Finite Group Databasebeta

← #16791731

Subgroups — #16791731

Order 3328.

1342 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719060C211yesmaximal, characteristic
2C2×C4×C4⋊#261C211yesmaximal, characteristic
3#13130025C212yesmaximal
4#13130023C212yesmaximal
5#13130015C212yesmaximal
6#13130014C211yesmaximal, characteristic
7#13130014C211yesmaximal, characteristic
8#13130014C211yesmaximal, characteristic
9#13130014C211yesmaximal, characteristic
10#13130011C212yesmaximal
11C4×C4⋊C4×D13C211yesmaximal, characteristic
12C22×C4⋊#261C2211yescharacteristic
13C22×C4⋊#261C2211yescharacteristic
14C22×C4⋊#261C2211yescharacteristic
15C22×C4⋊#261C2211yescharacteristic
16C22×C4×#261C2212yes—
17C2×C4⋊C4×D13C2211yescharacteristic
18C2×C4⋊C4×D13C2211yescharacteristic
19C2×C42×D13C2211yescharacteristic
20C2×C42×D13C2211yescharacteristic
21C2×C42×D13C2211yescharacteristic
22C2×(C2×#261)⋊C4C2212yes—
23C2×(C2×#261)⋊C4C2212yes—
24C2×(C2×#261)⋊C4C2212yes—
25C2×(C2×#261)⋊C4C2212yes—
26C2×(C2×#261)⋊C4C2212yes—
27C2×(C2×#261)⋊C4C2212yes—
28C2×(C2×#261)⋊C4C2212yes—
29C2×(C2×#261)⋊C4C2212yes—
30C2×(C2×#261)⋊C4C2212yes—
31C2×(C2×#261)⋊C4C2212yes—
32C2×(C2×#261)⋊C4C2212yes—
33#11719060—24no—
34C4×C4⋊#261—24no—
35C4×C13×C4⋊C4C411yescharacteristic, complemented
36C4⋊C4×Dic13C411yescharacteristic, complemented
37C4⋊C4×Dic13C411yescharacteristic, complemented
38C4×C4⋊Dic13C411yescharacteristic, complemented
39C4×#6101C411yescharacteristic, complemented
40C4×#6101C411yescharacteristic, complemented
41D13×#95C2211yescharacteristic
42D13×#95C2211yescharacteristic
43#11718310C411yescharacteristic, complemented
44#11718310C411yescharacteristic, complemented
45C23×#261C2312yes—
46C23×#261C2312yes—
47C23×#261C2312yes—
48C23×#261C2312yes—
49C22×C4×D13C2311yescharacteristic
50C22×C4×D13C2311yescharacteristic
51C22×C4×D13C2311yescharacteristic
52C22×C4×D13C2311yescharacteristic
53C22×C4×D13C2311yescharacteristic
54C22×C4×D13C2311yescharacteristic
55C22×C4×D13C2311yescharacteristic
56C2×C4⋊#261—22no—
57C2×C4⋊#261—22no—
58C2×C4⋊#261—22no—
59C2×C4⋊#261—22no—
60C2×C4⋊#261—22no—
61C2×C4⋊#261—22no—
62C2×C4⋊#261—22no—
63C2×C4⋊#261—22no—
64C2×C4⋊#261—22no—
65C2×C4⋊#261—22no—
66C2×C4⋊#261D414yes—
67C2×C4⋊#261Q814yes—
68C2×C4×#261—24no—
69C2×C4×#261—24no—
70C2×C4×#261—42no—
71C2×C13×C4⋊C4C2×C411yescharacteristic
72C2×C13×C4⋊C4C2×C411yescharacteristic
73C2×C42×C13C2×C411yescharacteristic
74C2×C42×C13C2×C411yescharacteristic
75C2×C42×C13C2×C411yescharacteristic
76C2×C4⋊Dic13C2×C411yescharacteristic
77C2×C4⋊Dic13C2×C411yescharacteristic
78C2×#6101C2×C411yescharacteristic
79C2×#6101C2×C411yescharacteristic
80C2×#6101C2×C411yescharacteristic
81C2×#6101C2×C411yescharacteristic
82C2×C4×Dic13C2×C411yescharacteristic
83C2×C4×Dic13C2×C411yescharacteristic
84C2×C4×Dic13C2×C411yescharacteristic
85C2×C4×Dic13C2×C411yescharacteristic
86C2×C4×Dic13C2×C411yescharacteristic
87C2×C4×Dic13C2×C411yescharacteristic
88C2×C4×Dic13C2×C411yescharacteristic
89C2×C4×Dic13C2×C411yescharacteristic
90C2×C4×Dic13C2×C411yescharacteristic
91C4⋊C4×D13—22no—
92C4⋊C4×D13—22no—
93C4⋊C4×D13—22no—
94C4⋊C4×D13—22no—
95C42×D13—22no—
96C42×D13—22no—
97C42×D13—22no—
98C42×D13—22no—
99C42×D13—22no—
100C42×D13—22no—
101(C2×#261)⋊C4—24no—
102(C2×#261)⋊C4—24no—
103(C2×#261)⋊C4—24no—
104(C2×#261)⋊C4—24no—
105(C2×#261)⋊C4—24no—
106(C2×#261)⋊C4—24no—
107(C2×#261)⋊C4—42no—
108(C2×#261)⋊C4—42no—
109(C2×#261)⋊C4—42no—
110(C2×#261)⋊C4—42no—
111(C2×#261)⋊C4—42no—
112C13×#95C2×C411yescharacteristic
113C13×#95C2×C411yescharacteristic
114#88071C2×C411yescharacteristic
115#88071C2×C411yescharacteristic
116#88071C2×C411yescharacteristic
117#88071C2×C411yescharacteristic
118#88071C2×C411yescharacteristic
119#88071C2×C411yescharacteristic
120#13885—131nomaximal, Sylow
121C23×D13C2411yescharacteristic
122C22×#261—22no—
123C22×#261—22no—
124C22×#261—22no—
125C22×#261—22no—
126C22×#261—22no—
127C22×#261—22no—
128C22×#261—22no—
129C22×#261—22no—
130C22×#261—22no—
131C22×#261—22no—
132C22×#261—22no—
133C22×#261—22no—
134C22×#261—22no—
135C22×#261—22no—
136C22×#261—22no—
137C22×#261—22no—
138C22×#261—22no—
139C22×#261—22no—
140C22×#261—22no—
141C22×#261—22no—
142C22×#261—22no—
143C22×#261—22no—
144C22×#261—22no—
145C22×#261—22no—
146C22×#261—22no—
147C22×#261—22no—
148C22×#261C2×D414yes—
149C22×#261C2×Q814yes—
150C22×C4×C13C22×C411yescharacteristic
151C22×C4×C13C22×C411yescharacteristic
152C22×C4×C13C22×C411yescharacteristic
153C22×C4×C13C22×C411yescharacteristic
154C22×C4×C13C22×C411yescharacteristic
155C22×C4×C13C22×C411yescharacteristic
156C22×C4×C13C22×C411yescharacteristic
157C22×Dic13C22×C411yescharacteristic
158C22×Dic13C22×C411yescharacteristic
159C22×Dic13C22×C411yescharacteristic
160C22×Dic13C22×C411yescharacteristic
161C22×Dic13C22×C411yescharacteristic
162C22×Dic13C22×C411yescharacteristic
163C22×Dic13C22×C411yescharacteristic
164C2×C4×D13—21no—
165C2×C4×D13—21no—
166C2×C4×D13—21no—
167C2×C4×D13—21no—
168C2×C4×D13—21no—
169C2×C4×D13—21no—
170C2×C4×D13—21no—
171C2×C4×D13—21no—
172C2×C4×D13—21no—
173C2×C4×D13—21no—
174C2×C4×D13—21no—
175C2×C4×D13—21no—
176C2×C4×D13—21no—
177C2×C4×D13—21no—
178C2×C4×D13—21no—
179C2×C4×D13—21no—
180C2×C4×D13—21no—
181C2×C4×D13—21no—
182C2×C4×D13—21no—
183C2×C4×D13—21no—
184C2×C4×D13—21no—
185C2×C4×D13—21no—
186C2×C4×D13—21no—
187C2×C4×D13—21no—
188C2×C4×D13—21no—
189C2×C4×D13—21no—
190C2×C4×D13—21no—
191C2×C4×D13—21no—
192C2×C4×D13—21no—
193C2×C4×D13—21no—
194C2×C4×D13—21no—
195C2×C4×D13—21no—
196C2×C4×D13C2×D412yes—
197C2×C4×D13C2×Q812yes—
198C2×C4×D13#4112yes—
199C2×C4×D13#4112yes—
200C2×C4×D13#4112yes—
201C2×C4×D13#4112yes—
202C2×C4×D13#4112yes—
203C2×C4×D13#4112yes—
204C2×C4×D13#4112yes—
205C2×C4×D13#4112yes—
206C4⋊#261—28no—
207C4⋊#261—28no—
208C4⋊#261—44no—
209C4⋊#261—44no—
210C4×#261—48no—
211C13×C4⋊C4—22no—
212C13×C4⋊C4—22no—
213C42×C13—22no—
214C42×C13—22no—
215C42×C13—22no—
216C4⋊Dic13—22no—
217C4⋊Dic13—22no—
218#6101—22no—
219#6101—22no—
220#6101—22no—
221#6101—22no—
222C4×Dic13—22no—
223C4×Dic13—22no—
224C4×Dic13—22no—
225C4×Dic13—22no—
226C4×Dic13—22no—
227C4×Dic13—22no—
228C4×Dic13—22no—
229C4×Dic13—22no—
230C4×Dic13—22no—
231C2×#382—131no—
232C2×C4×C4⋊C4—131no—
233C2×C4×C4⋊C4—131no—
234#1445—132no—
235#1443—132no—
236#1436—132no—
237C4⋊#95—131no—
238C4⋊#95—131no—
239C4⋊#95—131no—
240C4⋊#95—131no—
241#1434—132no—
242C23×C13C23×C411yescharacteristic
243C22×D13C22×D411yescharacteristic
244C22×D13C22×Q811yescharacteristic
245C22×D13C2×#4111yescharacteristic
246C22×D13C2×#4111yescharacteristic
247C22×D13C2×#4111yescharacteristic
248C22×D13C2×#4111yescharacteristic
249C22×D13C2×#4111yescharacteristic
250C22×D13C2×#4111yescharacteristic
251C22×D13C2×#4111yescharacteristic
252C22×D13C2×#4111yescharacteristic
253C22×D13H(5,𝔽2)11yescharacteristic
254C22×D13H(5,𝔽2)11yescharacteristic
255C22×D132−1+411yescharacteristic
256C22×D132−1+411yescharacteristic
257C2×#261—24no—
258C2×#261—24no—
259C2×#261—24no—
260C2×#261—24no—
261C2×#261—24no—
262C2×#261—24no—
263C2×#261—42no—
264C2×#261—42no—
265C2×#261—42no—
266C2×#261—42no—
267C2×#261—42no—
268C2×#261—42no—
269C2×#261—42no—
270C2×#261—42no—
271C2×#261—42no—
272C2×#261—42no—
273C2×#261—42no—
274C2×#261—42no—
275C2×#261—42no—
276C2×#261—42no—
277C2×#261—42no—
278C2×#261—42no—
279C2×#261—42no—
280C2×#261—42no—
281C2×#261—42no—
282C2×#261—42no—
283C2×#261—42no—
284C2×#261—42no—
285C2×C4×C13—21no—
286C2×C4×C13—21no—
287C2×C4×C13—21no—
288C2×C4×C13—21no—
289C2×C4×C13—21no—
290C2×C4×C13—21no—
291C2×C4×C13—21no—
292C2×C4×C13—21no—
293C2×C4×C13—21no—
294C2×C4×C13—21no—
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#11712yes—
302C2×C4×C13#11712yes—
303C2×C4×C13#11712yes—
304C2×C4×C13C4×D412yes—
305C2×C4×C13C4×Q812yes—
306C2×Dic13—21no—
307C2×Dic13—21no—
308C2×Dic13—21no—
309C2×Dic13—21no—
310C2×Dic13—21no—
311C2×Dic13—21no—
312C2×Dic13—21no—
313C2×Dic13—21no—
314C2×Dic13—21no—
315C2×Dic13—21no—
316C2×Dic13—21no—
317C2×Dic13—21no—
318C2×Dic13—21no—
319C2×Dic13—21no—
320C2×Dic13—21no—
321C2×Dic13—21no—
322C2×Dic13#11712yes—
323C2×Dic13#11712yes—
324C2×Dic13#11712yes—
325C2×Dic13C4×D412yes—
326C2×Dic13C4×Q812yes—
327C4×D13—22no—
328C4×D13—22no—
329C4×D13—22no—
330C4×D13—22no—
331C4×D13—22no—
332C4×D13—22no—
333C4×D13—22no—
334C4×D13—22no—
335C4×D13—41no—
336C4×D13—41no—
337C4×D13—41no—
338C4×D13—41no—
339C4×D13—41no—
340C4×D13—41no—
341C4×D13—41no—
342C4×D13—41no—
343C4×D13—41no—
344C4×D13—41no—
345C4×D13—41no—
346C4×D13—41no—
347C4×D13—41no—
348C4×D13—41no—
349C4×D13—41no—
350C4×D13—41no—
351C4×D13C22⋊Q814yes—
352C4×D13#12314yes—
353C4×D13#12514yes—
354C4×D13#12614yes—
355C22×C4⋊C4—131no—
356C22×C4⋊C4—131no—
357C22×C4⋊C4—131no—
358C22×C4⋊C4—131no—
359C22×C4⋊C4—131no—
360C22×C4⋊C4—131no—
361C22×C42—131no—
362C22×C42—131no—
363C22×C42—131no—
364C22×C42—132no—
365#382—264no—
366C4×C4⋊C4—131no—
367C4×C4⋊C4—131no—
368C4×C4⋊C4—131no—
369C4×C4⋊C4—131no—
370C4×C4⋊C4—131no—
371C4×C4⋊C4—131no—
372C4×C4⋊C4—131no—
373C4×C4⋊C4—264no—
374C4×C4⋊C4#26111yescharacteristic, complemented
375C2×#95—131no—
376C2×#95—131no—
377C2×#95—132no—
378C2×#95—132no—
379C2×#95—132no—
380C2×#95—132no—
381C2×#95—132no—
382C2×#95—132no—
383C2×#95—132no—
384C2×#95—132no—
385C2×#95—132no—
386C2×#95—132no—
387C2×#95—132no—
388C22×C13C2×#11711yescharacteristic
389C22×C13C2×#11711yescharacteristic
390C22×C13C2×#11711yescharacteristic
391C22×C13C2×C4×D411yescharacteristic
392C22×C13C2×C4×Q811yescharacteristic
393C22×C13#52011yescharacteristic
394C22×C13#52011yescharacteristic
395C2×D13C2×C22⋊Q811yescharacteristic
396C2×D13C2×#12311yescharacteristic
397C2×D13C2×#12511yescharacteristic
398C2×D13C2×#12611yescharacteristic
399C2×D13#52911yescharacteristic
400C2×D13#52911yescharacteristic
401C2×D13#52911yescharacteristic
402C2×D13#52911yescharacteristic
403C2×D13#54011yescharacteristic
404C2×D13#54111yescharacteristic
405C2×D13#54211yescharacteristic
406C2×D13#54211yescharacteristic
407C2×D13#54611yescharacteristic
408C2×D13#54711yescharacteristic
409C2×D13#54811yescharacteristic
410C2×D13#55011yescharacteristic
411C2×D13#55211yescharacteristic
412C2×D13#55311yescharacteristic
413C2×D13#55411yescharacteristic
414C2×D13#55411yescharacteristic
415C2×D13#55511yescharacteristic
416C2×D13#55611yescharacteristic
417C2×D13#55611yescharacteristic
418C2×D13#55611yescharacteristic
419C2×D13#55711yescharacteristic
420C2×D13#55711yescharacteristic
421C2×D13#55911yescharacteristic
422C2×D13#55911yescharacteristic
423#261—44no—
424#261—44no—
425#261—82no—
426#261—82no—
427C4×C13—22no—
428C4×C13—22no—
429C4×C13—41no—
430C4×C13—41no—
431C4×C13—41no—
432C4×C13—41no—
433C4×C13#38714yes—
434Dic13—22no—
435Dic13—22no—
436Dic13—41no—
437Dic13—41no—
438Dic13—41no—
439Dic13—41no—
440Dic13#38714yes—
441C23×C4—131no—
442C23×C4—131no—
443C23×C4—131no—
444C23×C4—132no—
445C23×C4—132no—
446C23×C4—131no—
447C23×C4—131no—
448C23×C4—131no—
449C23×C4—131no—
450C23×C4—132no—
451C23×C4—132no—
452C2×C4⋊C4—134no—
453C2×C4⋊C4—134no—
454C2×C4⋊C4—131no—
455C2×C4⋊C4—131no—
456C2×C4⋊C4—131no—
457C2×C4⋊C4—131no—
458C2×C4⋊C4—131no—
459C2×C4⋊C4—131no—
460C2×C4⋊C4—262no—
461C2×C4⋊C4—262no—
462C2×C4⋊C4—262no—
463C2×C4⋊C4—262no—
464C2×C4⋊C4—262no—
465C2×C4⋊C4—262no—
466C2×C4⋊C4—262no—
467C2×C4⋊C4—262no—
468C2×C4⋊C4—262no—
469C2×C4⋊C4—262no—
470C2×C4⋊C4—262no—
471C2×C4⋊C4—262no—
472C2×C4⋊C4—262no—
473C2×C4⋊C4—262no—
474C2×C4⋊C4C2×#26111yescharacteristic
475C2×C4⋊C4C2×#26111yescharacteristic
476C2×C42—131no—
477C2×C42—131no—
478C2×C42—131no—
479C2×C42—131no—
480C2×C42—131no—
481C2×C42—131no—
482C2×C42—131no—
483C2×C42—131no—
484C2×C42—131no—
485C2×C42—262no—
486C2×C42—262no—
487C2×C42—262no—
488C2×C42—262no—
489C2×C42—262no—
490C2×C42—262no—
491C2×C42—264no—
492C2×C42—264no—
493C2×C42—522no—
494C2×C42C2×#26111yescharacteristic
495C2×C42C2×#26111yescharacteristic
496C2×C42C2×#26111yescharacteristic
497#95—131no—
498#95—131no—
499#95—131no—
500#95—131no—
501#95—131no—
502#95—131no—
503#95—264no—
504#95—264no—
505#95—264no—
506#95—264no—
507#95—264no—
508#95—264no—
509#95—522no—
510#95—522no—
511#95—522no—
512#95—522no—
513#95—522no—
514#95C2×#26111yescharacteristic
515#95C2×#26111yescharacteristic
516C2×C13#228311yescharacteristic
517C2×C13C2×#38711yescharacteristic
518C2×C13#231411yescharacteristic
519C2×C13#235211yescharacteristic
520C2×C13#235411yescharacteristic
521C2×C13#235511yescharacteristic
522C2×C13#235511yescharacteristic
523D13#244711yescharacteristic
524D13#244811yescharacteristic
525D13#245311yescharacteristic
526D13#245411yescharacteristic
527D13#250811yescharacteristic
528D13#250911yescharacteristic
529D13#251311yescharacteristic
530D13#251411yescharacteristic
531C24—131no—
532C22×C4—131no—
533C22×C4—132no—
534C22×C4—132no—
535C22×C4—132no—
536C22×C4—132no—
537C22×C4—132no—
538C22×C4—132no—
539C22×C4—131no—
540C22×C4—131no—
541C22×C4—132no—
542C22×C4—132no—
543C22×C4—132no—
544C22×C4—132no—
545C22×C4—134no—
546C22×C4—134no—
547C22×C4—131no—
548C22×C4—131no—
549C22×C4—131no—
550C22×C4—131no—
551C22×C4—261no—
552C22×C4—261no—
553C22×C4—261no—
554C22×C4—261no—
555C22×C4—261no—
556C22×C4—261no—
557C22×C4—261no—
558C22×C4—261no—
559C22×C4—261no—
560C22×C4—261no—
561C22×C4—261no—
562C22×C4—261no—
563C22×C4—261no—
564C22×C4—261no—
565C22×C4—261no—
566C22×C4—261no—
567C22×C4—261no—
568C22×C4—261no—
569C22×C4—261no—
570C22×C4—261no—
571C22×C4—261no—
572C22×C4—261no—
573C22×C4—261no—
574C22×C4—261no—
575C22×C4—261no—
576C22×C4—261no—
577C22×C4—261no—
578C22×C4—261no—
579C22×C4—261no—
580C22×C4—261no—
581C22×C4—261no—
582C22×C4—261no—
583C22×C4—262no—
584C22×C4—262no—
585C22×C4—262no—
586C22×C4—262no—
587C22×C4—262no—
588C22×C4—262no—
589C22×C4—262no—
590C22×C4—262no—
591C22×C4—262no—
592C22×C4—262no—
593C22×C4—262no—
594C22×C4—262no—
595C22×C4—262no—
596C22×C4—262no—
597C22×C4—262no—
598C22×C4—262no—
599C22×C4—262no—
600C22×C4—262no—
601C22×C4—262no—
602C22×C4—262no—
603C22×C4—262no—
604C22×C4—262no—
605C22×C4—262no—
606C22×C4—262no—
607C22×C4—262no—
608C22×C4—262no—
609C22×C4C22×#26111yescharacteristic
610C22×C4C22×#26111yescharacteristic
611C22×C4C22×#26111yescharacteristic
612C22×C4C22×#26111yescharacteristic
613C22×C4C22×#26111yescharacteristic
614C22×C4C22×#26111yescharacteristic
615C22×C4C22×#26111yescharacteristic
616C4⋊C4—22no—
617C4⋊C4—22no—
618C4⋊C4—262no—
619C4⋊C4—262no—
620C4⋊C4—262no—
621C4⋊C4—262no—
622C4⋊C4—268no—
623C4⋊C4—268no—
624C4⋊C4—262no—
625C4⋊C4—262no—
626C4⋊C4—524no—
627C4⋊C4—524no—
628C42—22no—
629C42—22no—
630C42—22no—
631C42—262no—
632C42—262no—
633C42—262no—
634C42—262no—
635C42—262no—
636C42—262no—
637C42—262no—
638C42—262no—
639C42—262no—
640C42—528no—
641C13#1388511yescharacteristic, complemented, Sylow
642C23—131no—
643C23—131no—
644C23—131no—
645C23—131no—
646C23—131no—
647C23—131no—
648C23—131no—
649C23—131no—
650C23—131no—
651C23—131no—
652C23—131no—
653C23—131no—
654C23—131no—
655C23—131no—
656C23C23×#26111yescharacteristic
657C2×C4—21no—
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—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—132no—
674C2×C4—132no—
675C2×C4—132no—
676C2×C4—134no—
677C2×C4—134no—
678C2×C4—134no—
679C2×C4—134no—
680C2×C4—132no—
681C2×C4—132no—
682C2×C4—262no—
683C2×C4—262no—
684C2×C4—262no—
685C2×C4—262no—
686C2×C4—262no—
687C2×C4—262no—
688C2×C4—262no—
689C2×C4—262no—
690C2×C4—261no—
691C2×C4—261no—
692C2×C4—261no—
693C2×C4—261no—
694C2×C4—264no—
695C2×C4—264no—
696C2×C4—264no—
697C2×C4—264no—
698C2×C4—264no—
699C2×C4—264no—
700C2×C4—261no—
701C2×C4—261no—
702C2×C4—261no—
703C2×C4—261no—
704C2×C4—261no—
705C2×C4—261no—
706C2×C4—261no—
707C2×C4—261no—
708C2×C4—261no—
709C2×C4—261no—
710C2×C4—261no—
711C2×C4—261no—
712C2×C4—521no—
713C2×C4—521no—
714C2×C4—521no—
715C2×C4—521no—
716C2×C4—521no—
717C2×C4—521no—
718C2×C4—521no—
719C2×C4—521no—
720C2×C4—521no—
721C2×C4—521no—
722C2×C4—521no—
723C2×C4—521no—
724C2×C4—521no—
725C2×C4—521no—
726C2×C4—521no—
727C2×C4—521no—
728C2×C4—522no—
729C2×C4—522no—
730C2×C4—522no—
731C2×C4—522no—
732C2×C4—522no—
733C2×C4—522no—
734C2×C4—522no—
735C2×C4—522no—
736C2×C4—522no—
737C2×C4—522no—
738C2×C4—522no—
739C2×C4—522no—
740C2×C4—522no—
741C2×C4—522no—
742C2×C4—522no—
743C2×C4—522no—
744C2×C4—522no—
745C2×C4—522no—
746C2×C4—522no—
747C2×C4—522no—
748C2×C4—522no—
749C2×C4—522no—
750C2×C4#8823712yes—
751C2×C4#8823712yes—
752C2×C4#8823712yes—
753C2×C4D4×#26112yes—
754C2×C4Q8×#26112yes—
755C22—131no—
756C22—131no—
757C22—131no—
758C22—131no—
759C22—131no—
760C22—131no—
761C22—131no—
762C22—131no—
763C22—131no—
764C22—131no—
765C22—131no—
766C22—131no—
767C22—131no—
768C22—131no—
769C22—131no—
770C22—131no—
771C22—131no—
772C22—131no—
773C22—131no—
774C22—131no—
775C22—131no—
776C22—131no—
777C22—131no—
778C22—131no—
779C22—131no—
780C22—131no—
781C22—131no—
782C22—131no—
783C22C2×#8823711yescharacteristic
784C22C2×#8823711yescharacteristic
785C22C2×#8823711yescharacteristic
786C22C2×D4×#26111yescharacteristic
787C22C2×Q8×#26111yescharacteristic
788C22#1171963111yescharacteristic
789C22#1171963111yescharacteristic
790C4—22no—
791C4—22no—
792C4—41no—
793C4—41no—
794C4—41no—
795C4—41no—
796C4—134no—
797C4—262no—
798C4—262no—
799C4—524no—
800C4—524no—
801C4—521no—
802C4—521no—
803C4—521no—
804C4—521no—
805C4—1042no—
806C4—1042no—
807C4#1171908214yes—
808C2—131no—
809C2—131no—
810C2—131no—
811C2—131no—
812C2—131no—
813C2—131no—
814C2—131no—
815C2—131no—
816C2#1313128311yescharacteristic
817C2C2×#1171908211yescharacteristic
818C2#1313131411yescharacteristic
819C2#1313135211yescharacteristic
820C2#1313135411yescharacteristic
821C2#1313135511yescharacteristic
822C2#1313135511yescharacteristic
subgroupG/H
center, FrattiniC23C23×#261
commutator, socleC23×C13C23×C4
FittingC4×C13×C4⋊C4C4
prime radical, cosocleC23×D13C24
hypercenterC4×C4⋊C4#261
hypocenterC13#13885
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
35. C4×C13×C4⋊C4C4semidirect
36. C4⋊C4×Dic13C4semidirect
37. C4⋊C4×Dic13C4semidirect
38. C4×C4⋊Dic13C4semidirect
39. C4×#6101C4semidirect
40. C4×#6101C4semidirect
43. #11718310C4semidirect
44. #11718310C4semidirect
374. C4×C4⋊C4#261semidirect
641. C13#13885semidirect

Maximal subgroups

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

subgroupindex
C2×#117190602
C2×C4×C4⋊#2612
#131300252
#131300232
#131300152
#131300142
#131300112
C4×C4⋊C4×D132
#1388513