Finite Group Databasebeta

← C2×#13126083 #16735102

Subgroups — C2×#13126083 #16735102

Order 3328.

1806 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719224C211yesmaximal, characteristic, complemented
2#13126083C2116yesmaximal, direct product factor
3C2×#11718726C211yesmaximal, characteristic, complemented
4C2×#11718725C211yesmaximal, characteristic, complemented
5C2×#11718732C211yesmaximal, characteristic, complemented
6C2×#11718731C211yesmaximal, characteristic, complemented
7C2×#11718695C211yesmaximal, characteristic, complemented
8C2×#11718696C211yesmaximal, characteristic, complemented
9C2×#11718696C211yesmaximal, characteristic, complemented
10C2×#11718694C211yesmaximal, characteristic, complemented
11C2×#11718670C211yesmaximal, characteristic, complemented
12C2×#11718670C211yesmaximal, characteristic, complemented
13C2×#11718669C211yesmaximal, characteristic, complemented
14C2×#11718668C211yesmaximal, characteristic, complemented
15C2×#11718661C211yesmaximal, characteristic, complemented
16C2×C13×#540C211yesmaximal, characteristic
17C13×#540—24no—
18C13×#540C2218yes—
19C2×C13×#127C2211yescharacteristic
20C2×C13×#125C2211yescharacteristic
21C2×C13×#123—21no—
22C2×C13×#123—21no—
23C2×C13×#121—21no—
24C2×C13×#121—21no—
25C2×C13×#121C2211yescharacteristic
26C2×C13×#121C2211yescharacteristic
27C2×C4×D4×C13C2211yescharacteristic
28C2×C4×D4×C13C2211yescharacteristic
29C2×C13×#117C2211yescharacteristic
30C2×#88180C2211yescharacteristic
31C22×C4⋊Dic13C2211yescharacteristic
32#11719224—24no—
33#11719224C2218yescomplemented
34C2×#88144—21no—
35C2×#88142—21no—
36C2×#88132—21no—
37C2×#88132—21no—
38C2×#88124C2211yescharacteristic
39C2×#88124C2211yescharacteristic
40C2×#88123C2211yescharacteristic
41C2×#88123C2211yescharacteristic
42C2×#88072C2211yescharacteristic
43C2×#88072C2211yescharacteristic
44C2×#88072C2211yescharacteristic
45C2×#88072C2211yescharacteristic
46C2×#88072C2211yescharacteristic
47C2×#88072C2211yescharacteristic
48C2×#88072C2211yescharacteristic
49C2×#88072C2211yescharacteristic
50C2×C22⋊#1055C2211yescharacteristic
51C2×C22⋊#1055C2211yescharacteristic
52#11718732C2218yescomplemented
53#11718731C2218yescomplemented
54#11718726C2218yescomplemented
55#11718725C2218yescomplemented
56#11718696C2218yescomplemented
57#11718696C2218yescomplemented
58#11718695C2218yescomplemented
59#11718694C2218yescomplemented
60#11718670C2218yescomplemented
61#11718670C2218yescomplemented
62#11718669C2218yescomplemented
63#11718668C2218yescomplemented
64#11718661C2218yescomplemented
65C2×#88048C2211yescharacteristic
66C2×#88048C2211yescharacteristic
67C2×#88048C2211yescharacteristic
68C2×#88048C2211yescharacteristic
69C2×#88047C2211yescharacteristic
70C2×#88047C2211yescharacteristic
71C2×#88047C2211yescharacteristic
72C2×#88047C2211yescharacteristic
73C2×C4⋊#1055C2211yescharacteristic
74C2×C4⋊#1055C2211yescharacteristic
75C2×#88043C2211yescharacteristic
76C2×C4×#1055C2211yescharacteristic
77C22×D4×C13—21no—
78C22×D4×C13—21no—
79C22×D4×C13—21no—
80C22×D4×C13—21no—
81C22×D4×C13C2311yescharacteristic
82C22×D4×C13C2311yescharacteristic
83C23×C4×C13—21no—
84C23×C4×C13—21no—
85C23×C4×C13C2311yescharacteristic
86C23×Dic13—21no—
87C22×Dic26—21no—
88C22×Dic26—21no—
89C13×#127—22no—
90C13×#127C2314yes—
91C13×#125—22no—
92C13×#125C2314yes—
93C13×#123—28no—
94C13×#123—28no—
95C13×#121—22no—
96C13×#121—22no—
97C13×#121—28no—
98C13×#121—28no—
99C13×#121C2314yes—
100C13×#121C2314yes—
101C4×D4×C13—22no—
102C4×D4×C13—22no—
103C4×D4×C13C2314yes—
104C4×D4×C13C2314yes—
105C13×#117D414yes—
106C13×#117C2314yes—
107C2×C13×C4⋊C4—21no—
108C2×C13×C4⋊C4—21no—
109C2×C13×C4⋊C4D411yescharacteristic
110C2×C13×C4⋊C4D411yescharacteristic
111C2×C13×C4⋊C4C2311yescharacteristic
112C2×C13×C4⋊C4C2311yescharacteristic
113C2×C13×C22⋊C4—21no—
114C2×C13×C22⋊C4—21no—
115C2×C13×C22⋊C4—21no—
116C2×C13×C22⋊C4—21no—
117C2×C13×C22⋊C4D411yescharacteristic
118C2×C13×C22⋊C4D411yescharacteristic
119C2×C42×C13C2311yescharacteristic
120C2×C42×C13C2311yescharacteristic
121C2×C22⋊Dic13—21no—
122#88180—22no—
123#88180C2314yes—
124C2×C4⋊Dic13—21no—
125C2×C4⋊Dic13—21no—
126C2×C4⋊Dic13—21no—
127C2×C4⋊Dic13—22no—
128C2×C4⋊Dic13C2311yescharacteristic
129C2×C4⋊Dic13C2311yescharacteristic
130C2×C4⋊Dic13C2311yescharacteristic
131C2×C4⋊Dic13C2311yescharacteristic
132C2×C4⋊Dic13C2314yes—
133C2×#6101—21no—
134C2×#6101—21no—
135C2×#6101—21no—
136C2×#6101—21no—
137C2×C4×Dic13—21no—
138C22×#1055C2311yescharacteristic
139C22×#1055C2311yescharacteristic
140C22×#1055C2311yescharacteristic
141C22×#1055C2311yescharacteristic
142#88144—28no—
143#88142—28no—
144#88132—28no—
145#88132—28no—
146#88124—22no—
147#88124—22no—
148#88124C2314yes—
149#88124C2314yes—
150#88123—22no—
151#88123—22no—
152#88123C2314yes—
153#88123C2314yes—
154#88072C2314yes—
155#88072C2314yes—
156#88072C2314yes—
157#88072C2314yes—
158#88072C2314yes—
159#88072C2314yes—
160#88072C2314yes—
161#88072C2314yes—
162C22⋊#1055C2314yes—
163C22⋊#1055C2314yes—
164#88048C2314yes—
165#88048C2314yes—
166#88048C2314yes—
167#88048C2314yes—
168#88047C2314yes—
169#88047C2314yes—
170#88047C2314yes—
171#88047C2314yes—
172C4⋊#1055C2314yes—
173C4⋊#1055C2314yes—
174#88043C2314yes—
175C4×#1055C2314yes—
176C2×#3241—131nomaximal, Sylow
177C24×C13—21no—
178C24×C13—21no—
179C24×C13C2×D411yescharacteristic
180C2×D4×C13—24no—
181C2×D4×C13—24no—
182C2×D4×C13—21no—
183C2×D4×C13—21no—
184C2×D4×C13—24no—
185C2×D4×C13—24no—
186C2×D4×C13—22no—
187C2×D4×C13—22no—
188C2×D4×C13—22no—
189C2×D4×C13—22no—
190C2×D4×C13—82no—
191C2×D4×C13—82no—
192C2×D4×C13—82no—
193C2×D4×C13—82no—
194C2×D4×C13C2412yes—
195C2×D4×C13C2412yes—
196C22×C4×C13—22no—
197C22×C4×C13—22no—
198C22×C4×C13—21no—
199C22×C4×C13—21no—
200C22×C4×C13—24no—
201C22×C4×C13—24no—
202C22×C4×C13—82no—
203C22×C4×C13—82no—
204C22×C4×C13C2×D411yescharacteristic
205C22×C4×C13C2×D411yescharacteristic
206C22×C4×C13C2×D411yescharacteristic
207C22×C4×C13C2×D411yescharacteristic
208C22×C4×C13C2×D411yescharacteristic
209C22×C4×C13C2×D412yes—
210C22×C4×C13C2412yes—
211C22×C4×C13C2411yescharacteristic
212C22×Dic13—21no—
213C22×Dic13—21no—
214C22×Dic13—21no—
215C22×Dic13—21no—
216C22×Dic13—24no—
217C22×Dic13—82no—
218C2×Dic26—24no—
219C2×Dic26—24no—
220C2×Dic26—82no—
221C2×Dic26—82no—
222C13×C4⋊C4—24no—
223C13×C4⋊C4—24no—
224C13×C4⋊C4—21no—
225C13×C4⋊C4—21no—
226C13×C4⋊C4C2×D414yes—
227C13×C4⋊C4C2×D414yes—
228C13×C4⋊C4C2412yes—
229C13×C4⋊C4C2412yes—
230C13×C22⋊C4—24no—
231C13×C22⋊C4—24no—
232C13×C22⋊C4—24no—
233C13×C22⋊C4—24no—
234C13×C22⋊C4C2×D414yes—
235C13×C22⋊C4C2×D414yes—
236C42×C13C2×D412yes—
237C42×C13C2×D412yes—
238C42×C13C2412yes—
239C42×C13C2412yes—
240C22⋊Dic13—24no—
241C4⋊Dic13—21no—
242C4⋊Dic13—21no—
243C4⋊Dic13—21no—
244C4⋊Dic13—24no—
245C4⋊Dic13—24no—
246C4⋊Dic13—21no—
247C4⋊Dic13—24no—
248C4⋊Dic13C2412yes—
249C4⋊Dic13C2412yes—
250C4⋊Dic13C2412yes—
251C4⋊Dic13C2412yes—
252#6101—24no—
253#6101—24no—
254#6101—24no—
255#6101—24no—
256C4×Dic13—24no—
257C2×#1055—22no—
258C2×#1055—22no—
259C2×#1055—22no—
260C2×#1055—22no—
261C2×#1055C2412yes—
262C2×#1055C2412yes—
263C2×#1055C2412yes—
264C2×#1055C2412yes—
265C2×#544—131no—
266C2×#540D1311yescharacteristic
267#3241—1316no—
268C2×#501—131no—
269C2×#499—131no—
270C2×#490—131no—
271C2×#486—131no—
272C2×#481—131no—
273C2×#482—131no—
274C2×#482—131no—
275C2×#480—131no—
276C2×#478—131no—
277C2×#478—131no—
278C2×#476—131no—
279C2×#474—131no—
280C2×#433—131no—
281C23×C13—22no—
282C23×C13—22no—
283C23×C13—22no—
284C23×C13—22no—
285C23×C13—22no—
286C23×C13—42no—
287C23×C13—42no—
288C23×C13—42no—
289C23×C13—42no—
290C23×C13—42no—
291C23×C13—42no—
292C23×C13C22×D412yes—
293C23×C13C22×D411yescharacteristic
294D4×C13—22no—
295D4×C13—22no—
296D4×C13—22no—
297D4×C13—22no—
298D4×C13—42no—
299D4×C13—42no—
300D4×C13—84no—
301D4×C13—84no—
302D4×C13—84no—
303D4×C13—84no—
304C2×C4×C13—22no—
305C2×C4×C13—22no—
306C2×C4×C13—22no—
307C2×C4×C13—22no—
308C2×C4×C13—22no—
309C2×C4×C13—24no—
310C2×C4×C13—22no—
311C2×C4×C13—22no—
312C2×C4×C13—22no—
313C2×C4×C13—22no—
314C2×C4×C13—42no—
315C2×C4×C13—42no—
316C2×C4×C13—84no—
317C2×C4×C13—84no—
318C2×C4×C13C22×D412yes—
319C2×C4×C13C22×D412yes—
320C2×C4×C13C22×D412yes—
321C2×C4×C13C22×D412yes—
322C2×C4×C13C22×D412yes—
323C2×C4×C13C22×D411yescharacteristic
324C2×C4×C132−1+412yes—
325C2×C4×C132−1+412yes—
326C2×C4×C13C2511yescharacteristic
327C2×Dic13—22no—
328C2×Dic13—22no—
329C2×Dic13—22no—
330C2×Dic13—22no—
331C2×Dic13—42no—
332C2×Dic13—42no—
333C2×Dic13—42no—
334C2×Dic13—42no—
335C2×Dic13—84no—
336Dic26—84no—
337Dic26—84no—
338#1055—22no—
339#1055—22no—
340#1055—22no—
341#1055—22no—
342#544—138no—
343#544—264no—
344#540—24no—
345#540C2×D1318yes—
346C2×C4⋊Q8—131no—
347C2×C4⋊Q8—131no—
348C2×C4⋊Q8—261no—
349C2×#127C2×D1311yescharacteristic
350C2×#125—131no—
351C2×#125—131no—
352C2×#125—261no—
353C2×#125C2×D1311yescharacteristic
354C2×#123—21no—
355C2×#123—21no—
356C2×C22⋊Q8—261no—
357C2×C22⋊Q8—261no—
358C2×#121—21no—
359C2×#121—21no—
360C2×#121C2×D1311yescharacteristic
361C2×#121C2×D1311yescharacteristic
362C2×C4×D4C2×D1311yescharacteristic
363C2×C4×D4C2×D1311yescharacteristic
364C2×#117—131no—
365C2×#117C2×D1311yescharacteristic
366C22×C4⋊C4—131no—
367#501—138no—
368#499—138no—
369#490—138no—
370#486—138no—
371#482—138no—
372#482—138no—
373#481—138no—
374#480—138no—
375#478—138no—
376#478—138no—
377#476—138no—
378#474—138no—
379#433—138no—
380C2×#107—131no—
381C2×#107—131no—
382C2×#107—131no—
383C2×#107—131no—
384C2×#106—131no—
385C2×#106—131no—
386C2×#106—131no—
387C2×#106—131no—
388C2×C4⋊C8—131no—
389C2×C4⋊C8—131no—
390C2×#102—131no—
391C2×#102—131no—
392C2×#102—131no—
393C2×#102—131no—
394C2×#102—131no—
395C2×#102—131no—
396C2×#102—131no—
397C2×#102—131no—
398C2×C22⋊C8—131no—
399C2×C22⋊C8—131no—
400C2×#97—131no—
401C2×C4×C8—131no—
402C22×C13—22no—
403C22×C13—22no—
404C22×C13—22no—
405C22×C13—44no—
406C22×C13—42no—
407C22×C13—42no—
408C22×C13—42no—
409C22×C13—42no—
410C22×C13—42no—
411C22×C13—42no—
412C22×C13—84no—
413C22×C13—84no—
414C22×C13#53612yes—
415C22×C13#57612yes—
416C22×C13#57712yes—
417C22×C13C23×D411yescharacteristic
418C4×C13—22no—
419C4×C13—22no—
420C4×C13—22no—
421C4×C13—22no—
422C4×C13—22no—
423C4×C13—42no—
424C4×C13—42no—
425C4×C13#53612yes—
426C4×C13C2×2−1+411yescharacteristic
427C4×C13C2×2−1+411yescharacteristic
428Dic13—42no—
429Dic13—42no—
430Dic13—42no—
431Dic13—42no—
432C22×Q8—261no—
433C22×Q8—261no—
434C22×D4—21no—
435C22×D4—21no—
436C22×D4—21no—
437C22×D4—21no—
438C22×D4C22×D1311yescharacteristic
439C22×D4C22×D1311yescharacteristic
440C23×C4—21no—
441C23×C4—21no—
442C23×C4—261no—
443C23×C4C22×D1311yescharacteristic
444C22×C8—131no—
445C22×C8—131no—
446C22×C8—131no—
447C22×C8—131no—
448C4⋊Q8—134no—
449C4⋊Q8—134no—
450C4⋊Q8—268no—
451C4⋊Q8—262no—
452C4⋊Q8—262no—
453#127—22no—
454#127C22×D1314yes—
455#125—22no—
456#125—134no—
457#125—134no—
458#125—268no—
459#125—262no—
460#125—262no—
461#125C22×D1314yes—
462#123—28no—
463#123—28no—
464C22⋊Q8—268no—
465C22⋊Q8—268no—
466#121—22no—
467#121—22no—
468#121—28no—
469#121—28no—
470#121C22×D1314yes—
471#121C22×D1314yes—
472C4×D4—22no—
473C4×D4—22no—
474C4×D4C22×D1314yes—
475C4×D4C22×D1314yes—
476#117—134no—
477#117—262no—
478#117C22⋊D1314yes—
479#117C22×D1314yes—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—131no—
483C2×C4⋊C4—131no—
484C2×C4⋊C4—134no—
485C2×C4⋊C4—131no—
486C2×C4⋊C4—131no—
487C2×C4⋊C4—261no—
488C2×C4⋊C4—262no—
489C2×C4⋊C4—261no—
490C2×C4⋊C4—261no—
491C2×C4⋊C4—261no—
492C2×C4⋊C4—261no—
493C2×C4⋊C4—261no—
494C2×C4⋊C4—261no—
495C2×C4⋊C4C22⋊D1311yescharacteristic
496C2×C4⋊C4C22⋊D1311yescharacteristic
497C2×C4⋊C4C22×D1311yescharacteristic
498C2×C4⋊C4C22×D1311yescharacteristic
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—261no—
504C2×C22⋊C4C22⋊D1311yescharacteristic
505C2×C22⋊C4C22⋊D1311yescharacteristic
506C2×C42—261no—
507C2×C42C22×D1311yescharacteristic
508C2×C42C22×D1311yescharacteristic
509#107—134no—
510#107—134no—
511#107—134no—
512#107—134no—
513#106—134no—
514#106—134no—
515#106—134no—
516#106—134no—
517C4⋊C8—134no—
518C4⋊C8—134no—
519#102—134no—
520#102—134no—
521#102—134no—
522#102—134no—
523#102—134no—
524#102—134no—
525#102—134no—
526#102—134no—
527C22⋊C8—134no—
528C22⋊C8—134no—
529#97—134no—
530C4×C8—134no—
531C2×C13—42no—
532C2×C13—82no—
533C2×C13—82no—
534C2×C13#324114yescomplemented
535C2×C13C2×#53611yescharacteristic
536C2×C13C2×#57611yescharacteristic
537C2×C13C2×#57711yescharacteristic
538C24—21no—
539C24—21no—
540C24C2×C22⋊D1311yescharacteristic
541C2×Q8—264no—
542C2×Q8—264no—
543C2×Q8—1042no—
544C2×Q8—1042no—
545C2×D4—24no—
546C2×D4—24no—
547C2×D4—22no—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—24no—
554C2×D4—24no—
555C2×D4—82no—
556C2×D4—82no—
557C2×D4—82no—
558C2×D4—82no—
559C2×D4C23×D1312yes—
560C2×D4C23×D1312yes—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—82no—
568C22×C4—82no—
569C22×C4—261no—
570C22×C4—261no—
571C22×C4—261no—
572C22×C4—261no—
573C22×C4—264no—
574C22×C4—1042no—
575C22×C4C2×C22⋊D1312yes—
576C22×C4C2×C22⋊D1311yescharacteristic
577C22×C4C2×C22⋊D1311yescharacteristic
578C22×C4C2×C22⋊D1311yescharacteristic
579C22×C4C2×C22⋊D1311yescharacteristic
580C22×C4C2×C22⋊D1311yescharacteristic
581C22×C4C23×D1312yes—
582C22×C4C23×D1311yescharacteristic
583C2×C8—132no—
584C2×C8—132no—
585C2×C8—132no—
586C2×C8—132no—
587C2×C8—262no—
588C2×C8—262no—
589C2×C8—262no—
590C2×C8—262no—
591C4⋊C4—24no—
592C4⋊C4—24no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—132no—
596C4⋊C4—132no—
597C4⋊C4—132no—
598C4⋊C4—132no—
599C4⋊C4—264no—
600C4⋊C4—261no—
601C4⋊C4—261no—
602C4⋊C4—261no—
603C4⋊C4—261no—
604C4⋊C4—264no—
605C4⋊C4—264no—
606C4⋊C4—264no—
607C4⋊C4—264no—
608C4⋊C4—264no—
609C4⋊C4—264no—
610C4⋊C4C2×C22⋊D1314yes—
611C4⋊C4C2×C22⋊D1314yes—
612C4⋊C4C23×D1312yes—
613C4⋊C4C23×D1312yes—
614C22⋊C4—24no—
615C22⋊C4—24no—
616C22⋊C4—24no—
617C22⋊C4—24no—
618C22⋊C4—264no—
619C22⋊C4C2×C22⋊D1314yes—
620C22⋊C4C2×C22⋊D1314yes—
621C42—264no—
622C42C2×C22⋊D1312yes—
623C42C2×C22⋊D1312yes—
624C42C23×D1312yes—
625C42C23×D1312yes—
626C13C2×#324111yescharacteristic, complemented, Sylow
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23C22×C22⋊D1312yes—
639C23C22×C22⋊D1311yescharacteristic
640Q8—1044no—
641Q8—1044no—
642D4—22no—
643D4—22no—
644D4—22no—
645D4—22no—
646D4—42no—
647D4—42no—
648D4—84no—
649D4—84no—
650D4—84no—
651D4—84no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—24no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—84no—
665C2×C4—84no—
666C2×C4—262no—
667C2×C4—262no—
668C2×C4—262no—
669C2×C4—262no—
670C2×C4—522no—
671C2×C4—522no—
672C2×C4—522no—
673C2×C4—522no—
674C2×C4—1044no—
675C2×C4#8825712yes—
676C2×C4#8825712yes—
677C2×C4C22×C22⋊D1312yes—
678C2×C4C22×C22⋊D1312yes—
679C2×C4C22×C22⋊D1312yes—
680C2×C4C22×C22⋊D1312yes—
681C2×C4C22×C22⋊D1312yes—
682C2×C4C22×C22⋊D1311yescharacteristic
683C2×C4C24×D1311yescharacteristic
684C8—262no—
685C8—262no—
686C8—262no—
687C8—262no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—44no—
692C22—42no—
693C22—42no—
694C22—42no—
695C22—42no—
696C22—42no—
697C22—42no—
698C22—84no—
699C22—84no—
700C22#1171953012yes—
701C22#1171954012yes—
702C22#1171954112yes—
703C22C23×C22⋊D1311yescharacteristic
704C4—22no—
705C4—22no—
706C4—22no—
707C4—22no—
708C4—22no—
709C4—42no—
710C4—42no—
711C4—522no—
712C4—522no—
713C4—522no—
714C4—522no—
715C4#1171953012yes—
716C4C2×#8825711yescharacteristic
717C4C2×#8825711yescharacteristic
718C2—42no—
719C2—82no—
720C2—82no—
721C2#1312608314yesdirect product factor
722C2C2×#1171953011yescharacteristic
723C2C2×#1171954011yescharacteristic
724C2C2×#1171954111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
Fitting, prime radicalC2×C13×#540C2
socleC23×C13C22×D4
hypercenterC2×#540D13
hypocenterC13C2×#3241
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#540

Complements

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

NH ≅ G/Ntype
1. C2×#11719224C2semidirect
2. #13126083C2direct (N × H)
3. C2×#11718726C2semidirect
4. C2×#11718725C2semidirect
5. C2×#11718732C2semidirect
6. C2×#11718731C2semidirect
7. C2×#11718695C2semidirect
8. C2×#11718696C2semidirect
9. C2×#11718696C2semidirect
10. C2×#11718694C2semidirect
11. C2×#11718670C2semidirect
12. C2×#11718670C2semidirect
13. C2×#11718669C2semidirect
14. C2×#11718668C2semidirect
15. C2×#11718661C2semidirect
33. #11719224C22semidirect
52. #11718732C22semidirect
53. #11718731C22semidirect
54. #11718726C22semidirect
55. #11718725C22semidirect
56. #11718696C22semidirect
57. #11718696C22semidirect
58. #11718695C22semidirect
59. #11718694C22semidirect
60. #11718670C22semidirect
61. #11718670C22semidirect
62. #11718669C22semidirect
63. #11718668C22semidirect
64. #11718661C22semidirect
534. C2×C13#3241semidirect
626. C13C2×#3241semidirect
721. C2#13126083direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192242
#131260832
C2×#117187262
C2×#117187252
C2×#117187322
C2×#117187312
C2×#117186952
C2×#117186962
C2×#117186942
C2×#117186702
C2×#117186692
C2×#117186682
C2×#117186612
C2×C13×#5402
C2×#324113