Finite Group Databasebeta

← C2×#13125130 #16731269

Subgroups — C2×#13125130 #16731269

Order 3328.

1994 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719330C211yesmaximal, characteristic
2C2×#11719517C211yesmaximal, characteristic
3#13125130C2116yesmaximal, direct product factor
4C2×#11718384C211yesmaximal, characteristic
5C2×#11718706C211yesmaximal, characteristic
6C2×#11718457C211yesmaximal, characteristic, complemented
7C2×#11718460C211yesmaximal, characteristic, complemented
8C2×#11718843C211yesmaximal, characteristic, complemented
9C2×#11718843C211yesmaximal, characteristic, complemented
10C2×#11718889C211yesmaximal, characteristic
11C2×#11718845C211yesmaximal, characteristic, complemented
12C2×#11718450C211yesmaximal, characteristic, complemented
13C2×Q16×Dic13C211yesmaximal, characteristic, complemented
14C2×#11718451C211yesmaximal, characteristic, complemented
15C2×#11718381C211yesmaximal, characteristic
16C2×C13×#451C211yesmaximal, characteristic
17C23×Q8×C13C2211yescharacteristic
18C22×C13×Q16C2211yescharacteristic
19C22×C13×Q16C2211yescharacteristic
20C2×C13×C22⋊Q8C2211yescharacteristic
21#11719517—24no—
22#11719517C2218yes—
23C2×Q8×Dic13—21no—
24C2×Q8×Dic13—21no—
25C2×Q8×Dic13C2211yescharacteristic
26C2×Q8×Dic13C2211yescharacteristic
27C2×Q8×Dic13C2211yescharacteristic
28C2×Q8×Dic13C2211yescharacteristic
29C2×Q8×Dic13C2211yescharacteristic
30C2×#88198C2211yescharacteristic
31C22×#6107C2211yescharacteristic
32C22×#6107C2211yescharacteristic
33C2×#88180—21no—
34C2×#88180—21no—
35C2×#88180C2211yescharacteristic
36C2×#88180C2211yescharacteristic
37C2×#88178C2211yescharacteristic
38#11719330—24no—
39#11719330C2218yes—
40C2×#88144—21no—
41C2×#88144C2211yescharacteristic
42C2×#88143—21no—
43C2×#88141C2211yescharacteristic
44C2×#88133—21no—
45C2×#88133—21no—
46C13×#451C2218yes—
47C2×C13×#103C2211yescharacteristic
48C2×C13×#103C2211yescharacteristic
49C2×C13×C22⋊C8C2211yescharacteristic
50#11718889C2218yes—
51C2×#88075C2211yescharacteristic
52C2×#88075C2211yescharacteristic
53C2×#88075C2211yescharacteristic
54C2×#88075C2211yescharacteristic
55C2×C22⋊#1055C2211yescharacteristic
56#11718845C2218yescomplemented
57Q16×Dic13C2218yescomplemented
58#11718843C2218yescomplemented
59#11718843C2218yescomplemented
60C2×#88058C2211yescharacteristic
61C2×#88057C2211yescharacteristic
62C2×#88056C2211yescharacteristic
63C2×#88056C2211yescharacteristic
64C2×#88055C2211yescharacteristic
65C2×#88054C2211yescharacteristic
66C2×#88054C2211yescharacteristic
67C2×C8×Dic13C2211yescharacteristic
68#11718706C2218yes—
69C2×#88048C2211yescharacteristic
70C2×#88047C2211yescharacteristic
71#11718460C2218yescomplemented
72#11718457C2218yescomplemented
73#11718451C2218yescomplemented
74#11718450C2218yescomplemented
75#11718384C2218yes—
76#11718381C2218yes—
77C22×Q8×C13—24no—
78C22×Q8×C13—24no—
79C22×Q8×C13—21no—
80C22×Q8×C13—22no—
81C22×Q8×C13C2314yes—
82C22×Q8×C13C2311yescharacteristic
83C22×Q8×C13C2311yescharacteristic
84C22×Q8×C13C2311yescharacteristic
85C23×C4×C13—21no—
86C23×C4×C13C2311yescharacteristic
87C22×Dic26C2311yescharacteristic
88C2×C13×Q16—24no—
89C2×C13×Q16—24no—
90C2×C13×Q16C2314yes—
91C2×C13×Q16C2314yes—
92C22×C8×C13C2311yescharacteristic
93C22×C8×C13C2311yescharacteristic
94C13×C22⋊Q8—22no—
95C13×C22⋊Q8C2314yes—
96C2×C13×C4⋊C4—21no—
97C2×C13×C4⋊C4C2311yescharacteristic
98C2×C13×C22⋊C4—21no—
99C2×C22⋊Dic13—21no—
100C2×C22⋊Dic13—21no—
101C2×C22⋊Dic13D411yescharacteristic
102C2×C22⋊Dic13D411yescharacteristic
103Q8×Dic13—28no—
104Q8×Dic13—28no—
105Q8×Dic13—22no—
106Q8×Dic13—22no—
107Q8×Dic13—22no—
108Q8×Dic13—22no—
109Q8×Dic13—22no—
110Q8×Dic13C2314yes—
111Q8×Dic13C2314yes—
112Q8×Dic13C2314yes—
113Q8×Dic13C2314yes—
114Q8×Dic13C2314yes—
115#88198—22no—
116#88198C2314yes—
117C2×#6107—24no—
118C2×#6107—24no—
119C2×#6107C2314yes—
120C2×#6107C2314yes—
121#88180—22no—
122#88180—28no—
123#88180—28no—
124#88180D414yes—
125#88180C2314yes—
126#88180C2314yes—
127C2×C4⋊Dic13—21no—
128C2×C4⋊Dic13—21no—
129C2×C4⋊Dic13—21no—
130C2×C4⋊Dic13—21no—
131C2×C4⋊Dic13—21no—
132C2×C4⋊Dic13—21no—
133C2×C4⋊Dic13D411yescharacteristic
134C2×C4⋊Dic13D411yescharacteristic
135C2×C4⋊Dic13C2311yescharacteristic
136C2×C4⋊Dic13C2311yescharacteristic
137C2×C4⋊Dic13C2311yescharacteristic
138#88178—22no—
139#88178C2314yes—
140C2×#6101—21no—
141C2×#6101—21no—
142C2×#6101—21no—
143C2×#6101—21no—
144C2×#6101—21no—
145C2×C4×Dic13—21no—
146C2×C4×Dic13—21no—
147C2×C4×Dic13—21no—
148C2×C4×Dic13—21no—
149C2×C4×Dic13—21no—
150C2×C4×Dic13—21no—
151C2×C4×Dic13—21no—
152C2×C4×Dic13C2311yescharacteristic
153C2×C4×Dic13C2311yescharacteristic
154C22×#1055C2311yescharacteristic
155C22×#1055C2311yescharacteristic
156#88144—28no—
157#88144—22no—
158#88144C2314yes—
159#88143—28no—
160#88141—22no—
161#88141C2314yes—
162#88133—28no—
163#88133—28no—
164C13×#103C2314yes—
165C13×#103C2314yes—
166C13×C22⋊C8C2314yes—
167#88075C2314yes—
168#88075C2314yes—
169#88075C2314yes—
170#88075C2314yes—
171C22⋊#1055C2314yes—
172#88058C2314yes—
173#88057C2314yes—
174#88056C2314yes—
175#88056C2314yes—
176#88055C2314yes—
177#88054C2314yes—
178#88054C2314yes—
179C8×Dic13C2314yes—
180#88048C2314yes—
181#88047C2314yes—
182C2×#3127—131nomaximal, Sylow
183C24×C13C2×D411yescharacteristic
184C2×Q8×C13—216no—
185C2×Q8×C13—28no—
186C2×Q8×C13—28no—
187C2×Q8×C13—28no—
188C2×Q8×C13—24no—
189C2×Q8×C13—21no—
190C2×Q8×C13—21no—
191C2×Q8×C13—21no—
192C2×Q8×C13—22no—
193C2×Q8×C13—22no—
194C2×Q8×C13—22no—
195C2×Q8×C13—22no—
196C2×Q8×C13#4114yes—
197C2×Q8×C13#4114yes—
198C2×Q8×C13C2412yes—
199C2×Q8×C13C2412yes—
200C2×Q8×C13C2412yes—
201C22×C4×C13—28no—
202C22×C4×C13—21no—
203C22×C4×C13—21no—
204C22×C4×C13—24no—
205C22×C4×C13—22no—
206C22×C4×C13—22no—
207C22×C4×C13—21no—
208C22×C4×C13—21no—
209C22×C4×C13C2×D411yescharacteristic
210C22×C4×C13C2×D412yes—
211C22×C4×C13C2412yes—
212C22×C4×C13C2411yescharacteristic
213C22×Dic13—21no—
214C22×Dic13—21no—
215C22×Dic13—21no—
216C22×Dic13—21no—
217C22×Dic13C2×D411yescharacteristic
218C22×Dic13C2×D411yescharacteristic
219C22×Dic13C2×D411yescharacteristic
220C22×Dic13C2×D411yescharacteristic
221C2×Dic26—22no—
222C2×Dic26—22no—
223C2×Dic26—21no—
224C2×Dic26C2412yes—
225C13×Q16—28no—
226C13×Q16—28no—
227C2×C8×C13—22no—
228C2×C8×C13—22no—
229C2×C8×C13C2412yes—
230C2×C8×C13C2412yes—
231C13×C4⋊C4—21no—
232C13×C4⋊C4—24no—
233C13×C4⋊C4C2412yes—
234C13×C22⋊C4—24no—
235C22⋊Dic13—24no—
236C22⋊Dic13—24no—
237C22⋊Dic13C2×D414yes—
238C22⋊Dic13C2×D414yes—
239#6107—28no—
240#6107—28no—
241C4⋊Dic13—21no—
242C4⋊Dic13—21no—
243C4⋊Dic13—21no—
244C4⋊Dic13—24no—
245C4⋊Dic13—24no—
246C4⋊Dic13—24no—
247C4⋊Dic13—24no—
248C4⋊Dic13—24no—
249C4⋊Dic13—24no—
250C4⋊Dic13C2×D414yes—
251C4⋊Dic13C2×D414yes—
252C4⋊Dic13C2412yes—
253C4⋊Dic13C2412yes—
254C4⋊Dic13C2412yes—
255#6101—24no—
256#6101—24no—
257#6101—24no—
258#6101—24no—
259#6101—24no—
260C4×Dic13—24no—
261C4×Dic13—24no—
262C4×Dic13—24no—
263C4×Dic13—24no—
264C4×Dic13—24no—
265C4×Dic13—24no—
266C4×Dic13—24no—
267C4×Dic13C2×D412yes—
268C4×Dic13C2×D412yes—
269C4×Dic13C2412yes—
270C4×Dic13C2412yes—
271C2×#1055—22no—
272C2×#1055—22no—
273C2×#1055C2412yes—
274C2×#1055C2412yes—
275C2×#541—131no—
276C2×#519—131no—
277#3127—1316no—
278C2×#485—131no—
279C2×#485—131no—
280C2×#479—131no—
281C2×#479—131no—
282C2×#462—131no—
283C2×#462—131no—
284C2×#451—131no—
285C2×#451D1311yescharacteristic
286C2×#441—131no—
287C2×#441—131no—
288C2×C4×Q16—131no—
289C2×C4×Q16—131no—
290C2×#433—131no—
291C23×C13—22no—
292C23×C13—22no—
293C23×C13—22no—
294C23×C13C22×D412yes—
295C23×C13C22×D411yescharacteristic
296Q8×C13—216no—
297Q8×C13—24no—
298Q8×C13—24no—
299Q8×C13—22no—
300Q8×C13—22no—
301Q8×C13—22no—
302Q8×C13—22no—
303Q8×C13—42no—
304Q8×C13C2×#4114yes—
305Q8×C13C2×#4114yes—
306C2×C4×C13—216no—
307C2×C4×C13—24no—
308C2×C4×C13—24no—
309C2×C4×C13—22no—
310C2×C4×C13—22no—
311C2×C4×C13—22no—
312C2×C4×C13—24no—
313C2×C4×C13—22no—
314C2×C4×C13—22no—
315C2×C4×C13—22no—
316C2×C4×C13—22no—
317C2×C4×C13—42no—
318C2×C4×C13—42no—
319C2×C4×C13C22×D412yes—
320C2×C4×C13C22×D411yescharacteristic
321C2×C4×C13C2×#4112yes—
322C2×C4×C13C2×#4112yes—
323C2×C4×C13C2511yescharacteristic
324C2×Dic13—22no—
325C2×Dic13—22no—
326C2×Dic13—22no—
327C2×Dic13—22no—
328C2×Dic13—22no—
329C2×Dic13—22no—
330C2×Dic13—22no—
331C2×Dic13—22no—
332C2×Dic13—42no—
333C2×Dic13—42no—
334C2×Dic13—42no—
335C2×Dic13—42no—
336C2×Dic13C22×D412yes—
337C2×Dic13C22×D412yes—
338C2×Dic13C22×D412yes—
339C2×Dic13C22×D412yes—
340Dic26—22no—
341Dic26—22no—
342Dic26—42no—
343C8×C13—22no—
344C8×C13—22no—
345#1055—22no—
346#1055—22no—
347C23×Q8C2×D1311yescharacteristic
348C22×Q16—131no—
349C22×Q16—131no—
350C22×Q16C2×D1311yescharacteristic
351C22×Q16C2×D1311yescharacteristic
352#541—138no—
353#541—264no—
354C2×C4⋊Q8—131no—
355C2×#126—261no—
356C2×#126—261no—
357C2×#125—131no—
358C2×#125—261no—
359C2×#125—261no—
360C2×C22⋊Q8—131no—
361C2×C22⋊Q8C2×D1311yescharacteristic
362#519—138no—
363#519—264no—
364C2×C4×Q8—131no—
365C2×C4×Q8—131no—
366C2×C4×Q8—131no—
367C2×C4×Q8—131no—
368C2×C4×Q8—131no—
369C2×C4×Q8—131no—
370C2×C4×Q8—261no—
371C2×C4×Q8—261no—
372C2×#117—131no—
373C2×#117—131no—
374C2×#117—261no—
375C2×#117—261no—
376#485—138no—
377#485—138no—
378#479—138no—
379#479—138no—
380#462—138no—
381#462—138no—
382#451—138no—
383#451C2×D1318yes—
384#441—138no—
385#441—138no—
386C4×Q16—138no—
387C4×Q16—138no—
388#433—138no—
389C2×#107—131no—
390C2×#107—131no—
391C2×#106—131no—
392C2×#106—131no—
393C2×C4⋊C8—131no—
394C2×C4⋊C8—131no—
395C2×#103—131no—
396C2×#103—131no—
397C2×#103—131no—
398C2×#103—131no—
399C2×#103—131no—
400C2×#103—131no—
401C2×#103C2×D1311yescharacteristic
402C2×#103C2×D1311yescharacteristic
403C2×C22⋊C8—131no—
404C2×C22⋊C8C2×D1311yescharacteristic
405C2×#97—131no—
406C2×C4×C8—131no—
407C22×C13—22no—
408C22×C13—22no—
409C22×C13—22no—
410C22×C13—44no—
411C22×C13#52512yes—
412C22×C13#57812yes—
413C22×C13#57812yes—
414C22×C13C23×D411yescharacteristic
415C4×C13—24no—
416C4×C13—24no—
417C4×C13—22no—
418C4×C13—42no—
419C4×C13—42no—
420C4×C13#52512yes—
421C4×C13C22×#4111yescharacteristic
422C4×C13C22×#4111yescharacteristic
423Dic13—22no—
424Dic13—22no—
425Dic13—22no—
426Dic13—22no—
427Dic13—42no—
428Dic13—42no—
429Dic13—42no—
430Dic13—42no—
431C22×Q8—24no—
432C22×Q8—24no—
433C22×Q8—21no—
434C22×Q8—22no—
435C22×Q8—131no—
436C22×Q8C22×D1311yescharacteristic
437C22×Q8C22×D1314yes—
438C22×Q8C22×D1311yescharacteristic
439C22×Q8C22×D1311yescharacteristic
440C23×C4—21no—
441C23×C4C22×D1311yescharacteristic
442C2×Q16—24no—
443C2×Q16—24no—
444C2×Q16—134no—
445C2×Q16—134no—
446C2×Q16—264no—
447C2×Q16—264no—
448C2×Q16C22×D1314yes—
449C2×Q16C22×D1314yes—
450C22×C8—131no—
451C22×C8—131no—
452C22×C8C22×D1311yescharacteristic
453C22×C8C22×D1311yescharacteristic
454C4⋊Q8—134no—
455C4⋊Q8—262no—
456#126—268no—
457#126—268no—
458#125—134no—
459#125—262no—
460#125—268no—
461#125—268no—
462C22⋊Q8—22no—
463C22⋊Q8—134no—
464C22⋊Q8—262no—
465C22⋊Q8C22×D1314yes—
466C4×Q8—134no—
467C4×Q8—134no—
468C4×Q8—134no—
469C4×Q8—134no—
470C4×Q8—134no—
471C4×Q8—134no—
472C4×Q8—262no—
473C4×Q8—262no—
474C4×Q8—262no—
475C4×Q8—262no—
476C4×Q8—262no—
477C4×Q8—262no—
478C4×Q8—268no—
479C4×Q8—268no—
480#117—134no—
481#117—134no—
482#117—134no—
483#117—268no—
484#117—268no—
485#117—262no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—131no—
488C2×C4⋊C4—131no—
489C2×C4⋊C4—131no—
490C2×C4⋊C4—131no—
491C2×C4⋊C4—131no—
492C2×C4⋊C4—261no—
493C2×C4⋊C4—261no—
494C2×C4⋊C4—261no—
495C2×C4⋊C4—261no—
496C2×C4⋊C4—261no—
497C2×C4⋊C4—261no—
498C2×C4⋊C4—261no—
499C2×C4⋊C4—261no—
500C2×C4⋊C4—261no—
501C2×C4⋊C4—261no—
502C2×C4⋊C4—261no—
503C2×C4⋊C4C22×D1311yescharacteristic
504C2×C22⋊C4—21no—
505C2×C22⋊C4—131no—
506C2×C22⋊C4—131no—
507C2×C22⋊C4—261no—
508C2×C22⋊C4—261no—
509C2×C42—131no—
510C2×C42—131no—
511C2×C42—261no—
512C2×C42—261no—
513C2×C42—261no—
514C2×C42—261no—
515C2×C42—261no—
516C2×C42—261no—
517C2×C42—261no—
518#107—134no—
519#107—134no—
520#106—134no—
521#106—134no—
522C4⋊C8—134no—
523C4⋊C8—134no—
524#103—134no—
525#103—134no—
526#103—134no—
527#103—134no—
528#103—134no—
529#103—134no—
530#103C22×D1314yes—
531#103C22×D1314yes—
532C22⋊C8—134no—
533C22⋊C8C22×D1314yes—
534#97—134no—
535C4×C8—134no—
536C2×C13—42no—
537C2×C13#312714yescomplemented
538C2×C13C2×#52511yescharacteristic
539C2×C13C2×#57811yescharacteristic
540C2×C13C2×#57811yescharacteristic
541C24D4×D1311yescharacteristic
542C2×Q8—216no—
543C2×Q8—28no—
544C2×Q8—28no—
545C2×Q8—28no—
546C2×Q8—24no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—22no—
551C2×Q8—22no—
552C2×Q8—22no—
553C2×Q8—22no—
554C2×Q8—132no—
555C2×Q8—261no—
556C2×Q8—262no—
557C2×Q8—262no—
558C2×Q8#612914yes—
559C2×Q8#612914yes—
560C2×Q8C23×D1312yes—
561C2×Q8C23×D1312yes—
562C2×Q8C23×D1312yes—
563C22×C4—28no—
564C22×C4—24no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—131no—
572C22×C4—131no—
573C22×C4—131no—
574C22×C4—131no—
575C22×C4—261no—
576C22×C4—261no—
577C22×C4—261no—
578C22×C4—261no—
579C22×C4D4×D1312yes—
580C22×C4D4×D1311yescharacteristic
581C22×C4C23×D1312yes—
582C22×C4C23×D1311yescharacteristic
583Q16—28no—
584Q16—28no—
585Q16—268no—
586Q16—268no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—132no—
590C2×C8—132no—
591C2×C8—262no—
592C2×C8—262no—
593C2×C8C23×D1312yes—
594C2×C8C23×D1312yes—
595C4⋊C4—24no—
596C4⋊C4—21no—
597C4⋊C4—134no—
598C4⋊C4—134no—
599C4⋊C4—132no—
600C4⋊C4—132no—
601C4⋊C4—132no—
602C4⋊C4—264no—
603C4⋊C4—264no—
604C4⋊C4—264no—
605C4⋊C4—264no—
606C4⋊C4—264no—
607C4⋊C4—264no—
608C4⋊C4—264no—
609C4⋊C4—264no—
610C4⋊C4—264no—
611C4⋊C4—264no—
612C4⋊C4—261no—
613C4⋊C4—261no—
614C4⋊C4—261no—
615C4⋊C4—264no—
616C4⋊C4C23×D1312yes—
617C22⋊C4—24no—
618C22⋊C4—134no—
619C22⋊C4—134no—
620C22⋊C4—264no—
621C22⋊C4—264no—
622C42—132no—
623C42—132no—
624C42—132no—
625C42—132no—
626C42—264no—
627C42—264no—
628C42—264no—
629C42—264no—
630C42—264no—
631C42—264no—
632C42—264no—
633C13C2×#312711yescharacteristic, complemented, Sylow
634C23—22no—
635C23—22no—
636C23—22no—
637C23C2×D4×D1312yes—
638C23C2×D4×D1311yescharacteristic
639Q8—216no—
640Q8—24no—
641Q8—24no—
642Q8—22no—
643Q8—22no—
644Q8—22no—
645Q8—22no—
646Q8—42no—
647Q8—262no—
648Q8—262no—
649Q8—522no—
650Q8C2×#612914yes—
651Q8C2×#612914yes—
652C2×C4—216no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—24no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—132no—
666C2×C4—132no—
667C2×C4—132no—
668C2×C4—132no—
669C2×C4—262no—
670C2×C4—262no—
671C2×C4—262no—
672C2×C4—262no—
673C2×C4—262no—
674C2×C4—262no—
675C2×C4—262no—
676C2×C4—262no—
677C2×C4—522no—
678C2×C4—522no—
679C2×C4—522no—
680C2×C4—522no—
681C2×C4C2×D4×D1312yes—
682C2×C4C2×D4×D1311yescharacteristic
683C2×C4C2×#612912yes—
684C2×C4C2×#612912yes—
685C2×C4C24×D1311yescharacteristic
686C8—22no—
687C8—22no—
688C8—262no—
689C8—262no—
690C22—22no—
691C22—22no—
692C22—22no—
693C22—44no—
694C22#1171929112yes—
695C22#1171947112yes—
696C22#1171948412yes—
697C22C22×D4×D1311yescharacteristic
698C4—24no—
699C4—24no—
700C4—22no—
701C4—42no—
702C4—42no—
703C4—262no—
704C4—262no—
705C4—262no—
706C4—262no—
707C4—522no—
708C4—522no—
709C4—522no—
710C4—522no—
711C4#1171929112yes—
712C4C22×#612911yescharacteristic
713C4C22×#612911yescharacteristic
714C2—42no—
715C2#1312513014yesdirect product factor
716C2C2×#1171929111yescharacteristic
717C2C2×#1171947111yescharacteristic
718C2C2×#1171948411yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#451C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenterC2×#451D13
hypocenterC13C2×#3127
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
3. #13125130C2direct (N × H)
6. C2×#11718457C2semidirect
7. C2×#11718460C2semidirect
8. C2×#11718843C2semidirect
9. C2×#11718843C2semidirect
11. C2×#11718845C2semidirect
12. C2×#11718450C2semidirect
13. C2×Q16×Dic13C2semidirect
14. C2×#11718451C2semidirect
56. #11718845C22semidirect
57. Q16×Dic13C22semidirect
58. #11718843C22semidirect
59. #11718843C22semidirect
71. #11718460C22semidirect
72. #11718457C22semidirect
73. #11718451C22semidirect
74. #11718450C22semidirect
537. C2×C13#3127semidirect
633. C13C2×#3127semidirect
715. C2#13125130direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117193302
C2×#117195172
#131251302
C2×#117183842
C2×#117187062
C2×#117184572
C2×#117184602
C2×#117188432
C2×#117188892
C2×#117188452
C2×#117184502
C2×Q16×Dic132
C2×#117184512
C2×#117183812
C2×C13×#4512
C2×#312713