Finite Group Databasebeta

← #15786053

Subgroups — #15786053

Order 3328.

2106 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88178C211yesmaximal, characteristic
2C2×#11718590C211yesmaximal, characteristic, complemented
3C2×#11718590C211yesmaximal, characteristic, complemented
4C2×#11718589C211yesmaximal, characteristic, complemented
5C2×#11718873C211yesmaximal, characteristic
6C2×C4×C4⋊Dic13C211yesmaximal, characteristic, complemented
7#13113102C212yesmaximal, complemented
8#13113079C212yesmaximal
9#13113073C212yesmaximal
10#13113064C212yesmaximal, complemented
11C2×C4×C13×C22⋊C4C211yesmaximal, characteristic
12C24×C4×C13C2211yescharacteristic
13C23×Dic26C2211yescharacteristic
14C22×C13×C22⋊C4C2211yescharacteristic
15C22×C13×C22⋊C4C2211yescharacteristic
16C22×C42×C13C2211yescharacteristic
17C22×C42×C13C2211yescharacteristic
18C22×C22⋊Dic13C2212yes—
19C22×C22⋊Dic13C2212yes—
20C22×C4⋊Dic13C2211yescharacteristic
21C22×C4⋊Dic13C2211yescharacteristic
22C22×C4⋊Dic13C2211yescharacteristic
23C2×#88178—24no—
24C2×#88178—24no—
25C2×#88178C418yescomplemented
26C22×#6101C2212yes—
27C22×#6101C2212yes—
28C22×C4×Dic13C2212yes—
29C4×C13×C22⋊C4—24no—
30C2×C13×#95C2211yescharacteristic
31C2×C13×#95C2211yescharacteristic
32#11718873—24no—
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35C2×#88071C2212yes—
36C2×#88071C2212yes—
37C2×#88071C2212yes—
38C2×#88071C2212yes—
39C2×#88071C2212yes—
40C4×C4⋊Dic13—24no—
41#11718590—24no—
42#11718590—24no—
43#11718589—24no—
44C25×C13C2311yescharacteristic
45C23×C4×C13—22no—
46C23×C4×C13—22no—
47C23×C4×C13—22no—
48C23×C4×C13—22no—
49C23×C4×C13—22no—
50C23×C4×C13—22no—
51C23×C4×C13C2×C414yes—
52C23×C4×C13C2311yescharacteristic
53C23×C4×C13C2311yescharacteristic
54C23×C4×C13C2311yescharacteristic
55C23×C4×C13C2311yescharacteristic
56C23×C4×C13C2311yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×Dic13C2312yes—
59C23×Dic13C2312yes—
60C23×Dic13C2312yes—
61C23×Dic13C2312yes—
62C22×Dic26—22no—
63C22×Dic26—22no—
64C22×Dic26—22no—
65C22×Dic26—22no—
66C22×Dic26—22no—
67C22×Dic26—22no—
68C22×Dic26C2×C414yes—
69C2×C13×C22⋊C4—22no—
70C2×C13×C22⋊C4—22no—
71C2×C13×C22⋊C4—22no—
72C2×C13×C22⋊C4—22no—
73C2×C13×C22⋊C4—22no—
74C2×C13×C22⋊C4Q814yescomplemented
75C2×C42×C13—22no—
76C2×C42×C13—22no—
77C2×C42×C13—22no—
78C2×C42×C13—22no—
79C2×C42×C13—22no—
80C2×C42×C13D414yes—
81C2×C22⋊Dic13—24no—
82C2×C22⋊Dic13—24no—
83C2×C22⋊Dic13—24no—
84C2×C22⋊Dic13—24no—
85C2×C22⋊Dic13—42no—
86C2×C22⋊Dic13C2×C418yes—
87C2×C4⋊Dic13—22no—
88C2×C4⋊Dic13—22no—
89C2×C4⋊Dic13—22no—
90C2×C4⋊Dic13—22no—
91C2×C4⋊Dic13—22no—
92C2×C4⋊Dic13C2×C414yes—
93C2×C4⋊Dic13D414yes—
94C2×C4⋊Dic13D414yes—
95C2×C4⋊Dic13D414yes—
96#88178—232no—
97C2×#6101—24no—
98C2×#6101—24no—
99C2×#6101—24no—
100C2×#6101—24no—
101C2×#6101—42no—
102C2×#6101C2×C418yes—
103C2×C4×Dic13—24no—
104C2×C4×Dic13—24no—
105C2×C4×Dic13—42no—
106C13×#95—22no—
107C13×#95—22no—
108#88071—24no—
109#88071—24no—
110#88071—24no—
111#88071—24no—
112#88071—24no—
113#88071—24no—
114#88071—24no—
115#13997—131nomaximal, Sylow
116C24×C13—21no—
117C24×C13—21no—
118C24×C13—21no—
119C24×C13—21no—
120C24×C13—21no—
121C24×C13—21no—
122C24×C13—21no—
123C24×C13—21no—
124C24×C13—21no—
125C24×C13—21no—
126C24×C13—21no—
127C24×C13—21no—
128C24×C13C22×C412yes—
129C24×C13C2×Q812yes—
130C24×C13#4112yes—
131C24×C13C2411yescharacteristic
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13—21no—
145C22×C4×C13—21no—
146C22×C4×C13—21no—
147C22×C4×C13—21no—
148C22×C4×C13—21no—
149C22×C4×C13—21no—
150C22×C4×C13—21no—
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13—21no—
154C22×C4×C13—21no—
155C22×C4×C13—21no—
156C22×C4×C13—21no—
157C22×C4×C13—21no—
158C22×C4×C13—21no—
159C22×C4×C13—21no—
160C22×C4×C13—28no—
161C22×C4×C13—28no—
162C22×C4×C13—28no—
163C22×C4×C13—44no—
164C22×C4×C13—44no—
165C22×C4×C13—44no—
166C22×C4×C13—44no—
167C22×C4×C13C22×C412yes—
168C22×C4×C13C22×C412yes—
169C22×C4×C13C2×D412yes—
170C22×C4×C13C2×D412yes—
171C22×C4×C13C2×D412yes—
172C22×C4×C13C2×D412yes—
173C22×C4×C13C2×D412yes—
174C22×C4×C13C2×D412yes—
175C22×C4×C13C2×Q812yes—
176C22×C4×C13C2×Q812yes—
177C22×C4×C13#4112yes—
178C22×C4×C13#4112yes—
179C22×C4×C13#4112yes—
180C22×C4×C13#4112yes—
181C22×Dic13—22no—
182C22×Dic13—22no—
183C22×Dic13—22no—
184C22×Dic13—22no—
185C22×Dic13—22no—
186C22×Dic13—22no—
187C22×Dic13—22no—
188C22×Dic13—22no—
189C22×Dic13—22no—
190C22×Dic13—22no—
191C22×Dic13—22no—
192C22×Dic13—22no—
193C22×Dic13—22no—
194C22×Dic13—22no—
195C22×Dic13—22no—
196C22×Dic13—22no—
197C22×Dic13—22no—
198C22×Dic13—22no—
199C22×Dic13—22no—
200C22×Dic13—22no—
201C22×Dic13—22no—
202C22×Dic13—22no—
203C22×Dic13—22no—
204C22×Dic13C22×C414yes—
205C22×Dic13C22×C414yes—
206C22×Dic13C2×D414yes—
207C22×Dic13C2×D414yes—
208C22×Dic13C2×D414yes—
209C2×Dic26—28no—
210C2×Dic26—28no—
211C2×Dic26—28no—
212C2×Dic26—44no—
213C2×Dic26—44no—
214C2×Dic26—44no—
215C2×Dic26—44no—
216C13×C22⋊C4—28no—
217C13×C22⋊C4—28no—
218C42×C13—28no—
219C42×C13—44no—
220C22⋊Dic13—216no—
221C22⋊Dic13—48no—
222C4⋊Dic13—28no—
223C4⋊Dic13—44no—
224C4⋊Dic13C22⋊C4116yescomplemented
225#6101—216no—
226#6101—48no—
227C4×Dic13—48no—
228C22×C22⋊Q8—131no—
229C2×#391—131no—
230C2×#391—131no—
231C2×#389—131no—
232C2×#380—131no—
233C2×C4×C4⋊C4—131no—
234C2×C4×C22⋊C4D1311yescharacteristic
235#1445—132no—
236#1439—132no—
237#1437—132no—
238C4⋊#95—132no—
239C23×C13—22no—
240C23×C13—22no—
241C23×C13—22no—
242C23×C13—22no—
243C23×C13—22no—
244C23×C13—22no—
245C23×C13—22no—
246C23×C13—22no—
247C23×C13—22no—
248C23×C13—22no—
249C23×C13—22no—
250C23×C13—22no—
251C23×C13—22no—
252C23×C13—22no—
253C23×C13—22no—
254C23×C13—22no—
255C23×C13—22no—
256C23×C13—22no—
257C23×C13—41no—
258C23×C13—41no—
259C23×C13—41no—
260C23×C13—41no—
261C23×C13—41no—
262C23×C13—41no—
263C23×C13—41no—
264C23×C13—41no—
265C23×C13—41no—
266C23×C13—41no—
267C23×C13—41no—
268C23×C13—41no—
269C23×C13—41no—
270C23×C13—41no—
271C23×C13—41no—
272C23×C13—41no—
273C23×C13C4×Q814yes—
274C23×C13C23×C411yescharacteristic
275C23×C13C22×D411yescharacteristic
276C23×C13C22×D411yescharacteristic
277C23×C13C22×D411yescharacteristic
278C23×C13C22×D411yescharacteristic
279C23×C13C22×Q811yescharacteristic
280C23×C13C2×#4111yescharacteristic
281C23×C13C2×#4111yescharacteristic
282C23×C13C2×#4111yescharacteristic
283C23×C13C2×#4111yescharacteristic
284C23×C13C2×#4111yescharacteristic
285C23×C13H(5,𝔽2)11yescharacteristic
286C23×C132−1+411yescharacteristic
287C23×C132−1+411yescharacteristic
288C23×C132−1+411yescharacteristic
289C2×C4×C13—22no—
290C2×C4×C13—22no—
291C2×C4×C13—22no—
292C2×C4×C13—22no—
293C2×C4×C13—22no—
294C2×C4×C13—22no—
295C2×C4×C13—22no—
296C2×C4×C13—22no—
297C2×C4×C13—22no—
298C2×C4×C13—22no—
299C2×C4×C13—22no—
300C2×C4×C13—22no—
301C2×C4×C13—22no—
302C2×C4×C13—22no—
303C2×C4×C13—22no—
304C2×C4×C13—22no—
305C2×C4×C13—22no—
306C2×C4×C13—22no—
307C2×C4×C13—41no—
308C2×C4×C13—41no—
309C2×C4×C13—41no—
310C2×C4×C13—41no—
311C2×C4×C13—41no—
312C2×C4×C13—41no—
313C2×C4×C13—41no—
314C2×C4×C13—41no—
315C2×C4×C13—41no—
316C2×C4×C13—41no—
317C2×C4×C13—41no—
318C2×C4×C13—41no—
319C2×C4×C13—41no—
320C2×C4×C13—41no—
321C2×C4×C13—41no—
322C2×C4×C13—41no—
323C2×C4×C13—416no—
324C2×C4×C13C2×C22⋊C414yes—
325C2×C4×C13C4×D414yes—
326C2×C4×C13C4×D414yes—
327C2×C4×C13#12114yes—
328C2×C4×C13#12114yes—
329C2×C4×C13C22⋊Q814yescomplemented
330C2×C4×C13#12414yes—
331C2×C4×C13#12714yes—
332C2×Dic13—24no—
333C2×Dic13—24no—
334C2×Dic13—24no—
335C2×Dic13—24no—
336C2×Dic13—24no—
337C2×Dic13—24no—
338C2×Dic13—24no—
339C2×Dic13—24no—
340C2×Dic13—24no—
341C2×Dic13—24no—
342C2×Dic13—24no—
343C2×Dic13—24no—
344C2×Dic13—42no—
345C2×Dic13—42no—
346C2×Dic13—42no—
347C2×Dic13—42no—
348C2×Dic13—42no—
349C2×Dic13—42no—
350C2×Dic13—42no—
351C2×Dic13—42no—
352C2×Dic13—42no—
353C2×Dic13—42no—
354C2×Dic13—42no—
355C2×Dic13—42no—
356C2×Dic13—42no—
357C2×Dic13—42no—
358C2×Dic13—42no—
359C2×Dic13C2×C22⋊C418yes—
360Dic26—416no—
361C23×Q8—131no—
362C24×C4C2×D1311yescharacteristic
363C2×C22⋊Q8—138no—
364C2×C22⋊Q8—264no—
365C2×C22⋊Q8—264no—
366C22×C4⋊C4—131no—
367C22×C4⋊C4—132no—
368C22×C4⋊C4—131no—
369C22×C4⋊C4—131no—
370C22×C4⋊C4—132no—
371C22×C22⋊C4—132no—
372C22×C22⋊C4—132no—
373C22×C22⋊C4C2×D1311yescharacteristic
374C22×C22⋊C4C2×D1311yescharacteristic
375C22×C42—132no—
376C22×C42C2×D1311yescharacteristic
377C22×C42C2×D1311yescharacteristic
378#391—264no—
379#391—264no—
380#389—264no—
381#380—264no—
382C4×C4⋊C4—264no—
383C4×C22⋊C4—24no—
384C2×#95—132no—
385C2×#95—132no—
386C2×#95—132no—
387C2×#95—132no—
388C2×#95—132no—
389C2×#95—132no—
390C2×#95—132no—
391C2×#95C2×D1311yescharacteristic
392C2×#95C2×D1311yescharacteristic
393C22×C13—24no—
394C22×C13—24no—
395C22×C13—24no—
396C22×C13—42no—
397C22×C13—42no—
398C22×C13—42no—
399C22×C13—42no—
400C22×C13—42no—
401C22×C13—42no—
402C22×C13—42no—
403C22×C13—42no—
404C22×C13—42no—
405C22×C13—42no—
406C22×C13—42no—
407C22×C13—42no—
408C22×C13C22×C22⋊C411yescharacteristic
409C22×C13C2×C4×D411yescharacteristic
410C22×C13C2×C4×D411yescharacteristic
411C22×C13C2×C4×Q811yescharacteristic
412C22×C13C4×#4111yescharacteristic
413C22×C13#51911yescharacteristic
414C22×C13#52011yescharacteristic
415C22×C13C2×#12111yescharacteristic
416C22×C13C2×#12111yescharacteristic
417C22×C13C2×C22⋊Q811yescharacteristic
418C22×C13#52511yescharacteristic
419C22×C13C2×#12411yescharacteristic
420C22×C13#52911yescharacteristic
421C22×C13C2×#12711yescharacteristic
422C22×C13#53311yescharacteristic
423C22×C13#53611yescharacteristic
424C22×C13#53711yescharacteristic
425C22×C13#54111yescharacteristic
426C22×C13#54211yescharacteristic
427C22×C13#54611yescharacteristic
428C22×C13#54611yescharacteristic
429C22×C13#54611yescharacteristic
430C22×C13#54711yescharacteristic
431C22×C13#54711yescharacteristic
432C22×C13#54711yescharacteristic
433C22×C13#54811yescharacteristic
434C22×C13#54811yescharacteristic
435C22×C13#54811yescharacteristic
436C22×C13D4×Q811yescharacteristic
437C22×C13D4×Q811yescharacteristic
438C22×C13D4×Q811yescharacteristic
439C22×C13#55211yescharacteristic
440C22×C13#55211yescharacteristic
441C22×C13#55411yescharacteristic
442C22×C13#55611yescharacteristic
443C4×C13—24no—
444C4×C13—42no—
445C4×C13—42no—
446C4×C13—42no—
447C4×C13—42no—
448C4×C13#39018yes—
449Dic13—28no—
450Dic13—44no—
451Dic13—44no—
452Dic13—82no—
453C25C22×D1311yescharacteristic
454C22×Q8—134no—
455C22×Q8—262no—
456C22×Q8—262no—
457C22×Q8—262no—
458C22×Q8—262no—
459C22×Q8—262no—
460C22×Q8—262no—
461C23×C4—22no—
462C23×C4—22no—
463C23×C4—22no—
464C23×C4—22no—
465C23×C4—22no—
466C23×C4—22no—
467C23×C4—132no—
468C23×C4—132no—
469C23×C4—132no—
470C23×C4—132no—
471C23×C4C4×D1314yes—
472C23×C4C22×D1311yescharacteristic
473C23×C4C22×D1311yescharacteristic
474C23×C4C22×D1311yescharacteristic
475C23×C4C22×D1311yescharacteristic
476C23×C4C22×D1311yescharacteristic
477C23×C4C22×D1311yescharacteristic
478C22⋊Q8—2632no—
479C2×C4⋊C4—134no—
480C2×C4⋊C4—134no—
481C2×C4⋊C4—134no—
482C2×C4⋊C4—138no—
483C2×C4⋊C4—134no—
484C2×C4⋊C4—264no—
485C2×C4⋊C4—264no—
486C2×C4⋊C4—262no—
487C2×C4⋊C4—262no—
488C2×C4⋊C4—264no—
489C2×C4⋊C4—264no—
490C2×C4⋊C4—262no—
491C2×C4⋊C4—262no—
492C2×C4⋊C4—262no—
493C2×C4⋊C4—522no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—138no—
500C2×C22⋊C4—264no—
501C2×C22⋊C4—264no—
502C2×C22⋊C4—264no—
503C2×C22⋊C4—264no—
504C2×C22⋊C4—522no—
505C2×C22⋊C4Dic2614yescomplemented
506C2×C42—22no—
507C2×C42—22no—
508C2×C42—22no—
509C2×C42—22no—
510C2×C42—22no—
511C2×C42—264no—
512C2×C42—264no—
513C2×C42—522no—
514C2×C42C22⋊D1314yes—
515#95—22no—
516#95—22no—
517#95—264no—
518#95—264no—
519#95—264no—
520#95—264no—
521#95—264no—
522#95—264no—
523#95—264no—
524C2×C13—44no—
525C2×C13C2×#39011yescharacteristic
526C2×C13C4×C22⋊Q811yescharacteristic
527C2×C13#232311yescharacteristic
528C2×C13#233911yescharacteristic
529C2×C13Q8×C22⋊C411yescharacteristic
530C2×C13#236011yescharacteristic
531C2×C13#236211yescharacteristic
532C2×C13#241511yescharacteristic
533C2×C13#241711yescharacteristic
534C2×C13#242711yescharacteristic
535C2×C13#242911yescharacteristic
536C2×C13#248911yescharacteristic
537C2×C13#249211yescharacteristic
538C2×C13#254011yescharacteristic
539C2×C13#254211yescharacteristic
540C24—21no—
541C24—21no—
542C24—21no—
543C24—21no—
544C24—21no—
545C24—21no—
546C24—21no—
547C24—21no—
548C24—21no—
549C24—21no—
550C24—21no—
551C24—21no—
552C24C2×Dic2612yes—
553C24C2×C4×D1312yes—
554C24#612712yes—
555C24C23×D1311yescharacteristic
556C2×Q8—268no—
557C2×Q8—268no—
558C2×Q8—268no—
559C2×Q8—524no—
560C2×Q8—524no—
561C2×Q8—524no—
562C2×Q8—524no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—28no—
592C22×C4—28no—
593C22×C4—28no—
594C22×C4—44no—
595C22×C4—44no—
596C22×C4—44no—
597C22×C4—44no—
598C22×C4—134no—
599C22×C4—134no—
600C22×C4—134no—
601C22×C4—134no—
602C22×C4—134no—
603C22×C4—262no—
604C22×C4—262no—
605C22×C4—262no—
606C22×C4—262no—
607C22×C4—262no—
608C22×C4—262no—
609C22×C4—262no—
610C22×C4—262no—
611C22×C4—262no—
612C22×C4—262no—
613C22×C4—262no—
614C22×C4—262no—
615C22×C4—262no—
616C22×C4—262no—
617C22×C4—262no—
618C22×C4—262no—
619C22×C4—262no—
620C22×C4—262no—
621C22×C4—262no—
622C22×C4—262no—
623C22×C4—262no—
624C22×C4—262no—
625C22×C4—262no—
626C22×C4C2×Dic2612yes—
627C22×C4C2×Dic2612yes—
628C22×C4C2×C4×D1312yes—
629C22×C4C2×C4×D1312yes—
630C22×C4#612712yes—
631C22×C4#612712yes—
632C22×C4#612712yes—
633C22×C4D4×D1312yes—
634C22×C4D4×D1312yes—
635C22×C4D4×D1312yes—
636C22×C4#612912yes—
637C22×C4C2×C22⋊D1312yes—
638C22×C4C2×C22⋊D1312yes—
639C22×C4C2×C22⋊D1312yes—
640C4⋊C4—1316no—
641C4⋊C4—2616no—
642C4⋊C4—268no—
643C4⋊C4—528no—
644C4⋊C4—524no—
645C22⋊C4—28no—
646C22⋊C4—28no—
647C22⋊C4—2616no—
648C22⋊C4—528no—
649C42—28no—
650C42—44no—
651C42—528no—
652C13#1399711yescharacteristic, complemented, Sylow
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23C4×Dic2614yes—
688C23C22×Dic2611yescharacteristic
689C23C22×C4×D1311yescharacteristic
690C23C2×#612711yescharacteristic
691C23C2×#612711yescharacteristic
692C23C2×#612711yescharacteristic
693C23C2×#612711yescharacteristic
694C23C2×D4×D1311yescharacteristic
695C23C2×D4×D1311yescharacteristic
696C23C2×D4×D1311yescharacteristic
697C23C2×#612911yescharacteristic
698C23#8825611yescharacteristic
699C23#8825711yescharacteristic
700C23#8825711yescharacteristic
701C23#8825711yescharacteristic
702C23C22×C22⋊D1311yescharacteristic
703Q8—5216no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—416no—
739C2×C4—138no—
740C2×C4—264no—
741C2×C4—264no—
742C2×C4—264no—
743C2×C4—264no—
744C2×C4—264no—
745C2×C4—264no—
746C2×C4—264no—
747C2×C4—264no—
748C2×C4—264no—
749C2×C4—264no—
750C2×C4—264no—
751C2×C4—264no—
752C2×C4—522no—
753C2×C4—522no—
754C2×C4—522no—
755C2×C4—522no—
756C2×C4—522no—
757C2×C4—522no—
758C2×C4—522no—
759C2×C4—522no—
760C2×C4—522no—
761C2×C4—522no—
762C2×C4—522no—
763C2×C4—522no—
764C2×C4—522no—
765C2×C4—522no—
766C2×C4—522no—
767C2×C4C22⋊C4×D1314yes—
768C2×C4#8813514yes—
769C2×C4#8813814yes—
770C2×C4#8813914yes—
771C2×C4#8817814yescomplemented
772C2×C4C4×C22⋊D1314yes—
773C2×C4#8819314yes—
774C2×C4#8819414yes—
775C22—24no—
776C22—24no—
777C22—24no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22C2×C4×Dic2611yescharacteristic
791C22#1171917511yescharacteristic
792C22C4×#612711yescharacteristic
793C22#1171918411yescharacteristic
794C22C2×C22⋊C4×D1311yescharacteristic
795C22C2×#8813511yescharacteristic
796C22C2×#8813811yescharacteristic
797C22C2×#8813911yescharacteristic
798C22#1171922111yescharacteristic
799C22#1171922311yescharacteristic
800C22#1171922811yescharacteristic
801C22#1171923911yescharacteristic
802C22D4×Dic2611yescharacteristic
803C22D4×Dic2611yescharacteristic
804C22D4×Dic2611yescharacteristic
805C22#1171924611yescharacteristic
806C22#1171924611yescharacteristic
807C22#1171924711yescharacteristic
808C22#1171924811yescharacteristic
809C22#1171925511yescharacteristic
810C22#1171925511yescharacteristic
811C22#1171925511yescharacteristic
812C22#1171925611yescharacteristic
813C22#1171925611yescharacteristic
814C22#1171925611yescharacteristic
815C22#1171925711yescharacteristic
816C22#1171925711yescharacteristic
817C22#1171925711yescharacteristic
818C22C2×#8817811yescharacteristic
819C22C2×C4×C22⋊D1311yescharacteristic
820C22#1171949611yescharacteristic
821C22C2×#8819311yescharacteristic
822C22C2×#8819411yescharacteristic
823C22#1171953011yescharacteristic
824C22#1171953811yescharacteristic
825C4—24no—
826C4—42no—
827C4—42no—
828C4—42no—
829C4—42no—
830C4—268no—
831C4—524no—
832C4—524no—
833C4—1042no—
834C4#1171861818yes—
835C2—44no—
836C2C2×#1171861811yescharacteristic
837C2C4×#8817811yescharacteristic
838C2#1311751811yescharacteristic
839C2#1311766711yescharacteristic
840C2C22⋊C4×Dic2611yescharacteristic
841C2#1311783911yescharacteristic
842C2#1311786111yescharacteristic
843C2#1311826511yescharacteristic
844C2#1311828711yescharacteristic
845C2#1311841311yescharacteristic
846C2#1311843511yescharacteristic
847C2#1311917711yescharacteristic
848C2#1311921011yescharacteristic
849C2#1311977511yescharacteristic
850C2#1311978911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C4×C13×C22⋊C4C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC2×C4×C22⋊C4D13
hypocenterC13#13997
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#11718590C2semidirect
3. C2×#11718590C2semidirect
4. C2×#11718589C2semidirect
6. C2×C4×C4⋊Dic13C2semidirect
7. #13113102C2semidirect
10. #13113064C2semidirect
25. C2×#88178C4semidirect
74. C2×C13×C22⋊C4Q8semidirect
224. C4⋊Dic13C22⋊C4semidirect
329. C2×C4×C13C22⋊Q8semidirect
505. C2×C22⋊C4Dic26semidirect
652. C13#13997semidirect
771. C2×C4#88178semidirect

Maximal subgroups

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

subgroupindex
C22×#881782
C2×#117185902
C2×#117185892
C2×#117188732
C2×C4×C4⋊Dic132
#131131022
#131130792
#131130732
#131130642
C2×C4×C13×C22⋊C42
#1399713