Finite Group Databasebeta

← C4×#11718655 #15784775

Subgroups — C4×#11718655 #15784775

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×#11718655C211yesmaximal, characteristic
2C2×C4×#6101C211yesmaximal, characteristic, complemented
3C2×C4×C4⋊Dic13C211yesmaximal, characteristic, complemented
4C2×C4×#6103C211yesmaximal, characteristic
5C2×C4×#6103C211yesmaximal, characteristic
6C2×C4×#6103C211yesmaximal, characteristic
7#13113096C211yesmaximal, characteristic, complemented
8#13113089C211yesmaximal, characteristic, complemented
9#13113088C211yesmaximal, characteristic, complemented
10#13113086C211yesmaximal, characteristic, complemented
11#13113082C211yesmaximal, characteristic
12#13113080C211yesmaximal, characteristic
13#13113078C211yesmaximal, characteristic
14C4×#88071C211yesmaximal, characteristic, complemented
15C2×C4×C13×C4⋊C4C211yesmaximal, characteristic, complemented
16C23×C4×D13C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C42×C13C2211yescharacteristic
20C22×C42×C13C2211yescharacteristic
21C22×C42×C13C2211yescharacteristic
22C22×#6103C2211yescharacteristic
23C22×#6103C2211yescharacteristic
24C22×#6103C2211yescharacteristic
25C22×#6103C2211yescharacteristic
26C22×#6103C2211yescharacteristic
27C22×#6103C2211yescharacteristic
28C22×C4⋊Dic13C2211yescharacteristic
29C22×C4⋊Dic13C2211yescharacteristic
30C22×#6101C2211yescharacteristic
31C22×#6101C2211yescharacteristic
32C22×C4×Dic13C2211yescharacteristic
33C22×C4×Dic13C2211yescharacteristic
34C22×C4×Dic13C2211yescharacteristic
35C4×C13×C4⋊C4—24no—
36C2×C13×#95C2211yescharacteristic
37C2×C13×#95C2211yescharacteristic
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
51C2×#88071C2211yescharacteristic
52#11718655C418yesdirect product factor
53C4×#6103—24no—
54C4×#6103—24no—
55C4×#6103—24no—
56C4×C4⋊Dic13—24no—
57C4×#6101—24no—
58C24×D13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C23×C4×C13C2311yescharacteristic
64C23×C4×C13C2311yescharacteristic
65C23×C4×C13C2311yescharacteristic
66C23×Dic13C2311yescharacteristic
67C23×Dic13C2311yescharacteristic
68C23×Dic13C2311yescharacteristic
69C23×Dic13C2311yescharacteristic
70C23×Dic13C2311yescharacteristic
71C23×Dic13C2311yescharacteristic
72C23×Dic13C2311yescharacteristic
73C22×C4×D13—22no—
74C22×C4×D13—22no—
75C22×C4×D13—22no—
76C22×C4×D13—22no—
77C22×C4×D13—22no—
78C22×C4×D13—22no—
79C22×C4×D13Q814yes—
80C2×C13×C4⋊C4—22no—
81C2×C13×C4⋊C4—22no—
82C2×C13×C4⋊C4—22no—
83C2×C13×C4⋊C4—22no—
84C2×C13×C4⋊C4—22no—
85C2×C13×C4⋊C4C2×C414yescomplemented
86C2×C42×C13—22no—
87C2×C42×C13—22no—
88C2×C42×C13—22no—
89C2×C42×C13—22no—
90C2×C42×C13—22no—
91C2×C42×C13—22no—
92C2×C42×C13—22no—
93C2×C42×C13D414yes—
94C2×C42×C13D414yes—
95C2×#6103—22no—
96C2×#6103—22no—
97C2×#6103—22no—
98C2×#6103—22no—
99C2×#6103—22no—
100C2×#6103—22no—
101C2×#6103—22no—
102C2×#6103—22no—
103C2×#6103—22no—
104C2×#6103—22no—
105C2×#6103—22no—
106C2×#6103—22no—
107C2×#6103—22no—
108C2×#6103—22no—
109C2×#6103—22no—
110C2×#6103C2×C414yes—
111C2×#6103C2×C414yes—
112C2×#6103C2×C414yes—
113C2×C4⋊Dic13—22no—
114C2×C4⋊Dic13—22no—
115C2×C4⋊Dic13—22no—
116C2×C4⋊Dic13—22no—
117C2×C4⋊Dic13—22no—
118C2×C4⋊Dic13C2×C414yescomplemented
119C2×#6101—22no—
120C2×#6101—22no—
121C2×#6101—22no—
122C2×#6101—22no—
123C2×#6101—22no—
124C2×#6101C2×C414yescomplemented
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×Dic13—22no—
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×C13C2411yescharacteristic
152C23×D13—21no—
153C23×D13—21no—
154C23×D13—21no—
155C23×D13—21no—
156C23×D13—21no—
157C23×D13—21no—
158C23×D13—21no—
159C23×D13—21no—
160C23×D13—21no—
161C23×D13—21no—
162C23×D13—21no—
163C23×D13—21no—
164C23×D13C22×C412yes—
165C23×D13C2×Q812yes—
166C23×D13#4112yes—
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—21no—
196C22×C4×C13—21no—
197C22×C4×C13—21no—
198C22×C4×C13—21no—
199C22×C4×C13C22×C412yes—
200C22×C4×C13C22×C412yes—
201C22×C4×C13C22×C412yes—
202C22×C4×C13C2×D412yes—
203C22×C4×C13C2×D412yes—
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×C13#4112yes—
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×Dic13C22×C412yes—
257C22×Dic13C22×C412yes—
258C22×Dic13C22×C412yes—
259C22×Dic13C2×D412yes—
260C22×Dic13C2×D412yes—
261C22×Dic13C2×Q812yes—
262C22×Dic13#4112yes—
263C22×Dic13#4112yes—
264C22×Dic13#4112yes—
265C2×C4×D13—28no—
266C2×C4×D13—28no—
267C2×C4×D13—28no—
268C2×C4×D13—44no—
269C2×C4×D13—44no—
270C2×C4×D13—44no—
271C2×C4×D13—44no—
272C13×C4⋊C4—28no—
273C13×C4⋊C4—28no—
274C42×C13—28no—
275C42×C13—28no—
276C42×C13—44no—
277#6103—28no—
278#6103—28no—
279#6103—28no—
280#6103—28no—
281#6103—28no—
282#6103—28no—
283C4⋊Dic13—28no—
284C4⋊Dic13—28no—
285#6101—28no—
286#6101—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⋊C4D1311yescharacteristic, complemented
294C2×C4×C22⋊C4—131no—
295C2×C4×C22⋊C4—131no—
296C2×C4×C22⋊C4—131no—
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×C13C23×C411yescharacteristic
306C23×C13C22×D411yescharacteristic
307C23×C13C22×D411yescharacteristic
308C23×C13C22×D411yescharacteristic
309C23×C13C22×Q811yescharacteristic
310C23×C13C2×#4111yescharacteristic
311C23×C13C2×#4111yescharacteristic
312C23×C13C2×#4111yescharacteristic
313C23×C13C2×#4111yescharacteristic
314C23×C13C2×#4111yescharacteristic
315C23×C13C2×#4111yescharacteristic
316C23×C13C2×#4111yescharacteristic
317C23×C13C2×#4111yescharacteristic
318C23×C13C2×#4111yescharacteristic
319C23×C13C2×#4111yescharacteristic
320C22×D13—22no—
321C22×D13—22no—
322C22×D13—22no—
323C22×D13—22no—
324C22×D13—22no—
325C22×D13—22no—
326C22×D13—22no—
327C22×D13—22no—
328C22×D13—22no—
329C22×D13—22no—
330C22×D13—22no—
331C22×D13—22no—
332C22×D13—22no—
333C22×D13—22no—
334C22×D13—22no—
335C22×D13—22no—
336C22×D13—22no—
337C22×D13—22no—
338C22×D13—41no—
339C22×D13—41no—
340C22×D13—41no—
341C22×D13—41no—
342C22×D13—41no—
343C22×D13—41no—
344C22×D13—41no—
345C22×D13—41no—
346C22×D13—41no—
347C22×D13—41no—
348C22×D13—41no—
349C22×D13—41no—
350C22×D13—41no—
351C22×D13—41no—
352C22×D13—41no—
353C22×D13—41no—
354C22×D13C4×Q814yes—
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—22no—
374C2×C4×C13—22no—
375C2×C4×C13—22no—
376C2×C4×C13—22no—
377C2×C4×C13—22no—
378C2×C4×C13—22no—
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—41no—
390C2×C4×C13—41no—
391C2×C4×C13—41no—
392C2×C4×C13—41no—
393C2×C4×C13—41no—
394C2×C4×C13—41no—
395C2×C4×C13C4×D414yes—
396C2×C4×C13C4×D414yes—
397C2×C4×C13#12114yes—
398C2×C4×C13#12114yes—
399C2×C4×C13#12114yes—
400C2×C4×C13C22⋊Q814yes—
401C2×C4×C13C22⋊Q814yes—
402C2×C4×C13C22⋊Q814yes—
403C2×C4×C13#12614yes—
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—
453C4×D13—416no—
454C24×C4—131no—
455C22×C4⋊C4—131no—
456C22×C4⋊C4—131no—
457C22×C4⋊C4—131no—
458C22×C4⋊C4—131no—
459C22×C4⋊C4C2×D1311yescharacteristic
460C22×C4⋊C4C2×D1311yescharacteristic
461C22×C22⋊C4—131no—
462C22×C22⋊C4—131no—
463C22×C22⋊C4—131no—
464C22×C22⋊C4—131no—
465C22×C22⋊C4—131no—
466C22×C22⋊C4—131no—
467C22×C42—131no—
468C22×C42—131no—
469C22×C42—131no—
470C22×C42C2×D1311yescharacteristic
471C22×C42C2×D1311yescharacteristic
472C22×C42C2×D1311yescharacteristic
473#396—138no—
474C4×C4⋊C4—24no—
475C4×C4⋊C4—264no—
476C4×C4⋊C4—264no—
477C4×C22⋊C4—264no—
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×C13C2×C4×D411yescharacteristic
497C22×C13C2×C4×D411yescharacteristic
498C22×C13C2×C4×D411yescharacteristic
499C22×C13C2×C4×Q811yescharacteristic
500C22×C13C4×#4111yescharacteristic
501C22×C13C4×#4111yescharacteristic
502C22×C13C4×#4111yescharacteristic
503C22×C13C2×#12111yescharacteristic
504C22×C13C2×#12111yescharacteristic
505C22×C13C2×#12111yescharacteristic
506C22×C13C2×C22⋊Q811yescharacteristic
507C22×C13C2×C22⋊Q811yescharacteristic
508C22×C13C2×C22⋊Q811yescharacteristic
509C22×C13#52511yescharacteristic
510C22×C13#52511yescharacteristic
511C22×C13#52511yescharacteristic
512C22×C13#52511yescharacteristic
513C22×C13#52511yescharacteristic
514C22×C13#52511yescharacteristic
515C22×C13C2×#12611yescharacteristic
516C22×C13#52911yescharacteristic
517C22×C13#52911yescharacteristic
518C22×C13#52911yescharacteristic
519C22×C13#52911yescharacteristic
520C22×C13#52911yescharacteristic
521C22×C13#52911yescharacteristic
522C22×C13#52911yescharacteristic
523C22×C13#52911yescharacteristic
524C22×C13#52911yescharacteristic
525C22×C13#53211yescharacteristic
526C22×C13#53211yescharacteristic
527C22×C13#53211yescharacteristic
528C22×C13#53311yescharacteristic
529C22×C13#53311yescharacteristic
530C22×C13#53311yescharacteristic
531C2×D13—24no—
532C2×D13—24no—
533C2×D13—24no—
534C2×D13—42no—
535C2×D13—42no—
536C2×D13—42no—
537C2×D13—42no—
538C2×D13—42no—
539C2×D13—42no—
540C2×D13—42no—
541C2×D13—42no—
542C2×D13—42no—
543C2×D13—42no—
544C2×D13—42no—
545C2×D13—42no—
546C4×C13—24no—
547C4×C13—24no—
548C4×C13—42no—
549C4×C13—42no—
550C4×C13—42no—
551C4×C13—42no—
552C4×C13#39618yescomplemented
553Dic13—24no—
554Dic13—42no—
555Dic13—42no—
556Dic13—42no—
557Dic13—42no—
558Dic13—42no—
559Dic13—42no—
560C25—131no—
561C23×C4—131no—
562C23×C4—131no—
563C23×C4—131no—
564C23×C4—131no—
565C23×C4—131no—
566C23×C4—131no—
567C23×C4—131no—
568C23×C4—134no—
569C23×C4—262no—
570C23×C4—262no—
571C23×C4—262no—
572C23×C4—262no—
573C23×C4—262no—
574C23×C4—262no—
575C23×C4C22×D1311yescharacteristic
576C23×C4C22×D1311yescharacteristic
577C23×C4C22×D1311yescharacteristic
578C23×C4C22×D1311yescharacteristic
579C23×C4C22×D1311yescharacteristic
580C23×C4C22×D1311yescharacteristic
581C23×C4C22×D1311yescharacteristic
582C2×C4⋊C4—22no—
583C2×C4⋊C4—22no—
584C2×C4⋊C4—22no—
585C2×C4⋊C4—22no—
586C2×C4⋊C4—22no—
587C2×C4⋊C4—134no—
588C2×C4⋊C4—134no—
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⋊C4C4×D1314yescomplemented
600C2×C22⋊C4—134no—
601C2×C22⋊C4—134no—
602C2×C22⋊C4—134no—
603C2×C22⋊C4—262no—
604C2×C22⋊C4—262no—
605C2×C22⋊C4—262no—
606C2×C22⋊C4—262no—
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⋊C4—262no—
618C2×C42—22no—
619C2×C42—22no—
620C2×C42—22no—
621C2×C42—22no—
622C2×C42—22no—
623C2×C42—22no—
624C2×C42—22no—
625C2×C42—134no—
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×C42D5214yes—
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×C13C4×#12111yescharacteristic
653C2×C13C4×#12111yescharacteristic
654C2×C13C4×#12111yescharacteristic
655C2×C13C4×C22⋊Q811yescharacteristic
656C2×C13C4×C22⋊Q811yescharacteristic
657C2×C13C4×C22⋊Q811yescharacteristic
658C2×C13C4×#12611yescharacteristic
659C2×C13C2×#39611yescharacteristic
660C2×C13#239211yescharacteristic
661C2×C13#239211yescharacteristic
662C2×C13#239211yescharacteristic
663C2×C13#239611yescharacteristic
664C2×C13#239611yescharacteristic
665C2×C13#239611yescharacteristic
666C2×C13#240111yescharacteristic
667D13—44no—
668C24—132no—
669C24—132no—
670C24—132no—
671C24—261no—
672C24—261no—
673C24—261no—
674C24—261no—
675C24—261no—
676C24—261no—
677C24—261no—
678C24—261no—
679C24—261no—
680C24—261no—
681C24—261no—
682C24—261no—
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—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—132no—
717C22×C4—132no—
718C22×C4—132no—
719C22×C4—132no—
720C22×C4—132no—
721C22×C4—132no—
722C22×C4—132no—
723C22×C4—132no—
724C22×C4—132no—
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—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—268no—
766C22×C4—268no—
767C22×C4—268no—
768C22×C4—524no—
769C22×C4—524no—
770C22×C4—524no—
771C22×C4—524no—
772C22×C4C2×C4×D1312yes—
773C22×C4C2×C4×D1312yes—
774C22×C4C2×C4×D1312yes—
775C22×C4C2×D5212yes—
776C22×C4C2×D5212yes—
777C22×C4C2×D5212yes—
778C22×C4#612712yes—
779C22×C4#612712yes—
780C22×C4#612712yes—
781C22×C4#612712yes—
782C22×C4D4×D1312yes—
783C22×C4#612912yes—
784C22×C4Q8×D1312yes—
785C22×C4#613112yes—
786C22×C4C2×C22⋊D1312yes—
787C22×C4C2×C22⋊D1312yes—
788C22×C4C2×C22⋊D1312yes—
789C4⋊C4—28no—
790C4⋊C4—28no—
791C4⋊C4—268no—
792C4⋊C4—268no—
793C4⋊C4—268no—
794C4⋊C4—268no—
795C22⋊C4—268no—
796C22⋊C4—268no—
797C22⋊C4—268no—
798C22⋊C4—268no—
799C22⋊C4—268no—
800C22⋊C4—268no—
801C42—28no—
802C42—28no—
803C42—44no—
804C42—268no—
805C42—524no—
806C42—524no—
807C13C4×#39611yescharacteristic, complemented, Sylow
808C23—134no—
809C23—262no—
810C23—262no—
811C23—262no—
812C23—262no—
813C23—262no—
814C23—262no—
815C23—262no—
816C23—262no—
817C23—262no—
818C23—262no—
819C23—262no—
820C23—262no—
821C23—262no—
822C23—262no—
823C23—262no—
824C23—262no—
825C23—262no—
826C23—262no—
827C23—521no—
828C23—521no—
829C23—521no—
830C23—521no—
831C23—521no—
832C23—521no—
833C23—521no—
834C23—521no—
835C23—521no—
836C23—521no—
837C23—521no—
838C23—521no—
839C23—521no—
840C23—521no—
841C23—521no—
842C23—521no—
843C23C22×C4×D1311yescharacteristic
844C23C22×D5211yescharacteristic
845C23C2×#612711yescharacteristic
846C23C2×#612711yescharacteristic
847C23C2×#612711yescharacteristic
848C23C2×#612711yescharacteristic
849C23C2×D4×D1311yescharacteristic
850C23C2×#612911yescharacteristic
851C23C2×Q8×D1311yescharacteristic
852C23C2×#613111yescharacteristic
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—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
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—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—134no—
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—521no—
924C2×C4—521no—
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—5216no—
948C2×C4C4×D5214yes—
949C2×C4#8814914yes—
950C2×C4#8815014yes—
951C2×C4#8815114yes—
952C2×C4#8815214yes—
953C2×C4C4×C22⋊D1314yes—
954C2×C4#8818414yes—
955C2×C4#8819314yes—
956C2×C4#8820014yes—
957C22—264no—
958C22—264no—
959C22—264no—
960C22—522no—
961C22—522no—
962C22—522no—
963C22—522no—
964C22—522no—
965C22—522no—
966C22—522no—
967C22—522no—
968C22—522no—
969C22—522no—
970C22—522no—
971C22—522no—
972C22C2×C4×D5211yescharacteristic
973C22C4×#612711yescharacteristic
974C22#1171918211yescharacteristic
975C22#1171918411yescharacteristic
976C22C2×#8814911yescharacteristic
977C22C2×#8815011yescharacteristic
978C22C2×#8815111yescharacteristic
979C22C2×#8815211yescharacteristic
980C22#1171922911yescharacteristic
981C22#1171922911yescharacteristic
982C22#1171923311yescharacteristic
983C22#1171923311yescharacteristic
984C22C4×#612911yescharacteristic
985C22#1171924311yescharacteristic
986C22#1171924311yescharacteristic
987C22C4×D4×D1311yescharacteristic
988C22#1171925211yescharacteristic
989C22#1171925211yescharacteristic
990C22#1171925311yescharacteristic
991C22#1171926211yescharacteristic
992C22C4×Q8×D1311yescharacteristic
993C22C4×#613111yescharacteristic
994C22#1171928311yescharacteristic
995C22#1171928311yescharacteristic
996C22#1171928311yescharacteristic
997C22#1171928511yescharacteristic
998C22#1171928511yescharacteristic
999C22#1171928511yescharacteristic
1000C22C2×C4×C22⋊D1311yescharacteristic
1001C22C2×#8818411yescharacteristic
1002C22#1171949611yescharacteristic
1003C22C2×#8819311yescharacteristic
1004C22C2×#8820011yescharacteristic
1005C22#1171953311yescharacteristic
1006C22#1171953711yescharacteristic
1007C4—24no—
1008C4—24no—
1009C4—42no—
1010C4—42no—
1011C4—42no—
1012C4—42no—
1013C4—264no—
1014C4—522no—
1015C4—522no—
1016C4—522no—
1017C4—522no—
1018C4—522no—
1019C4—522no—
1020C4#1171865518yesdirect product factor
1021C2—524no—
1022C2C4×#8819311yescharacteristic
1023C2C4×#8818411yescharacteristic
1024C2C4×#8814911yescharacteristic
1025C2C4×#8820011yescharacteristic
1026C2C4×#8815011yescharacteristic
1027C2C4×#8815111yescharacteristic
1028C2C4×#8815211yescharacteristic
1029C2C2×#1171865511yescharacteristic
1030C2#1311807211yescharacteristic
1031C2#1311807611yescharacteristic
1032C2#1311807811yescharacteristic
1033C2#1311810611yescharacteristic
1034C2#1311810811yescharacteristic
1035C2#1311811211yescharacteristic
1036C2#1311813711yescharacteristic
subgroupG/H
centerC23×C4C22×D13
commutatorC23×C13C23×C4
FrattiniC24C23×D13
FittingC2×C4×C13×C4⋊C4C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenterC2×C4×C4⋊C4D13
hypocenterC13C4×#396
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23×C4 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×#6101C2semidirect
3. C2×C4×C4⋊Dic13C2semidirect
7. #13113096C2semidirect
8. #13113089C2semidirect
9. #13113088C2semidirect
10. #13113086C2semidirect
14. C4×#88071C2semidirect
15. C2×C4×C13×C4⋊C4C2semidirect
52. #11718655C4direct (N × H)
85. C2×C13×C4⋊C4C2×C4semidirect
118. C2×C4⋊Dic13C2×C4semidirect
124. C2×#6101C2×C4semidirect
149. #88071C2×C4semidirect
293. C2×C4×C4⋊C4D13semidirect
552. C4×C13#396semidirect
599. C2×C4⋊C4C4×D13semidirect
807. C13C4×#396semidirect
1020. C4#11718655direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117186552
C2×C4×#61012
C2×C4×C4⋊Dic132
C2×C4×#61032
#131130962
#131130892
#131130882
#131130862
#131130822
#131130802
#131130782
C4×#880712
C2×C4×C13×C4⋊C42
C4×#39613