Finite Group Databasebeta

← C2×#20275264 #27386118

Subgroups — C2×#20275264 #27386118

Order 13568.

1670 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811389C211yesmaximal, characteristic
2C2×#16811197C211yesmaximal, characteristic
3C2×#16810605C211yesmaximal, characteristic
4C22×#13133136C211yesmaximal, characteristic, complemented
5#20275264C218yesmaximal, direct product factor
6C2×#16810395C211yesmaximal, characteristic, complemented
7C2×#16810394C211yesmaximal, characteristic, complemented
8C22×#101×C53C211yesmaximal, characteristic, complemented
9C22×#11719945C2211yescharacteristic
10#16811389—22no—
11#16811389—22no—
12#16811389—22no—
13#16811389C2214yes—
14C2×#13133225—22no—
15C2×#13133223—22no—
16C22×#11719917C2211yescharacteristic
17C22×#11719917C2211yescharacteristic
18C2×M16×D53—22no—
19#16811197—22no—
20#16811197—22no—
21#16811197C414yes—
22#16811197C2214yes—
23C2×#13133215—21no—
24C2×#13133206—21no—
25C2×#13133200C414yes—
26C2×#13133193—22no—
27C2×#13133176C2211yescharacteristic
28#16810605—22no—
29#16810605C2214yes—
30C2×#13133136—22no—
31C2×#13133136—22no—
32C2×#13133136C2214yescomplemented
33C2×#13133135—21no—
34C2×#13133133—21no—
35#16810395C2214yescomplemented
36#16810394C2214yescomplemented
37C23×Q8×C53C2211yescharacteristic
38C22×M16×C53C2211yescharacteristic
39C22×M16×C53C2211yescharacteristic
40C2×#101×C53—22no—
41C2×#101×C53—22no—
42C2×#101×C53C2214yescomplemented
43C2×#11719945—21no—
44C2×#11719945—21no—
45C2×#11719945—21no—
46C2×#11719945—21no—
47C2×#11719945—21no—
48C2×#11719945—21no—
49C2×#11719945—21no—
50C2×#11719945—21no—
51C2×#11719945C2×C412yes—
52C2×#11719945D412yes—
53C2×#11719945D412yes—
54C2×#11719945C2312yes—
55C22×Dic106D411yescharacteristic
56C22×D212D411yescharacteristic
57C22×C22⋊D53C2×C412yes—
58C22×C4×D53D412yes—
59#13133225—28no—
60#13133225—28no—
61#13133223—28no—
62#13133223—28no—
63C2×#11719917—21no—
64C2×#11719917—21no—
65C2×#11719917—21no—
66C2×#11719917—21no—
67C2×#11719917—21no—
68C2×#11719917—21no—
69C2×#11719917—21no—
70C2×#11719917—21no—
71C2×#11719917D412yes—
72C2×#11719917D412yes—
73C2×#11719917C2312yes—
74C2×#11719917C2312yes—
75C2×#11719912—24no—
76M16×D53—28no—
77M16×D53—28no—
78C22×#88322—21no—
79C22×#88322—21no—
80C2×C8×D53—24no—
81#13133215—24no—
82#13133215—24no—
83#13133206—24no—
84#13133206—24no—
85#13133200—28no—
86#13133200C2×C4116yes—
87#13133193—28no—
88#13133193—28no—
89#13133176—21no—
90#13133176—21no—
91#13133176C2×C412yes—
92#13133176C2312yes—
93C2×C4⋊Dic53—21no—
94C2×#11719919—24no—
95C2×C22⋊Dic53C2×C412yes—
96C2×#11719921—24no—
97C2×C4×Dic53—21no—
98#13133136—28no—
99#13133135—24no—
100#13133133—24no—
101C22×Q8×C53—21no—
102C22×Q8×C53—21no—
103C22×Q8×C53—21no—
104C22×Q8×C53—21no—
105C22×Q8×C53—21no—
106C22×Q8×C53—21no—
107C22×Q8×C53—21no—
108C22×Q8×C53—21no—
109C22×Q8×C53—21no—
110C22×Q8×C53—21no—
111C22×Q8×C53—21no—
112C22×Q8×C53—21no—
113C22×Q8×C53C2×C412yes—
114C22×Q8×C53C2312yes—
115C23×C4×C53C2×C412yes—
116C23×C4×C53C2311yescharacteristic
117C2×M16×C53—21no—
118C2×M16×C53—21no—
119C2×M16×C53—21no—
120C2×M16×C53—21no—
121C2×M16×C53—21no—
122C2×M16×C53—21no—
123C2×M16×C53—21no—
124C2×M16×C53—21no—
125C2×M16×C53D412yes—
126C2×M16×C53D412yes—
127C2×M16×C53C2312yes—
128C2×M16×C53C2312yes—
129C22×C8×C53—21no—
130C22×C8×C53—21no—
131#101×C53—28no—
132C24×C53C22×C411yescharacteristic
133C23×D53C22⋊C412yes—
134C2×Q8×C53—22no—
135C2×Q8×C53—22no—
136C2×Q8×C53—22no—
137C2×Q8×C53—22no—
138C2×Q8×C53—22no—
139C2×Q8×C53—22no—
140C2×Q8×C53—22no—
141C2×Q8×C53—22no—
142C2×Q8×C53—22no—
143C2×Q8×C53—22no—
144C2×Q8×C53—22no—
145C2×Q8×C53—22no—
146C2×Q8×C53—41no—
147C2×Q8×C53—41no—
148C2×Q8×C53—41no—
149C2×Q8×C53—41no—
150C2×Q8×C53—41no—
151C2×Q8×C53—41no—
152C2×Q8×C53—41no—
153C2×Q8×C53—41no—
154C2×Q8×C53—41no—
155C2×Q8×C53—41no—
156C2×Q8×C53—41no—
157C2×Q8×C53—41no—
158C2×Q8×C53—41no—
159C2×Q8×C53—41no—
160C2×Q8×C53—41no—
161C2×Q8×C53—41no—
162C22×C4×C53—22no—
163C22×C4×C53—22no—
164C22×C4×C53—22no—
165C22×C4×C53—22no—
166C22×C4×C53—22no—
167C22×C4×C53—22no—
168C22×C4×C53C22×C414yes—
169C22×C4×C53C22×C411yescharacteristic
170C22×C4×C53C2×D411yescharacteristic
171C22×C4×C53C2×D411yescharacteristic
172C22×C4×C53C2×D411yescharacteristic
173C22×C4×C53C2×D411yescharacteristic
174C22×C4×C53C2×D411yescharacteristic
175C22×C4×C53C2×D411yescharacteristic
176C22×C4×C53C2×D411yescharacteristic
177C22×C4×C53C2×D411yescharacteristic
178C22×C4×C53#4111yescharacteristic
179C22×C4×C53#4111yescharacteristic
180C22×C4×C53#4111yescharacteristic
181C22×C4×C53#4111yescharacteristic
182C22×C4×C53C2411yescharacteristic
183C2×C22⋊D53—22no—
184C2×C22⋊D53—22no—
185C2×C22⋊D53—22no—
186C2×C22⋊D53—22no—
187C2×C22⋊D53C22⋊C414yes—
188C2×C22⋊D53C22×C414yes—
189C22×Dic53—22no—
190C22×Dic53C22⋊C412yes—
191#11719945—22no—
192#11719945—22no—
193#11719945—22no—
194#11719945—22no—
195#11719945—22no—
196#11719945—22no—
197#11719945—22no—
198#11719945—22no—
199#11719945—22no—
200#11719945—22no—
201#11719945—22no—
202#11719945—22no—
203#11719945—22no—
204#11719945—22no—
205#11719945—22no—
206#11719945—22no—
207C2×D212—21no—
208C2×D212—21no—
209C2×D212—21no—
210C2×D212—21no—
211C2×D212C22⋊C412yes—
212C2×D212C2×D412yes—
213C2×C4×D53—22no—
214C2×C4×D53—22no—
215C2×C4×D53—22no—
216C2×C4×D53—22no—
217C2×C4×D53C22⋊C414yes—
218C2×C4×D53C2×D414yes—
219C2×Dic106—21no—
220C2×Dic106—21no—
221C2×Dic106—21no—
222C2×Dic106—21no—
223C2×Dic106C22⋊C412yes—
224C2×Dic106C2×D412yes—
225M16×C53—22no—
226M16×C53—22no—
227M16×C53—22no—
228M16×C53—22no—
229M16×C53—22no—
230M16×C53—41no—
231M16×C53—41no—
232M16×C53C2×D414yes—
233C2×C8×C53—22no—
234C2×C8×C53—22no—
235C2×C8×C53—22no—
236C2×C8×C53—22no—
237C2×C8×C53—41no—
238C2×C8×C53—41no—
239C22⋊Dic53—22no—
240C22⋊Dic53C22×C414yes—
241#11719921—216no—
242C4⋊Dic53—22no—
243C4⋊Dic53—22no—
244#11719919—216no—
245C4×Dic53—22no—
246C4×Dic53—22no—
247#11719917—22no—
248#11719917—22no—
249#11719917—22no—
250#11719917—22no—
251#11719917—22no—
252#11719917—41no—
253#11719917—41no—
254#11719917C2×D414yes—
255C2×#88322—22no—
256C2×#88322—22no—
257C2×#88322—22no—
258C2×#88322—22no—
259C2×#88322—41no—
260C2×#88322—41no—
261#11719912—216no—
262C8×D53—216no—
263C23×C53—42no—
264C23×C53C2×C22⋊C411yescharacteristic
265C23×C53C2×C22⋊C411yescharacteristic
266C23×C53C4×D411yescharacteristic
267C23×C53C4×D411yescharacteristic
268C23×C53C4×D411yescharacteristic
269C23×C53C4×D411yescharacteristic
270C23×C53C23×C411yescharacteristic
271C22×D53—22no—
272C22×D53—22no—
273C22×D53—44no—
274C22×D53C2×C22⋊C414yes—
275Q8×C53—42no—
276Q8×C53—42no—
277Q8×C53—42no—
278Q8×C53—42no—
279Q8×C53—42no—
280Q8×C53—42no—
281Q8×C53—42no—
282Q8×C53—42no—
283C2×C4×C53—24no—
284C2×C4×C53—24no—
285C2×C4×C53—24no—
286C2×C4×C53—42no—
287C2×C4×C53—42no—
288C2×C4×C53—42no—
289C2×C4×C53—42no—
290C2×C4×C53C2×C22⋊C411yescharacteristic
291C2×C4×C53C2×C22⋊C411yescharacteristic
292C2×C4×C53C4×D411yescharacteristic
293C2×C4×C53C4×D411yescharacteristic
294C2×C4×C53C4×D411yescharacteristic
295C2×C4×C53C4×D411yescharacteristic
296C2×C4×C53#12011yescharacteristic
297C2×C4×C53#12011yescharacteristic
298C2×C4×C53#12011yescharacteristic
299C2×C4×C53#12011yescharacteristic
300C2×C4×C53#12111yescharacteristic
301C2×C4×C53#12111yescharacteristic
302C2×C4×C53#12111yescharacteristic
303C2×C4×C53#12111yescharacteristic
304C2×C4×C53#12111yescharacteristic
305C2×C4×C53#12111yescharacteristic
306C2×C4×C53#12111yescharacteristic
307C2×C4×C53#12111yescharacteristic
308C2×C4×C53#12311yescharacteristic
309C2×C4×C53#12311yescharacteristic
310C2×C4×C53#12311yescharacteristic
311C2×C4×C53#12311yescharacteristic
312C2×C4×C53C22×D411yescharacteristic
313C2×C4×C53C22×D411yescharacteristic
314C2×C4×C53C22×D411yescharacteristic
315C2×C4×C53C22×D411yescharacteristic
316C2×C4×C53C2×#4111yescharacteristic
317C2×C4×C53C2×#4111yescharacteristic
318C22⋊D53—24no—
319C22⋊D53—24no—
320C22⋊D53—24no—
321C22⋊D53—24no—
322C2×Dic53—22no—
323C2×Dic53—22no—
324C2×Dic53—24no—
325C2×Dic53—44no—
326C2×Dic53C2×C22⋊C414yes—
327D212—22no—
328D212—22no—
329D212—22no—
330D212—22no—
331C4×D53—24no—
332C4×D53—24no—
333C4×D53—24no—
334C4×D53—24no—
335Dic106—22no—
336Dic106—22no—
337Dic106—22no—
338Dic106—22no—
339C8×C53—24no—
340C8×C53—42no—
341#88322—24no—
342#88322—42no—
343C2×#1915—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#38611yescharacteristic
352C22×C53#38611yescharacteristic
353C22×C53#38611yescharacteristic
354C22×C53#38611yescharacteristic
355C22×C53C22×C22⋊C411yescharacteristic
356C22×C53C2×C4×D411yescharacteristic
357C22×C53C2×C4×D411yescharacteristic
358C2×D53—24no—
359C2×D53—44no—
360C2×D53—44no—
361C2×D53—82no—
362C4×C53—44no—
363C4×C53#38611yescharacteristic
364C4×C53#38611yescharacteristic
365C4×C53#38611yescharacteristic
366C4×C53#38611yescharacteristic
367C4×C53C2×#12011yescharacteristic
368C4×C53C2×#12111yescharacteristic
369C4×C53C2×#12111yescharacteristic
370C4×C53C2×#12311yescharacteristic
371Dic53—24no—
372Dic53—44no—
373C2×#568—531no—
374C2×#536—531no—
375C2×#413—531no—
376C22×#101—531no—
377C22×#101D5311yescharacteristic, complemented
378#1915—538no—
379C2×#344—531no—
380C2×#344—531no—
381C2×C53—21no—
382C2×C53—21no—
383C2×C53—21no—
384C2×C53—21no—
385C2×C53—21no—
386C2×C53—21no—
387C2×C53#191512yescomplemented
388C2×C53C2×#38611yescharacteristic
389D53—44no—
390C22×#41—531no—
391C23×Q8C2×D5311yescharacteristic
392#568—534no—
393#568—1062no—
394#568—1062no—
395#568—1062no—
396C2×#131—1062no—
397C2×#131—1062no—
398C22×M16—531no—
399C22×M16—531no—
400C22×M16—1062no—
401C22×M16C2×D5311yescharacteristic
402C22×M16C2×D5311yescharacteristic
403#536—534no—
404#536—534no—
405#536—1062no—
406#536—1062no—
407C2×C4⋊Q8—1061no—
408C2×#124—1061no—
409C2×#123—534no—
410C2×C22⋊Q8—1062no—
411C2×#117—531no—
412#413—534no—
413#413—1062no—
414C2×#101—22no—
415C2×#101—22no—
416C2×#101—534no—
417C2×#101—1061no—
418C2×#101—1062no—
419C2×#101—1062no—
420C2×#101C2×D5314yescomplemented
421C2×#100—1061no—
422#344—534no—
423#344—534no—
424C53C2×#191511yescharacteristic, complemented, Sylow
425C2×#41—532no—
426C2×#41—532no—
427C2×#41—532no—
428C2×#41—532no—
429C2×#41—1061no—
430C2×#41—1061no—
431C2×#41—1061no—
432C2×#41—1061no—
433C2×#41—1061no—
434C2×#41—1061no—
435C2×#41—1061no—
436C2×#41—1061no—
437C22×Q8—21no—
438C22×Q8—21no—
439C22×Q8—21no—
440C22×Q8—21no—
441C22×Q8—21no—
442C22×Q8—21no—
443C22×Q8—21no—
444C22×Q8—21no—
445C22×Q8—21no—
446C22×Q8—21no—
447C22×Q8—21no—
448C22×Q8—21no—
449C22×Q8—531no—
450C22×Q8C4×D5312yes—
451C22×Q8C22×D5312yes—
452C22×D4—532no—
453C22×D4—531no—
454C23×C4—532no—
455C23×C4C4×D5312yes—
456C23×C4C22×D5311yescharacteristic
457#131—1068no—
458#131—1068no—
459#131—1068no—
460#131—1068no—
461C2×M16—21no—
462C2×M16—21no—
463C2×M16—21no—
464C2×M16—21no—
465C2×M16—21no—
466C2×M16—21no—
467C2×M16—21no—
468C2×M16—21no—
469C2×M16—532no—
470C2×M16—532no—
471C2×M16—532no—
472C2×M16—532no—
473C2×M16—1064no—
474C2×M16—1068no—
475C2×M16—1068no—
476C2×M16—1061no—
477C2×M16—1061no—
478C2×M16—1061no—
479C2×M16—1061no—
480C2×M16—1061no—
481C2×M16—1061no—
482C2×M16—1061no—
483C2×M16—1061no—
484C2×M16C22⋊D5312yes—
485C2×M16C22⋊D5312yes—
486C2×M16C22×D5312yes—
487C2×M16C22×D5312yes—
488C22×C8—21no—
489C22×C8—21no—
490C22×C8—1064no—
491C22×C8—1061no—
492C22×C8—1061no—
493C4⋊Q8—1064no—
494C4⋊Q8—1064no—
495#124—1064no—
496#124—1064no—
497#123—5316no—
498#123—1068no—
499C22⋊Q8—1068no—
500C22⋊Q8—1068no—
501#117—532no—
502#117—532no—
503#117—1061no—
504#117—1061no—
505C2×C4⋊C4—1064no—
506C2×C4⋊C4—1061no—
507C2×C22⋊C4—532no—
508C2×C22⋊C4—1064no—
509C2×C42—1061no—
510#101—28no—
511#101—1064no—
512#101—1068no—
513#100—1064no—
514C24—532no—
515C24C2×C4×D5311yescharacteristic
516#41—1062no—
517#41—1062no—
518#41—1062no—
519#41—1062no—
520#41—1062no—
521#41—1062no—
522#41—1062no—
523#41—1062no—
524#41—1062no—
525#41—1062no—
526#41—1062no—
527#41—1062no—
528#41—1062no—
529#41—1062no—
530#41—1062no—
531#41—1062no—
532C2×Q8—22no—
533C2×Q8—22no—
534C2×Q8—22no—
535C2×Q8—22no—
536C2×Q8—22no—
537C2×Q8—22no—
538C2×Q8—22no—
539C2×Q8—22no—
540C2×Q8—22no—
541C2×Q8—22no—
542C2×Q8—22no—
543C2×Q8—22no—
544C2×Q8—41no—
545C2×Q8—41no—
546C2×Q8—41no—
547C2×Q8—41no—
548C2×Q8—41no—
549C2×Q8—41no—
550C2×Q8—41no—
551C2×Q8—41no—
552C2×Q8—41no—
553C2×Q8—41no—
554C2×Q8—41no—
555C2×Q8—41no—
556C2×Q8—41no—
557C2×Q8—41no—
558C2×Q8—41no—
559C2×Q8—41no—
560C2×Q8—532no—
561C2×Q8—532no—
562C2×Q8—1061no—
563C2×Q8—1061no—
564C2×Q8—1061no—
565C2×Q8—1061no—
566C2×D4—534no—
567C2×D4—534no—
568C2×D4—532no—
569C2×D4—532no—
570C2×D4—1062no—
571C2×D4—1062no—
572C2×D4—1062no—
573C2×D4—1062no—
574C2×D4—1061no—
575C2×D4—1061no—
576C2×D4—1061no—
577C2×D4—1061no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—532no—
585C22×C4—534no—
586C22×C4—534no—
587C22×C4—1062no—
588C22×C4—1062no—
589C22×C4—1062no—
590C22×C4—1062no—
591C22×C4—1062no—
592C22×C4C2×C4×D5314yes—
593C22×C4C2×C4×D5311yescharacteristic
594C22×C4#1171994511yescharacteristic
595C22×C4#1171994511yescharacteristic
596C22×C4D4×D5311yescharacteristic
597C22×C4D4×D5311yescharacteristic
598C22×C4D4×D5311yescharacteristic
599C22×C4D4×D5311yescharacteristic
600C22×C4D4×D5311yescharacteristic
601C22×C4D4×D5311yescharacteristic
602C22×C4#1171994711yescharacteristic
603C22×C4#1171994711yescharacteristic
604C22×C4C2×C22⋊D5311yescharacteristic
605C22×C4C2×C22⋊D5311yescharacteristic
606C22×C4C23×D5311yescharacteristic
607M16—22no—
608M16—22no—
609M16—22no—
610M16—22no—
611M16—22no—
612M16—41no—
613M16—41no—
614M16—534no—
615M16—10616no—
616M16—1062no—
617M16—1062no—
618M16—1062no—
619M16—1062no—
620M16—1062no—
621M16—2121no—
622M16—2121no—
623M16C2×C22⋊D5314yes—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8—41no—
629C2×C8—41no—
630C2×C8—10616no—
631C2×C8—1062no—
632C2×C8—1062no—
633C2×C8—1062no—
634C2×C8—1062no—
635C2×C8—2121no—
636C2×C8—2121no—
637C4⋊C4—10616no—
638C4⋊C4—1062no—
639C4⋊C4—1062no—
640C22⋊C4—534no—
641C22⋊C4—10616no—
642C22⋊C4—1062no—
643C42—1062no—
644C42—1062no—
645C23—42no—
646C23—534no—
647C23—1062no—
648C23—1062no—
649C23—2124no—
650C23C22⋊C4×D5311yescharacteristic
651C23C22⋊C4×D5311yescharacteristic
652C23#1313317711yescharacteristic
653C23#1313317711yescharacteristic
654C23C4×C22⋊D5311yescharacteristic
655C23C4×C22⋊D5311yescharacteristic
656C23C22×C4×D5311yescharacteristic
657Q8—42no—
658Q8—42no—
659Q8—42no—
660Q8—42no—
661Q8—42no—
662Q8—42no—
663Q8—42no—
664Q8—42no—
665Q8—1062no—
666Q8—1062no—
667Q8—1062no—
668Q8—1062no—
669D4—1064no—
670D4—1064no—
671D4—1064no—
672D4—1064no—
673D4—1062no—
674D4—1062no—
675D4—1062no—
676D4—1062no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—534no—
685C2×C4—1062no—
686C2×C4—1062no—
687C2×C4—1064no—
688C2×C4—1064no—
689C2×C4—1064no—
690C2×C4—1064no—
691C2×C4—1064no—
692C2×C4—2124no—
693C2×C4C22⋊C4×D5311yescharacteristic
694C2×C4C22⋊C4×D5311yescharacteristic
695C2×C4#1313317711yescharacteristic
696C2×C4#1313317711yescharacteristic
697C2×C4C4×C22⋊D5311yescharacteristic
698C2×C4C4×C22⋊D5311yescharacteristic
699C2×C4#1313318511yescharacteristic
700C2×C4#1313318511yescharacteristic
701C2×C4#1313318511yescharacteristic
702C2×C4#1313318511yescharacteristic
703C2×C4#1313318811yescharacteristic
704C2×C4#1313318811yescharacteristic
705C2×C4#1313318811yescharacteristic
706C2×C4#1313318811yescharacteristic
707C2×C4#1313319011yescharacteristic
708C2×C4#1313319011yescharacteristic
709C2×C4#1313319011yescharacteristic
710C2×C4#1313319011yescharacteristic
711C2×C4#1313319911yescharacteristic
712C2×C4#1313319911yescharacteristic
713C2×C4#1313319911yescharacteristic
714C2×C4#1313319911yescharacteristic
715C2×C4C2×D4×D5311yescharacteristic
716C2×C4C2×D4×D5311yescharacteristic
717C2×C4C2×D4×D5311yescharacteristic
718C2×C4C22×C22⋊D5311yescharacteristic
719C2×C4C2×#1171994711yescharacteristic
720C2×C4C2×#1171994511yescharacteristic
721C8—24no—
722C8—42no—
723C8—1064no—
724C8—2122no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—1064no—
733C22—4242no—
734C22—2124no—
735C22—2124no—
736C22#1681049911yescharacteristic
737C22#1681049911yescharacteristic
738C22#1681049911yescharacteristic
739C22#1681049911yescharacteristic
740C22C2×C22⋊C4×D5311yescharacteristic
741C22C2×#1313317711yescharacteristic
742C22C2×C4×C22⋊D5311yescharacteristic
743C4—44no—
744C4—1064no—
745C4—2124no—
746C4#1681049911yescharacteristic
747C4#1681049911yescharacteristic
748C4#1681049911yescharacteristic
749C4#1681049911yescharacteristic
750C4C2×#1313318511yescharacteristic
751C4C2×#1313318811yescharacteristic
752C4C2×#1313319011yescharacteristic
753C4C2×#1313319911yescharacteristic
754C2—21no—
755C2—21no—
756C2—21no—
757C2—21no—
758C2—21no—
759C2—21no—
760C2—2124no—
761C2#2027526412yesdirect product factor
762C2C2×#1681049911yescharacteristic
subgroupG/H
centerC22#16810499
commutatorC23×C53C23×C4
FrattiniC22×C4C23×D53
FittingC22×#101×C53C2
socleC22×C53#386
prime radicalC22×#11719945C22
cosocleC22×C4×C53C24
hypercenterC22×#101D53
hypocenterC53C2×#1915
LCSG ▷ C23×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#101

Complements

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

NH ≅ G/Ntype
4. C22×#13133136C2semidirect
5. #20275264C2direct (N × H)
6. C2×#16810395C2semidirect
7. C2×#16810394C2semidirect
8. C22×#101×C53C2semidirect
32. C2×#13133136C22semidirect
35. #16810395C22semidirect
36. #16810394C22semidirect
42. C2×#101×C53C22semidirect
377. C22×#101D53semidirect
387. C2×C53#1915semidirect
420. C2×#101C2×D53semidirect
424. C53C2×#1915semidirect
761. C2#20275264direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113892
C2×#168111972
C2×#168106052
C22×#131331362
#202752642
C2×#168103952
C2×#168103942
C22×#101×C532
C2×#191553