Finite Group Databasebeta

← C4×#11718336 #15784741

Subgroups — C4×#11718336 #15784741

Order 3328.

1790 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718336C211yesmaximal, characteristic
2C2×C4×#6101C211yesmaximal, characteristic, complemented
3C2×C4×#6103C211yesmaximal, characteristic
4C2×C4×#6103C211yesmaximal, characteristic
5C2×C4×#6103C211yesmaximal, characteristic
6#13113102C211yesmaximal, characteristic, complemented
7#13113098C211yesmaximal, characteristic, complemented
8#13113097C211yesmaximal, characteristic, complemented
9#13113094C211yesmaximal, characteristic, complemented
10#13113084C211yesmaximal, characteristic
11#13113084C211yesmaximal, characteristic
12#13113080C211yesmaximal, characteristic
13C4×#88071C211yesmaximal, characteristic, complemented
14C4×#88071C211yesmaximal, characteristic, complemented
15C4×C13×#95C211yesmaximal, characteristic, complemented
16C23×C4×D13C2211yescharacteristic
17C22×C42×C13C2211yescharacteristic
18C22×C42×C13C2211yescharacteristic
19C22×C42×C13C2211yescharacteristic
20C22×#6103C2211yescharacteristic
21C22×#6103C2211yescharacteristic
22C22×#6103C2211yescharacteristic
23C22×#6103C2211yescharacteristic
24C22×#6103C2211yescharacteristic
25C22×#6103C2211yescharacteristic
26C22×#6101C2211yescharacteristic
27C22×#6101C2211yescharacteristic
28C22×C4×Dic13C2211yescharacteristic
29C22×C4×Dic13C2211yescharacteristic
30C22×C4×Dic13C2211yescharacteristic
31C2×C13×#95C2211yescharacteristic
32C2×C13×#95C2211yescharacteristic
33C2×C13×#95C2211yescharacteristic
34C2×C13×#95C2211yescharacteristic
35C2×#88071C2211yescharacteristic
36C2×#88071C2211yescharacteristic
37C2×#88071C2211yescharacteristic
38C2×#88071C2211yescharacteristic
39C2×#88071C2211yescharacteristic
40C2×#88071C2211yescharacteristic
41C2×#88071C2211yescharacteristic
42C2×#88071C2211yescharacteristic
43C2×#88071C2211yescharacteristic
44C2×#88071C2211yescharacteristic
45C2×#88071C2211yescharacteristic
46C2×#88071C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C4×#6103—24no—
52C4×#6103—24no—
53C4×#6103—24no—
54C4×#6101—24no—
55#11718336C418yesdirect product factor
56C24×D13C2311yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C23×C4×C13C2311yescharacteristic
64C23×Dic13C2311yescharacteristic
65C23×Dic13C2311yescharacteristic
66C23×Dic13C2311yescharacteristic
67C23×Dic13C2311yescharacteristic
68C23×Dic13C2311yescharacteristic
69C23×Dic13C2311yescharacteristic
70C23×Dic13C2311yescharacteristic
71C22×C4×D13—22no—
72C22×C4×D13—22no—
73C22×C4×D13—22no—
74C22×C4×D13—22no—
75C22×C4×D13—22no—
76C22×C4×D13—22no—
77C22×C4×D13D414yes—
78C2×C42×C13—22no—
79C2×C42×C13—22no—
80C2×C42×C13—22no—
81C2×C42×C13—22no—
82C2×C42×C13—22no—
83C2×C42×C13—22no—
84C2×C42×C13—22no—
85C2×C42×C13—22no—
86C2×C42×C13—22no—
87C2×#6103—22no—
88C2×#6103—22no—
89C2×#6103—22no—
90C2×#6103—22no—
91C2×#6103—22no—
92C2×#6103—22no—
93C2×#6103—22no—
94C2×#6103—22no—
95C2×#6103—22no—
96C2×#6103—22no—
97C2×#6103—22no—
98C2×#6103—22no—
99C2×#6103—22no—
100C2×#6103—22no—
101C2×#6103—22no—
102C2×#6103C2×C414yes—
103C2×#6103C2×C414yes—
104C2×#6103C2×C414yes—
105C2×#6101—22no—
106C2×#6101—22no—
107C2×#6101—22no—
108C2×#6101—22no—
109C2×#6101—22no—
110C2×#6101C2×C414yescomplemented
111C2×C4×Dic13—22no—
112C2×C4×Dic13—22no—
113C2×C4×Dic13—22no—
114C2×C4×Dic13—22no—
115C2×C4×Dic13—22no—
116C2×C4×Dic13—22no—
117C2×C4×Dic13—22no—
118C2×C4×Dic13—22no—
119C2×C4×Dic13D414yes—
120C13×#95—22no—
121C13×#95—22no—
122C13×#95—22no—
123C13×#95C2×C414yescomplemented
124#88071—22no—
125#88071—22no—
126#88071—22no—
127#88071—22no—
128#88071—22no—
129#88071—22no—
130#88071—22no—
131#88071—22no—
132#88071—22no—
133#88071—22no—
134#88071—22no—
135#88071—22no—
136#88071—22no—
137#88071—22no—
138#88071C2×C414yescomplemented
139#88071C2×C414yescomplemented
140C4×#397—131nomaximal, Sylow
141C24×C13C2411yescharacteristic
142C23×D13—21no—
143C23×D13—21no—
144C23×D13—21no—
145C23×D13—21no—
146C23×D13—21no—
147C23×D13—21no—
148C23×D13—21no—
149C23×D13—21no—
150C23×D13—21no—
151C23×D13—21no—
152C23×D13—21no—
153C23×D13—21no—
154C23×D13C22×C412yes—
155C23×D13C2×D412yes—
156C23×D13#4112yes—
157C22×C4×C13—21no—
158C22×C4×C13—21no—
159C22×C4×C13—21no—
160C22×C4×C13—21no—
161C22×C4×C13—21no—
162C22×C4×C13—21no—
163C22×C4×C13—21no—
164C22×C4×C13—21no—
165C22×C4×C13—21no—
166C22×C4×C13—21no—
167C22×C4×C13—21no—
168C22×C4×C13—21no—
169C22×C4×C13—21no—
170C22×C4×C13—21no—
171C22×C4×C13—21no—
172C22×C4×C13—21no—
173C22×C4×C13—21no—
174C22×C4×C13—21no—
175C22×C4×C13—21no—
176C22×C4×C13—21no—
177C22×C4×C13—21no—
178C22×C4×C13—21no—
179C22×C4×C13—21no—
180C22×C4×C13—21no—
181C22×C4×C13—21no—
182C22×C4×C13—21no—
183C22×C4×C13—21no—
184C22×C4×C13—21no—
185C22×C4×C13—21no—
186C22×C4×C13—21no—
187C22×C4×C13—21no—
188C22×C4×C13—21no—
189C22×C4×C13—21no—
190C22×C4×C13—21no—
191C22×C4×C13—21no—
192C22×C4×C13—21no—
193C22×C4×C13C22×C412yes—
194C22×C4×C13C22×C412yes—
195C22×C4×C13C22×C412yes—
196C22×C4×C13C2×D412yes—
197C22×C4×C13C2×D412yes—
198C22×C4×C13#4112yes—
199C22×C4×C13#4112yes—
200C22×C4×C13#4112yes—
201C22×C4×C13#4112yes—
202C22×C4×C13#4112yes—
203C22×C4×C13#4112yes—
204C22×C4×C13#4112yes—
205C22×C4×C13#4112yes—
206C22×Dic13—21no—
207C22×Dic13—21no—
208C22×Dic13—21no—
209C22×Dic13—21no—
210C22×Dic13—21no—
211C22×Dic13—21no—
212C22×Dic13—21no—
213C22×Dic13—21no—
214C22×Dic13—21no—
215C22×Dic13—21no—
216C22×Dic13—21no—
217C22×Dic13—21no—
218C22×Dic13—21no—
219C22×Dic13—21no—
220C22×Dic13—21no—
221C22×Dic13—21no—
222C22×Dic13—21no—
223C22×Dic13—21no—
224C22×Dic13—21no—
225C22×Dic13—21no—
226C22×Dic13—21no—
227C22×Dic13—21no—
228C22×Dic13—21no—
229C22×Dic13—21no—
230C22×Dic13—21no—
231C22×Dic13—21no—
232C22×Dic13—21no—
233C22×Dic13—21no—
234C22×Dic13—21no—
235C22×Dic13—21no—
236C22×Dic13—21no—
237C22×Dic13—21no—
238C22×Dic13—21no—
239C22×Dic13—21no—
240C22×Dic13—21no—
241C22×Dic13—21no—
242C22×Dic13—21no—
243C22×Dic13—21no—
244C22×Dic13—21no—
245C22×Dic13—21no—
246C22×Dic13C22×C412yes—
247C22×Dic13C22×C412yes—
248C22×Dic13C22×C412yes—
249C22×Dic13C2×D412yes—
250C22×Dic13C2×D412yes—
251C22×Dic13C2×D412yes—
252C22×Dic13#4112yes—
253C22×Dic13#4112yes—
254C22×Dic13#4112yes—
255C2×C4×D13—28no—
256C2×C4×D13—28no—
257C2×C4×D13—28no—
258C2×C4×D13—44no—
259C2×C4×D13—44no—
260C2×C4×D13—44no—
261C2×C4×D13—44no—
262C42×C13—44no—
263C42×C13—44no—
264C42×C13—44no—
265#6103—28no—
266#6103—28no—
267#6103—28no—
268#6103—28no—
269#6103—28no—
270#6103—28no—
271#6101—28no—
272#6101—28no—
273C4×Dic13—28no—
274C4×Dic13—44no—
275C4×Dic13—44no—
276C2×#397—131no—
277C2×C4×C4⋊C4—131no—
278C2×C4×C22⋊C4—131no—
279C2×C4×C22⋊C4—131no—
280C2×C4×C22⋊C4—131no—
281#1445—131no—
282#1443—131no—
283#1443—131no—
284#1442—131no—
285#1440—131no—
286#1440—131no—
287#1439—131no—
288C4×#95—131no—
289C4×#95—131no—
290C4×#95D1311yescharacteristic, complemented
291C23×C13C23×C411yescharacteristic
292C23×C13C22×D411yescharacteristic
293C23×C13C22×D411yescharacteristic
294C23×C13C2×#4111yescharacteristic
295C23×C13C2×#4111yescharacteristic
296C23×C13C2×#4111yescharacteristic
297C23×C13C2×#4111yescharacteristic
298C23×C13C2×#4111yescharacteristic
299C23×C13C2×#4111yescharacteristic
300C23×C13C2×#4111yescharacteristic
301C23×C13C2×#4111yescharacteristic
302C23×C13C2×#4111yescharacteristic
303C23×C13C2×#4111yescharacteristic
304C23×C13C2×#4111yescharacteristic
305C23×C13C2×#4111yescharacteristic
306C22×D13—22no—
307C22×D13—22no—
308C22×D13—22no—
309C22×D13—22no—
310C22×D13—22no—
311C22×D13—22no—
312C22×D13—22no—
313C22×D13—22no—
314C22×D13—22no—
315C22×D13—22no—
316C22×D13—22no—
317C22×D13—22no—
318C22×D13—22no—
319C22×D13—22no—
320C22×D13—22no—
321C22×D13—22no—
322C22×D13—22no—
323C22×D13—22no—
324C22×D13—41no—
325C22×D13—41no—
326C22×D13—41no—
327C22×D13—41no—
328C22×D13—41no—
329C22×D13—41no—
330C22×D13—41no—
331C22×D13—41no—
332C22×D13—41no—
333C22×D13—41no—
334C22×D13—41no—
335C22×D13—41no—
336C22×D13—41no—
337C22×D13—41no—
338C22×D13—41no—
339C22×D13—41no—
340C22×D13C4×D414yes—
341C2×C4×C13—22no—
342C2×C4×C13—22no—
343C2×C4×C13—22no—
344C2×C4×C13—22no—
345C2×C4×C13—22no—
346C2×C4×C13—22no—
347C2×C4×C13—22no—
348C2×C4×C13—22no—
349C2×C4×C13—22no—
350C2×C4×C13—22no—
351C2×C4×C13—22no—
352C2×C4×C13—22no—
353C2×C4×C13—22no—
354C2×C4×C13—22no—
355C2×C4×C13—22no—
356C2×C4×C13—22no—
357C2×C4×C13—22no—
358C2×C4×C13—22no—
359C2×C4×C13—41no—
360C2×C4×C13—41no—
361C2×C4×C13—41no—
362C2×C4×C13—41no—
363C2×C4×C13—41no—
364C2×C4×C13—41no—
365C2×C4×C13—41no—
366C2×C4×C13—41no—
367C2×C4×C13—41no—
368C2×C4×C13—41no—
369C2×C4×C13—41no—
370C2×C4×C13—41no—
371C2×C4×C13—41no—
372C2×C4×C13—41no—
373C2×C4×C13—41no—
374C2×C4×C13—41no—
375C2×C4×C13—41no—
376C2×C4×C13—41no—
377C2×C4×C13—41no—
378C2×C4×C13—41no—
379C2×C4×C13—41no—
380C2×C4×C13—41no—
381C2×C4×C13—41no—
382C2×C4×C13—41no—
383C2×C4×C13#12114yes—
384C2×C4×C13#12314yes—
385C2×C4×C13#12314yes—
386C2×C4×C13#12314yes—
387C2×C4×C13#12414yes—
388C2×C4×C13#12614yes—
389C2×C4×C13#12614yes—
390C2×Dic13—22no—
391C2×Dic13—22no—
392C2×Dic13—22no—
393C2×Dic13—22no—
394C2×Dic13—22no—
395C2×Dic13—22no—
396C2×Dic13—22no—
397C2×Dic13—22no—
398C2×Dic13—22no—
399C2×Dic13—22no—
400C2×Dic13—22no—
401C2×Dic13—22no—
402C2×Dic13—22no—
403C2×Dic13—22no—
404C2×Dic13—22no—
405C2×Dic13—22no—
406C2×Dic13—22no—
407C2×Dic13—22no—
408C2×Dic13—22no—
409C2×Dic13—22no—
410C2×Dic13—22no—
411C2×Dic13—22no—
412C2×Dic13—22no—
413C2×Dic13—22no—
414C2×Dic13—41no—
415C2×Dic13—41no—
416C2×Dic13—41no—
417C2×Dic13—41no—
418C2×Dic13—41no—
419C2×Dic13—41no—
420C2×Dic13—41no—
421C2×Dic13—41no—
422C2×Dic13—41no—
423C2×Dic13—41no—
424C2×Dic13—41no—
425C2×Dic13—41no—
426C2×Dic13—41no—
427C2×Dic13—41no—
428C2×Dic13—41no—
429C2×Dic13—41no—
430C2×Dic13—41no—
431C2×Dic13—41no—
432C2×Dic13—41no—
433C2×Dic13—41no—
434C2×Dic13—41no—
435C2×Dic13—41no—
436C2×Dic13—41no—
437C2×Dic13—41no—
438C2×Dic13C4×D414yes—
439C4×D13—416no—
440C24×C4—131no—
441C22×C4⋊C4—131no—
442C22×C4⋊C4—131no—
443C22×C22⋊C4—131no—
444C22×C22⋊C4—131no—
445C22×C22⋊C4—131no—
446C22×C22⋊C4—131no—
447C22×C22⋊C4—131no—
448C22×C22⋊C4—131no—
449C22×C42—131no—
450C22×C42—131no—
451C22×C42—131no—
452C22×C42C2×D1311yescharacteristic
453C22×C42C2×D1311yescharacteristic
454C22×C42C2×D1311yescharacteristic
455#397—138no—
456C4×C4⋊C4—264no—
457C4×C22⋊C4—264no—
458C4×C22⋊C4—264no—
459C4×C22⋊C4—264no—
460C2×#95—131no—
461C2×#95—131no—
462C2×#95—131no—
463C2×#95—131no—
464C2×#95—131no—
465C2×#95—131no—
466C2×#95—131no—
467C2×#95—131no—
468C2×#95—131no—
469C2×#95—131no—
470C2×#95—131no—
471C2×#95—131no—
472C2×#95—131no—
473C2×#95—131no—
474C2×#95—131no—
475C2×#95—131no—
476C2×#95C2×D1311yescharacteristic
477C2×#95C2×D1311yescharacteristic
478C2×#95C2×D1311yescharacteristic
479C2×#95C2×D1311yescharacteristic
480C22×C13C2×C4×D411yescharacteristic
481C22×C13C2×C4×D411yescharacteristic
482C22×C13C4×#4111yescharacteristic
483C22×C13C4×#4111yescharacteristic
484C22×C13C4×#4111yescharacteristic
485C22×C13C4×#4111yescharacteristic
486C22×C13C4×#4111yescharacteristic
487C22×C13C2×#12111yescharacteristic
488C22×C13C2×#12311yescharacteristic
489C22×C13C2×#12311yescharacteristic
490C22×C13C2×#12311yescharacteristic
491C22×C13#52511yescharacteristic
492C22×C13#52511yescharacteristic
493C22×C13#52511yescharacteristic
494C22×C13#52511yescharacteristic
495C22×C13C2×#12411yescharacteristic
496C22×C13C2×#12611yescharacteristic
497C22×C13C2×#12611yescharacteristic
498C22×C13#52911yescharacteristic
499C22×C13#52911yescharacteristic
500C22×C13#52911yescharacteristic
501C22×C13#52911yescharacteristic
502C22×C13#52911yescharacteristic
503C22×C13#52911yescharacteristic
504C22×C13#52911yescharacteristic
505C22×C13#52911yescharacteristic
506C22×C13#52911yescharacteristic
507C22×C13#52911yescharacteristic
508C22×C13#52911yescharacteristic
509C22×C13#52911yescharacteristic
510C22×C13#52911yescharacteristic
511C22×C13#52911yescharacteristic
512C22×C13#52911yescharacteristic
513C22×C13#53211yescharacteristic
514C22×C13#53211yescharacteristic
515C2×D13—24no—
516C2×D13—24no—
517C2×D13—24no—
518C2×D13—42no—
519C2×D13—42no—
520C2×D13—42no—
521C2×D13—42no—
522C2×D13—42no—
523C2×D13—42no—
524C2×D13—42no—
525C2×D13—42no—
526C2×D13—42no—
527C2×D13—42no—
528C2×D13—42no—
529C2×D13—42no—
530C4×C13—42no—
531C4×C13—42no—
532C4×C13—42no—
533C4×C13—42no—
534C4×C13—42no—
535C4×C13—42no—
536C4×C13#39718yescomplemented
537Dic13—24no—
538Dic13—42no—
539Dic13—42no—
540Dic13—42no—
541Dic13—42no—
542Dic13—42no—
543Dic13—42no—
544C25—131no—
545C23×C4—131no—
546C23×C4—131no—
547C23×C4—131no—
548C23×C4—131no—
549C23×C4—131no—
550C23×C4—131no—
551C23×C4—131no—
552C23×C4—134no—
553C23×C4—262no—
554C23×C4—262no—
555C23×C4—262no—
556C23×C4—262no—
557C23×C4—262no—
558C23×C4—262no—
559C23×C4C22×D1311yescharacteristic
560C23×C4C22×D1311yescharacteristic
561C23×C4C22×D1311yescharacteristic
562C23×C4C22×D1311yescharacteristic
563C23×C4C22×D1311yescharacteristic
564C23×C4C22×D1311yescharacteristic
565C23×C4C22×D1311yescharacteristic
566C2×C4⋊C4—134no—
567C2×C4⋊C4—262no—
568C2×C4⋊C4—262no—
569C2×C4⋊C4—262no—
570C2×C4⋊C4—262no—
571C2×C4⋊C4—262no—
572C2×C22⋊C4—134no—
573C2×C22⋊C4—134no—
574C2×C22⋊C4—134no—
575C2×C22⋊C4—262no—
576C2×C22⋊C4—262no—
577C2×C22⋊C4—262no—
578C2×C22⋊C4—262no—
579C2×C22⋊C4—262no—
580C2×C22⋊C4—262no—
581C2×C22⋊C4—262no—
582C2×C22⋊C4—262no—
583C2×C22⋊C4—262no—
584C2×C22⋊C4—262no—
585C2×C22⋊C4—262no—
586C2×C22⋊C4—262no—
587C2×C22⋊C4—262no—
588C2×C22⋊C4—262no—
589C2×C22⋊C4—262no—
590C2×C42—22no—
591C2×C42—22no—
592C2×C42—22no—
593C2×C42—22no—
594C2×C42—22no—
595C2×C42—22no—
596C2×C42—22no—
597C2×C42—22no—
598C2×C42—22no—
599C2×C42—134no—
600C2×C42—262no—
601C2×C42—262no—
602C2×C42—262no—
603C2×C42—262no—
604C2×C42—262no—
605C2×C42—262no—
606C2×C42—262no—
607C2×C42—262no—
608#95—22no—
609#95—22no—
610#95—22no—
611#95—134no—
612#95—134no—
613#95—262no—
614#95—262no—
615#95—262no—
616#95—262no—
617#95—262no—
618#95—262no—
619#95—262no—
620#95—262no—
621#95—262no—
622#95—262no—
623#95—262no—
624#95—262no—
625#95—262no—
626#95—262no—
627#95C4×D1314yescomplemented
628C2×C13C4×#12111yescharacteristic
629C2×C13C4×#12311yescharacteristic
630C2×C13C4×#12311yescharacteristic
631C2×C13C4×#12311yescharacteristic
632C2×C13C4×#12411yescharacteristic
633C2×C13C4×#12611yescharacteristic
634C2×C13C4×#12611yescharacteristic
635C2×C13C2×#39711yescharacteristic
636C2×C13#239211yescharacteristic
637C2×C13#239511yescharacteristic
638C2×C13#239511yescharacteristic
639C2×C13#239511yescharacteristic
640C2×C13#239811yescharacteristic
641C2×C13#240111yescharacteristic
642C2×C13#240111yescharacteristic
643D13—44no—
644C24—132no—
645C24—132no—
646C24—132no—
647C24—261no—
648C24—261no—
649C24—261no—
650C24—261no—
651C24—261no—
652C24—261no—
653C24—261no—
654C24—261no—
655C24—261no—
656C24—261no—
657C24—261no—
658C24—261no—
659C24C23×D1311yescharacteristic
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—132no—
697C22×C4—132no—
698C22×C4—132no—
699C22×C4—132no—
700C22×C4—132no—
701C22×C4—132no—
702C22×C4—132no—
703C22×C4—132no—
704C22×C4—132no—
705C22×C4—261no—
706C22×C4—261no—
707C22×C4—261no—
708C22×C4—261no—
709C22×C4—261no—
710C22×C4—261no—
711C22×C4—261no—
712C22×C4—261no—
713C22×C4—261no—
714C22×C4—261no—
715C22×C4—261no—
716C22×C4—261no—
717C22×C4—261no—
718C22×C4—261no—
719C22×C4—261no—
720C22×C4—261no—
721C22×C4—261no—
722C22×C4—261no—
723C22×C4—261no—
724C22×C4—261no—
725C22×C4—261no—
726C22×C4—261no—
727C22×C4—261no—
728C22×C4—261no—
729C22×C4—261no—
730C22×C4—261no—
731C22×C4—261no—
732C22×C4—261no—
733C22×C4—261no—
734C22×C4—261no—
735C22×C4—261no—
736C22×C4—261no—
737C22×C4—261no—
738C22×C4—261no—
739C22×C4—261no—
740C22×C4—261no—
741C22×C4—261no—
742C22×C4—261no—
743C22×C4—261no—
744C22×C4—261no—
745C22×C4—268no—
746C22×C4—268no—
747C22×C4—268no—
748C22×C4—524no—
749C22×C4—524no—
750C22×C4—524no—
751C22×C4—524no—
752C22×C4C2×C4×D1312yes—
753C22×C4C2×C4×D1312yes—
754C22×C4C2×C4×D1312yes—
755C22×C4#612712yes—
756C22×C4#612712yes—
757C22×C4#612712yes—
758C22×C4#612712yes—
759C22×C4#612712yes—
760C22×C4#612712yes—
761C22×C4D4×D1312yes—
762C22×C4D4×D1312yes—
763C22×C4#612912yes—
764C22×C4#613112yes—
765C4⋊C4—268no—
766C4⋊C4—268no—
767C22⋊C4—268no—
768C22⋊C4—268no—
769C22⋊C4—268no—
770C22⋊C4—268no—
771C22⋊C4—268no—
772C22⋊C4—268no—
773C42—44no—
774C42—44no—
775C42—44no—
776C42—268no—
777C42—524no—
778C42—524no—
779C13C4×#39711yescharacteristic, complemented, Sylow
780C23—134no—
781C23—262no—
782C23—262no—
783C23—262no—
784C23—262no—
785C23—262no—
786C23—262no—
787C23—262no—
788C23—262no—
789C23—262no—
790C23—262no—
791C23—262no—
792C23—262no—
793C23—262no—
794C23—262no—
795C23—262no—
796C23—262no—
797C23—262no—
798C23—262no—
799C23—521no—
800C23—521no—
801C23—521no—
802C23—521no—
803C23—521no—
804C23—521no—
805C23—521no—
806C23—521no—
807C23—521no—
808C23—521no—
809C23—521no—
810C23—521no—
811C23—521no—
812C23—521no—
813C23—521no—
814C23—521no—
815C23C22×C4×D1311yescharacteristic
816C23C2×#612711yescharacteristic
817C23C2×#612711yescharacteristic
818C23C2×#612711yescharacteristic
819C23C2×#612711yescharacteristic
820C23C2×#612711yescharacteristic
821C23C2×#612711yescharacteristic
822C23C2×D4×D1311yescharacteristic
823C23C2×D4×D1311yescharacteristic
824C23C2×#612911yescharacteristic
825C23C2×#613111yescharacteristic
826C23#41×D1311yescharacteristic
827C23#41×D1311yescharacteristic
828C23#41×D1311yescharacteristic
829C23#41×D1311yescharacteristic
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—134no—
873C2×C4—262no—
874C2×C4—262no—
875C2×C4—262no—
876C2×C4—262no—
877C2×C4—262no—
878C2×C4—262no—
879C2×C4—262no—
880C2×C4—262no—
881C2×C4—262no—
882C2×C4—262no—
883C2×C4—262no—
884C2×C4—262no—
885C2×C4—262no—
886C2×C4—262no—
887C2×C4—262no—
888C2×C4—262no—
889C2×C4—262no—
890C2×C4—262no—
891C2×C4—262no—
892C2×C4—262no—
893C2×C4—262no—
894C2×C4—262no—
895C2×C4—262no—
896C2×C4—262no—
897C2×C4—521no—
898C2×C4—521no—
899C2×C4—521no—
900C2×C4—521no—
901C2×C4—521no—
902C2×C4—521no—
903C2×C4—521no—
904C2×C4—521no—
905C2×C4—521no—
906C2×C4—521no—
907C2×C4—521no—
908C2×C4—521no—
909C2×C4—521no—
910C2×C4—521no—
911C2×C4—521no—
912C2×C4—521no—
913C2×C4—521no—
914C2×C4—521no—
915C2×C4—521no—
916C2×C4—521no—
917C2×C4—521no—
918C2×C4—521no—
919C2×C4—521no—
920C2×C4—521no—
921C2×C4—5216no—
922C2×C4#8813014yes—
923C2×C4#8813714yes—
924C2×C4#8813814yes—
925C2×C4#8813914yes—
926C2×C4#8814814yes—
927C2×C4#8814814yes—
928C2×C4#8815214yes—
929C22—264no—
930C22—264no—
931C22—264no—
932C22—522no—
933C22—522no—
934C22—522no—
935C22—522no—
936C22—522no—
937C22—522no—
938C22—522no—
939C22—522no—
940C22—522no—
941C22—522no—
942C22—522no—
943C22—522no—
944C22C4×#612711yescharacteristic
945C22C4×#612711yescharacteristic
946C22C4×#612711yescharacteristic
947C22C2×#8813011yescharacteristic
948C22#1171918411yescharacteristic
949C22#1171918411yescharacteristic
950C22#1171918411yescharacteristic
951C22C2×#8813711yescharacteristic
952C22C2×#8813811yescharacteristic
953C22C2×#8813911yescharacteristic
954C22C2×#8814811yescharacteristic
955C22C2×#8814811yescharacteristic
956C22C2×#8815211yescharacteristic
957C22#1171923311yescharacteristic
958C22#1171923311yescharacteristic
959C22#1171923311yescharacteristic
960C22#1171923311yescharacteristic
961C22#1171923311yescharacteristic
962C22#1171923311yescharacteristic
963C22C4×#612911yescharacteristic
964C22#1171924311yescharacteristic
965C22#1171924311yescharacteristic
966C22C4×D4×D1311yescharacteristic
967C22C4×D4×D1311yescharacteristic
968C22#1171925211yescharacteristic
969C22#1171925211yescharacteristic
970C22#1171925211yescharacteristic
971C22#1171925211yescharacteristic
972C22#1171925311yescharacteristic
973C22#1171925311yescharacteristic
974C22#1171926211yescharacteristic
975C22C4×#613111yescharacteristic
976C22#1171928511yescharacteristic
977C22#1171928511yescharacteristic
978C22#1171928511yescharacteristic
979C4—42no—
980C4—42no—
981C4—42no—
982C4—42no—
983C4—42no—
984C4—42no—
985C4—264no—
986C4—522no—
987C4—522no—
988C4—522no—
989C4—522no—
990C4—522no—
991C4—522no—
992C4#1171833618yesdirect product factor
993C2—524no—
994C2C4×#8813811yescharacteristic
995C2C4×#8813711yescharacteristic
996C2C4×#8814811yescharacteristic
997C2C4×#8814811yescharacteristic
998C2C4×#8813911yescharacteristic
999C2C4×#8813011yescharacteristic
1000C2C4×#8815211yescharacteristic
1001C2C2×#1171833611yescharacteristic
1002C2#1311808011yescharacteristic
1003C2#1311809711yescharacteristic
1004C2#1311809911yescharacteristic
1005C2#1311809911yescharacteristic
1006C2#1311812311yescharacteristic
1007C2#1311813411yescharacteristic
1008C2#1311813711yescharacteristic
subgroupG/H
centerC23×C4C22×D13
commutatorC23×C13C23×C4
FrattiniC24C23×D13
FittingC4×C13×#95C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenterC4×#95D13
hypocenterC13C4×#397
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23×C4 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
2. C2×C4×#6101C2semidirect
6. #13113102C2semidirect
7. #13113098C2semidirect
8. #13113097C2semidirect
9. #13113094C2semidirect
13. C4×#88071C2semidirect
14. C4×#88071C2semidirect
15. C4×C13×#95C2semidirect
55. #11718336C4direct (N × H)
110. C2×#6101C2×C4semidirect
123. C13×#95C2×C4semidirect
138. #88071C2×C4semidirect
139. #88071C2×C4semidirect
290. C4×#95D13semidirect
536. C4×C13#397semidirect
627. #95C4×D13semidirect
779. C13C4×#397semidirect
992. C4#11718336direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117183362
C2×C4×#61012
C2×C4×#61032
#131131022
#131130982
#131130972
#131130942
#131130842
#131130802
C4×#880712
C4×C13×#952
C4×#39713