Finite Group Databasebeta

← C2×#20275989 #27411923

Subgroups — C2×#20275989 #27411923

Order 13568.

1450 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133242C211yesmaximal, characteristic
2C2×#16810672C211yesmaximal, characteristic, complemented
3C2×#16810627C211yesmaximal, characteristic, complemented
4C2×#16810607C211yesmaximal, characteristic, complemented
5C22×#13133133C211yesmaximal, characteristic, complemented
6#20275989C218yesmaximal, direct product factor
7C2×#16810393C211yesmaximal, characteristic, complemented
8C2×C53×#421C211yesmaximal, characteristic, complemented
9C23×D212C2211yescharacteristic
10C2×#13133242—22no—
11C2×#13133242—22no—
12C2×#13133242—22no—
13C2×#13133242—22no—
14C2×#13133242—22no—
15C2×#13133242C2214yes—
16C22×#11719924—21no—
17C22×#11719922—21no—
18C22×#11719917C2211yescharacteristic
19C22×#11719917C2211yescharacteristic
20C22×#11719917C2211yescharacteristic
21#16810672—22no—
22#16810672C2214yescomplemented
23C2×#13133153—22no—
24#16810627—22no—
25#16810627C2214yescomplemented
26C2×#13133137—22no—
27#16810607—22no—
28#16810607C2214yescomplemented
29C2×#13133136—21no—
30C2×#13133134—21no—
31C2×#13133133—22no—
32C2×#13133133—22no—
33C2×#13133133C2214yescomplemented
34#16810393C2214yescomplemented
35C22×#41×C53C2211yescharacteristic
36C22×M16×C53C2211yescharacteristic
37C2×#117×C53C2211yescharacteristic
38C53×#421—22no—
39C53×#421C2214yescomplemented
40C2×#104×C53—22no—
41C24×D53—21no—
42C22×D212—21no—
43C22×D212—21no—
44C22×D212—21no—
45C22×D212—21no—
46C22×D212—21no—
47C22×D212—21no—
48C22×D212—21no—
49C22×D212—21no—
50C22×D212—21no—
51C22×D212—21no—
52C22×D212—21no—
53C22×D212D412yes—
54C22×D212D412yes—
55C22×D212C2312yes—
56#13133242—28no—
57#13133242—28no—
58#13133242—28no—
59#13133242—28no—
60C2×#11719924—24no—
61C2×#11719924—24no—
62C2×#11719924—24no—
63C2×#11719922—24no—
64C2×#11719922—24no—
65C2×#11719922—24no—
66C2×#11719917—21no—
67C2×#11719917—21no—
68C2×#11719917—21no—
69C2×#11719917—21no—
70C2×#11719917—21no—
71C2×#11719917—21no—
72C2×#11719917—21no—
73C2×#11719917—21no—
74C2×#11719917—21no—
75C2×#11719917—21no—
76C2×#11719917—21no—
77C2×#11719917—21no—
78C2×#11719917—21no—
79C2×#11719917D412yes—
80C2×#11719917D412yes—
81C2×#11719917C2312yes—
82C2×#11719917C2312yes—
83C2×#11719917C2312yes—
84C22×#88322—21no—
85C22×#88322—21no—
86C22×#88322—21no—
87#13133153—28no—
88#13133137—28no—
89#13133136—24no—
90#13133134—24no—
91#13133133—28no—
92C2×#41×C53—21no—
93C2×#41×C53—21no—
94C2×#41×C53—21no—
95C2×#41×C53—21no—
96C2×#41×C53—21no—
97C2×#41×C53—21no—
98C2×#41×C53—21no—
99C2×#41×C53—21no—
100C2×#41×C53—21no—
101C2×#41×C53—21no—
102C2×#41×C53D412yes—
103C2×#41×C53C2312yes—
104C22×Q8×C53D411yescharacteristic
105C22×D4×C53—21no—
106C22×D4×C53D411yescharacteristic
107C23×C4×C53—21no—
108C23×C4×C53C2311yescharacteristic
109C2×M16×C53—21no—
110C2×M16×C53—21no—
111C2×M16×C53—21no—
112C2×M16×C53D412yes—
113C2×M16×C53D412yes—
114C2×M16×C53C2312yes—
115C22×C8×C53—21no—
116#117×C53—21no—
117#117×C53—21no—
118#117×C53—21no—
119#117×C53C2312yes—
120C2×C4⋊C4×C53—21no—
121C2×C22⋊C4×C53—21no—
122C2×C42×C53—21no—
123#104×C53—28no—
124C24×C53—21no—
125C24×C53#4111yescharacteristic
126C23×D53—22no—
127C23×D53—22no—
128C23×D53—22no—
129C23×D53—41no—
130C23×D53—41no—
131C23×D53—41no—
132C23×D53—41no—
133C23×D53—84no—
134#41×C53—22no—
135#41×C53—22no—
136#41×C53—22no—
137#41×C53—22no—
138#41×C53—22no—
139#41×C53—22no—
140#41×C53—22no—
141#41×C53—22no—
142#41×C53—41no—
143#41×C53—41no—
144#41×C53—41no—
145#41×C53—41no—
146#41×C53—41no—
147#41×C53—41no—
148#41×C53—41no—
149#41×C53—41no—
150C2×Q8×C53—21no—
151C2×Q8×C53—21no—
152C2×Q8×C53—21no—
153C2×Q8×C53—21no—
154C2×Q8×C53—21no—
155C2×Q8×C53C2×D412yes—
156C2×D4×C53—22no—
157C2×D4×C53—22no—
158C2×D4×C53—21no—
159C2×D4×C53—21no—
160C2×D4×C53—21no—
161C2×D4×C53—21no—
162C2×D4×C53—21no—
163C2×D4×C53—41no—
164C2×D4×C53—41no—
165C2×D4×C53—41no—
166C2×D4×C53—41no—
167C2×D4×C53C2×D412yes—
168C22×C4×C53—21no—
169C22×C4×C53—22no—
170C22×C4×C53—22no—
171C22×C4×C53—41no—
172C22×C4×C53—41no—
173C22×C4×C53—41no—
174C22×C4×C53—41no—
175C22×C4×C53—41no—
176C22×C4×C53C2×D411yescharacteristic
177C22×C4×C53C2×D411yescharacteristic
178C22×C4×C53C2×D411yescharacteristic
179C22×C4×C53C2×D411yescharacteristic
180C22×C4×C53C2×D411yescharacteristic
181C22×C4×C53C2×D411yescharacteristic
182C22×C4×C53C2×D411yescharacteristic
183C22×C4×C53C2×D411yescharacteristic
184C22×C4×C53#4111yescharacteristic
185C22×C4×C53#4111yescharacteristic
186C22×C4×C53#4111yescharacteristic
187C22×C4×C53#4111yescharacteristic
188C22×C4×C53#4111yescharacteristic
189C22×C4×C53C2411yescharacteristic
190C2×D212—22no—
191C2×D212—22no—
192C2×D212—22no—
193C2×D212—22no—
194C2×D212—22no—
195C2×D212—22no—
196C2×D212—22no—
197C2×D212—22no—
198C2×D212—22no—
199C2×D212—22no—
200C2×D212—22no—
201C2×D212—22no—
202C2×D212—22no—
203C2×D212—22no—
204C2×D212—22no—
205C2×D212—41no—
206C2×D212—41no—
207C2×D212—41no—
208C2×D212—41no—
209C2×D212—41no—
210C2×D212—41no—
211C2×D212—41no—
212C2×D212—41no—
213C2×D212—41no—
214C2×D212—41no—
215C2×D212—41no—
216C2×D212—41no—
217C2×D212C2×D414yes—
218M16×C53—22no—
219M16×C53—22no—
220M16×C53—22no—
221M16×C53C2×D414yes—
222C2×C8×C53—22no—
223C2×C8×C53—22no—
224C2×C8×C53—22no—
225C4⋊C4×C53—22no—
226C4⋊C4×C53—41no—
227C22⋊C4×C53—22no—
228C22⋊C4×C53—41no—
229C42×C53—22no—
230C42×C53—41no—
231#11719924—216no—
232#11719922—216no—
233#11719917—22no—
234#11719917—22no—
235#11719917—22no—
236#11719917—22no—
237#11719917—22no—
238#11719917—22no—
239#11719917—22no—
240#11719917—41no—
241#11719917—41no—
242#11719917—41no—
243#11719917—41no—
244#11719917C2×D414yes—
245C2×#88322—22no—
246C2×#88322—22no—
247C2×#88322—22no—
248C2×#88322—22no—
249C2×#88322—22no—
250C2×#88322—41no—
251C2×#88322—41no—
252C2×#88322—41no—
253C2×#88322—41no—
254C23×C53—22no—
255C23×C53—42no—
256C23×C53—41no—
257C23×C53—41no—
258C23×C53—82no—
259C23×C53#12111yescharacteristic
260C23×C53#12111yescharacteristic
261C23×C53#12311yescharacteristic
262C23×C53#12311yescharacteristic
263C23×C53#12411yescharacteristic
264C23×C53#12411yescharacteristic
265C23×C53C2×#4111yescharacteristic
266C22×D53—24no—
267C22×D53—42no—
268C22×D53—42no—
269C22×D53—42no—
270C22×D53—42no—
271C22×D53—42no—
272C22×D53—42no—
273C22×D53—84no—
274C22×D53—84no—
275C22×D53—84no—
276C22×D53—84no—
277C22×D53—84no—
278C22×D53—84no—
279C22×D53—84no—
280Q8×C53—22no—
281Q8×C53—22no—
282Q8×C53—41no—
283Q8×C53—41no—
284D4×C53—22no—
285D4×C53—22no—
286D4×C53—42no—
287D4×C53—42no—
288D4×C53—42no—
289D4×C53—42no—
290D4×C53—41no—
291D4×C53—41no—
292C2×C4×C53—22no—
293C2×C4×C53—41no—
294C2×C4×C53—41no—
295C2×C4×C53—42no—
296C2×C4×C53—42no—
297C2×C4×C53—42no—
298C2×C4×C53—42no—
299C2×C4×C53—42no—
300C2×C4×C53—82no—
301C2×C4×C53#12011yescharacteristic
302C2×C4×C53#12011yescharacteristic
303C2×C4×C53#12011yescharacteristic
304C2×C4×C53#12011yescharacteristic
305C2×C4×C53#12111yescharacteristic
306C2×C4×C53#12111yescharacteristic
307C2×C4×C53#12111yescharacteristic
308C2×C4×C53#12111yescharacteristic
309C2×C4×C53#12111yescharacteristic
310C2×C4×C53#12111yescharacteristic
311C2×C4×C53#12111yescharacteristic
312C2×C4×C53#12111yescharacteristic
313C2×C4×C53#12111yescharacteristic
314C2×C4×C53#12111yescharacteristic
315C2×C4×C53#12311yescharacteristic
316C2×C4×C53#12311yescharacteristic
317C2×C4×C53#12311yescharacteristic
318C2×C4×C53#12311yescharacteristic
319C2×C4×C53#12311yescharacteristic
320C2×C4×C53#12311yescharacteristic
321C2×C4×C53#12411yescharacteristic
322C2×C4×C53#12411yescharacteristic
323C2×C4×C53C22×D411yescharacteristic
324C2×C4×C53C22×D411yescharacteristic
325C2×C4×C53C22×D411yescharacteristic
326C2×C4×C53C22×D411yescharacteristic
327C2×C4×C53C2×#4111yescharacteristic
328C2×C4×C53C2×#4111yescharacteristic
329D212—24no—
330D212—24no—
331D212—42no—
332D212—42no—
333D212—42no—
334D212—42no—
335D212—42no—
336D212—42no—
337C8×C53—24no—
338#88322—24no—
339#88322—42no—
340#88322—42no—
341C2×#2048—531nomaximal, Sylow
342C22×C53—22no—
343C22×C53—22no—
344C22×C53—22no—
345C22×C53—41no—
346C22×C53—41no—
347C22×C53—41no—
348C22×C53—41no—
349C22×C53—42no—
350C22×C53—82no—
351C22×C53—82no—
352C22×C53—82no—
353C22×C53#39411yescharacteristic
354C22×C53#39411yescharacteristic
355C22×C53#39411yescharacteristic
356C22×C53#39411yescharacteristic
357C22×C53C2×#12111yescharacteristic
358C22×C53C2×#12311yescharacteristic
359C22×C53C2×#12411yescharacteristic
360C2×D53—44no—
361C2×D53—84no—
362C2×D53—84no—
363C2×D53—84no—
364C2×D53—84no—
365C2×D53—84no—
366C2×D53—84no—
367C2×D53—84no—
368C4×C53—42no—
369C4×C53—82no—
370C4×C53#39411yescharacteristic
371C4×C53#39411yescharacteristic
372C4×C53#39411yescharacteristic
373C4×C53#39411yescharacteristic
374C4×C53C2×#12011yescharacteristic
375C4×C53C2×#12111yescharacteristic
376C4×C53C2×#12111yescharacteristic
377C4×C53C2×#12311yescharacteristic
378C22×AGL(1,ℤ/8)—531no—
379C2×#430—531no—
380C2×#421D5311yescharacteristic, complemented
381C2×#418—531no—
382C2×#413—531no—
383C22×#100—531no—
384#2048—538no—
385C2×#344—531no—
386C2×C53—21no—
387C2×C53—21no—
388C2×C53—21no—
389C2×C53—21no—
390C2×C53—21no—
391C2×C53—21no—
392C2×C53—82no—
393C2×C53#204812yescomplemented
394C2×C53C2×#39411yescharacteristic
395D53—84no—
396C22×#41C2×D5311yescharacteristic
397C23×D4—531no—
398C2×AGL(1,ℤ/8)—534no—
399C2×AGL(1,ℤ/8)—1062no—
400C2×AGL(1,ℤ/8)—1062no—
401C2×AGL(1,ℤ/8)—1062no—
402C2×AGL(1,ℤ/8)—1062no—
403C2×AGL(1,ℤ/8)—1062no—
404C22×SD16—1061no—
405C22×D8—1061no—
406C22×M16—531no—
407C22×M16—531no—
408C22×M16—531no—
409C22×M16C2×D5311yescharacteristic
410C2×#117C2×D5311yescharacteristic
411#430—534no—
412#430—1062no—
413C2×#108—1062no—
414#421—22no—
415#421C2×D5314yescomplemented
416C2×#104—22no—
417#418—534no—
418#418—1062no—
419C2×#102—1062no—
420#413—534no—
421#413—1062no—
422C2×#101—1061no—
423C2×#100—534no—
424C2×#100—1061no—
425C2×#100—1062no—
426C2×#100—1062no—
427#344—534no—
428C53C2×#204811yescharacteristic, complemented, Sylow
429C25—1061no—
430C2×#41—21no—
431C2×#41—21no—
432C2×#41—21no—
433C2×#41—21no—
434C2×#41—21no—
435C2×#41—21no—
436C2×#41—21no—
437C2×#41—21no—
438C2×#41—21no—
439C2×#41—21no—
440C2×#41D21212yes—
441C2×#41C22×D5312yes—
442C22×Q8D21211yescharacteristic
443C22×D4—21no—
444C22×D4—532no—
445C22×D4—532no—
446C22×D4—532no—
447C22×D4—1061no—
448C22×D4—1061no—
449C22×D4—1061no—
450C22×D4—1061no—
451C22×D4—1061no—
452C22×D4—1061no—
453C22×D4—1061no—
454C22×D4—1061no—
455C22×D4—1061no—
456C22×D4—1061no—
457C22×D4—1061no—
458C22×D4D21211yescharacteristic
459C23×C4—21no—
460C23×C4C22×D5311yescharacteristic
461AGL(1,ℤ/8)—1068no—
462AGL(1,ℤ/8)—1068no—
463AGL(1,ℤ/8)—1068no—
464AGL(1,ℤ/8)—1068no—
465C2×SD16—1064no—
466C2×SD16—1064no—
467C2×SD16—1064no—
468C2×D8—1064no—
469C2×D8—1064no—
470C2×D8—1064no—
471C2×M16—21no—
472C2×M16—21no—
473C2×M16—21no—
474C2×M16—532no—
475C2×M16—532no—
476C2×M16—532no—
477C2×M16—532no—
478C2×M16—532no—
479C2×M16—1061no—
480C2×M16—1061no—
481C2×M16—1061no—
482C2×M16—1061no—
483C2×M16—1061no—
484C2×M16—1061no—
485C2×M16—1061no—
486C2×M16—1061no—
487C2×M16—1061no—
488C2×M16—1061no—
489C2×M16—1061no—
490C2×M16—1061no—
491C2×M16—1061no—
492C2×M16C22⋊D5312yes—
493C2×M16C22⋊D5312yes—
494C2×M16C22×D5312yes—
495C22×C8—21no—
496C22×C8—1061no—
497C22×C8—1061no—
498C22×C8—1061no—
499#117—21no—
500#117—21no—
501#117—21no—
502#117C22×D5312yes—
503C2×C4⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C42—21no—
506#108—1068no—
507#104—28no—
508#102—1068no—
509#101—1064no—
510#100—1064no—
511#100—1068no—
512C24—21no—
513C24—1062no—
514C24—1062no—
515C24—1062no—
516C24—4244no—
517C24—2121no—
518C24—2121no—
519C24—2121no—
520C24—2121no—
521C24#1171994711yescharacteristic
522#41—22no—
523#41—22no—
524#41—22no—
525#41—22no—
526#41—22no—
527#41—22no—
528#41—22no—
529#41—22no—
530#41—41no—
531#41—41no—
532#41—41no—
533#41—41no—
534#41—41no—
535#41—41no—
536#41—41no—
537#41—41no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8C2×D21212yes—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—41no—
552C2×D4—41no—
553C2×D4—41no—
554C2×D4—41no—
555C2×D4—534no—
556C2×D4—1062no—
557C2×D4—1062no—
558C2×D4—1062no—
559C2×D4—1062no—
560C2×D4—1062no—
561C2×D4—1062no—
562C2×D4—1062no—
563C2×D4—1062no—
564C2×D4—1062no—
565C2×D4—1062no—
566C2×D4—1062no—
567C2×D4—1062no—
568C2×D4—1062no—
569C2×D4—1062no—
570C2×D4—1062no—
571C2×D4—2121no—
572C2×D4—2121no—
573C2×D4—2121no—
574C2×D4—2121no—
575C2×D4—2121no—
576C2×D4—2121no—
577C2×D4—2121no—
578C2×D4—2121no—
579C2×D4—2121no—
580C2×D4—2121no—
581C2×D4—2121no—
582C2×D4—2121no—
583C2×D4C2×D21212yes—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4C2×D21211yescharacteristic
593C22×C4C2×D21211yescharacteristic
594C22×C4#1171994511yescharacteristic
595C22×C4#1171994511yescharacteristic
596C22×C4D4×D5311yescharacteristic
597C22×C4D4×D5311yescharacteristic
598C22×C4D4×D5311yescharacteristic
599C22×C4D4×D5311yescharacteristic
600C22×C4#1171994711yescharacteristic
601C22×C4#1171994711yescharacteristic
602C22×C4#1171994711yescharacteristic
603C22×C4C2×C22⋊D5311yescharacteristic
604C22×C4C2×C22⋊D5311yescharacteristic
605C22×C4C23×D5311yescharacteristic
606SD16—10616no—
607D8—10616no—
608M16—22no—
609M16—22no—
610M16—22no—
611M16—534no—
612M16—1062no—
613M16—1062no—
614M16—1062no—
615M16—1062no—
616M16—1062no—
617M16—1062no—
618M16—1062no—
619M16—2121no—
620M16—2121no—
621M16—2121no—
622M16—2121no—
623M16C2×C22⋊D5314yes—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8—1062no—
628C2×C8—1062no—
629C2×C8—1062no—
630C2×C8—1062no—
631C2×C8—1062no—
632C2×C8—2121no—
633C2×C8—2121no—
634C2×C8—2121no—
635C2×C8—2121no—
636C4⋊C4—22no—
637C4⋊C4—41no—
638C22⋊C4—22no—
639C22⋊C4—41no—
640C42—22no—
641C42—41no—
642C23—22no—
643C23—42no—
644C23—41no—
645C23—41no—
646C23—82no—
647C23—1064no—
648C23—4244no—
649C23—4244no—
650C23—4244no—
651C23—4244no—
652C23—4244no—
653C23—4244no—
654C23—4244no—
655C23—2122no—
656C23—2122no—
657C23—2122no—
658C23—2122no—
659C23—2122no—
660C23—2122no—
661C23#1313318811yescharacteristic
662C23#1313318811yescharacteristic
663C23#1313320111yescharacteristic
664C23#1313320111yescharacteristic
665C23#1313320311yescharacteristic
666C23#1313320311yescharacteristic
667C23C2×#1171994711yescharacteristic
668Q8—22no—
669Q8—22no—
670Q8—41no—
671Q8—41no—
672D4—22no—
673D4—22no—
674D4—42no—
675D4—42no—
676D4—42no—
677D4—42no—
678D4—41no—
679D4—41no—
680D4—1064no—
681D4—1064no—
682D4—2122no—
683D4—2122no—
684D4—2122no—
685D4—2122no—
686D4—2122no—
687D4—2122no—
688C2×C4—22no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—82no—
697C2×C4#1313318711yescharacteristic
698C2×C4#1313318711yescharacteristic
699C2×C4#1313318711yescharacteristic
700C2×C4#1313318711yescharacteristic
701C2×C4#1313318811yescharacteristic
702C2×C4#1313318811yescharacteristic
703C2×C4#1313318911yescharacteristic
704C2×C4#1313318911yescharacteristic
705C2×C4#1313318911yescharacteristic
706C2×C4#1313318911yescharacteristic
707C2×C4#1313319111yescharacteristic
708C2×C4#1313319111yescharacteristic
709C2×C4#1313319111yescharacteristic
710C2×C4#1313319111yescharacteristic
711C2×C4#1313319911yescharacteristic
712C2×C4#1313319911yescharacteristic
713C2×C4#1313319911yescharacteristic
714C2×C4#1313319911yescharacteristic
715C2×C4#1313320111yescharacteristic
716C2×C4#1313320111yescharacteristic
717C2×C4#1313320311yescharacteristic
718C2×C4#1313320311yescharacteristic
719C2×C4C2×D4×D5311yescharacteristic
720C2×C4C2×D4×D5311yescharacteristic
721C2×C4C22×C22⋊D5311yescharacteristic
722C2×C4C22×D21211yescharacteristic
723C2×C4C2×#1171994711yescharacteristic
724C2×C4C2×#1171994511yescharacteristic
725C8—24no—
726C8—1064no—
727C8—2122no—
728C8—2122no—
729C22—22no—
730C22—22no—
731C22—22no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—42no—
737C22—82no—
738C22—82no—
739C22—82no—
740C22—4244no—
741C22—4244no—
742C22—4244no—
743C22—4244no—
744C22—4244no—
745C22—4244no—
746C22—4244no—
747C22—2124no—
748C22#1681053911yescharacteristic
749C22#1681053911yescharacteristic
750C22#1681053911yescharacteristic
751C22#1681053911yescharacteristic
752C22C2×#1313318811yescharacteristic
753C22C2×#1313320111yescharacteristic
754C22C2×#1313320311yescharacteristic
755C4—42no—
756C4—82no—
757C4#1681053911yescharacteristic
758C4#1681053911yescharacteristic
759C4#1681053911yescharacteristic
760C4#1681053911yescharacteristic
761C4C2×#1313318711yescharacteristic
762C4C2×#1313318911yescharacteristic
763C4C2×#1313319111yescharacteristic
764C4C2×#1313319911yescharacteristic
765C2—21no—
766C2—21no—
767C2—21no—
768C2—21no—
769C2—21no—
770C2—21no—
771C2—82no—
772C2—4244no—
773C2#2027598912yesdirect product factor
774C2C2×#1681053911yescharacteristic
subgroupG/H
centerC22#16810539
commutator, cosocleC22×C4×C53C24
FrattiniC22×C4C23×D53
FittingC2×C53×#421C2
socleC22×C53#394
prime radicalC22×#13133242C2
hypercenterC2×#421D53
hypocenterC53C2×#2048
LCSG ▷ C22×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
2. C2×#16810672C2semidirect
3. C2×#16810627C2semidirect
4. C2×#16810607C2semidirect
5. C22×#13133133C2semidirect
6. #20275989C2direct (N × H)
7. C2×#16810393C2semidirect
8. C2×C53×#421C2semidirect
22. #16810672C22semidirect
25. #16810627C22semidirect
28. #16810607C22semidirect
33. C2×#13133133C22semidirect
34. #16810393C22semidirect
39. C53×#421C22semidirect
380. C2×#421D53semidirect
393. C2×C53#2048semidirect
415. #421C2×D53semidirect
428. C53C2×#2048semidirect
773. C2#20275989direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131332422
C2×#168106722
C2×#168106272
C2×#168106072
C22×#131331332
#202759892
C2×#168103932
C2×C53×#4212
C2×#204853