Finite Group Databasebeta

← C2×C113×#1913 #43289033

Subgroups — C2×C113×#1913 #43289033

Order 28928.

2078 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#534×C113C211yesmaximal, characteristic
2C2×#518×C113C211yesmaximal, characteristic, complemented
3C22×#99×C113C211yesmaximal, characteristic, complemented
4C22×#99×C113C212yesmaximal, complemented
5C113×#1913C218yesmaximal, direct product factor
6C2×#342×C113C212yesmaximal, complemented
7C23×D4×C113C2211yescharacteristic
8C23×D4×C113C2211yescharacteristic
9#534×C113—22no—
10#534×C113—22no—
11#534×C113C414yescomplemented
12#534×C113C2214yes—
13C2×#123×C113—21no—
14C2×#123×C113C412yescomplemented
15C2×#121×C113—22no—
16C2×#120×C113—21no—
17C2×#120×C113C412yescomplemented
18#518×C113—22no—
19#518×C113—24no—
20#518×C113C2214yescomplemented
21C2×C4×D4×C113—24no—
22C2×#117×C113—21no—
23C22×C22⋊C4×C113—21no—
24C22×C22⋊C4×C113C2212yes—
25C22×C22⋊C4×C113C2211yescharacteristic
26C22×C22⋊C4×C113C2212yes—
27C2×#99×C113—22no—
28C2×#99×C113—22no—
29C2×#99×C113—24no—
30C2×#99×C113—24no—
31C2×#99×C113C2214yescomplemented
32C2×#99×C113C2218yescomplemented
33#342×C113C2218yescomplemented
34C25×C113C2×C411yescharacteristic, complemented
35C25×C113D411yescharacteristic
36C25×C113C2311yescharacteristic
37C22×D4×C113—22no—
38C22×D4×C113—22no—
39C22×D4×C113—22no—
40C22×D4×C113—22no—
41C22×D4×C113—21no—
42C22×D4×C113—21no—
43C22×D4×C113—21no—
44C22×D4×C113—21no—
45C22×D4×C113—22no—
46C22×D4×C113—22no—
47C22×D4×C113—22no—
48C22×D4×C113—22no—
49C22×D4×C113—22no—
50C22×D4×C113C2×C412yes—
51C22×D4×C113C2×C412yes—
52C22×D4×C113C2×C412yescomplemented
53C22×D4×C113D412yes—
54C22×D4×C113D412yes—
55C22×D4×C113D412yes—
56C22×D4×C113C2312yes—
57C22×D4×C113C2312yes—
58C23×C4×C113—22no—
59C23×C4×C113—22no—
60C23×C4×C113—21no—
61C23×C4×C113—22no—
62C23×C4×C113C2×C411yescharacteristic, complemented
63C23×C4×C113D411yescharacteristic
64#123×C113—24no—
65#123×C113—24no—
66#123×C113—24no—
67#123×C113C2×C418yescomplemented
68#121×C113—28no—
69#121×C113—28no—
70#120×C113—24no—
71#120×C113—24no—
72#120×C113—24no—
73#120×C113C2×C418yescomplemented
74C4×D4×C113—216no—
75C4×D4×C113—216no—
76#117×C113—24no—
77#117×C113—24no—
78C2×C4⋊C4×C113—22no—
79C2×C4⋊C4×C113—22no—
80C2×C22⋊C4×C113—22no—
81C2×C22⋊C4×C113—24no—
82C2×C22⋊C4×C113—22no—
83C2×C22⋊C4×C113—22no—
84C2×C22⋊C4×C113—24no—
85C2×C22⋊C4×C113—22no—
86C2×C22⋊C4×C113—22no—
87C2×C22⋊C4×C113—21no—
88C2×C22⋊C4×C113—21no—
89C2×C22⋊C4×C113—21no—
90C2×C22⋊C4×C113—22no—
91C2×C22⋊C4×C113—22no—
92C2×C22⋊C4×C113—22no—
93C2×C22⋊C4×C113—22no—
94C2×C22⋊C4×C113—22no—
95C2×C22⋊C4×C113—22no—
96C2×C22⋊C4×C113C2×C412yescomplemented
97C2×C22⋊C4×C113C2×C412yescomplemented
98C2×C22⋊C4×C113D414yescomplemented
99C2×C22⋊C4×C113D414yescomplemented
100C2×C22⋊C4×C113C2314yes—
101C2×C22⋊C4×C113C2312yes—
102C2×C22⋊C4×C113C2314yes—
103C2×C42×C113—22no—
104#99×C113—28no—
105#99×C113—216no—
106C24×C113—21no—
107C24×C113—21no—
108C24×C113—21no—
109C24×C113—21no—
110C24×C113—21no—
111C24×C113—21no—
112C24×C113—22no—
113C24×C113—22no—
114C24×C113—82no—
115C24×C113—82no—
116C24×C113—82no—
117C24×C113C22⋊C412yes—
118C24×C113C22⋊C412yes—
119C24×C113C22×C411yescharacteristic
120C24×C113C22×C411yescharacteristic
121C24×C113C22×C412yescomplemented
122C24×C113C2×D412yes—
123C24×C113C2×D411yescharacteristic
124C24×C113C2×D411yescharacteristic
125C24×C113C2×D412yes—
126C24×C113C2×D411yescharacteristic
127C24×C113C2×D411yescharacteristic
128C24×C113C2×D412yes—
129C24×C113#4112yes—
130C24×C113#4112yes—
131C24×C113C2411yescharacteristic
132C2×D4×C113—24no—
133C2×D4×C113—24no—
134C2×D4×C113—24no—
135C2×D4×C113—24no—
136C2×D4×C113—24no—
137C2×D4×C113—24no—
138C2×D4×C113—24no—
139C2×D4×C113—24no—
140C2×D4×C113—24no—
141C2×D4×C113—24no—
142C2×D4×C113—24no—
143C2×D4×C113—24no—
144C2×D4×C113—22no—
145C2×D4×C113—22no—
146C2×D4×C113—24no—
147C2×D4×C113—24no—
148C2×D4×C113—24no—
149C2×D4×C113—22no—
150C2×D4×C113—22no—
151C2×D4×C113—24no—
152C2×D4×C113—28no—
153C2×D4×C113—41no—
154C2×D4×C113—42no—
155C2×D4×C113—41no—
156C2×D4×C113—42no—
157C2×D4×C113—42no—
158C2×D4×C113—42no—
159C2×D4×C113—42no—
160C2×D4×C113—41no—
161C2×D4×C113—42no—
162C2×D4×C113—41no—
163C2×D4×C113—84no—
164C2×D4×C113C22⋊C414yes—
165C2×D4×C113C22⋊C414yes—
166C2×D4×C113C22×C414yes—
167C2×D4×C113C2×D414yes—
168C22×C4×C113—21no—
169C22×C4×C113—21no—
170C22×C4×C113—21no—
171C22×C4×C113—21no—
172C22×C4×C113—22no—
173C22×C4×C113—21no—
174C22×C4×C113—21no—
175C22×C4×C113—22no—
176C22×C4×C113—22no—
177C22×C4×C113—24no—
178C22×C4×C113—28no—
179C22×C4×C113—22no—
180C22×C4×C113—24no—
181C22×C4×C113—24no—
182C22×C4×C113—22no—
183C22×C4×C113—24no—
184C22×C4×C113—42no—
185C22×C4×C113—42no—
186C22×C4×C113—84no—
187C22×C4×C113—84no—
188C22×C4×C113—82no—
189C22×C4×C113—84no—
190C22×C4×C113C22⋊C412yes—
191C22×C4×C113C22⋊C412yes—
192C22×C4×C113C22×C412yescomplemented
193C22×C4×C113C2×D412yes—
194C4⋊C4×C113—28no—
195C4⋊C4×C113—28no—
196C22⋊C4×C113—28no—
197C22⋊C4×C113—22no—
198C22⋊C4×C113—22no—
199C22⋊C4×C113—28no—
200C22⋊C4×C113—24no—
201C22⋊C4×C113—24no—
202C22⋊C4×C113—24no—
203C22⋊C4×C113—22no—
204C22⋊C4×C113—28no—
205C22⋊C4×C113—24no—
206C22⋊C4×C113—24no—
207C22⋊C4×C113—42no—
208C22⋊C4×C113—42no—
209C22⋊C4×C113C22×C414yescomplemented
210C22⋊C4×C113C2×D418yescomplemented
211C42×C113—28no—
212C23×C113—22no—
213C23×C113—22no—
214C23×C113—22no—
215C23×C113—22no—
216C23×C113—22no—
217C23×C113—22no—
218C23×C113—22no—
219C23×C113—24no—
220C23×C113—44no—
221C23×C113—42no—
222C23×C113—44no—
223C23×C113—42no—
224C23×C113—42no—
225C23×C113—44no—
226C23×C113—44no—
227C23×C113—44no—
228C23×C113—41no—
229C23×C113—42no—
230C23×C113—41no—
231C23×C113—82no—
232C23×C113—84no—
233C23×C113—81no—
234C23×C113—81no—
235C23×C113—82no—
236C23×C113—81no—
237C23×C113—82no—
238C23×C113—81no—
239C23×C113—82no—
240C23×C113—82no—
241C23×C113—82no—
242C23×C113—82no—
243C23×C113—82no—
244C23×C113—82no—
245C23×C113—84no—
246C23×C113C2×C22⋊C411yescharacteristic
247C23×C113C2×C22⋊C414yes—
248C23×C113C2×C22⋊C411yescharacteristic
249C23×C113C2×C22⋊C411yescharacteristic
250C23×C113C2×C22⋊C411yescharacteristic
251C23×C113C4×D412yes—
252C23×C113C4×D412yes—
253C23×C113C4×D412yes—
254C23×C113C4×D412yes—
255C23×C113#12011yescharacteristic
256C23×C113#12011yescharacteristic
257C23×C113#12012yes—
258C23×C113#12112yes—
259C23×C113#12112yes—
260C23×C113#12112yes—
261C23×C113#12112yes—
262C23×C113#12311yescharacteristic
263C23×C113#12311yescharacteristic
264C23×C113#12312yes—
265C23×C113C23×C411yescharacteristic
266C23×C113C22×D411yescharacteristic
267C23×C113C22×D411yescharacteristic
268C23×C113C22×D412yes—
269C23×C113C2×#4112yes—
270D4×C113—28no—
271D4×C113—28no—
272D4×C113—28no—
273D4×C113—28no—
274D4×C113—42no—
275D4×C113—44no—
276D4×C113—42no—
277D4×C113—42no—
278D4×C113—42no—
279D4×C113—44no—
280D4×C113—88no—
281C2×C4×C113—22no—
282C2×C4×C113—22no—
283C2×C4×C113—22no—
284C2×C4×C113—22no—
285C2×C4×C113—22no—
286C2×C4×C113—22no—
287C2×C4×C113—24no—
288C2×C4×C113—22no—
289C2×C4×C113—24no—
290C2×C4×C113—28no—
291C2×C4×C113—48no—
292C2×C4×C113—44no—
293C2×C4×C113—41no—
294C2×C4×C113—42no—
295C2×C4×C113—41no—
296C2×C4×C113—44no—
297C2×C4×C113—84no—
298C2×C4×C113—84no—
299C2×C4×C113—88no—
300C2×C4×C113—82no—
301C2×C4×C113—82no—
302C2×C4×C113—84no—
303C2×C4×C113—84no—
304C2×C4×C113—84no—
305C2×C4×C113C2×C22⋊C414yes—
306C22×C113—22no—
307C22×C113—22no—
308C22×C113—24no—
309C22×C113—24no—
310C22×C113—22no—
311C22×C113—24no—
312C22×C113—41no—
313C22×C113—42no—
314C22×C113—42no—
315C22×C113—42no—
316C22×C113—41no—
317C22×C113—42no—
318C22×C113—41no—
319C22×C113—41no—
320C22×C113—42no—
321C22×C113—41no—
322C22×C113—41no—
323C22×C113—41no—
324C22×C113—41no—
325C22×C113—42no—
326C22×C113—42no—
327C22×C113—42no—
328C22×C113—42no—
329C22×C113—42no—
330C22×C113—44no—
331C22×C113—44no—
332C22×C113—44no—
333C22×C113—44no—
334C22×C113—44no—
335C22×C113—42no—
336C22×C113—82no—
337C22×C113—82no—
338C22×C113—82no—
339C22×C113—84no—
340C22×C113—82no—
341C22×C113—84no—
342C22×C113—82no—
343C22×C113#38611yescharacteristic
344C22×C113#38611yescharacteristic
345C22×C113#38611yescharacteristic
346C22×C113#38612yes—
347C22×C113#38612yes—
348C22×C113#38611yescharacteristic
349C22×C113C22×C22⋊C411yescharacteristic
350C22×C113C2×C4×D412yes—
351C22×C113C2×#12011yescharacteristic
352C22×C113C2×#12112yes—
353C22×C113C2×#12311yescharacteristic
354C4×C113—24no—
355C4×C113—48no—
356C4×C113—44no—
357C4×C113—42no—
358C4×C113—84no—
359C2×#1913C11311yesmaximal, characteristic, direct product factor, Sylow
360C2×C113—21no—
361C2×C113—21no—
362C2×C113—22no—
363C2×C113—21no—
364C2×C113—21no—
365C2×C113—22no—
366C2×C113—21no—
367C2×C113—22no—
368C2×C113—21no—
369C2×C113—22no—
370C2×C113—44no—
371C2×C113—82no—
372C2×C113#191312yesdirect product factor
373C2×C113C2×#38611yescharacteristic
374C2×#534C2×C11311yescharacteristic
375C2×#518C2×C11311yescharacteristic, complemented
376C22×#99C2×C11311yescharacteristic, complemented
377C22×#99C2×C11312yescomplemented
378#1913C2×C11318yesdirect product factor
379C2×#342C2×C11312yescomplemented
380C113C2×#191311yescharacteristic, direct product factor, Sylow
381C23×D4C22×C11311yescharacteristic
382C23×D4C22×C11311yescharacteristic
383#534—22no—
384#534—22no—
385#534C4×C11314yescomplemented
386#534C22×C11314yes—
387C2×#123—21no—
388C2×#123C4×C11312yescomplemented
389C2×#121—22no—
390C2×#120—21no—
391C2×#120C4×C11312yescomplemented
392#518—22no—
393#518—24no—
394#518C22×C11314yescomplemented
395C2×C4×D4—24no—
396C2×#117—21no—
397C22×C22⋊C4—21no—
398C22×C22⋊C4C22×C11312yes—
399C22×C22⋊C4C22×C11311yescharacteristic
400C22×C22⋊C4C22×C11312yes—
401C2×#99—22no—
402C2×#99—22no—
403C2×#99—24no—
404C2×#99—24no—
405C2×#99C22×C11314yescomplemented
406C2×#99C22×C11318yescomplemented
407#342C22×C11318yescomplemented
408C25C2×C4×C11311yescharacteristic, complemented
409C25D4×C11311yescharacteristic
410C25C23×C11311yescharacteristic
411C22×D4—22no—
412C22×D4—22no—
413C22×D4—22no—
414C22×D4—22no—
415C22×D4—21no—
416C22×D4—21no—
417C22×D4—21no—
418C22×D4—21no—
419C22×D4—22no—
420C22×D4—22no—
421C22×D4—22no—
422C22×D4—22no—
423C22×D4—22no—
424C22×D4C2×C4×C11312yes—
425C22×D4C2×C4×C11312yes—
426C22×D4C2×C4×C11312yescomplemented
427C22×D4D4×C11312yes—
428C22×D4D4×C11312yes—
429C22×D4D4×C11312yes—
430C22×D4C23×C11312yes—
431C22×D4C23×C11312yes—
432C23×C4—22no—
433C23×C4—22no—
434C23×C4—21no—
435C23×C4—22no—
436C23×C4C2×C4×C11311yescharacteristic, complemented
437C23×C4D4×C11311yescharacteristic
438#123—24no—
439#123—24no—
440#123—24no—
441#123C2×C4×C11318yescomplemented
442#121—28no—
443#121—28no—
444#120—24no—
445#120—24no—
446#120—24no—
447#120C2×C4×C11318yescomplemented
448C4×D4—216no—
449C4×D4—216no—
450#117—24no—
451#117—24no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—22no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—24no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—24no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4C2×C4×C11312yescomplemented
471C2×C22⋊C4C2×C4×C11312yescomplemented
472C2×C22⋊C4D4×C11314yescomplemented
473C2×C22⋊C4D4×C11314yescomplemented
474C2×C22⋊C4C23×C11314yes—
475C2×C22⋊C4C23×C11312yes—
476C2×C22⋊C4C23×C11314yes—
477C2×C42—22no—
478#99—28no—
479#99—216no—
480C24—21no—
481C24—21no—
482C24—21no—
483C24—21no—
484C24—21no—
485C24—21no—
486C24—22no—
487C24—22no—
488C24—82no—
489C24—82no—
490C24—82no—
491C24C22⋊C4×C11312yes—
492C24C22⋊C4×C11312yes—
493C24C22×C4×C11311yescharacteristic
494C24C22×C4×C11311yescharacteristic
495C24C22×C4×C11312yescomplemented
496C24C2×D4×C11312yes—
497C24C2×D4×C11311yescharacteristic
498C24C2×D4×C11311yescharacteristic
499C24C2×D4×C11312yes—
500C24C2×D4×C11311yescharacteristic
501C24C2×D4×C11311yescharacteristic
502C24C2×D4×C11312yes—
503C24#41×C11312yes—
504C24#41×C11312yes—
505C24C24×C11311yescharacteristic
506C2×D4—24no—
507C2×D4—24no—
508C2×D4—24no—
509C2×D4—24no—
510C2×D4—24no—
511C2×D4—24no—
512C2×D4—24no—
513C2×D4—24no—
514C2×D4—24no—
515C2×D4—24no—
516C2×D4—24no—
517C2×D4—24no—
518C2×D4—22no—
519C2×D4—22no—
520C2×D4—24no—
521C2×D4—24no—
522C2×D4—24no—
523C2×D4—22no—
524C2×D4—22no—
525C2×D4—24no—
526C2×D4—28no—
527C2×D4—41no—
528C2×D4—41no—
529C2×D4—42no—
530C2×D4—42no—
531C2×D4—42no—
532C2×D4—42no—
533C2×D4—42no—
534C2×D4—41no—
535C2×D4—41no—
536C2×D4—42no—
537C2×D4—84no—
538C2×D4C22⋊C4×C11314yes—
539C2×D4C22⋊C4×C11314yes—
540C2×D4C22×C4×C11314yes—
541C2×D4C2×D4×C11314yes—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—24no—
552C22×C4—28no—
553C22×C4—22no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—22no—
557C22×C4—24no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—84no—
561C22×C4—84no—
562C22×C4—82no—
563C22×C4—84no—
564C22×C4C22⋊C4×C11312yes—
565C22×C4C22⋊C4×C11312yes—
566C22×C4C22×C4×C11312yescomplemented
567C22×C4C2×D4×C11312yes—
568C4⋊C4—28no—
569C4⋊C4—28no—
570C22⋊C4—28no—
571C22⋊C4—22no—
572C22⋊C4—22no—
573C22⋊C4—28no—
574C22⋊C4—24no—
575C22⋊C4—24no—
576C22⋊C4—24no—
577C22⋊C4—22no—
578C22⋊C4—28no—
579C22⋊C4—24no—
580C22⋊C4—24no—
581C22⋊C4—42no—
582C22⋊C4—42no—
583C22⋊C4C22×C4×C11314yescomplemented
584C22⋊C4C2×D4×C11318yescomplemented
585C42—28no—
586C23—22no—
587C23—22no—
588C23—22no—
589C23—22no—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—24no—
594C23—44no—
595C23—42no—
596C23—44no—
597C23—42no—
598C23—42no—
599C23—44no—
600C23—44no—
601C23—44no—
602C23—41no—
603C23—42no—
604C23—41no—
605C23—82no—
606C23—84no—
607C23—81no—
608C23—81no—
609C23—82no—
610C23—81no—
611C23—82no—
612C23—81no—
613C23—82no—
614C23—82no—
615C23—82no—
616C23—82no—
617C23—82no—
618C23—82no—
619C23—84no—
620C23C2×C22⋊C4×C11311yescharacteristic
621C23C2×C22⋊C4×C11314yes—
622C23C2×C22⋊C4×C11311yescharacteristic
623C23C2×C22⋊C4×C11311yescharacteristic
624C23C2×C22⋊C4×C11311yescharacteristic
625C23C4×D4×C11312yes—
626C23C4×D4×C11312yes—
627C23C4×D4×C11312yes—
628C23C4×D4×C11312yes—
629C23#120×C11311yescharacteristic
630C23#120×C11311yescharacteristic
631C23#120×C11312yes—
632C23#121×C11312yes—
633C23#121×C11312yes—
634C23#121×C11312yes—
635C23#121×C11312yes—
636C23#123×C11311yescharacteristic
637C23#123×C11311yescharacteristic
638C23#123×C11312yes—
639C23C23×C4×C11311yescharacteristic
640C23C22×D4×C11311yescharacteristic
641C23C22×D4×C11311yescharacteristic
642C23C22×D4×C11312yes—
643C23C2×#41×C11312yes—
644D4—28no—
645D4—28no—
646D4—28no—
647D4—28no—
648D4—42no—
649D4—44no—
650D4—42no—
651D4—42no—
652D4—42no—
653D4—44no—
654D4—88no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—24no—
662C2×C4—22no—
663C2×C4—24no—
664C2×C4—28no—
665C2×C4—48no—
666C2×C4—44no—
667C2×C4—41no—
668C2×C4—42no—
669C2×C4—41no—
670C2×C4—44no—
671C2×C4—84no—
672C2×C4—84no—
673C2×C4—88no—
674C2×C4—82no—
675C2×C4—82no—
676C2×C4—84no—
677C2×C4—84no—
678C2×C4—84no—
679C2×C4C2×C22⋊C4×C11314yes—
680C22—22no—
681C22—22no—
682C22—24no—
683C22—24no—
684C22—22no—
685C22—24no—
686C22—41no—
687C22—42no—
688C22—42no—
689C22—42no—
690C22—41no—
691C22—42no—
692C22—41no—
693C22—41no—
694C22—42no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—42no—
700C22—42no—
701C22—42no—
702C22—42no—
703C22—42no—
704C22—44no—
705C22—44no—
706C22—44no—
707C22—44no—
708C22—44no—
709C22—42no—
710C22—82no—
711C22—82no—
712C22—82no—
713C22—84no—
714C22—82no—
715C22—84no—
716C22—82no—
717C22#386×C11311yescharacteristic
718C22#386×C11311yescharacteristic
719C22#386×C11311yescharacteristic
720C22#386×C11312yes—
721C22#386×C11312yes—
722C22#386×C11311yescharacteristic
723C22C22×C22⋊C4×C11311yescharacteristic
724C22C2×C4×D4×C11312yes—
725C22C2×#120×C11311yescharacteristic
726C22C2×#121×C11312yes—
727C22C2×#123×C11311yescharacteristic
728C4—24no—
729C4—48no—
730C4—44no—
731C4—42no—
732C4—84no—
733C2—21no—
734C2—21no—
735C2—22no—
736C2—21no—
737C2—21no—
738C2—22no—
739C2—21no—
740C2—22no—
741C2—21no—
742C2—22no—
743C2—44no—
744C2—82no—
745C2C113×#191312yesdirect product factor
746C2C2×#386×C11311yescharacteristic
subgroupG/H
center, socleC22×C113#386
commutatorC23C23×C4×C113
Frattini, cosocleC24C24×C113
prime radicalC2×#534×C113C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C113 ◁ C25×C113 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#518×C113C2semidirect
3. C22×#99×C113C2semidirect
4. C22×#99×C113C2semidirect
5. C113×#1913C2direct (N × H)
6. C2×#342×C113C2semidirect
11. #534×C113C4semidirect
14. C2×#123×C113C4semidirect
17. C2×#120×C113C4semidirect
20. #518×C113C22semidirect
31. C2×#99×C113C22semidirect
32. C2×#99×C113C22semidirect
33. #342×C113C22semidirect
34. C25×C113C2×C4semidirect
52. C22×D4×C113C2×C4semidirect
62. C23×C4×C113C2×C4semidirect
67. #123×C113C2×C4semidirect
73. #120×C113C2×C4semidirect
96. C2×C22⋊C4×C113C2×C4semidirect
97. C2×C22⋊C4×C113C2×C4semidirect
98. C2×C22⋊C4×C113D4semidirect
99. C2×C22⋊C4×C113D4semidirect
121. C24×C113C22×C4semidirect
192. C22×C4×C113C22×C4semidirect
209. C22⋊C4×C113C22×C4semidirect
210. C22⋊C4×C113C2×D4semidirect
359. C2×#1913C113direct (N × H)
372. C2×C113#1913direct (N × H)
375. C2×#518C2×C113semidirect
376. C22×#99C2×C113semidirect
377. C22×#99C2×C113semidirect
378. #1913C2×C113direct (N × H)
379. C2×#342C2×C113semidirect
380. C113C2×#1913direct (N × H)
385. #534C4×C113semidirect
388. C2×#123C4×C113semidirect
391. C2×#120C4×C113semidirect
394. #518C22×C113semidirect
405. C2×#99C22×C113semidirect
406. C2×#99C22×C113semidirect
407. #342C22×C113semidirect
408. C25C2×C4×C113semidirect
426. C22×D4C2×C4×C113semidirect
436. C23×C4C2×C4×C113semidirect
441. #123C2×C4×C113semidirect
447. #120C2×C4×C113semidirect
470. C2×C22⋊C4C2×C4×C113semidirect
471. C2×C22⋊C4C2×C4×C113semidirect
472. C2×C22⋊C4D4×C113semidirect
473. C2×C22⋊C4D4×C113semidirect
495. C24C22×C4×C113semidirect
566. C22×C4C22×C4×C113semidirect
583. C22⋊C4C22×C4×C113semidirect
584. C22⋊C4C2×D4×C113semidirect
745. C2C113×#1913direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#534×C1132
C2×#518×C1132
C22×#99×C1132
C113×#19132
C2×#342×C1132
C2×#1913113