Finite Group Databasebeta

← C2×#13120632 #16029989

Subgroups — C2×#13120632 #16029989

Order 3328.

2590 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88132C211yesmaximal, characteristic
2C22×#88131C211yesmaximal, characteristic
3#13120632C2116yesmaximal, direct product factor
4C2×#11718321C211yesmaximal, characteristic, complemented
5C2×#11718319C211yesmaximal, characteristic, complemented
6C2×#11718318C211yesmaximal, characteristic, complemented
7C2×#11718645C211yesmaximal, characteristic, complemented
8C2×#11718613C211yesmaximal, characteristic
9C2×#11718613C211yesmaximal, characteristic
10C2×#11718614C211yesmaximal, characteristic
11C2×#11718307C211yesmaximal, characteristic, complemented
12C2×#11718307C211yesmaximal, characteristic, complemented
13C2×#11718308C211yesmaximal, characteristic, complemented
14C2×#11718633C211yesmaximal, characteristic, complemented
15C2×#11718603C211yesmaximal, characteristic
16C2×C13×#397C211yesmaximal, characteristic
17C24×Dic13C2211yescharacteristic
18C23×Dic26C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C13×C22⋊C4C2211yescharacteristic
21C22×C13×C22⋊C4C2211yescharacteristic
22C22×C13×C22⋊C4C2211yescharacteristic
23C22×C22⋊Dic13C2211yescharacteristic
24C22×C22⋊Dic13C2211yescharacteristic
25C22×C22⋊Dic13C2211yescharacteristic
26C22×C4⋊Dic13C2211yescharacteristic
27C22×C4⋊Dic13C2211yescharacteristic
28C22×#6101C2211yescharacteristic
29C22×#6101C2211yescharacteristic
30C22×#6101C2211yescharacteristic
31C22×#6101C2211yescharacteristic
32C22×#6101C2211yescharacteristic
33C22×#6101C2211yescharacteristic
34C22×#6101C2211yescharacteristic
35C22×#6101C2211yescharacteristic
36C22×C4×Dic13C2211yescharacteristic
37C22×C4×Dic13C2211yescharacteristic
38C2×#88132—28no—
39C2×#88132C2218yes—
40C2×#88131—28no—
41C2×#88131C2218yes—
42C13×#397C2218yes—
43C2×C13×#95C2211yescharacteristic
44C2×C13×#95C2211yescharacteristic
45C2×C13×#95C2211yescharacteristic
46C2×#88071C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57#11718645C2218yescomplemented
58#11718633C2218yescomplemented
59#11718614C2218yes—
60#11718613C2218yes—
61#11718613C2218yes—
62#11718603C2218yes—
63#11718321C2218yescomplemented
64#11718319C2218yescomplemented
65#11718318C2218yescomplemented
66#11718308C2218yescomplemented
67#11718307C2218yescomplemented
68#11718307C2218yescomplemented
69C25×C13C2311yescharacteristic
70C23×C4×C13C2311yescharacteristic
71C23×C4×C13C2311yescharacteristic
72C23×C4×C13C2311yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×Dic13—24no—
77C23×Dic13—24no—
78C23×Dic13D418yes—
79C23×Dic13C2311yescharacteristic
80C23×Dic13C2311yescharacteristic
81C23×Dic13C2311yescharacteristic
82C23×Dic13C2311yescharacteristic
83C23×Dic13C2311yescharacteristic
84C23×Dic13C2311yescharacteristic
85C23×Dic13C2314yes—
86C23×Dic13C2311yescharacteristic
87C23×Dic13C2311yescharacteristic
88C22×Dic26—24no—
89C22×Dic26—24no—
90C22×Dic26—24no—
91C22×Dic26C2314yes—
92C2×C13×C4⋊C4—42no—
93C2×C13×C4⋊C4C2314yes—
94C2×C13×C22⋊C4—24no—
95C2×C13×C22⋊C4—24no—
96C2×C13×C22⋊C4—42no—
97C2×C13×C22⋊C4C2314yes—
98C2×C13×C22⋊C4C2314yes—
99C2×C13×C22⋊C4C2314yes—
100C2×C22⋊Dic13—24no—
101C2×C22⋊Dic13—24no—
102C2×C22⋊Dic13—42no—
103C2×C22⋊Dic13C2314yes—
104C2×C22⋊Dic13C2314yes—
105C2×C22⋊Dic13C2314yes—
106C2×C4⋊Dic13—24no—
107C2×C4⋊Dic13—42no—
108C2×C4⋊Dic13C2314yes—
109C2×C4⋊Dic13C2314yes—
110C2×#6101—24no—
111C2×#6101—24no—
112C2×#6101—24no—
113C2×#6101—24no—
114C2×#6101—24no—
115C2×#6101—24no—
116C2×#6101—42no—
117C2×#6101—42no—
118C2×#6101C2314yes—
119C2×#6101C2314yes—
120C2×#6101C2314yes—
121C2×#6101C2314yes—
122C2×#6101C2314yes—
123C2×#6101C2314yes—
124C2×#6101C2314yes—
125C2×#6101C2314yes—
126C2×C4×Dic13—24no—
127C2×C4×Dic13—24no—
128C2×C4×Dic13C2314yes—
129C2×C4×Dic13C2314yes—
130#88132—232no—
131#88131—232no—
132C13×#95C2314yes—
133C13×#95C2314yes—
134C13×#95C2314yes—
135#88071C2314yes—
136#88071C2314yes—
137#88071C2314yes—
138#88071C2314yes—
139#88071C2314yes—
140#88071C2314yes—
141#88071C2314yes—
142#88071C2314yes—
143#88071C2314yes—
144#88071C2314yes—
145#88071C2314yes—
146C2×#2625—131nomaximal, Sylow
147C24×C13—22no—
148C24×C13—22no—
149C24×C13—22no—
150C24×C13—22no—
151C24×C13—22no—
152C24×C13—22no—
153C24×C13C2×D414yes—
154C24×C13C2412yes—
155C24×C13C2411yescharacteristic
156C22×C4×C13—22no—
157C22×C4×C13—22no—
158C22×C4×C13—22no—
159C22×C4×C13—22no—
160C22×C4×C13—22no—
161C22×C4×C13—22no—
162C22×C4×C13—22no—
163C22×C4×C13—22no—
164C22×C4×C13—22no—
165C22×C4×C13—22no—
166C22×C4×C13—22no—
167C22×C4×C13—22no—
168C22×C4×C13—22no—
169C22×C4×C13—22no—
170C22×C4×C13—22no—
171C22×C4×C13—22no—
172C22×C4×C13—22no—
173C22×C4×C13—22no—
174C22×C4×C13C2412yes—
175C22×C4×C13C2412yes—
176C22×C4×C13C2412yes—
177C22×C4×C13C2412yes—
178C22×C4×C13C2412yes—
179C22×C4×C13C2412yes—
180C22×Dic13—22no—
181C22×Dic13—22no—
182C22×Dic13—232no—
183C22×Dic13—28no—
184C22×Dic13—28no—
185C22×Dic13—22no—
186C22×Dic13—22no—
187C22×Dic13—22no—
188C22×Dic13—22no—
189C22×Dic13—22no—
190C22×Dic13—22no—
191C22×Dic13—22no—
192C22×Dic13—22no—
193C22×Dic13—22no—
194C22×Dic13—22no—
195C22×Dic13—22no—
196C22×Dic13—22no—
197C22×Dic13—22no—
198C22×Dic13—22no—
199C22×Dic13—22no—
200C22×Dic13—22no—
201C22×Dic13—22no—
202C22×Dic13—22no—
203C22×Dic13C2×D4116yes—
204C22×Dic13C2×D414yes—
205C22×Dic13C2×D414yes—
206C22×Dic13#4114yes—
207C22×Dic13#4114yes—
208C22×Dic13C2412yes—
209C22×Dic13C2412yes—
210C22×Dic13C2412yes—
211C22×Dic13C2412yes—
212C22×Dic13C2412yes—
213C22×Dic13C2412yes—
214C22×Dic13C2412yes—
215C22×Dic13C2412yes—
216C2×Dic26—28no—
217C2×Dic26—28no—
218C2×Dic26—28no—
219C2×Dic26—416no—
220C13×C4⋊C4—44no—
221C13×C22⋊C4—28no—
222C13×C22⋊C4—28no—
223C13×C22⋊C4—44no—
224C22⋊Dic13—28no—
225C22⋊Dic13—28no—
226C22⋊Dic13—44no—
227C4⋊Dic13—28no—
228C4⋊Dic13—44no—
229#6101—28no—
230#6101—28no—
231#6101—28no—
232#6101—28no—
233#6101—28no—
234#6101—28no—
235#6101—44no—
236#6101—44no—
237C4×Dic13—28no—
238C4×Dic13—28no—
239C22×C22⋊Q8—131no—
240C22×#117—131no—
241#2625—1316no—
242C2×#400—131no—
243C2×#400—131no—
244C2×#398—131no—
245C2×#398—131no—
246C2×#397—131no—
247C2×#397—131no—
248C2×#397—131no—
249C2×#397D1311yescharacteristic
250C2×#391—131no—
251C2×#391—131no—
252C2×#389—131no—
253C2×#389—131no—
254C2×#380—131no—
255C23×C13—28no—
256C23×C13—28no—
257C23×C13—28no—
258C23×C13—22no—
259C23×C13—22no—
260C23×C13—22no—
261C23×C13—22no—
262C23×C13—22no—
263C23×C13—22no—
264C23×C13—44no—
265C23×C13—44no—
266C23×C13—44no—
267C23×C13—44no—
268C23×C13C22×D414yes—
269C23×C13C22×D412yes—
270C23×C13C2×#4112yes—
271C23×C13C2×#4112yes—
272C23×C13H(5,𝔽2)12yes—
273C23×C132−1+412yes—
274C23×C132−1+412yes—
275C23×C132−1+412yes—
276C23×C13C2511yescharacteristic
277C2×C4×C13—22no—
278C2×C4×C13—22no—
279C2×C4×C13—22no—
280C2×C4×C13—22no—
281C2×C4×C13—22no—
282C2×C4×C13—22no—
283C2×C4×C13—22no—
284C2×C4×C13—22no—
285C2×C4×C13—22no—
286C2×C4×C13—22no—
287C2×C4×C13—22no—
288C2×C4×C13—22no—
289C2×C4×C13—22no—
290C2×C4×C13—22no—
291C2×C4×C13—22no—
292C2×C4×C13—22no—
293C2×C4×C13—22no—
294C2×C4×C13—22no—
295C2×C4×C13—44no—
296C2×C4×C13—44no—
297C2×C4×C13—44no—
298C2×C4×C13—44no—
299C2×C4×C13—44no—
300C2×C4×C13—44no—
301C2×Dic13—28no—
302C2×Dic13—22no—
303C2×Dic13—22no—
304C2×Dic13—232no—
305C2×Dic13—22no—
306C2×Dic13—22no—
307C2×Dic13—22no—
308C2×Dic13—22no—
309C2×Dic13—22no—
310C2×Dic13—22no—
311C2×Dic13—22no—
312C2×Dic13—22no—
313C2×Dic13—22no—
314C2×Dic13—22no—
315C2×Dic13—22no—
316C2×Dic13—22no—
317C2×Dic13—22no—
318C2×Dic13—22no—
319C2×Dic13—22no—
320C2×Dic13—22no—
321C2×Dic13—22no—
322C2×Dic13—22no—
323C2×Dic13—44no—
324C2×Dic13—44no—
325C2×Dic13—44no—
326C2×Dic13—44no—
327C2×Dic13—44no—
328C2×Dic13—44no—
329C2×Dic13#123116yes—
330C2×Dic13C22×D414yes—
331C2×Dic13C22×D414yes—
332C2×Dic13C2×#4114yes—
333C2×Dic13C2×#4114yes—
334Dic26—416no—
335C23×Q8—131no—
336C24×C4—131no—
337C2×C22⋊Q8—138no—
338C2×C22⋊Q8—268no—
339C2×#117—138no—
340C2×#117—268no—
341C22×C4⋊C4—131no—
342C22×C4⋊C4—131no—
343C22×C4⋊C4—131no—
344C22×C4⋊C4—131no—
345C22×C4⋊C4—131no—
346C22×C4⋊C4—131no—
347C22×C4⋊C4—131no—
348C22×C4⋊C4—131no—
349C22×C4⋊C4—131no—
350C22×C4⋊C4—131no—
351C22×C4⋊C4C2×D1311yescharacteristic
352C22×C22⋊C4—131no—
353C22×C22⋊C4—131no—
354C22×C22⋊C4—131no—
355C22×C22⋊C4C2×D1311yescharacteristic
356C22×C22⋊C4C2×D1311yescharacteristic
357C22×C22⋊C4C2×D1311yescharacteristic
358C22×C42—131no—
359C22×C42—131no—
360#400—138no—
361#400—138no—
362#398—138no—
363#398—138no—
364#397—138no—
365#397—138no—
366#397—138no—
367#397C2×D1318yes—
368#391—138no—
369#391—138no—
370#389—138no—
371#389—138no—
372#380—138no—
373C2×#95—131no—
374C2×#95—131no—
375C2×#95—131no—
376C2×#95—131no—
377C2×#95—131no—
378C2×#95—131no—
379C2×#95—131no—
380C2×#95—131no—
381C2×#95—131no—
382C2×#95—131no—
383C2×#95—131no—
384C2×#95C2×D1311yescharacteristic
385C2×#95C2×D1311yescharacteristic
386C2×#95C2×D1311yescharacteristic
387C22×C13—24no—
388C22×C13—24no—
389C22×C13—24no—
390C22×C13—416no—
391C22×C13—42no—
392C22×C13—42no—
393C22×C13—42no—
394C22×C13—42no—
395C22×C13C2×#12314yes—
396C22×C13#53614yes—
397C22×C13#53714yes—
398C22×C13#54114yes—
399C22×C13#54114yes—
400C22×C13#54214yes—
401C22×C13#54214yes—
402C22×C13C23×D411yescharacteristic
403C22×C13C22×#4111yescharacteristic
404C22×C13C22×#4111yescharacteristic
405C22×C13C2×H(5,𝔽2)11yescharacteristic
406C22×C13C2×2−1+411yescharacteristic
407C22×C13C2×2−1+411yescharacteristic
408C22×C13C2×2−1+411yescharacteristic
409C4×C13—42no—
410C4×C13—42no—
411C4×C13—42no—
412C4×C13—42no—
413C4×C13—42no—
414C4×C13—42no—
415Dic13—24no—
416Dic13—42no—
417Dic13—42no—
418Dic13—42no—
419Dic13—42no—
420Dic13—42no—
421Dic13—42no—
422Dic13C2×#12318yes—
423C25C22×D1311yescharacteristic
424C22×Q8—134no—
425C22×Q8—264no—
426C22×Q8—264no—
427C22×Q8—264no—
428C23×C4—131no—
429C23×C4—138no—
430C23×C4—134no—
431C23×C4—131no—
432C23×C4—131no—
433C23×C4—131no—
434C23×C4—131no—
435C23×C4—131no—
436C23×C4—131no—
437C23×C4—131no—
438C23×C4—264no—
439C23×C4—264no—
440C23×C4C22×D1311yescharacteristic
441C23×C4C22×D1311yescharacteristic
442C23×C4C22×D1311yescharacteristic
443C23×C4C22×D1311yescharacteristic
444C23×C4C22×D1311yescharacteristic
445C23×C4C22×D1311yescharacteristic
446C22⋊Q8—2632no—
447#117—2632no—
448C2×C4⋊C4—42no—
449C2×C4⋊C4—134no—
450C2×C4⋊C4—134no—
451C2×C4⋊C4—134no—
452C2×C4⋊C4—134no—
453C2×C4⋊C4—134no—
454C2×C4⋊C4—134no—
455C2×C4⋊C4—134no—
456C2×C4⋊C4—134no—
457C2×C4⋊C4—134no—
458C2×C4⋊C4—134no—
459C2×C4⋊C4—264no—
460C2×C4⋊C4—264no—
461C2×C4⋊C4—264no—
462C2×C4⋊C4—264no—
463C2×C4⋊C4—264no—
464C2×C4⋊C4—264no—
465C2×C4⋊C4—264no—
466C2×C4⋊C4—522no—
467C2×C4⋊C4—522no—
468C2×C4⋊C4—522no—
469C2×C4⋊C4C22×D1314yes—
470C2×C22⋊C4—24no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—42no—
473C2×C22⋊C4—134no—
474C2×C22⋊C4—134no—
475C2×C22⋊C4—134no—
476C2×C22⋊C4—264no—
477C2×C22⋊C4—264no—
478C2×C22⋊C4—522no—
479C2×C22⋊C4C22×D1314yes—
480C2×C22⋊C4C22×D1314yes—
481C2×C22⋊C4C22×D1314yes—
482C2×C42—134no—
483C2×C42—134no—
484C2×C42—264no—
485C2×C42—264no—
486#95—134no—
487#95—134no—
488#95—134no—
489#95—134no—
490#95—134no—
491#95—134no—
492#95—134no—
493#95—134no—
494#95—134no—
495#95—134no—
496#95—134no—
497#95C22×D1314yes—
498#95C22×D1314yes—
499#95C22×D1314yes—
500C2×C13—44no—
501C2×C13#262518yescomplemented
502C2×C13C22×#12311yescharacteristic
503C2×C13C2×#53611yescharacteristic
504C2×C13C2×#53711yescharacteristic
505C2×C13C2×#54111yescharacteristic
506C2×C13C2×#54111yescharacteristic
507C2×C13C2×#54211yescharacteristic
508C2×C13C2×#54211yescharacteristic
509C24—22no—
510C24—22no—
511C24—22no—
512C24—22no—
513C24—22no—
514C24—22no—
515C24D4×D1314yes—
516C24C23×D1312yes—
517C24C23×D1311yescharacteristic
518C2×Q8—268no—
519C2×Q8—268no—
520C2×Q8—268no—
521C2×Q8—5216no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—134no—
541C22×C4—134no—
542C22×C4—134no—
543C22×C4—132no—
544C22×C4—134no—
545C22×C4—1316no—
546C22×C4—132no—
547C22×C4—132no—
548C22×C4—132no—
549C22×C4—132no—
550C22×C4—132no—
551C22×C4—132no—
552C22×C4—132no—
553C22×C4—2632no—
554C22×C4—268no—
555C22×C4—268no—
556C22×C4—262no—
557C22×C4—262no—
558C22×C4—262no—
559C22×C4—262no—
560C22×C4—262no—
561C22×C4—262no—
562C22×C4—262no—
563C22×C4—262no—
564C22×C4—262no—
565C22×C4—262no—
566C22×C4—262no—
567C22×C4—262no—
568C22×C4—262no—
569C22×C4—262no—
570C22×C4—262no—
571C22×C4—262no—
572C22×C4—262no—
573C22×C4—262no—
574C22×C4—262no—
575C22×C4—262no—
576C22×C4C23×D1312yes—
577C22×C4C23×D1312yes—
578C22×C4C23×D1312yes—
579C22×C4C23×D1312yes—
580C22×C4C23×D1312yes—
581C22×C4C23×D1312yes—
582C4⋊C4—44no—
583C4⋊C4—268no—
584C4⋊C4—268no—
585C4⋊C4—268no—
586C4⋊C4—268no—
587C4⋊C4—268no—
588C4⋊C4—268no—
589C4⋊C4—268no—
590C4⋊C4—524no—
591C4⋊C4—524no—
592C4⋊C4—524no—
593C22⋊C4—28no—
594C22⋊C4—28no—
595C22⋊C4—44no—
596C22⋊C4—268no—
597C22⋊C4—268no—
598C22⋊C4—524no—
599C42—268no—
600C42—268no—
601C13C2×#262511yescharacteristic, complemented, Sylow
602C23—28no—
603C23—28no—
604C23—28no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—44no—
612C23—44no—
613C23—44no—
614C23—44no—
615C23C2×D4×D1314yes—
616C23C2×D4×D1312yes—
617C23#8825112yes—
618C23#41×D1312yes—
619C23#41×D1312yes—
620C23#8825712yes—
621C23#8825712yes—
622C23#8825712yes—
623C23C24×D1311yescharacteristic
624Q8—5216no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—44no—
644C2×C4—44no—
645C2×C4—44no—
646C2×C4—44no—
647C2×C4—44no—
648C2×C4—44no—
649C2×C4—1316no—
650C2×C4—134no—
651C2×C4—134no—
652C2×C4—134no—
653C2×C4—134no—
654C2×C4—2632no—
655C2×C4—268no—
656C2×C4—262no—
657C2×C4—262no—
658C2×C4—262no—
659C2×C4—262no—
660C2×C4—262no—
661C2×C4—262no—
662C2×C4—262no—
663C2×C4—262no—
664C2×C4—262no—
665C2×C4—262no—
666C2×C4—262no—
667C2×C4—262no—
668C2×C4—262no—
669C2×C4—262no—
670C2×C4—262no—
671C2×C4—262no—
672C2×C4—262no—
673C2×C4—262no—
674C2×C4—262no—
675C2×C4—262no—
676C2×C4—524no—
677C2×C4—524no—
678C2×C4—524no—
679C2×C4—524no—
680C2×C4—524no—
681C2×C4—524no—
682C22—24no—
683C22—24no—
684C22—24no—
685C22—42no—
686C22—42no—
687C22—42no—
688C22—42no—
689C22—416no—
690C22#1171930214yes—
691C22#1171935314yes—
692C22D13×#12314yes—
693C22#1171936714yes—
694C22#1171937414yes—
695C22#1171940614yes—
696C22#1171940614yes—
697C22C22×D4×D1311yescharacteristic
698C22C2×#8825111yescharacteristic
699C22C2×#41×D1311yescharacteristic
700C22C2×#41×D1311yescharacteristic
701C22C2×#8825711yescharacteristic
702C22C2×#8825711yescharacteristic
703C22C2×#8825711yescharacteristic
704C4—42no—
705C4—42no—
706C4—42no—
707C4—42no—
708C4—42no—
709C4—42no—
710C4—138no—
711C4—264no—
712C4—522no—
713C4—522no—
714C4—522no—
715C4—522no—
716C4—522no—
717C4—522no—
718C2—44no—
719C2#1312063218yesdirect product factor
720C2C2×D13×#12311yescharacteristic
721C2C2×#1171935311yescharacteristic
722C2C2×#1171930211yescharacteristic
723C2C2×#1171940611yescharacteristic
724C2C2×#1171940611yescharacteristic
725C2C2×#1171937411yescharacteristic
726C2C2×#1171936711yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#397C2
socleC24×C13C24
prime radicalC25×C13C23
hypercenterC2×#397D13
hypocenterC13C2×#2625
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
3. #13120632C2direct (N × H)
4. C2×#11718321C2semidirect
5. C2×#11718319C2semidirect
6. C2×#11718318C2semidirect
7. C2×#11718645C2semidirect
11. C2×#11718307C2semidirect
12. C2×#11718307C2semidirect
13. C2×#11718308C2semidirect
14. C2×#11718633C2semidirect
57. #11718645C22semidirect
58. #11718633C22semidirect
63. #11718321C22semidirect
64. #11718319C22semidirect
65. #11718318C22semidirect
66. #11718308C22semidirect
67. #11718307C22semidirect
68. #11718307C22semidirect
501. C2×C13#2625semidirect
601. C13C2×#2625semidirect
719. C2#13120632direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881322
C22×#881312
#131206322
C2×#117183212
C2×#117183192
C2×#117183182
C2×#117186452
C2×#117186132
C2×#117186142
C2×#117183072
C2×#117183082
C2×#117186332
C2×#117186032
C2×C13×#3972
C2×#262513