Finite Group Databasebeta

← C2×#13127323 #16741500

Subgroups — C2×#13127323 #16741500

Order 3328.

1942 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×#11719248C211yesmaximal, characteristic, complemented
2C2×#11719270C211yesmaximal, characteristic
3#13127323C2116yesmaximal, direct product factor
4C2×#11718363C211yesmaximal, characteristic, complemented
5C2×#11718383C211yesmaximal, characteristic, complemented
6C2×#11718396C211yesmaximal, characteristic, complemented
7C2×#11718384C211yesmaximal, characteristic, complemented
8C2×#11718397C211yesmaximal, characteristic, complemented
9C2×#11718490C211yesmaximal, characteristic, complemented
10C2×#11718507C211yesmaximal, characteristic, complemented
11C2×#11718795C211yesmaximal, characteristic, complemented
12C2×#11718775C211yesmaximal, characteristic, complemented
13C2×#11718371C211yesmaximal, characteristic, complemented
14C2×#11718782C211yesmaximal, characteristic, complemented
15C22×#88058C211yesmaximal, characteristic, complemented
16C2×C13×#435C211yesmaximal, characteristic, complemented
17C22×C13×M16C2211yescharacteristic
18C23×C8×C13C2211yescharacteristic
19C2×C4×D4×C13C2211yescharacteristic
20C2×#88193—21no—
21C2×D4×Dic13—21no—
22C2×#88184C2211yescharacteristic
23C2×#88184C2211yescharacteristic
24C2×#88180C2211yescharacteristic
25C22×C4⋊Dic13C2211yescharacteristic
26C22×C4⋊Dic13C2211yescharacteristic
27C22×C4⋊Dic13C2211yescharacteristic
28C2×#88178C2211yescharacteristic
29C2×#88178C2211yescharacteristic
30C22×#6095C2211yescharacteristic
31#11719270—24no—
32#11719270C2218yes—
33#11719248—24no—
34#11719248C2218yescomplemented
35C2×#88152—21no—
36C2×#88144—21no—
37C2×#88137—21no—
38C2×#88135—21no—
39C2×#88132—21no—
40C2×#88132—21no—
41C2×C4×D52C2211yescharacteristic
42C2×#88124C2211yescharacteristic
43C2×#88123C2211yescharacteristic
44C2×C4×Dic26C2211yescharacteristic
45C13×#435C2218yescomplemented
46C2×C13×C4⋊C8C2211yescharacteristic
47C2×C13×C22⋊C8C2211yescharacteristic
48C2×C13×C22⋊C8C2211yescharacteristic
49C2×C13×#97C2211yescharacteristic
50#11718795C2218yescomplemented
51#11718782C2218yescomplemented
52#11718775C2218yescomplemented
53C2×#88061C2211yescharacteristic
54C2×#88061C2211yescharacteristic
55C2×#88061C2211yescharacteristic
56C2×#88058C2211yescharacteristic
57C2×#88058C2211yescharacteristic
58C2×#88058C2211yescharacteristic
59C2×#88058C2211yescharacteristic
60C2×#88058C2211yescharacteristic
61C2×#88058C2211yescharacteristic
62C2×#88058C2218yescomplemented
63C2×#88057C2211yescharacteristic
64C2×#88057C2211yescharacteristic
65C2×#88057C2211yescharacteristic
66C2×#88056C2211yescharacteristic
67C2×#88056C2211yescharacteristic
68C2×#88056C2211yescharacteristic
69#11718507C2218yescomplemented
70#11718490C2218yescomplemented
71#11718397C2218yescomplemented
72#11718396C2218yescomplemented
73#11718384C2218yescomplemented
74#11718383C2218yescomplemented
75#11718371C2218yescomplemented
76#11718363C2218yescomplemented
77C22×D4×C13D411yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C23×C4×C13C2311yescharacteristic
80C22×C22⋊D13—21no—
81C22×C22⋊D13—21no—
82C23×Dic13—21no—
83C23×Dic13—21no—
84C23×Dic13—21no—
85C22×D52C2311yescharacteristic
86C22×C4×D13—21no—
87C22×Dic26—21no—
88C22×Dic26C2311yescharacteristic
89C2×C13×M16—24no—
90C2×C13×M16C2314yes—
91C22×C8×C13—24no—
92C22×C8×C13C2311yescharacteristic
93C22×C8×C13C2311yescharacteristic
94C22×C8×C13C2311yescharacteristic
95C22×C8×C13C2314yes—
96C22×C8×C13C2311yescharacteristic
97C4×D4×C13D414yes—
98C4×D4×C13C2314yes—
99C2×C13×C4⋊C4D411yescharacteristic
100C2×C13×C22⋊C4D411yescharacteristic
101C2×C13×C22⋊C4D411yescharacteristic
102C2×C42×C13C2311yescharacteristic
103C2×C22⋊Dic13—21no—
104C2×C22⋊Dic13—21no—
105C2×C22⋊Dic13—21no—
106#88193—28no—
107D4×Dic13—28no—
108#88184—22no—
109#88184—22no—
110#88184C2314yes—
111#88184C2314yes—
112C2×#6103—21no—
113C2×#6103—21no—
114C2×#6103—21no—
115#88180—22no—
116#88180C2314yes—
117C2×C4⋊Dic13—21no—
118C2×C4⋊Dic13—21no—
119C2×C4⋊Dic13—21no—
120C2×C4⋊Dic13—21no—
121C2×C4⋊Dic13—22no—
122C2×C4⋊Dic13—22no—
123C2×C4⋊Dic13—22no—
124C2×C4⋊Dic13C2311yescharacteristic
125C2×C4⋊Dic13C2311yescharacteristic
126C2×C4⋊Dic13C2311yescharacteristic
127C2×C4⋊Dic13C2311yescharacteristic
128C2×C4⋊Dic13C2311yescharacteristic
129C2×C4⋊Dic13C2311yescharacteristic
130C2×C4⋊Dic13C2314yes—
131C2×C4⋊Dic13C2314yes—
132C2×C4⋊Dic13C2314yes—
133#88178—22no—
134#88178—22no—
135#88178C2314yes—
136#88178C2314yes—
137C2×#6101—21no—
138C2×#6101—21no—
139C2×#6101—21no—
140C2×#6101—21no—
141C2×#6101—21no—
142C2×C4×Dic13—21no—
143C2×C4×Dic13—21no—
144C2×#6095—24no—
145C2×#6095C2314yes—
146#88152—28no—
147#88144—28no—
148#88137—28no—
149#88135—28no—
150#88132—28no—
151#88132—28no—
152C4×D52—22no—
153C4×D52C2314yes—
154#88124—22no—
155#88124C2314yes—
156#88123—22no—
157#88123C2314yes—
158C4×Dic26—22no—
159C4×Dic26C2314yes—
160C13×C4⋊C8C2314yes—
161C13×C22⋊C8C2314yes—
162C13×C22⋊C8C2314yes—
163C13×#97C2314yes—
164#88061C2314yes—
165#88061C2314yes—
166#88061C2314yes—
167#88058C2314yes—
168#88058C2314yes—
169#88058C2314yes—
170#88058C2314yes—
171#88058C2314yes—
172#88058C2314yes—
173#88057C2314yes—
174#88057C2314yes—
175#88057C2314yes—
176#88056C2314yes—
177#88056C2314yes—
178#88056C2314yes—
179C2×#3346—131nomaximal, Sylow
180C24×C13C2×D411yescharacteristic
181C24×C13C2×D411yescharacteristic
182C23×D13—21no—
183C2×D4×C13—24no—
184C2×D4×C13C2×D414yes—
185C22×C4×C13—22no—
186C22×C4×C13—22no—
187C22×C4×C13—22no—
188C22×C4×C13—22no—
189C22×C4×C13C2×D411yescharacteristic
190C22×C4×C13C2×D411yescharacteristic
191C22×C4×C13C2×D411yescharacteristic
192C22×C4×C13C2×D411yescharacteristic
193C22×C4×C13C2×D412yes—
194C22×C4×C13C2×D412yes—
195C22×C4×C13C2412yes—
196C22×C4×C13C2412yes—
197C22×C4×C13C2411yescharacteristic
198C2×C22⋊D13—24no—
199C2×C22⋊D13—24no—
200C2×C22⋊D13—44no—
201C2×C22⋊D13—82no—
202C22×Dic13—21no—
203C22×Dic13—21no—
204C22×Dic13—21no—
205C22×Dic13—21no—
206C22×Dic13—21no—
207C22×Dic13—21no—
208C22×Dic13—21no—
209C22×Dic13—24no—
210C22×Dic13—24no—
211C22×Dic13—24no—
212C22×Dic13—82no—
213C22×Dic13—82no—
214C22×Dic13—82no—
215C2×D52—22no—
216C2×D52—22no—
217C2×D52—21no—
218C2×D52C2412yes—
219C2×C4×D13—24no—
220C2×C4×D13—82no—
221C2×Dic26—22no—
222C2×Dic26—22no—
223C2×Dic26—21no—
224C2×Dic26—24no—
225C2×Dic26—82no—
226C2×Dic26C2412yes—
227C13×M16—28no—
228C2×C8×C13—22no—
229C2×C8×C13—22no—
230C2×C8×C13—22no—
231C2×C8×C13—28no—
232C2×C8×C13#4114yes—
233C2×C8×C13C2412yes—
234C2×C8×C13C2412yes—
235C2×C8×C13C2412yes—
236C2×C8×C13C2412yes—
237C13×C4⋊C4C2×D414yes—
238C13×C22⋊C4C2×D414yes—
239C13×C22⋊C4C2×D414yes—
240C42×C13C2×D412yes—
241C42×C13C2412yes—
242C22⋊Dic13—24no—
243C22⋊Dic13—24no—
244C22⋊Dic13—24no—
245#6103—24no—
246#6103—24no—
247#6103—24no—
248C4⋊Dic13—21no—
249C4⋊Dic13—21no—
250C4⋊Dic13—21no—
251C4⋊Dic13—24no—
252C4⋊Dic13—21no—
253C4⋊Dic13—21no—
254C4⋊Dic13—21no—
255C4⋊Dic13—24no—
256C4⋊Dic13—24no—
257C4⋊Dic13—24no—
258C4⋊Dic13C2412yes—
259C4⋊Dic13C2412yes—
260C4⋊Dic13C2412yes—
261C4⋊Dic13C2412yes—
262C4⋊Dic13C2412yes—
263C4⋊Dic13C2412yes—
264#6101—24no—
265#6101—24no—
266#6101—24no—
267#6101—24no—
268#6101—24no—
269C4×Dic13—24no—
270C4×Dic13—24no—
271#6095—28no—
272C2×#554—131no—
273C2×#553—131no—
274#3346—1316no—
275C2×#501—131no—
276C2×#484—131no—
277C2×#481—131no—
278C2×#485—131no—
279C2×#480—131no—
280C2×#479—131no—
281C2×#474—131no—
282C2×#468—131no—
283C2×#465—131no—
284C2×#440—131no—
285C2×#435D1311yescharacteristic, complemented
286C2×#428—131no—
287C22×#107—131no—
288C23×C13—22no—
289C23×C13—22no—
290C23×C13—22no—
291C23×C13—22no—
292C23×C13—22no—
293C23×C13#13714yes—
294C23×C13C22×D412yes—
295C23×C13C22×D412yes—
296C23×C13C22×D411yescharacteristic
297C22×D13—22no—
298C22×D13—42no—
299C22×D13—42no—
300C22×D13—42no—
301D4×C13—28no—
302C2×C4×C13—22no—
303C2×C4×C13—22no—
304C2×C4×C13—22no—
305C2×C4×C13—22no—
306C2×C4×C13—24no—
307C2×C4×C13—24no—
308C2×C4×C13—22no—
309C2×C4×C13—22no—
310C2×C4×C13—22no—
311C2×C4×C13—22no—
312C2×C4×C13C22×D412yes—
313C2×C4×C13C22×D412yes—
314C2×C4×C13C22×D412yes—
315C2×C4×C13C22×D412yes—
316C2×C4×C13C22×D411yescharacteristic
317C2×C4×C13C2×#4112yes—
318C2×C4×C132−1+412yes—
319C2×C4×C13C2511yescharacteristic
320C22⋊D13—48no—
321C22⋊D13—84no—
322C2×Dic13—22no—
323C2×Dic13—22no—
324C2×Dic13—22no—
325C2×Dic13—22no—
326C2×Dic13—22no—
327C2×Dic13—22no—
328C2×Dic13—22no—
329C2×Dic13—42no—
330C2×Dic13—42no—
331C2×Dic13—42no—
332C2×Dic13—42no—
333C2×Dic13—42no—
334C2×Dic13—42no—
335C2×Dic13—42no—
336C2×Dic13—84no—
337C2×Dic13—84no—
338C2×Dic13—84no—
339D52—22no—
340D52—22no—
341D52—42no—
342C4×D13—84no—
343Dic26—22no—
344Dic26—22no—
345Dic26—42no—
346Dic26—84no—
347C8×C13—22no—
348C8×C13—22no—
349C8×C13—22no—
350C8×C13C2×#4114yes—
351C22×SD16—131no—
352C22×M16C2×D1311yescharacteristic
353C23×C8C2×D1311yescharacteristic
354#554—138no—
355#554—264no—
356#553—138no—
357#553—264no—
358C2×C4⋊Q8—131no—
359C2×#126—261no—
360C2×#125—131no—
361C2×#125—261no—
362C2×#123—261no—
363C2×C22⋊Q8—131no—
364C2×C22⋊Q8—131no—
365C2×C22⋊Q8—261no—
366C2×C22⋊Q8—261no—
367C2×#121—131no—
368C2×#121—131no—
369C2×#121—261no—
370C2×C4×Q8—131no—
371C2×C4×D4—131no—
372C2×C4×D4—261no—
373C2×C4×D4—261no—
374C2×C4×D4C2×D1311yescharacteristic
375C2×#117—131no—
376C22×C4⋊C4—131no—
377C22×C4⋊C4—131no—
378C22×C4⋊C4—131no—
379#501—138no—
380#485—138no—
381#484—138no—
382#481—138no—
383#480—138no—
384#479—138no—
385#474—138no—
386#468—138no—
387#465—138no—
388#440—138no—
389#435C2×D1318yescomplemented
390#428—138no—
391C2×#107—131no—
392C2×#107—131no—
393C2×#107—131no—
394C2×#107—131no—
395C2×#107—138no—
396C2×#107—131no—
397C2×#107—131no—
398C2×#106—131no—
399C2×#106—131no—
400C2×#106—131no—
401C2×C4⋊C8C2×D1311yescharacteristic
402C2×#103—131no—
403C2×#103—131no—
404C2×#103—131no—
405C2×#102—131no—
406C2×#102—131no—
407C2×#102—131no—
408C2×C22⋊C8C2×D1311yescharacteristic
409C2×C22⋊C8C2×D1311yescharacteristic
410C2×#97C2×D1311yescharacteristic
411C22×C13—28no—
412C22×C13—22no—
413C22×C13—22no—
414C22×C13—22no—
415C22×C13—22no—
416C22×C13—22no—
417C22×C13—44no—
418C22×C13#54712yes—
419C22×C13C2×#13714yes—
420C22×C13C2×#13712yes—
421C22×C13#57612yes—
422C22×C13C23×D411yescharacteristic
423C2×D13—42no—
424C2×D13—42no—
425C2×D13—42no—
426C2×D13—84no—
427C4×C13—22no—
428C4×C13—22no—
429C4×C13—22no—
430C4×C13—22no—
431C4×C13#54712yes—
432C4×C13C22×#4111yescharacteristic
433C4×C13C2×2−1+411yescharacteristic
434Dic13—42no—
435Dic13—42no—
436Dic13—42no—
437Dic13—42no—
438Dic13—42no—
439Dic13—42no—
440Dic13—42no—
441C22×Q8—131no—
442C22×Q8—261no—
443C22×D4—131no—
444C22×D4—261no—
445C22×D4—261no—
446C22×D4D5211yescharacteristic
447C23×C4—261no—
448C23×C4—261no—
449C23×C4—261no—
450C23×C4—261no—
451C23×C4C22×D1311yescharacteristic
452C23×C4C22×D1311yescharacteristic
453C2×SD16—134no—
454C2×SD16—264no—
455C2×M16—24no—
456C2×M16C22×D1314yes—
457C22×C8—24no—
458C22×C8C22×D1311yescharacteristic
459C22×C8C22×D1314yes—
460C22×C8C22×D1311yescharacteristic
461C22×C8C22×D1311yescharacteristic
462C22×C8C22×D1311yescharacteristic
463C4⋊Q8—134no—
464C4⋊Q8—262no—
465#126—268no—
466#125—134no—
467#125—268no—
468#125—262no—
469#123—268no—
470C22⋊Q8—134no—
471C22⋊Q8—134no—
472C22⋊Q8—262no—
473C22⋊Q8—262no—
474C22⋊Q8—268no—
475C22⋊Q8—268no—
476#121—134no—
477#121—134no—
478#121—268no—
479#121—262no—
480#121—262no—
481C4×Q8—134no—
482C4×Q8—262no—
483C4×D4—134no—
484C4×D4—268no—
485C4×D4—268no—
486C4×D4—262no—
487C4×D4D5214yes—
488C4×D4C22×D1314yes—
489#117—134no—
490#117—262no—
491C2×C4⋊C4—131no—
492C2×C4⋊C4—131no—
493C2×C4⋊C4—131no—
494C2×C4⋊C4—131no—
495C2×C4⋊C4—131no—
496C2×C4⋊C4—134no—
497C2×C4⋊C4—134no—
498C2×C4⋊C4—134no—
499C2×C4⋊C4—131no—
500C2×C4⋊C4—261no—
501C2×C4⋊C4—261no—
502C2×C4⋊C4—261no—
503C2×C4⋊C4—262no—
504C2×C4⋊C4—262no—
505C2×C4⋊C4—262no—
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⋊C4D5211yescharacteristic
513C2×C22⋊C4—261no—
514C2×C22⋊C4—261no—
515C2×C22⋊C4—261no—
516C2×C22⋊C4—261no—
517C2×C22⋊C4—261no—
518C2×C22⋊C4—261no—
519C2×C22⋊C4D5211yescharacteristic
520C2×C22⋊C4D5211yescharacteristic
521C2×C42—261no—
522C2×C42—261no—
523C2×C42C22×D1311yescharacteristic
524#107—134no—
525#107—134no—
526#107—134no—
527#107—134no—
528#107—134no—
529#107—134no—
530#106—134no—
531#106—134no—
532#106—134no—
533C4⋊C8C22×D1314yes—
534#103—134no—
535#103—134no—
536#103—134no—
537#102—134no—
538#102—134no—
539#102—134no—
540C22⋊C8C22×D1314yes—
541C22⋊C8C22×D1314yes—
542#97C22×D1314yes—
543C2×C13—24no—
544C2×C13—42no—
545C2×C13#334614yescomplemented
546C2×C13C2×#54711yescharacteristic
547C2×C13C22×#13711yescharacteristic
548C2×C13C2×#57611yescharacteristic
549D13—82no—
550C24—261no—
551C24C2×D5211yescharacteristic
552C24C2×D5211yescharacteristic
553C2×Q8—132no—
554C2×Q8—261no—
555C2×Q8—264no—
556C2×Q8—262no—
557C2×Q8—262no—
558C2×Q8—1042no—
559C2×D4—24no—
560C2×D4—132no—
561C2×D4—264no—
562C2×D4—264no—
563C2×D4—261no—
564C2×D4—262no—
565C2×D4—262no—
566C2×D4—524no—
567C2×D4—1042no—
568C2×D4C2×D5214yes—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—261no—
574C22×C4—261no—
575C22×C4—261no—
576C22×C4—261no—
577C22×C4—261no—
578C22×C4—261no—
579C22×C4—261no—
580C22×C4—264no—
581C22×C4—264no—
582C22×C4—264no—
583C22×C4—264no—
584C22×C4—1042no—
585C22×C4—1042no—
586C22×C4—1042no—
587C22×C4—1042no—
588C22×C4C2×D5212yes—
589C22×C4C2×D5212yes—
590C22×C4C2×D5211yescharacteristic
591C22×C4C2×D5211yescharacteristic
592C22×C4C2×D5211yescharacteristic
593C22×C4C2×D5211yescharacteristic
594C22×C4C23×D1312yes—
595C22×C4C23×D1312yes—
596C22×C4C23×D1311yescharacteristic
597SD16—268no—
598M16—28no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—28no—
603C2×C8#612914yes—
604C2×C8C23×D1312yes—
605C2×C8C23×D1312yes—
606C2×C8C23×D1312yes—
607C2×C8C23×D1312yes—
608C4⋊C4—132no—
609C4⋊C4—132no—
610C4⋊C4—132no—
611C4⋊C4—132no—
612C4⋊C4—132no—
613C4⋊C4—132no—
614C4⋊C4—261no—
615C4⋊C4—261no—
616C4⋊C4—261no—
617C4⋊C4—264no—
618C4⋊C4—264no—
619C4⋊C4—261no—
620C4⋊C4—261no—
621C4⋊C4—264no—
622C4⋊C4—261no—
623C4⋊C4—264no—
624C4⋊C4—264no—
625C4⋊C4—264no—
626C4⋊C4—264no—
627C4⋊C4—264no—
628C4⋊C4—264no—
629C4⋊C4C2×D5214yes—
630C22⋊C4—264no—
631C22⋊C4—264no—
632C22⋊C4—264no—
633C22⋊C4—264no—
634C22⋊C4—264no—
635C22⋊C4—264no—
636C22⋊C4C2×D5214yes—
637C22⋊C4C2×D5214yes—
638C42—264no—
639C42—264no—
640C42C2×D5212yes—
641C42C23×D1312yes—
642C13C2×#334611yescharacteristic, complemented, Sylow
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—262no—
649C23—522no—
650C23—522no—
651C23—522no—
652C23#8816314yes—
653C23C22×D5212yes—
654C23C22×D5212yes—
655C23C22×D5211yescharacteristic
656Q8—262no—
657Q8—262no—
658Q8—522no—
659Q8—1044no—
660D4—28no—
661D4—262no—
662D4—262no—
663D4—528no—
664D4—522no—
665D4—1044no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—262no—
677C2×C4—262no—
678C2×C4—262no—
679C2×C4—262no—
680C2×C4—262no—
681C2×C4—262no—
682C2×C4—262no—
683C2×C4—522no—
684C2×C4—522no—
685C2×C4—522no—
686C2×C4—522no—
687C2×C4—522no—
688C2×C4—522no—
689C2×C4—522no—
690C2×C4—1044no—
691C2×C4—1044no—
692C2×C4—1044no—
693C2×C4—1044no—
694C2×C4C22×D5212yes—
695C2×C4C22×D5212yes—
696C2×C4C22×D5212yes—
697C2×C4C22×D5212yes—
698C2×C4C22×D5211yescharacteristic
699C2×C4C2×#612912yes—
700C2×C4#8825712yes—
701C2×C4C24×D1311yescharacteristic
702C8—22no—
703C8—22no—
704C8—22no—
705C8C2×#612914yes—
706C22—22no—
707C22—22no—
708C22—28no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—44no—
713C22—522no—
714C22—522no—
715C22—522no—
716C22—1044no—
717C22#1171926012yes—
718C22C2×#8816314yes—
719C22C2×#8816312yes—
720C22#1171945712yes—
721C22C23×D5211yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—522no—
727C4—522no—
728C4—522no—
729C4—522no—
730C4—522no—
731C4—522no—
732C4—522no—
733C4#1171926012yes—
734C4C22×#612911yescharacteristic
735C4C2×#8825711yescharacteristic
736C2—24no—
737C2—42no—
738C2—1042no—
739C2#1312732314yesdirect product factor
740C2C2×#1171926011yescharacteristic
741C2C22×#8816311yescharacteristic
742C2C2×#1171945711yescharacteristic
subgroupG/H
centerC23C22×D52
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#435C2
socleC23×C13C22×D4
prime radicalC2×#11719270C2
hypercenterC2×#435D13
hypocenterC13C2×#3346
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#11719248C2semidirect
3. #13127323C2direct (N × H)
4. C2×#11718363C2semidirect
5. C2×#11718383C2semidirect
6. C2×#11718396C2semidirect
7. C2×#11718384C2semidirect
8. C2×#11718397C2semidirect
9. C2×#11718490C2semidirect
10. C2×#11718507C2semidirect
11. C2×#11718795C2semidirect
12. C2×#11718775C2semidirect
13. C2×#11718371C2semidirect
14. C2×#11718782C2semidirect
15. C22×#88058C2semidirect
16. C2×C13×#435C2semidirect
34. #11719248C22semidirect
45. C13×#435C22semidirect
50. #11718795C22semidirect
51. #11718782C22semidirect
52. #11718775C22semidirect
62. C2×#88058C22semidirect
69. #11718507C22semidirect
70. #11718490C22semidirect
71. #11718397C22semidirect
72. #11718396C22semidirect
73. #11718384C22semidirect
74. #11718383C22semidirect
75. #11718371C22semidirect
76. #11718363C22semidirect
285. C2×#435D13semidirect
389. #435C2×D13semidirect
545. C2×C13#3346semidirect
642. C13C2×#3346semidirect
739. C2#13127323direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192482
C2×#117192702
#131273232
C2×#117183632
C2×#117183832
C2×#117183962
C2×#117183842
C2×#117183972
C2×#117184902
C2×#117185072
C2×#117187952
C2×#117187752
C2×#117183712
C2×#117187822
C22×#880582
C2×C13×#4352
C2×#334613