Finite Group Databasebeta

← C2×#13127321 #16741498

Subgroups — C2×#13127321 #16741498

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
2#13127321C2116yesmaximal, direct product factor
3C2×#11718726C211yesmaximal, characteristic, complemented
4C2×#11718631C211yesmaximal, characteristic, complemented
5C2×#11718695C211yesmaximal, characteristic, complemented
6C2×#11718657C211yesmaximal, characteristic, complemented
7C2×#11718694C211yesmaximal, characteristic, complemented
8C2×#11718724C211yesmaximal, characteristic, complemented
9C2×#11718668C211yesmaximal, characteristic, complemented
10C2×#11718703C211yesmaximal, characteristic, complemented
11C2×#11718702C211yesmaximal, characteristic, complemented
12C2×#11718679C211yesmaximal, characteristic, complemented
13C2×#11718672C211yesmaximal, characteristic, complemented
14C2×#11718656C211yesmaximal, characteristic, complemented
15C22×#88047C211yesmaximal, characteristic, complemented
16C2×C13×#553C211yesmaximal, characteristic
17C13×#553—24no—
18C13×#553C2218yes—
19C2×C13×#126—21no—
20C2×C13×#125C2211yescharacteristic
21C2×C13×#123—21no—
22C2×C13×#121—21no—
23C2×C13×#121C2211yescharacteristic
24C2×C13×#121C2211yescharacteristic
25C2×C4×D4×C13—21no—
26C2×C4×D4×C13C2211yescharacteristic
27C2×C4×D4×C13C2211yescharacteristic
28C2×C13×#117C2211yescharacteristic
29C22×C13×C4⋊C4C2211yescharacteristic
30C2×D4×Dic13—21no—
31C22×#6105C2211yescharacteristic
32C22×C4⋊Dic13C2211yescharacteristic
33C22×C4⋊Dic13C2211yescharacteristic
34C2×#88178C2211yescharacteristic
35C2×#88178C2211yescharacteristic
36C22×#6099C2211yescharacteristic
37C23×#1055C2211yescharacteristic
38#11719248—24no—
39#11719248C2218yescomplemented
40C2×#88144—21no—
41C2×#88132—21no—
42C2×#88132—21no—
43C2×#88123C2211yescharacteristic
44C2×C4×Dic26C2211yescharacteristic
45C2×#88072C2211yescharacteristic
46C2×#88072C2211yescharacteristic
47C2×#88072C2211yescharacteristic
48C2×C22⋊#1055C2211yescharacteristic
49C2×C22⋊#1055C2211yescharacteristic
50#11718726C2218yescomplemented
51#11718724C2218yescomplemented
52#11718703C2218yescomplemented
53#11718702C2218yescomplemented
54#11718695C2218yescomplemented
55#11718694C2218yescomplemented
56#11718679C2218yescomplemented
57#11718672C2218yescomplemented
58#11718668C2218yescomplemented
59#11718657C2218yescomplemented
60#11718656C2218yescomplemented
61#11718631C2218yescomplemented
62C2×#88050C2211yescharacteristic
63C2×#88050C2211yescharacteristic
64C2×#88050C2211yescharacteristic
65C2×#88048C2211yescharacteristic
66C2×#88048C2211yescharacteristic
67C2×#88048C2211yescharacteristic
68C2×#88047C2211yescharacteristic
69C2×#88047C2211yescharacteristic
70C2×#88047C2211yescharacteristic
71C2×#88047C2211yescharacteristic
72C2×#88047C2211yescharacteristic
73C2×#88047C2211yescharacteristic
74C2×#88047C2218yescomplemented
75C2×C4⋊#1055C2211yescharacteristic
76C2×#88043C2211yescharacteristic
77C22×D4×C13—21no—
78C22×D4×C13—21no—
79C22×D4×C13D411yescharacteristic
80C22×D4×C13C2311yescharacteristic
81C23×C4×C13—21no—
82C23×C4×C13—21no—
83C23×C4×C13C2311yescharacteristic
84C23×C4×C13C2311yescharacteristic
85C23×Dic13—21no—
86C23×Dic13—21no—
87C22×Dic26—21no—
88C22×Dic26C2311yescharacteristic
89C13×#126—28no—
90C13×#125—22no—
91C13×#125C2314yes—
92C13×#123—28no—
93C13×#121—28no—
94C13×#121—22no—
95C13×#121—22no—
96C13×#121C2314yes—
97C13×#121C2314yes—
98C4×D4×C13—28no—
99C4×D4×C13—22no—
100C4×D4×C13D414yes—
101C4×D4×C13C2314yes—
102C4×D4×C13C2314yes—
103C13×#117—22no—
104C13×#117C2314yes—
105C2×C13×C4⋊C4—21no—
106C2×C13×C4⋊C4—22no—
107C2×C13×C4⋊C4—21no—
108C2×C13×C4⋊C4—21no—
109C2×C13×C4⋊C4D411yescharacteristic
110C2×C13×C4⋊C4C2311yescharacteristic
111C2×C13×C4⋊C4C2311yescharacteristic
112C2×C13×C4⋊C4C2314yes—
113C2×C13×C4⋊C4C2311yescharacteristic
114C2×C13×C22⋊C4—21no—
115C2×C13×C22⋊C4—21no—
116C2×C13×C22⋊C4—21no—
117C2×C13×C22⋊C4—21no—
118C2×C13×C22⋊C4D411yescharacteristic
119C2×C13×C22⋊C4D411yescharacteristic
120C2×C42×C13—21no—
121C2×C42×C13C2311yescharacteristic
122C2×C22⋊Dic13—21no—
123C2×C22⋊Dic13—21no—
124D4×Dic13—28no—
125C2×#6105—24no—
126C2×#6105C2314yes—
127C2×C4⋊Dic13—21no—
128C2×C4⋊Dic13—21no—
129C2×C4⋊Dic13—21no—
130C2×C4⋊Dic13—22no—
131C2×C4⋊Dic13—22no—
132C2×C4⋊Dic13C2314yes—
133C2×C4⋊Dic13C2311yescharacteristic
134C2×C4⋊Dic13C2311yescharacteristic
135C2×C4⋊Dic13C2311yescharacteristic
136C2×C4⋊Dic13C2314yes—
137#88178—22no—
138#88178—22no—
139#88178C2314yes—
140#88178C2314yes—
141C2×#6101—21no—
142C2×#6101—21no—
143C2×#6101—21no—
144C2×C4×Dic13—21no—
145C2×#6099—24no—
146C2×#6099C2314yes—
147C22×#1055—24no—
148C22×#1055C2314yes—
149C22×#1055C2311yescharacteristic
150C22×#1055C2311yescharacteristic
151C22×#1055C2311yescharacteristic
152C22×#1055C2311yescharacteristic
153#88144—28no—
154#88132—28no—
155#88132—28no—
156#88123—22no—
157#88123C2314yes—
158C4×Dic26—22no—
159C4×Dic26C2314yes—
160#88072C2314yes—
161#88072C2314yes—
162#88072C2314yes—
163C22⋊#1055C2314yes—
164C22⋊#1055C2314yes—
165#88050C2314yes—
166#88050C2314yes—
167#88050C2314yes—
168#88048C2314yes—
169#88048C2314yes—
170#88048C2314yes—
171#88047C2314yes—
172#88047C2314yes—
173#88047C2314yes—
174#88047C2314yes—
175#88047C2314yes—
176#88047C2314yes—
177C4⋊#1055C2314yes—
178#88043C2314yes—
179C2×#3346—131nomaximal, Sylow
180C24×C13—21no—
181C24×C13C2×D411yescharacteristic
182C24×C13C2×D411yescharacteristic
183C2×D4×C13—24no—
184C2×D4×C13—24no—
185C2×D4×C13—24no—
186C2×D4×C13—21no—
187C2×D4×C13—22no—
188C2×D4×C13—22no—
189C2×D4×C13—44no—
190C2×D4×C13—82no—
191C2×D4×C13C2×D414yes—
192C2×D4×C13C2412yes—
193C22×C4×C13—22no—
194C22×C4×C13—22no—
195C22×C4×C13—22no—
196C22×C4×C13—22no—
197C22×C4×C13—21no—
198C22×C4×C13—21no—
199C22×C4×C13—21no—
200C22×C4×C13—24no—
201C22×C4×C13—24no—
202C22×C4×C13—82no—
203C22×C4×C13—82no—
204C22×C4×C13C2×D411yescharacteristic
205C22×C4×C13C2×D411yescharacteristic
206C22×C4×C13C2×D411yescharacteristic
207C22×C4×C13C2×D411yescharacteristic
208C22×C4×C13C2×D412yes—
209C22×C4×C13C2×D412yes—
210C22×C4×C13C2412yes—
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—82no—
220C22×Dic13—82no—
221C2×Dic26—22no—
222C2×Dic26—22no—
223C2×Dic26—21no—
224C2×Dic26—24no—
225C2×Dic26—82no—
226C2×Dic26C2412yes—
227C13×C4⋊C4—21no—
228C13×C4⋊C4—21no—
229C13×C4⋊C4—24no—
230C13×C4⋊C4—24no—
231C13×C4⋊C4—24no—
232C13×C4⋊C4—21no—
233C13×C4⋊C4C2×D414yes—
234C13×C4⋊C4C2412yes—
235C13×C4⋊C4C2412yes—
236C13×C4⋊C4C2412yes—
237C13×C22⋊C4—24no—
238C13×C22⋊C4—24no—
239C13×C22⋊C4—24no—
240C13×C22⋊C4—24no—
241C13×C22⋊C4C2×D414yes—
242C13×C22⋊C4C2×D414yes—
243C42×C13—24no—
244C42×C13C2×D412yes—
245C42×C13C2412yes—
246C22⋊Dic13—24no—
247C22⋊Dic13—24no—
248#6105—28no—
249C4⋊Dic13—21no—
250C4⋊Dic13—21no—
251C4⋊Dic13—21no—
252C4⋊Dic13—24no—
253C4⋊Dic13—24no—
254C4⋊Dic13—24no—
255C4⋊Dic13C2412yes—
256C4⋊Dic13C2412yes—
257C4⋊Dic13C2412yes—
258#6101—24no—
259#6101—24no—
260#6101—24no—
261C4×Dic13—24no—
262#6099—28no—
263C2×#1055—22no—
264C2×#1055—22no—
265C2×#1055—22no—
266C2×#1055—28no—
267C2×#1055#4114yes—
268C2×#1055C2412yes—
269C2×#1055C2412yes—
270C2×#1055C2412yes—
271C2×#1055C2412yes—
272C2×#554—131no—
273C2×#553D1311yescharacteristic
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×#435—131no—
286C2×#428—131no—
287C22×#107—131no—
288C23×C13—22no—
289C23×C13—22no—
290C23×C13—22no—
291C23×C13—22no—
292C23×C13—22no—
293C23×C13—22no—
294C23×C13—42no—
295C23×C13—42no—
296C23×C13—42no—
297C23×C13#13714yes—
298C23×C13C22×D412yes—
299C23×C13C22×D412yes—
300C23×C13C22×D411yescharacteristic
301D4×C13—28no—
302D4×C13—22no—
303D4×C13—22no—
304D4×C13—48no—
305D4×C13—42no—
306D4×C13—84no—
307C2×C4×C13—22no—
308C2×C4×C13—22no—
309C2×C4×C13—22no—
310C2×C4×C13—22no—
311C2×C4×C13—24no—
312C2×C4×C13—24no—
313C2×C4×C13—22no—
314C2×C4×C13—22no—
315C2×C4×C13—22no—
316C2×C4×C13—22no—
317C2×C4×C13—22no—
318C2×C4×C13—22no—
319C2×C4×C13—22no—
320C2×C4×C13—42no—
321C2×C4×C13—42no—
322C2×C4×C13—42no—
323C2×C4×C13—84no—
324C2×C4×C13—84no—
325C2×C4×C13C22×D412yes—
326C2×C4×C13C22×D412yes—
327C2×C4×C13C22×D412yes—
328C2×C4×C13C22×D412yes—
329C2×C4×C13C22×D411yescharacteristic
330C2×C4×C13C2×#4112yes—
331C2×C4×C132−1+412yes—
332C2×C4×C13C2511yescharacteristic
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—
343Dic26—22no—
344Dic26—22no—
345Dic26—42no—
346Dic26—84no—
347#1055—22no—
348#1055—22no—
349#1055—22no—
350#1055C2×#4114yes—
351C22×SD16—131no—
352C22×M16—131no—
353C23×C8—131no—
354#554—138no—
355#554—264no—
356#553—24no—
357#553C2×D1318yes—
358C2×C4⋊Q8—131no—
359C2×#126—21no—
360C2×#125—261no—
361C2×#125C2×D1311yescharacteristic
362C2×#123—21no—
363C2×C22⋊Q8—131no—
364C2×C22⋊Q8—131no—
365C2×C22⋊Q8—261no—
366C2×C22⋊Q8—261no—
367C2×#121—21no—
368C2×#121C2×D1311yescharacteristic
369C2×#121C2×D1311yescharacteristic
370C2×C4×Q8—131no—
371C2×C4×D4—21no—
372C2×C4×D4—261no—
373C2×C4×D4C2×D1311yescharacteristic
374C2×C4×D4C2×D1311yescharacteristic
375C2×#117C2×D1311yescharacteristic
376C22×C4⋊C4—131no—
377C22×C4⋊C4—131no—
378C22×C4⋊C4C2×D1311yescharacteristic
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#435—138no—
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⋊C8—131no—
402C2×#103—131no—
403C2×#103—131no—
404C2×#103—131no—
405C2×#102—131no—
406C2×#102—131no—
407C2×#102—131no—
408C2×C22⋊C8—131no—
409C2×C22⋊C8—131no—
410C2×#97—131no—
411C22×C13—28no—
412C22×C13—22no—
413C22×C13—22no—
414C22×C13—22no—
415C22×C13—22no—
416C22×C13—22no—
417C22×C13—44no—
418C22×C13—42no—
419C22×C13—42no—
420C22×C13—42no—
421C22×C13—84no—
422C22×C13#54712yes—
423C22×C13C2×#13714yes—
424C22×C13C2×#13712yes—
425C22×C13#57612yes—
426C22×C13C23×D411yescharacteristic
427C4×C13—22no—
428C4×C13—22no—
429C4×C13—22no—
430C4×C13—22no—
431C4×C13—42no—
432C4×C13—42no—
433C4×C13—42no—
434C4×C13#54712yes—
435C4×C13C22×#4111yescharacteristic
436C4×C13C2×2−1+411yescharacteristic
437Dic13—42no—
438Dic13—42no—
439Dic13—42no—
440Dic13—42no—
441C22×Q8—131no—
442C22×Q8—261no—
443C22×D4—21no—
444C22×D4—21no—
445C22×D4C22⋊D1311yescharacteristic
446C22×D4C22×D1311yescharacteristic
447C23×C4—21no—
448C23×C4—21no—
449C23×C4—261no—
450C23×C4—261no—
451C23×C4C22×D1311yescharacteristic
452C23×C4C22×D1311yescharacteristic
453C2×SD16—134no—
454C2×SD16—264no—
455C2×M16—134no—
456C2×M16—264no—
457C22×C8—131no—
458C22×C8—131no—
459C22×C8—134no—
460C22×C8—131no—
461C22×C8—131no—
462C22×C8—264no—
463C4⋊Q8—134no—
464C4⋊Q8—262no—
465#126—28no—
466#125—22no—
467#125—268no—
468#125C22×D1314yes—
469#123—28no—
470C22⋊Q8—134no—
471C22⋊Q8—134no—
472C22⋊Q8—262no—
473C22⋊Q8—262no—
474C22⋊Q8—268no—
475C22⋊Q8—268no—
476#121—28no—
477#121—22no—
478#121—22no—
479#121C22×D1314yes—
480#121C22×D1314yes—
481C4×Q8—134no—
482C4×Q8—262no—
483C4×D4—28no—
484C4×D4—22no—
485C4×D4—268no—
486C4×D4C22⋊D1314yes—
487C4×D4C22×D1314yes—
488C4×D4C22×D1314yes—
489#117—22no—
490#117C22×D1314yes—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—22no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—131no—
496C2×C4⋊C4—131no—
497C2×C4⋊C4—131no—
498C2×C4⋊C4—134no—
499C2×C4⋊C4—134no—
500C2×C4⋊C4—261no—
501C2×C4⋊C4—261no—
502C2×C4⋊C4—262no—
503C2×C4⋊C4—262no—
504C2×C4⋊C4—261no—
505C2×C4⋊C4—261no—
506C2×C4⋊C4—261no—
507C2×C4⋊C4—261no—
508C2×C4⋊C4C22⋊D1311yescharacteristic
509C2×C4⋊C4C22×D1311yescharacteristic
510C2×C4⋊C4C22×D1311yescharacteristic
511C2×C4⋊C4C22×D1314yes—
512C2×C4⋊C4C22×D1311yescharacteristic
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—261no—
518C2×C22⋊C4—261no—
519C2×C22⋊C4C22⋊D1311yescharacteristic
520C2×C22⋊C4C22⋊D1311yescharacteristic
521C2×C42—21no—
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⋊C8—134no—
534#103—134no—
535#103—134no—
536#103—134no—
537#102—134no—
538#102—134no—
539#102—134no—
540C22⋊C8—134no—
541C22⋊C8—134no—
542#97—134no—
543C2×C13—24no—
544C2×C13—42no—
545C2×C13—82no—
546C2×C13#334614yescomplemented
547C2×C13C2×#54711yescharacteristic
548C2×C13C22×#13711yescharacteristic
549C2×C13C2×#57611yescharacteristic
550C24—21no—
551C24C2×C22⋊D1311yescharacteristic
552C24C2×C22⋊D1311yescharacteristic
553C2×Q8—132no—
554C2×Q8—261no—
555C2×Q8—264no—
556C2×Q8—262no—
557C2×Q8—262no—
558C2×Q8—1042no—
559C2×D4—24no—
560C2×D4—24no—
561C2×D4—24no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—21no—
565C2×D4—44no—
566C2×D4—82no—
567C2×D4C2×C22⋊D1314yes—
568C2×D4C23×D1312yes—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—82no—
579C22×C4—82no—
580C22×C4—261no—
581C22×C4—261no—
582C22×C4—261no—
583C22×C4—261no—
584C22×C4—264no—
585C22×C4—264no—
586C22×C4—1042no—
587C22×C4—1042no—
588C22×C4C2×C22⋊D1312yes—
589C22×C4C2×C22⋊D1312yes—
590C22×C4C2×C22⋊D1311yescharacteristic
591C22×C4C2×C22⋊D1311yescharacteristic
592C22×C4C2×C22⋊D1311yescharacteristic
593C22×C4C2×C22⋊D1311yescharacteristic
594C22×C4C23×D1312yes—
595C22×C4C23×D1312yes—
596C22×C4C23×D1311yescharacteristic
597SD16—268no—
598M16—268no—
599C2×C8—134no—
600C2×C8—132no—
601C2×C8—132no—
602C2×C8—132no—
603C2×C8—132no—
604C2×C8—268no—
605C2×C8—262no—
606C2×C8—262no—
607C2×C8—262no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—24no—
611C4⋊C4—24no—
612C4⋊C4—24no—
613C4⋊C4—21no—
614C4⋊C4—132no—
615C4⋊C4—132no—
616C4⋊C4—132no—
617C4⋊C4—261no—
618C4⋊C4—264no—
619C4⋊C4—264no—
620C4⋊C4—261no—
621C4⋊C4—261no—
622C4⋊C4—264no—
623C4⋊C4—264no—
624C4⋊C4—264no—
625C4⋊C4—264no—
626C4⋊C4C2×C22⋊D1314yes—
627C4⋊C4C23×D1312yes—
628C4⋊C4C23×D1312yes—
629C4⋊C4C23×D1312yes—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—24no—
634C22⋊C4—264no—
635C22⋊C4—264no—
636C22⋊C4C2×C22⋊D1314yes—
637C22⋊C4C2×C22⋊D1314yes—
638C42—24no—
639C42—264no—
640C42C2×C22⋊D1312yes—
641C42C23×D1312yes—
642C13C2×#334611yescharacteristic, complemented, Sylow
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23#8820514yes—
653C23C22×C22⋊D1312yes—
654C23C22×C22⋊D1312yes—
655C23C22×C22⋊D1311yescharacteristic
656Q8—262no—
657Q8—262no—
658Q8—522no—
659Q8—1044no—
660D4—28no—
661D4—22no—
662D4—22no—
663D4—48no—
664D4—42no—
665D4—84no—
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—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—84no—
683C2×C4—84no—
684C2×C4—262no—
685C2×C4—262no—
686C2×C4—262no—
687C2×C4—262no—
688C2×C4—522no—
689C2×C4—522no—
690C2×C4—522no—
691C2×C4—522no—
692C2×C4—1044no—
693C2×C4—1044no—
694C2×C4#41×D1312yes—
695C2×C4#8825712yes—
696C2×C4C22×C22⋊D1312yes—
697C2×C4C22×C22⋊D1312yes—
698C2×C4C22×C22⋊D1312yes—
699C2×C4C22×C22⋊D1312yes—
700C2×C4C22×C22⋊D1311yescharacteristic
701C2×C4C24×D1311yescharacteristic
702C8—134no—
703C8—262no—
704C8—262no—
705C8—262no—
706C22—22no—
707C22—22no—
708C22—28no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—44no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—84no—
717C22C2×#8820514yes—
718C22C2×#8820512yes—
719C22#1171952912yes—
720C22#1171954012yes—
721C22C23×C22⋊D1311yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—42no—
727C4—42no—
728C4—42no—
729C4—522no—
730C4—522no—
731C4—522no—
732C4—522no—
733C4#1171952912yes—
734C4C2×#41×D1311yescharacteristic
735C4C2×#8825711yescharacteristic
736C2—24no—
737C2—42no—
738C2—82no—
739C2#1312732114yesdirect product factor
740C2C2×#1171952911yescharacteristic
741C2C22×#8820511yescharacteristic
742C2C2×#1171954011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
Fitting, prime radicalC2×C13×#553C2
socleC23×C13C22×D4
hypercenterC2×#553D13
hypocenterC13C2×#3346
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×#11719248C2semidirect
2. #13127321C2direct (N × H)
3. C2×#11718726C2semidirect
4. C2×#11718631C2semidirect
5. C2×#11718695C2semidirect
6. C2×#11718657C2semidirect
7. C2×#11718694C2semidirect
8. C2×#11718724C2semidirect
9. C2×#11718668C2semidirect
10. C2×#11718703C2semidirect
11. C2×#11718702C2semidirect
12. C2×#11718679C2semidirect
13. C2×#11718672C2semidirect
14. C2×#11718656C2semidirect
15. C22×#88047C2semidirect
39. #11719248C22semidirect
50. #11718726C22semidirect
51. #11718724C22semidirect
52. #11718703C22semidirect
53. #11718702C22semidirect
54. #11718695C22semidirect
55. #11718694C22semidirect
56. #11718679C22semidirect
57. #11718672C22semidirect
58. #11718668C22semidirect
59. #11718657C22semidirect
60. #11718656C22semidirect
61. #11718631C22semidirect
74. C2×#88047C22semidirect
546. C2×C13#3346semidirect
642. C13C2×#3346semidirect
739. C2#13127321direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192482
#131273212
C2×#117187262
C2×#117186312
C2×#117186952
C2×#117186572
C2×#117186942
C2×#117187242
C2×#117186682
C2×#117187032
C2×#117187022
C2×#117186792
C2×#117186722
C2×#117186562
C22×#880472
C2×C13×#5532
C2×#334613