Finite Group Databasebeta

← C2×#13127223 #16741375

Subgroups — C2×#13127223 #16741375

Order 3328.

1942 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
1C2×#11719340C211yesmaximal, characteristic
2C2×#11719216C211yesmaximal, characteristic
3#13127223C2116yesmaximal, direct product factor
4C2×#11718535C211yesmaximal, characteristic, complemented
5C2×#11718545C211yesmaximal, characteristic, complemented
6C2×#11718383C211yesmaximal, characteristic, complemented
7C2×#11718470C211yesmaximal, characteristic, complemented
8C2×#11718536C211yesmaximal, characteristic, complemented
9C2×#11718455C211yesmaximal, characteristic, complemented
10C2×#11718474C211yesmaximal, characteristic, complemented
11C2×#11718712C211yesmaximal, characteristic, complemented
12C2×#11718451C211yesmaximal, characteristic, complemented
13C2×#11718386C211yesmaximal, characteristic
14C22×#88047C211yesmaximal, characteristic, complemented
15C2×D13×#107C211yesmaximal, characteristic, complemented
16C2×C13×#484C211yesmaximal, characteristic, complemented
17C2×C13×C22⋊Q8C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C2×#88200C2211yescharacteristic
20C2×Q8×Dic13C2211yescharacteristic
21C22×#6107C2211yescharacteristic
22C2×C4×C22⋊D13—21no—
23C2×C4×C22⋊D13C2211yescharacteristic
24C22×C4⋊Dic13C2211yescharacteristic
25C2×#88178—21no—
26C2×#88178C2211yescharacteristic
27C23×#1055C2211yescharacteristic
28C22×C8×D13C2211yescharacteristic
29#11719340—24no—
30#11719340C2218yes—
31#11719216—24no—
32#11719216C2218yes—
33C2×#88151—21no—
34C2×#88151C2211yescharacteristic
35C2×#88150—21no—
36C2×C4⋊C4×D13C2211yescharacteristic
37C2×C4⋊C4×D13C2211yescharacteristic
38C2×#88143—21no—
39C2×#88143—21no—
40C2×#88142C2211yescharacteristic
41C2×#88142C2211yescharacteristic
42C2×#88141C2211yescharacteristic
43C2×#88135—21no—
44C2×#88132—21no—
45C13×#484C2218yescomplemented
46C2×C13×#107C2211yescharacteristic
47C2×C13×#107C2211yescharacteristic
48C2×C13×#103C2211yescharacteristic
49C2×C13×#103C2211yescharacteristic
50C2×C13×C22⋊C8C2211yescharacteristic
51C2×#88075C2211yescharacteristic
52C2×#88060C2211yescharacteristic
53C2×#88058C2211yescharacteristic
54C2×#88058C2211yescharacteristic
55C2×#88056C2211yescharacteristic
56C2×#88056C2211yescharacteristic
57C2×#88054C2211yescharacteristic
58C2×C8×Dic13C2211yescharacteristic
59#11718712C2218yescomplemented
60C2×#88050C2211yescharacteristic
61C2×#88047C2211yescharacteristic
62C2×#88047C2211yescharacteristic
63C2×#88047C2211yescharacteristic
64C2×#88047C2211yescharacteristic
65C2×#88047C2211yescharacteristic
66C2×#88047C2218yescomplemented
67#11718545C2218yescomplemented
68D13×#107C2218yescomplemented
69#11718536C2218yescomplemented
70#11718535C2218yescomplemented
71#11718474C2218yescomplemented
72#11718470C2218yescomplemented
73#11718455C2218yescomplemented
74#11718451C2218yescomplemented
75#11718386C2218yes—
76#11718383C2218yescomplemented
77C22×Q8×C13C2311yescharacteristic
78C23×C4×C13—21no—
79C23×C4×C13C2311yescharacteristic
80C22×C22⋊D13D411yescharacteristic
81C23×Dic13—21no—
82C22×C4×D13—21no—
83C22×C4×D13—21no—
84C22×C4×D13C2311yescharacteristic
85C22×Dic26—21no—
86C22×Dic26—21no—
87C22×Dic26C2311yescharacteristic
88C22×C8×C13C2311yescharacteristic
89C22×C8×C13C2311yescharacteristic
90C13×C22⋊Q8—22no—
91C13×C22⋊Q8C2314yes—
92C2×C13×C4⋊C4—21no—
93C2×C13×C4⋊C4—21no—
94C2×C13×C4⋊C4—22no—
95C2×C13×C4⋊C4C2311yescharacteristic
96C2×C13×C4⋊C4C2311yescharacteristic
97C2×C13×C4⋊C4C2311yescharacteristic
98C2×C13×C4⋊C4C2314yes—
99C2×C13×C22⋊C4—21no—
100C2×C22⋊Dic13—21no—
101C2×C22⋊Dic13D411yescharacteristic
102#88200—22no—
103#88200C2314yes—
104Q8×Dic13—22no—
105Q8×Dic13C2314yes—
106C2×#6107—24no—
107C2×#6107C2314yes—
108C4×C22⋊D13—28no—
109C4×C22⋊D13D414yes—
110C4×C22⋊D13C2314yes—
111C2×#6103—21no—
112C2×#6103—21no—
113C2×#6103D411yescharacteristic
114C2×C4⋊Dic13—21no—
115C2×C4⋊Dic13—22no—
116C2×C4⋊Dic13—21no—
117C2×C4⋊Dic13—21no—
118C2×C4⋊Dic13C2311yescharacteristic
119C2×C4⋊Dic13C2311yescharacteristic
120C2×C4⋊Dic13C2311yescharacteristic
121C2×C4⋊Dic13C2314yes—
122#88178—22no—
123#88178—28no—
124#88178C2314yes—
125C2×#6101—21no—
126C2×#6101—21no—
127C2×#6101—21no—
128C2×#6101—21no—
129C2×#6101—21no—
130C2×#6101—21no—
131C2×#6101—21no—
132C2×#6101D411yescharacteristic
133C2×C4×Dic13—21no—
134C2×C4×Dic13—21no—
135C2×C4×Dic13C2311yescharacteristic
136C22×#1055—24no—
137C22×#1055C2314yes—
138C22×#1055C2311yescharacteristic
139C22×#1055C2311yescharacteristic
140C2×C8×D13—24no—
141C2×C8×D13C2314yes—
142#88151—22no—
143#88151—28no—
144#88151C2314yes—
145#88150—28no—
146C4⋊C4×D13—22no—
147C4⋊C4×D13—22no—
148C4⋊C4×D13C2314yes—
149C4⋊C4×D13C2314yes—
150#88143—28no—
151#88143—28no—
152#88142—22no—
153#88142—22no—
154#88142C2314yes—
155#88142C2314yes—
156#88141—22no—
157#88141C2314yes—
158#88135—28no—
159#88132—28no—
160C13×#107C2314yes—
161C13×#107C2314yes—
162C13×#103C2314yes—
163C13×#103C2314yes—
164C13×C22⋊C8C2314yes—
165#88075C2314yes—
166#88060C2314yes—
167#88058C2314yes—
168#88058C2314yes—
169#88056C2314yes—
170#88056C2314yes—
171#88054C2314yes—
172C8×Dic13C2314yes—
173#88050C2314yes—
174#88047C2314yes—
175#88047C2314yes—
176#88047C2314yes—
177#88047C2314yes—
178#88047C2314yes—
179C2×#3338—131nomaximal, Sylow
180C24×C13C2×D411yescharacteristic
181C23×D13C2×D411yescharacteristic
182C2×Q8×C13—21no—
183C2×Q8×C13—22no—
184C2×Q8×C13—22no—
185C2×Q8×C13C2412yes—
186C22×C4×C13—22no—
187C22×C4×C13—22no—
188C22×C4×C13—21no—
189C22×C4×C13—21no—
190C22×C4×C13—21no—
191C22×C4×C13—21no—
192C22×C4×C13—24no—
193C22×C4×C13—82no—
194C22×C4×C13C2×D411yescharacteristic
195C22×C4×C13C2×D412yes—
196C22×C4×C13C2412yes—
197C22×C4×C13C2411yescharacteristic
198C2×C22⋊D13Q1618yescomplemented
199C2×C22⋊D13C2×D414yes—
200C22×Dic13—21no—
201C22×Dic13—21no—
202C22×Dic13—21no—
203C22×Dic13—21no—
204C22×Dic13—24no—
205C22×Dic13—82no—
206C22×Dic13C2×D411yescharacteristic
207C22×Dic13C2×D411yescharacteristic
208C22×Dic13C2×D411yescharacteristic
209C2×C4×D13—22no—
210C2×C4×D13—22no—
211C2×C4×D13—24no—
212C2×C4×D13—24no—
213C2×C4×D13—82no—
214C2×C4×D13—82no—
215C2×C4×D13C2×D412yes—
216C2×C4×D13C2412yes—
217C2×Dic26—22no—
218C2×Dic26—22no—
219C2×Dic26—21no—
220C2×Dic26—24no—
221C2×Dic26—24no—
222C2×Dic26—82no—
223C2×Dic26—82no—
224C2×Dic26C2412yes—
225C2×C8×C13—22no—
226C2×C8×C13—22no—
227C2×C8×C13C2412yes—
228C2×C8×C13C2412yes—
229C13×C4⋊C4—21no—
230C13×C4⋊C4—21no—
231C13×C4⋊C4—21no—
232C13×C4⋊C4—24no—
233C13×C4⋊C4—24no—
234C13×C4⋊C4C2412yes—
235C13×C4⋊C4C2412yes—
236C13×C4⋊C4C2412yes—
237C13×C22⋊C4—24no—
238C22⋊Dic13—24no—
239C22⋊Dic13C2×D414yes—
240#6107—28no—
241#6103—24no—
242#6103—24no—
243#6103C2×D414yes—
244C4⋊Dic13—21no—
245C4⋊Dic13—21no—
246C4⋊Dic13—24no—
247C4⋊Dic13—21no—
248C4⋊Dic13—24no—
249C4⋊Dic13—24no—
250C4⋊Dic13C2412yes—
251C4⋊Dic13C2412yes—
252C4⋊Dic13C2412yes—
253#6101—24no—
254#6101—24no—
255#6101—24no—
256#6101—24no—
257#6101—24no—
258#6101—24no—
259#6101—24no—
260#6101C2×D414yes—
261C4×Dic13—24no—
262C4×Dic13—24no—
263C4×Dic13C2×D412yes—
264C4×Dic13C2412yes—
265C2×#1055—22no—
266C2×#1055—28no—
267C2×#1055#4114yes—
268C2×#1055C2412yes—
269C2×#1055C2412yes—
270C8×D13—28no—
271C2×#554—131no—
272C2×#554—131no—
273#3338—1316no—
274C2×#500—131no—
275C2×#484—131no—
276C2×#484—131no—
277C2×#484—131no—
278C2×#484D1311yescharacteristic, complemented
279C2×#477—131no—
280C2×#477—131no—
281C2×#467—131no—
282C2×#467—131no—
283C2×C4×Q16—131no—
284C2×C8×D4—131no—
285C22×#107—131no—
286C22×#107—131no—
287C23×C13—22no—
288C23×C13—22no—
289C23×C13C2×Q1614yes—
290C23×C13C22×D412yes—
291C23×C13C22×D411yescharacteristic
292C22×D13—22no—
293C22×D13—22no—
294C22×D13C2×Q1614yes—
295C22×D13C22×D412yes—
296Q8×C13—22no—
297Q8×C13—22no—
298Q8×C13—42no—
299C2×C4×C13—22no—
300C2×C4×C13—24no—
301C2×C4×C13—22no—
302C2×C4×C13—22no—
303C2×C4×C13—22no—
304C2×C4×C13—22no—
305C2×C4×C13—22no—
306C2×C4×C13—22no—
307C2×C4×C13—42no—
308C2×C4×C13—42no—
309C2×C4×C13—42no—
310C2×C4×C13—42no—
311C2×C4×C13—84no—
312C2×C4×C13C22×D412yes—
313C2×C4×C13C22×D411yescharacteristic
314C2×C4×C13C2×#4112yes—
315C2×C4×C132−1+412yes—
316C2×C4×C13C2511yescharacteristic
317C22⋊D13C2×Q16116yescomplemented
318C2×Dic13—22no—
319C2×Dic13—22no—
320C2×Dic13—22no—
321C2×Dic13—22no—
322C2×Dic13—22no—
323C2×Dic13—22no—
324C2×Dic13—42no—
325C2×Dic13—42no—
326C2×Dic13—42no—
327C2×Dic13—42no—
328C2×Dic13—84no—
329C2×Dic13C2×Q1614yes—
330C2×Dic13C22×D412yes—
331C2×Dic13C22×D412yes—
332C2×Dic13C22×D412yes—
333C4×D13—24no—
334C4×D13—22no—
335C4×D13—22no—
336C4×D13—84no—
337C4×D13—84no—
338Dic26—22no—
339Dic26—22no—
340Dic26—42no—
341Dic26—84no—
342Dic26—84no—
343C8×C13—22no—
344C8×C13—22no—
345#1055—22no—
346#1055C2×#4114yes—
347C22×Q16—131no—
348C23×C8—131no—
349C23×C8—131no—
350#554—138no—
351#554—138no—
352#554—264no—
353#554—264no—
354C2×C4⋊Q8—131no—
355C2×C4⋊Q8—131no—
356C2×#125—261no—
357C2×#125—261no—
358C2×C22⋊Q8—131no—
359C2×C22⋊Q8—131no—
360C2×C22⋊Q8—131no—
361C2×C22⋊Q8—261no—
362C2×C22⋊Q8—261no—
363C2×C22⋊Q8—261no—
364C2×C22⋊Q8—261no—
365C2×C22⋊Q8C2×D1311yescharacteristic
366C2×C4×Q8—131no—
367C2×C4×Q8—131no—
368C2×C4×D4—131no—
369C2×C4×D4—261no—
370C2×C4×D4—261no—
371C22×C4⋊C4—131no—
372C22×C4⋊C4—131no—
373C22×C4⋊C4—131no—
374C22×C4⋊C4C2×D1311yescharacteristic
375#500—138no—
376#484—138no—
377#484—138no—
378#484—138no—
379#484C2×D1318yescomplemented
380#477—138no—
381#477—138no—
382#467—138no—
383#467—138no—
384C4×Q16—138no—
385C8×D4—138no—
386C2×#107—131no—
387C2×#107—131no—
388C2×#107—131no—
389C2×#107—131no—
390C2×#107—138no—
391C2×#107—131no—
392C2×#107—131no—
393C2×#107—131no—
394C2×#107—138no—
395C2×#107C2×D1311yescharacteristic
396C2×#107C2×D1311yescharacteristic
397C2×C4⋊C8—131no—
398C2×#103—131no—
399C2×#103—131no—
400C2×#103—131no—
401C2×#103—131no—
402C2×#103C2×D1311yescharacteristic
403C2×#103C2×D1311yescharacteristic
404C2×C22⋊C8—131no—
405C2×C22⋊C8C2×D1311yescharacteristic
406C2×C4×C8—131no—
407C22×C13—28no—
408C22×C13—22no—
409C22×C13—22no—
410C22×C13#54712yes—
411C22×C13C22×Q1614yes—
412C22×C13C22×Q1612yes—
413C22×C13#57612yes—
414C22×C13C23×D411yescharacteristic
415C2×D13—28no—
416C2×D13—22no—
417C2×D13—22no—
418C2×D13C22×Q1614yes—
419C4×C13—22no—
420C4×C13—42no—
421C4×C13—42no—
422C4×C13—42no—
423C4×C13—42no—
424C4×C13#54712yes—
425C4×C13C22×#4111yescharacteristic
426C4×C13C2×2−1+411yescharacteristic
427Dic13—22no—
428Dic13—22no—
429Dic13—42no—
430Dic13—42no—
431Dic13—42no—
432Dic13—42no—
433Dic13C22×Q1614yes—
434C22×Q8—131no—
435C22×Q8—261no—
436C22×Q8—261no—
437C22×Q8C22×D1311yescharacteristic
438C22×D4—131no—
439C23×C4—21no—
440C23×C4—131no—
441C23×C4—261no—
442C23×C4—261no—
443C23×C4—261no—
444C23×C4C22×D1311yescharacteristic
445C2×Q16—134no—
446C2×Q16—264no—
447C22×C8—131no—
448C22×C8—131no—
449C22×C8—134no—
450C22×C8—134no—
451C22×C8—264no—
452C22×C8—264no—
453C22×C8C22×D1311yescharacteristic
454C22×C8C22×D1311yescharacteristic
455C4⋊Q8—134no—
456C4⋊Q8—134no—
457C4⋊Q8—262no—
458C4⋊Q8—262no—
459#125—268no—
460#125—268no—
461C22⋊Q8—22no—
462C22⋊Q8—134no—
463C22⋊Q8—134no—
464C22⋊Q8—134no—
465C22⋊Q8—268no—
466C22⋊Q8—268no—
467C22⋊Q8—268no—
468C22⋊Q8—268no—
469C22⋊Q8—262no—
470C22⋊Q8—262no—
471C22⋊Q8—262no—
472C22⋊Q8C22×D1314yes—
473C4×Q8—134no—
474C4×Q8—134no—
475C4×Q8—262no—
476C4×Q8—262no—
477C4×D4—134no—
478C4×D4—134no—
479C4×D4—268no—
480C4×D4—268no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—131no—
485C2×C4⋊C4—131no—
486C2×C4⋊C4—131no—
487C2×C4⋊C4—131no—
488C2×C4⋊C4—134no—
489C2×C4⋊C4—134no—
490C2×C4⋊C4—134no—
491C2×C4⋊C4—262no—
492C2×C4⋊C4—262no—
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—262no—
503C2×C4⋊C4—261no—
504C2×C4⋊C4C22×D1311yescharacteristic
505C2×C4⋊C4C22×D1311yescharacteristic
506C2×C4⋊C4C22×D1311yescharacteristic
507C2×C4⋊C4C22×D1314yes—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—131no—
510C2×C22⋊C4—131no—
511C2×C22⋊C4—261no—
512C2×C22⋊C4—261no—
513C2×C22⋊C4—261no—
514C2×C42—131no—
515C2×C42—261no—
516C2×C42—261no—
517#107—134no—
518#107—134no—
519#107—134no—
520#107—134no—
521#107—134no—
522#107—134no—
523#107—134no—
524#107C22×D1314yes—
525#107C22×D1314yes—
526C4⋊C8—134no—
527#103—134no—
528#103—134no—
529#103—134no—
530#103—134no—
531#103C22×D1314yes—
532#103C22×D1314yes—
533C22⋊C8—134no—
534C22⋊C8C22×D1314yes—
535C4×C8—134no—
536C2×C13—24no—
537C2×C13#333814yescomplemented
538C2×C13C2×#54711yescharacteristic
539C2×C13C23×Q1611yescharacteristic
540C2×C13C2×#57611yescharacteristic
541D13—24no—
542C24—131no—
543C24D4×D1311yescharacteristic
544C2×Q8—21no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—132no—
548C2×Q8—264no—
549C2×Q8—264no—
550C2×Q8—261no—
551C2×Q8—262no—
552C2×Q8—262no—
553C2×Q8—1042no—
554C2×Q8—1042no—
555C2×Q8C23×D1312yes—
556C2×D4—138no—
557C2×D4—134no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—24no—
565C22×C4—82no—
566C22×C4—131no—
567C22×C4—131no—
568C22×C4—131no—
569C22×C4—132no—
570C22×C4—132no—
571C22×C4—264no—
572C22×C4—264no—
573C22×C4—262no—
574C22×C4—262no—
575C22×C4—261no—
576C22×C4—261no—
577C22×C4—261no—
578C22×C4—261no—
579C22×C4—264no—
580C22×C4—1042no—
581C22×C4—1042no—
582C22×C4—1042no—
583C22×C4D4×D1312yes—
584C22×C4D4×D1311yescharacteristic
585C22×C4C23×D1312yes—
586C22×C4C23×D1311yescharacteristic
587Q16—268no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—134no—
591C2×C8—132no—
592C2×C8—132no—
593C2×C8—268no—
594C2×C8—268no—
595C2×C8—262no—
596C2×C8C23×D1312yes—
597C2×C8C23×D1312yes—
598C4⋊C4—21no—
599C4⋊C4—24no—
600C4⋊C4—21no—
601C4⋊C4—24no—
602C4⋊C4—21no—
603C4⋊C4—134no—
604C4⋊C4—132no—
605C4⋊C4—132no—
606C4⋊C4—132no—
607C4⋊C4—264no—
608C4⋊C4—264no—
609C4⋊C4—264no—
610C4⋊C4—264no—
611C4⋊C4—264no—
612C4⋊C4—264no—
613C4⋊C4—264no—
614C4⋊C4—264no—
615C4⋊C4—261no—
616C4⋊C4—264no—
617C4⋊C4—261no—
618C4⋊C4—261no—
619C4⋊C4—264no—
620C4⋊C4C23×D1312yes—
621C4⋊C4C23×D1312yes—
622C4⋊C4C23×D1312yes—
623C22⋊C4—24no—
624C22⋊C4—134no—
625C22⋊C4—134no—
626C22⋊C4—264no—
627C22⋊C4—264no—
628C22⋊C4—264no—
629C42—132no—
630C42—132no—
631C42—264no—
632C42—264no—
633C13C2×#333811yescharacteristic, complemented, Sylow
634C23—22no—
635C23—22no—
636C23—134no—
637C23—132no—
638C23—262no—
639C23—262no—
640C23Q16×D1314yes—
641C23C2×D4×D1312yes—
642C23C2×D4×D1311yescharacteristic
643Q8—22no—
644Q8—22no—
645Q8—42no—
646Q8—262no—
647Q8—262no—
648Q8—522no—
649Q8—1044no—
650Q8—1044no—
651D4—1316no—
652C2×C4—22no—
653C2×C4—24no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—84no—
665C2×C4—134no—
666C2×C4—132no—
667C2×C4—132no—
668C2×C4—132no—
669C2×C4—262no—
670C2×C4—262no—
671C2×C4—264no—
672C2×C4—262no—
673C2×C4—262no—
674C2×C4—262no—
675C2×C4—262no—
676C2×C4—262no—
677C2×C4—262no—
678C2×C4—522no—
679C2×C4—522no—
680C2×C4—522no—
681C2×C4—522no—
682C2×C4—1044no—
683C2×C4—1044no—
684C2×C4—1044no—
685C2×C4C2×D4×D1312yes—
686C2×C4C2×D4×D1311yescharacteristic
687C2×C4#41×D1312yes—
688C2×C4#8825712yes—
689C2×C4C24×D1311yescharacteristic
690C8—22no—
691C8—22no—
692C8—134no—
693C8—262no—
694C22—28no—
695C22—22no—
696C22—22no—
697C22—134no—
698C22—268no—
699C22—262no—
700C22—262no—
701C22#1171936012yes—
702C22C2×Q16×D1314yes—
703C22C2×Q16×D1312yes—
704C22#1171947912yes—
705C22C22×D4×D1311yescharacteristic
706C4—22no—
707C4—42no—
708C4—42no—
709C4—42no—
710C4—42no—
711C4—134no—
712C4—262no—
713C4—262no—
714C4—522no—
715C4—522no—
716C4—522no—
717C4—522no—
718C4#1171936012yes—
719C4C2×#41×D1311yescharacteristic
720C4C2×#8825711yescharacteristic
721C2—24no—
722C2—264no—
723C2#1312722314yesdirect product factor
724C2C2×#1171936011yescharacteristic
725C2C22×Q16×D1311yescharacteristic
726C2C2×#1171947911yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#484C2
socleC23×C13C22×D4
prime radicalC22×C22⋊D13D4
hypercenterC2×#484D13
hypocenterC13C2×#3338
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#484

Complements

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

NH ≅ G/Ntype
3. #13127223C2direct (N × H)
4. C2×#11718535C2semidirect
5. C2×#11718545C2semidirect
6. C2×#11718383C2semidirect
7. C2×#11718470C2semidirect
8. C2×#11718536C2semidirect
9. C2×#11718455C2semidirect
10. C2×#11718474C2semidirect
11. C2×#11718712C2semidirect
12. C2×#11718451C2semidirect
14. C22×#88047C2semidirect
15. C2×D13×#107C2semidirect
16. C2×C13×#484C2semidirect
45. C13×#484C22semidirect
59. #11718712C22semidirect
66. C2×#88047C22semidirect
67. #11718545C22semidirect
68. D13×#107C22semidirect
69. #11718536C22semidirect
70. #11718535C22semidirect
71. #11718474C22semidirect
72. #11718470C22semidirect
73. #11718455C22semidirect
74. #11718451C22semidirect
76. #11718383C22semidirect
198. C2×C22⋊D13Q16semidirect
278. C2×#484D13semidirect
317. C22⋊D13C2×Q16semidirect
379. #484C2×D13semidirect
537. C2×C13#3338semidirect
633. C13C2×#3338semidirect
723. C2#13127223direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117193402
C2×#117192162
#131272232
C2×#117185352
C2×#117185452
C2×#117183832
C2×#117184702
C2×#117185362
C2×#117184552
C2×#117184742
C2×#117187122
C2×#117184512
C2×#117183862
C22×#880472
C2×D13×#1072
C2×C13×#4842
C2×#333813