Finite Group Databasebeta

← #15883187

Subgroups — #15883187

Order 3328.

1170 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×#11718888C211yesmaximal, characteristic
2C2×#11718687C211yesmaximal, characteristic, complemented
3C22×#88075C211yesmaximal, characteristic, complemented
4#13117850C211yesmaximal, characteristic
5#13115720C211yesmaximal, characteristic, complemented
6#13115529C211yesmaximal, characteristic, complemented
7#13115474C211yesmaximal, characteristic, complemented
8#13115262C211yesmaximal, characteristic
9#13115191C211yesmaximal, characteristic, complemented
10#13115173C211yesmaximal, characteristic, complemented
11#13115090C211yesmaximal, characteristic, complemented
12#13115023C211yesmaximal, characteristic, complemented
13#13114666C211yesmaximal, characteristic, complemented
14#13114614C211yesmaximal, characteristic, complemented
15Q8×C13×C22⋊C4C211yesmaximal, characteristic, complemented
16C23×Q8×C13C2211yescharacteristic
17C2×C4×Q8×C13C2211yescharacteristic
18C2×C4×Q8×C13C2211yescharacteristic
19C22×#6106C2211yescharacteristic
20C22×#6106C2211yescharacteristic
21C2×#88184C2211yescharacteristic
22C22×C4⋊Dic13C2211yescharacteristic
23C23×#1055C2211yescharacteristic
24C2×#88135—21no—
25C2×C4×D52C2211yescharacteristic
26C13×#391—21no—
27C13×#391—21no—
28C13×#391C2211yescharacteristic
29C13×#391C2211yescharacteristic
30C13×#380—21no—
31C13×#380C2211yescharacteristic
32C4×C13×C22⋊C4—21no—
33C4×C13×C22⋊C4C2211yescharacteristic
34#11718888C418yescomplemented
35C2×#88075—24no—
36C2×#88075C2211yescharacteristic
37C2×#88075C2211yescharacteristic
38C2×#88075C2211yescharacteristic
39C2×#88075C2211yescharacteristic
40C2×#88075C2211yescharacteristic
41C2×#88075C2211yescharacteristic
42C2×C22⋊#1055C2211yescharacteristic
43#11718687—24no—
44C2×#88049C2211yescharacteristic
45C2×#88049C2211yescharacteristic
46C2×#88047C2211yescharacteristic
47C2×#88047C2211yescharacteristic
48#11718619—21no—
49#11718600C2211yescharacteristic
50C4×C4⋊Dic13C2211yescharacteristic
51#11718589C2211yescharacteristic
52C2×#88043C2211yescharacteristic
53C2×#88043C2211yescharacteristic
54#11718331—21no—
55#11718329—21no—
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60#11718116C2211yescharacteristic
61#11718116C2211yescharacteristic
62C22×Q8×C13—21no—
63C22×Q8×C13—22no—
64C22×Q8×C13—22no—
65C22×Q8×C13—22no—
66C22×Q8×C13—41no—
67C22×Q8×C13—41no—
68C22×Q8×C13C2×C414yescomplemented
69C22×Q8×C13C2311yescharacteristic
70C22×Q8×C13C2311yescharacteristic
71C23×C4×C13—21no—
72C23×C4×C13C2311yescharacteristic
73C22×C22⋊D13—21no—
74C23×Dic13—21no—
75C22×D52C2311yescharacteristic
76C22×C4×D13—21no—
77C4×Q8×C13—22no—
78C4×Q8×C13—22no—
79C4×Q8×C13—41no—
80C4×Q8×C13—41no—
81C2×C13×C4⋊C4—21no—
82C2×C13×C4⋊C4—21no—
83C2×C13×C4⋊C4C2311yescharacteristic
84C2×C13×C4⋊C4C2311yescharacteristic
85C2×C13×C22⋊C4—21no—
86C2×C13×C22⋊C4D411yescharacteristic
87C2×C13×C22⋊C4D411yescharacteristic
88C2×C42×C13—21no—
89C2×C42×C13—21no—
90C2×C42×C13C2311yescharacteristic
91C2×C42×C13C2311yescharacteristic
92C2×#6106—22no—
93C2×#6106—22no—
94C2×#6106—41no—
95C2×#6106—41no—
96C2×#6106C2×C414yescomplemented
97C2×#6106C2×C414yescomplemented
98#88184—22no—
99#88184C2×C414yes—
100C2×#6103—21no—
101C2×#6103—21no—
102C2×#6103—21no—
103C2×#6103—21no—
104C2×C4⋊Dic13—22no—
105C2×C4⋊Dic13—21no—
106C2×C4⋊Dic13—41no—
107C2×C4⋊Dic13C2311yescharacteristic
108C2×C4⋊Dic13C2311yescharacteristic
109C2×C4⋊Dic13C2311yescharacteristic
110C2×#6101—21no—
111C2×C4×Dic13—21no—
112C22×#1055—22no—
113C22×#1055—22no—
114C22×#1055—41no—
115C22×#1055C2311yescharacteristic
116C22×#1055C2311yescharacteristic
117C22×#1055C2311yescharacteristic
118C22×#1055C2311yescharacteristic
119#88135—44no—
120C4×D52—22no—
121C4×D52—41no—
122C13×#95—21no—
123C13×#95—21no—
124C13×#95—21no—
125C13×#95—21no—
126C13×#95—21no—
127C13×#95D411yescharacteristic
128C13×#95D411yescharacteristic
129#88075—22no—
130#88075—22no—
131#88075—22no—
132#88075C2×C414yescomplemented
133#88075C2×C414yescomplemented
134#88075D414yescomplemented
135#88071—21no—
136#88071—21no—
137C22⋊#1055C2×C414yescomplemented
138#88049—22no—
139#88049—41no—
140#88047—22no—
141#88047—41no—
142#88043—22no—
143#88043—41no—
144#22855—131nomaximal, Sylow
145C24×C13C2×D411yescharacteristic
146C23×D13—21no—
147C2×Q8×C13—24no—
148C2×Q8×C13—21no—
149C2×Q8×C13—21no—
150C2×Q8×C13—21no—
151C2×Q8×C13—21no—
152C2×Q8×C13—28no—
153C2×Q8×C13—21no—
154C2×Q8×C13—21no—
155C2×Q8×C13—21no—
156C2×Q8×C13—21no—
157C2×Q8×C13—42no—
158C2×Q8×C13—42no—
159C2×Q8×C13—44no—
160C2×Q8×C13—44no—
161C2×Q8×C13—44no—
162C2×Q8×C13C22×C412yes—
163C2×Q8×C13C22×C412yes—
164C2×Q8×C13C2×D412yes—
165C2×Q8×C13#4112yes—
166C22×C4×C13—21no—
167C22×C4×C13—21no—
168C22×C4×C13—21no—
169C22×C4×C13—21no—
170C22×C4×C13—21no—
171C22×C4×C13—24no—
172C22×C4×C13—21no—
173C22×C4×C13—21no—
174C22×C4×C13—21no—
175C22×C4×C13—42no—
176C22×C4×C13—42no—
177C22×C4×C13C22×C412yes—
178C22×C4×C13C2×D411yescharacteristic
179C22×C4×C13C2×D411yescharacteristic
180C22×C4×C13C2×D411yescharacteristic
181C22×C4×C13C2×D411yescharacteristic
182C22×C4×C13C2×D411yescharacteristic
183C22×C4×C13#4112yes—
184C22×C4×C13C2411yescharacteristic
185C2×C22⋊D13—24no—
186C2×C22⋊D13—42no—
187C2×C22⋊D13—42no—
188C22×Dic13—21no—
189C22×Dic13—21no—
190C22×Dic13—21no—
191C22×Dic13—42no—
192C22×Dic13—42no—
193C22×Dic13—81no—
194C2×D52—21no—
195C2×D52—21no—
196C2×D52—21no—
197C2×D52—21no—
198C2×D52—21no—
199C2×D52C22×C412yes—
200C2×C4×D13—42no—
201C2×C4×D13—42no—
202C2×C4×D13—81no—
203C13×C4⋊C4—21no—
204C13×C4⋊C4—21no—
205C13×C4⋊C4—21no—
206C13×C4⋊C4—21no—
207C13×C4⋊C4—42no—
208C13×C4⋊C4—42no—
209C13×C22⋊C4—22no—
210C13×C22⋊C4—22no—
211C13×C22⋊C4—42no—
212C42×C13—21no—
213C42×C13—21no—
214C42×C13—21no—
215C42×C13—21no—
216C42×C13—42no—
217C42×C13—42no—
218#6106—28no—
219#6106—44no—
220#6103—24no—
221#6103—42no—
222#6103—42no—
223#6103—81no—
224C4⋊Dic13—21no—
225C4⋊Dic13—21no—
226C4⋊Dic13—21no—
227C4⋊Dic13—21no—
228C4⋊Dic13—42no—
229C4⋊Dic13C22×C412yes—
230C4⋊Dic13C2×D412yes—
231#6101—42no—
232C4×Dic13—42no—
233C2×#1055—21no—
234C2×#1055—21no—
235C2×#1055—21no—
236C2×#1055—21no—
237C2×#1055—21no—
238C2×#1055—21no—
239C2×#1055—21no—
240C2×#1055—21no—
241C2×#1055—21no—
242C2×#1055—44no—
243C2×#1055C22×C412yes—
244C2×#1055C22×C412yes—
245C2×#1055C2×D412yes—
246C2×#448—131no—
247C2×#440—131no—
248C22×#103—131no—
249#2361—131no—
250Q8×C22⋊C4D1311yescharacteristic, complemented
251#1973—131no—
252#1935—131no—
253#1928—131no—
254#1893—131no—
255#1880—131no—
256#1877—131no—
257#1863—131no—
258#1852—131no—
259#1763—131no—
260#1752—131no—
261C23×C13—21no—
262C23×C13—21no—
263C23×C13—21no—
264C23×C13—21no—
265C23×C13C4×D412yes—
266C23×C13AGL(1,ℤ/8)12yes—
267C23×C13#13712yes—
268C23×C13C22×D411yescharacteristic
269C22×D13—22no—
270C22×D13—41no—
271C22×D13—41no—
272C22×D13—41no—
273C22×D13—41no—
274C22×D13—41no—
275C22×D13—41no—
276Q8×C13—22no—
277Q8×C13—22no—
278Q8×C13—22no—
279Q8×C13—22no—
280Q8×C13—22no—
281Q8×C13—48no—
282Q8×C13—41no—
283Q8×C13—41no—
284Q8×C13C4×D414yescomplemented
285C2×C4×C13—22no—
286C2×C4×C13—21no—
287C2×C4×C13—22no—
288C2×C4×C13—22no—
289C2×C4×C13—21no—
290C2×C4×C13—22no—
291C2×C4×C13—22no—
292C2×C4×C13—22no—
293C2×C4×C13—22no—
294C2×C4×C13—22no—
295C2×C4×C13—21no—
296C2×C4×C13—21no—
297C2×C4×C13—21no—
298C2×C4×C13—21no—
299C2×C4×C13—21no—
300C2×C4×C13—21no—
301C2×C4×C13—21no—
302C2×C4×C13—21no—
303C2×C4×C13—21no—
304C2×C4×C13—21no—
305C2×C4×C13—21no—
306C2×C4×C13—21no—
307C2×C4×C13—48no—
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×C13C4×D412yes—
317C2×C4×C13C23×C411yescharacteristic
318C2×C4×C13C22×D411yescharacteristic
319C2×C4×C13C2×#4111yescharacteristic
320C2×C4×C13C2×#4111yescharacteristic
321C2×C4×C13H(5,𝔽2)11yescharacteristic
322C2×C4×C13H(5,𝔽2)11yescharacteristic
323C22⋊D13—48no—
324C2×Dic13—22no—
325C2×Dic13—22no—
326C2×Dic13—41no—
327C2×Dic13—41no—
328C2×Dic13—41no—
329C2×Dic13—41no—
330C2×Dic13—41no—
331C2×Dic13—41no—
332C2×Dic13—41no—
333C2×Dic13—84no—
334D52—22no—
335D52—22no—
336D52—41no—
337D52—41no—
338C4×D13—84no—
339#1055—22no—
340#1055—22no—
341#1055—22no—
342#1055—41no—
343C23×Q8C2×D1311yescharacteristic
344C22×SD16—131no—
345C22×SD16—131no—
346C23×C8—131no—
347C2×#121—131no—
348C2×C4×Q8C2×D1311yescharacteristic
349C2×C4×Q8C2×D1311yescharacteristic
350C2×C4×D4—131no—
351C2×C4×D4—261no—
352C22×C4⋊C4—131no—
353#448—138no—
354#440—264no—
355C2×#107—131no—
356C2×#107—131no—
357C2×#103—131no—
358C2×#103—131no—
359C2×#103—131no—
360C2×#103—131no—
361C2×#103—131no—
362C2×#103—131no—
363C2×#103—264no—
364C2×#102—131no—
365C2×#102—131no—
366C2×C22⋊C8—131no—
367C2×#97—131no—
368C2×#97—131no—
369#391—21no—
370#391—21no—
371#391C2×D1311yescharacteristic
372#391C2×D1311yescharacteristic
373#390—131no—
374#389—131no—
375#388—261no—
376#386—261no—
377#385—261no—
378#380—21no—
379#380C2×D1311yescharacteristic
380C4×C4⋊C4—131no—
381C4×C22⋊C4—21no—
382C4×C22⋊C4C2×D1311yescharacteristic
383#340—131no—
384#340—131no—
385#340—131no—
386#340—131no—
387#336—131no—
388#336—131no—
389C22×C13—22no—
390C22×C13—22no—
391C22×C13—22no—
392C22×C13—22no—
393C22×C13—22no—
394C22×C13—22no—
395C22×C13#44014yescomplemented
396C22×C13C2×C4×D411yescharacteristic
397C22×C13D4211yescharacteristic
398C22×C13#54611yescharacteristic
399C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
400C22×C13C2×#13711yescharacteristic
401C22×C13#57711yescharacteristic
402C22×C13#57811yescharacteristic
403C2×D13—42no—
404C2×D13—42no—
405C2×D13—42no—
406C2×D13—81no—
407C2×D13—81no—
408C2×D13—81no—
409C2×D13—81no—
410C4×C13—22no—
411C4×C13—24no—
412C4×C13—42no—
413C4×C13—41no—
414C4×C13—41no—
415C4×C13—41no—
416C4×C13—41no—
417C4×C13—81no—
418C4×C13—81no—
419C4×C13C2×C4×D411yescharacteristic
420C4×C13#51811yescharacteristic
421C4×C13#54611yescharacteristic
422C4×C13#55111yescharacteristic
423Dic13—42no—
424Dic13—42no—
425Dic13—81no—
426C22×Q8—22no—
427C22×Q8—21no—
428C22×Q8—22no—
429C22×Q8—22no—
430C22×Q8—41no—
431C22×Q8—41no—
432C22×Q8C4×D1314yescomplemented
433C22×Q8C22×D1311yescharacteristic
434C22×Q8C22×D1311yescharacteristic
435C22×D4—131no—
436C22×D4—261no—
437C23×C4—21no—
438C23×C4—261no—
439C23×C4—261no—
440C23×C4C22×D1311yescharacteristic
441C2×SD16—134no—
442C2×SD16—134no—
443C2×SD16—262no—
444C2×SD16—262no—
445C2×SD16—521no—
446C2×SD16—521no—
447C22×C8—131no—
448C22×C8—131no—
449C22×C8—131no—
450C22×C8—131no—
451C22×C8—262no—
452C22×C8—262no—
453C22×C8—521no—
454#121—134no—
455#121—262no—
456C4×Q8—22no—
457C4×Q8—22no—
458C4×Q8—41no—
459C4×Q8—41no—
460C4×D4—262no—
461C4×D4—521no—
462C4×D4—524no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—131no—
466C2×C4⋊C4—131no—
467C2×C4⋊C4—131no—
468C2×C4⋊C4—262no—
469C2×C4⋊C4—261no—
470C2×C4⋊C4—261no—
471C2×C4⋊C4—521no—
472C2×C4⋊C4C22×D1311yescharacteristic
473C2×C4⋊C4C22×D1311yescharacteristic
474C2×C22⋊C4—21no—
475C2×C22⋊C4—261no—
476C2×C22⋊C4—261no—
477C2×C22⋊C4—261no—
478C2×C22⋊C4—261no—
479C2×C22⋊C4C22⋊D1311yescharacteristic
480C2×C22⋊C4C22⋊D1311yescharacteristic
481C2×C42—21no—
482C2×C42—21no—
483C2×C42—261no—
484C2×C42C22×D1311yescharacteristic
485C2×C42C22×D1311yescharacteristic
486#107—262no—
487#107—521no—
488#103—134no—
489#103—134no—
490#103—134no—
491#103—262no—
492#103—262no—
493#103—262no—
494#102—262no—
495#102—521no—
496C22⋊C8—134no—
497#97—262no—
498#97—521no—
499#95—21no—
500#95—21no—
501#95—21no—
502#95—21no—
503#95—21no—
504#95—261no—
505#95—261no—
506#95C22⋊D1311yescharacteristic
507#95C22⋊D1311yescharacteristic
508C2×C13—24no—
509C2×C13#235811yescharacteristic
510C2×C13C2×#44011yescharacteristic
511C2×C13#294711yescharacteristic
512C2×C13#326511yescharacteristic
513C2×C13#327011yescharacteristic
514C2×C13#330811yescharacteristic
515C2×C13#332011yescharacteristic
516D13—82no—
517C24—261no—
518C24C2×C22⋊D1311yescharacteristic
519C2×Q8—24no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—28no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—42no—
530C2×Q8—42no—
531C2×Q8—44no—
532C2×Q8—44no—
533C2×Q8—44no—
534C2×Q8C2×C4×D1312yes—
535C2×Q8C2×C4×D1312yes—
536C2×Q8D4×D1312yes—
537C2×Q8#612912yes—
538C2×D4—132no—
539C2×D4—264no—
540C2×D4—261no—
541C2×D4—261no—
542C2×D4—261no—
543C2×D4—261no—
544C2×D4—261no—
545C2×D4—522no—
546C2×D4—522no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—24no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—261no—
559C22×C4—261no—
560C22×C4—261no—
561C22×C4—522no—
562C22×C4—522no—
563C22×C4—522no—
564C22×C4—522no—
565C22×C4—1041no—
566C22×C4—1041no—
567C22×C4C2×C4×D1312yes—
568C22×C4#612712yes—
569C22×C4C2×C22⋊D1311yescharacteristic
570C22×C4C2×C22⋊D1311yescharacteristic
571C22×C4C2×C22⋊D1311yescharacteristic
572C22×C4C2×C22⋊D1311yescharacteristic
573C22×C4C2×C22⋊D1311yescharacteristic
574C22×C4C23×D1311yescharacteristic
575SD16—268no—
576SD16—524no—
577C2×C8—132no—
578C2×C8—132no—
579C2×C8—132no—
580C2×C8—261no—
581C2×C8—261no—
582C2×C8—261no—
583C2×C8—261no—
584C2×C8—261no—
585C2×C8—261no—
586C2×C8—261no—
587C2×C8—261no—
588C2×C8—261no—
589C2×C8—524no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—42no—
595C4⋊C4—42no—
596C4⋊C4—132no—
597C4⋊C4—132no—
598C4⋊C4—261no—
599C4⋊C4—261no—
600C4⋊C4—261no—
601C4⋊C4—261no—
602C4⋊C4—522no—
603C4⋊C4—522no—
604C22⋊C4—22no—
605C22⋊C4—22no—
606C22⋊C4—42no—
607C22⋊C4—264no—
608C22⋊C4—522no—
609C22⋊C4—522no—
610C22⋊C4—1041no—
611C42—21no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—42no—
616C42—42no—
617C42—522no—
618C13#2285511yescharacteristic, complemented, Sylow
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—262no—
624C23—521no—
625C23—521no—
626C23—521no—
627C23—521no—
628C23—521no—
629C23—521no—
630C23C4×C22⋊D1312yes—
631C23#8819612yes—
632C23#8820312yes—
633C23C22×C22⋊D1311yescharacteristic
634Q8—22no—
635Q8—22no—
636Q8—22no—
637Q8—22no—
638Q8—22no—
639Q8—48no—
640Q8—41no—
641Q8—41no—
642Q8#8813514yescomplemented
643D4—262no—
644D4—262no—
645D4—528no—
646D4—521no—
647D4—521no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—48no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—262no—
680C2×C4—262no—
681C2×C4—521no—
682C2×C4—521no—
683C2×C4—521no—
684C2×C4—521no—
685C2×C4—521no—
686C2×C4—521no—
687C2×C4—521no—
688C2×C4—1044no—
689C2×C4—1044no—
690C2×C4C4×C22⋊D1312yes—
691C2×C4C22×C4×D1311yescharacteristic
692C2×C4C2×#612711yescharacteristic
693C2×C4C2×D4×D1311yescharacteristic
694C2×C4C2×#612911yescharacteristic
695C2×C4#8825111yescharacteristic
696C2×C4#8825111yescharacteristic
697C8—262no—
698C8—262no—
699C8—262no—
700C8—521no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—522no—
708C22—522no—
709C22—522no—
710C22—1041no—
711C22—1041no—
712C22—1041no—
713C22—1041no—
714C22#1171868714yescomplemented
715C22C2×C4×C22⋊D1311yescharacteristic
716C22D4×C22⋊D1311yescharacteristic
717C22#1171951111yescharacteristic
718C22C2×#8819611yescharacteristic
719C22C2×#8820311yescharacteristic
720C22#1171954211yescharacteristic
721C22#1171954311yescharacteristic
722C4—22no—
723C4—24no—
724C4—41no—
725C4—41no—
726C4—42no—
727C4—41no—
728C4—41no—
729C4—81no—
730C4—81no—
731C4—522no—
732C4—522no—
733C4—1041no—
734C4C2×#8813511yescharacteristic
735C4#1171919111yescharacteristic
736C4#1171919511yescharacteristic
737C4#1171920011yescharacteristic
738C2—24no—
739C2—1042no—
740C2#1311781511yescharacteristic
741C2C2×#1171868711yescharacteristic
742C2#1312367911yescharacteristic
743C2#1312633211yescharacteristic
744C2#1312640711yescharacteristic
745C2#1312682711yescharacteristic
746C2#1312700711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingQ8×C13×C22⋊C4C2
socleC23×C13C22×D4
prime radicalC2×#88184C22
cosocleC22×C4×C13C24
hypercenterQ8×C22⋊C4D13
hypocenterC13#22855
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ Q8×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#11718687C2semidirect
3. C22×#88075C2semidirect
5. #13115720C2semidirect
6. #13115529C2semidirect
7. #13115474C2semidirect
9. #13115191C2semidirect
10. #13115173C2semidirect
11. #13115090C2semidirect
12. #13115023C2semidirect
13. #13114666C2semidirect
14. #13114614C2semidirect
15. Q8×C13×C22⋊C4C2semidirect
34. #11718888C4semidirect
68. C22×Q8×C13C2×C4semidirect
96. C2×#6106C2×C4semidirect
97. C2×#6106C2×C4semidirect
132. #88075C2×C4semidirect
133. #88075C2×C4semidirect
134. #88075D4semidirect
137. C22⋊#1055C2×C4semidirect
250. Q8×C22⋊C4D13semidirect
284. Q8×C13C4×D4semidirect
395. C22×C13#440semidirect
432. C22×Q8C4×D13semidirect
618. C13#22855semidirect
642. Q8#88135semidirect
714. C22#11718687semidirect

Maximal subgroups

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

subgroupindex
C2×#117188882
C2×#117186872
C22×#880752
#131178502
#131157202
#131155292
#131154742
#131152622
#131151912
#131151732
#131150902
#131150232
#131146662
#131146142
Q8×C13×C22⋊C42
#2285513