Finite Group Databasebeta

← C4×#11718609 #15784777

Subgroups — C4×#11718609 #15784777

Order 3328.

1966 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718609C211yesmaximal, characteristic
2C2×C4×#6101C211yesmaximal, characteristic, complemented
3C2×C4×#6101C211yesmaximal, characteristic, complemented
4C2×C4×C4⋊Dic13C211yesmaximal, characteristic, complemented
5C2×C4×C22⋊Dic13C211yesmaximal, characteristic
6C2×C4×C22⋊Dic13C211yesmaximal, characteristic
7#13113097C211yesmaximal, characteristic, complemented
8#13113090C211yesmaximal, characteristic, complemented
9#13113088C211yesmaximal, characteristic, complemented
10#13113087C211yesmaximal, characteristic, complemented
11#13113081C211yesmaximal, characteristic
12#13113079C211yesmaximal, characteristic
13#13113079C211yesmaximal, characteristic
14C4×#88071C211yesmaximal, characteristic, complemented
15C2×C4×C13×C22⋊C4C211yesmaximal, characteristic
16C24×C4×C13C2211yescharacteristic
17C22×C13×C22⋊C4C2211yescharacteristic
18C22×C13×C22⋊C4C2211yescharacteristic
19C22×C42×C13C2211yescharacteristic
20C22×C42×C13C2211yescharacteristic
21C22×C22⋊Dic13C2211yescharacteristic
22C22×C22⋊Dic13C2211yescharacteristic
23C22×C22⋊Dic13C2211yescharacteristic
24C22×C22⋊Dic13C2211yescharacteristic
25C22×C4⋊Dic13C2211yescharacteristic
26C22×C4⋊Dic13C2211yescharacteristic
27C22×#6101C2211yescharacteristic
28C22×#6101C2211yescharacteristic
29C22×#6101C2211yescharacteristic
30C22×#6101C2211yescharacteristic
31C22×C4×Dic13C2211yescharacteristic
32C22×C4×Dic13C2211yescharacteristic
33C22×C4×Dic13C2211yescharacteristic
34C22×C4×Dic13C2211yescharacteristic
35C4×C13×C22⋊C4—24no—
36C2×C13×#95C2211yescharacteristic
37C2×C13×#95C2211yescharacteristic
38C4×C22⋊Dic13—24no—
39C4×C22⋊Dic13—24no—
40C2×#88071C2211yescharacteristic
41C2×#88071C2211yescharacteristic
42C2×#88071C2211yescharacteristic
43C2×#88071C2211yescharacteristic
44C2×#88071C2211yescharacteristic
45C2×#88071C2211yescharacteristic
46C2×#88071C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54#11718609C418yesdirect product factor
55C4×C4⋊Dic13—24no—
56C4×#6101—24no—
57C4×#6101—24no—
58C25×C13C2311yescharacteristic
59C23×C4×C13—22no—
60C23×C4×C13—22no—
61C23×C4×C13—22no—
62C23×C4×C13—22no—
63C23×C4×C13—22no—
64C23×C4×C13—22no—
65C23×C4×C13Q814yes—
66C23×C4×C13C2311yescharacteristic
67C23×C4×C13C2311yescharacteristic
68C23×C4×C13C2311yescharacteristic
69C23×C4×C13C2311yescharacteristic
70C23×C4×C13C2311yescharacteristic
71C23×C4×C13C2311yescharacteristic
72C23×Dic13C2311yescharacteristic
73C23×Dic13C2311yescharacteristic
74C23×Dic13C2311yescharacteristic
75C23×Dic13C2311yescharacteristic
76C23×Dic13C2311yescharacteristic
77C23×Dic13C2311yescharacteristic
78C23×Dic13C2311yescharacteristic
79C23×Dic13C2311yescharacteristic
80C2×C13×C22⋊C4—22no—
81C2×C13×C22⋊C4—22no—
82C2×C13×C22⋊C4—22no—
83C2×C13×C22⋊C4—22no—
84C2×C13×C22⋊C4—22no—
85C2×C13×C22⋊C4C2×C414yes—
86C2×C42×C13—22no—
87C2×C42×C13—22no—
88C2×C42×C13—22no—
89C2×C42×C13—22no—
90C2×C42×C13—22no—
91C2×C42×C13D414yes—
92C2×C22⋊Dic13—22no—
93C2×C22⋊Dic13—22no—
94C2×C22⋊Dic13—22no—
95C2×C22⋊Dic13—22no—
96C2×C22⋊Dic13—22no—
97C2×C22⋊Dic13—22no—
98C2×C22⋊Dic13—22no—
99C2×C22⋊Dic13—22no—
100C2×C22⋊Dic13—22no—
101C2×C22⋊Dic13—22no—
102C2×C22⋊Dic13C2×C414yes—
103C2×C22⋊Dic13C2×C414yes—
104C2×C4⋊Dic13—22no—
105C2×C4⋊Dic13—22no—
106C2×C4⋊Dic13—22no—
107C2×C4⋊Dic13—22no—
108C2×C4⋊Dic13—22no—
109C2×C4⋊Dic13C2×C414yescomplemented
110C2×#6101—22no—
111C2×#6101—22no—
112C2×#6101—22no—
113C2×#6101—22no—
114C2×#6101—22no—
115C2×#6101—22no—
116C2×#6101—22no—
117C2×#6101—22no—
118C2×#6101—22no—
119C2×#6101—22no—
120C2×#6101C2×C414yescomplemented
121C2×#6101C2×C414yescomplemented
122C2×C4×Dic13—22no—
123C2×C4×Dic13—22no—
124C2×C4×Dic13—22no—
125C2×C4×Dic13—22no—
126C2×C4×Dic13—22no—
127C2×C4×Dic13—22no—
128C2×C4×Dic13—22no—
129C2×C4×Dic13—22no—
130C2×C4×Dic13—22no—
131C2×C4×Dic13—22no—
132C2×C4×Dic13D414yes—
133C2×C4×Dic13D414yes—
134C13×#95—22no—
135C13×#95—22no—
136#88071—22no—
137#88071—22no—
138#88071—22no—
139#88071—22no—
140#88071—22no—
141#88071—22no—
142#88071—22no—
143#88071—22no—
144#88071—22no—
145#88071—22no—
146#88071—22no—
147#88071—22no—
148#88071—22no—
149#88071C2×C414yescomplemented
150C4×#396—131nomaximal, Sylow
151C24×C13—21no—
152C24×C13—21no—
153C24×C13—21no—
154C24×C13—21no—
155C24×C13—21no—
156C24×C13—21no—
157C24×C13—21no—
158C24×C13—21no—
159C24×C13—21no—
160C24×C13—21no—
161C24×C13—21no—
162C24×C13—21no—
163C24×C13C22×C412yes—
164C24×C13C2×Q812yes—
165C24×C13#4112yes—
166C24×C13C2411yescharacteristic
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×C13—21no—
194C22×C4×C13—21no—
195C22×C4×C13—28no—
196C22×C4×C13—28no—
197C22×C4×C13—28no—
198C22×C4×C13—44no—
199C22×C4×C13—44no—
200C22×C4×C13—44no—
201C22×C4×C13—44no—
202C22×C4×C13C22×C412yes—
203C22×C4×C13C22×C412yes—
204C22×C4×C13C2×D412yes—
205C22×C4×C13C2×D412yes—
206C22×C4×C13C2×D412yes—
207C22×C4×C13C2×D412yes—
208C22×C4×C13C2×D412yes—
209C22×C4×C13C2×Q812yes—
210C22×C4×C13C2×Q812yes—
211C22×C4×C13#4112yes—
212C22×C4×C13#4112yes—
213C22×C4×C13#4112yes—
214C22×C4×C13#4112yes—
215C22×C4×C13#4112yes—
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×Dic13—21no—
247C22×Dic13—21no—
248C22×Dic13—21no—
249C22×Dic13—21no—
250C22×Dic13—21no—
251C22×Dic13—21no—
252C22×Dic13—21no—
253C22×Dic13—21no—
254C22×Dic13—21no—
255C22×Dic13—21no—
256C22×Dic13—21no—
257C22×Dic13—21no—
258C22×Dic13—21no—
259C22×Dic13—21no—
260C22×Dic13C22×C412yes—
261C22×Dic13C22×C412yes—
262C22×Dic13C22×C412yes—
263C22×Dic13C22×C412yes—
264C22×Dic13C2×D412yes—
265C22×Dic13C2×D412yes—
266C22×Dic13C2×D412yes—
267C22×Dic13C2×D412yes—
268C22×Dic13#4112yes—
269C22×Dic13#4112yes—
270C22×Dic13#4112yes—
271C22×Dic13#4112yes—
272C13×C22⋊C4—28no—
273C13×C22⋊C4—28no—
274C42×C13—28no—
275C42×C13—44no—
276C22⋊Dic13—28no—
277C22⋊Dic13—28no—
278C22⋊Dic13—28no—
279C22⋊Dic13—28no—
280C4⋊Dic13—28no—
281C4⋊Dic13—28no—
282#6101—28no—
283#6101—28no—
284#6101—28no—
285#6101—28no—
286C4×Dic13—28no—
287C4×Dic13—28no—
288C4×Dic13—44no—
289C4×Dic13—44no—
290C2×#396—131no—
291C2×C4×C4⋊C4—131no—
292C2×C4×C4⋊C4—131no—
293C2×C4×C4⋊C4—131no—
294C2×C4×C22⋊C4—131no—
295C2×C4×C22⋊C4—131no—
296C2×C4×C22⋊C4D1311yescharacteristic
297#1443—131no—
298#1441—131no—
299#1441—131no—
300#1441—131no—
301#1439—131no—
302#1439—131no—
303#1439—131no—
304C4×#95—131no—
305C23×C13—22no—
306C23×C13—22no—
307C23×C13—22no—
308C23×C13—22no—
309C23×C13—22no—
310C23×C13—22no—
311C23×C13—22no—
312C23×C13—22no—
313C23×C13—22no—
314C23×C13—22no—
315C23×C13—22no—
316C23×C13—22no—
317C23×C13—22no—
318C23×C13—22no—
319C23×C13—22no—
320C23×C13—22no—
321C23×C13—22no—
322C23×C13—22no—
323C23×C13—41no—
324C23×C13—41no—
325C23×C13—41no—
326C23×C13—41no—
327C23×C13—41no—
328C23×C13—41no—
329C23×C13—41no—
330C23×C13—41no—
331C23×C13—41no—
332C23×C13—41no—
333C23×C13—41no—
334C23×C13—41no—
335C23×C13—41no—
336C23×C13—41no—
337C23×C13—41no—
338C23×C13—41no—
339C23×C13C4×Q814yes—
340C23×C13C23×C411yescharacteristic
341C23×C13C22×D411yescharacteristic
342C23×C13C22×D411yescharacteristic
343C23×C13C22×D411yescharacteristic
344C23×C13C22×Q811yescharacteristic
345C23×C13C2×#4111yescharacteristic
346C23×C13C2×#4111yescharacteristic
347C23×C13C2×#4111yescharacteristic
348C23×C13C2×#4111yescharacteristic
349C23×C13C2×#4111yescharacteristic
350C23×C13C2×#4111yescharacteristic
351C23×C13C2×#4111yescharacteristic
352C23×C13C2×#4111yescharacteristic
353C23×C13C2×#4111yescharacteristic
354C23×C13C2×#4111yescharacteristic
355C2×C4×C13—22no—
356C2×C4×C13—22no—
357C2×C4×C13—22no—
358C2×C4×C13—22no—
359C2×C4×C13—22no—
360C2×C4×C13—22no—
361C2×C4×C13—22no—
362C2×C4×C13—22no—
363C2×C4×C13—22no—
364C2×C4×C13—22no—
365C2×C4×C13—22no—
366C2×C4×C13—22no—
367C2×C4×C13—22no—
368C2×C4×C13—22no—
369C2×C4×C13—22no—
370C2×C4×C13—22no—
371C2×C4×C13—22no—
372C2×C4×C13—22no—
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—41no—
384C2×C4×C13—41no—
385C2×C4×C13—41no—
386C2×C4×C13—41no—
387C2×C4×C13—41no—
388C2×C4×C13—41no—
389C2×C4×C13—416no—
390C2×C4×C13C4×D414yes—
391C2×C4×C13#12114yes—
392C2×C4×C13#12114yes—
393C2×C4×C13#12114yes—
394C2×C4×C13C22⋊Q814yes—
395C2×C4×C13C22⋊Q814yes—
396C2×C4×C13C22⋊Q814yes—
397C2×C4×C13#12614yes—
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—22no—
415C2×Dic13—22no—
416C2×Dic13—22no—
417C2×Dic13—22no—
418C2×Dic13—22no—
419C2×Dic13—22no—
420C2×Dic13—22no—
421C2×Dic13—22no—
422C2×Dic13—22no—
423C2×Dic13—22no—
424C2×Dic13—22no—
425C2×Dic13—22no—
426C2×Dic13—22no—
427C2×Dic13—22no—
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×Dic13—41no—
439C2×Dic13—41no—
440C2×Dic13—41no—
441C2×Dic13—41no—
442C2×Dic13—41no—
443C2×Dic13—41no—
444C2×Dic13—41no—
445C2×Dic13—41no—
446C2×Dic13—41no—
447C2×Dic13—41no—
448C2×Dic13—41no—
449C2×Dic13—41no—
450C2×Dic13—41no—
451C2×Dic13—41no—
452C2×Dic13C4×D414yes—
453C2×Dic13C4×D414yes—
454C24×C4C2×D1311yescharacteristic
455C22×C4⋊C4—131no—
456C22×C4⋊C4—131no—
457C22×C4⋊C4—131no—
458C22×C4⋊C4—131no—
459C22×C4⋊C4—131no—
460C22×C4⋊C4—131no—
461C22×C22⋊C4—131no—
462C22×C22⋊C4—131no—
463C22×C22⋊C4—131no—
464C22×C22⋊C4—131no—
465C22×C22⋊C4C2×D1311yescharacteristic
466C22×C22⋊C4C2×D1311yescharacteristic
467C22×C42—131no—
468C22×C42—131no—
469C22×C42—131no—
470C22×C42—131no—
471C22×C42C2×D1311yescharacteristic
472C22×C42C2×D1311yescharacteristic
473#396—138no—
474C4×C4⋊C4—264no—
475C4×C4⋊C4—264no—
476C4×C4⋊C4—264no—
477C4×C22⋊C4—24no—
478C4×C22⋊C4—264no—
479C4×C22⋊C4—264no—
480C2×#95—131no—
481C2×#95—131no—
482C2×#95—131no—
483C2×#95—131no—
484C2×#95—131no—
485C2×#95—131no—
486C2×#95—131no—
487C2×#95—131no—
488C2×#95—131no—
489C2×#95—131no—
490C2×#95—131no—
491C2×#95—131no—
492C2×#95—131no—
493C2×#95—131no—
494C2×#95C2×D1311yescharacteristic
495C2×#95C2×D1311yescharacteristic
496C22×C13—24no—
497C22×C13—24no—
498C22×C13—24no—
499C22×C13—42no—
500C22×C13—42no—
501C22×C13—42no—
502C22×C13—42no—
503C22×C13—42no—
504C22×C13—42no—
505C22×C13—42no—
506C22×C13—42no—
507C22×C13—42no—
508C22×C13—42no—
509C22×C13—42no—
510C22×C13—42no—
511C22×C13C2×C4×D411yescharacteristic
512C22×C13C2×C4×D411yescharacteristic
513C22×C13C2×C4×D411yescharacteristic
514C22×C13C2×C4×Q811yescharacteristic
515C22×C13C4×#4111yescharacteristic
516C22×C13C4×#4111yescharacteristic
517C22×C13C4×#4111yescharacteristic
518C22×C13C2×#12111yescharacteristic
519C22×C13C2×#12111yescharacteristic
520C22×C13C2×#12111yescharacteristic
521C22×C13C2×C22⋊Q811yescharacteristic
522C22×C13C2×C22⋊Q811yescharacteristic
523C22×C13C2×C22⋊Q811yescharacteristic
524C22×C13#52511yescharacteristic
525C22×C13#52511yescharacteristic
526C22×C13#52511yescharacteristic
527C22×C13#52511yescharacteristic
528C22×C13#52511yescharacteristic
529C22×C13#52511yescharacteristic
530C22×C13C2×#12611yescharacteristic
531C22×C13#52911yescharacteristic
532C22×C13#52911yescharacteristic
533C22×C13#52911yescharacteristic
534C22×C13#52911yescharacteristic
535C22×C13#52911yescharacteristic
536C22×C13#52911yescharacteristic
537C22×C13#52911yescharacteristic
538C22×C13#52911yescharacteristic
539C22×C13#52911yescharacteristic
540C22×C13#53211yescharacteristic
541C22×C13#53211yescharacteristic
542C22×C13#53211yescharacteristic
543C22×C13#53311yescharacteristic
544C22×C13#53311yescharacteristic
545C22×C13#53311yescharacteristic
546C4×C13—24no—
547C4×C13—42no—
548C4×C13—42no—
549C4×C13—42no—
550C4×C13—42no—
551C4×C13#39618yescomplemented
552Dic13—24no—
553Dic13—24no—
554Dic13—42no—
555Dic13—42no—
556Dic13—42no—
557Dic13—42no—
558Dic13—42no—
559Dic13—42no—
560C25C22×D1311yescharacteristic
561C23×C4—22no—
562C23×C4—22no—
563C23×C4—22no—
564C23×C4—22no—
565C23×C4—22no—
566C23×C4—22no—
567C23×C4—131no—
568C23×C4—131no—
569C23×C4—131no—
570C23×C4—131no—
571C23×C4—131no—
572C23×C4—131no—
573C23×C4—131no—
574C23×C4—131no—
575C23×C4Dic2614yes—
576C23×C4C22×D1311yescharacteristic
577C23×C4C22×D1311yescharacteristic
578C23×C4C22×D1311yescharacteristic
579C23×C4C22×D1311yescharacteristic
580C23×C4C22×D1311yescharacteristic
581C23×C4C22×D1311yescharacteristic
582C2×C4⋊C4—134no—
583C2×C4⋊C4—134no—
584C2×C4⋊C4—134no—
585C2×C4⋊C4—262no—
586C2×C4⋊C4—262no—
587C2×C4⋊C4—262no—
588C2×C4⋊C4—262no—
589C2×C4⋊C4—262no—
590C2×C4⋊C4—262no—
591C2×C4⋊C4—262no—
592C2×C4⋊C4—262no—
593C2×C4⋊C4—262no—
594C2×C4⋊C4—262no—
595C2×C4⋊C4—262no—
596C2×C4⋊C4—262no—
597C2×C4⋊C4—262no—
598C2×C4⋊C4—262no—
599C2×C4⋊C4—262no—
600C2×C22⋊C4—22no—
601C2×C22⋊C4—22no—
602C2×C22⋊C4—22no—
603C2×C22⋊C4—22no—
604C2×C22⋊C4—22no—
605C2×C22⋊C4—134no—
606C2×C22⋊C4—134no—
607C2×C22⋊C4—262no—
608C2×C22⋊C4—262no—
609C2×C22⋊C4—262no—
610C2×C22⋊C4—262no—
611C2×C22⋊C4—262no—
612C2×C22⋊C4—262no—
613C2×C22⋊C4—262no—
614C2×C22⋊C4—262no—
615C2×C22⋊C4—262no—
616C2×C22⋊C4—262no—
617C2×C22⋊C4C4×D1314yes—
618C2×C42—22no—
619C2×C42—22no—
620C2×C42—22no—
621C2×C42—22no—
622C2×C42—22no—
623C2×C42—134no—
624C2×C42—134no—
625C2×C42—262no—
626C2×C42—262no—
627C2×C42—262no—
628C2×C42—262no—
629C2×C42—262no—
630C2×C42—262no—
631C2×C42—262no—
632C2×C42—262no—
633C2×C42—262no—
634C2×C42—262no—
635C2×C42C22⋊D1314yes—
636#95—22no—
637#95—22no—
638#95—134no—
639#95—262no—
640#95—262no—
641#95—262no—
642#95—262no—
643#95—262no—
644#95—262no—
645#95—262no—
646#95—262no—
647#95—262no—
648#95—262no—
649#95—262no—
650#95—262no—
651#95—262no—
652C2×C13—44no—
653C2×C13C4×#12111yescharacteristic
654C2×C13C4×#12111yescharacteristic
655C2×C13C4×#12111yescharacteristic
656C2×C13C4×C22⋊Q811yescharacteristic
657C2×C13C4×C22⋊Q811yescharacteristic
658C2×C13C4×C22⋊Q811yescharacteristic
659C2×C13C4×#12611yescharacteristic
660C2×C13C2×#39611yescharacteristic
661C2×C13#239211yescharacteristic
662C2×C13#239211yescharacteristic
663C2×C13#239211yescharacteristic
664C2×C13#239611yescharacteristic
665C2×C13#239611yescharacteristic
666C2×C13#239611yescharacteristic
667C2×C13#240111yescharacteristic
668C24—21no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24C2×Dic2612yes—
681C24C2×C4×D1312yes—
682C24#612712yes—
683C24C23×D1311yescharacteristic
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—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—28no—
713C22×C4—28no—
714C22×C4—28no—
715C22×C4—44no—
716C22×C4—44no—
717C22×C4—44no—
718C22×C4—44no—
719C22×C4—132no—
720C22×C4—132no—
721C22×C4—132no—
722C22×C4—132no—
723C22×C4—132no—
724C22×C4—132no—
725C22×C4—132no—
726C22×C4—132no—
727C22×C4—132no—
728C22×C4—132no—
729C22×C4—132no—
730C22×C4—132no—
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—261no—
746C22×C4—261no—
747C22×C4—261no—
748C22×C4—261no—
749C22×C4—261no—
750C22×C4—261no—
751C22×C4—261no—
752C22×C4—261no—
753C22×C4—261no—
754C22×C4—261no—
755C22×C4—261no—
756C22×C4—261no—
757C22×C4—261no—
758C22×C4—261no—
759C22×C4—261no—
760C22×C4—261no—
761C22×C4—261no—
762C22×C4—261no—
763C22×C4—261no—
764C22×C4—261no—
765C22×C4—261no—
766C22×C4—261no—
767C22×C4—261no—
768C22×C4—261no—
769C22×C4—261no—
770C22×C4—261no—
771C22×C4—261no—
772C22×C4—261no—
773C22×C4—261no—
774C22×C4—261no—
775C22×C4C2×Dic2612yes—
776C22×C4C2×Dic2612yes—
777C22×C4C2×C4×D1312yes—
778C22×C4C2×C4×D1312yes—
779C22×C4#612712yes—
780C22×C4#612712yes—
781C22×C4#612712yes—
782C22×C4D4×D1312yes—
783C22×C4D4×D1312yes—
784C22×C4#612912yes—
785C22×C4#612912yes—
786C22×C4C2×C22⋊D1312yes—
787C22×C4C2×C22⋊D1312yes—
788C22×C4C2×C22⋊D1312yes—
789C4⋊C4—268no—
790C4⋊C4—268no—
791C4⋊C4—268no—
792C4⋊C4—268no—
793C4⋊C4—268no—
794C4⋊C4—268no—
795C22⋊C4—28no—
796C22⋊C4—28no—
797C22⋊C4—268no—
798C22⋊C4—268no—
799C22⋊C4—268no—
800C22⋊C4—268no—
801C42—28no—
802C42—44no—
803C42—268no—
804C42—268no—
805C42—524no—
806C42—524no—
807C13C4×#39611yescharacteristic, complemented, Sylow
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23C4×Dic2614yes—
843C23C22×Dic2611yescharacteristic
844C23C22×C4×D1311yescharacteristic
845C23C2×#612711yescharacteristic
846C23C2×#612711yescharacteristic
847C23C2×#612711yescharacteristic
848C23C2×#612711yescharacteristic
849C23C2×D4×D1311yescharacteristic
850C23C2×D4×D1311yescharacteristic
851C23C2×#612911yescharacteristic
852C23C2×#612911yescharacteristic
853C23#41×D1311yescharacteristic
854C23#41×D1311yescharacteristic
855C23#41×D1311yescharacteristic
856C23#41×D1311yescharacteristic
857C23C22×C22⋊D1311yescharacteristic
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—416no—
893C2×C4—134no—
894C2×C4—134no—
895C2×C4—262no—
896C2×C4—262no—
897C2×C4—262no—
898C2×C4—262no—
899C2×C4—262no—
900C2×C4—262no—
901C2×C4—262no—
902C2×C4—262no—
903C2×C4—262no—
904C2×C4—262no—
905C2×C4—262no—
906C2×C4—262no—
907C2×C4—262no—
908C2×C4—262no—
909C2×C4—262no—
910C2×C4—262no—
911C2×C4—262no—
912C2×C4—262no—
913C2×C4—262no—
914C2×C4—262no—
915C2×C4—262no—
916C2×C4—262no—
917C2×C4—262no—
918C2×C4—262no—
919C2×C4—262no—
920C2×C4—262no—
921C2×C4—262no—
922C2×C4—262no—
923C2×C4—262no—
924C2×C4—262no—
925C2×C4—521no—
926C2×C4—521no—
927C2×C4—521no—
928C2×C4—521no—
929C2×C4—521no—
930C2×C4—521no—
931C2×C4—521no—
932C2×C4—521no—
933C2×C4—521no—
934C2×C4—521no—
935C2×C4—521no—
936C2×C4—521no—
937C2×C4—521no—
938C2×C4—521no—
939C2×C4—521no—
940C2×C4—521no—
941C2×C4—521no—
942C2×C4—521no—
943C2×C4—521no—
944C2×C4—521no—
945C2×C4—521no—
946C2×C4—521no—
947C2×C4—521no—
948C2×C4—521no—
949C2×C4#8813214yes—
950C2×C4#8813214yes—
951C2×C4#8813314yes—
952C2×C4#8813814yes—
953C2×C4#8817814yes—
954C2×C4C4×C22⋊D1314yes—
955C2×C4#8819214yes—
956C2×C4#8819314yes—
957C22—24no—
958C22—24no—
959C22—24no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22C2×C4×Dic2611yescharacteristic
973C22#1171917511yescharacteristic
974C22C4×#612711yescharacteristic
975C22#1171918411yescharacteristic
976C22C2×#8813211yescharacteristic
977C22C2×#8813211yescharacteristic
978C22C2×#8813311yescharacteristic
979C22C2×#8813811yescharacteristic
980C22#1171922211yescharacteristic
981C22#1171922211yescharacteristic
982C22#1171923311yescharacteristic
983C22#1171923311yescharacteristic
984C22C4×#612911yescharacteristic
985C22C4×#612911yescharacteristic
986C22#1171924311yescharacteristic
987C22#1171924311yescharacteristic
988C22#1171924311yescharacteristic
989C22#1171924311yescharacteristic
990C22C4×D4×D1311yescharacteristic
991C22C4×D4×D1311yescharacteristic
992C22#1171925211yescharacteristic
993C22#1171925211yescharacteristic
994C22#1171925211yescharacteristic
995C22#1171925211yescharacteristic
996C22#1171925311yescharacteristic
997C22#1171925311yescharacteristic
998C22#1171926211yescharacteristic
999C22#1171926211yescharacteristic
1000C22C2×#8817811yescharacteristic
1001C22C2×C4×C22⋊D1311yescharacteristic
1002C22#1171949611yescharacteristic
1003C22C2×#8819211yescharacteristic
1004C22C2×#8819311yescharacteristic
1005C22#1171953311yescharacteristic
1006C22#1171953711yescharacteristic
1007C4—24no—
1008C4—42no—
1009C4—42no—
1010C4—42no—
1011C4—42no—
1012C4—264no—
1013C4—264no—
1014C4—522no—
1015C4—522no—
1016C4—522no—
1017C4—522no—
1018C4—522no—
1019C4—522no—
1020C4#1171860918yesdirect product factor
1021C2—44no—
1022C2C4×#8819211yescharacteristic
1023C2C4×#8819311yescharacteristic
1024C2C4×#8813811yescharacteristic
1025C2C4×#8813211yescharacteristic
1026C2C4×#8813211yescharacteristic
1027C2C4×#8817811yescharacteristic
1028C2C4×#8813311yescharacteristic
1029C2C2×#1171860911yescharacteristic
1030C2#1311807411yescharacteristic
1031C2#1311807811yescharacteristic
1032C2#1311808011yescharacteristic
1033C2#1311810411yescharacteristic
1034C2#1311811011yescharacteristic
1035C2#1311811011yescharacteristic
1036C2#1311813611yescharacteristic
subgroupG/H
centerC23×C4C22×D13
commutatorC23×C13C23×C4
FrattiniC24C23×D13
FittingC2×C4×C13×C22⋊C4C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC2×C4×C22⋊C4D13
hypocenterC13C4×#396
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×#6101C2semidirect
3. C2×C4×#6101C2semidirect
4. C2×C4×C4⋊Dic13C2semidirect
7. #13113097C2semidirect
8. #13113090C2semidirect
9. #13113088C2semidirect
10. #13113087C2semidirect
14. C4×#88071C2semidirect
54. #11718609C4direct (N × H)
109. C2×C4⋊Dic13C2×C4semidirect
120. C2×#6101C2×C4semidirect
121. C2×#6101C2×C4semidirect
149. #88071C2×C4semidirect
551. C4×C13#396semidirect
807. C13C4×#396semidirect
1020. C4#11718609direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117186092
C2×C4×#61012
C2×C4×C4⋊Dic132
C2×C4×C22⋊Dic132
#131130972
#131130902
#131130882
#131130872
#131130812
#131130792
C4×#880712
C2×C4×C13×C22⋊C42
C4×#39613