Finite Group Databasebeta

← #15785713

Subgroups — #15785713

Order 3328.

2266 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88178C211yesmaximal, characteristic
2C22×C4×Dic26C211yesmaximal, characteristic, complemented
3C2×#11718590C211yesmaximal, characteristic, complemented
4C2×#11718873C211yesmaximal, characteristic
5#13113087C212yesmaximal, complemented
6#13113079C212yesmaximal
7#13113073C212yesmaximal
8#13113067C212yesmaximal, complemented
9#13113066C211yesmaximal, characteristic, complemented
10#13113066C211yesmaximal, characteristic, 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—
29C2×C4×Dic26—24no—
30C2×C4×Dic26—24no—
31C2×C4×Dic26—24no—
32C4×C13×C22⋊C4—24no—
33C2×C13×#95C2211yescharacteristic
34C2×C13×#95C2211yescharacteristic
35#11718873—24no—
36C2×#88071C2212yes—
37C2×#88071C2212yes—
38C2×#88071C2212yes—
39C2×#88071C2212yes—
40C2×#88071C2212yes—
41C2×#88071C2212yes—
42C2×#88071C2212yes—
43#11718590—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×Dic26C2×C414yes—
67C22×Dic26D414yes—
68C22×Dic26D414yes—
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⋊Dic13—22no—
93C2×C4⋊Dic13—22no—
94C2×C4⋊Dic13C2×C414yes—
95C2×C4⋊Dic13D414yes—
96#88178—232no—
97C2×#6101—24no—
98C2×#6101—24no—
99C2×#6101—24no—
100C2×#6101—24no—
101C2×#6101—24no—
102C2×#6101C2×C418yes—
103C2×C4×Dic13—24no—
104C2×C4×Dic13—24no—
105C2×C4×Dic13—24no—
106C4×Dic26—232no—
107C13×#95—22no—
108C13×#95—22no—
109#88071—24no—
110#88071—24no—
111#88071—24no—
112#88071—24no—
113#88071—24no—
114#88071—42no—
115#88071—42no—
116#13969—131nomaximal, Sylow
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×C13—21no—
129C24×C13C22×C412yes—
130C24×C13C2×Q812yes—
131C24×C13#4112yes—
132C24×C13C2411yescharacteristic
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—21no—
161C22×C4×C13—28no—
162C22×C4×C13—28no—
163C22×C4×C13—28no—
164C22×C4×C13—44no—
165C22×C4×C13—44no—
166C22×C4×C13—44no—
167C22×C4×C13—44no—
168C22×C4×C13C22×C412yes—
169C22×C4×C13C22×C412yes—
170C22×C4×C13C2×D412yes—
171C22×C4×C13C2×D412yes—
172C22×C4×C13C2×D412yes—
173C22×C4×C13C2×D412yes—
174C22×C4×C13C2×D412yes—
175C22×C4×C13C2×D412yes—
176C22×C4×C13C2×Q812yes—
177C22×C4×C13C2×Q812yes—
178C22×C4×C13#4112yes—
179C22×C4×C13#4112yes—
180C22×C4×C13#4112yes—
181C22×C4×C13#4112yes—
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×Dic13—22no—
205C22×Dic13C22×C414yes—
206C22×Dic13C22×C414yes—
207C22×Dic13C2×D414yes—
208C22×Dic13C2×D414yes—
209C22×Dic13C2×D414yes—
210C2×Dic26—28no—
211C2×Dic26—28no—
212C2×Dic26—28no—
213C2×Dic26—28no—
214C2×Dic26—28no—
215C2×Dic26—28no—
216C2×Dic26C22⋊C4116yescomplemented
217C13×C22⋊C4—28no—
218C13×C22⋊C4—28no—
219C42×C13—28no—
220C42×C13—44no—
221C22⋊Dic13—216no—
222C22⋊Dic13—48no—
223C4⋊Dic13—28no—
224C4⋊Dic13—28no—
225C4⋊Dic13—44no—
226#6101—216no—
227#6101—216no—
228C4×Dic13—216no—
229C22×C22⋊Q8—131no—
230C22×C4×Q8—131no—
231C2×#391—131no—
232C2×#380—131no—
233C2×C4×C22⋊C4D1311yescharacteristic
234#1441—132no—
235#1439—132no—
236#1437—132no—
237#1436—132no—
238C4⋊#95—131no—
239C4⋊#95—131no—
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—22no—
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×C13—41no—
274C23×C13C4×Q814yescomplemented
275C23×C13C23×C411yescharacteristic
276C23×C13C22×D411yescharacteristic
277C23×C13C22×D411yescharacteristic
278C23×C13C22×D411yescharacteristic
279C23×C13C22×D411yescharacteristic
280C23×C13C22×Q811yescharacteristic
281C23×C13C2×#4111yescharacteristic
282C23×C13C2×#4111yescharacteristic
283C23×C13C2×#4111yescharacteristic
284C23×C13C2×#4111yescharacteristic
285C23×C13C2×#4111yescharacteristic
286C23×C13H(5,𝔽2)11yescharacteristic
287C23×C132−1+411yescharacteristic
288C23×C132−1+411yescharacteristic
289C23×C132−1+411yescharacteristic
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—22no—
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—41no—
324C2×C4×C13—416no—
325C2×C4×C13C2×C22⋊C414yes—
326C2×C4×C13C4×D414yes—
327C2×C4×C13C4×D414yes—
328C2×C4×C13#12014yes—
329C2×C4×C13#12114yes—
330C2×C4×C13#12114yes—
331C2×C4×C13C22⋊Q814yescomplemented
332C2×C4×C13#12314yes—
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—24no—
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×Dic13—42no—
360C2×Dic13C2×C22⋊C418yes—
361Dic26—232no—
362C23×Q8—131no—
363C24×C4C2×D1311yescharacteristic
364C2×C22⋊Q8—138no—
365C2×C22⋊Q8—264no—
366C2×C22⋊Q8—264no—
367C2×C4×Q8—264no—
368C2×C4×Q8—264no—
369C2×C4×Q8—264no—
370C22×C4⋊C4—132no—
371C22×C4⋊C4—131no—
372C22×C4⋊C4—131no—
373C22×C4⋊C4—132no—
374C22×C4⋊C4—131no—
375C22×C22⋊C4—132no—
376C22×C22⋊C4—132no—
377C22×C22⋊C4C2×D1311yescharacteristic
378C22×C22⋊C4C2×D1311yescharacteristic
379C22×C42—132no—
380C22×C42C2×D1311yescharacteristic
381C22×C42C2×D1311yescharacteristic
382#391—264no—
383#380—264no—
384C4×C22⋊C4—24no—
385C2×#95—132no—
386C2×#95—132no—
387C2×#95—132no—
388C2×#95—132no—
389C2×#95—132no—
390C2×#95—132no—
391C2×#95—132no—
392C2×#95C2×D1311yescharacteristic
393C2×#95C2×D1311yescharacteristic
394C22×C13—24no—
395C22×C13—24no—
396C22×C13—24no—
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×C13—42no—
409C22×C13C22×C22⋊C411yescharacteristic
410C22×C13C2×C4×D411yescharacteristic
411C22×C13C2×C4×D411yescharacteristic
412C22×C13C2×C4×Q811yescharacteristic
413C22×C13C4×#4111yescharacteristic
414C22×C13#51911yescharacteristic
415C22×C13#52011yescharacteristic
416C22×C13C2×#12011yescharacteristic
417C22×C13C2×#12111yescharacteristic
418C22×C13C2×#12111yescharacteristic
419C22×C13C2×C22⋊Q811yescharacteristic
420C22×C13C2×#12311yescharacteristic
421C22×C13#52511yescharacteristic
422C22×C13#52911yescharacteristic
423C22×C13#53311yescharacteristic
424C22×C13#53611yescharacteristic
425C22×C13#53711yescharacteristic
426C22×C13#54111yescharacteristic
427C22×C13#54211yescharacteristic
428C22×C13#54611yescharacteristic
429C22×C13#54711yescharacteristic
430C22×C13#54811yescharacteristic
431C22×C13#54811yescharacteristic
432C22×C13#54811yescharacteristic
433C22×C13#54811yescharacteristic
434C22×C13#54811yescharacteristic
435C22×C13D4×Q811yescharacteristic
436C22×C13D4×Q811yescharacteristic
437C22×C13D4×Q811yescharacteristic
438C22×C13#55011yescharacteristic
439C22×C13#55011yescharacteristic
440C22×C13#55211yescharacteristic
441C22×C13#55211yescharacteristic
442C22×C13#55411yescharacteristic
443C22×C13#55611yescharacteristic
444C4×C13—24no—
445C4×C13—42no—
446C4×C13—42no—
447C4×C13—42no—
448C4×C13—42no—
449C4×C13#38618yes—
450Dic13—28no—
451Dic13—44no—
452Dic13—44no—
453Dic13—82no—
454C25C22×D1311yescharacteristic
455C22×Q8—134no—
456C22×Q8—134no—
457C22×Q8—134no—
458C22×Q8—262no—
459C22×Q8—262no—
460C22×Q8—262no—
461C22×Q8—262no—
462C23×C4—22no—
463C23×C4—22no—
464C23×C4—22no—
465C23×C4—22no—
466C23×C4—22no—
467C23×C4—22no—
468C23×C4—132no—
469C23×C4—132no—
470C23×C4—132no—
471C23×C4—132no—
472C23×C4C4×D1314yes—
473C23×C4C22×D1311yescharacteristic
474C23×C4C22×D1311yescharacteristic
475C23×C4C22×D1311yescharacteristic
476C23×C4C22×D1311yescharacteristic
477C23×C4C22×D1311yescharacteristic
478C23×C4C22×D1311yescharacteristic
479C22⋊Q8—2632no—
480C4×Q8—2632no—
481C2×C4⋊C4—138no—
482C2×C4⋊C4—134no—
483C2×C4⋊C4—134no—
484C2×C4⋊C4—264no—
485C2×C4⋊C4—264no—
486C2×C4⋊C4—264no—
487C2×C4⋊C4—264no—
488C2×C4⋊C4—262no—
489C2×C4⋊C4—262no—
490C2×C4⋊C4—262no—
491C2×C4⋊C4—264no—
492C2×C4⋊C4—262no—
493C2×C4⋊C4—262no—
494C2×C4⋊C4—262no—
495C2×C4⋊C4—262no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—138no—
502C2×C22⋊C4—264no—
503C2×C22⋊C4—264no—
504C2×C22⋊C4—264no—
505C2×C22⋊C4—264no—
506C2×C22⋊C4—522no—
507C2×C22⋊C4Dic2614yescomplemented
508C2×C42—22no—
509C2×C42—22no—
510C2×C42—22no—
511C2×C42—22no—
512C2×C42—22no—
513C2×C42—264no—
514C2×C42—264no—
515C2×C42—264no—
516C2×C42C22⋊D1314yes—
517#95—22no—
518#95—22no—
519#95—264no—
520#95—264no—
521#95—264no—
522#95—264no—
523#95—264no—
524#95—522no—
525#95—522no—
526C2×C13—44no—
527C2×C13C2×#38611yescharacteristic
528C2×C13C4×C22⋊Q811yescharacteristic
529C2×C13#232311yescharacteristic
530C2×C13Q8×C22⋊C411yescharacteristic
531C2×C13#234111yescharacteristic
532C2×C13#236011yescharacteristic
533C2×C13#236211yescharacteristic
534C2×C13#240711yescharacteristic
535C2×C13#240911yescharacteristic
536C2×C13#242111yescharacteristic
537C2×C13#242311yescharacteristic
538C2×C13#242611yescharacteristic
539C2×C13#242911yescharacteristic
540C2×C13#253611yescharacteristic
541C2×C13#253811yescharacteristic
542C24—21no—
543C24—21no—
544C24—21no—
545C24—21no—
546C24—21no—
547C24—21no—
548C24—21no—
549C24—21no—
550C24—21no—
551C24—21no—
552C24—21no—
553C24—21no—
554C24C2×Dic2612yes—
555C24C2×C4×D1312yes—
556C24#612712yes—
557C24C23×D1311yescharacteristic
558C2×Q8—1316no—
559C2×Q8—268no—
560C2×Q8—268no—
561C2×Q8—268no—
562C2×Q8—268no—
563C2×Q8—268no—
564C2×Q8—268no—
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—21no—
592C22×C4—21no—
593C22×C4—28no—
594C22×C4—28no—
595C22×C4—28no—
596C22×C4—44no—
597C22×C4—44no—
598C22×C4—44no—
599C22×C4—44no—
600C22×C4—134no—
601C22×C4—134no—
602C22×C4—134no—
603C22×C4—134no—
604C22×C4—134no—
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×C4—262no—
627C22×C4—262no—
628C22×C4C2×Dic2612yes—
629C22×C4C2×Dic2612yes—
630C22×C4C2×C4×D1312yes—
631C22×C4C2×C4×D1312yes—
632C22×C4#612712yes—
633C22×C4#612712yes—
634C22×C4#612712yes—
635C22×C4D4×D1312yes—
636C22×C4D4×D1312yes—
637C22×C4D4×D1312yes—
638C22×C4#612912yes—
639C22×C4C2×C22⋊D1312yes—
640C22×C4C2×C22⋊D1312yes—
641C22×C4C2×C22⋊D1312yes—
642C4⋊C4—2616no—
643C4⋊C4—2616no—
644C4⋊C4—268no—
645C4⋊C4—268no—
646C4⋊C4—524no—
647C22⋊C4—28no—
648C22⋊C4—28no—
649C22⋊C4—2616no—
650C22⋊C4—528no—
651C42—28no—
652C42—44no—
653C42—2616no—
654C13#1396911yescharacteristic, complemented, Sylow
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—22no—
672C23—22no—
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—
687C23—41no—
688C23—41no—
689C23C4×Dic2614yescomplemented
690C23C22×Dic2611yescharacteristic
691C23C22×C4×D1311yescharacteristic
692C23C2×#612711yescharacteristic
693C23C2×#612711yescharacteristic
694C23C2×#612711yescharacteristic
695C23C2×#612711yescharacteristic
696C23C2×D4×D1311yescharacteristic
697C23C2×D4×D1311yescharacteristic
698C23C2×D4×D1311yescharacteristic
699C23C2×#612911yescharacteristic
700C23#8825611yescharacteristic
701C23#8825711yescharacteristic
702C23#8825711yescharacteristic
703C23#8825711yescharacteristic
704C23C22×C22⋊D1311yescharacteristic
705Q8—2632no—
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—22no—
723C2×C4—22no—
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—41no—
739C2×C4—41no—
740C2×C4—416no—
741C2×C4—138no—
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—264no—
753C2×C4—264no—
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×C4—522no—
768C2×C4—522no—
769C2×C4C22⋊C4×D1314yes—
770C2×C4#8813514yes—
771C2×C4#8813714yes—
772C2×C4#8813814yes—
773C2×C4#8817814yescomplemented
774C2×C4C4×C22⋊D1314yes—
775C2×C4#8819114yes—
776C2×C4#8819214yes—
777C22—24no—
778C22—24no—
779C22—24no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22C2×C4×Dic2611yescharacteristic
793C22#1171917511yescharacteristic
794C22C4×#612711yescharacteristic
795C22#1171918411yescharacteristic
796C22C2×C22⋊C4×D1311yescharacteristic
797C22C2×#8813511yescharacteristic
798C22C2×#8813711yescharacteristic
799C22C2×#8813811yescharacteristic
800C22#1171922111yescharacteristic
801C22#1171922311yescharacteristic
802C22#1171922811yescharacteristic
803C22#1171923911yescharacteristic
804C22D4×Dic2611yescharacteristic
805C22D4×Dic2611yescharacteristic
806C22D4×Dic2611yescharacteristic
807C22#1171924611yescharacteristic
808C22#1171924611yescharacteristic
809C22#1171924711yescharacteristic
810C22#1171924811yescharacteristic
811C22#1171925511yescharacteristic
812C22#1171925611yescharacteristic
813C22#1171925711yescharacteristic
814C22#1171925711yescharacteristic
815C22#1171925711yescharacteristic
816C22#1171925711yescharacteristic
817C22#1171925711yescharacteristic
818C22#1171925811yescharacteristic
819C22#1171925811yescharacteristic
820C22C2×#8817811yescharacteristic
821C22C2×C4×C22⋊D1311yescharacteristic
822C22#1171949611yescharacteristic
823C22C2×#8819111yescharacteristic
824C22C2×#8819211yescharacteristic
825C22#1171953011yescharacteristic
826C22#1171953811yescharacteristic
827C4—24no—
828C4—42no—
829C4—42no—
830C4—42no—
831C4—42no—
832C4—268no—
833C4—524no—
834C4—524no—
835C4—1042no—
836C4#1171861718yes—
837C2—44no—
838C2C2×#1171861711yescharacteristic
839C2C4×#8817811yescharacteristic
840C2#1311751811yescharacteristic
841C2C22⋊C4×Dic2611yescharacteristic
842C2#1311767611yescharacteristic
843C2#1311783911yescharacteristic
844C2#1311786111yescharacteristic
845C2#1311818111yescharacteristic
846C2#1311820111yescharacteristic
847C2#1311833911yescharacteristic
848C2#1311836111yescharacteristic
849C2#1311840211yescharacteristic
850C2#1311843511yescharacteristic
851C2#1311974511yescharacteristic
852C2#1311975811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C4×C13×C22⋊C4C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC2×C4×C22⋊C4D13
hypocenterC13#13969
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. C22×C4×Dic26C2semidirect
3. C2×#11718590C2semidirect
5. #13113087C2semidirect
8. #13113067C2semidirect
9. #13113066C2semidirect
10. #13113066C2semidirect
25. C2×#88178C4semidirect
74. C2×C13×C22⋊C4Q8semidirect
216. C2×Dic26C22⋊C4semidirect
274. C23×C13C4×Q8semidirect
331. C2×C4×C13C22⋊Q8semidirect
507. C2×C22⋊C4Dic26semidirect
654. C13#13969semidirect
689. C23C4×Dic26semidirect
773. 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
C22×C4×Dic262
C2×#117185902
C2×#117188732
#131130872
#131130792
#131130732
#131130672
#131130662
C2×C4×C13×C22⋊C42
#1396913