Finite Group Databasebeta

← #15769214

Subgroups — #15769214

Order 3328.

1354 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88061C211yesmaximal, characteristic
2C22×#88049C211yesmaximal, characteristic
3C2×#11718649C211yesmaximal, characteristic
4C2×C4⋊C4×Dic13C211yesmaximal, characteristic, complemented
5C2×#11718121C211yesmaximal, characteristic, complemented
6C2×#11718142C211yesmaximal, characteristic, complemented
7C2×C13×#340C211yesmaximal, characteristic, complemented
8C23×D52C2211yescharacteristic
9C23×C8×C13C2211yescharacteristic
10C22×C13×C4⋊C4C2211yescharacteristic
11C22×C13×C4⋊C4C2211yescharacteristic
12C22×#6103—21no—
13C22×#6103—21no—
14C22×C4⋊Dic13C2211yescharacteristic
15C22×C4×Dic13—21no—
16C22×C4×Dic13C2211yescharacteristic
17C23×#1055C2211yescharacteristic
18C2×#88071—21no—
19C2×#88061—22no—
20C2×#88061—22no—
21C2×#88061C414yescomplemented
22#11718649—22no—
23#11718649C414yescomplemented
24C4⋊C4×Dic13—22no—
25C4⋊C4×Dic13—22no—
26C2×#88049—22no—
27C2×#88049—22no—
28C2×#88049C414yescomplemented
29C13×#340—22no—
30#11718142—22no—
31#11718121—22no—
32C24×D13—21no—
33C23×C4×C13—21no—
34C23×C4×C13—21no—
35C23×C4×C13C2311yescharacteristic
36C23×Dic13—21no—
37C23×Dic13D411yescharacteristic
38C23×Dic13D411yescharacteristic
39C22×D52—21no—
40C22×D52—21no—
41C22×D52—21no—
42C22×D52—21no—
43C22×D52—21no—
44C22×D52—21no—
45C22×D52—21no—
46C22×D52—21no—
47C22×D52—21no—
48C22×D52—21no—
49C22×D52—21no—
50C22×D52C2×C412yes—
51C22×D52C2×C412yes—
52C22×D52C2×C412yes—
53C22×C8×C13—21no—
54C22×C8×C13—21no—
55C22×C8×C13—21no—
56C22×C8×C13—21no—
57C22×C8×C13—21no—
58C22×C8×C13—21no—
59C22×C8×C13C2×C412yes—
60C2×C13×C4⋊C4—21no—
61C2×C13×C4⋊C4—21no—
62C2×C13×C4⋊C4—21no—
63C2×C13×C4⋊C4—21no—
64C2×C13×C4⋊C4—21no—
65C2×C13×C4⋊C4—21no—
66C2×C13×C4⋊C4—21no—
67C2×C13×C4⋊C4—21no—
68C2×C13×C4⋊C4C2×C412yes—
69C2×C13×C4⋊C4C2×C412yes—
70C2×C13×C4⋊C4D412yes—
71C2×C13×C4⋊C4D412yes—
72C2×#6103—24no—
73C2×#6103—24no—
74C2×#6103—42no—
75C2×#6103—42no—
76C2×#6103—42no—
77C2×#6103—42no—
78C2×C4⋊Dic13—21no—
79C2×C4⋊Dic13—21no—
80C2×C4⋊Dic13—21no—
81C2×C4⋊Dic13C2×C412yes—
82C2×C4⋊Dic13D412yes—
83C2×C4⋊Dic13D412yes—
84C2×C4×Dic13—21no—
85C2×C4×Dic13—21no—
86C2×C4×Dic13—21no—
87C2×C4×Dic13—21no—
88C2×C4×Dic13—24no—
89C2×C4×Dic13—42no—
90C2×C4×Dic13—42no—
91C2×C4×Dic13C2×C412yes—
92C2×C4×Dic13D412yes—
93C22×#1055—21no—
94C22×#1055—21no—
95C22×#1055—21no—
96C22×#1055—21no—
97C22×#1055—21no—
98C22×#1055—21no—
99C22×#1055C2×C412yes—
100#88071—24no—
101#88061—28no—
102#88049—28no—
103#10931—131nomaximal, Sylow
104C24×C13C2×D411yescharacteristic
105C23×D13—22no—
106C23×D13—22no—
107C23×D13—22no—
108C23×D13—41no—
109C23×D13—41no—
110C23×D13—41no—
111C23×D13—41no—
112C23×D13—41no—
113C23×D13—41no—
114C23×D13—41no—
115C23×D13—41no—
116C23×D13—41no—
117C23×D13—41no—
118C23×D13—41no—
119C23×D13—41no—
120C22×C4×C13—22no—
121C22×C4×C13—22no—
122C22×C4×C13—22no—
123C22×C4×C13—22no—
124C22×C4×C13—41no—
125C22×C4×C13—41no—
126C22×C4×C13—41no—
127C22×C4×C13—41no—
128C22×C4×C13—41no—
129C22×C4×C13—41no—
130C22×C4×C13—41no—
131C22×C4×C13—41no—
132C22×C4×C13—41no—
133C22×C4×C13—41no—
134C22×C4×C13C22×C411yescharacteristic
135C22×C4×C13C22×C411yescharacteristic
136C22×C4×C13C22×C411yescharacteristic
137C22×C4×C13C2×D411yescharacteristic
138C22×C4×C13C2×D411yescharacteristic
139C22×C4×C13C2×D411yescharacteristic
140C22×C4×C13C2×D411yescharacteristic
141C22×C4×C13C2×D411yescharacteristic
142C22×C4×C13#4111yescharacteristic
143C22×C4×C13#4111yescharacteristic
144C22×C4×C13#4111yescharacteristic
145C22×C4×C13#4111yescharacteristic
146C22×C4×C13#4111yescharacteristic
147C22×C4×C13#4111yescharacteristic
148C22×Dic13—21no—
149C22×Dic13—21no—
150C22×Dic13—21no—
151C22×Dic13—21no—
152C22×Dic13—22no—
153C22×Dic13—21no—
154C22×Dic13—22no—
155C22×Dic13—22no—
156C22×Dic13—21no—
157C22×Dic13—21no—
158C22×Dic13—21no—
159C22×Dic13—21no—
160C22×Dic13—21no—
161C22×Dic13—41no—
162C22×Dic13—41no—
163C22×Dic13—41no—
164C22×Dic13—41no—
165C22×Dic13C22⋊C412yes—
166C22×Dic13C22⋊C412yes—
167C22×Dic13D812yes—
168C22×Dic13SD1612yes—
169C2×D52—22no—
170C2×D52—22no—
171C2×D52—22no—
172C2×D52—22no—
173C2×D52—22no—
174C2×D52—22no—
175C2×D52—22no—
176C2×D52—22no—
177C2×D52—22no—
178C2×D52—22no—
179C2×D52—22no—
180C2×D52—22no—
181C2×D52—22no—
182C2×D52—22no—
183C2×D52—22no—
184C2×D52—41no—
185C2×D52—41no—
186C2×D52—41no—
187C2×D52—41no—
188C2×D52—41no—
189C2×D52—41no—
190C2×D52—41no—
191C2×D52—41no—
192C2×D52—41no—
193C2×D52—41no—
194C2×D52—41no—
195C2×D52—41no—
196C2×D52C4214yescomplemented
197C2×C8×C13—22no—
198C2×C8×C13—22no—
199C2×C8×C13—22no—
200C2×C8×C13—41no—
201C2×C8×C13—41no—
202C2×C8×C13—41no—
203C2×C8×C13—41no—
204C13×C4⋊C4—22no—
205C13×C4⋊C4—22no—
206C13×C4⋊C4—22no—
207C13×C4⋊C4—22no—
208C13×C4⋊C4—22no—
209C13×C4⋊C4—41no—
210C13×C4⋊C4—41no—
211C13×C4⋊C4C22⋊C414yescomplemented
212#6103—48no—
213#6103—48no—
214C4⋊Dic13—22no—
215C4⋊Dic13—22no—
216C4⋊Dic13—22no—
217C4⋊Dic13C22⋊C414yescomplemented
218C4×Dic13—22no—
219C4×Dic13—22no—
220C4×Dic13—22no—
221C4×Dic13—22no—
222C4×Dic13—48no—
223C2×#1055—22no—
224C2×#1055—22no—
225C2×#1055—22no—
226C2×#1055—41no—
227C2×#1055—41no—
228C2×#1055—41no—
229C2×#1055—41no—
230C22×#102—131no—
231C22×#102—131no—
232C2×#390—131no—
233C2×C4×C4⋊C4—131no—
234C2×#340—131no—
235C2×#340D1311yescharacteristic, complemented
236C2×#336—131no—
237C23×C13C2×C22⋊C411yescharacteristic
238C23×C13C4×D411yescharacteristic
239C23×C13C4×D411yescharacteristic
240C23×C13#12011yescharacteristic
241C23×C13#12111yescharacteristic
242C23×C13#12111yescharacteristic
243C23×C13#12311yescharacteristic
244C23×C13C2×D811yescharacteristic
245C23×C13C2×SD1611yescharacteristic
246C23×C13#13511yescharacteristic
247C23×C13#13511yescharacteristic
248C23×C13AGL(1,ℤ/8)11yescharacteristic
249C23×C13AGL(1,ℤ/8)11yescharacteristic
250C23×C13AGL(1,ℤ/8)11yescharacteristic
251C23×C13#13711yescharacteristic
252C22×D13—24no—
253C22×D13—42no—
254C22×D13—42no—
255C22×D13—42no—
256C22×D13—42no—
257C22×D13—42no—
258C22×D13—42no—
259C22×D13—42no—
260C22×D13—42no—
261C22×D13—42no—
262C22×D13—42no—
263C22×D13—42no—
264C22×D13—42no—
265C22×D13—42no—
266C22×D13—42no—
267C22×D13—42no—
268C22×D13—42no—
269C22×D13—42no—
270C22×D13—42no—
271C22×D13—81no—
272C22×D13—81no—
273C22×D13—81no—
274C22×D13—81no—
275C22×D13—81no—
276C22×D13—81no—
277C22×D13—81no—
278C22×D13—81no—
279C22×D13—81no—
280C22×D13—81no—
281C22×D13—81no—
282C22×D13—81no—
283C22×D13—81no—
284C22×D13—81no—
285C22×D13—81no—
286C22×D13—81no—
287C2×C4×C13—24no—
288C2×C4×C13—42no—
289C2×C4×C13—42no—
290C2×C4×C13—42no—
291C2×C4×C13—42no—
292C2×C4×C13—42no—
293C2×C4×C13—42no—
294C2×C4×C13—42no—
295C2×C4×C13—42no—
296C2×C4×C13—42no—
297C2×C4×C13—81no—
298C2×C4×C13—81no—
299C2×C4×C13—81no—
300C2×C4×C13—81no—
301C2×C4×C13C2×C4211yescharacteristic
302C2×C4×C13C2×C22⋊C411yescharacteristic
303C2×C4×C13C2×C22⋊C411yescharacteristic
304C2×C4×C13#11711yescharacteristic
305C2×C4×C13#11711yescharacteristic
306C2×C4×C13#11711yescharacteristic
307C2×C4×C13C4×D411yescharacteristic
308C2×C4×C13C4×D411yescharacteristic
309C2×C4×C13C4×D411yescharacteristic
310C2×C4×C13C4×D411yescharacteristic
311C2×C4×C13C4×D411yescharacteristic
312C2×C4×C13C4×D411yescharacteristic
313C2×C4×C13C4×D411yescharacteristic
314C2×C4×C13C4×D411yescharacteristic
315C2×C4×C13C4×D411yescharacteristic
316C2×C4×C13C4×D411yescharacteristic
317C2×C4×C13#12111yescharacteristic
318C2×C4×C13#12111yescharacteristic
319C2×C4×C13#12111yescharacteristic
320C2×C4×C13#12111yescharacteristic
321C2×C4×C13#12311yescharacteristic
322C2×C4×C13#12311yescharacteristic
323C2×C4×C13#12411yescharacteristic
324C2×C4×C13#12411yescharacteristic
325C2×C4×C13#12411yescharacteristic
326C2×C4×C13#12611yescharacteristic
327C2×C4×C13#12611yescharacteristic
328C2×C4×C13#12711yescharacteristic
329C2×Dic13—22no—
330C2×Dic13—22no—
331C2×Dic13—22no—
332C2×Dic13—22no—
333C2×Dic13—22no—
334C2×Dic13—22no—
335C2×Dic13—22no—
336C2×Dic13—24no—
337C2×Dic13—22no—
338C2×Dic13—22no—
339C2×Dic13—42no—
340C2×Dic13—42no—
341C2×Dic13—42no—
342C2×Dic13—41no—
343C2×Dic13—41no—
344C2×Dic13—42no—
345C2×Dic13—42no—
346C2×Dic13—42no—
347C2×Dic13—41no—
348C2×Dic13—41no—
349C2×Dic13#10214yescomplemented
350D52—24no—
351D52—24no—
352D52—42no—
353D52—42no—
354D52—42no—
355D52—42no—
356D52—42no—
357D52—42no—
358C8×C13—42no—
359#1055—42no—
360C23×D4—131no—
361C23×C8—131no—
362C23×C8C2×D1311yescharacteristic
363C22×C4⋊C4—131no—
364C22×C4⋊C4C2×D1311yescharacteristic
365C22×C4⋊C4C2×D1311yescharacteristic
366C22×C22⋊C4—261no—
367C22×C22⋊C4—261no—
368C22×C42—131no—
369C22×C42—261no—
370C2×#102—134no—
371C2×#102—134no—
372C2×#102—262no—
373C2×#102—262no—
374C2×#102—262no—
375C2×#102—262no—
376#390—134no—
377#390—262no—
378C4×C4⋊C4—262no—
379C4×C4⋊C4—262no—
380C2×#95—261no—
381#340—22no—
382#340—262no—
383#336—262no—
384C22×C13C4×C22⋊C411yescharacteristic
385C22×C13#38611yescharacteristic
386C22×C13#38611yescharacteristic
387C22×C13#38611yescharacteristic
388C22×C13#38811yescharacteristic
389C22×C13#38811yescharacteristic
390C22×C13#39011yescharacteristic
391C22×C13C2×#10211yescharacteristic
392C22×C13#41611yescharacteristic
393C22×C13#41711yescharacteristic
394C22×C13#41811yescharacteristic
395C22×C13C4×D811yescharacteristic
396C22×C13C4×D811yescharacteristic
397C22×C13C4×SD1611yescharacteristic
398C22×C13C4×SD1611yescharacteristic
399C22×C13#44011yescharacteristic
400C22×C13#44011yescharacteristic
401C22×C13#44211yescharacteristic
402C22×C13#44211yescharacteristic
403C22×C13#44711yescharacteristic
404C22×C13#44811yescharacteristic
405C22×C13#44911yescharacteristic
406C22×C13#44911yescharacteristic
407C22×C13#45911yescharacteristic
408C22×C13#45911yescharacteristic
409C22×C13#46011yescharacteristic
410C22×C13#46011yescharacteristic
411C22×C13#46311yescharacteristic
412C22×C13#46311yescharacteristic
413C22×C13#46411yescharacteristic
414C22×C13#46411yescharacteristic
415C22×C13#48011yescharacteristic
416C22×C13#48111yescharacteristic
417C22×C13#48211yescharacteristic
418C22×C13#48211yescharacteristic
419C2×D13—44no—
420C2×D13—44no—
421C2×D13—44no—
422C2×D13—82no—
423C2×D13—82no—
424C2×D13—82no—
425C2×D13—82no—
426C2×D13—82no—
427C2×D13—82no—
428C2×D13—82no—
429C2×D13—82no—
430C2×D13—82no—
431C2×D13—82no—
432C2×D13—82no—
433C2×D13—82no—
434C4×C13—44no—
435C4×C13—82no—
436C4×C13C4×C22⋊C411yescharacteristic
437C4×C13C4×C22⋊C411yescharacteristic
438C4×C13#38811yescharacteristic
439C4×C13#38811yescharacteristic
440C4×C13#38811yescharacteristic
441C4×C13#38811yescharacteristic
442C4×C13#39011yescharacteristic
443C4×C13#39011yescharacteristic
444Dic13—24no—
445Dic13—42no—
446Dic13—44no—
447C25—261no—
448C22×D4—132no—
449C22×D4—132no—
450C22×D4—132no—
451C22×D4—261no—
452C22×D4—261no—
453C22×D4—261no—
454C22×D4—261no—
455C22×D4—261no—
456C22×D4—261no—
457C22×D4—261no—
458C22×D4—261no—
459C22×D4—261no—
460C22×D4—261no—
461C22×D4—261no—
462C23×C4—21no—
463C23×C4—21no—
464C23×C4—131no—
465C23×C4—131no—
466C23×C4—261no—
467C23×C4C22×D1311yescharacteristic
468C22×C8—21no—
469C22×C8—21no—
470C22×C8—21no—
471C22×C8—21no—
472C22×C8—21no—
473C22×C8—21no—
474C22×C8—132no—
475C22×C8—261no—
476C22×C8—261no—
477C22×C8—261no—
478C22×C8—261no—
479C22×C8—261no—
480C22×C8—261no—
481C22×C8C4×D1312yes—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—132no—
491C2×C4⋊C4—132no—
492C2×C4⋊C4—132no—
493C2×C4⋊C4—261no—
494C2×C4⋊C4—261no—
495C2×C4⋊C4—261no—
496C2×C4⋊C4C4×D1312yes—
497C2×C4⋊C4C4×D1312yes—
498C2×C4⋊C4D5212yes—
499C2×C4⋊C4C22⋊D1312yes—
500C2×C22⋊C4—264no—
501C2×C22⋊C4—264no—
502C2×C22⋊C4—522no—
503C2×C22⋊C4—522no—
504C2×C22⋊C4—522no—
505C2×C22⋊C4—522no—
506C2×C42—132no—
507C2×C42—132no—
508C2×C42—261no—
509C2×C42—261no—
510C2×C42—261no—
511C2×C42—261no—
512C2×C42—264no—
513C2×C42—522no—
514C2×C42—522no—
515#102—268no—
516#102—268no—
517#95—264no—
518C2×C13#143711yescharacteristic
519C2×C13C4×#10211yescharacteristic
520C2×C13#176211yescharacteristic
521C2×C13#187411yescharacteristic
522C2×C13#187511yescharacteristic
523C2×C13#187911yescharacteristic
524C2×C13#187911yescharacteristic
525C2×C13#188011yescharacteristic
526C2×C13#188011yescharacteristic
527C2×C13#192511yescharacteristic
528C2×C13#192511yescharacteristic
529C2×C13#192611yescharacteristic
530C2×C13#192611yescharacteristic
531C2×C13#198211yescharacteristic
532C2×C13#198311yescharacteristic
533D13—84no—
534C24—262no—
535C24—262no—
536C24—262no—
537C24—521no—
538C24—521no—
539C24—521no—
540C24—521no—
541C24—521no—
542C24—521no—
543C24—521no—
544C24—521no—
545C24—521no—
546C24—521no—
547C24—521no—
548C24—521no—
549C24D4×D1311yescharacteristic
550C2×D4—134no—
551C2×D4—262no—
552C2×D4—262no—
553C2×D4—262no—
554C2×D4—262no—
555C2×D4—262no—
556C2×D4—262no—
557C2×D4—262no—
558C2×D4—262no—
559C2×D4—262no—
560C2×D4—262no—
561C2×D4—262no—
562C2×D4—262no—
563C2×D4—262no—
564C2×D4—262no—
565C2×D4—262no—
566C2×D4—521no—
567C2×D4—521no—
568C2×D4—521no—
569C2×D4—521no—
570C2×D4—521no—
571C2×D4—521no—
572C2×D4—521no—
573C2×D4—521no—
574C2×D4—521no—
575C2×D4—521no—
576C2×D4—521no—
577C2×D4—521no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4—132no—
593C22×C4—132no—
594C22×C4—132no—
595C22×C4—132no—
596C22×C4—261no—
597C22×C4—261no—
598C22×C4—261no—
599C22×C4—261no—
600C22×C4—261no—
601C22×C4—262no—
602C22×C4—262no—
603C22×C4—262no—
604C22×C4—261no—
605C22×C4—261no—
606C22×C4—261no—
607C22×C4—261no—
608C22×C4—261no—
609C22×C4—521no—
610C22×C4—521no—
611C22×C4—521no—
612C22×C4—521no—
613C22×C4C2×C4×D1311yescharacteristic
614C22×C4C2×C4×D1311yescharacteristic
615C22×C4C2×C4×D1311yescharacteristic
616C22×C4C2×D5211yescharacteristic
617C22×C4#612711yescharacteristic
618C22×C4#612711yescharacteristic
619C22×C4D4×D1311yescharacteristic
620C22×C4D4×D1311yescharacteristic
621C22×C4D4×D1311yescharacteristic
622C22×C4#612911yescharacteristic
623C22×C4#612911yescharacteristic
624C22×C4#613111yescharacteristic
625C22×C4#613111yescharacteristic
626C22×C4C2×C22⋊D1311yescharacteristic
627C2×C8—22no—
628C2×C8—22no—
629C2×C8—22no—
630C2×C8—41no—
631C2×C8—41no—
632C2×C8—41no—
633C2×C8—41no—
634C2×C8—262no—
635C2×C8—262no—
636C2×C8—262no—
637C2×C8—521no—
638C2×C8—521no—
639C2×C8—521no—
640C2×C8—521no—
641C4⋊C4—22no—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—41no—
647C4⋊C4—41no—
648C4⋊C4—134no—
649C4⋊C4—262no—
650C4⋊C4—262no—
651C4⋊C4—262no—
652C4⋊C4#610314yescomplemented
653C22⋊C4—528no—
654C22⋊C4—528no—
655C42—262no—
656C42—262no—
657C42—262no—
658C42—262no—
659C42—528no—
660C13#1093111yescharacteristic, complemented, Sylow
661C23—264no—
662C23—522no—
663C23—522no—
664C23—522no—
665C23—522no—
666C23—522no—
667C23—522no—
668C23—522no—
669C23—522no—
670C23—522no—
671C23—522no—
672C23—522no—
673C23—522no—
674C23—522no—
675C23—522no—
676C23—522no—
677C23—522no—
678C23—522no—
679C23—522no—
680C23—1041no—
681C23—1041no—
682C23—1041no—
683C23—1041no—
684C23—1041no—
685C23—1041no—
686C23—1041no—
687C23—1041no—
688C23—1041no—
689C23—1041no—
690C23—1041no—
691C23—1041no—
692C23—1041no—
693C23—1041no—
694C23—1041no—
695C23—1041no—
696C23C22⋊C4×D1311yescharacteristic
697C23#8813511yescharacteristic
698C23#8813611yescharacteristic
699C23#8813811yescharacteristic
700C23#8814711yescharacteristic
701C23#8814811yescharacteristic
702C23D8×D1311yescharacteristic
703C23#8816511yescharacteristic
704C23SD16×D1311yescharacteristic
705C23#8816811yescharacteristic
706C23#8816811yescharacteristic
707C23#8817011yescharacteristic
708C23#8817211yescharacteristic
709C23#8817311yescharacteristic
710C23#8819311yescharacteristic
711D4—264no—
712D4—264no—
713D4—522no—
714D4—522no—
715D4—522no—
716D4—522no—
717D4—522no—
718D4—522no—
719C2×C4—24no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—81no—
730C2×C4—81no—
731C2×C4—81no—
732C2×C4—81no—
733C2×C4—134no—
734C2×C4—262no—
735C2×C4—262no—
736C2×C4—262no—
737C2×C4—262no—
738C2×C4—262no—
739C2×C4—262no—
740C2×C4—262no—
741C2×C4—262no—
742C2×C4—262no—
743C2×C4—264no—
744C2×C4—522no—
745C2×C4—521no—
746C2×C4—522no—
747C2×C4—521no—
748C2×C4—522no—
749C2×C4—522no—
750C2×C4—521no—
751C2×C4—522no—
752C2×C4—522no—
753C2×C4—521no—
754C2×C4C42×D1311yescharacteristic
755C2×C4#8812611yescharacteristic
756C2×C4C4×D5211yescharacteristic
757C2×C4C4×D5211yescharacteristic
758C2×C4C22⋊C4×D1311yescharacteristic
759C2×C4#8813511yescharacteristic
760C2×C4#8813511yescharacteristic
761C2×C4#8813511yescharacteristic
762C2×C4#8813811yescharacteristic
763C2×C4#8813911yescharacteristic
764C2×C4#8813911yescharacteristic
765C2×C4#8814011yescharacteristic
766C2×C4#8814611yescharacteristic
767C2×C4#8814611yescharacteristic
768C2×C4#8814711yescharacteristic
769C2×C4#8814711yescharacteristic
770C2×C4#8814711yescharacteristic
771C2×C4#8814811yescharacteristic
772C2×C4#8814911yescharacteristic
773C2×C4#8814911yescharacteristic
774C2×C4#8815211yescharacteristic
775C2×C4#8815211yescharacteristic
776C2×C4C2×#610311yescharacteristic
777C2×C4C4×C22⋊D1311yescharacteristic
778C2×C4C4×C22⋊D1311yescharacteristic
779C2×C4#8819311yescharacteristic
780C2×C4#8819411yescharacteristic
781C2×C4#8820111yescharacteristic
782C8—42no—
783C8—522no—
784C22—524no—
785C22—524no—
786C22—524no—
787C22—1042no—
788C22—1042no—
789C22—1042no—
790C22—1042no—
791C22—1042no—
792C22—1042no—
793C22—1042no—
794C22—1042no—
795C22—1042no—
796C22—1042no—
797C22—1042no—
798C22—1042no—
799C22#1171832611yescharacteristic
800C22#1171832611yescharacteristic
801C22#1171832711yescharacteristic
802C22#1171833011yescharacteristic
803C22#1171841711yescharacteristic
804C22#1171842311yescharacteristic
805C22D13×#10211yescharacteristic
806C22#1171843111yescharacteristic
807C22#1171843411yescharacteristic
808C22#1171844211yescharacteristic
809C22#1171844611yescharacteristic
810C22#1171844711yescharacteristic
811C22#1171844911yescharacteristic
812C22#1171845911yescharacteristic
813C22#1171846411yescharacteristic
814C22#1171846511yescharacteristic
815C22#1171846711yescharacteristic
816C22#1171847211yescharacteristic
817C22#1171847811yescharacteristic
818C22#1171848011yescharacteristic
819C22#1171851311yescharacteristic
820C22#1171852411yescharacteristic
821C22#1171852711yescharacteristic
822C22#1171853011yescharacteristic
823C22#1171853311yescharacteristic
824C22#1171854311yescharacteristic
825C22#1171854611yescharacteristic
826C22#1171855011yescharacteristic
827C22#1171861811yescharacteristic
828C22#1171861911yescharacteristic
829C22#1171865111yescharacteristic
830C22#1171881111yescharacteristic
831C22#1171882411yescharacteristic
832C22#1171882611yescharacteristic
833C22#1171884611yescharacteristic
834C4—44no—
835C4—82no—
836C4—264no—
837C4—522no—
838C4—524no—
839C4#1171832711yescharacteristic
840C4#1171833011yescharacteristic
841C4#1171833111yescharacteristic
842C4#1171833111yescharacteristic
843C4C4×#610311yescharacteristic
844C4#1171861811yescharacteristic
845C4#1171864911yescharacteristic
846C4#1171865111yescharacteristic
847C2—1044no—
848C2#1311307211yescharacteristic
849C2#1311465011yescharacteristic
850C2#1311466011yescharacteristic
851C2#1311515211yescharacteristic
852C2#1311515711yescharacteristic
853C2#1311518211yescharacteristic
854C2#1311518511yescharacteristic
855C2#1311518911yescharacteristic
856C2#1311519211yescharacteristic
857C2#1311545411yescharacteristic
858C2#1311545511yescharacteristic
859C2#1311546111yescharacteristic
860C2#1311546211yescharacteristic
861C2#1311576111yescharacteristic
862C2#1311576511yescharacteristic
subgroupG/H
centerC24D4×D13
commutatorC2×C4×C13C2×C42
FrattiniC23×C4C22×D13
FittingC2×C13×#340C2
socleC24×C13C2×D4
prime radicalC23×D52C22
cosocleC23×C4×C13C23
hypercenterC2×#340D13
hypocenterC13#10931
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
4. C2×C4⋊C4×Dic13C2semidirect
5. C2×#11718121C2semidirect
6. C2×#11718142C2semidirect
7. C2×C13×#340C2semidirect
21. C2×#88061C4semidirect
23. #11718649C4semidirect
28. C2×#88049C4semidirect
196. C2×D52C42semidirect
211. C13×C4⋊C4C22⋊C4semidirect
217. C4⋊Dic13C22⋊C4semidirect
235. C2×#340D13semidirect
349. C2×Dic13#102semidirect
652. C4⋊C4#6103semidirect
660. C13#10931semidirect

Maximal subgroups

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

subgroupindex
C22×#880612
C22×#880492
C2×#117186492
C2×C4⋊C4×Dic132
C2×#117181212
C2×#117181422
C2×C13×#3402
#1093113