Finite Group Databasebeta

← #30603224

Subgroups — #30603224

Order 15616.

1262 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊#92420C211yesmaximal, characteristic, complemented
2C22×#14519834C212yesmaximal
3C2×#16840628C212yesmaximal, complemented
4C2×#16840628C211yesmaximal, characteristic, complemented
5C2×#16839609C211yesmaximal, characteristic
6C23×#92420C2212yes—
7C23×#92420C2212yes—
8C2×C4⋊#92420—22no—
9C2×C4⋊#92420—24no—
10C2×#14519834—24no—
11C2×#14519834—24no—
12C2×#14519834—24no—
13#16840628—22no—
14#16840628—24no—
15C23×C4×D61C2211yescharacteristic
16C22×#11758198C411yescharacteristic
17C22×#11758198C411yescharacteristic
18C22×C4×Dic61C2211yescharacteristic
19C22×C4×Dic61C2211yescharacteristic
20#16839609—22no—
21#16839609—22no—
22C2×#14519684C411yescharacteristic
23C2×#95×C61C411yescharacteristic
24C22×#92420—22no—
25C22×#92420—22no—
26C22×#92420—22no—
27C22×#92420—22no—
28C22×#92420—22no—
29C22×#92420—22no—
30C22×#92420—22no—
31C22×#92420—22no—
32C22×#92420—22no—
33C22×#92420—22no—
34C22×#92420—22no—
35C22×#92420—22no—
36C22×#92420D414yes—
37C22×#92420D414yes—
38C4⋊#92420—28no—
39#14519834—216no—
40C24×D61C2×C411yescharacteristic
41C23×Dic61C2×C411yescharacteristic
42C23×Dic61C2×C411yescharacteristic
43C23×Dic61C2311yescharacteristic
44C22×C4×D61—22no—
45C22×C4×D61—22no—
46C22×C4×D61—21no—
47C22×C4×D61—21no—
48C22×C4×D61—21no—
49C22×C4×D61—21no—
50C22×C4×D61—22no—
51C22×C4×D61—22no—
52C22×C4×D61D412yes—
53C22×C4×D61Q812yes—
54C2×#11758198—22no—
55C2×#11758198—22no—
56C2×#11758198—22no—
57C2×#11758198—22no—
58C2×#11758198—22no—
59C2×#11758198C814yescomplemented
60C2×C4×Dic61—22no—
61C2×C4×Dic61—22no—
62C2×C4×Dic61—22no—
63C2×C4×Dic61—21no—
64C2×C4×Dic61—21no—
65C2×C4×Dic61—22no—
66C2×C4×Dic61D412yes—
67C2×C4×Dic61D412yes—
68#14519684—22no—
69C23×C4×C61C2×C411yescharacteristic
70C23×C4×C61C2×C411yescharacteristic
71C23×C4×C61C2×C411yescharacteristic
72#95×C61—22no—
73C24×C61C22×C411yescharacteristic
74C23×D61—21no—
75C23×D61—21no—
76C23×D61—22no—
77C23×D61—22no—
78C23×D61—21no—
79C23×D61—21no—
80C23×D61—22no—
81C23×D61—22no—
82C23×D61C4⋊C412yes—
83C23×D61C2×C812yes—
84C23×D61M1612yes—
85C22×C4×C61—22no—
86C22×C4×C61—22no—
87C22×C4×C61—21no—
88C22×C4×C61—21no—
89C22×C4×C61—21no—
90C22×C4×C61—22no—
91C22×C4×C61—22no—
92C22×C4×C61—22no—
93C22×C4×C61—21no—
94C22×C4×C61—22no—
95C22×C4×C61C22⋊C412yes—
96C22×C4×C61C4⋊C412yes—
97C22×C4×C61C2×C812yes—
98C22×C4×C61M1612yes—
99C22×C4×C61M1612yes—
100C22×Dic61—21no—
101C22×Dic61—22no—
102C22×Dic61—22no—
103C22×Dic61—21no—
104C22×Dic61—21no—
105C22×Dic61—21no—
106C22×Dic61—22no—
107C22×Dic61—22no—
108C22×Dic61C22⋊C412yes—
109C22×Dic61C2×C812yes—
110C22×Dic61C2×D412yes—
111C22×Dic61C2×D411yescharacteristic
112C22×Dic61C2×D412yes—
113C22×Dic61C2×D411yescharacteristic
114C22×Dic61C2×D411yescharacteristic
115C22×Dic61C2×Q811yescharacteristic
116C22×Dic61#4111yescharacteristic
117C22×Dic61#4112yes—
118C22×Dic61#4111yescharacteristic
119C22×Dic61#4112yes—
120C2×C4×D61—24no—
121C2×C4×D61—22no—
122C2×C4×D61—22no—
123C2×C4×D61—24no—
124C2×C4×D61—22no—
125C2×C4×D61—22no—
126C2×C4×D61—24no—
127C2×C4×D61—24no—
128C2×C4×D61—41no—
129C2×C4×D61—42no—
130C2×C4×D61—42no—
131C2×C4×D61—42no—
132C2×C4×D61—42no—
133C2×C4×D61—41no—
134C2×C4×D61—42no—
135C2×C4×D61—41no—
136C2×C4×D61—42no—
137C2×C4×D61—41no—
138C2×#92420—24no—
139C2×#92420—24no—
140C2×#92420—24no—
141C2×#92420—24no—
142C2×#92420—24no—
143C2×#92420—24no—
144C2×#92420—42no—
145C2×#92420—42no—
146C2×#92420—42no—
147C2×#92420—42no—
148C2×#92420—42no—
149C2×#92420—42no—
150C2×#92420—42no—
151C2×#92420—42no—
152#11758198—28no—
153#11758198—28no—
154C4×Dic61—22no—
155C4×Dic61—24no—
156C4×Dic61—22no—
157C4×Dic61—42no—
158C4×Dic61—41no—
159C4×Dic61—41no—
160C23×C61C2×C22⋊C411yescharacteristic
161C23×C61C2×C4⋊C411yescharacteristic
162C23×C61#11711yescharacteristic
163C23×C61C4×D412yes—
164C23×C61C4×D412yes—
165C23×C61C22×C811yescharacteristic
166C23×C61C2×M1611yescharacteristic
167C23×C61C2×M1611yescharacteristic
168C23×C61C2×M1611yescharacteristic
169C23×C61#13112yes—
170C23×C61#13112yes—
171C22×D61—22no—
172C22×D61—24no—
173C22×D61—22no—
174C22×D61—22no—
175C22×D61—22no—
176C22×D61—24no—
177C22×D61—22no—
178C22×D61—22no—
179C22×D61—24no—
180C22×D61—24no—
181C22×D61—24no—
182C22×D61—24no—
183C22×D61—41no—
184C22×D61—42no—
185C22×D61—41no—
186C22×D61—41no—
187C22×D61—41no—
188C22×D61—42no—
189C22×D61—42no—
190C22×D61—42no—
191C22×D61—42no—
192C22×D61—42no—
193C22×D61C4⋊C814yescomplemented
194C2×C4×C61—22no—
195C2×C4×C61—22no—
196C2×C4×C61—24no—
197C2×C4×C61—24no—
198C2×C4×C61—22no—
199C2×C4×C61—24no—
200C2×C4×C61—22no—
201C2×C4×C61—24no—
202C2×C4×C61—41no—
203C2×C4×C61—42no—
204C2×C4×C61—41no—
205C2×C4×C61—41no—
206C2×C4×C61—41no—
207C2×C4×C61—42no—
208C2×C4×C61C22⋊C814yescomplemented
209C2×Dic61—22no—
210C2×Dic61—22no—
211C2×Dic61—22no—
212C2×Dic61—22no—
213C2×Dic61—24no—
214C2×Dic61—41no—
215C2×Dic61—41no—
216C2×Dic61—42no—
217C2×Dic61—42no—
218C2×Dic61—42no—
219C2×Dic61#12011yescharacteristic
220C2×Dic61#12012yes—
221C2×Dic61#12112yes—
222C2×Dic61#12111yescharacteristic
223C2×Dic61#12111yescharacteristic
224C2×Dic61#12112yes—
225C2×Dic61#12112yes—
226C2×Dic61C22⋊Q812yes—
227C2×Dic61C22⋊Q811yescharacteristic
228C2×Dic61C22⋊Q811yescharacteristic
229C2×Dic61C22⋊Q812yes—
230C2×Dic61#12312yes—
231C2×Dic61#12312yes—
232C2×Dic61#12311yescharacteristic
233C2×Dic61#12412yes—
234C2×Dic61#12411yescharacteristic
235C2×Dic61#12612yes—
236C2×Dic61#12711yescharacteristic
237C4×D61—42no—
238C4×D61—42no—
239C4×D61—44no—
240C4×D61—44no—
241C4×D61—42no—
242C4×D61—42no—
243#92420—44no—
244#92420—44no—
245#11042—611nomaximal, Sylow
246C22×C61#38011yescharacteristic
247C22×C61#38512yes—
248C22×C61#38611yescharacteristic
249C22×C61#38812yes—
250C22×C61#39011yescharacteristic
251C22×C61C2×C22⋊C811yescharacteristic
252C22×C61#40711yescharacteristic
253C22×C61#40811yescharacteristic
254C22×C61#40811yescharacteristic
255C22×C61C2×C4⋊C811yescharacteristic
256C22×C61#42311yescharacteristic
257C22×C61#42412yes—
258C22×C61#43111yescharacteristic
259C22×C61#43211yescharacteristic
260C22×C61#43312yes—
261C22×C61C8×D412yes—
262C22×C61C8×D412yes—
263C22×C61#43512yes—
264C22×C61#43512yes—
265C22×C61#43512yes—
266C22×C61#43512yes—
267C22×C61#43612yes—
268C22×C61#43612yes—
269C2×D61—24no—
270C2×D61—28no—
271C2×D61—42no—
272C2×D61—44no—
273C2×D61—42no—
274C2×D61—42no—
275C2×D61—44no—
276C2×D61—44no—
277C2×D61—42no—
278C2×D61—42no—
279C2×D61—42no—
280C4×C61—24no—
281C4×C61—42no—
282C4×C61—42no—
283Dic61—42no—
284Dic61—42no—
285Dic61#39211yescharacteristic
286Dic61#39311yescharacteristic
287Dic61#39412yes—
288Dic61#39612yes—
289Dic61#39711yescharacteristic
290Dic61#39911yescharacteristic
291C22×C4⋊C8—611no—
292C22×C22⋊C8—612no—
293C2×C4×C22⋊C4—611no—
294C2×#336—612no—
295C2×#336—611no—
296C2×C61#143911yescharacteristic
297C2×C61#179711yescharacteristic
298C2×C61#179811yescharacteristic
299C2×C61#185012yes—
300C2×C61#185112yes—
301C2×C61#186911yescharacteristic
302C2×C61#187011yescharacteristic
303C2×C61#192312yes—
304C2×C61#192412yes—
305C2×C61#195411yescharacteristic
306C2×C61#195511yescharacteristic
307D61—44no—
308C24×C4—611no—
309C23×C8—612no—
310C23×C8—612no—
311C22×C22⋊C4—611no—
312C22×C22⋊C4—611no—
313C22×C42—611no—
314C22×C42—611no—
315C2×C4⋊C8—1222no—
316C2×C4⋊C8—1224no—
317C2×C22⋊C8—1224no—
318C2×C22⋊C8—1224no—
319C2×C22⋊C8—1224no—
320C4×C22⋊C4—1222no—
321C4×C22⋊C4—1222no—
322C2×#95—611no—
323C2×#95#692311yescharacteristic
324#336—1222no—
325#336—1224no—
326C61#1104211yescharacteristic, complemented, Sylow
327C25—611no—
328C23×C4—611no—
329C23×C4—611no—
330C23×C4—611no—
331C23×C4—612no—
332C23×C4—612no—
333C23×C4—1221no—
334C23×C4—1221no—
335C23×C4—1222no—
336C23×C4—1222no—
337C23×C4—1221no—
338C23×C4—1221no—
339C23×C4—1222no—
340C23×C4—1222no—
341C23×C4C2×#692311yescharacteristic
342C23×C4C2×#692311yescharacteristic
343C23×C4C2×#692311yescharacteristic
344C22×C8—614no—
345C22×C8—614no—
346C22×C8—1222no—
347C22×C8—1222no—
348C22×C8—1222no—
349C22×C8—1222no—
350C22×C8—1222no—
351C22×C8—1222no—
352C22×C8—1222no—
353C22×C8—1222no—
354C22×C8—1222no—
355C22×C8—1222no—
356C22×C8—1222no—
357C22×C8—1222no—
358C2×C22⋊C4—614no—
359C2×C22⋊C4—1222no—
360C2×C22⋊C4—1222no—
361C2×C22⋊C4—1222no—
362C2×C22⋊C4—1222no—
363C2×C22⋊C4—1222no—
364C2×C42—612no—
365C2×C42—612no—
366C2×C42—1222no—
367C2×C42—1222no—
368C2×C42—1222no—
369C2×C42—1221no—
370C2×C42—1221no—
371C2×C42—1222no—
372C4⋊C8—1228no—
373C22⋊C8—12216no—
374#95—22no—
375#95—1222no—
376C24—612no—
377C24—612no—
378C24—612no—
379C24—1221no—
380C24—1221no—
381C24—1222no—
382C24—1222no—
383C24—1221no—
384C24—1221no—
385C24—1222no—
386C24—1222no—
387C24C22×#692311yescharacteristic
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—611no—
399C22×C4—611no—
400C22×C4—611no—
401C22×C4—611no—
402C22×C4—611no—
403C22×C4—611no—
404C22×C4—612no—
405C22×C4—612no—
406C22×C4—612no—
407C22×C4—612no—
408C22×C4—612no—
409C22×C4—612no—
410C22×C4—1224no—
411C22×C4—1222no—
412C22×C4—1222no—
413C22×C4—1222no—
414C22×C4—1222no—
415C22×C4—1224no—
416C22×C4—1224no—
417C22×C4—1224no—
418C22×C4—1221no—
419C22×C4—1222no—
420C22×C4—1222no—
421C22×C4—1221no—
422C22×C4—1221no—
423C22×C4—1221no—
424C22×C4—1222no—
425C22×C4—1222no—
426C22×C4—2441no—
427C22×C4—2442no—
428C22×C4—2441no—
429C22×C4—2442no—
430C22×C4—2442no—
431C22×C4—2442no—
432C22×C4—2442no—
433C22×C4—2442no—
434C22×C4—2441no—
435C22×C4—2441no—
436C22×C4D61⋊C812yes—
437C22×C4#1175821312yes—
438C22×C4#1175821312yes—
439C22×C4C4⋊#692312yes—
440C22×C4C22⋊#692312yes—
441C2×C8—1224no—
442C2×C8—1224no—
443C2×C8—1224no—
444C2×C8—1224no—
445C2×C8—1224no—
446C2×C8—1224no—
447C2×C8—2442no—
448C2×C8—2442no—
449C2×C8—2442no—
450C2×C8—2442no—
451C2×C8—2442no—
452C2×C8—2442no—
453C2×C8—2442no—
454C2×C8—2442no—
455C22⋊C4—1228no—
456C22⋊C4—1228no—
457C42—1222no—
458C42—1224no—
459C42—1222no—
460C42—2442no—
461C42—2441no—
462C42—2441no—
463C23—614no—
464C23—1222no—
465C23—1224no—
466C23—1222no—
467C23—1222no—
468C23—1222no—
469C23—1224no—
470C23—1222no—
471C23—1222no—
472C23—1224no—
473C23—1224no—
474C23—1224no—
475C23—1224no—
476C23—2441no—
477C23—2442no—
478C23—2441no—
479C23—2441no—
480C23—2441no—
481C23—2442no—
482C23—2442no—
483C23—2442no—
484C23—2442no—
485C23—2442no—
486C23C2×C22⋊#692311yescharacteristic
487C23C2×C4⋊#692311yescharacteristic
488C23#1451985611yescharacteristic
489C23D4×#692312yes—
490C23D4×#692312yes—
491C23C2×D61⋊C811yescharacteristic
492C23D61⋊M1611yescharacteristic
493C23C2×#1175821311yescharacteristic
494C23C2×#1175821311yescharacteristic
495C23#1451986412yes—
496C23#1451986512yes—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—24no—
500C2×C4—24no—
501C2×C4—22no—
502C2×C4—24no—
503C2×C4—22no—
504C2×C4—24no—
505C2×C4—41no—
506C2×C4—42no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—42no—
511C2×C4—611no—
512C2×C4—611no—
513C2×C4—611no—
514C2×C4—611no—
515C2×C4—612no—
516C2×C4—612no—
517C2×C4—612no—
518C2×C4—612no—
519C2×C4—611no—
520C2×C4—612no—
521C2×C4—611no—
522C2×C4—612no—
523C2×C4—612no—
524C2×C4—612no—
525C2×C4—612no—
526C2×C4—612no—
527C2×C4—611no—
528C2×C4—611no—
529C2×C4—1222no—
530C2×C4—1222no—
531C2×C4—1222no—
532C2×C4—1222no—
533C2×C4—1224no—
534C2×C4—2442no—
535C2×C4—2442no—
536C2×C4—2444no—
537C2×C4—2444no—
538C2×C4—2442no—
539C2×C4—2442no—
540C2×C4—2441no—
541C2×C4—2441no—
542C2×C4—2442no—
543C2×C4—2442no—
544C2×C4—2442no—
545C2×C4#1451983414yescomplemented
546C8—2444no—
547C8—2444no—
548C22—1228no—
549C22—1224no—
550C22—2444no—
551C22—2442no—
552C22—2442no—
553C22—2442no—
554C22—2444no—
555C22—2444no—
556C22—2442no—
557C22—2442no—
558C22—2442no—
559C22#1684070411yescharacteristic
560C22#1684070912yes—
561C22#1684071011yescharacteristic
562C22#1684071212yes—
563C22#1684071411yescharacteristic
564C22C2×#1451983411yescharacteristic
565C22#1684073311yescharacteristic
566C22#1684073511yescharacteristic
567C22#1684073711yescharacteristic
568C22D61⋊(C4⋊C8)11yescharacteristic
569C22#1684076611yescharacteristic
570C22#1684076912yes—
571C22#1684078111yescharacteristic
572C22#1684078411yescharacteristic
573C22#1684078712yes—
574C22#1684078912yes—
575C22#1684079012yes—
576C22#1684079112yes—
577C22#1684079112yes—
578C22#1684079212yes—
579C22#1684079412yes—
580C22#1684079612yes—
581C22#1684079612yes—
582C4—24no—
583C4—42no—
584C4—42no—
585C4—611no—
586C4—611no—
587C4—612no—
588C4—612no—
589C4—611no—
590C4—611no—
591C4—2442no—
592C4—2442no—
593C2—2444no—
594C2#2146100211yescharacteristic
595C2#2146167411yescharacteristic
596C2#2146167811yescharacteristic
597C2#2146176412yes—
598C2#2146176512yes—
599C2#2146179411yescharacteristic
600C2#2146179911yescharacteristic
601C2#2146189112yes—
602C2#2146189412yes—
603C2#2146194111yescharacteristic
604C2#2146194411yescharacteristic
subgroupG/H
center, FrattiniC24C22×#6923
commutatorC23×C61C22×C8
FittingC2×#95×C61C4
socleC24×C61C22×C4
prime radicalC24×D61C2×C4
cosocleC23×Dic61C23
hypercenterC2×#95#6923
hypocenterC61#11042
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
1. C22×C4⋊#92420C2semidirect
3. C2×#16840628C2semidirect
4. C2×#16840628C2semidirect
59. C2×#11758198C8semidirect
193. C22×D61C4⋊C8semidirect
208. C2×C4×C61C22⋊C8semidirect
326. C61#11042semidirect
545. C2×C4#14519834semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊#924202
C22×#145198342
C2×#168406282
C2×#168396092
#1104261