Finite Group Databasebeta

← C2×#13115819 #15867557

Subgroups — C2×#13115819 #15867557

Order 3328.

1698 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88132C211yesmaximal, characteristic
2C2×#11718603C211yesmaximal, characteristic
3C2×C22⋊C4×Dic13C211yesmaximal, characteristic
4#13115819C218yesmaximal, direct product factor
5C2×#11718118C211yesmaximal, characteristic
6C2×#11718119C211yesmaximal, characteristic
7C2×#11718119C211yesmaximal, characteristic
8C2×C13×#342C211yesmaximal, characteristic
9C24×Dic13C2211yescharacteristic
10C23×Dic26C411yescharacteristic, complemented
11C22×C13×C22⋊C4C2211yescharacteristic
12C22×C13×C22⋊C4C2211yescharacteristic
13C22×C13×C22⋊C4C2211yescharacteristic
14C22×C22⋊Dic13C2211yescharacteristic
15C22×C22⋊Dic13C2211yescharacteristic
16C22×C22⋊Dic13C2211yescharacteristic
17C22×C4⋊Dic13C411yescharacteristic, complemented
18C22×#6101—21no—
19C22×#6101C411yescharacteristic, complemented
20C22×#6101C411yescharacteristic, complemented
21C22×C4×Dic13—21no—
22C2×#88132—21no—
23C2×#88132—21no—
24C2×#88132—22no—
25C2×#88132—22no—
26C2×#88132—21no—
27C2×#88132—21no—
28C2×#88132C414yescomplemented
29C2×#88132C2214yes—
30C2×#88071—21no—
31C2×#88071—21no—
32#11718603—22no—
33#11718603C2214yes—
34C22⋊C4×Dic13—22no—
35C22⋊C4×Dic13C2214yes—
36C13×#342C2214yes—
37#11718119C2214yes—
38#11718119C2214yes—
39#11718118C2214yes—
40C25×C13C2311yescharacteristic
41C23×C4×C13—21no—
42C23×C4×C13—21no—
43C23×C4×C13C2×C411yescharacteristic
44C23×C4×C13C2×C411yescharacteristic
45C23×Dic13—21no—
46C23×Dic13—21no—
47C23×Dic13—44no—
48C23×Dic13C2×C411yescharacteristic
49C23×Dic13C2×C411yescharacteristic
50C23×Dic13C2×C411yescharacteristic
51C23×Dic13C2×C412yes—
52C23×Dic13C2×C411yescharacteristic
53C23×Dic13D411yescharacteristic
54C23×Dic13D411yescharacteristic
55C23×Dic13D412yes—
56C23×Dic13D412yes—
57C23×Dic13D411yescharacteristic
58C23×Dic13D411yescharacteristic
59C23×Dic13C2312yes—
60C22×Dic26—22no—
61C22×Dic26—21no—
62C22×Dic26—21no—
63C22×Dic26—44no—
64C22×Dic26C2×C414yescomplemented
65C2×C13×C22⋊C4—21no—
66C2×C13×C22⋊C4—21no—
67C2×C13×C22⋊C4—21no—
68C2×C13×C22⋊C4—21no—
69C2×C13×C22⋊C4—21no—
70C2×C13×C22⋊C4—22no—
71C2×C13×C22⋊C4—22no—
72C2×C13×C22⋊C4—22no—
73C2×C13×C22⋊C4—21no—
74C2×C13×C22⋊C4C2×C412yes—
75C2×C13×C22⋊C4Q814yescomplemented
76C2×C13×C22⋊C4C2312yes—
77C2×C13×C22⋊C4C2312yes—
78C2×C13×C22⋊C4C2312yes—
79C2×C22⋊Dic13—21no—
80C2×C22⋊Dic13—21no—
81C2×C22⋊Dic13—21no—
82C2×C22⋊Dic13—21no—
83C2×C22⋊Dic13—21no—
84C2×C22⋊Dic13—22no—
85C2×C22⋊Dic13—22no—
86C2×C22⋊Dic13—22no—
87C2×C22⋊Dic13—21no—
88C2×C22⋊Dic13C2×C412yes—
89C2×C22⋊Dic13Q814yescomplemented
90C2×C22⋊Dic13C2312yes—
91C2×C22⋊Dic13C2312yes—
92C2×C22⋊Dic13C2312yes—
93C2×C4⋊Dic13—21no—
94C2×C4⋊Dic13—21no—
95C2×C4⋊Dic13—22no—
96C2×C4⋊Dic13C2×C414yescomplemented
97C2×#6101—21no—
98C2×#6101—21no—
99C2×#6101—22no—
100C2×#6101—21no—
101C2×#6101—22no—
102C2×#6101—21no—
103C2×#6101—24no—
104C2×#6101—44no—
105C2×#6101C2×C414yescomplemented
106C2×#6101C2×C414yescomplemented
107C2×C4×Dic13—24no—
108C2×C4×Dic13—44no—
109#88132—24no—
110#88132—24no—
111#88132—24no—
112#88132—24no—
113#88132—24no—
114#88132—24no—
115#88132—24no—
116#88132—24no—
117#88071—24no—
118#88071—24no—
119C2×#1996—131nomaximal, Sylow
120C24×C13—42no—
121C24×C13—42no—
122C24×C13C22×C411yescharacteristic
123C24×C13C22×C411yescharacteristic
124C24×C13C2×D411yescharacteristic
125C24×C13C2×D411yescharacteristic
126C24×C13C2×D411yescharacteristic
127C24×C13C2×D411yescharacteristic
128C24×C13C2×Q812yes—
129C24×C13C2×Q812yes—
130C24×C13#4112yes—
131C24×C13#4112yes—
132C24×C13C2411yescharacteristic
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—24no—
138C22×C4×C13—22no—
139C22×C4×C13—22no—
140C22×C4×C13—42no—
141C22×C4×C13—42no—
142C22×C4×C13—42no—
143C22×C4×C13—42no—
144C22×C4×C13—42no—
145C22×C4×C13—42no—
146C22×C4×C13—42no—
147C22×C4×C13C22×C412yes—
148C22×C4×C13C22×C412yes—
149C22×Dic13—24no—
150C22×Dic13—24no—
151C22×Dic13—24no—
152C22×Dic13—21no—
153C22×Dic13—21no—
154C22×Dic13—21no—
155C22×Dic13—21no—
156C22×Dic13—24no—
157C22×Dic13—22no—
158C22×Dic13—22no—
159C22×Dic13—44no—
160C22×Dic13—44no—
161C22×Dic13—44no—
162C22×Dic13—44no—
163C22×Dic13—42no—
164C22×Dic13—42no—
165C22×Dic13—42no—
166C22×Dic13—42no—
167C22×Dic13—42no—
168C22×Dic13—42no—
169C22×Dic13—42no—
170C22×Dic13—42no—
171C22×Dic13—42no—
172C22×Dic13—42no—
173C22×Dic13C22⋊C412yes—
174C22×Dic13C22⋊C412yes—
175C22×Dic13C22⋊C411yescharacteristic
176C22×Dic13C22⋊C411yescharacteristic
177C22×Dic13C22⋊C411yescharacteristic
178C22×Dic13C22⋊C412yes—
179C22×Dic13C22⋊C412yes—
180C22×Dic13C22⋊C412yes—
181C22×Dic13C22⋊C412yes—
182C22×Dic13C22⋊C411yescharacteristic
183C22×Dic13C22×C412yes—
184C22×Dic13C22×C412yes—
185C22×Dic13C22×C412yes—
186C22×Dic13C22×C412yes—
187C22×Dic13C2×D412yes—
188C22×Dic13C2×D412yes—
189C22×Dic13C2×D412yes—
190C22×Dic13C2×D412yes—
191C2×Dic26—24no—
192C2×Dic26—24no—
193C2×Dic26—44no—
194C2×Dic26—48no—
195C2×Dic26—44no—
196C2×Dic26—48no—
197C13×C22⋊C4—22no—
198C13×C22⋊C4—22no—
199C13×C22⋊C4—24no—
200C13×C22⋊C4—22no—
201C13×C22⋊C4—22no—
202C13×C22⋊C4—22no—
203C13×C22⋊C4—22no—
204C13×C22⋊C4—22no—
205C13×C22⋊C4—42no—
206C13×C22⋊C4C2×Q814yescomplemented
207C22⋊Dic13—22no—
208C22⋊Dic13—22no—
209C22⋊Dic13—24no—
210C22⋊Dic13—22no—
211C22⋊Dic13—22no—
212C22⋊Dic13—22no—
213C22⋊Dic13—22no—
214C22⋊Dic13—22no—
215C22⋊Dic13—42no—
216C22⋊Dic13C2×Q814yescomplemented
217C4⋊Dic13—24no—
218C4⋊Dic13—24no—
219#6101—24no—
220#6101—24no—
221#6101—24no—
222#6101—24no—
223#6101—48no—
224C4×Dic13—48no—
225C22×C22⋊Q8—131no—
226C2×#380—131no—
227C2×C4×C22⋊C4—131no—
228#1996—138no—
229C2×#342—131no—
230C2×#342—131no—
231C2×#342—131no—
232C2×#342D1311yescharacteristic
233C23×C13—22no—
234C23×C13—22no—
235C23×C13—22no—
236C23×C13—22no—
237C23×C13—22no—
238C23×C13—22no—
239C23×C13—41no—
240C23×C13—41no—
241C23×C13—41no—
242C23×C13—41no—
243C23×C13—41no—
244C23×C13—41no—
245C23×C13—41no—
246C23×C13—44no—
247C23×C13—44no—
248C23×C13—44no—
249C23×C13—44no—
250C23×C13—41no—
251C23×C13C2×C22⋊C411yescharacteristic
252C23×C13C2×C22⋊C411yescharacteristic
253C23×C13C2×C22⋊C411yescharacteristic
254C23×C13C2×C22⋊C411yescharacteristic
255C23×C13C4×Q812yes—
256C23×C13C4×Q812yes—
257C23×C13C4×Q812yes—
258C23×C13C4×Q812yes—
259C23×C13C22⋊Q812yes—
260C23×C13C22⋊Q812yes—
261C23×C13C22⋊Q812yes—
262C23×C13C22⋊Q812yes—
263C23×C13#12412yes—
264C23×C13#12412yes—
265C23×C13C4⋊Q812yes—
266C23×C13C4⋊Q812yes—
267C23×C13C23×C411yescharacteristic
268C23×C13C22×D411yescharacteristic
269C23×C13C22×D411yescharacteristic
270C23×C13C22×Q811yescharacteristic
271C23×C13C22×Q811yescharacteristic
272C23×C13C2×#4111yescharacteristic
273C23×C13C2×#4111yescharacteristic
274C2×C4×C13—22no—
275C2×C4×C13—22no—
276C2×C4×C13—24no—
277C2×C4×C13—42no—
278C2×C4×C13—42no—
279C2×C4×C13—42no—
280C2×C4×C13—48no—
281C2×C4×C13—42no—
282C2×C4×C13—42no—
283C2×C4×C13—42no—
284C2×C4×C13—42no—
285C2×C4×C13—42no—
286C2×C4×C13—42no—
287C2×C4×C13—42no—
288C2×C4×C13—42no—
289C2×C4×C13—84no—
290C2×Dic13—22no—
291C2×Dic13—22no—
292C2×Dic13—22no—
293C2×Dic13—24no—
294C2×Dic13—24no—
295C2×Dic13—24no—
296C2×Dic13—24no—
297C2×Dic13—24no—
298C2×Dic13—24no—
299C2×Dic13—22no—
300C2×Dic13—22no—
301C2×Dic13—24no—
302C2×Dic13—42no—
303C2×Dic13—42no—
304C2×Dic13—42no—
305C2×Dic13—42no—
306C2×Dic13—42no—
307C2×Dic13—42no—
308C2×Dic13—42no—
309C2×Dic13—42no—
310C2×Dic13—42no—
311C2×Dic13—48no—
312C2×Dic13—42no—
313C2×Dic13—42no—
314C2×Dic13—42no—
315C2×Dic13—42no—
316C2×Dic13—42no—
317C2×Dic13—42no—
318C2×Dic13—42no—
319C2×Dic13—42no—
320C2×Dic13—84no—
321C2×Dic13#9914yes—
322C2×Dic13C2×C22⋊C412yes—
323C2×Dic13C2×C22⋊C412yes—
324C2×Dic13C2×C22⋊C412yes—
325C2×Dic13C2×C22⋊C412yes—
326Dic26—48no—
327Dic26—48no—
328C23×Q8—131no—
329C24×C4—131no—
330C2×C22⋊Q8—134no—
331C2×C22⋊Q8—134no—
332C2×C22⋊Q8—261no—
333C2×C22⋊Q8—261no—
334C2×C22⋊Q8—261no—
335C2×C22⋊Q8—261no—
336C2×C22⋊Q8—262no—
337C2×C22⋊Q8—262no—
338C22×C4⋊C4—131no—
339C22×C4⋊C4—131no—
340C22×C4⋊C4—131no—
341C22×C4⋊C4—261no—
342C22×C22⋊C4—131no—
343C22×C22⋊C4—131no—
344C22×C22⋊C4—131no—
345C22×C22⋊C4C2×D1311yescharacteristic
346C22×C22⋊C4C2×D1311yescharacteristic
347C22×C22⋊C4C2×D1311yescharacteristic
348C22×C42—261no—
349#380—134no—
350#380—262no—
351C4×C22⋊C4—134no—
352C4×C22⋊C4—262no—
353C2×#95—261no—
354C2×#95—261no—
355#342—134no—
356#342—134no—
357#342—134no—
358#342C2×D1314yes—
359C22×C13—21no—
360C22×C13—21no—
361C22×C13—21no—
362C22×C13—21no—
363C22×C13—21no—
364C22×C13—21no—
365C22×C13—21no—
366C22×C13—21no—
367C22×C13—21no—
368C22×C13—21no—
369C22×C13—21no—
370C22×C13—21no—
371C22×C13—24no—
372C22×C13—24no—
373C22×C13—24no—
374C22×C13—24no—
375C22×C13—24no—
376C22×C13—24no—
377C22×C13—42no—
378C22×C13—42no—
379C22×C13—42no—
380C22×C13—42no—
381C22×C13—42no—
382C22×C13—42no—
383C22×C13—41no—
384C22×C13—41no—
385C22×C13—41no—
386C22×C13—41no—
387C22×C13#39112yes—
388C22×C13#39112yes—
389C22×C13#39112yes—
390C22×C13#39112yes—
391C22×C13C2×#9912yes—
392C22×C13#41012yes—
393C22×C13C22×C22⋊C411yescharacteristic
394C22×C13C2×C4×Q811yescharacteristic
395C22×C13C2×C4×Q811yescharacteristic
396C22×C13C2×C22⋊Q811yescharacteristic
397C22×C13C2×C22⋊Q811yescharacteristic
398C22×C13C2×#12411yescharacteristic
399C22×C13C2×C4⋊Q811yescharacteristic
400C4×C13—44no—
401C4×C13—42no—
402C4×C13—42no—
403C4×C13—82no—
404Dic13—22no—
405Dic13—22no—
406Dic13—22no—
407Dic13—44no—
408Dic13—42no—
409Dic13—42no—
410Dic13—82no—
411Dic13C2×#9914yes—
412C25C22×D1311yescharacteristic
413C22×Q8—134no—
414C22×Q8—262no—
415C22×Q8—261no—
416C22×Q8—261no—
417C22×Q8—524no—
418C23×C4—21no—
419C23×C4—21no—
420C23×C4—131no—
421C23×C4—131no—
422C23×C4—131no—
423C23×C4—131no—
424C23×C4—132no—
425C23×C4—131no—
426C23×C4—131no—
427C23×C4—132no—
428C23×C4—132no—
429C23×C4—132no—
430C23×C4—131no—
431C23×C4—131no—
432C23×C4—261no—
433C23×C4—261no—
434C23×C4—524no—
435C23×C4C4×D1311yescharacteristic
436C23×C4C4×D1311yescharacteristic
437C22⋊Q8—264no—
438C22⋊Q8—264no—
439C22⋊Q8—264no—
440C22⋊Q8—264no—
441C22⋊Q8—264no—
442C22⋊Q8—264no—
443C22⋊Q8—264no—
444C22⋊Q8—264no—
445C2×C4⋊C4—134no—
446C2×C4⋊C4—134no—
447C2×C4⋊C4—134no—
448C2×C4⋊C4—262no—
449C2×C4⋊C4—262no—
450C2×C4⋊C4—261no—
451C2×C4⋊C4—261no—
452C2×C4⋊C4—261no—
453C2×C4⋊C4—261no—
454C2×C4⋊C4—262no—
455C2×C4⋊C4—261no—
456C2×C4⋊C4—261no—
457C2×C4⋊C4—264no—
458C2×C4⋊C4—524no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—134no—
469C2×C22⋊C4—132no—
470C2×C22⋊C4—132no—
471C2×C22⋊C4—132no—
472C2×C22⋊C4—132no—
473C2×C22⋊C4—262no—
474C2×C22⋊C4—261no—
475C2×C22⋊C4—261no—
476C2×C22⋊C4—261no—
477C2×C22⋊C4—261no—
478C2×C22⋊C4—261no—
479C2×C22⋊C4—262no—
480C2×C22⋊C4—262no—
481C2×C22⋊C4—261no—
482C2×C22⋊C4Dic2614yescomplemented
483C2×C22⋊C4C4×D1312yes—
484C2×C22⋊C4C22×D1312yes—
485C2×C22⋊C4C22×D1312yes—
486C2×C22⋊C4C22×D1312yes—
487C2×C42—264no—
488C2×C42—524no—
489#95—264no—
490#95—264no—
491C2×C13—21no—
492C2×C13—21no—
493C2×C13—21no—
494C2×C13—21no—
495C2×C13—21no—
496C2×C13—21no—
497C2×C13—22no—
498C2×C13—22no—
499C2×C13—22no—
500C2×C13#199614yescomplemented
501C2×C13C2×#39111yescharacteristic
502C2×C13C22×#9911yescharacteristic
503C2×C13C2×#41011yescharacteristic
504C24—42no—
505C24—42no—
506C24C2×Dic2612yes—
507C24C2×C4×D1311yescharacteristic
508C24C2×C4×D1311yescharacteristic
509C24#612712yes—
510C24D4×D1311yescharacteristic
511C24D4×D1311yescharacteristic
512C24D4×D1311yescharacteristic
513C24D4×D1311yescharacteristic
514C24#612912yes—
515C24Q8×D1312yes—
516C24C23×D1311yescharacteristic
517C2×Q8—264no—
518C2×Q8—264no—
519C2×Q8—524no—
520C2×Q8—528no—
521C2×Q8—528no—
522C2×Q8—524no—
523C22×C4—24no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—131no—
538C22×C4—132no—
539C22×C4—132no—
540C22×C4—132no—
541C22×C4—131no—
542C22×C4—131no—
543C22×C4—131no—
544C22×C4—132no—
545C22×C4—132no—
546C22×C4—132no—
547C22×C4—132no—
548C22×C4—132no—
549C22×C4—132no—
550C22×C4—132no—
551C22×C4—132no—
552C22×C4—132no—
553C22×C4—132no—
554C22×C4—132no—
555C22×C4—264no—
556C22×C4—264no—
557C22×C4—264no—
558C22×C4—261no—
559C22×C4—261no—
560C22×C4—261no—
561C22×C4—261no—
562C22×C4—264no—
563C22×C4—262no—
564C22×C4—262no—
565C22×C4—524no—
566C22×C4—524no—
567C22×C4—524no—
568C22×C4—524no—
569C22×C4—522no—
570C22×C4—522no—
571C22×C4—522no—
572C22×C4—522no—
573C22×C4—522no—
574C22×C4—522no—
575C22×C4—522no—
576C22×C4—522no—
577C22×C4—522no—
578C22×C4—522no—
579C22×C4C2×C4×D1312yes—
580C22×C4C2×C4×D1312yes—
581C4⋊C4—264no—
582C4⋊C4—264no—
583C4⋊C4—264no—
584C4⋊C4—264no—
585C4⋊C4—264no—
586C4⋊C4—264no—
587C4⋊C4—528no—
588C22⋊C4—24no—
589C22⋊C4—22no—
590C22⋊C4—22no—
591C22⋊C4—22no—
592C22⋊C4—22no—
593C22⋊C4—22no—
594C22⋊C4—22no—
595C22⋊C4—22no—
596C22⋊C4—42no—
597C22⋊C4—134no—
598C22⋊C4—262no—
599C22⋊C4—262no—
600C22⋊C4—264no—
601C22⋊C4—262no—
602C22⋊C4—262no—
603C22⋊C4—262no—
604C22⋊C4—262no—
605C22⋊C4—262no—
606C22⋊C4—522no—
607C22⋊C4C2×Dic2614yescomplemented
608C42—528no—
609C13C2×#199611yescharacteristic, complemented, Sylow
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—44no—
621C23—41no—
622C23—44no—
623C23—41no—
624C23—41no—
625C23—44no—
626C23—44no—
627C23—41no—
628C23C4×Dic2612yes—
629C23C4×Dic2612yes—
630C23#8813212yes—
631C23#8813212yes—
632C23C22⋊C4×D1311yescharacteristic
633C23C22⋊C4×D1311yescharacteristic
634C23C22⋊C4×D1311yescharacteristic
635C23C22⋊C4×D1311yescharacteristic
636C23#8813912yes—
637C23#8813912yes—
638C23#8814112yes—
639C23#8814112yes—
640C23#8814212yes—
641C23#8814212yes—
642C23#8815012yes—
643C23#8815012yes—
644C23C22×Dic2611yescharacteristic
645C23C22×C4×D1311yescharacteristic
646C23C2×#612711yescharacteristic
647C23C2×D4×D1311yescharacteristic
648C23C2×D4×D1311yescharacteristic
649C23C2×#612911yescharacteristic
650C23C2×Q8×D1311yescharacteristic
651Q8—528no—
652Q8—528no—
653C2×C4—24no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—42no—
657C2×C4—48no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—84no—
669C2×C4—134no—
670C2×C4—132no—
671C2×C4—132no—
672C2×C4—132no—
673C2×C4—132no—
674C2×C4—264no—
675C2×C4—264no—
676C2×C4—264no—
677C2×C4—264no—
678C2×C4—264no—
679C2×C4—264no—
680C2×C4—262no—
681C2×C4—262no—
682C2×C4—262no—
683C2×C4—262no—
684C2×C4—262no—
685C2×C4—264no—
686C2×C4—522no—
687C2×C4—522no—
688C2×C4—522no—
689C2×C4—522no—
690C2×C4—522no—
691C2×C4—522no—
692C2×C4—522no—
693C2×C4—528no—
694C2×C4—522no—
695C2×C4—522no—
696C2×C4—522no—
697C2×C4—522no—
698C2×C4—522no—
699C2×C4—522no—
700C2×C4—522no—
701C2×C4—522no—
702C2×C4—522no—
703C2×C4—522no—
704C2×C4—1044no—
705C22—24no—
706C22—24no—
707C22—24no—
708C22—24no—
709C22—24no—
710C22—24no—
711C22—21no—
712C22—21no—
713C22—21no—
714C22—21no—
715C22—21no—
716C22—21no—
717C22—21no—
718C22—21no—
719C22—21no—
720C22—21no—
721C22—21no—
722C22—21no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22#1171830712yes—
734C22#1171830712yes—
735C22#1171830712yes—
736C22#1171830712yes—
737C22#1171840112yes—
738C22D13×#9912yes—
739C22C2×C4×Dic2611yescharacteristic
740C22C2×#8813211yescharacteristic
741C22C2×C22⋊C4×D1311yescharacteristic
742C22C2×#8813911yescharacteristic
743C22C2×#8814111yescharacteristic
744C22C2×#8814211yescharacteristic
745C22C2×#8815011yescharacteristic
746C4—44no—
747C4—42no—
748C4—42no—
749C4—82no—
750C4—134no—
751C4—262no—
752C4—262no—
753C4—262no—
754C4—524no—
755C4—522no—
756C4—522no—
757C4—1042no—
758C2—21no—
759C2—21no—
760C2—21no—
761C2—21no—
762C2—21no—
763C2—21no—
764C2—22no—
765C2—22no—
766C2—22no—
767C2#1311581914yesdirect product factor
768C2C2×#1171830711yescharacteristic
769C2C2×D13×#9911yescharacteristic
770C2C2×#1171840111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D13
commutatorC23×C13C23×C4
FrattiniC24C23×D13
FittingC2×C13×#342C2
socleC23×C13C2×C22⋊C4
prime radicalC25×C13C23
cosocleC24×C13C24
hypercenterC2×#342D13
hypocenterC13C2×#1996
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
4. #13115819C2direct (N × H)
10. C23×Dic26C4semidirect
17. C22×C4⋊Dic13C4semidirect
19. C22×#6101C4semidirect
20. C22×#6101C4semidirect
28. C2×#88132C4semidirect
64. C22×Dic26C2×C4semidirect
75. C2×C13×C22⋊C4Q8semidirect
89. C2×C22⋊Dic13Q8semidirect
96. C2×C4⋊Dic13C2×C4semidirect
105. C2×#6101C2×C4semidirect
106. C2×#6101C2×C4semidirect
206. C13×C22⋊C4C2×Q8semidirect
216. C22⋊Dic13C2×Q8semidirect
482. C2×C22⋊C4Dic26semidirect
500. C2×C13#1996semidirect
607. C22⋊C4C2×Dic26semidirect
609. C13C2×#1996semidirect
767. C2#13115819direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881322
C2×#117186032
C2×C22⋊C4×Dic132
#131158192
C2×#117181182
C2×#117181192
C2×C13×#3422
C2×#199613