Finite Group Databasebeta

← #15786301

Subgroups — #15786301

Order 3328.

1810 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88141C211yesmaximal, characteristic
2C2×#11718590C211yesmaximal, characteristic
3C2×#11718635C211yesmaximal, characteristic
4C2×#11718634C211yesmaximal, characteristic
5C2×C4×C4⋊Dic13C211yesmaximal, characteristic
6#13113100C212yesmaximal
7#13113091C212yesmaximal
8#13113071C212yesmaximal
9#13113070C212yesmaximal
10#13113065C211yesmaximal, characteristic
11C13×C4⋊#95C211yesmaximal, characteristic
12C23×Dic26C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C4⋊C4C2211yescharacteristic
15C22×C42×C13C2211yescharacteristic
16C22×C4⋊Dic13C2211yescharacteristic
17C22×C4⋊Dic13C2211yescharacteristic
18C22×C4⋊Dic13C2211yescharacteristic
19C22×#6101C2212yes—
20C22×#6101C2212yes—
21C22×C4×Dic13C2212yes—
22C22×C4×Dic13C2211yescharacteristic
23C22×C4×Dic13C2211yescharacteristic
24C2×#88141—24no—
25C2×#88141—24no—
26C2×#88141—24no—
27C2×C13×#95C2212yes—
28C2×C13×#95C2212yes—
29C2×#88071C2211yescharacteristic
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2211yescharacteristic
35C2×#88071C2212yes—
36C2×#88071C2212yes—
37C2×#88071C2212yes—
38#11718635—24no—
39#11718634—24no—
40C4×C4⋊Dic13—24no—
41#11718590C418yescomplemented
42C23×C4×C13C2312yes—
43C23×C4×C13C2311yescharacteristic
44C23×C4×C13C2312yes—
45C23×C4×C13C2311yescharacteristic
46C23×C4×C13C2311yescharacteristic
47C23×Dic13C2312yes—
48C23×Dic13C2311yescharacteristic
49C23×Dic13C2311yescharacteristic
50C23×Dic13C2311yescharacteristic
51C23×Dic13C2312yes—
52C23×Dic13C2311yescharacteristic
53C22×Dic26—22no—
54C22×Dic26—22no—
55C22×Dic26—22no—
56C22×Dic26—22no—
57C22×Dic26C2×C414yes—
58C22×Dic26D414yes—
59C22×Dic26Q814yes—
60C2×C13×C4⋊C4—22no—
61C2×C13×C4⋊C4—22no—
62C2×C13×C4⋊C4—22no—
63C2×C13×C4⋊C4—22no—
64C2×C13×C4⋊C4—22no—
65C2×C13×C4⋊C4D414yes—
66C2×C42×C13—22no—
67C2×C42×C13—22no—
68C2×C42×C13C2×C414yes—
69C2×C4⋊Dic13—22no—
70C2×C4⋊Dic13—22no—
71C2×C4⋊Dic13—22no—
72C2×C4⋊Dic13—22no—
73C2×C4⋊Dic13—22no—
74C2×C4⋊Dic13—22no—
75C2×C4⋊Dic13—22no—
76C2×C4⋊Dic13C2×C414yes—
77C2×C4⋊Dic13Q814yescomplemented
78C2×#6101—24no—
79C2×#6101—24no—
80C2×#6101—24no—
81C2×#6101—24no—
82C2×#6101—24no—
83C2×#6101—42no—
84C2×C4×Dic13—24no—
85C2×C4×Dic13—22no—
86C2×C4×Dic13—22no—
87C2×C4×Dic13—24no—
88C2×C4×Dic13—24no—
89C2×C4×Dic13—22no—
90C2×C4×Dic13—22no—
91C2×C4×Dic13—22no—
92C2×C4×Dic13D414yes—
93#88141—232no—
94C13×#95—24no—
95C13×#95—42no—
96#88071—24no—
97#88071—22no—
98#88071—22no—
99#88071—24no—
100#88071—24no—
101#88071—24no—
102#88071—42no—
103#88071C2×C418yes—
104#88071C2×C418yes—
105#14017—131nomaximal, Sylow
106C24×C13C2411yescharacteristic
107C22×C4×C13—21no—
108C22×C4×C13—21no—
109C22×C4×C13—21no—
110C22×C4×C13—21no—
111C22×C4×C13—21no—
112C22×C4×C13—22no—
113C22×C4×C13—22no—
114C22×C4×C13—22no—
115C22×C4×C13—22no—
116C22×C4×C13—21no—
117C22×C4×C13—21no—
118C22×C4×C13—22no—
119C22×C4×C13—21no—
120C22×C4×C13—21no—
121C22×C4×C13—21no—
122C22×C4×C13—22no—
123C22×C4×C13—22no—
124C22×C4×C13—22no—
125C22×C4×C13—22no—
126C22×C4×C13—22no—
127C22×C4×C13—22no—
128C22×C4×C13—22no—
129C22×C4×C13—22no—
130C22×C4×C13C22×C412yes—
131C22×C4×C13C22×C412yes—
132C22×C4×C13C22×C412yes—
133C22×C4×C13C2×D414yes—
134C22×C4×C13C2×D412yes—
135C22×C4×C13C2×D412yes—
136C22×C4×C13C2×D412yes—
137C22×C4×C13C2×Q812yes—
138C22×C4×C13C2×Q812yes—
139C22×C4×C13#4112yes—
140C22×C4×C13#4112yes—
141C22×C4×C13#4112yes—
142C22×Dic13—21no—
143C22×Dic13—21no—
144C22×Dic13—22no—
145C22×Dic13—22no—
146C22×Dic13—22no—
147C22×Dic13—22no—
148C22×Dic13—21no—
149C22×Dic13—21no—
150C22×Dic13—21no—
151C22×Dic13—21no—
152C22×Dic13—21no—
153C22×Dic13—21no—
154C22×Dic13—21no—
155C22×Dic13—22no—
156C22×Dic13—21no—
157C22×Dic13—21no—
158C22×Dic13—21no—
159C22×Dic13—22no—
160C22×Dic13—22no—
161C22×Dic13—22no—
162C22×Dic13—21no—
163C22×Dic13—21no—
164C22×Dic13—21no—
165C22×Dic13—21no—
166C22×Dic13—21no—
167C22×Dic13—22no—
168C22×Dic13—21no—
169C22×Dic13—22no—
170C22×Dic13—21no—
171C22×Dic13—21no—
172C22×Dic13—21no—
173C22×Dic13—21no—
174C22×Dic13C22×C414yes—
175C22×Dic13C22×C414yes—
176C22×Dic13C2×D412yes—
177C22×Dic13C2×D414yes—
178C22×Dic13C2×D412yes—
179C22×Dic13C2×Q812yes—
180C22×Dic13C2×Q814yes—
181C22×Dic13C2×Q812yes—
182C22×Dic13#4112yes—
183C22×Dic13#4112yes—
184C2×Dic26—28no—
185C2×Dic26—28no—
186C2×Dic26—28no—
187C2×Dic26—28no—
188C2×Dic26—28no—
189C2×Dic26—28no—
190C2×Dic26C4⋊C4116yescomplemented
191C13×C4⋊C4—28no—
192C13×C4⋊C4—44no—
193C42×C13—28no—
194C4⋊Dic13—28no—
195C4⋊Dic13—28no—
196C4⋊Dic13—28no—
197#6101—216no—
198#6101—48no—
199C4×Dic13—216no—
200C4×Dic13—28no—
201C4×Dic13—44no—
202C22×C4×Q8—131no—
203C2×#391—131no—
204C2×#391—131no—
205C2×#389—131no—
206C2×C4×C4⋊C4—131no—
207#1444—132no—
208#1442—132no—
209#1436—132no—
210#1436—132no—
211C4⋊#95—131no—
212C4⋊#95D1311yescharacteristic
213C23×C13C23×C411yescharacteristic
214C23×C13C22×D411yescharacteristic
215C23×C13C22×D411yescharacteristic
216C23×C13C22×D411yescharacteristic
217C23×C13C22×Q811yescharacteristic
218C23×C13C22×Q811yescharacteristic
219C23×C13C2×#4111yescharacteristic
220C23×C13C2×#4111yescharacteristic
221C23×C13C2×#4111yescharacteristic
222C23×C13C2×#4111yescharacteristic
223C23×C13C2×#4111yescharacteristic
224C23×C13H(5,𝔽2)11yescharacteristic
225C23×C132−1+411yescharacteristic
226C23×C132−1+411yescharacteristic
227C23×C132−1+411yescharacteristic
228C2×C4×C13—22no—
229C2×C4×C13—22no—
230C2×C4×C13—22no—
231C2×C4×C13—22no—
232C2×C4×C13—22no—
233C2×C4×C13—22no—
234C2×C4×C13—22no—
235C2×C4×C13—22no—
236C2×C4×C13—22no—
237C2×C4×C13—24no—
238C2×C4×C13—24no—
239C2×C4×C13—24no—
240C2×C4×C13—42no—
241C2×C4×C13—41no—
242C2×C4×C13—41no—
243C2×C4×C13—42no—
244C2×C4×C13—41no—
245C2×C4×C13—41no—
246C2×C4×C13—42no—
247C2×C4×C13—42no—
248C2×C4×C13—42no—
249C2×C4×C13—42no—
250C2×C4×C13—42no—
251C2×C4×C13—42no—
252C2×C4×C13—42no—
253C2×C4×C13—42no—
254C2×C4×C13—42no—
255C2×C4×C13C2×C4⋊C414yes—
256C2×C4×C13C4×D414yes—
257C2×C4×C13C4×D414yes—
258C2×C4×C13C4×Q814yescomplemented
259C2×C4×C13#12014yes—
260C2×C4×C13C22⋊Q814yes—
261C2×C4×C13C22⋊Q814yes—
262C2×C4×C13#12314yes—
263C2×Dic13—24no—
264C2×Dic13—24no—
265C2×Dic13—22no—
266C2×Dic13—24no—
267C2×Dic13—24no—
268C2×Dic13—24no—
269C2×Dic13—24no—
270C2×Dic13—22no—
271C2×Dic13—22no—
272C2×Dic13—22no—
273C2×Dic13—22no—
274C2×Dic13—22no—
275C2×Dic13—24no—
276C2×Dic13—24no—
277C2×Dic13—24no—
278C2×Dic13—22no—
279C2×Dic13—22no—
280C2×Dic13—22no—
281C2×Dic13—22no—
282C2×Dic13—22no—
283C2×Dic13—22no—
284C2×Dic13—22no—
285C2×Dic13—22no—
286C2×Dic13—22no—
287C2×Dic13—41no—
288C2×Dic13—41no—
289C2×Dic13—41no—
290C2×Dic13—41no—
291C2×Dic13—42no—
292C2×Dic13—41no—
293C2×Dic13—41no—
294C2×Dic13—41no—
295C2×Dic13—42no—
296C2×Dic13—41no—
297C2×Dic13—41no—
298C2×Dic13—41no—
299C2×Dic13—41no—
300C2×Dic13—41no—
301C2×Dic13—42no—
302C2×Dic13—42no—
303C2×Dic13C2×C4⋊C418yes—
304C2×Dic13C22⋊Q814yes—
305Dic26—232no—
306C23×Q8—131no—
307C2×C4×Q8—264no—
308C2×C4×Q8—264no—
309C2×C4×Q8—264no—
310C22×C4⋊C4—131no—
311C22×C4⋊C4—131no—
312C22×C4⋊C4—132no—
313C22×C4⋊C4—131no—
314C22×C4⋊C4—132no—
315C22×C4⋊C4C2×D1311yescharacteristic
316C22×C4⋊C4C2×D1311yescharacteristic
317C22×C42—131no—
318C22×C42—132no—
319C22×C42—131no—
320C22×C42C2×D1311yescharacteristic
321#391—138no—
322#391—264no—
323#389—264no—
324C4×C4⋊C4—264no—
325C2×#95—132no—
326C2×#95—132no—
327C2×#95—132no—
328C2×#95—131no—
329C2×#95—132no—
330C2×#95—132no—
331C2×#95—132no—
332C2×#95—131no—
333C2×#95—132no—
334C2×#95C2×D1312yes—
335C2×#95C2×D1312yes—
336C22×C13C22×C4⋊C411yescharacteristic
337C22×C13C2×C4×D411yescharacteristic
338C22×C13C2×C4×D411yescharacteristic
339C22×C13C2×C4×Q811yescharacteristic
340C22×C13C4×#4111yescharacteristic
341C22×C13#51911yescharacteristic
342C22×C13#52011yescharacteristic
343C22×C13C2×#12011yescharacteristic
344C22×C13C2×C22⋊Q811yescharacteristic
345C22×C13C2×C22⋊Q811yescharacteristic
346C22×C13C2×C22⋊Q811yescharacteristic
347C22×C13C2×#12311yescharacteristic
348C22×C13#52511yescharacteristic
349C22×C13#52911yescharacteristic
350C22×C13#53311yescharacteristic
351C22×C13#53611yescharacteristic
352C22×C13#53711yescharacteristic
353C22×C13#54111yescharacteristic
354C22×C13#54211yescharacteristic
355C22×C13#54611yescharacteristic
356C22×C13#54711yescharacteristic
357C22×C13#54811yescharacteristic
358C22×C13#54811yescharacteristic
359C22×C13#54811yescharacteristic
360C22×C13D4×Q811yescharacteristic
361C22×C13D4×Q811yescharacteristic
362C22×C13#55011yescharacteristic
363C22×C13#55611yescharacteristic
364C22×C13#55611yescharacteristic
365C22×C13#55711yescharacteristic
366C22×C13#55711yescharacteristic
367C22×C13#55711yescharacteristic
368C22×C13#55711yescharacteristic
369C22×C13Q8211yescharacteristic
370C22×C13#55911yescharacteristic
371C4×C13—24no—
372C4×C13—42no—
373C4×C13—44no—
374C4×C13—82no—
375C4×C13#38518yes—
376Dic13—24no—
377Dic13—28no—
378Dic13—44no—
379Dic13—42no—
380Dic13—42no—
381Dic13—42no—
382C22×Q8—134no—
383C22×Q8—134no—
384C22×Q8—134no—
385C22×Q8—262no—
386C22×Q8—262no—
387C22×Q8—262no—
388C22×Q8—262no—
389C23×C4—132no—
390C23×C4—131no—
391C23×C4—131no—
392C23×C4—131no—
393C23×C4—132no—
394C23×C4—131no—
395C23×C4C22×D1312yes—
396C23×C4C22×D1311yescharacteristic
397C23×C4C22×D1312yes—
398C23×C4C22×D1311yescharacteristic
399C23×C4C22×D1311yescharacteristic
400C4×Q8—2632no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—134no—
407C2×C4⋊C4—134no—
408C2×C4⋊C4—264no—
409C2×C4⋊C4—264no—
410C2×C4⋊C4—262no—
411C2×C4⋊C4—262no—
412C2×C4⋊C4—262no—
413C2×C4⋊C4—262no—
414C2×C4⋊C4—264no—
415C2×C4⋊C4—262no—
416C2×C4⋊C4—262no—
417C2×C4⋊C4—262no—
418C2×C4⋊C4—264no—
419C2×C4⋊C4—264no—
420C2×C4⋊C4—522no—
421C2×C4⋊C4D5214yes—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—134no—
425C2×C42—264no—
426C2×C42—264no—
427C2×C42—264no—
428C2×C42—262no—
429C2×C42—262no—
430C2×C42—262no—
431C2×C42—262no—
432C2×C42—262no—
433C2×C42C4×D1314yes—
434#95—24no—
435#95—42no—
436#95—138no—
437#95—138no—
438#95—264no—
439#95—262no—
440#95—262no—
441#95—264no—
442#95—264no—
443#95—264no—
444#95—522no—
445C2×C13C2×#38511yescharacteristic
446C2×C13C4×C22⋊Q811yescharacteristic
447C2×C13#232311yescharacteristic
448C2×C13Q8×C4⋊C411yescharacteristic
449C2×C13#235111yescharacteristic
450C2×C13#236511yescharacteristic
451C2×C13#236711yescharacteristic
452C2×C13#240711yescharacteristic
453C2×C13#240911yescharacteristic
454C2×C13#244611yescharacteristic
455C2×C13#244811yescharacteristic
456C2×C13#245111yescharacteristic
457C2×C13#245311yescharacteristic
458C2×C13#258111yescharacteristic
459C2×C13#258211yescharacteristic
460C24C23×D1311yescharacteristic
461C2×Q8—1316no—
462C2×Q8—268no—
463C2×Q8—268no—
464C2×Q8—268no—
465C2×Q8—268no—
466C2×Q8—268no—
467C2×Q8—268no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—134no—
492C22×C4—134no—
493C22×C4—132no—
494C22×C4—132no—
495C22×C4—134no—
496C22×C4—132no—
497C22×C4—134no—
498C22×C4—132no—
499C22×C4—132no—
500C22×C4—132no—
501C22×C4—261no—
502C22×C4—262no—
503C22×C4—262no—
504C22×C4—261no—
505C22×C4—262no—
506C22×C4—262no—
507C22×C4—261no—
508C22×C4—261no—
509C22×C4—261no—
510C22×C4—262no—
511C22×C4—261no—
512C22×C4—261no—
513C22×C4—262no—
514C22×C4—261no—
515C22×C4—261no—
516C22×C4—261no—
517C22×C4—261no—
518C22×C4—261no—
519C22×C4—261no—
520C22×C4—261no—
521C22×C4—261no—
522C22×C4—262no—
523C22×C4—261no—
524C22×C4—261no—
525C22×C4—262no—
526C22×C4—262no—
527C22×C4—262no—
528C22×C4—261no—
529C22×C4—261no—
530C22×C4—261no—
531C22×C4—261no—
532C22×C4—261no—
533C22×C4C2×C4×D1312yes—
534C22×C4C2×C4×D1312yes—
535C22×C4C2×C4×D1312yes—
536C22×C4C2×D5214yes—
537C22×C4C2×D5212yes—
538C22×C4#612712yes—
539C22×C4D4×D1312yes—
540C22×C4D4×D1312yes—
541C22×C4#612912yes—
542C22×C4#612912yes—
543C22×C4Q8×D1312yes—
544C22×C4Q8×D1312yes—
545C4⋊C4—28no—
546C4⋊C4—44no—
547C4⋊C4—268no—
548C4⋊C4—2616no—
549C4⋊C4—268no—
550C4⋊C4—268no—
551C4⋊C4—528no—
552C42—28no—
553C42—2616no—
554C42—268no—
555C42—524no—
556C13#1401711yescharacteristic, complemented, Sylow
557C23C22×C4×D1311yescharacteristic
558C23C22×D5211yescharacteristic
559C23C2×#612711yescharacteristic
560C23C2×D4×D1311yescharacteristic
561C23C2×D4×D1311yescharacteristic
562C23C2×#612911yescharacteristic
563C23C2×#612911yescharacteristic
564C23#8825111yescharacteristic
565C23C2×Q8×D1311yescharacteristic
566C23C2×Q8×D1311yescharacteristic
567C23#8825411yescharacteristic
568C23#41×D1311yescharacteristic
569C23#41×D1311yescharacteristic
570C23#8825711yescharacteristic
571C23#8825711yescharacteristic
572Q8—2632no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—24no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—24no—
584C2×C4—24no—
585C2×C4—41no—
586C2×C4—42no—
587C2×C4—41no—
588C2×C4—42no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—138no—
601C2×C4—134no—
602C2×C4—262no—
603C2×C4—264no—
604C2×C4—264no—
605C2×C4—262no—
606C2×C4—264no—
607C2×C4—264no—
608C2×C4—264no—
609C2×C4—264no—
610C2×C4—262no—
611C2×C4—262no—
612C2×C4—262no—
613C2×C4—262no—
614C2×C4—262no—
615C2×C4—264no—
616C2×C4—262no—
617C2×C4—264no—
618C2×C4—264no—
619C2×C4—262no—
620C2×C4—262no—
621C2×C4—262no—
622C2×C4—262no—
623C2×C4—262no—
624C2×C4—262no—
625C2×C4—262no—
626C2×C4—521no—
627C2×C4—521no—
628C2×C4—522no—
629C2×C4—521no—
630C2×C4—521no—
631C2×C4—521no—
632C2×C4—522no—
633C2×C4—522no—
634C2×C4—522no—
635C2×C4—521no—
636C2×C4—521no—
637C2×C4—521no—
638C2×C4—521no—
639C2×C4—521no—
640C2×C4—521no—
641C2×C4—521no—
642C2×C4C4×D5214yes—
643C2×C4#8813514yes—
644C2×C4#8813614yes—
645C2×C4#8813714yes—
646C2×C4#8814114yescomplemented
647C2×C4C4⋊C4×D1314yes—
648C2×C4#8815014yes—
649C2×C4#8815114yes—
650C22C2×C4×D5211yescharacteristic
651C22C2×#8813511yescharacteristic
652C22C2×#8813611yescharacteristic
653C22C2×#8813711yescharacteristic
654C22C2×#8814111yescharacteristic
655C22C2×C4⋊C4×D1311yescharacteristic
656C22#1171920911yescharacteristic
657C22C2×#8815011yescharacteristic
658C22C2×#8815111yescharacteristic
659C22#1171922111yescharacteristic
660C22#1171922711yescharacteristic
661C22#1171924711yescharacteristic
662C22#1171925911yescharacteristic
663C22#1171926011yescharacteristic
664C22#1171926411yescharacteristic
665C22#1171927211yescharacteristic
666C22#1171927311yescharacteristic
667C22Q8×D5211yescharacteristic
668C22#1171928111yescharacteristic
669C22#1171930511yescharacteristic
670C22#1171930811yescharacteristic
671C22#1171931111yescharacteristic
672C22#1171931311yescharacteristic
673C22#1171932711yescharacteristic
674C22#1171933011yescharacteristic
675C22D13×C22⋊Q811yescharacteristic
676C22#1171933311yescharacteristic
677C22#1171938211yescharacteristic
678C22#1171938211yescharacteristic
679C22#1171939011yescharacteristic
680C22#1171939011yescharacteristic
681C22#1171942311yescharacteristic
682C22#1171942611yescharacteristic
683C22#1171942711yescharacteristic
684C22#1171943211yescharacteristic
685C4—24no—
686C4—42no—
687C4—44no—
688C4—82no—
689C4—268no—
690C4—264no—
691C4—524no—
692C4—522no—
693C4—522no—
694C4—522no—
695C4#1171832918yes—
696C2C2×#1171832911yescharacteristic
697C2#1311736411yescharacteristic
698C2#1311751411yescharacteristic
699C2#1311774811yescharacteristic
700C2#1311775311yescharacteristic
701C2#1311789411yescharacteristic
702C2#1311790711yescharacteristic
703C2#1311817911yescharacteristic
704C2#1311819911yescharacteristic
705C2#1311861511yescharacteristic
706C2#1311863711yescharacteristic
707C2#1311867311yescharacteristic
708C2#1311869511yescharacteristic
709C2#1312020411yescharacteristic
710C2#1312020811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×C4⋊#95C2
socle, prime radical, cosocleC24×C13C24
hypercenterC4⋊#95D13
hypocenterC13#14017
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
41. #11718590C4semidirect
77. C2×C4⋊Dic13Q8semidirect
190. C2×Dic26C4⋊C4semidirect
258. C2×C4×C13C4×Q8semidirect
556. C13#14017semidirect
646. C2×C4#88141semidirect

Maximal subgroups

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

subgroupindex
C22×#881412
C2×#117185902
C2×#117186352
C2×#117186342
C2×C4×C4⋊Dic132
#131131002
#131130912
#131130712
#131130702
#131130652
C13×C4⋊#952
#1401713