Finite Group Databasebeta

← C2×#13125051 #16731183

Subgroups — C2×#13125051 #16731183

Order 3328.

2070 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719330C211yesmaximal, characteristic, complemented
2C2×#11719532C211yesmaximal, characteristic
3#13125051C2116yesmaximal, direct product factor
4C2×#11718383C211yesmaximal, characteristic, complemented
5C2×#11718704C211yesmaximal, characteristic, complemented
6C2×#11718457C211yesmaximal, characteristic, complemented
7C2×#11718427C211yesmaximal, characteristic, complemented
8C2×#11718843C211yesmaximal, characteristic, complemented
9C2×#11718823C211yesmaximal, characteristic, complemented
10C2×#11718900C211yesmaximal, characteristic
11C2×#11718450C211yesmaximal, characteristic, complemented
12C2×#11718825C211yesmaximal, characteristic, complemented
13C2×Q16×Dic13C211yesmaximal, characteristic, complemented
14C2×#11718419C211yesmaximal, characteristic, complemented
15C2×#11718381C211yesmaximal, characteristic, complemented
16C2×C13×#452C211yesmaximal, characteristic
17C22×C13×#41C2211yescharacteristic
18C22×C13×Q16C2211yescharacteristic
19C22×C13×SD16C2211yescharacteristic
20C2×C13×C22⋊Q8C2211yescharacteristic
21#11719532—24no—
22#11719532C2218yes—
23C2×Q8×Dic13C2211yescharacteristic
24C2×Q8×Dic13C2211yescharacteristic
25C2×Q8×Dic13C2211yescharacteristic
26C2×#88198C2211yescharacteristic
27C22×#6107C2211yescharacteristic
28C2×D4×Dic13—21no—
29C2×D4×Dic13—21no—
30C2×D4×Dic13C2211yescharacteristic
31C2×D4×Dic13C2211yescharacteristic
32C22×#6105C2211yescharacteristic
33C2×#88180—21no—
34C2×#88180C2211yescharacteristic
35C22×C4⋊Dic13—21no—
36C22×C4⋊Dic13C2211yescharacteristic
37C2×#88178C2211yescharacteristic
38#11719330—24no—
39#11719330C2218yescomplemented
40C2×#88144—21no—
41C2×#88144C2211yescharacteristic
42C2×#88143—21no—
43C2×#88141C2211yescharacteristic
44C2×#88133—21no—
45C2×#88133—21no—
46C13×#452C2218yes—
47C2×C13×#103C2211yescharacteristic
48C2×C13×#102C2211yescharacteristic
49C2×C13×C22⋊C8C2211yescharacteristic
50#11718900C2218yes—
51C2×#88075C2211yescharacteristic
52C2×#88075C2211yescharacteristic
53C2×#88075C2211yescharacteristic
54C2×#88072C2211yescharacteristic
55C2×C22⋊#1055C2211yescharacteristic
56Q16×Dic13C2218yescomplemented
57#11718843C2218yescomplemented
58#11718825C2218yescomplemented
59#11718823C2218yescomplemented
60C2×#88058C2211yescharacteristic
61C2×#88058C2211yescharacteristic
62C2×#88056C2211yescharacteristic
63C2×#88056C2211yescharacteristic
64C2×#88055C2211yescharacteristic
65C2×#88054C2211yescharacteristic
66C2×#88054C2211yescharacteristic
67C2×C8×Dic13C2211yescharacteristic
68#11718704C2218yescomplemented
69C2×#88048C2211yescharacteristic
70C2×#88048C2211yescharacteristic
71#11718457C2218yescomplemented
72#11718450C2218yescomplemented
73#11718427C2218yescomplemented
74#11718419C2218yescomplemented
75#11718383C2218yescomplemented
76#11718381C2218yescomplemented
77C2×C13×#41—24no—
78C2×C13×#41—24no—
79C2×C13×#41—22no—
80C2×C13×#41C2314yes—
81C22×Q8×C13C2311yescharacteristic
82C22×Q8×C13C2311yescharacteristic
83C22×D4×C13—21no—
84C22×D4×C13C2311yescharacteristic
85C23×C4×C13—21no—
86C23×C4×C13C2311yescharacteristic
87C23×Dic13—21no—
88C23×Dic13—21no—
89C23×Dic13—21no—
90C22×Dic26C2311yescharacteristic
91C2×C13×Q16—24no—
92C2×C13×Q16C2314yes—
93C2×C13×SD16—24no—
94C2×C13×SD16C2314yes—
95C22×C8×C13C2311yescharacteristic
96C22×C8×C13C2311yescharacteristic
97C13×C22⋊Q8—22no—
98C13×C22⋊Q8C2314yes—
99C2×C13×C4⋊C4—21no—
100C2×C13×C4⋊C4C2311yescharacteristic
101C2×C13×C22⋊C4—21no—
102C2×C22⋊Dic13—21no—
103C2×C22⋊Dic13—21no—
104C2×C22⋊Dic13—21no—
105C2×C22⋊Dic13D411yescharacteristic
106C2×C22⋊Dic13D411yescharacteristic
107Q8×Dic13—22no—
108Q8×Dic13—22no—
109Q8×Dic13—22no—
110Q8×Dic13C2314yes—
111Q8×Dic13C2314yes—
112Q8×Dic13C2314yes—
113#88198—22no—
114#88198C2314yes—
115C2×#6107—24no—
116C2×#6107C2314yes—
117D4×Dic13—28no—
118D4×Dic13—28no—
119D4×Dic13—22no—
120D4×Dic13—22no—
121D4×Dic13C2314yes—
122D4×Dic13C2314yes—
123C2×#6105—24no—
124C2×#6105C2314yes—
125#88180—28no—
126#88180D414yes—
127#88180C2314yes—
128C2×C4⋊Dic13—21no—
129C2×C4⋊Dic13—22no—
130C2×C4⋊Dic13—21no—
131C2×C4⋊Dic13—21no—
132C2×C4⋊Dic13—21no—
133C2×C4⋊Dic13—21no—
134C2×C4⋊Dic13—28no—
135C2×C4⋊Dic13D411yescharacteristic
136C2×C4⋊Dic13D411yescharacteristic
137C2×C4⋊Dic13C2311yescharacteristic
138C2×C4⋊Dic13C2314yes—
139C2×C4⋊Dic13C2311yescharacteristic
140C2×C4⋊Dic13C2311yescharacteristic
141#88178—22no—
142#88178C2314yes—
143C2×#6101—21no—
144C2×#6101—21no—
145C2×#6101—21no—
146C2×#6101—21no—
147C2×#6101—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×#102C2314yes—
166C13×C22⋊C8C2314yes—
167#88075C2314yes—
168#88075C2314yes—
169#88075C2314yes—
170#88072C2314yes—
171C22⋊#1055C2314yes—
172#88058C2314yes—
173#88058C2314yes—
174#88056C2314yes—
175#88056C2314yes—
176#88055C2314yes—
177#88054C2314yes—
178#88054C2314yes—
179C8×Dic13C2314yes—
180#88048C2314yes—
181#88048C2314yes—
182C2×#3120—131nomaximal, Sylow
183C24×C13—21no—
184C24×C13C2×D411yescharacteristic
185C13×#41—216no—
186C13×#41—28no—
187C13×#41—28no—
188C2×Q8×C13—21no—
189C2×Q8×C13—21no—
190C2×Q8×C13—22no—
191C2×Q8×C13—22no—
192C2×Q8×C13—22no—
193C2×Q8×C13#4114yes—
194C2×Q8×C13C2412yes—
195C2×Q8×C13C2412yes—
196C2×D4×C13—28no—
197C2×D4×C13—24no—
198C2×D4×C13—21no—
199C2×D4×C13—22no—
200C2×D4×C13#4114yes—
201C2×D4×C13C2412yes—
202C22×C4×C13—28no—
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×Dic13—24no—
218C22×Dic13—24no—
219C22×Dic13—24no—
220C22×Dic13—82no—
221C22×Dic13—82no—
222C22×Dic13—82no—
223C22×Dic13C2×D411yescharacteristic
224C22×Dic13C2×D411yescharacteristic
225C22×Dic13C2×D411yescharacteristic
226C22×Dic13C2×D411yescharacteristic
227C2×Dic26—22no—
228C2×Dic26—22no—
229C2×Dic26—21no—
230C2×Dic26C2412yes—
231C13×Q16—28no—
232C13×SD16—28no—
233C2×C8×C13—22no—
234C2×C8×C13—22no—
235C2×C8×C13C2412yes—
236C2×C8×C13C2412yes—
237C13×C4⋊C4—21no—
238C13×C4⋊C4—24no—
239C13×C4⋊C4C2412yes—
240C13×C22⋊C4—24no—
241C22⋊Dic13—24no—
242C22⋊Dic13—24no—
243C22⋊Dic13—24no—
244C22⋊Dic13C2×D414yes—
245C22⋊Dic13C2×D414yes—
246#6107—28no—
247#6105—28no—
248C4⋊Dic13—21no—
249C4⋊Dic13—24no—
250C4⋊Dic13—21no—
251C4⋊Dic13—21no—
252C4⋊Dic13—24no—
253C4⋊Dic13—24no—
254C4⋊Dic13—24no—
255C4⋊Dic13—24no—
256C4⋊Dic13C2×D414yes—
257C4⋊Dic13C2×D414yes—
258C4⋊Dic13C2412yes—
259C4⋊Dic13C2412yes—
260C4⋊Dic13C2412yes—
261#6101—24no—
262#6101—24no—
263#6101—24no—
264#6101—24no—
265#6101—24no—
266C4×Dic13—24no—
267C4×Dic13—24no—
268C4×Dic13—24no—
269C4×Dic13—24no—
270C4×Dic13C2×D412yes—
271C4×Dic13C2×D412yes—
272C4×Dic13C2412yes—
273C4×Dic13C2412yes—
274C2×#1055—22no—
275C2×#1055—22no—
276C2×#1055C2412yes—
277C2×#1055C2412yes—
278C2×#541—131no—
279C2×#520—131no—
280#3120—1316no—
281C2×#484—131no—
282C2×#483—131no—
283C2×#479—131no—
284C2×#478—131no—
285C2×#462—131no—
286C2×#461—131no—
287C2×#452—131no—
288C2×#452D1311yescharacteristic
289C2×#441—131no—
290C2×#440—131no—
291C2×C4×Q16—131no—
292C2×C4×SD16—131no—
293C2×#433—131no—
294C23×C13—22no—
295C23×C13—24no—
296C23×C13—22no—
297C23×C13—22no—
298C23×C13—22no—
299C23×C13—42no—
300C23×C13—42no—
301C23×C13C22×D412yes—
302C23×C13C22×D411yescharacteristic
303Q8×C13—24no—
304Q8×C13—22no—
305Q8×C13—22no—
306Q8×C13—22no—
307Q8×C13—42no—
308Q8×C13C2×#4114yes—
309D4×C13—216no—
310D4×C13—24no—
311D4×C13—22no—
312D4×C13C2×#4114yes—
313C2×C4×C13—216no—
314C2×C4×C13—22no—
315C2×C4×C13—24no—
316C2×C4×C13—22no—
317C2×C4×C13—24no—
318C2×C4×C13—22no—
319C2×C4×C13—22no—
320C2×C4×C13—22no—
321C2×C4×C13—22no—
322C2×C4×C13—42no—
323C2×C4×C13—42no—
324C2×C4×C13C22×D412yes—
325C2×C4×C13C22×D411yescharacteristic
326C2×C4×C13C2×#4112yes—
327C2×C4×C13C2×#4112yes—
328C2×C4×C13C2511yescharacteristic
329C2×Dic13—22no—
330C2×Dic13—22no—
331C2×Dic13—22no—
332C2×Dic13—22no—
333C2×Dic13—22no—
334C2×Dic13—22no—
335C2×Dic13—22no—
336C2×Dic13—22no—
337C2×Dic13—42no—
338C2×Dic13—42no—
339C2×Dic13—42no—
340C2×Dic13—42no—
341C2×Dic13—84no—
342C2×Dic13—84no—
343C2×Dic13—84no—
344C2×Dic13C22×D412yes—
345C2×Dic13C22×D412yes—
346C2×Dic13C22×D412yes—
347C2×Dic13C22×D412yes—
348Dic26—22no—
349Dic26—22no—
350Dic26—42no—
351C8×C13—22no—
352C8×C13—22no—
353#1055—22no—
354#1055—22no—
355C22×#41C2×D1311yescharacteristic
356C22×Q16—131no—
357C22×Q16C2×D1311yescharacteristic
358C22×SD16—131no—
359C22×SD16C2×D1311yescharacteristic
360#541—138no—
361#541—264no—
362C2×C4⋊Q8—131no—
363C2×#126—261no—
364C2×#126—261no—
365C2×#125—131no—
366C2×#125—261no—
367C2×#125—261no—
368C2×C22⋊Q8—131no—
369C2×C22⋊Q8C2×D1311yescharacteristic
370#520—138no—
371#520—264no—
372C2×C4×Q8—131no—
373C2×C4×Q8—131no—
374C2×C4×Q8—131no—
375C2×C4×Q8—131no—
376C2×C4×D4—131no—
377C2×C4×D4—131no—
378C2×C4×D4—261no—
379C2×C4×D4—261no—
380C2×#117—131no—
381C2×#117—261no—
382C22×C4⋊C4—131no—
383C22×C4⋊C4—261no—
384#484—138no—
385#483—138no—
386#479—138no—
387#478—138no—
388#462—138no—
389#461—138no—
390#452—138no—
391#452C2×D1318yes—
392#441—138no—
393#440—138no—
394C4×Q16—138no—
395C4×SD16—138no—
396#433—138no—
397C2×#107—131no—
398C2×#107—131no—
399C2×#106—131no—
400C2×#106—131no—
401C2×C4⋊C8—131no—
402C2×C4⋊C8—131no—
403C2×#103—131no—
404C2×#103—131no—
405C2×#103—131no—
406C2×#103—131no—
407C2×#103—131no—
408C2×#103C2×D1311yescharacteristic
409C2×#102—131no—
410C2×#102C2×D1311yescharacteristic
411C2×C22⋊C8—131no—
412C2×C22⋊C8C2×D1311yescharacteristic
413C2×#97—131no—
414C2×C4×C8—131no—
415C22×C13—22no—
416C22×C13—24no—
417C22×C13—22no—
418C22×C13—22no—
419C22×C13—44no—
420C22×C13—48no—
421C22×C13—42no—
422C22×C13—42no—
423C22×C13#52512yes—
424C22×C13#57712yes—
425C22×C13#57812yes—
426C22×C13C23×D411yescharacteristic
427C4×C13—22no—
428C4×C13—24no—
429C4×C13—42no—
430C4×C13—42no—
431C4×C13#52512yes—
432C4×C13C22×#4111yescharacteristic
433C4×C13C22×#4111yescharacteristic
434Dic13—22no—
435Dic13—22no—
436Dic13—22no—
437Dic13—22no—
438Dic13—42no—
439Dic13—42no—
440Dic13—42no—
441Dic13—42no—
442C2×#41—24no—
443C2×#41—24no—
444C2×#41—22no—
445C2×#41C22×D1314yes—
446C22×Q8—131no—
447C22×Q8C22×D1311yescharacteristic
448C22×Q8C22×D1311yescharacteristic
449C22×D4—21no—
450C22×D4C22×D1311yescharacteristic
451C23×C4—21no—
452C23×C4—261no—
453C23×C4—261no—
454C23×C4—261no—
455C23×C4C22×D1311yescharacteristic
456C2×Q16—24no—
457C2×Q16—134no—
458C2×Q16—264no—
459C2×Q16C22×D1314yes—
460C2×SD16—24no—
461C2×SD16—134no—
462C2×SD16—264no—
463C2×SD16C22×D1314yes—
464C22×C8—131no—
465C22×C8—131no—
466C22×C8C22×D1311yescharacteristic
467C22×C8C22×D1311yescharacteristic
468C4⋊Q8—134no—
469C4⋊Q8—262no—
470#126—268no—
471#126—268no—
472#125—134no—
473#125—262no—
474#125—268no—
475#125—268no—
476C22⋊Q8—22no—
477C22⋊Q8—134no—
478C22⋊Q8—262no—
479C22⋊Q8C22×D1314yes—
480C4×Q8—134no—
481C4×Q8—134no—
482C4×Q8—134no—
483C4×Q8—134no—
484C4×Q8—262no—
485C4×Q8—262no—
486C4×Q8—262no—
487C4×Q8—262no—
488C4×D4—134no—
489C4×D4—134no—
490C4×D4—262no—
491C4×D4—262no—
492C4×D4—268no—
493C4×D4—268no—
494#117—134no—
495#117—134no—
496#117—268no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—131no—
499C2×C4⋊C4—131no—
500C2×C4⋊C4—131no—
501C2×C4⋊C4—131no—
502C2×C4⋊C4—134no—
503C2×C4⋊C4—131no—
504C2×C4⋊C4—268no—
505C2×C4⋊C4—261no—
506C2×C4⋊C4—261no—
507C2×C4⋊C4—261no—
508C2×C4⋊C4—261no—
509C2×C4⋊C4—261no—
510C2×C4⋊C4—261no—
511C2×C4⋊C4—261no—
512C2×C4⋊C4—261no—
513C2×C4⋊C4—261no—
514C2×C4⋊C4—262no—
515C2×C4⋊C4—261no—
516C2×C4⋊C4C22×D1311yescharacteristic
517C2×C22⋊C4—21no—
518C2×C22⋊C4—131no—
519C2×C22⋊C4—131no—
520C2×C22⋊C4—261no—
521C2×C22⋊C4—261no—
522C2×C22⋊C4—261no—
523C2×C42—131no—
524C2×C42—131no—
525C2×C42—261no—
526C2×C42—261no—
527C2×C42—261no—
528C2×C42—261no—
529#107—134no—
530#107—134no—
531#106—134no—
532#106—134no—
533C4⋊C8—134no—
534C4⋊C8—134no—
535#103—134no—
536#103—134no—
537#103—134no—
538#103—134no—
539#103—134no—
540#103C22×D1314yes—
541#102—134no—
542#102C22×D1314yes—
543C22⋊C8—134no—
544C22⋊C8C22×D1314yes—
545#97—134no—
546C4×C8—134no—
547C2×C13—42no—
548C2×C13—44no—
549C2×C13#312014yescomplemented
550C2×C13C2×#52511yescharacteristic
551C2×C13C2×#57711yescharacteristic
552C2×C13C2×#57811yescharacteristic
553C24—21no—
554C24D4×D1311yescharacteristic
555#41—216no—
556#41—28no—
557#41—28no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—22no—
561C2×Q8—22no—
562C2×Q8—22no—
563C2×Q8—132no—
564C2×Q8—261no—
565C2×Q8—262no—
566C2×Q8—262no—
567C2×Q8#612914yes—
568C2×Q8C23×D1312yes—
569C2×Q8C23×D1312yes—
570C2×D4—28no—
571C2×D4—24no—
572C2×D4—21no—
573C2×D4—22no—
574C2×D4#612914yes—
575C2×D4C23×D1312yes—
576C22×C4—28no—
577C22×C4—21no—
578C22×C4—24no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—131no—
584C22×C4—131no—
585C22×C4—131no—
586C22×C4—131no—
587C22×C4—264no—
588C22×C4—264no—
589C22×C4—261no—
590C22×C4—261no—
591C22×C4—261no—
592C22×C4—261no—
593C22×C4—264no—
594C22×C4—1042no—
595C22×C4—1042no—
596C22×C4—1042no—
597C22×C4D4×D1312yes—
598C22×C4D4×D1311yescharacteristic
599C22×C4C23×D1312yes—
600C22×C4C23×D1311yescharacteristic
601Q16—28no—
602Q16—268no—
603SD16—28no—
604SD16—268no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—132no—
608C2×C8—132no—
609C2×C8—262no—
610C2×C8—262no—
611C2×C8C23×D1312yes—
612C2×C8C23×D1312yes—
613C4⋊C4—24no—
614C4⋊C4—21no—
615C4⋊C4—134no—
616C4⋊C4—134no—
617C4⋊C4—132no—
618C4⋊C4—132no—
619C4⋊C4—132no—
620C4⋊C4—264no—
621C4⋊C4—264no—
622C4⋊C4—264no—
623C4⋊C4—264no—
624C4⋊C4—264no—
625C4⋊C4—264no—
626C4⋊C4—264no—
627C4⋊C4—264no—
628C4⋊C4—264no—
629C4⋊C4—261no—
630C4⋊C4—261no—
631C4⋊C4—261no—
632C4⋊C4—264no—
633C4⋊C4C23×D1312yes—
634C22⋊C4—24no—
635C22⋊C4—134no—
636C22⋊C4—134no—
637C22⋊C4—264no—
638C22⋊C4—264no—
639C22⋊C4—264no—
640C42—132no—
641C42—132no—
642C42—132no—
643C42—132no—
644C42—264no—
645C42—264no—
646C42—264no—
647C42—264no—
648C13C2×#312011yescharacteristic, complemented, Sylow
649C23—22no—
650C23—22no—
651C23—22no—
652C23—24no—
653C23—22no—
654C23—42no—
655C23—42no—
656C23C2×D4×D1312yes—
657C23C2×D4×D1311yescharacteristic
658Q8—24no—
659Q8—22no—
660Q8—22no—
661Q8—22no—
662Q8—42no—
663Q8—262no—
664Q8—262no—
665Q8—522no—
666Q8C2×#612914yes—
667D4—216no—
668D4—24no—
669D4—22no—
670D4C2×#612914yes—
671C2×C4—216no—
672C2×C4—22no—
673C2×C4—24no—
674C2×C4—22no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—132no—
683C2×C4—132no—
684C2×C4—132no—
685C2×C4—132no—
686C2×C4—262no—
687C2×C4—262no—
688C2×C4—262no—
689C2×C4—262no—
690C2×C4—262no—
691C2×C4—262no—
692C2×C4—262no—
693C2×C4—262no—
694C2×C4—522no—
695C2×C4—522no—
696C2×C4—522no—
697C2×C4—522no—
698C2×C4—1044no—
699C2×C4—1044no—
700C2×C4—1044no—
701C2×C4C2×D4×D1312yes—
702C2×C4C2×D4×D1311yescharacteristic
703C2×C4C2×#612912yes—
704C2×C4C2×#612912yes—
705C2×C4C24×D1311yescharacteristic
706C8—22no—
707C8—22no—
708C8—262no—
709C8—262no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—24no—
714C22—42no—
715C22—42no—
716C22—44no—
717C22—48no—
718C22#1171929112yes—
719C22#1171947612yes—
720C22#1171948312yes—
721C22C22×D4×D1311yescharacteristic
722C4—22no—
723C4—24no—
724C4—42no—
725C4—42no—
726C4—262no—
727C4—262no—
728C4—262no—
729C4—262no—
730C4—522no—
731C4—522no—
732C4—522no—
733C4—522no—
734C4#1171929112yes—
735C4C22×#612911yescharacteristic
736C4C22×#612911yescharacteristic
737C2—42no—
738C2—44no—
739C2#1312505114yesdirect product factor
740C2C2×#1171929111yescharacteristic
741C2C2×#1171948311yescharacteristic
742C2C2×#1171947611yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#452C2
socleC23×C13C22×D4
prime radicalC22×C13×#41C22
hypercenterC2×#452D13
hypocenterC13C2×#3120
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C2×#11719330C2semidirect
3. #13125051C2direct (N × H)
4. C2×#11718383C2semidirect
5. C2×#11718704C2semidirect
6. C2×#11718457C2semidirect
7. C2×#11718427C2semidirect
8. C2×#11718843C2semidirect
9. C2×#11718823C2semidirect
11. C2×#11718450C2semidirect
12. C2×#11718825C2semidirect
13. C2×Q16×Dic13C2semidirect
14. C2×#11718419C2semidirect
15. C2×#11718381C2semidirect
39. #11719330C22semidirect
56. Q16×Dic13C22semidirect
57. #11718843C22semidirect
58. #11718825C22semidirect
59. #11718823C22semidirect
68. #11718704C22semidirect
71. #11718457C22semidirect
72. #11718450C22semidirect
73. #11718427C22semidirect
74. #11718419C22semidirect
75. #11718383C22semidirect
76. #11718381C22semidirect
549. C2×C13#3120semidirect
648. C13C2×#3120semidirect
739. C2#13125051direct (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×#117195322
#131250512
C2×#117183832
C2×#117187042
C2×#117184572
C2×#117184272
C2×#117188432
C2×#117188232
C2×#117189002
C2×#117184502
C2×#117188252
C2×Q16×Dic132
C2×#117184192
C2×#117183812
C2×C13×#4522
C2×#312013