Finite Group Databasebeta

← C2×#20286290 #28259142

Subgroups — C2×#20286290 #28259142

Order 13568.

2742 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133250C211yesmaximal, characteristic, complemented
2C23×Dic212C211yesmaximal, characteristic, complemented
3C2×D4×Dic106C211yesmaximal, characteristic, complemented
4C2×#16811282C211yesmaximal, characteristic
5#20286290C2116yesmaximal, direct product factor
6C2×#16811017C211yesmaximal, characteristic, complemented
7C2×#16810881C211yesmaximal, characteristic, complemented
8C2×#16810852C211yesmaximal, characteristic, complemented
9C2×#16810846C211yesmaximal, characteristic, complemented
10C2×#16810834C211yesmaximal, characteristic, complemented
11C2×#16810787C211yesmaximal, characteristic, complemented
12C2×#16810781C211yesmaximal, characteristic, complemented
13C2×#16810781C211yesmaximal, characteristic, complemented
14C2×#16810764C211yesmaximal, characteristic, complemented
15C2×#16810731C211yesmaximal, characteristic, complemented
16C2×C53×#435C211yesmaximal, characteristic, complemented
17C22×#11719945C2211yescharacteristic
18C23×Dic106C2211yescharacteristic
19C23×Dic106C2211yescharacteristic
20C23×Dic106C2211yescharacteristic
21C2×#13133250—28no—
22C2×#13133250C2218yescomplemented
23C22×Dic212—28no—
24C22×Dic212C2211yescharacteristic
25C22×Dic212C2211yescharacteristic
26C22×Dic212C2211yescharacteristic
27C22×Dic212C2211yescharacteristic
28C22×Dic212C2211yescharacteristic
29C22×Dic212C2211yescharacteristic
30C22×Dic212C2218yescomplemented
31C22×#11719913C2211yescharacteristic
32C22×#11719913C2211yescharacteristic
33C22×#11719913C2211yescharacteristic
34D4×Dic106—24no—
35D4×Dic106C2218yescomplemented
36#16811282—24no—
37#16811282C2218yes—
38C2×#13133217C2211yescharacteristic
39C2×#13133216—21no—
40C2×#13133205C2211yescharacteristic
41C2×#13133203—21no—
42C2×#13133196C2211yescharacteristic
43C2×#13133196C2211yescharacteristic
44C2×#13133196C2211yescharacteristic
45C2×#13133195—21no—
46C2×#13133194—21no—
47C2×#13133194—21no—
48C2×#13133191C2211yescharacteristic
49C2×#13133189—21no—
50C2×C4×Dic106C2211yescharacteristic
51C2×C4×Dic106C2211yescharacteristic
52C2×D4×Dic53—21no—
53C2×#13133177—21no—
54#16811017C2218yescomplemented
55#16810881C2218yescomplemented
56#16810852C2218yescomplemented
57#16810846C2218yescomplemented
58#16810834C2218yescomplemented
59#16810787C2218yescomplemented
60#16810781C2218yescomplemented
61#16810781C2218yescomplemented
62#16810764C2218yescomplemented
63#16810731C2218yescomplemented
64C2×#13133149C2211yescharacteristic
65C2×#13133142C2211yescharacteristic
66C2×#13133142C2211yescharacteristic
67C2×#13133142C2211yescharacteristic
68C2×#13133142C2211yescharacteristic
69C2×#13133142C2211yescharacteristic
70C2×#13133139C2211yescharacteristic
71C22×M16×C53C2211yescharacteristic
72C23×C8×C53C2211yescharacteristic
73C2×C4×D4×C53C2211yescharacteristic
74C53×#435C2218yescomplemented
75C2×C4⋊C8×C53C2211yescharacteristic
76C2×C22⋊C8×C53C2211yescharacteristic
77C2×C22⋊C8×C53C2211yescharacteristic
78C2×#97×C53C2211yescharacteristic
79C2×#11719945—22no—
80C2×#11719945—24no—
81C2×#11719945—42no—
82C2×#11719945C2314yes—
83C22×Dic106—24no—
84C22×Dic106—24no—
85C22×Dic106—24no—
86C22×Dic106—22no—
87C22×Dic106—22no—
88C22×Dic106—22no—
89C22×Dic106—21no—
90C22×Dic106—21no—
91C22×Dic106—21no—
92C22×Dic106—42no—
93C22×Dic106—42no—
94C22×Dic106—42no—
95C22×Dic106C2311yescharacteristic
96C22×Dic106C2311yescharacteristic
97C22×Dic106C2311yescharacteristic
98C22×Dic106C2314yes—
99C22×Dic106C2314yes—
100C22×Dic106C2314yes—
101C22×Dic106C2311yescharacteristic
102C22×Dic106C2311yescharacteristic
103C22×D212C2311yescharacteristic
104C22×C22⋊D53—21no—
105C22×C22⋊D53—21no—
106C23×Dic53—21no—
107C23×Dic53—21no—
108C23×Dic53—21no—
109C22×C4×D53—21no—
110#13133250—232no—
111C2×Dic212—24no—
112C2×Dic212—232no—
113C2×Dic212—24no—
114C2×Dic212—24no—
115C2×Dic212—24no—
116C2×Dic212—42no—
117C2×Dic212D418yescomplemented
118C2×Dic212C2314yes—
119C2×Dic212C2314yes—
120C2×Dic212C2314yes—
121C2×Dic212C2314yes—
122C2×Dic212C2314yes—
123C2×Dic212C2314yes—
124C2×#11719913—24no—
125C2×#11719913—24no—
126C2×#11719913—42no—
127C2×#11719913C2314yes—
128C2×#11719913C2314yes—
129C2×#11719913C2314yes—
130#13133217—22no—
131#13133217C2314yes—
132#13133216—28no—
133#13133205—22no—
134#13133205C2314yes—
135#13133203—28no—
136#13133196—22no—
137#13133196—22no—
138#13133196—22no—
139#13133196C2314yes—
140#13133196C2314yes—
141#13133196C2314yes—
142#13133195—28no—
143#13133194—28no—
144#13133194—28no—
145#13133191—22no—
146#13133191C2314yes—
147#13133189—28no—
148C4×Dic106—22no—
149C4×Dic106—22no—
150C4×Dic106C2314yes—
151C4×Dic106C2314yes—
152D4×Dic53—28no—
153#13133177—28no—
154C2×C4⋊Dic53—21no—
155C2×C4⋊Dic53—21no—
156C2×C4⋊Dic53C2311yescharacteristic
157C2×C4⋊Dic53C2311yescharacteristic
158C2×#11719919—21no—
159C2×#11719919—21no—
160C2×#11719919—21no—
161C2×#11719919—21no—
162C2×#11719919—21no—
163C2×C22⋊Dic53—21no—
164C2×C22⋊Dic53—21no—
165C2×C22⋊Dic53—21no—
166C2×#11719921—21no—
167C2×#11719921—21no—
168C2×#11719921—21no—
169C2×C4×Dic53—21no—
170C2×C4×Dic53—21no—
171#13133149C2314yes—
172#13133142C2314yes—
173#13133142C2314yes—
174#13133142C2314yes—
175#13133142C2314yes—
176#13133142C2314yes—
177#13133139C2314yes—
178C22×D4×C53D411yescharacteristic
179C23×C4×C53C2311yescharacteristic
180C23×C4×C53C2311yescharacteristic
181C2×M16×C53—24no—
182C2×M16×C53C2314yes—
183C22×C8×C53—24no—
184C22×C8×C53C2314yes—
185C22×C8×C53C2311yescharacteristic
186C22×C8×C53C2311yescharacteristic
187C22×C8×C53C2311yescharacteristic
188C22×C8×C53C2311yescharacteristic
189C4×D4×C53D414yes—
190C4×D4×C53C2314yes—
191C2×C4⋊C4×C53D411yescharacteristic
192C2×C22⋊C4×C53D411yescharacteristic
193C2×C22⋊C4×C53D411yescharacteristic
194C2×C42×C53C2311yescharacteristic
195C4⋊C8×C53C2314yes—
196C22⋊C8×C53C2314yes—
197C22⋊C8×C53C2314yes—
198#97×C53C2314yes—
199C24×C53C2×D411yescharacteristic
200C24×C53C2×D411yescharacteristic
201C23×D53—21no—
202C2×D4×C53—24no—
203C2×D4×C53C2×D414yes—
204C22×C4×C53—22no—
205C22×C4×C53—22no—
206C22×C4×C53—22no—
207C22×C4×C53—22no—
208C22×C4×C53C2×D411yescharacteristic
209C22×C4×C53C2×D411yescharacteristic
210C22×C4×C53C2×D411yescharacteristic
211C22×C4×C53C2×D411yescharacteristic
212C22×C4×C53C2×D412yes—
213C22×C4×C53C2×D412yes—
214C22×C4×C53C2412yes—
215C22×C4×C53C2412yes—
216C22×C4×C53C2411yescharacteristic
217C2×C22⋊D53—24no—
218C2×C22⋊D53—24no—
219C2×C22⋊D53—44no—
220C2×C22⋊D53—44no—
221C22×Dic53—21no—
222C22×Dic53—21no—
223C22×Dic53—21no—
224C22×Dic53—21no—
225C22×Dic53—21no—
226C22×Dic53—21no—
227C22×Dic53—21no—
228C22×Dic53—24no—
229C22×Dic53—24no—
230C22×Dic53—24no—
231C22×Dic53—44no—
232C22×Dic53—44no—
233C22×Dic53—44no—
234#11719945—28no—
235#11719945—44no—
236#11719945—48no—
237C2×D212—22no—
238C2×D212—22no—
239C2×D212—21no—
240C2×D212C2412yes—
241C2×C4×D53—24no—
242C2×C4×D53—44no—
243C2×Dic106—21no—
244C2×Dic106—21no—
245C2×Dic106—22no—
246C2×Dic106—22no—
247C2×Dic106—22no—
248C2×Dic106—22no—
249C2×Dic106—22no—
250C2×Dic106—22no—
251C2×Dic106—22no—
252C2×Dic106—22no—
253C2×Dic106—28no—
254C2×Dic106—28no—
255C2×Dic106—28no—
256C2×Dic106—24no—
257C2×Dic106—24no—
258C2×Dic106—24no—
259C2×Dic106—21no—
260C2×Dic106—21no—
261C2×Dic106—21no—
262C2×Dic106—44no—
263C2×Dic106—44no—
264C2×Dic106—44no—
265C2×Dic106—48no—
266C2×Dic106—48no—
267C2×Dic106—48no—
268C2×Dic106—44no—
269C2×Dic106—44no—
270C2×Dic106—44no—
271C2×Dic106C2×D414yes—
272C2×Dic106C2×D414yes—
273C2×Dic106C2412yes—
274C2×Dic106C2412yes—
275C2×Dic106C2412yes—
276C2×Dic106C2412yes—
277C2×Dic106C2412yes—
278M16×C53—28no—
279C2×C8×C53—22no—
280C2×C8×C53—22no—
281C2×C8×C53—22no—
282C2×C8×C53—28no—
283C2×C8×C53C2×D414yes—
284C2×C8×C53C2412yes—
285C2×C8×C53C2412yes—
286C2×C8×C53C2412yes—
287C2×C8×C53C2412yes—
288C4⋊C4×C53C2×D414yes—
289C22⋊C4×C53C2×D414yes—
290C22⋊C4×C53C2×D414yes—
291C42×C53C2×D412yes—
292C42×C53C2412yes—
293C22⋊Dic53—24no—
294C22⋊Dic53—24no—
295C22⋊Dic53—24no—
296#11719921—24no—
297#11719921—24no—
298#11719921—24no—
299C4⋊Dic53—24no—
300C4⋊Dic53—24no—
301C4⋊Dic53—21no—
302C4⋊Dic53—21no—
303C4⋊Dic53C2412yes—
304C4⋊Dic53C2412yes—
305#11719919—24no—
306#11719919—24no—
307#11719919—24no—
308#11719919—24no—
309#11719919—24no—
310C4×Dic53—24no—
311C4×Dic53—24no—
312Dic212—28no—
313Dic212—28no—
314Dic212—28no—
315Dic212—28no—
316Dic212—44no—
317Dic212C2×D4116yescomplemented
318#11719913—28no—
319#11719913—28no—
320#11719913—44no—
321C23×C53—22no—
322C23×C53—22no—
323C23×C53—22no—
324C23×C53—22no—
325C23×C53—22no—
326C23×C53#13714yescomplemented
327C23×C53C22×D412yes—
328C23×C53C22×D412yes—
329C23×C53C22×D411yescharacteristic
330C22×D53—22no—
331C22×D53—42no—
332C22×D53—42no—
333C22×D53—42no—
334D4×C53—28no—
335C2×C4×C53—22no—
336C2×C4×C53—22no—
337C2×C4×C53—22no—
338C2×C4×C53—22no—
339C2×C4×C53—24no—
340C2×C4×C53—24no—
341C2×C4×C53—22no—
342C2×C4×C53—22no—
343C2×C4×C53—22no—
344C2×C4×C53—22no—
345C2×C4×C53C22×D412yes—
346C2×C4×C53C22×D412yes—
347C2×C4×C53C22×D412yes—
348C2×C4×C53C22×D412yes—
349C2×C4×C53C22×D412yes—
350C2×C4×C53C22×D411yescharacteristic
351C2×C4×C53H(5,𝔽2)12yes—
352C2×C4×C53C2511yescharacteristic
353C22⋊D53—48no—
354C22⋊D53—48no—
355C2×Dic53—24no—
356C2×Dic53—24no—
357C2×Dic53—22no—
358C2×Dic53—22no—
359C2×Dic53—22no—
360C2×Dic53—22no—
361C2×Dic53—22no—
362C2×Dic53—22no—
363C2×Dic53—22no—
364C2×Dic53—48no—
365C2×Dic53—48no—
366C2×Dic53—48no—
367C2×Dic53—42no—
368C2×Dic53—42no—
369C2×Dic53—42no—
370C2×Dic53—42no—
371C2×Dic53—42no—
372D212—22no—
373D212—22no—
374D212—42no—
375C4×D53—48no—
376Dic106—24no—
377Dic106—24no—
378Dic106—22no—
379Dic106—22no—
380Dic106—22no—
381Dic106—22no—
382Dic106—22no—
383Dic106—22no—
384Dic106—22no—
385Dic106—22no—
386Dic106—48no—
387Dic106—48no—
388Dic106—48no—
389Dic106—42no—
390Dic106—42no—
391Dic106—42no—
392Dic106C22×D414yes—
393Dic106C22×D414yes—
394C8×C53—22no—
395C8×C53—22no—
396C8×C53—22no—
397C8×C53C22×D414yes—
398C2×#3270—531nomaximal, Sylow
399C22×C53—22no—
400C22×C53—28no—
401C22×C53—22no—
402C22×C53—22no—
403C22×C53—22no—
404C22×C53—22no—
405C22×C53—44no—
406C22×C53D4212yes—
407C22×C53C2×#13712yes—
408C22×C53C2×#13714yescomplemented
409C22×C53#57812yes—
410C22×C53C23×D411yescharacteristic
411C2×D53—42no—
412C2×D53—42no—
413C2×D53—42no—
414C2×D53—84no—
415C4×C53—22no—
416C4×C53—22no—
417C4×C53—22no—
418C4×C53—22no—
419C4×C53D4212yes—
420C4×C53C23×D411yescharacteristic
421C4×C53C2×H(5,𝔽2)11yescharacteristic
422Dic53—24no—
423Dic53—24no—
424Dic53—42no—
425Dic53—42no—
426Dic53—42no—
427Dic53—42no—
428Dic53—42no—
429C22×#137—531no—
430C23×Q16—531no—
431C2×D4×Q8—531no—
432C2×#548—531no—
433#3270—5316no—
434C2×#497—531no—
435C2×#470—531no—
436C2×#465—531no—
437C2×#464—531no—
438C2×#462—531no—
439C2×#452—531no—
440C2×#451—531no—
441C2×#451—531no—
442C2×#448—531no—
443C2×#441—531no—
444C2×#435D5311yescharacteristic, complemented
445C2×C53—24no—
446C2×C53—42no—
447C2×C53#327014yescomplemented
448C2×C53C2×D4211yescharacteristic
449C2×C53C22×#13711yescharacteristic
450C2×C53C2×#57811yescharacteristic
451D53—82no—
452C22×#41—531no—
453C23×Q8—531no—
454C23×Q8—531no—
455C23×Q8—531no—
456C2×#137—538no—
457C2×#137—1068no—
458C22×Q16—531no—
459C22×Q16—531no—
460C22×Q16—531no—
461C22×Q16—531no—
462C22×Q16—531no—
463C22×Q16—538no—
464C22×Q16—531no—
465C22×Q16—1068no—
466C22×SD16—531no—
467C22×SD16—531no—
468C22×SD16—531no—
469C22×M16C2×D5311yescharacteristic
470C23×C8C2×D5311yescharacteristic
471D4×Q8—538no—
472D4×Q8—1064no—
473#548—538no—
474#548—1064no—
475C2×C4⋊Q8—531no—
476C2×C4⋊Q8—1061no—
477C2×#124—531no—
478C2×#124—1061no—
479C2×C22⋊Q8—531no—
480C2×C22⋊Q8—531no—
481C2×C22⋊Q8—531no—
482C2×C22⋊Q8—1061no—
483C2×C22⋊Q8—1061no—
484C2×C22⋊Q8—1061no—
485C2×#121—531no—
486C2×#121—1061no—
487C2×C4×Q8—531no—
488C2×C4×Q8—531no—
489C2×C4×D4—1061no—
490C2×C4×D4—1061no—
491C2×C4×D4C2×D5311yescharacteristic
492#497—538no—
493#470—538no—
494#465—538no—
495#464—538no—
496#462—538no—
497#452—538no—
498#451—538no—
499#451—538no—
500#448—538no—
501#441—538no—
502#435C2×D5318yescomplemented
503C2×#106—531no—
504C2×C4⋊C8C2×D5311yescharacteristic
505C2×#103—531no—
506C2×#103—531no—
507C2×#103—531no—
508C2×#103—531no—
509C2×#103—531no—
510C2×#102—531no—
511C2×C22⋊C8C2×D5311yescharacteristic
512C2×C22⋊C8C2×D5311yescharacteristic
513C2×#97C2×D5311yescharacteristic
514C53C2×#327011yescharacteristic, complemented, Sylow
515C2×#41—534no—
516C2×#41—1064no—
517C2×#41—1062no—
518C2×#41—2122no—
519C22×Q8—531no—
520C22×Q8—531no—
521C22×Q8—531no—
522C22×Q8—531no—
523C22×Q8—531no—
524C22×Q8—534no—
525C22×Q8—534no—
526C22×Q8—534no—
527C22×Q8—1064no—
528C22×Q8—1064no—
529C22×Q8—1064no—
530C22×Q8—1061no—
531C22×Q8—1061no—
532C22×Q8—1061no—
533C22×Q8—1062no—
534C22×Q8—1062no—
535C22×Q8—1062no—
536C22×Q8—2122no—
537C22×Q8—2122no—
538C22×Q8—2122no—
539C22×D4—531no—
540C22×D4—1061no—
541C22×D4—1061no—
542C22×D4D21211yescharacteristic
543C23×C4—1061no—
544C23×C4—1061no—
545C23×C4—1061no—
546C23×C4—1061no—
547C23×C4C22×D5311yescharacteristic
548C23×C4C22×D5311yescharacteristic
549#137—10632no—
550C2×Q16—538no—
551C2×Q16—534no—
552C2×Q16—534no—
553C2×Q16—534no—
554C2×Q16—534no—
555C2×Q16—534no—
556C2×Q16—534no—
557C2×Q16—10632no—
558C2×Q16—1064no—
559C2×Q16—1064no—
560C2×Q16—1064no—
561C2×Q16—1064no—
562C2×Q16—2122no—
563C2×SD16—534no—
564C2×SD16—534no—
565C2×SD16—534no—
566C2×SD16—1064no—
567C2×SD16—1064no—
568C2×SD16—2122no—
569C2×M16—24no—
570C2×M16C22×D5314yes—
571C22×C8—24no—
572C22×C8C22×D5311yescharacteristic
573C22×C8C22×D5314yes—
574C22×C8C22×D5311yescharacteristic
575C22×C8C22×D5311yescharacteristic
576C22×C8C22×D5311yescharacteristic
577C4⋊Q8—534no—
578C4⋊Q8—1068no—
579C4⋊Q8—1062no—
580#124—534no—
581#124—1068no—
582#124—1062no—
583C22⋊Q8—534no—
584C22⋊Q8—534no—
585C22⋊Q8—534no—
586C22⋊Q8—1062no—
587C22⋊Q8—1062no—
588C22⋊Q8—1062no—
589C22⋊Q8—1068no—
590C22⋊Q8—1068no—
591C22⋊Q8—1068no—
592#121—534no—
593#121—1068no—
594#121—1062no—
595C4×Q8—534no—
596C4×Q8—534no—
597C4×Q8—1062no—
598C4×Q8—1062no—
599C4×D4—1068no—
600C4×D4—1068no—
601C4×D4D21214yes—
602C4×D4C22×D5314yes—
603C2×C4⋊C4—531no—
604C2×C4⋊C4—531no—
605C2×C4⋊C4—1061no—
606C2×C4⋊C4—1061no—
607C2×C4⋊C4—1061no—
608C2×C4⋊C4—1061no—
609C2×C4⋊C4—1061no—
610C2×C4⋊C4—1061no—
611C2×C4⋊C4—1061no—
612C2×C4⋊C4D21211yescharacteristic
613C2×C22⋊C4—1061no—
614C2×C22⋊C4—1061no—
615C2×C22⋊C4—1061no—
616C2×C22⋊C4—1061no—
617C2×C22⋊C4—1061no—
618C2×C22⋊C4—1061no—
619C2×C22⋊C4D21211yescharacteristic
620C2×C22⋊C4D21211yescharacteristic
621C2×C42—1061no—
622C2×C42—1061no—
623C2×C42C22×D5311yescharacteristic
624#106—534no—
625C4⋊C8C22×D5314yes—
626#103—534no—
627#103—534no—
628#103—534no—
629#103—534no—
630#103—534no—
631#102—534no—
632C22⋊C8C22×D5314yes—
633C22⋊C8C22×D5314yes—
634#97C22×D5314yes—
635C24—1061no—
636C24C2×D21211yescharacteristic
637C24C2×D21211yescharacteristic
638#41—1068no—
639#41—2124no—
640#41—2128no—
641C2×Q8—534no—
642C2×Q8—534no—
643C2×Q8—532no—
644C2×Q8—532no—
645C2×Q8—532no—
646C2×Q8—532no—
647C2×Q8—532no—
648C2×Q8—1068no—
649C2×Q8—1068no—
650C2×Q8—1068no—
651C2×Q8—1061no—
652C2×Q8—1061no—
653C2×Q8—1064no—
654C2×Q8—1061no—
655C2×Q8—1064no—
656C2×Q8—1064no—
657C2×Q8—1061no—
658C2×Q8—1061no—
659C2×Q8—1062no—
660C2×Q8—1062no—
661C2×Q8—1062no—
662C2×Q8—1062no—
663C2×Q8—1062no—
664C2×Q8—1062no—
665C2×Q8—1062no—
666C2×Q8—1062no—
667C2×Q8—2124no—
668C2×Q8—2124no—
669C2×Q8—2124no—
670C2×Q8—2124no—
671C2×Q8—2124no—
672C2×Q8—2124no—
673C2×Q8—2128no—
674C2×Q8—2128no—
675C2×Q8—2128no—
676C2×D4—24no—
677C2×D4—532no—
678C2×D4—1064no—
679C2×D4—1064no—
680C2×D4—1062no—
681C2×D4—1061no—
682C2×D4—1062no—
683C2×D4—2124no—
684C2×D4—2124no—
685C2×D4C2×D21214yes—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—1061no—
691C22×C4—1061no—
692C22×C4—1064no—
693C22×C4—1064no—
694C22×C4—1064no—
695C22×C4—1061no—
696C22×C4—1061no—
697C22×C4—1061no—
698C22×C4—1061no—
699C22×C4—1061no—
700C22×C4—1064no—
701C22×C4—2124no—
702C22×C4—2124no—
703C22×C4—2124no—
704C22×C4—2124no—
705C22×C4C2×D21212yes—
706C22×C4C2×D21212yes—
707C22×C4C2×D21211yescharacteristic
708C22×C4C2×D21211yescharacteristic
709C22×C4C2×D21211yescharacteristic
710C22×C4C2×D21211yescharacteristic
711C22×C4C23×D5312yes—
712C22×C4C23×D5312yes—
713C22×C4C23×D5311yescharacteristic
714Q16—5316no—
715Q16—1068no—
716Q16—1068no—
717Q16—1068no—
718Q16—1068no—
719Q16—2124no—
720SD16—1068no—
721SD16—1068no—
722SD16—2124no—
723M16—28no—
724C2×C8—22no—
725C2×C8—22no—
726C2×C8—22no—
727C2×C8—28no—
728C2×C8D4×D5314yes—
729C2×C8C23×D5312yes—
730C2×C8C23×D5312yes—
731C2×C8C23×D5312yes—
732C2×C8C23×D5312yes—
733C4⋊C4—532no—
734C4⋊C4—532no—
735C4⋊C4—1061no—
736C4⋊C4—1061no—
737C4⋊C4—1064no—
738C4⋊C4—1064no—
739C4⋊C4—1064no—
740C4⋊C4—1064no—
741C4⋊C4—1064no—
742C4⋊C4—1064no—
743C4⋊C4—1064no—
744C4⋊C4C2×D21214yes—
745C22⋊C4—1064no—
746C22⋊C4—1064no—
747C22⋊C4—1064no—
748C22⋊C4—1064no—
749C22⋊C4—1064no—
750C22⋊C4—1064no—
751C22⋊C4C2×D21214yes—
752C22⋊C4C2×D21214yes—
753C42—1064no—
754C42—1064no—
755C42C2×D21212yes—
756C42C23×D5312yes—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—1062no—
763C23—2122no—
764C23—2122no—
765C23—2122no—
766C23#1313325014yescomplemented
767C23C22×D21212yes—
768C23C22×D21212yes—
769C23C22×D21211yescharacteristic
770Q8—534no—
771Q8—534no—
772Q8—1062no—
773Q8—1062no—
774Q8—1064no—
775Q8—1064no—
776Q8—1062no—
777Q8—1062no—
778Q8—1062no—
779Q8—1062no—
780Q8—1062no—
781Q8—1062no—
782Q8—2128no—
783Q8—2128no—
784Q8—2128no—
785Q8—2122no—
786Q8—2122no—
787Q8—2122no—
788D4—28no—
789D4—1062no—
790D4—1062no—
791D4—2128no—
792D4—2128no—
793D4—2122no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—24no—
803C2×C4—24no—
804C2×C4—1062no—
805C2×C4—1062no—
806C2×C4—1064no—
807C2×C4—1064no—
808C2×C4—1062no—
809C2×C4—1062no—
810C2×C4—1062no—
811C2×C4—1062no—
812C2×C4—1062no—
813C2×C4—2128no—
814C2×C4—2128no—
815C2×C4—2128no—
816C2×C4—2128no—
817C2×C4—2122no—
818C2×C4—2122no—
819C2×C4—2122no—
820C2×C4—2122no—
821C2×C4—2122no—
822C2×C4C2×D4×D5312yes—
823C2×C4C22×D21212yes—
824C2×C4C22×D21212yes—
825C2×C4C22×D21212yes—
826C2×C4C22×D21212yes—
827C2×C4C22×D21211yescharacteristic
828C2×C4#1313326312yes—
829C2×C4C24×D5311yescharacteristic
830C8—22no—
831C8—22no—
832C8—22no—
833C8C2×D4×D5314yes—
834C22—28no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—22no—
840C22—44no—
841C22—4244no—
842C22—2122no—
843C22—2122no—
844C22—2122no—
845C22D4×D21212yes—
846C22C2×#1313325012yes—
847C22C2×#1313325014yescomplemented
848C22#1681144012yes—
849C22C23×D21211yescharacteristic
850C4—22no—
851C4—22no—
852C4—22no—
853C4—22no—
854C4—1064no—
855C4—1064no—
856C4—2122no—
857C4—2122no—
858C4—2122no—
859C4—2122no—
860C4—2122no—
861C4D4×D21212yes—
862C4C22×D4×D5311yescharacteristic
863C4C2×#1313326311yescharacteristic
864C2—24no—
865C2—42no—
866C2—4242no—
867C2#2028629014yesdirect product factor
868C2C2×D4×D21211yescharacteristic
869C2C22×#1313325011yescharacteristic
870C2C2×#1681144011yescharacteristic
subgroupG/H
centerC23C22×D212
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#435C2
socleC23×C53C22×D4
prime radicalC2×#16811282C2
hypercenterC2×#435D53
hypocenterC53C2×#3270
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C22×#13133250C2semidirect
2. C23×Dic212C2semidirect
3. C2×D4×Dic106C2semidirect
5. #20286290C2direct (N × H)
6. C2×#16811017C2semidirect
7. C2×#16810881C2semidirect
8. C2×#16810852C2semidirect
9. C2×#16810846C2semidirect
10. C2×#16810834C2semidirect
11. C2×#16810787C2semidirect
12. C2×#16810781C2semidirect
13. C2×#16810781C2semidirect
14. C2×#16810764C2semidirect
15. C2×#16810731C2semidirect
16. C2×C53×#435C2semidirect
22. C2×#13133250C22semidirect
30. C22×Dic212C22semidirect
35. D4×Dic106C22semidirect
54. #16811017C22semidirect
55. #16810881C22semidirect
56. #16810852C22semidirect
57. #16810846C22semidirect
58. #16810834C22semidirect
59. #16810787C22semidirect
60. #16810781C22semidirect
61. #16810781C22semidirect
62. #16810764C22semidirect
63. #16810731C22semidirect
74. C53×#435C22semidirect
117. C2×Dic212D4semidirect
317. Dic212C2×D4semidirect
326. C23×C53#137semidirect
408. C22×C53C2×#137semidirect
444. C2×#435D53semidirect
447. C2×C53#3270semidirect
502. #435C2×D53semidirect
514. C53C2×#3270semidirect
766. C23#13133250semidirect
847. C22C2×#13133250semidirect
867. C2#20286290direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131332502
C23×Dic2122
C2×D4×Dic1062
C2×#168112822
#202862902
C2×#168110172
C2×#168108812
C2×#168108522
C2×#168108462
C2×#168108342
C2×#168107872
C2×#168107812
C2×#168107642
C2×#168107312
C2×C53×#4352
C2×#327053