Finite Group Databasebeta

← C2×#13118911 #16031125

Subgroups — C2×#13118911 #16031125

Order 3328.

2594 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88152C211yesmaximal, characteristic
2#13118911C2116yesmaximal, direct product factor
3C2×#11718647C211yesmaximal, characteristic, complemented
4C2×#11718655C211yesmaximal, characteristic
5C2×#11718890C211yesmaximal, characteristic, complemented
6C2×#11718892C211yesmaximal, characteristic
7C2×#11718589C211yesmaximal, characteristic, complemented
8C2×#11718601C211yesmaximal, characteristic
9C2×#11718601C211yesmaximal, characteristic
10C2×#11718601C211yesmaximal, characteristic
11C2×#11718651C211yesmaximal, characteristic
12C2×#11718642C211yesmaximal, characteristic, complemented
13C2×#11718594C211yesmaximal, characteristic, complemented
14C2×#11718639C211yesmaximal, characteristic, complemented
15C2×C4×#6101C211yesmaximal, characteristic, complemented
16C22×C4×Q8×C13C211yesmaximal, characteristic, complemented
17C23×Q8×C13C2211yescharacteristic
18C2×C4×Q8×C13—28no—
19C2×C4×Q8×C13C2218yescomplemented
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C13×C4⋊C4C2211yescharacteristic
22C22×C13×C4⋊C4C2211yescharacteristic
23C22×C42×C13C2211yescharacteristic
24C22×C42×C13C2211yescharacteristic
25C22×C42×C13C2211yescharacteristic
26C22×#6103C2211yescharacteristic
27C22×#6103C2211yescharacteristic
28C22×#6103C2211yescharacteristic
29C22×#6103C2211yescharacteristic
30C22×#6103C2211yescharacteristic
31C22×#6103C2211yescharacteristic
32C22×#6103C2211yescharacteristic
33C22×C4⋊Dic13C2211yescharacteristic
34C22×C4⋊Dic13C2211yescharacteristic
35C22×#6101C2211yescharacteristic
36C22×#6101C2211yescharacteristic
37C22×#6101C2211yescharacteristic
38C22×#6101C2211yescharacteristic
39C22×#6101C2211yescharacteristic
40C22×C4×Dic13C2211yescharacteristic
41C22×C4×Dic13C2211yescharacteristic
42C2×#88152—28no—
43C2×#88152C2218yes—
44#11718892C2218yes—
45#11718890C2218yescomplemented
46C2×#88071C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57C2×#88071C2211yescharacteristic
58#11718655C2218yes—
59#11718651C2218yes—
60#11718647C2218yescomplemented
61#11718642C2218yescomplemented
62#11718639C2218yescomplemented
63#11718601C2218yes—
64#11718601C2218yes—
65#11718601C2218yes—
66#11718594C2218yescomplemented
67C4×#6101C2218yescomplemented
68#11718589C2218yescomplemented
69C24×D13C2311yescharacteristic
70C22×Q8×C13—24no—
71C22×Q8×C13—24no—
72C22×Q8×C13—24no—
73C22×Q8×C13C2314yes—
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C23×C4×C13C2311yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C23×C4×C13C2311yescharacteristic
80C23×C4×C13C2311yescharacteristic
81C23×Dic13C2311yescharacteristic
82C23×Dic13C2311yescharacteristic
83C23×Dic13C2311yescharacteristic
84C23×Dic13C2311yescharacteristic
85C23×Dic13C2311yescharacteristic
86C23×Dic13C2311yescharacteristic
87C23×Dic13C2311yescharacteristic
88C4×Q8×C13—232no—
89C2×C13×C4⋊C4—24no—
90C2×C13×C4⋊C4—24no—
91C2×C13×C4⋊C4D418yes—
92C2×C13×C4⋊C4C2314yes—
93C2×C13×C4⋊C4C2314yes—
94C2×C13×C4⋊C4C2314yes—
95C2×C42×C13—24no—
96C2×C42×C13—24no—
97C2×C42×C13—24no—
98C2×C42×C13C2314yes—
99C2×C42×C13C2314yes—
100C2×C42×C13C2314yes—
101C2×#6103—24no—
102C2×#6103—24no—
103C2×#6103—24no—
104C2×#6103—24no—
105C2×#6103—24no—
106C2×#6103—24no—
107C2×#6103—24no—
108C2×#6103C2314yes—
109C2×#6103C2314yes—
110C2×#6103C2314yes—
111C2×#6103C2314yes—
112C2×#6103C2314yes—
113C2×#6103C2314yes—
114C2×#6103C2314yes—
115C2×C4⋊Dic13—24no—
116C2×C4⋊Dic13—24no—
117C2×C4⋊Dic13C2314yes—
118C2×C4⋊Dic13C2314yes—
119C2×#6101—24no—
120C2×#6101—24no—
121C2×#6101—24no—
122C2×#6101—24no—
123C2×#6101—24no—
124C2×#6101C2314yes—
125C2×#6101C2314yes—
126C2×#6101C2314yes—
127C2×#6101C2314yes—
128C2×#6101C2314yes—
129C2×C4×Dic13—24no—
130C2×C4×Dic13—24no—
131C2×C4×Dic13C2314yes—
132C2×C4×Dic13C2314yes—
133#88152—232no—
134#88071C2314yes—
135#88071C2314yes—
136#88071C2314yes—
137#88071C2314yes—
138#88071C2314yes—
139#88071C2314yes—
140#88071C2314yes—
141#88071C2314yes—
142#88071C2314yes—
143#88071C2314yes—
144#88071C2314yes—
145#88071C2314yes—
146C2×#2469—131nomaximal, Sylow
147C24×C13C2411yescharacteristic
148C23×D13—22no—
149C23×D13—22no—
150C23×D13—22no—
151C23×D13—22no—
152C23×D13—22no—
153C23×D13—22no—
154C23×D13—22no—
155C23×D13C2412yes—
156C2×Q8×C13—232no—
157C2×Q8×C13—28no—
158C2×Q8×C13—28no—
159C2×Q8×C13—28no—
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×C13—22no—
175C22×C4×C13C2×D414yes—
176C22×C4×C13C2×D414yes—
177C22×C4×C13C2×D414yes—
178C22×C4×C13#4114yes—
179C22×C4×C13#4114yes—
180C22×C4×C13#4114yes—
181C22×C4×C13C2412yes—
182C22×C4×C13C2412yes—
183C22×C4×C13C2412yes—
184C22×C4×C13C2412yes—
185C22×C4×C13C2412yes—
186C22×C4×C13C2412yes—
187C22×C4×C13C2412yes—
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×Dic13—22no—
204C22×Dic13—22no—
205C22×Dic13—22no—
206C22×Dic13—22no—
207C22×Dic13—22no—
208C22×Dic13#4114yes—
209C22×Dic13C2412yes—
210C22×Dic13C2412yes—
211C22×Dic13C2412yes—
212C22×Dic13C2412yes—
213C22×Dic13C2412yes—
214C22×Dic13C2412yes—
215C22×Dic13C2412yes—
216C13×C4⋊C4—28no—
217C13×C4⋊C4—28no—
218C13×C4⋊C4C2×D4116yes—
219C42×C13—28no—
220C42×C13—28no—
221C42×C13—28no—
222#6103—28no—
223#6103—28no—
224#6103—28no—
225#6103—28no—
226#6103—28no—
227#6103—28no—
228#6103—28no—
229C4⋊Dic13—28no—
230C4⋊Dic13—28no—
231#6101—28no—
232#6101—28no—
233#6101—28no—
234#6101—28no—
235#6101—28no—
236C4×Dic13—28no—
237C4×Dic13—28no—
238C22×#126—131no—
239C22×C4×Q8D1311yescharacteristic, complemented
240#2469—1316no—
241C2×#400—131no—
242C2×#396—131no—
243C2×#395—131no—
244C2×#393—131no—
245C2×#389—131no—
246C2×#388—131no—
247C2×#388—131no—
248C2×#388—131no—
249C2×#388—131no—
250C2×#387—131no—
251C2×#387—131no—
252C2×#387—131no—
253C2×C4×C4⋊C4—131no—
254C23×C13C22×D412yes—
255C23×C13C2×#4112yes—
256C23×C13C2×#4112yes—
257C23×C13C2×#4112yes—
258C23×C13C2×#4112yes—
259C23×C132−1+412yes—
260C23×C132−1+412yes—
261C23×C13C2511yescharacteristic
262C22×D13—22no—
263C22×D13—22no—
264C22×D13—22no—
265C22×D13—22no—
266C22×D13—22no—
267C22×D13—22no—
268C22×D13—22no—
269C22×D13—44no—
270C22×D13—44no—
271C22×D13—44no—
272C22×D13—44no—
273C22×D13—44no—
274C22×D13—44no—
275C22×D13—44no—
276Q8×C13—232no—
277C2×C4×C13—28no—
278C2×C4×C13—28no—
279C2×C4×C13—28no—
280C2×C4×C13—28no—
281C2×C4×C13—28no—
282C2×C4×C13—28no—
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—22no—
296C2×C4×C13—22no—
297C2×C4×C13—22no—
298C2×C4×C13—44no—
299C2×C4×C13C22×D414yes—
300C2×C4×C13C22×D414yes—
301C2×C4×C13C22×D414yes—
302C2×C4×C13C2×#4114yes—
303C2×C4×C13C2×#4114yes—
304C2×C4×C13C2×#4114yes—
305C2×Dic13—28no—
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—22no—
324C2×Dic13—22no—
325C2×Dic13—22no—
326C2×Dic13—44no—
327C2×Dic13—44no—
328C2×Dic13—44no—
329C2×Dic13—44no—
330C2×Dic13—44no—
331C2×Dic13—44no—
332C2×Dic13C2×#4114yes—
333C23×Q8C2×D1311yescharacteristic
334C2×#126—138no—
335C2×#126—268no—
336C2×C4×Q8—28no—
337C2×C4×Q8C2×D1318yescomplemented
338C22×C4⋊C4—131no—
339C22×C4⋊C4—131no—
340C22×C4⋊C4—131no—
341C22×C4⋊C4—131no—
342C22×C4⋊C4—131no—
343C22×C4⋊C4—131no—
344C22×C4⋊C4—131no—
345C22×C4⋊C4C2×D1311yescharacteristic
346C22×C4⋊C4C2×D1311yescharacteristic
347C22×C4⋊C4C2×D1311yescharacteristic
348C22×C22⋊C4—131no—
349C22×C22⋊C4—131no—
350C22×C22⋊C4—131no—
351C22×C22⋊C4—131no—
352C22×C22⋊C4—131no—
353C22×C22⋊C4—131no—
354C22×C22⋊C4—131no—
355C22×C42—131no—
356C22×C42—131no—
357C22×C42C2×D1311yescharacteristic
358C22×C42C2×D1311yescharacteristic
359C22×C42C2×D1311yescharacteristic
360#400—138no—
361#396—138no—
362#395—138no—
363#393—138no—
364#389—138no—
365#388—138no—
366#388—138no—
367#388—138no—
368#388—138no—
369#387—138no—
370#387—138no—
371#387—138no—
372C4×C4⋊C4—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×#95—131no—
385C22×C13#52514yes—
386C22×C13#52914yes—
387C22×C13#54114yes—
388C22×C13#54714yes—
389C22×C13#54814yes—
390C22×C13#55614yes—
391C22×C13#55614yes—
392C22×C13C23×D411yescharacteristic
393C22×C13C22×#4111yescharacteristic
394C22×C13C22×#4111yescharacteristic
395C22×C13C22×#4111yescharacteristic
396C22×C13C22×#4111yescharacteristic
397C22×C13C2×2−1+411yescharacteristic
398C22×C13C2×2−1+411yescharacteristic
399C2×D13—42no—
400C2×D13—42no—
401C2×D13—42no—
402C2×D13—42no—
403C2×D13—42no—
404C2×D13—42no—
405C2×D13—42no—
406C2×D13—88no—
407C4×C13—24no—
408C4×C13—24no—
409C4×C13—24no—
410C4×C13—24no—
411C4×C13—24no—
412C4×C13—24no—
413C4×C13—42no—
414Dic13—24no—
415Dic13—42no—
416Dic13—42no—
417Dic13—42no—
418Dic13—42no—
419Dic13—42no—
420Dic13—42no—
421C25—131no—
422C22×Q8—24no—
423C22×Q8—24no—
424C22×Q8—24no—
425C22×Q8C22×D1314yes—
426C23×C4—131no—
427C23×C4—131no—
428C23×C4—131no—
429C23×C4—131no—
430C23×C4—131no—
431C23×C4—131no—
432C23×C4—131no—
433C23×C4C22×D1311yescharacteristic
434C23×C4C22×D1311yescharacteristic
435C23×C4C22×D1311yescharacteristic
436C23×C4C22×D1311yescharacteristic
437C23×C4C22×D1311yescharacteristic
438C23×C4C22×D1311yescharacteristic
439C23×C4C22×D1311yescharacteristic
440#126—2632no—
441C4×Q8—232no—
442C2×C4⋊C4—24no—
443C2×C4⋊C4—24no—
444C2×C4⋊C4—134no—
445C2×C4⋊C4—134no—
446C2×C4⋊C4—134no—
447C2×C4⋊C4—134no—
448C2×C4⋊C4—134no—
449C2×C4⋊C4—134no—
450C2×C4⋊C4—134no—
451C2×C4⋊C4—264no—
452C2×C4⋊C4—264no—
453C2×C4⋊C4—264no—
454C2×C4⋊C4—264no—
455C2×C4⋊C4—264no—
456C2×C4⋊C4—264no—
457C2×C4⋊C4—264no—
458C2×C4⋊C4C22⋊D1318yes—
459C2×C4⋊C4C22×D1314yes—
460C2×C4⋊C4C22×D1314yes—
461C2×C4⋊C4C22×D1314yes—
462C2×C22⋊C4—134no—
463C2×C22⋊C4—134no—
464C2×C22⋊C4—134no—
465C2×C22⋊C4—134no—
466C2×C22⋊C4—134no—
467C2×C22⋊C4—134no—
468C2×C22⋊C4—134no—
469C2×C22⋊C4—264no—
470C2×C22⋊C4—264no—
471C2×C22⋊C4—264no—
472C2×C22⋊C4—264no—
473C2×C22⋊C4—264no—
474C2×C22⋊C4—264no—
475C2×C22⋊C4—264no—
476C2×C42—24no—
477C2×C42—24no—
478C2×C42—24no—
479C2×C42—134no—
480C2×C42—134no—
481C2×C42—264no—
482C2×C42—264no—
483C2×C42C22×D1314yes—
484C2×C42C22×D1314yes—
485C2×C42C22×D1314yes—
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#95—134no—
498C2×C13#246918yescomplemented
499C2×C13C2×#52511yescharacteristic
500C2×C13C2×#52911yescharacteristic
501C2×C13C2×#54111yescharacteristic
502C2×C13C2×#54711yescharacteristic
503C2×C13C2×#54811yescharacteristic
504C2×C13C2×#55611yescharacteristic
505C2×C13C2×#55611yescharacteristic
506D13—82no—
507C24—132no—
508C24—262no—
509C24—262no—
510C24—262no—
511C24—262no—
512C24—262no—
513C24—262no—
514C24—262no—
515C24C23×D1311yescharacteristic
516C2×Q8—232no—
517C2×Q8—28no—
518C2×Q8—28no—
519C2×Q8—28no—
520C22×C4—22no—
521C22×C4—22no—
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—134no—
536C22×C4—132no—
537C22×C4—132no—
538C22×C4—132no—
539C22×C4—132no—
540C22×C4—132no—
541C22×C4—132no—
542C22×C4—132no—
543C22×C4—262no—
544C22×C4—262no—
545C22×C4—262no—
546C22×C4—262no—
547C22×C4—262no—
548C22×C4—262no—
549C22×C4—262no—
550C22×C4—262no—
551C22×C4—262no—
552C22×C4—262no—
553C22×C4—262no—
554C22×C4—262no—
555C22×C4—262no—
556C22×C4—262no—
557C22×C4—262no—
558C22×C4—262no—
559C22×C4—262no—
560C22×C4—262no—
561C22×C4—262no—
562C22×C4—262no—
563C22×C4#612714yes—
564C22×C4#612714yes—
565C22×C4#613114yes—
566C22×C4C2×C22⋊D1314yes—
567C22×C4C2×C22⋊D1314yes—
568C22×C4C2×C22⋊D1314yes—
569C22×C4C23×D1312yes—
570C22×C4C23×D1312yes—
571C22×C4C23×D1312yes—
572C22×C4C23×D1312yes—
573C22×C4C23×D1312yes—
574C22×C4C23×D1312yes—
575C22×C4C23×D1312yes—
576C4⋊C4—28no—
577C4⋊C4—28no—
578C4⋊C4—268no—
579C4⋊C4—268no—
580C4⋊C4—268no—
581C4⋊C4—268no—
582C4⋊C4—268no—
583C4⋊C4—268no—
584C4⋊C4—268no—
585C4⋊C4C2×C22⋊D13116yes—
586C22⋊C4—268no—
587C22⋊C4—268no—
588C22⋊C4—268no—
589C22⋊C4—268no—
590C22⋊C4—268no—
591C22⋊C4—268no—
592C22⋊C4—268no—
593C42—28no—
594C42—28no—
595C42—28no—
596C42—268no—
597C42—268no—
598C13C2×#246911yescharacteristic, complemented, Sylow
599C23—262no—
600C23—262no—
601C23—262no—
602C23—262no—
603C23—262no—
604C23—262no—
605C23—262no—
606C23—524no—
607C23—524no—
608C23—524no—
609C23—524no—
610C23—524no—
611C23—524no—
612C23—524no—
613C23C2×#612712yes—
614C23C2×#612712yes—
615C23C2×#613112yes—
616C23#8825412yes—
617C23#41×D1312yes—
618C23#8825712yes—
619C23C22×C22⋊D1312yes—
620C23C24×D1311yescharacteristic
621Q8—232no—
622C2×C4—28no—
623C2×C4—28no—
624C2×C4—28no—
625C2×C4—28no—
626C2×C4—28no—
627C2×C4—28no—
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—134no—
645C2×C4—268no—
646C2×C4—262no—
647C2×C4—262no—
648C2×C4—262no—
649C2×C4—262no—
650C2×C4—262no—
651C2×C4—262no—
652C2×C4—262no—
653C2×C4—262no—
654C2×C4—262no—
655C2×C4—262no—
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—524no—
667C2×C4—524no—
668C2×C4—524no—
669C2×C4—524no—
670C2×C4—524no—
671C2×C4—524no—
672C2×C4C2×#612714yes—
673C2×C4C2×#612714yes—
674C2×C4C2×#613114yes—
675C2×C4C22×C22⋊D1314yes—
676C2×C4C22×C22⋊D1314yes—
677C2×C4C22×C22⋊D1314yes—
678C22—522no—
679C22—522no—
680C22—522no—
681C22—522no—
682C22—522no—
683C22—522no—
684C22—522no—
685C22—1048no—
686C22#1171927314yes—
687C22#1171928514yes—
688C22#1171928814yes—
689C22#1171928914yes—
690C22#1171949614yes—
691C22#1171952214yes—
692C22#1171952914yes—
693C22C22×#612711yescharacteristic
694C22C22×#612711yescharacteristic
695C22C22×#613111yescharacteristic
696C22C2×#8825411yescharacteristic
697C22C2×#41×D1311yescharacteristic
698C22C2×#8825711yescharacteristic
699C22C23×C22⋊D1311yescharacteristic
700C4—24no—
701C4—24no—
702C4—24no—
703C4—24no—
704C4—24no—
705C4—24no—
706C4—42no—
707C4—264no—
708C4—522no—
709C4—522no—
710C4—522no—
711C4—522no—
712C4—522no—
713C4—522no—
714C2—1042no—
715C2#1311891118yesdirect product factor
716C2C2×#1171949611yescharacteristic
717C2C2×#1171928511yescharacteristic
718C2C2×#1171928811yescharacteristic
719C2C2×#1171952911yescharacteristic
720C2C2×#1171952211yescharacteristic
721C2C2×#1171927311yescharacteristic
722C2C2×#1171928911yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC22×C4×Q8×C13C2
socleC24×C13C24
prime radicalC24×D13C23
hypercenterC22×C4×Q8D13
hypocenterC13C2×#2469
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C4×Q8

Complements

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

NH ≅ G/Ntype
2. #13118911C2direct (N × H)
3. C2×#11718647C2semidirect
5. C2×#11718890C2semidirect
7. C2×#11718589C2semidirect
12. C2×#11718642C2semidirect
13. C2×#11718594C2semidirect
14. C2×#11718639C2semidirect
15. C2×C4×#6101C2semidirect
16. C22×C4×Q8×C13C2semidirect
19. C2×C4×Q8×C13C22semidirect
45. #11718890C22semidirect
60. #11718647C22semidirect
61. #11718642C22semidirect
62. #11718639C22semidirect
66. #11718594C22semidirect
67. C4×#6101C22semidirect
68. #11718589C22semidirect
239. C22×C4×Q8D13semidirect
337. C2×C4×Q8C2×D13semidirect
498. C2×C13#2469semidirect
598. C13C2×#2469semidirect
715. C2#13118911direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881522
#131189112
C2×#117186472
C2×#117186552
C2×#117188902
C2×#117188922
C2×#117185892
C2×#117186012
C2×#117186512
C2×#117186422
C2×#117185942
C2×#117186392
C2×C4×#61012
C22×C4×Q8×C132
C2×#246913