Finite Group Databasebeta

← C2×#20275249 #27386087

Subgroups — C2×#20275249 #27386087

Order 13568.

1694 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811194C211yesmaximal, characteristic
2C2×#16811100C211yesmaximal, characteristic, complemented
3C2×#16810640C211yesmaximal, characteristic
4C22×#13133135C211yesmaximal, characteristic, complemented
5#20275249C218yesmaximal, direct product factor
6C2×#16810380C211yesmaximal, characteristic, complemented
7C2×#16810379C211yesmaximal, characteristic, complemented
8C2×C53×#421C211yesmaximal, characteristic
9C23×Dic106C2211yescharacteristic
10C22×#11719917C2211yescharacteristic
11#16811194—22no—
12#16811194—22no—
13#16811194C414yescomplemented
14#16811194C2214yes—
15C2×#13133215C412yescomplemented
16C2×#13133204C412yescomplemented
17C2×#13133198—22no—
18C2×#13133196—22no—
19#16811100—22no—
20#16811100—22no—
21#16811100—22no—
22#16811100C2214yescomplemented
23C2×C4×Dic106—22no—
24C2×#13133182—22no—
25C2×#13133176C2211yescharacteristic
26C2×#13133176C2211yescharacteristic
27C2×#13133173—22no—
28#16810640—22no—
29#16810640C2214yes—
30C2×#13133144—22no—
31C2×#13133135—22no—
32C2×#13133135—22no—
33C2×#13133135C2214yescomplemented
34#16810380C2214yescomplemented
35#16810379C2214yescomplemented
36C22×#41×C53C2211yescharacteristic
37C22×M16×C53C2211yescharacteristic
38C2×#117×C53C2211yescharacteristic
39C53×#421—22no—
40C53×#421C2214yes—
41C2×#104×C53—22no—
42C22×Dic106—21no—
43C22×Dic106—21no—
44C22×Dic106—21no—
45C22×Dic106—21no—
46C22×Dic106—21no—
47C22×Dic106—21no—
48C22×Dic106—21no—
49C22×Dic106—21no—
50C22×Dic106C2×C412yes—
51C22×Dic106C2×C412yes—
52C22×Dic106D412yes—
53C22×Dic106D412yes—
54C22×Dic106D412yes—
55C22×Dic106C2312yes—
56C23×Dic53D412yes—
57C2×#11719917—21no—
58C2×#11719917—21no—
59C2×#11719917—21no—
60C2×#11719917—21no—
61C2×#11719917—21no—
62C2×#11719917C2312yes—
63C22×#88322—21no—
64#13133215—24no—
65#13133215C2×C418yescomplemented
66#13133204—24no—
67#13133204C2×C418yescomplemented
68#13133198—28no—
69#13133198—28no—
70#13133196—28no—
71#13133196—28no—
72C4×Dic106—28no—
73C4×Dic106—28no—
74#13133182—28no—
75#13133182—28no—
76#13133176—21no—
77#13133176—21no—
78#13133176—21no—
79#13133176—21no—
80#13133176C2×C412yes—
81#13133176D412yes—
82#13133176C2312yes—
83#13133176C2312yes—
84#13133173—28no—
85#13133173—28no—
86C2×C4⋊Dic53—21no—
87C2×C4⋊Dic53—21no—
88C2×#11719919—24no—
89C2×#11719919—24no—
90C2×C22⋊Dic53—21no—
91C2×C22⋊Dic53—21no—
92C2×C22⋊Dic53—24no—
93C2×C4×Dic53—24no—
94C2×C4×Dic53C2×C412yes—
95C2×C4×Dic53D412yes—
96#13133144—28no—
97#13133135—28no—
98C2×#41×C53—21no—
99C2×#41×C53—21no—
100C2×#41×C53—21no—
101C2×#41×C53—21no—
102C2×#41×C53—21no—
103C2×#41×C53—21no—
104C2×#41×C53—21no—
105C2×#41×C53—21no—
106C2×#41×C53—21no—
107C2×#41×C53—21no—
108C2×#41×C53C2×C412yes—
109C2×#41×C53C2312yes—
110C22×Q8×C53C2×C411yescharacteristic
111C22×D4×C53—21no—
112C22×D4×C53C2×C411yescharacteristic
113C23×C4×C53—21no—
114C23×C4×C53C2311yescharacteristic
115C2×M16×C53—21no—
116C2×M16×C53—21no—
117C2×M16×C53—21no—
118C2×M16×C53—21no—
119C2×M16×C53—21no—
120C2×M16×C53C2312yes—
121C22×C8×C53—21no—
122#117×C53—21no—
123#117×C53—21no—
124#117×C53D412yes—
125#117×C53C2312yes—
126C2×C4⋊C4×C53—21no—
127C2×C22⋊C4×C53—21no—
128C2×C42×C53D412yes—
129#104×C53—28no—
130C24×C53—21no—
131C24×C53C2×D411yescharacteristic
132#41×C53—22no—
133#41×C53—22no—
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—41no—
141#41×C53—41no—
142#41×C53—41no—
143#41×C53—41no—
144#41×C53—41no—
145#41×C53—41no—
146#41×C53—41no—
147#41×C53—41no—
148C2×Q8×C53—21no—
149C2×Q8×C53—21no—
150C2×Q8×C53—21no—
151C2×Q8×C53—21no—
152C2×Q8×C53—21no—
153C2×Q8×C53C22×C412yes—
154C2×D4×C53—22no—
155C2×D4×C53—22no—
156C2×D4×C53—21no—
157C2×D4×C53—21no—
158C2×D4×C53—21no—
159C2×D4×C53—21no—
160C2×D4×C53—21no—
161C2×D4×C53—41no—
162C2×D4×C53—41no—
163C2×D4×C53—41no—
164C2×D4×C53—41no—
165C2×D4×C53C22×C412yes—
166C22×C4×C53—21no—
167C22×C4×C53—22no—
168C22×C4×C53—22no—
169C22×C4×C53—22no—
170C22×C4×C53—41no—
171C22×C4×C53—41no—
172C22×C4×C53—41no—
173C22×C4×C53—41no—
174C22×C4×C53C22×C411yescharacteristic
175C22×C4×C53C22×C411yescharacteristic
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×C53#4111yescharacteristic
184C22×C4×C53#4111yescharacteristic
185C22×C4×C53#4111yescharacteristic
186C22×C4×C53#4111yescharacteristic
187C22×C4×C53C2411yescharacteristic
188C22×Dic53—22no—
189C22×Dic53—22no—
190C22×Dic53—22no—
191C22×Dic53—22no—
192C22×Dic53—22no—
193C22×Dic53—22no—
194C22×Dic53C22⋊C414yes—
195C22×Dic53C22⋊C414yes—
196C22×Dic53C2×D414yes—
197C2×Dic106—22no—
198C2×Dic106—22no—
199C2×Dic106—22no—
200C2×Dic106—22no—
201C2×Dic106—22no—
202C2×Dic106—22no—
203C2×Dic106—22no—
204C2×Dic106—22no—
205C2×Dic106—22no—
206C2×Dic106—22no—
207C2×Dic106—22no—
208C2×Dic106—22no—
209C2×Dic106—22no—
210C2×Dic106—22no—
211C2×Dic106—22no—
212C2×Dic106—22no—
213C2×Dic106—22no—
214C2×Dic106—22no—
215C2×Dic106—22no—
216C2×Dic106—22no—
217C2×Dic106—22no—
218C2×Dic106—22no—
219C2×Dic106—22no—
220C2×Dic106—22no—
221C2×Dic106C22⋊C414yes—
222C2×Dic106C22⋊C414yes—
223C2×Dic106C22×C414yes—
224C2×Dic106C2×D414yes—
225M16×C53—22no—
226M16×C53—22no—
227M16×C53—41no—
228M16×C53—41no—
229C2×C8×C53—22no—
230C2×C8×C53—41no—
231C2×C8×C53—41no—
232C4⋊C4×C53—22no—
233C4⋊C4×C53—22no—
234C22⋊C4×C53—22no—
235C22⋊C4×C53—22no—
236C42×C53—22no—
237C42×C53C2×D414yes—
238C22⋊Dic53—22no—
239C22⋊Dic53—22no—
240C22⋊Dic53—22no—
241C22⋊Dic53—22no—
242C22⋊Dic53—216no—
243C4⋊Dic53—22no—
244C4⋊Dic53—22no—
245C4⋊Dic53—22no—
246C4⋊Dic53—22no—
247#11719919—216no—
248#11719919—216no—
249C4×Dic53—216no—
250C4×Dic53—22no—
251C4×Dic53—22no—
252C4×Dic53C22×C414yes—
253C4×Dic53C2×D414yes—
254#11719917—22no—
255#11719917—22no—
256#11719917—41no—
257#11719917—41no—
258C2×#88322—22no—
259C2×#88322—41no—
260C2×#88322—41no—
261C23×C53—22no—
262C23×C53—42no—
263C23×C53—44no—
264C23×C53—41no—
265C23×C53—41no—
266C23×C53C2×C22⋊C411yescharacteristic
267C23×C53C2×C22⋊C411yescharacteristic
268C23×C53#12011yescharacteristic
269C23×C53#12011yescharacteristic
270C23×C53#12311yescharacteristic
271C23×C53#12311yescharacteristic
272C23×C53C22×D411yescharacteristic
273Q8×C53—22no—
274Q8×C53—22no—
275Q8×C53—41no—
276Q8×C53—41no—
277D4×C53—22no—
278D4×C53—22no—
279D4×C53—42no—
280D4×C53—42no—
281D4×C53—42no—
282D4×C53—42no—
283D4×C53—41no—
284D4×C53—41no—
285C2×C4×C53—22no—
286C2×C4×C53—24no—
287C2×C4×C53—44no—
288C2×C4×C53—41no—
289C2×C4×C53—41no—
290C2×C4×C53—42no—
291C2×C4×C53—42no—
292C2×C4×C53—42no—
293C2×C4×C53—42no—
294C2×C4×C53C2×C22⋊C411yescharacteristic
295C2×C4×C53C2×C22⋊C411yescharacteristic
296C2×C4×C53C4×D411yescharacteristic
297C2×C4×C53C4×D411yescharacteristic
298C2×C4×C53C4×D411yescharacteristic
299C2×C4×C53C4×D411yescharacteristic
300C2×C4×C53C4×D411yescharacteristic
301C2×C4×C53C4×D411yescharacteristic
302C2×C4×C53C4×D411yescharacteristic
303C2×C4×C53C4×D411yescharacteristic
304C2×C4×C53#12011yescharacteristic
305C2×C4×C53#12011yescharacteristic
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#12311yescharacteristic
315C2×C4×C53#12311yescharacteristic
316C2×C4×C53C23×C411yescharacteristic
317C2×C4×C53C22×D411yescharacteristic
318C2×C4×C53C22×D411yescharacteristic
319C2×C4×C53C22×D411yescharacteristic
320C2×C4×C53C2×#4111yescharacteristic
321C2×C4×C53C2×#4111yescharacteristic
322C2×Dic53—24no—
323C2×Dic53—24no—
324C2×Dic53—24no—
325C2×Dic53—24no—
326C2×Dic53—24no—
327C2×Dic53—24no—
328C2×Dic53—24no—
329C2×Dic53—24no—
330C2×Dic53—44no—
331C2×Dic53—44no—
332C2×Dic53C2×C22⋊C418yes—
333Dic106—24no—
334Dic106—24no—
335Dic106—24no—
336Dic106—24no—
337Dic106—24no—
338Dic106—24no—
339Dic106—24no—
340Dic106—24no—
341C8×C53—42no—
342#88322—42no—
343C2×#1912—531nomaximal, Sylow
344C22×C53—22no—
345C22×C53—22no—
346C22×C53—22no—
347C22×C53—41no—
348C22×C53—41no—
349C22×C53—41no—
350C22×C53—41no—
351C22×C53—44no—
352C22×C53—42no—
353C22×C53—82no—
354C22×C53—82no—
355C22×C53#38611yescharacteristic
356C22×C53#38611yescharacteristic
357C22×C53#38611yescharacteristic
358C22×C53#38611yescharacteristic
359C22×C53C22×C22⋊C411yescharacteristic
360C22×C53C2×#12011yescharacteristic
361C22×C53C2×#12311yescharacteristic
362C4×C53—44no—
363C4×C53—42no—
364C4×C53#38611yescharacteristic
365C4×C53#38611yescharacteristic
366C4×C53#38611yescharacteristic
367C4×C53#38611yescharacteristic
368C4×C53C2×C4×D411yescharacteristic
369C4×C53C2×C4×D411yescharacteristic
370C4×C53C2×#12111yescharacteristic
371C4×C53C2×#12111yescharacteristic
372Dic53—28no—
373Dic53—44no—
374Dic53—44no—
375C2×#536—531no—
376C2×#519—531no—
377C2×#421—531no—
378C2×#421D5311yescharacteristic
379C22×#101—531no—
380#1912—538no—
381C2×H(3,ℤ/4)—531no—
382C2×H(3,ℤ/4)—531no—
383C2×C53—21no—
384C2×C53—21no—
385C2×C53—21no—
386C2×C53—21no—
387C2×C53—21no—
388C2×C53—21no—
389C2×C53—82no—
390C2×C53#191212yescomplemented
391C2×C53C2×#38611yescharacteristic
392C22×#41C2×D5311yescharacteristic
393C23×Q8—531no—
394C22×M16—531no—
395C22×M16C2×D5311yescharacteristic
396#536—534no—
397#536—534no—
398#536—1062no—
399#536—1062no—
400C2×C4⋊Q8—532no—
401C2×#124—532no—
402C2×#123—1062no—
403C2×C22⋊Q8—1062no—
404#519—534no—
405#519—1062no—
406#519—1062no—
407#519—1062no—
408C2×C4×Q8—1062no—
409C2×C4×Q8—1062no—
410C2×#117—531no—
411C2×#117—531no—
412C2×#117—1062no—
413C2×#117C2×D5311yescharacteristic
414#421—22no—
415#421—534no—
416#421—1062no—
417#421C2×D5314yes—
418C2×#104—22no—
419C2×#104—1062no—
420C2×#101—534no—
421C2×#101—1062no—
422C2×#101—1062no—
423H(3,ℤ/4)—534no—
424H(3,ℤ/4)—534no—
425C53C2×#191211yescharacteristic, complemented, Sylow
426C2×#41—21no—
427C2×#41—21no—
428C2×#41—21no—
429C2×#41—21no—
430C2×#41—21no—
431C2×#41—21no—
432C2×#41—21no—
433C2×#41—21no—
434C2×#41—21no—
435C2×#41—21no—
436C2×#41C4×D5312yes—
437C2×#41C22×D5312yes—
438C22×Q8—532no—
439C22×Q8—532no—
440C22×Q8—532no—
441C22×Q8—532no—
442C22×Q8—532no—
443C22×Q8—532no—
444C22×Q8—1061no—
445C22×Q8—1061no—
446C22×Q8—1061no—
447C22×Q8—1061no—
448C22×Q8—1061no—
449C22×Q8—1061no—
450C22×Q8—1061no—
451C22×Q8—1061no—
452C22×Q8C4×D5311yescharacteristic
453C22×D4—21no—
454C22×D4C4×D5311yescharacteristic
455C23×C4—21no—
456C23×C4—532no—
457C23×C4C22×D5311yescharacteristic
458C2×M16—21no—
459C2×M16—21no—
460C2×M16—21no—
461C2×M16—21no—
462C2×M16—21no—
463C2×M16—532no—
464C2×M16—1061no—
465C2×M16—1061no—
466C2×M16—1061no—
467C2×M16—1061no—
468C2×M16—1061no—
469C2×M16C22×D5312yes—
470C22×C8—21no—
471C22×C8—1061no—
472C4⋊Q8—538no—
473C4⋊Q8—1064no—
474#124—538no—
475#124—1064no—
476#123—1068no—
477#123—1068no—
478C22⋊Q8—1068no—
479C22⋊Q8—1068no—
480C4×Q8—1068no—
481C4×Q8—1068no—
482C4×Q8—1068no—
483C4×Q8—1068no—
484#117—21no—
485#117—21no—
486#117—532no—
487#117—532no—
488#117—532no—
489#117—532no—
490#117—1068no—
491#117—1068no—
492#117—1061no—
493#117—1061no—
494#117—1061no—
495#117—1061no—
496#117C22⋊D5312yes—
497#117C22×D5312yes—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—1064no—
500C2×C4⋊C4—1064no—
501C2×C4⋊C4—1061no—
502C2×C4⋊C4—1061no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—1064no—
505C2×C22⋊C4—1061no—
506C2×C22⋊C4—1061no—
507C2×C42—532no—
508C2×C42—532no—
509C2×C42—1064no—
510C2×C42C22⋊D5312yes—
511#104—28no—
512#104—1068no—
513#101—1068no—
514C24—21no—
515C24D4×D5311yescharacteristic
516#41—22no—
517#41—22no—
518#41—22no—
519#41—22no—
520#41—22no—
521#41—22no—
522#41—22no—
523#41—22no—
524#41—41no—
525#41—41no—
526#41—41no—
527#41—41no—
528#41—41no—
529#41—41no—
530#41—41no—
531#41—41no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—534no—
538C2×Q8—534no—
539C2×Q8—534no—
540C2×Q8—534no—
541C2×Q8—1062no—
542C2×Q8—1062no—
543C2×Q8—1062no—
544C2×Q8—1062no—
545C2×Q8—1062no—
546C2×Q8—1062no—
547C2×Q8—1062no—
548C2×Q8—1062no—
549C2×Q8—1062no—
550C2×Q8—1062no—
551C2×Q8—1062no—
552C2×Q8—1062no—
553C2×Q8—1062no—
554C2×Q8—1062no—
555C2×Q8—1062no—
556C2×Q8—1062no—
557C2×Q8—1062no—
558C2×Q8—1062no—
559C2×Q8—1062no—
560C2×Q8—1062no—
561C2×Q8—1062no—
562C2×Q8—1062no—
563C2×Q8—1062no—
564C2×Q8—1062no—
565C2×Q8C2×C4×D5312yes—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—41no—
574C2×D4—41no—
575C2×D4—41no—
576C2×D4—41no—
577C2×D4C2×C4×D5312yes—
578C22×C4—21no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—534no—
587C22×C4—534no—
588C22×C4—534no—
589C22×C4—1062no—
590C22×C4—1062no—
591C22×C4—1062no—
592C22×C4—1062no—
593C22×C4—1062no—
594C22×C4—1062no—
595C22×C4C2×C4×D5311yescharacteristic
596C22×C4C2×C4×D5311yescharacteristic
597C22×C4#1171994511yescharacteristic
598C22×C4#1171994511yescharacteristic
599C22×C4D4×D5311yescharacteristic
600C22×C4D4×D5311yescharacteristic
601C22×C4D4×D5311yescharacteristic
602C22×C4D4×D5311yescharacteristic
603C22×C4D4×D5311yescharacteristic
604C22×C4#1171994711yescharacteristic
605C22×C4#1171994711yescharacteristic
606C22×C4C2×C22⋊D5311yescharacteristic
607C22×C4C2×C22⋊D5311yescharacteristic
608C22×C4C23×D5311yescharacteristic
609M16—22no—
610M16—22no—
611M16—41no—
612M16—41no—
613M16—1062no—
614M16—1062no—
615M16—2121no—
616M16—2121no—
617C2×C8—22no—
618C2×C8—41no—
619C2×C8—41no—
620C2×C8—1062no—
621C2×C8—2121no—
622C2×C8—2121no—
623C4⋊C4—22no—
624C4⋊C4—22no—
625C4⋊C4—10616no—
626C4⋊C4—10616no—
627C4⋊C4—1062no—
628C4⋊C4—1062no—
629C4⋊C4—1062no—
630C4⋊C4—1062no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—10616no—
634C22⋊C4—1062no—
635C22⋊C4—1062no—
636C22⋊C4—1062no—
637C22⋊C4—1062no—
638C42—22no—
639C42—534no—
640C42—534no—
641C42—10616no—
642C42—1062no—
643C42—1062no—
644C42C2×C22⋊D5314yes—
645C23—22no—
646C23—42no—
647C23—44no—
648C23—41no—
649C23—41no—
650C23C22⋊C4×D5311yescharacteristic
651C23C22⋊C4×D5311yescharacteristic
652C23#1313318511yescharacteristic
653C23#1313318511yescharacteristic
654C23#1313319911yescharacteristic
655C23#1313319911yescharacteristic
656C23C2×D4×D5311yescharacteristic
657Q8—22no—
658Q8—22no—
659Q8—41no—
660Q8—41no—
661Q8—1064no—
662Q8—1064no—
663Q8—1064no—
664Q8—1064no—
665Q8—1064no—
666Q8—1064no—
667Q8—1064no—
668Q8—1064no—
669D4—22no—
670D4—22no—
671D4—42no—
672D4—42no—
673D4—42no—
674D4—42no—
675D4—41no—
676D4—41no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—44no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—538no—
687C2×C4—1064no—
688C2×C4—1064no—
689C2×C4—1064no—
690C2×C4—1064no—
691C2×C4—1064no—
692C2×C4—1064no—
693C2×C4—1064no—
694C2×C4—1064no—
695C2×C4—2124no—
696C2×C4—2124no—
697C2×C4C22⋊C4×D5311yescharacteristic
698C2×C4C22⋊C4×D5311yescharacteristic
699C2×C4#1313317711yescharacteristic
700C2×C4#1313317711yescharacteristic
701C2×C4#1313317711yescharacteristic
702C2×C4#1313317711yescharacteristic
703C2×C4C4×C22⋊D5311yescharacteristic
704C2×C4C4×C22⋊D5311yescharacteristic
705C2×C4C4×C22⋊D5311yescharacteristic
706C2×C4C4×C22⋊D5311yescharacteristic
707C2×C4#1313318511yescharacteristic
708C2×C4#1313318511yescharacteristic
709C2×C4#1313318811yescharacteristic
710C2×C4#1313318811yescharacteristic
711C2×C4#1313318811yescharacteristic
712C2×C4#1313318811yescharacteristic
713C2×C4#1313319011yescharacteristic
714C2×C4#1313319011yescharacteristic
715C2×C4#1313319011yescharacteristic
716C2×C4#1313319011yescharacteristic
717C2×C4#1313319911yescharacteristic
718C2×C4#1313319911yescharacteristic
719C2×C4C22×C4×D5311yescharacteristic
720C2×C4C2×D4×D5311yescharacteristic
721C2×C4C2×D4×D5311yescharacteristic
722C2×C4C22×C22⋊D5311yescharacteristic
723C2×C4C2×#1171994711yescharacteristic
724C2×C4C2×#1171994511yescharacteristic
725C8—42no—
726C8—2122no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—44no—
735C22—42no—
736C22—82no—
737C22—82no—
738C22#1681049911yescharacteristic
739C22#1681049911yescharacteristic
740C22#1681049911yescharacteristic
741C22#1681049911yescharacteristic
742C22C2×C22⋊C4×D5311yescharacteristic
743C22C2×#1313318511yescharacteristic
744C22C2×#1313319911yescharacteristic
745C4—44no—
746C4—42no—
747C4—1068no—
748C4—2124no—
749C4—2124no—
750C4#1681049911yescharacteristic
751C4#1681049911yescharacteristic
752C4#1681049911yescharacteristic
753C4#1681049911yescharacteristic
754C4C2×#1313317711yescharacteristic
755C4C2×C4×C22⋊D5311yescharacteristic
756C4C2×#1313318811yescharacteristic
757C4C2×#1313319011yescharacteristic
758C2—21no—
759C2—21no—
760C2—21no—
761C2—21no—
762C2—21no—
763C2—21no—
764C2—82no—
765C2#2027524912yesdirect product factor
766C2C2×#1681049911yescharacteristic
subgroupG/H
centerC22#16810499
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC2×C53×#421C2
socleC22×C53#386
prime radicalC22×#41×C53C22
cosocleC22×C4×C53C24
hypercenterC2×#421D53
hypocenterC53C2×#1912
LCSG ▷ C2×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×#16811100C2semidirect
4. C22×#13133135C2semidirect
5. #20275249C2direct (N × H)
6. C2×#16810380C2semidirect
7. C2×#16810379C2semidirect
13. #16811194C4semidirect
15. C2×#13133215C4semidirect
16. C2×#13133204C4semidirect
22. #16811100C22semidirect
33. C2×#13133135C22semidirect
34. #16810380C22semidirect
35. #16810379C22semidirect
65. #13133215C2×C4semidirect
67. #13133204C2×C4semidirect
390. C2×C53#1912semidirect
425. C53C2×#1912semidirect
765. C2#20275249direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168111942
C2×#168111002
C2×#168106402
C22×#131331352
#202752492
C2×#168103802
C2×#168103792
C2×C53×#4212
C2×#191253