377C2×D4—2442no—
378C2×D4C22⋊#692312yes—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—611no—
385C22×C4—612no—
386C22×C4—612no—
387C22×C4—611no—
388C22×C4—611no—
389C22×C4—611no—
390C22×C4—1224no—
391C22×C4—1222no—
392C22×C4—1222no—
393C22×C4—1222no—
394C22×C4—1222no—
395C22×C4—1224no—
396C22×C4—1221no—
397C22×C4—2441no—
398C22×C4—2441no—
399C22×C4—2442no—
400C22×C4—2441no—
401C22×C4—2441no—
402C22×C4—2442no—
403C22×C4—2441no—
404C22×C4C22⋊#692311yescharacteristic
405C22×C4C22×#692311yescharacteristic
406C2×C8—1224no—
407C2×C8—2442no—
408C2×C8—2442no—
409C2×C8—2442no—
410C2×C8—2442no—
411C2×C8—2442no—
412C4⋊C4—21no—
413C4⋊C4—612no—
414C4⋊C4—1224no—
415C4⋊C4—1221no—
416C4⋊C4C22⋊#692312yes—
417C22⋊C4—24no—
418C22⋊C4—1224no—
419C22⋊C4—1224no—
420C22⋊C4—1224no—
421C42—612no—
422C42—612no—
423C42—1222no—
424C42—1222no—
425C42—1221no—
426C42—1221no—
427C23—21no—
428C23—21no—
429C23—21no—
430C23—21no—
431C23—21no—
432C23—21no—
433C23—22no—
434C23—41no—
435C23—41no—
436C23—41no—
437C23—41no—
438C23—41no—
439C23—41no—
440C23—1222no—
441C23—2441no—
442C23—2441no—
443C23—2441no—
444C23—2441no—
445C23—2441no—
446C23—2441no—
447C23#1451983912yes—
448C23C2×C22⋊#692311yescharacteristic
449Q8—2448no—
450D4—24no—
451D4—48no—
452D4—42no—
453D4—1224no—
454D4—2448no—
455D4—2448no—
456D4—2448no—
457D4—2442no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—22no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—611no—
467C2×C4—611no—
468C2×C4—612no—
469C2×C4—612no—
470C2×C4—612no—
471C2×C4—612no—
472C2×C4—612no—
473C2×C4—1224no—
474C2×C4—1224no—
475C2×C4—1221no—
476C2×C4—1221no—
477C2×C4—1221no—
478C2×C4—1221no—
479C2×C4—1221no—
480C2×C4—1221no—
481C2×C4—1222no—
482C2×C4—2444no—
483C2×C4—2444no—
484C2×C4—2444no—
485C2×C4—2444no—
486C2×C4—2444no—
487C2×C4—2441no—
488C2×C4—2441no—
489C2×C4C2×C22⋊#692311yescharacteristic
490C2×C4C2×C22⋊#692311yescharacteristic
491C2×C4#1451986412yes—
492C2×C4#1451986412yes—
493C8—4882no—
494C8—2444no—
495C22—22no—
496C22—22no—
497C22—22no—
498C22—41no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—42no—
503C22—42no—
504C22—42no—
505C22—81no—
506C22—81no—
507C22—81no—
508C22—81no—
509C22—4881no—
510C22—4881no—
511C22—4881no—
512C22—4881no—
513C22—2442no—
514C22—2442no—
515C22—2442no—
516C22#1684070311yescharacteristic
517C22#1684073511yescharacteristic
518C22#1684073511yescharacteristic
519C22C2×#1451983911yescharacteristic
520C22#1684075411yescharacteristic
521C22D61⋊#10411yescharacteristic
522C22#1684075911yescharacteristic
523C4—41no—
524C4—42no—
525C4—612no—
526C4—612no—
527C4—1222no—
528C4—1222no—
529C4—1222no—
530C4—2442no—
531C4#1684073512yes—
532C4#1684073612yes—
533C2—42no—
534C2—82no—
535C2—4882no—
536C2#2146112411yescharacteristic
537C2#2146113811yescharacteristic
538C2#2146116411yescharacteristic
539C2#2146117811yescharacteristic
540C2#2146164311yescharacteristic
541C2#2146165711yescharacteristic
542C2#2146166111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#121×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC2×#16840307C2
cosocleC2×C4×Dic61C23
hypercenterC2×#121#6923
hypocenterC61#8313
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. #21461673C2semidirect
2. C4×C22⋊#92420C2semidirect
3. C2×#16840610C2semidirect
4. C2×D4⋊#92420C2semidirect
298. C61#8313semidirect

Maximal subgroups

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

subgroupindex
#214616732
C4×C22⋊#924202
C2×#168406102
C2×D4⋊#924202
C2×#168403072
#831361