Finite Group Databasebeta

← C2×#13127270 #16741444

Subgroups — C2×#13127270 #16741444

Order 3328.

2094 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719246C211yesmaximal, characteristic, complemented
2#13127270C2116yesmaximal, direct product factor
3C2×#11718741C211yesmaximal, characteristic, complemented
4C2×#11718631C211yesmaximal, characteristic, complemented
5C2×#11718696C211yesmaximal, characteristic, complemented
6C2×#11718632C211yesmaximal, characteristic, complemented
7C2×#11718694C211yesmaximal, characteristic, complemented
8C2×#11718752C211yesmaximal, characteristic, complemented
9C2×#11718670C211yesmaximal, characteristic, complemented
10C2×#11718703C211yesmaximal, characteristic, complemented
11C2×#11718702C211yesmaximal, characteristic, complemented
12C2×#11718679C211yesmaximal, characteristic, complemented
13C2×#11718672C211yesmaximal, characteristic, complemented
14C2×#11718625C211yesmaximal, characteristic, complemented
15C22×#88047C211yesmaximal, characteristic, complemented
16C2×C13×#547C211yesmaximal, characteristic
17C22×C13×#41—21no—
18C13×#547—24no—
19C13×#547C2218yes—
20C2×C13×C4⋊Q8C2211yescharacteristic
21C2×C13×#123—21no—
22C2×C13×#123—21no—
23C2×C13×C22⋊Q8—21no—
24C2×C13×#121C2211yescharacteristic
25C2×C13×#121C2211yescharacteristic
26C2×C4×D4×C13C2211yescharacteristic
27C2×C4×D4×C13C2211yescharacteristic
28C22×C13×C4⋊C4C2211yescharacteristic
29C22×C13×C4⋊C4C2211yescharacteristic
30C2×#88189—21no—
31C22×#6105C2211yescharacteristic
32C2×#88180C2211yescharacteristic
33C22×C4⋊Dic13C2211yescharacteristic
34C2×#88178C2211yescharacteristic
35C2×#88178C2211yescharacteristic
36C22×#6099C2211yescharacteristic
37C23×#1055C2211yescharacteristic
38#11719246—24no—
39#11719246C2218yescomplemented
40C2×#88143—21no—
41C2×#88133—21no—
42C2×#88131—21no—
43C2×#88124C2211yescharacteristic
44C2×C4×Dic26C2211yescharacteristic
45C2×#88072C2211yescharacteristic
46C2×#88072C2211yescharacteristic
47C2×#88072C2211yescharacteristic
48C2×C22⋊#1055C2211yescharacteristic
49C2×C22⋊#1055C2211yescharacteristic
50#11718752C2218yescomplemented
51#11718741C2218yescomplemented
52#11718703C2218yescomplemented
53#11718702C2218yescomplemented
54#11718696C2218yescomplemented
55#11718694C2218yescomplemented
56#11718679C2218yescomplemented
57#11718672C2218yescomplemented
58#11718670C2218yescomplemented
59#11718632C2218yescomplemented
60#11718631C2218yescomplemented
61C2×#88050C2211yescharacteristic
62C2×#88050C2211yescharacteristic
63C2×#88050C2211yescharacteristic
64#11718625C2218yescomplemented
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
77C2×C13×#41—28no—
78C2×C13×#41—48no—
79C22×Q8×C13—21no—
80C22×D4×C13—21no—
81C22×D4×C13—21no—
82C22×D4×C13D411yescharacteristic
83C22×D4×C13C2311yescharacteristic
84C23×C4×C13—21no—
85C23×C4×C13—21no—
86C23×C4×C13—21no—
87C23×C4×C13C2311yescharacteristic
88C23×C4×C13C2311yescharacteristic
89C23×Dic13—21no—
90C22×Dic26C2311yescharacteristic
91C13×C4⋊Q8—22no—
92C13×C4⋊Q8C2314yes—
93C13×#123—28no—
94C13×#123—28no—
95C13×C22⋊Q8—28no—
96C13×#121—22no—
97C13×#121—22no—
98C13×#121C2314yes—
99C13×#121C2314yes—
100C4×D4×C13—22no—
101C4×D4×C13D414yes—
102C4×D4×C13C2314yes—
103C4×D4×C13C2314yes—
104C2×C13×C4⋊C4—21no—
105C2×C13×C4⋊C4—21no—
106C2×C13×C4⋊C4—22no—
107C2×C13×C4⋊C4—22no—
108C2×C13×C4⋊C4—21no—
109C2×C13×C4⋊C4D411yescharacteristic
110C2×C13×C4⋊C4C2311yescharacteristic
111C2×C13×C4⋊C4C2311yescharacteristic
112C2×C13×C4⋊C4C2311yescharacteristic
113C2×C13×C4⋊C4C2314yes—
114C2×C13×C4⋊C4C2314yes—
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×C13C2311yescharacteristic
121C2×C22⋊Dic13—21no—
122C2×C22⋊Dic13—21no—
123C2×C22⋊Dic13—21no—
124#88189—28no—
125C2×#6105—24no—
126C2×#6105C2314yes—
127#88180—22no—
128#88180C2314yes—
129C2×C4⋊Dic13—21no—
130C2×C4⋊Dic13—22no—
131C2×C4⋊Dic13C2311yescharacteristic
132C2×C4⋊Dic13C2311yescharacteristic
133C2×C4⋊Dic13C2311yescharacteristic
134C2×C4⋊Dic13C2314yes—
135#88178—22no—
136#88178—22no—
137#88178C2314yes—
138#88178C2314yes—
139C2×#6101—21no—
140C2×#6101—21no—
141C2×#6101—21no—
142C2×#6101—21no—
143C2×#6101—21no—
144C2×C4×Dic13—21no—
145C2×C4×Dic13—21no—
146C2×#6099—24no—
147C2×#6099C2314yes—
148C22×#1055—24no—
149C22×#1055C2314yes—
150C22×#1055C2311yescharacteristic
151C22×#1055C2311yescharacteristic
152C22×#1055C2311yescharacteristic
153C22×#1055C2311yescharacteristic
154#88143—28no—
155#88133—28no—
156#88131—28no—
157#88124—22no—
158#88124C2314yes—
159C4×Dic26—22no—
160C4×Dic26C2314yes—
161#88072C2314yes—
162#88072C2314yes—
163#88072C2314yes—
164C22⋊#1055C2314yes—
165C22⋊#1055C2314yes—
166#88050C2314yes—
167#88050C2314yes—
168#88050C2314yes—
169#88048C2314yes—
170#88048C2314yes—
171#88048C2314yes—
172#88047C2314yes—
173#88047C2314yes—
174#88047C2314yes—
175#88047C2314yes—
176#88047C2314yes—
177#88047C2314yes—
178C4⋊#1055C2314yes—
179#88043C2314yes—
180C2×#3343—131nomaximal, Sylow
181C24×C13—21no—
182C24×C13C2×D411yescharacteristic
183C24×C13C2×D411yescharacteristic
184C13×#41—432no—
185C2×Q8×C13—24no—
186C2×Q8×C13—44no—
187C2×D4×C13—24no—
188C2×D4×C13—24no—
189C2×D4×C13—24no—
190C2×D4×C13—21no—
191C2×D4×C13—22no—
192C2×D4×C13—22no—
193C2×D4×C13—44no—
194C2×D4×C13—44no—
195C2×D4×C13C2×D414yes—
196C2×D4×C13C2412yes—
197C22×C4×C13—22no—
198C22×C4×C13—22no—
199C22×C4×C13—22no—
200C22×C4×C13—22no—
201C22×C4×C13—21no—
202C22×C4×C13—21no—
203C22×C4×C13—21no—
204C22×C4×C13—24no—
205C22×C4×C13—24no—
206C22×C4×C13—24no—
207C22×C4×C13—44no—
208C22×C4×C13—44no—
209C22×C4×C13—44no—
210C22×C4×C13C2×D411yescharacteristic
211C22×C4×C13C2×D411yescharacteristic
212C22×C4×C13C2×D411yescharacteristic
213C22×C4×C13C2×D411yescharacteristic
214C22×C4×C13C2×D412yes—
215C22×C4×C13C2×D412yes—
216C22×C4×C13C2412yes—
217C22×C4×C13C2412yes—
218C22×C4×C13C2411yescharacteristic
219C22×Dic13—24no—
220C22×Dic13—21no—
221C22×Dic13—21no—
222C22×Dic13—21no—
223C22×Dic13—21no—
224C22×Dic13—44no—
225C2×Dic26—22no—
226C2×Dic26—22no—
227C2×Dic26—21no—
228C2×Dic26C2412yes—
229C13×C4⋊C4—21no—
230C13×C4⋊C4—21no—
231C13×C4⋊C4—21no—
232C13×C4⋊C4—24no—
233C13×C4⋊C4—24no—
234C13×C4⋊C4—24no—
235C13×C4⋊C4C2×D414yes—
236C13×C4⋊C4C2412yes—
237C13×C4⋊C4C2412yes—
238C13×C4⋊C4C2412yes—
239C13×C22⋊C4—24no—
240C13×C22⋊C4—24no—
241C13×C22⋊C4—24no—
242C13×C22⋊C4C2×D414yes—
243C13×C22⋊C4C2×D414yes—
244C42×C13C2×D412yes—
245C42×C13C2412yes—
246C22⋊Dic13—24no—
247C22⋊Dic13—24no—
248C22⋊Dic13—24no—
249#6105—28no—
250C4⋊Dic13—21no—
251C4⋊Dic13—21no—
252C4⋊Dic13—21no—
253C4⋊Dic13—24no—
254C4⋊Dic13C2412yes—
255C4⋊Dic13C2412yes—
256C4⋊Dic13C2412yes—
257#6101—24no—
258#6101—24no—
259#6101—24no—
260#6101—24no—
261#6101—24no—
262C4×Dic13—24no—
263C4×Dic13—24no—
264#6099—28no—
265C2×#1055—22no—
266C2×#1055—22no—
267C2×#1055—22no—
268C2×#1055—28no—
269C2×#1055#4114yescomplemented
270C2×#1055C2412yes—
271C2×#1055C2412yes—
272C2×#1055C2412yes—
273C2×#1055C2412yes—
274C2×#552—131no—
275C2×#547D1311yescharacteristic
276#3343—1316no—
277C2×#501—131no—
278C2×#484—131no—
279C2×#482—131no—
280C2×#483—131no—
281C2×#480—131no—
282C2×#477—131no—
283C2×#478—131no—
284C2×#468—131no—
285C2×#465—131no—
286C2×#440—131no—
287C2×#435—131no—
288C2×#428—131no—
289C22×#107—131no—
290C23×C13—22no—
291C23×C13—22no—
292C23×C13—22no—
293C23×C13—22no—
294C23×C13—22no—
295C23×C13—22no—
296C23×C13—42no—
297C23×C13—42no—
298C23×C13—42no—
299C23×C13AGL(1,ℤ/8)14yes—
300C23×C13C22×D412yes—
301C23×C13C22×D412yes—
302C23×C13C22×D411yescharacteristic
303Q8×C13—48no—
304D4×C13—28no—
305D4×C13—22no—
306D4×C13—22no—
307D4×C13—48no—
308D4×C13—48no—
309D4×C13—42no—
310C2×C4×C13—22no—
311C2×C4×C13—22no—
312C2×C4×C13—22no—
313C2×C4×C13—22no—
314C2×C4×C13—24no—
315C2×C4×C13—24no—
316C2×C4×C13—22no—
317C2×C4×C13—22no—
318C2×C4×C13—22no—
319C2×C4×C13—22no—
320C2×C4×C13—22no—
321C2×C4×C13—22no—
322C2×C4×C13—22no—
323C2×C4×C13—48no—
324C2×C4×C13—48no—
325C2×C4×C13—42no—
326C2×C4×C13—42no—
327C2×C4×C13—42no—
328C2×C4×C13—48no—
329C2×C4×C13C22×D412yes—
330C2×C4×C13C22×D412yes—
331C2×C4×C13C22×D412yes—
332C2×C4×C13C22×D412yes—
333C2×C4×C13C22×D411yescharacteristic
334C2×C4×C13C2×#4112yes—
335C2×C4×C132−1+412yes—
336C2×C4×C13C2511yescharacteristic
337C2×Dic13—22no—
338C2×Dic13—22no—
339C2×Dic13—22no—
340C2×Dic13—22no—
341C2×Dic13—42no—
342C2×Dic13—48no—
343C2×Dic13—42no—
344C2×Dic13—42no—
345C2×Dic13—42no—
346Dic26—22no—
347Dic26—22no—
348Dic26—42no—
349#1055—22no—
350#1055—22no—
351#1055—22no—
352#1055C2×#4114yescomplemented
353C22×#41—21no—
354C22×SD16—131no—
355C22×M16—131no—
356C23×C8—131no—
357#552—138no—
358#552—264no—
359#547—24no—
360#547C2×D1318yes—
361C2×C4⋊Q8C2×D1311yescharacteristic
362C2×#126—261no—
363C2×#125—131no—
364C2×#125—261no—
365C2×#123—21no—
366C2×#123—21no—
367C2×#123—261no—
368C2×C22⋊Q8—21no—
369C2×C22⋊Q8—131no—
370C2×C22⋊Q8—131no—
371C2×#121C2×D1311yescharacteristic
372C2×#121C2×D1311yescharacteristic
373C2×C4×Q8—131no—
374C2×C4×D4C2×D1311yescharacteristic
375C2×C4×D4C2×D1311yescharacteristic
376C2×#117—131no—
377C2×#117—261no—
378C22×C4⋊C4—131no—
379C22×C4⋊C4C2×D1311yescharacteristic
380C22×C4⋊C4C2×D1311yescharacteristic
381#501—138no—
382#484—138no—
383#483—138no—
384#482—138no—
385#480—138no—
386#478—138no—
387#477—138no—
388#468—138no—
389#465—138no—
390#440—138no—
391#435—138no—
392#428—138no—
393C2×#107—131no—
394C2×#107—131no—
395C2×#107—131no—
396C2×#107—131no—
397C2×#107—138no—
398C2×#107—131no—
399C2×#107—131no—
400C2×#106—131no—
401C2×#106—131no—
402C2×#106—131no—
403C2×C4⋊C8—131no—
404C2×#103—131no—
405C2×#103—131no—
406C2×#103—131no—
407C2×#102—131no—
408C2×#102—131no—
409C2×#102—131no—
410C2×C22⋊C8—131no—
411C2×C22⋊C8—131no—
412C2×#97—131no—
413C22×C13—28no—
414C22×C13—22no—
415C22×C13—22no—
416C22×C13—22no—
417C22×C13—22no—
418C22×C13—22no—
419C22×C13—44no—
420C22×C13—42no—
421C22×C13—42no—
422C22×C13—42no—
423C22×C13—84no—
424C22×C13#54712yes—
425C22×C13C2×AGL(1,ℤ/8)14yes—
426C22×C13C2×AGL(1,ℤ/8)12yes—
427C22×C13#57812yes—
428C22×C13C23×D411yescharacteristic
429C4×C13—22no—
430C4×C13—22no—
431C4×C13—22no—
432C4×C13—22no—
433C4×C13—42no—
434C4×C13—42no—
435C4×C13—42no—
436C4×C13#54712yes—
437C4×C13C22×#4111yescharacteristic
438C4×C13C2×2−1+411yescharacteristic
439Dic13—42no—
440Dic13—42no—
441Dic13—42no—
442Dic13—42no—
443C2×#41—28no—
444C2×#41—48no—
445C22×Q8—21no—
446C22×Q8—131no—
447C22×D4—21no—
448C22×D4—21no—
449C22×D4C22⋊D1311yescharacteristic
450C22×D4C22×D1311yescharacteristic
451C23×C4—21no—
452C23×C4—21no—
453C23×C4—21no—
454C23×C4—261no—
455C23×C4C22×D1311yescharacteristic
456C23×C4C22×D1311yescharacteristic
457C2×SD16—134no—
458C2×SD16—264no—
459C2×M16—134no—
460C2×M16—264no—
461C22×C8—131no—
462C22×C8—131no—
463C22×C8—134no—
464C22×C8—131no—
465C22×C8—131no—
466C22×C8—264no—
467C4⋊Q8—22no—
468C4⋊Q8C22×D1314yes—
469#126—268no—
470#125—134no—
471#125—268no—
472#125—262no—
473#123—28no—
474#123—28no—
475#123—268no—
476C22⋊Q8—28no—
477C22⋊Q8—134no—
478C22⋊Q8—134no—
479C22⋊Q8—262no—
480C22⋊Q8—262no—
481#121—22no—
482#121—22no—
483#121C22×D1314yes—
484#121C22×D1314yes—
485C4×Q8—134no—
486C4×Q8—262no—
487C4×D4—22no—
488C4×D4C22⋊D1314yes—
489C4×D4C22×D1314yes—
490C4×D4C22×D1314yes—
491#117—134no—
492#117—262no—
493#117—268no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—131no—
500C2×C4⋊C4—131no—
501C2×C4⋊C4—134no—
502C2×C4⋊C4—131no—
503C2×C4⋊C4—261no—
504C2×C4⋊C4—262no—
505C2×C4⋊C4—261no—
506C2×C4⋊C4—261no—
507C2×C4⋊C4—261no—
508C2×C4⋊C4—261no—
509C2×C4⋊C4—261no—
510C2×C4⋊C4C22⋊D1311yescharacteristic
511C2×C4⋊C4C22×D1311yescharacteristic
512C2×C4⋊C4C22×D1311yescharacteristic
513C2×C4⋊C4C22×D1311yescharacteristic
514C2×C4⋊C4C22×D1314yes—
515C2×C4⋊C4C22×D1314yes—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—261no—
520C2×C22⋊C4—261no—
521C2×C22⋊C4—261no—
522C2×C22⋊C4C22⋊D1311yescharacteristic
523C2×C22⋊C4C22⋊D1311yescharacteristic
524C2×C42—261no—
525C2×C42—261no—
526C2×C42C22×D1311yescharacteristic
527#107—134no—
528#107—134no—
529#107—134no—
530#107—134no—
531#107—134no—
532#107—134no—
533#106—134no—
534#106—134no—
535#106—134no—
536C4⋊C8—134no—
537#103—134no—
538#103—134no—
539#103—134no—
540#102—134no—
541#102—134no—
542#102—134no—
543C22⋊C8—134no—
544C22⋊C8—134no—
545#97—134no—
546C2×C13—24no—
547C2×C13—42no—
548C2×C13—82no—
549C2×C13#334314yescomplemented
550C2×C13C2×#54711yescharacteristic
551C2×C13C22×AGL(1,ℤ/8)11yescharacteristic
552C2×C13C2×#57811yescharacteristic
553C24—21no—
554C24C2×C22⋊D1311yescharacteristic
555C24C2×C22⋊D1311yescharacteristic
556#41—432no—
557C2×Q8—24no—
558C2×Q8—44no—
559C2×Q8—132no—
560C2×Q8—261no—
561C2×Q8—262no—
562C2×Q8—262no—
563C2×D4—24no—
564C2×D4—24no—
565C2×D4—24no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—21no—
569C2×D4—44no—
570C2×D4—44no—
571C2×D4C2×C22⋊D1314yes—
572C2×D4C23×D1312yes—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—24no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—264no—
587C22×C4—261no—
588C22×C4—261no—
589C22×C4—261no—
590C22×C4—261no—
591C22×C4—524no—
592C22×C4C2×C22⋊D1312yes—
593C22×C4C2×C22⋊D1312yes—
594C22×C4C2×C22⋊D1311yescharacteristic
595C22×C4C2×C22⋊D1311yescharacteristic
596C22×C4C2×C22⋊D1311yescharacteristic
597C22×C4C2×C22⋊D1311yescharacteristic
598C22×C4C23×D1312yes—
599C22×C4C23×D1312yes—
600C22×C4C23×D1311yescharacteristic
601SD16—268no—
602M16—268no—
603C2×C8—134no—
604C2×C8—132no—
605C2×C8—132no—
606C2×C8—132no—
607C2×C8—132no—
608C2×C8—268no—
609C2×C8—262no—
610C2×C8—262no—
611C2×C8—262no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—24no—
618C4⋊C4—132no—
619C4⋊C4—132no—
620C4⋊C4—132no—
621C4⋊C4—261no—
622C4⋊C4—261no—
623C4⋊C4—264no—
624C4⋊C4—261no—
625C4⋊C4—264no—
626C4⋊C4—264no—
627C4⋊C4—264no—
628C4⋊C4—264no—
629C4⋊C4—264no—
630C4⋊C4C2×C22⋊D1314yes—
631C4⋊C4C23×D1312yes—
632C4⋊C4C23×D1312yes—
633C4⋊C4C23×D1312yes—
634C22⋊C4—24no—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—264no—
638C22⋊C4—264no—
639C22⋊C4—264no—
640C22⋊C4C2×C22⋊D1314yes—
641C22⋊C4C2×C22⋊D1314yes—
642C42—264no—
643C42—264no—
644C42C2×C22⋊D1312yes—
645C42C23×D1312yes—
646C13C2×#334311yescharacteristic, complemented, Sylow
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23#8818614yes—
657C23C22×C22⋊D1312yes—
658C23C22×C22⋊D1312yes—
659C23C22×C22⋊D1311yescharacteristic
660Q8—48no—
661Q8—262no—
662Q8—262no—
663Q8—522no—
664D4—28no—
665D4—22no—
666D4—22no—
667D4—48no—
668D4—48no—
669D4—42no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—48no—
684C2×C4—48no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—48no—
689C2×C4—262no—
690C2×C4—262no—
691C2×C4—262no—
692C2×C4—262no—
693C2×C4—528no—
694C2×C4—522no—
695C2×C4—522no—
696C2×C4—522no—
697C2×C4—522no—
698C2×C4#41×D1312yes—
699C2×C4#8825712yes—
700C2×C4C22×C22⋊D1312yes—
701C2×C4C22×C22⋊D1312yes—
702C2×C4C22×C22⋊D1312yes—
703C2×C4C22×C22⋊D1312yes—
704C2×C4C22×C22⋊D1311yescharacteristic
705C2×C4C24×D1311yescharacteristic
706C8—134no—
707C8—262no—
708C8—262no—
709C8—262no—
710C22—22no—
711C22—28no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—44no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—84no—
721C22C2×#8818614yes—
722C22C2×#8818612yes—
723C22#1171952912yes—
724C22#1171954312yes—
725C22C23×C22⋊D1311yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—42no—
731C4—42no—
732C4—42no—
733C4—522no—
734C4—522no—
735C4—522no—
736C4—522no—
737C4#1171952912yes—
738C4C2×#41×D1311yescharacteristic
739C4C2×#8825711yescharacteristic
740C2—24no—
741C2—42no—
742C2—82no—
743C2#1312727014yesdirect product factor
744C2C2×#1171952911yescharacteristic
745C2C22×#8818611yescharacteristic
746C2C2×#1171954311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
Fitting, prime radicalC2×C13×#547C2
socleC23×C13C22×D4
hypercenterC2×#547D13
hypocenterC13C2×#3343
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×#11719246C2semidirect
2. #13127270C2direct (N × H)
3. C2×#11718741C2semidirect
4. C2×#11718631C2semidirect
5. C2×#11718696C2semidirect
6. C2×#11718632C2semidirect
7. C2×#11718694C2semidirect
8. C2×#11718752C2semidirect
9. C2×#11718670C2semidirect
10. C2×#11718703C2semidirect
11. C2×#11718702C2semidirect
12. C2×#11718679C2semidirect
13. C2×#11718672C2semidirect
14. C2×#11718625C2semidirect
15. C22×#88047C2semidirect
39. #11719246C22semidirect
50. #11718752C22semidirect
51. #11718741C22semidirect
52. #11718703C22semidirect
53. #11718702C22semidirect
54. #11718696C22semidirect
55. #11718694C22semidirect
56. #11718679C22semidirect
57. #11718672C22semidirect
58. #11718670C22semidirect
59. #11718632C22semidirect
60. #11718631C22semidirect
64. #11718625C22semidirect
74. C2×#88047C22semidirect
269. C2×#1055#41semidirect
352. #1055C2×#41semidirect
549. C2×C13#3343semidirect
646. C13C2×#3343semidirect
743. C2#13127270direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192462
#131272702
C2×#117187412
C2×#117186312
C2×#117186962
C2×#117186322
C2×#117186942
C2×#117187522
C2×#117186702
C2×#117187032
C2×#117187022
C2×#117186792
C2×#117186722
C2×#117186252
C22×#880472
C2×C13×#5472
C2×#334313