Finite Group Databasebeta

← C2×#13126264 #16735847

Subgroups — C2×#13126264 #16735847

Order 3328.

1818 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719239C211yesmaximal, characteristic
2C2×#11719223C211yesmaximal, characteristic, complemented
3#13126264C2116yesmaximal, direct product factor
4C2×#11718490C211yesmaximal, characteristic, complemented
5C2×#11718511C211yesmaximal, characteristic, complemented
6C2×#11718512C211yesmaximal, characteristic, complemented
7C2×#11718508C211yesmaximal, characteristic, complemented
8C2×#11718798C211yesmaximal, characteristic, complemented
9C2×#11718795C211yesmaximal, characteristic
10C2×#11718777C211yesmaximal, characteristic, complemented
11C2×#11718775C211yesmaximal, characteristic
12C2×#11718506C211yesmaximal, characteristic, complemented
13C2×#11718506C211yesmaximal, characteristic, complemented
14C2×#11718510C211yesmaximal, characteristic, complemented
15C2×#11718502C211yesmaximal, characteristic, complemented
16C2×C13×#424C211yesmaximal, characteristic, complemented
17C22×C13×M16C2211yescharacteristic
18C23×C8×C13C2211yescharacteristic
19C2×C13×#117C2211yescharacteristic
20C2×#88184C2211yescharacteristic
21C2×#88178C2211yescharacteristic
22C2×#88178C2211yescharacteristic
23C2×#88178C2211yescharacteristic
24C22×Dic52C2211yescharacteristic
25C22×Dic52C2211yescharacteristic
26C22×#6095C2211yescharacteristic
27C22×#6095C2211yescharacteristic
28#11719239—24no—
29#11719239C2218yes—
30#11719223—24no—
31#11719223C2218yescomplemented
32C2×#88152—21no—
33C2×#88150—21no—
34C2×#88143—21no—
35C2×#88143—21no—
36C2×#88139—21no—
37C2×#88137—21no—
38C2×#88133—21no—
39C2×#88133—21no—
40C2×#88129C2211yescharacteristic
41C2×C4×D52C2211yescharacteristic
42C2×#88124C2211yescharacteristic
43C2×#88123C2211yescharacteristic
44C2×#88123C2211yescharacteristic
45C2×C4×Dic26C2211yescharacteristic
46C2×C4×Dic26C2211yescharacteristic
47C2×C4×Dic26C2211yescharacteristic
48C13×#424C2218yescomplemented
49C2×C13×C4⋊C8C2211yescharacteristic
50C2×C13×C4⋊C8C2211yescharacteristic
51C2×C13×C4⋊C8C2211yescharacteristic
52C2×C13×C4⋊C8C2211yescharacteristic
53#11718798C2218yescomplemented
54#11718795C2218yes—
55#11718777C2218yescomplemented
56#11718775C2218yes—
57C2×#88061C2211yescharacteristic
58C2×#88061C2211yescharacteristic
59C2×#88058C2211yescharacteristic
60C2×#88058C2211yescharacteristic
61C2×#88057C2211yescharacteristic
62C2×#88057C2211yescharacteristic
63C2×#88056C2211yescharacteristic
64C2×#88056C2211yescharacteristic
65C2×#88056C2211yescharacteristic
66C2×#88056C2211yescharacteristic
67C2×#88056C2211yescharacteristic
68C2×#88056C2211yescharacteristic
69#11718512C2218yescomplemented
70#11718511C2218yescomplemented
71#11718510C2218yescomplemented
72#11718508C2218yescomplemented
73#11718506C2218yescomplemented
74#11718506C2218yescomplemented
75#11718502C2218yescomplemented
76#11718490C2218yescomplemented
77C23×C4×C13C2311yescharacteristic
78C22×C22⋊D13—21no—
79C22×D52C2311yescharacteristic
80C22×C4×D13—21no—
81C22×Dic26—21no—
82C22×Dic26C2311yescharacteristic
83C22×Dic26C2311yescharacteristic
84C22×Dic26C2311yescharacteristic
85C2×C13×M16—42no—
86C2×C13×M16C2314yes—
87C22×C8×C13—42no—
88C22×C8×C13C2311yescharacteristic
89C22×C8×C13C2311yescharacteristic
90C22×C8×C13C2311yescharacteristic
91C22×C8×C13C2311yescharacteristic
92C22×C8×C13C2314yes—
93C13×#117D414yes—
94C13×#117C2314yes—
95C2×C13×C4⋊C4D411yescharacteristic
96C2×C13×C4⋊C4D411yescharacteristic
97C2×C13×C22⋊C4D411yescharacteristic
98C2×C13×C22⋊C4D411yescharacteristic
99C2×C42×C13C2311yescharacteristic
100C2×C42×C13C2311yescharacteristic
101C2×C22⋊Dic13—21no—
102C2×C22⋊Dic13—21no—
103C2×C22⋊Dic13—21no—
104#88184—22no—
105#88184C2314yes—
106C2×#6103—21no—
107C2×#6103—21no—
108C2×#6103—21no—
109C2×#6103—21no—
110C2×C4⋊Dic13—21no—
111C2×C4⋊Dic13—21no—
112C2×C4⋊Dic13—21no—
113C2×C4⋊Dic13C2311yescharacteristic
114C2×C4⋊Dic13C2311yescharacteristic
115C2×C4⋊Dic13C2311yescharacteristic
116C2×C4⋊Dic13C2311yescharacteristic
117#88178—22no—
118#88178—22no—
119#88178—22no—
120#88178C2314yes—
121#88178C2314yes—
122#88178C2314yes—
123C2×#6101—21no—
124C2×#6101—21no—
125C2×#6101—21no—
126C2×#6101—21no—
127C2×#6101—21no—
128C2×#6101—21no—
129C2×#6101—21no—
130C2×#6101—21no—
131C2×C4×Dic13—21no—
132C2×C4×Dic13—21no—
133C2×C4×Dic13—21no—
134C2×Dic52—42no—
135C2×Dic52—42no—
136C2×Dic52C2314yes—
137C2×Dic52C2314yes—
138C2×#6095—42no—
139C2×#6095—42no—
140C2×#6095C2314yes—
141C2×#6095C2314yes—
142#88152—28no—
143#88150—28no—
144#88143—28no—
145#88143—28no—
146#88139—28no—
147#88137—28no—
148#88133—28no—
149#88133—28no—
150#88129—22no—
151#88129C2314yes—
152C4×D52—22no—
153C4×D52C2314yes—
154#88124—22no—
155#88124C2314yes—
156#88123—22no—
157#88123—22no—
158#88123C2314yes—
159#88123C2314yes—
160C4×Dic26—22no—
161C4×Dic26—22no—
162C4×Dic26—22no—
163C4×Dic26C2314yes—
164C4×Dic26C2314yes—
165C4×Dic26C2314yes—
166C13×C4⋊C8C2314yes—
167C13×C4⋊C8C2314yes—
168C13×C4⋊C8C2314yes—
169C13×C4⋊C8C2314yes—
170#88061C2314yes—
171#88061C2314yes—
172#88058C2314yes—
173#88058C2314yes—
174#88057C2314yes—
175#88057C2314yes—
176#88056C2314yes—
177#88056C2314yes—
178#88056C2314yes—
179#88056C2314yes—
180#88056C2314yes—
181#88056C2314yes—
182C2×#3258—131nomaximal, Sylow
183C24×C13C2×D411yescharacteristic
184C23×D13—21no—
185C22×C4×C13—22no—
186C22×C4×C13—22no—
187C22×C4×C13C2×D411yescharacteristic
188C22×C4×C13C2×D411yescharacteristic
189C22×C4×C13C2×D411yescharacteristic
190C22×C4×C13C2×D411yescharacteristic
191C22×C4×C13C2×D411yescharacteristic
192C22×C4×C13C2×D412yes—
193C22×C4×C13C2412yes—
194C22×C4×C13C2411yescharacteristic
195C2×C22⋊D13—24no—
196C2×C22⋊D13—82no—
197C22×Dic13—21no—
198C22×Dic13—21no—
199C22×Dic13—21no—
200C22×Dic13—21no—
201C22×Dic13—21no—
202C22×Dic13—21no—
203C22×Dic13—21no—
204C2×D52—22no—
205C2×D52—22no—
206C2×D52—21no—
207C2×D52C2412yes—
208C2×C4×D13—24no—
209C2×C4×D13—82no—
210C2×Dic26—22no—
211C2×Dic26—22no—
212C2×Dic26—22no—
213C2×Dic26—22no—
214C2×Dic26—22no—
215C2×Dic26—22no—
216C2×Dic26—21no—
217C2×Dic26—21no—
218C2×Dic26—21no—
219C2×Dic26—24no—
220C2×Dic26—82no—
221C2×Dic26C2412yes—
222C2×Dic26C2412yes—
223C2×Dic26C2412yes—
224C13×M16—44no—
225C2×C8×C13—22no—
226C2×C8×C13—22no—
227C2×C8×C13—22no—
228C2×C8×C13—22no—
229C2×C8×C13—44no—
230C2×C8×C13C2412yes—
231C2×C8×C13C2412yes—
232C2×C8×C13C2412yes—
233C2×C8×C13C2412yes—
234C13×C4⋊C4C2×D414yes—
235C13×C4⋊C4C2×D414yes—
236C13×C22⋊C4C2×D414yes—
237C13×C22⋊C4C2×D414yes—
238C42×C13C2×D412yes—
239C42×C13C2×D412yes—
240C42×C13C2412yes—
241C42×C13C2412yes—
242C22⋊Dic13—24no—
243C22⋊Dic13—24no—
244C22⋊Dic13—24no—
245#6103—24no—
246#6103—24no—
247#6103—24no—
248#6103—24no—
249C4⋊Dic13—21no—
250C4⋊Dic13—21no—
251C4⋊Dic13—21no—
252C4⋊Dic13—21no—
253C4⋊Dic13—24no—
254C4⋊Dic13—24no—
255C4⋊Dic13—24no—
256C4⋊Dic13C2412yes—
257C4⋊Dic13C2412yes—
258C4⋊Dic13C2412yes—
259C4⋊Dic13C2412yes—
260#6101—24no—
261#6101—24no—
262#6101—24no—
263#6101—24no—
264#6101—24no—
265#6101—24no—
266#6101—24no—
267#6101—24no—
268C4×Dic13—24no—
269C4×Dic13—24no—
270C4×Dic13—24no—
271Dic52—44no—
272Dic52—44no—
273#6095—44no—
274#6095—44no—
275C2×#542—131no—
276C2×#541—131no—
277#3258—1316no—
278C2×#479—131no—
279C2×#477—131no—
280C2×#475—131no—
281C2×#478—131no—
282C2×#470—131no—
283C2×#468—131no—
284C2×#467—131no—
285C2×#465—131no—
286C2×#464—131no—
287C2×#464—131no—
288C2×#462—131no—
289C2×#461—131no—
290C2×#424D1311yescharacteristic, complemented
291C23×C13—22no—
292C23×C13—22no—
293C23×C13—22no—
294C23×C13C22×D412yes—
295C23×C13C22×D411yescharacteristic
296C22×D13—22no—
297C22×D13—42no—
298C22×D13—42no—
299C22×D13—42no—
300C2×C4×C13—22no—
301C2×C4×C13—22no—
302C2×C4×C13—22no—
303C2×C4×C13—22no—
304C2×C4×C13—22no—
305C2×C4×C13—24no—
306C2×C4×C13—22no—
307C2×C4×C13—22no—
308C2×C4×C13C22×D412yes—
309C2×C4×C13C22×D412yes—
310C2×C4×C13C22×D412yes—
311C2×C4×C13C22×D412yes—
312C2×C4×C13C22×D412yes—
313C2×C4×C13C22×D411yescharacteristic
314C2×C4×C13H(5,𝔽2)12yes—
315C2×C4×C132−1+412yes—
316C2×C4×C13C2511yescharacteristic
317C22⋊D13—84no—
318C2×Dic13—22no—
319C2×Dic13—22no—
320C2×Dic13—22no—
321C2×Dic13—22no—
322C2×Dic13—22no—
323C2×Dic13—22no—
324C2×Dic13—22no—
325C2×Dic13—42no—
326C2×Dic13—42no—
327C2×Dic13—42no—
328C2×Dic13—42no—
329C2×Dic13—42no—
330C2×Dic13—42no—
331C2×Dic13—42no—
332D52—22no—
333D52—22no—
334D52—42no—
335C4×D13—84no—
336Dic26—22no—
337Dic26—22no—
338Dic26—22no—
339Dic26—22no—
340Dic26—22no—
341Dic26—22no—
342Dic26—42no—
343Dic26—42no—
344Dic26—42no—
345Dic26—84no—
346C8×C13—22no—
347C8×C13—22no—
348C8×C13—22no—
349C8×C13—22no—
350C22×Q16—131no—
351C22×Q16—131no—
352C22×SD16—131no—
353C22×SD16—131no—
354C22×M16C2×D1311yescharacteristic
355C23×C8C2×D1311yescharacteristic
356#542—138no—
357#542—264no—
358#541—138no—
359#541—264no—
360C2×C4⋊Q8—131no—
361C2×C4⋊Q8—131no—
362C2×#126—261no—
363C2×#126—261no—
364C2×#126—261no—
365C2×#125—131no—
366C2×#125—261no—
367C2×#125—261no—
368C2×#124—131no—
369C2×#124—261no—
370C2×#123—261no—
371C2×C22⋊Q8—131no—
372C2×C22⋊Q8—131no—
373C2×C22⋊Q8—131no—
374C2×C22⋊Q8—261no—
375C2×#121—131no—
376C2×C4×Q8—131no—
377C2×C4×Q8—131no—
378C2×C4×Q8—131no—
379C2×C4×D4—131no—
380C2×#117C2×D1311yescharacteristic
381#479—138no—
382#478—138no—
383#477—138no—
384#475—138no—
385#470—138no—
386#468—138no—
387#467—138no—
388#465—138no—
389#464—138no—
390#464—138no—
391#462—138no—
392#461—138no—
393C2×#107—131no—
394C2×#107—131no—
395C2×#106—131no—
396C2×#106—131no—
397#424C2×D1318yescomplemented
398C2×C4⋊C8C2×D1311yescharacteristic
399C2×C4⋊C8C2×D1311yescharacteristic
400C2×C4⋊C8C2×D1311yescharacteristic
401C2×C4⋊C8C2×D1311yescharacteristic
402C2×#103—131no—
403C2×#103—131no—
404C2×#103—131no—
405C2×#103—131no—
406C2×#103—131no—
407C2×#103—131no—
408C2×#102—131no—
409C2×#102—131no—
410C22×C13—22no—
411C22×C13—22no—
412C22×C13—22no—
413C22×C13—44no—
414C22×C13#53712yes—
415C22×C13#57712yes—
416C22×C13#57812yes—
417C22×C13C23×D411yescharacteristic
418C2×D13—42no—
419C2×D13—42no—
420C2×D13—42no—
421C2×D13—84no—
422C4×C13—22no—
423C4×C13—22no—
424C4×C13—22no—
425C4×C13—22no—
426C4×C13—22no—
427C4×C13#53712yes—
428C4×C13C2×H(5,𝔽2)11yescharacteristic
429C4×C13C2×2−1+411yescharacteristic
430Dic13—42no—
431Dic13—42no—
432Dic13—42no—
433Dic13—42no—
434Dic13—42no—
435Dic13—42no—
436Dic13—42no—
437C22×Q8—131no—
438C22×Q8—131no—
439C22×Q8—131no—
440C22×Q8—261no—
441C22×D4—131no—
442C22×D4—261no—
443C23×C4—261no—
444C23×C4C22×D1311yescharacteristic
445C2×Q16—134no—
446C2×Q16—134no—
447C2×Q16—522no—
448C2×Q16—522no—
449C2×SD16—134no—
450C2×SD16—134no—
451C2×SD16—522no—
452C2×SD16—522no—
453C2×M16—42no—
454C2×M16C22×D1314yes—
455C22×C8—42no—
456C22×C8C22×D1311yescharacteristic
457C22×C8C22×D1311yescharacteristic
458C22×C8C22×D1311yescharacteristic
459C22×C8C22×D1311yescharacteristic
460C22×C8C22×D1314yes—
461C4⋊Q8—134no—
462C4⋊Q8—134no—
463C4⋊Q8—262no—
464C4⋊Q8—262no—
465#126—268no—
466#126—268no—
467#126—268no—
468#125—134no—
469#125—268no—
470#125—268no—
471#125—262no—
472#124—134no—
473#124—268no—
474#124—262no—
475#123—268no—
476C22⋊Q8—134no—
477C22⋊Q8—134no—
478C22⋊Q8—134no—
479C22⋊Q8—262no—
480C22⋊Q8—262no—
481C22⋊Q8—262no—
482C22⋊Q8—268no—
483#121—134no—
484#121—262no—
485C4×Q8—134no—
486C4×Q8—134no—
487C4×Q8—134no—
488C4×Q8—262no—
489C4×Q8—262no—
490C4×Q8—262no—
491C4×D4—134no—
492C4×D4—262no—
493#117D5214yes—
494#117C22×D1314yes—
495C2×C4⋊C4—131no—
496C2×C4⋊C4—131no—
497C2×C4⋊C4—131no—
498C2×C4⋊C4—131no—
499C2×C4⋊C4—261no—
500C2×C4⋊C4—261no—
501C2×C4⋊C4—261no—
502C2×C4⋊C4—261no—
503C2×C4⋊C4—261no—
504C2×C4⋊C4—261no—
505C2×C4⋊C4—261no—
506C2×C4⋊C4—261no—
507C2×C4⋊C4—261no—
508C2×C4⋊C4—261no—
509C2×C4⋊C4—261no—
510C2×C4⋊C4D5211yescharacteristic
511C2×C4⋊C4D5211yescharacteristic
512C2×C22⋊C4—261no—
513C2×C22⋊C4—261no—
514C2×C22⋊C4—261no—
515C2×C22⋊C4—261no—
516C2×C22⋊C4—261no—
517C2×C22⋊C4—261no—
518C2×C22⋊C4—261no—
519C2×C22⋊C4D5211yescharacteristic
520C2×C22⋊C4D5211yescharacteristic
521C2×C42—261no—
522C2×C42—261no—
523C2×C42—261no—
524C2×C42C22×D1311yescharacteristic
525C2×C42C22×D1311yescharacteristic
526#107—134no—
527#107—134no—
528#106—134no—
529#106—134no—
530C4⋊C8C22×D1314yes—
531C4⋊C8C22×D1314yes—
532C4⋊C8C22×D1314yes—
533C4⋊C8C22×D1314yes—
534#103—134no—
535#103—134no—
536#103—134no—
537#103—134no—
538#103—134no—
539#103—134no—
540#102—134no—
541#102—134no—
542C2×C13—42no—
543C2×C13#325814yescomplemented
544C2×C13C2×#53711yescharacteristic
545C2×C13C2×#57711yescharacteristic
546C2×C13C2×#57811yescharacteristic
547D13—82no—
548C24—261no—
549C24C2×D5211yescharacteristic
550C2×Q8—132no—
551C2×Q8—132no—
552C2×Q8—132no—
553C2×Q8—261no—
554C2×Q8—261no—
555C2×Q8—261no—
556C2×Q8—264no—
557C2×Q8—262no—
558C2×Q8—262no—
559C2×Q8—262no—
560C2×Q8—262no—
561C2×Q8—262no—
562C2×Q8—262no—
563C2×Q8—1042no—
564C2×D4—132no—
565C2×D4—264no—
566C2×D4—261no—
567C2×D4—262no—
568C2×D4—262no—
569C2×D4—1042no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—261no—
573C22×C4—261no—
574C22×C4—261no—
575C22×C4—261no—
576C22×C4—261no—
577C22×C4—261no—
578C22×C4—261no—
579C22×C4—264no—
580C22×C4—1042no—
581C22×C4C2×D5212yes—
582C22×C4C2×D5211yescharacteristic
583C22×C4C2×D5211yescharacteristic
584C22×C4C2×D5211yescharacteristic
585C22×C4C2×D5211yescharacteristic
586C22×C4C2×D5211yescharacteristic
587C22×C4C23×D1312yes—
588C22×C4C23×D1311yescharacteristic
589Q16—524no—
590Q16—524no—
591SD16—524no—
592SD16—524no—
593M16—44no—
594C2×C8—22no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—44no—
599C2×C8C23×D1312yes—
600C2×C8C23×D1312yes—
601C2×C8C23×D1312yes—
602C2×C8C23×D1312yes—
603C4⋊C4—132no—
604C4⋊C4—132no—
605C4⋊C4—132no—
606C4⋊C4—132no—
607C4⋊C4—261no—
608C4⋊C4—261no—
609C4⋊C4—261no—
610C4⋊C4—261no—
611C4⋊C4—264no—
612C4⋊C4—264no—
613C4⋊C4—264no—
614C4⋊C4—264no—
615C4⋊C4—264no—
616C4⋊C4—264no—
617C4⋊C4—264no—
618C4⋊C4—264no—
619C4⋊C4—264no—
620C4⋊C4—264no—
621C4⋊C4—264no—
622C4⋊C4C2×D5214yes—
623C4⋊C4C2×D5214yes—
624C22⋊C4—264no—
625C22⋊C4—264no—
626C22⋊C4—264no—
627C22⋊C4—264no—
628C22⋊C4—264no—
629C22⋊C4—264no—
630C22⋊C4—264no—
631C22⋊C4C2×D5214yes—
632C22⋊C4C2×D5214yes—
633C42—264no—
634C42—264no—
635C42—264no—
636C42C2×D5212yes—
637C42C2×D5212yes—
638C42C23×D1312yes—
639C42C23×D1312yes—
640C13C2×#325811yescharacteristic, complemented, Sylow
641C23—22no—
642C23—22no—
643C23—22no—
644C23—262no—
645C23—522no—
646C23—522no—
647C23—522no—
648C23C22×D5212yes—
649C23C22×D5211yescharacteristic
650Q8—262no—
651Q8—262no—
652Q8—262no—
653Q8—262no—
654Q8—262no—
655Q8—262no—
656Q8—522no—
657Q8—522no—
658Q8—522no—
659Q8—1044no—
660D4—262no—
661D4—262no—
662D4—522no—
663D4—1044no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—262no—
673C2×C4—262no—
674C2×C4—262no—
675C2×C4—262no—
676C2×C4—262no—
677C2×C4—262no—
678C2×C4—262no—
679C2×C4—522no—
680C2×C4—522no—
681C2×C4—522no—
682C2×C4—522no—
683C2×C4—522no—
684C2×C4—522no—
685C2×C4—522no—
686C2×C4—1044no—
687C2×C4C22×D5212yes—
688C2×C4C22×D5212yes—
689C2×C4C22×D5212yes—
690C2×C4C22×D5212yes—
691C2×C4C22×D5212yes—
692C2×C4C22×D5211yescharacteristic
693C2×C4#8825112yes—
694C2×C4#8825412yes—
695C2×C4C24×D1311yescharacteristic
696C8—22no—
697C8—22no—
698C8—22no—
699C8—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—44no—
704C22—522no—
705C22—522no—
706C22—522no—
707C22—1044no—
708C22#1171921512yes—
709C22#1171945612yes—
710C22#1171945812yes—
711C22C23×D5211yescharacteristic
712C4—22no—
713C4—22no—
714C4—22no—
715C4—22no—
716C4—22no—
717C4—522no—
718C4—522no—
719C4—522no—
720C4—522no—
721C4—522no—
722C4—522no—
723C4—522no—
724C4#1171921512yes—
725C4C2×#8825111yescharacteristic
726C4C2×#8825411yescharacteristic
727C2—42no—
728C2—1042no—
729C2#1312626414yesdirect product factor
730C2C2×#1171921511yescharacteristic
731C2C2×#1171945611yescharacteristic
732C2C2×#1171945811yescharacteristic
subgroupG/H
centerC23C22×D52
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#424C2
socleC23×C13C22×D4
prime radicalC2×#88184C22
hypercenterC2×#424D13
hypocenterC13C2×#3258
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#424

Complements

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

NH ≅ G/Ntype
2. C2×#11719223C2semidirect
3. #13126264C2direct (N × H)
4. C2×#11718490C2semidirect
5. C2×#11718511C2semidirect
6. C2×#11718512C2semidirect
7. C2×#11718508C2semidirect
8. C2×#11718798C2semidirect
10. C2×#11718777C2semidirect
12. C2×#11718506C2semidirect
13. C2×#11718506C2semidirect
14. C2×#11718510C2semidirect
15. C2×#11718502C2semidirect
16. C2×C13×#424C2semidirect
31. #11719223C22semidirect
48. C13×#424C22semidirect
53. #11718798C22semidirect
55. #11718777C22semidirect
69. #11718512C22semidirect
70. #11718511C22semidirect
71. #11718510C22semidirect
72. #11718508C22semidirect
73. #11718506C22semidirect
74. #11718506C22semidirect
75. #11718502C22semidirect
76. #11718490C22semidirect
290. C2×#424D13semidirect
397. #424C2×D13semidirect
543. C2×C13#3258semidirect
640. C13C2×#3258semidirect
729. C2#13126264direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192392
C2×#117192232
#131262642
C2×#117184902
C2×#117185112
C2×#117185122
C2×#117185082
C2×#117187982
C2×#117187952
C2×#117187772
C2×#117187752
C2×#117185062
C2×#117185102
C2×#117185022
C2×C13×#4242
C2×#325813