Finite Group Databasebeta

← #30620149

Subgroups — #30620149

Order 15616.

1404 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462557C212yesmaximal, complemented
2C2×#16840748C211yesmaximal, characteristic, complemented
3C22×#14519838C211yesmaximal, characteristic, complemented
4#21461963C212yesmaximal, complemented
5#21461847C212yesmaximal, complemented
6#21461844C212yesmaximal, complemented
7#21461685C211yesmaximal, characteristic, complemented
8#21461655C211yesmaximal, characteristic, complemented
9#21461653C211yesmaximal, characteristic, complemented
10C4×#14519838C211yesmaximal, characteristic, complemented
11C2×#16840421C211yesmaximal, characteristic
12C2×D61⋊M16C2212yes—
13C22×#11758217C2212yes—
14#16840795—22no—
15#16840794—22no—
16#16840791—22no—
17#16840789—22no—
18#16840765C2212yes—
19#16840748—24no—
20C2×#14519838—24no—
21C2×#14519838C2211yescharacteristic
22C2×#14519838C2212yes—
23C2×#14519838C2211yescharacteristic
24C2×#14519838C2211yescharacteristic
25C2×#14519838C2212yes—
26C2×#14519838C2211yescharacteristic
27C2×#14519837C2212yes—
28C2×#14519837C2212yes—
29#16840734C2212yes—
30#16840732C2212yes—
31C4×#11758217C2212yes—
32#16840642C2212yes—
33#16840642C2212yes—
34C22×#11758222C2211yescharacteristic
35C23×Dic122C2211yescharacteristic
36#16840421—22no—
37#16840421—22no—
38#16840421—22no—
39#16840421—22no—
40C2×#14519765C411yescharacteristic
41C2×#14519763C411yescharacteristic
42C2×#14519763C2211yescharacteristic
43C2×#14519756C411yescharacteristic
44C2×#14519755C411yescharacteristic
45C2×#14519755C2211yescharacteristic
46C2×#14519751C411yescharacteristic
47C2×#14519749C411yescharacteristic
48C2×#14519749C2211yescharacteristic
49C2×C4×Dic122C2211yescharacteristic
50C2×#14519737C411yescharacteristic
51C2×#14519737C2211yescharacteristic
52C2×C4×D4×C61C411yescharacteristic
53C2×#11758213—22no—
54D61⋊M16—24no—
55D61⋊M16—42no—
56C2×#11758217—22no—
57C2×#11758217—24no—
58C2×#11758217—42no—
59C2×#11758217C2312yes—
60C2×#11758217C2312yes—
61C2×#11758217C2312yes—
62C2×#11758217C2312yes—
63C2×D61⋊C8—22no—
64C22×#92420—22no—
65#14519844—22no—
66C4⋊#92420—22no—
67#14519838—22no—
68#14519838—22no—
69#14519838—22no—
70#14519838—24no—
71#14519838—42no—
72#14519838D414yescomplemented
73#14519837—24no—
74#14519837—42no—
75#14519834—22no—
76#14519834—22no—
77C22⋊#92420—22no—
78C22⋊#92420—22no—
79#14519832—22no—
80C4×#92420—22no—
81C2×#11758222—22no—
82C2×#11758222—22no—
83C2×#11758222—22no—
84C2×#11758222—22no—
85C2×#11758222—42no—
86C22×Dic122—22no—
87C22×Dic122—22no—
88C22×Dic122—22no—
89C22×Dic122—22no—
90C22×Dic122—42no—
91C22×Dic122C2×C411yescharacteristic
92C22×Dic122C2×C411yescharacteristic
93C22×Dic122C2311yescharacteristic
94C22×Dic122C2311yescharacteristic
95C22×D244C2×C411yescharacteristic
96C22×C22⋊D61C2×C411yescharacteristic
97C22×C22⋊D61C2×C411yescharacteristic
98C22×C22⋊D61C2×C411yescharacteristic
99C22×C22⋊D61C2311yescharacteristic
100C23×Dic61C2×C411yescharacteristic
101C23×Dic61C2311yescharacteristic
102C22×C4×D61C2×C411yescharacteristic
103C22×C4×D61C2311yescharacteristic
104#14519765—22no—
105#14519765—22no—
106#14519763—22no—
107#14519763—22no—
108#14519763—22no—
109#14519763—22no—
110#14519756—22no—
111#14519756—22no—
112#14519755—22no—
113#14519755—22no—
114#14519755—22no—
115#14519755—22no—
116#14519751—22no—
117#14519751—22no—
118#14519749—22no—
119#14519749—22no—
120#14519749—22no—
121#14519749—22no—
122C4×Dic122—22no—
123C4×Dic122—22no—
124#14519737—21no—
125#14519737—21no—
126#14519737—21no—
127#14519737—21no—
128#14519737D412yes—
129#14519737D412yes—
130#14519737D412yes—
131#14519737D412yes—
132C2×C4⋊Dic61C2×C411yescharacteristic
133C2×#11758196C2×C411yescharacteristic
134C2×#11758196C2×C411yescharacteristic
135C2×#11758196C2×C411yescharacteristic
136C2×#11758196C2311yescharacteristic
137C2×C22⋊Dic61C2×C411yescharacteristic
138C2×C22⋊Dic61C2×C411yescharacteristic
139C2×#11758198C2×C411yescharacteristic
140C2×#11758198C2×C411yescharacteristic
141C2×#11758198C2×C411yescharacteristic
142C2×#11758198C2×C411yescharacteristic
143C2×#11758198C2×C411yescharacteristic
144C2×#11758198C2×C411yescharacteristic
145C2×C4×Dic61C2×C411yescharacteristic
146C2×C4×Dic61C2311yescharacteristic
147C22×D4×C61C2×C411yescharacteristic
148C23×C4×C61C2×C411yescharacteristic
149C23×C4×C61C2×C411yescharacteristic
150C4×D4×C61—21no—
151C4×D4×C61—21no—
152C4×D4×C61—21no—
153C4×D4×C61—21no—
154C2×C4⋊C4×C61C2×C411yescharacteristic
155C2×C22⋊C4×C61C2×C411yescharacteristic
156C2×C22⋊C4×C61C2×C411yescharacteristic
157C2×C42×C61C2×C411yescharacteristic
158C24×C61C22×C411yescharacteristic
159C24×C61C22×C411yescharacteristic
160C23×D61C22×C411yescharacteristic
161C23×D61C22×C411yescharacteristic
162C2×D4×C61—21no—
163C2×D4×C61—21no—
164C2×D4×C61—42no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—22no—
170C22×C4×C61—22no—
171C22×C4×C61—41no—
172C22×C4×C61—41no—
173C22×C4×C61C22×C411yescharacteristic
174C22×C4×C61C22×C411yescharacteristic
175C22×C4×C61C22×C411yescharacteristic
176C22×C4×C61C22×C411yescharacteristic
177C22×C4×C61C22×C411yescharacteristic
178C2×C22⋊D61—21no—
179C2×C22⋊D61—21no—
180C2×C22⋊D61—22no—
181C2×C22⋊D61—22no—
182C2×C22⋊D61—21no—
183C2×C22⋊D61—22no—
184C2×C22⋊D61—21no—
185C2×C22⋊D61—22no—
186C2×C22⋊D61—41no—
187C2×C22⋊D61—42no—
188C2×C22⋊D61—42no—
189C2×C22⋊D61C22⋊C412yes—
190C2×C22⋊D61C22⋊C412yes—
191C22×Dic61—21no—
192C22×Dic61—21no—
193C22×Dic61—22no—
194C22×Dic61—21no—
195C22×Dic61—21no—
196C22×Dic61—22no—
197C22×Dic61—41no—
198C22×Dic61C22×C411yescharacteristic
199C22×Dic61C22×C411yescharacteristic
200C22×Dic61C22×C411yescharacteristic
201C22×Dic61C22×C411yescharacteristic
202C22×Dic61C22×C411yescharacteristic
203C22×Dic61C2×D412yes—
204C22×Dic61C2×D412yes—
205C22×Dic61C2411yescharacteristic
206#11758222—44no—
207#11758222—44no—
208#11758222—44no—
209#11758222—44no—
210C2×D244—22no—
211C2×D244—22no—
212C2×D244—41no—
213C2×C4×D61—21no—
214C2×C4×D61—21no—
215C2×C4×D61—22no—
216C2×C4×D61—21no—
217C2×C4×D61—21no—
218C2×C4×D61—22no—
219C2×C4×D61—41no—
220C2×C4×D61C2×D412yes—
221C2×C4×D61C2×D412yes—
222C2×Dic122—22no—
223C2×Dic122—22no—
224C2×Dic122—22no—
225C2×Dic122—22no—
226C2×Dic122—22no—
227C2×Dic122—22no—
228C2×Dic122—21no—
229C2×Dic122—22no—
230C2×Dic122—21no—
231C2×Dic122—22no—
232C2×Dic122—44no—
233C2×Dic122—44no—
234C2×Dic122—44no—
235C2×Dic122—44no—
236C2×Dic122—41no—
237C2×Dic122—41no—
238C2×Dic122C2×D412yes—
239C2×Dic122#4112yes—
240#11758217—22no—
241#11758217—22no—
242#11758217—22no—
243#11758217—22no—
244#11758217—22no—
245#11758217—22no—
246#11758217—22no—
247#11758217—44no—
248#11758217C2×D414yes—
249C2×#92420—22no—
250C2×#92420—22no—
251C2×#92420—22no—
252C2×#92420—22no—
253C2×#92420—44no—
254#11758213—44no—
255D61⋊C8—44no—
256C4⋊C4×C61—21no—
257C4⋊C4×C61—21no—
258C22⋊C4×C61—21no—
259C22⋊C4×C61—21no—
260C22⋊C4×C61C22⋊C411yescharacteristic
261C22⋊C4×C61C22⋊C411yescharacteristic
262C22⋊C4×C61C22⋊C411yescharacteristic
263C22⋊C4×C61C22⋊C411yescharacteristic
264C42×C61—21no—
265C42×C61—21no—
266C22⋊Dic61—22no—
267C22⋊Dic61—22no—
268#11758198—22no—
269#11758198—22no—
270#11758198—21no—
271#11758198—21no—
272#11758198—22no—
273#11758198—22no—
274#11758198C22⋊C412yes—
275#11758198C22⋊C412yes—
276C4⋊Dic61—22no—
277#11758196—21no—
278#11758196—21no—
279#11758196—22no—
280#11758196—22no—
281#11758196C22⋊C412yes—
282#11758196C22⋊C412yes—
283C4×Dic61—21no—
284C4×Dic61—21no—
285C4×Dic61C2×D412yes—
286C4×Dic61C2×D412yes—
287C23×C61—21no—
288C23×C61—21no—
289C23×C61—22no—
290C23×C61—21no—
291C23×C61—21no—
292C23×C61—21no—
293C23×C61—41no—
294C23×C61—41no—
295C23×C61—41no—
296C23×C61C2×C22⋊C411yescharacteristic
297C23×C61C2×C22⋊C411yescharacteristic
298C23×C61C23×C411yescharacteristic
299C22×D61—21no—
300C22×D61—21no—
301C22×D61—21no—
302C22×D61—21no—
303C22×D61—21no—
304C22×D61—41no—
305C22×D61—41no—
306C22×D61—41no—
307C22×D61—41no—
308C22×D61C2×C22⋊C412yes—
309D4×C61—42no—
310D4×C61—42no—
311C2×C4×C61—21no—
312C2×C4×C61—21no—
313C2×C4×C61—21no—
314C2×C4×C61—21no—
315C2×C4×C61—21no—
316C2×C4×C61—21no—
317C2×C4×C61—21no—
318C2×C4×C61—21no—
319C2×C4×C61—41no—
320C2×C4×C61—42no—
321C2×C4×C61—42no—
322C2×C4×C61—42no—
323C2×C4×C61—42no—
324C2×C4×C61—41no—
325C2×C4×C61C2×C22⋊C411yescharacteristic
326C2×C4×C61C2×C22⋊C411yescharacteristic
327C2×C4×C61C2×C22⋊C411yescharacteristic
328C2×C4×C61C2×C22⋊C411yescharacteristic
329C2×C4×C61C4×D412yes—
330C22⋊D61—24no—
331C22⋊D61—42no—
332C22⋊D61—44no—
333C22⋊D61—42no—
334C22⋊D61—42no—
335C22⋊D61—42no—
336C22⋊D61—42no—
337C2×Dic61—21no—
338C2×Dic61—21no—
339C2×Dic61—21no—
340C2×Dic61—21no—
341C2×Dic61—22no—
342C2×Dic61—22no—
343C2×Dic61—22no—
344C2×Dic61—22no—
345C2×Dic61—21no—
346C2×Dic61—21no—
347C2×Dic61—21no—
348C2×Dic61—21no—
349C2×Dic61—41no—
350C2×Dic61—42no—
351C2×Dic61—42no—
352C2×Dic61—41no—
353C2×Dic61C2×C22⋊C412yes—
354C2×Dic61C2×C22⋊C412yes—
355C2×Dic61C4×D412yes—
356C2×Dic61C22×D411yescharacteristic
357C2×Dic61C22×D412yes—
358C2×Dic61C2×#4111yescharacteristic
359C2×Dic61H(5,𝔽2)12yes—
360D244—44no—
361C4×D61—22no—
362C4×D61—22no—
363C4×D61—22no—
364C4×D61—22no—
365C4×D61—42no—
366C4×D61—42no—
367Dic122—24no—
368Dic122—24no—
369Dic122—44no—
370Dic122—44no—
371Dic122—42no—
372Dic122—42no—
373#92420—24no—
374#92420—42no—
375#92420—42no—
376#92420—42no—
377#22410—611nomaximal, Sylow
378C22×C61—21no—
379C22×C61—21no—
380C22×C61—21no—
381C22×C61—21no—
382C22×C61—21no—
383C22×C61—21no—
384C22×C61—21no—
385C22×C61—42no—
386C22×C61—42no—
387C22×C61—41no—
388C22×C61—41no—
389C22×C61—41no—
390C22×C61—81no—
391C22×C61—81no—
392C22×C61#41312yescomplemented
393C22×C61C22×C22⋊C411yescharacteristic
394C22×C61C2×C4×D411yescharacteristic
395C22×C61#51811yescharacteristic
396C2×D61—22no—
397C2×D61—22no—
398C2×D61—22no—
399C2×D61—41no—
400C2×D61—41no—
401C2×D61—41no—
402C2×D61—81no—
403C2×D61—81no—
404C2×D61—81no—
405C2×D61—81no—
406C4×C61—22no—
407C4×C61—21no—
408C4×C61—21no—
409C4×C61—21no—
410C4×C61—21no—
411C4×C61—41no—
412C4×C61—41no—
413Dic61—22no—
414Dic61—22no—
415Dic61—22no—
416Dic61—41no—
417Dic61—41no—
418Dic61D4212yes—
419Dic61#54612yes—
420C2×#548—611no—
421D4×M16—612no—
422C2×#413—611no—
423C22×#101—611no—
424#1967—612no—
425#1901—612no—
426#1900—612no—
427#1801—611no—
428#1785—611no—
429#1784—611no—
430C4×#101—611no—
431C2×C61—21no—
432C2×C61—21no—
433C2×C61—22no—
434C2×C61—41no—
435C2×C61—81no—
436C2×C61D4×C22⋊C411yescharacteristic
437C2×C61C2×#41311yescharacteristic
438C2×C61#288911yescharacteristic
439D61—42no—
440D61—81no—
441C22×#41—611no—
442C23×Q8—611no—
443C22×M16—612no—
444C22×M16—612no—
445#548—1222no—
446#548—1222no—
447#548—1222no—
448#548—1222no—
449C2×#124—611no—
450C2×#124—611no—
451C2×#124—611no—
452C2×C22⋊Q8—611no—
453C2×C22⋊Q8—611no—
454C2×C22⋊Q8—611no—
455C2×#121—611no—
456C2×#121—611no—
457C2×#121—611no—
458C2×C4×Q8—611no—
459C2×C4×D4—611no—
460C2×C4×D4—611no—
461C2×C4×D4#692311yescharacteristic
462#436—1222no—
463#435—1222no—
464#435—1222no—
465C8×D4—1222no—
466#423—612no—
467#413—1224no—
468C2×#101—611no—
469C2×#101—611no—
470C2×#101—611no—
471C2×#101—612no—
472C2×#101—611no—
473C2×#101—612no—
474C2×#101—1224no—
475C2×#100—612no—
476C2×#100—612no—
477#407—612no—
478#407—612no—
479C4×M16—612no—
480#343—612no—
481#343—612no—
482C61#2241011yescharacteristic, complemented, Sylow
483C2×#41—1222no—
484C2×#41—1222no—
485C2×#41—1222no—
486C2×#41—1222no—
487C2×#41—2442no—
488C22×Q8—611no—
489C22×Q8—611no—
490C22×Q8—611no—
491C22×Q8—611no—
492C22×Q8—1222no—
493C22×Q8—1222no—
494C22×Q8—1222no—
495C22×Q8—1222no—
496C22×Q8—2442no—
497C22×D4—611no—
498C22×D4—611no—
499C22×D4—611no—
500C22×D4—611no—
501C22×D4—611no—
502C22×D4C2×#692311yescharacteristic
503C23×C4—611no—
504C23×C4—611no—
505C23×C4—611no—
506C23×C4—611no—
507C23×C4C2×#692311yescharacteristic
508C23×C4C2×#692311yescharacteristic
509C2×M16—612no—
510C2×M16—612no—
511C2×M16—612no—
512C2×M16—612no—
513C2×M16—1222no—
514C2×M16—1222no—
515C2×M16—1224no—
516C2×M16—1224no—
517C2×M16—2442no—
518C2×M16—2442no—
519C22×C8—1222no—
520C22×C8—1222no—
521#124—1222no—
522#124—1222no—
523#124—1222no—
524#124—1222no—
525#124—1222no—
526#124—1222no—
527C22⋊Q8—1222no—
528C22⋊Q8—1222no—
529C22⋊Q8—1222no—
530C22⋊Q8—1222no—
531C22⋊Q8—1222no—
532C22⋊Q8—1222no—
533#121—1222no—
534#121—1222no—
535#121—1222no—
536#121—1222no—
537#121—1222no—
538#121—1222no—
539C4×Q8—1222no—
540C4×Q8—1222no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4—21no—
544C4×D4—21no—
545C4×D4—612no—
546C4×D4—612no—
547C4×D4—612no—
548C4×D4—612no—
549C4×D4—1221no—
550C4×D4—1221no—
551C4×D4—1221no—
552C4×D4—1221no—
553C2×C4⋊C4—611no—
554C2×C4⋊C4—611no—
555C2×C4⋊C4—611no—
556C2×C4⋊C4—611no—
557C2×C4⋊C4—611no—
558C2×C4⋊C4C2×#692311yescharacteristic
559C2×C22⋊C4—611no—
560C2×C22⋊C4—611no—
561C2×C22⋊C4—611no—
562C2×C22⋊C4—611no—
563C2×C22⋊C4—611no—
564C2×C22⋊C4—611no—
565C2×C22⋊C4—611no—
566C2×C22⋊C4—611no—
567C2×C22⋊C4C2×#692311yescharacteristic
568C2×C22⋊C4C2×#692311yescharacteristic
569C2×C42—611no—
570C2×C42—611no—
571C2×C42C2×#692311yescharacteristic
572C4⋊C8—1222no—
573C4⋊C8—1222no—
574#101—614no—
575#101—1224no—
576#101—1222no—
577#101—1222no—
578#101—1222no—
579#101—2442no—
580#100—1224no—
581#100—2442no—
582C22⋊C8—1222no—
583C22⋊C8—1222no—
584C22⋊C8—1222no—
585C22⋊C8—1222no—
586#97—1222no—
587C4×C8—1222no—
588C24—611no—
589C24—611no—
590C24C22×#692311yescharacteristic
591C24C22×#692311yescharacteristic
592#41—2444no—
593#41—2444no—
594#41—2444no—
595#41—2444no—
596C2×Q8—612no—
597C2×Q8—612no—
598C2×Q8—1222no—
599C2×Q8—1222no—
600C2×Q8—1221no—
601C2×Q8—1222no—
602C2×Q8—1222no—
603C2×Q8—1222no—
604C2×Q8—1222no—
605C2×Q8—1221no—
606C2×Q8—1222no—
607C2×Q8—1222no—
608C2×Q8—2441no—
609C2×Q8—2441no—
610C2×Q8—2444no—
611C2×Q8—2444no—
612C2×Q8—2444no—
613C2×Q8—2444no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—42no—
617C2×D4—612no—
618C2×D4—612no—
619C2×D4—1222no—
620C2×D4—1221no—
621C2×D4—1222no—
622C2×D4—1222no—
623C2×D4—1221no—
624C2×D4—1222no—
625C2×D4—1222no—
626C2×D4—1221no—
627C2×D4—1221no—
628C2×D4—1222no—
629C2×D4—2441no—
630C2×D4—2441no—
631C2×D4—2442no—
632C2×D4—2442no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—41no—
640C22×C4—41no—
641C22×C4—611no—
642C22×C4—612no—
643C22×C4—612no—
644C22×C4—611no—
645C22×C4—611no—
646C22×C4—611no—
647C22×C4—612no—
648C22×C4—612no—
649C22×C4—611no—
650C22×C4—611no—
651C22×C4—1221no—
652C22×C4—1222no—
653C22×C4—1221no—
654C22×C4—1222no—
655C22×C4—1221no—
656C22×C4—1222no—
657C22×C4—1221no—
658C22×C4—1222no—
659C22×C4—1221no—
660C22×C4—1221no—
661C22×C4—1221no—
662C22×C4—1221no—
663C22×C4—2441no—
664C22×C4—2441no—
665C22×C4C22×#692311yescharacteristic
666C22×C4C22×#692311yescharacteristic
667C22×C4C22×#692311yescharacteristic
668C22×C4C22×#692311yescharacteristic
669C22×C4C22×#692311yescharacteristic
670M16—614no—
671M16—1222no—
672M16—1222no—
673M16—1222no—
674M16—1222no—
675M16—1222no—
676M16—1222no—
677M16—1222no—
678M16—2444no—
679M16—2444no—
680C2×C8—1222no—
681C2×C8—1222no—
682C2×C8—1222no—
683C2×C8—1222no—
684C2×C8—2444no—
685C2×C8—2444no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—612no—
689C4⋊C4—612no—
690C4⋊C4—1222no—
691C4⋊C4—1222no—
692C4⋊C4—1222no—
693C4⋊C4—1221no—
694C4⋊C4—1221no—
695C22⋊C4—21no—
696C22⋊C4—21no—
697C22⋊C4—612no—
698C22⋊C4—612no—
699C22⋊C4—1222no—
700C22⋊C4—1222no—
701C22⋊C4—1222no—
702C22⋊C4—1222no—
703C22⋊C4—1222no—
704C22⋊C4—1222no—
705C22⋊C4—1221no—
706C22⋊C4—1221no—
707C22⋊C4C22⋊#692311yescharacteristic
708C22⋊C4C22⋊#692311yescharacteristic
709C22⋊C4C22⋊#692311yescharacteristic
710C22⋊C4C22⋊#692311yescharacteristic
711C42—21no—
712C42—21no—
713C42—612no—
714C42—612no—
715C42—1221no—
716C42—1221no—
717C23—22no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—612no—
727C23—1221no—
728C23—1221no—
729C23—1221no—
730C23—1221no—
731C23—1221no—
732C23—2441no—
733C23—2441no—
734C23—2441no—
735C23—2441no—
736C23C2×C22⋊#692311yescharacteristic
737C23C2×C22⋊#692311yescharacteristic
738C23C23×#692311yescharacteristic
739Q8—1224no—
740Q8—1224no—
741Q8—2444no—
742Q8—2442no—
743Q8—2442no—
744Q8—2444no—
745D4—42no—
746D4—42no—
747D4—1224no—
748D4—2444no—
749D4—2442no—
750D4—2442no—
751D4—2442no—
752D4—2444no—
753D4—2442no—
754D4—2442no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—41no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—41no—
769C2×C4—612no—
770C2×C4—611no—
771C2×C4—611no—
772C2×C4—612no—
773C2×C4—612no—
774C2×C4—612no—
775C2×C4—612no—
776C2×C4—1222no—
777C2×C4—1222no—
778C2×C4—1222no—
779C2×C4—1222no—
780C2×C4—1222no—
781C2×C4—1222no—
782C2×C4—1222no—
783C2×C4—1222no—
784C2×C4—1221no—
785C2×C4—1221no—
786C2×C4—1221no—
787C2×C4—1221no—
788C2×C4—1221no—
789C2×C4—1221no—
790C2×C4—1221no—
791C2×C4—1221no—
792C2×C4—2442no—
793C2×C4—2442no—
794C2×C4—2441no—
795C2×C4—2442no—
796C2×C4—2442no—
797C2×C4—2441no—
798C2×C4C2×C22⋊#692311yescharacteristic
799C2×C4C2×C22⋊#692311yescharacteristic
800C2×C4C2×C22⋊#692311yescharacteristic
801C2×C4C2×C22⋊#692311yescharacteristic
802C2×C4D4×#692312yes—
803C8—1224no—
804C8—2442no—
805C8—2442no—
806C8—2442no—
807C22—21no—
808C22—21no—
809C22—21no—
810C22—21no—
811C22—21no—
812C22—21no—
813C22—21no—
814C22—42no—
815C22—42no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—81no—
820C22—81no—
821C22—1222no—
822C22—1222no—
823C22—1222no—
824C22—4881no—
825C22—4881no—
826C22—4881no—
827C22—4881no—
828C22—2441no—
829C22—2441no—
830C22—2441no—
831C22#1684074812yescomplemented
832C22C22×C22⋊#692311yescharacteristic
833C22C2×D4×#692311yescharacteristic
834C22#1684082911yescharacteristic
835C4—22no—
836C4—21no—
837C4—21no—
838C4—21no—
839C4—21no—
840C4—41no—
841C4—41no—
842C4—612no—
843C4—612no—
844C4—1222no—
845C4—1222no—
846C4—1222no—
847C4—2441no—
848C4—2441no—
849C2—21no—
850C2—21no—
851C2—22no—
852C2—41no—
853C2—81no—
854C2—4881no—
855C2—2442no—
856C2D4×C22⋊#692311yescharacteristic
857C2C2×#1684074811yescharacteristic
858C2#2146243111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×C4×D4×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840421C2
cosocleC22×Dic61C24
hypercenterC2×C4×D4#6923
hypocenterC61#22410
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C22⋊C4 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #21462557C2semidirect
2. C2×#16840748C2semidirect
3. C22×#14519838C2semidirect
4. #21461963C2semidirect
5. #21461847C2semidirect
6. #21461844C2semidirect
7. #21461685C2semidirect
8. #21461655C2semidirect
9. #21461653C2semidirect
10. C4×#14519838C2semidirect
72. #14519838D4semidirect
392. C22×C61#413semidirect
482. C61#22410semidirect
831. C22#16840748semidirect

Maximal subgroups

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

subgroupindex
#214625572
C2×#168407482
C22×#145198382
#214619632
#214618472
#214618442
#214616852
#214616552
#214616532
C4×#145198382
C2×#168404212
#2241061