Finite Group Databasebeta

← C2×#13125447 #16732711

Subgroups — C2×#13125447 #16732711

Order 3328.

1970 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719239C211yesmaximal, characteristic, complemented
2#13125447C2116yesmaximal, direct product factor
3C2×#11718740C211yesmaximal, characteristic, complemented
4C2×#11718720C211yesmaximal, characteristic, complemented
5C2×#11718750C211yesmaximal, characteristic, complemented
6C2×#11718716C211yesmaximal, characteristic, complemented
7C2×#11718713C211yesmaximal, characteristic, complemented
8C2×#11718700C211yesmaximal, characteristic
9C2×#11718709C211yesmaximal, characteristic, complemented
10C2×#11718702C211yesmaximal, characteristic, complemented
11C2×#11718675C211yesmaximal, characteristic, complemented
12C2×#11718691C211yesmaximal, characteristic, complemented
13C2×C4×#6106C211yesmaximal, characteristic, complemented
14C2×C4×#6105C211yesmaximal, characteristic, complemented
15C2×#11718658C211yesmaximal, characteristic, complemented
16C2×C13×#542C211yesmaximal, characteristic, complemented
17C13×#542—24no—
18C13×#542C2218yescomplemented
19C2×C13×C4⋊Q8C2211yescharacteristic
20C2×C13×#126—21no—
21C2×C13×#124—21no—
22C2×C13×#124C2211yescharacteristic
23C2×C13×#123—21no—
24C2×C13×C22⋊Q8—21no—
25C2×C13×C22⋊Q8C2211yescharacteristic
26C2×C13×#121C2211yescharacteristic
27C2×C4×Q8×C13C2211yescharacteristic
28C2×C4×D4×C13C2211yescharacteristic
29C2×C13×#117C2211yescharacteristic
30C22×#6107C2211yescharacteristic
31C22×#6106C2211yescharacteristic
32C22×#6105C2211yescharacteristic
33C22×#6104C2211yescharacteristic
34C2×#88184C2211yescharacteristic
35C2×#88178C2211yescharacteristic
36C22×#6099C2211yescharacteristic
37C23×#1055C2211yescharacteristic
38#11719239—24no—
39#11719239C2218yescomplemented
40C2×#88152—21no—
41C2×#88150—21no—
42C2×#88139—21no—
43C2×#88137—21no—
44C2×#88129C2211yescharacteristic
45C2×C4×D52C2211yescharacteristic
46C2×#88123C2211yescharacteristic
47C2×C4×Dic26C2211yescharacteristic
48C2×#88075C2211yescharacteristic
49C2×#88075C2211yescharacteristic
50C2×#88072C2211yescharacteristic
51C2×#88072C2211yescharacteristic
52#11718750C2218yescomplemented
53#11718740C2218yescomplemented
54#11718720C2218yescomplemented
55#11718716C2218yescomplemented
56#11718713C2218yescomplemented
57#11718709C2218yescomplemented
58#11718702C2218yescomplemented
59#11718700C2218yes—
60#11718691C2218yescomplemented
61C4×#6106C2218yescomplemented
62C4×#6105C2218yescomplemented
63#11718675C2218yescomplemented
64#11718658C2218yescomplemented
65C2×#88050C2211yescharacteristic
66C2×#88050C2211yescharacteristic
67C2×#88049C2211yescharacteristic
68C2×#88049C2211yescharacteristic
69C2×#88048C2211yescharacteristic
70C2×#88048C2211yescharacteristic
71C2×#88048C2211yescharacteristic
72C2×#88048C2211yescharacteristic
73C2×#88043C2211yescharacteristic
74C2×#88043C2211yescharacteristic
75C2×C4×#1055C2211yescharacteristic
76C2×C4×#1055C2211yescharacteristic
77C22×Q8×C13—21no—
78C22×Q8×C13C2311yescharacteristic
79C22×D4×C13—21no—
80C22×D4×C13C2311yescharacteristic
81C23×C4×C13—21no—
82C23×C4×C13C2311yescharacteristic
83C22×C22⋊D13—21no—
84C22×D52C2311yescharacteristic
85C22×C4×D13—21no—
86C22×Dic26—21no—
87C22×Dic26C2311yescharacteristic
88C13×C4⋊Q8—22no—
89C13×C4⋊Q8C2314yes—
90C13×#126—28no—
91C13×#124—28no—
92C13×#124—22no—
93C13×#124C2314yes—
94C13×#123—28no—
95C13×C22⋊Q8—22no—
96C13×C22⋊Q8—28no—
97C13×C22⋊Q8C2314yes—
98C13×#121—22no—
99C13×#121C2314yes—
100C4×Q8×C13—22no—
101C4×Q8×C13C2314yes—
102C4×D4×C13—22no—
103C4×D4×C13C2314yes—
104C13×#117D414yes—
105C13×#117C2314yes—
106C2×C13×C4⋊C4—21no—
107C2×C13×C4⋊C4—21no—
108C2×C13×C4⋊C4—21no—
109C2×C13×C4⋊C4D411yescharacteristic
110C2×C13×C4⋊C4D411yescharacteristic
111C2×C13×C4⋊C4C2311yescharacteristic
112C2×C13×C4⋊C4C2311yescharacteristic
113C2×C13×C22⋊C4—21no—
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×C42×C13C2311yescharacteristic
123C2×C22⋊Dic13—21no—
124C2×#6107—24no—
125C2×#6107C2314yes—
126C2×#6106—24no—
127C2×#6106C2314yes—
128C2×#6105—24no—
129C2×#6105C2314yes—
130C2×#6104—24no—
131C2×#6104C2314yes—
132#88184—22no—
133#88184C2314yes—
134C2×#6103—21no—
135C2×#6103—21no—
136C2×#6103—21no—
137C2×#6103—21no—
138C2×C4⋊Dic13—21no—
139C2×C4⋊Dic13C2311yescharacteristic
140C2×C4⋊Dic13C2311yescharacteristic
141#88178—22no—
142#88178C2314yes—
143C2×#6101—21no—
144C2×#6101—21no—
145C2×C4×Dic13—21no—
146C2×#6099—24no—
147C2×#6099C2314yes—
148C22×#1055—24no—
149C22×#1055C2314yes—
150C22×#1055C2311yescharacteristic
151C22×#1055C2311yescharacteristic
152C22×#1055C2311yescharacteristic
153C22×#1055C2311yescharacteristic
154#88152—28no—
155#88150—28no—
156#88139—28no—
157#88137—28no—
158#88129—22no—
159#88129C2314yes—
160C4×D52—22no—
161C4×D52C2314yes—
162#88123—22no—
163#88123C2314yes—
164C4×Dic26—22no—
165C4×Dic26C2314yes—
166#88075C2314yes—
167#88075C2314yes—
168#88072C2314yes—
169#88072C2314yes—
170#88050C2314yes—
171#88050C2314yes—
172#88049C2314yes—
173#88049C2314yes—
174#88048C2314yes—
175#88048C2314yes—
176#88048C2314yes—
177#88048C2314yes—
178#88043C2314yes—
179#88043C2314yes—
180C4×#1055C2314yes—
181C4×#1055C2314yes—
182C2×#3173—131nomaximal, Sylow
183C24×C13—21no—
184C24×C13C2×D411yescharacteristic
185C23×D13—21no—
186C2×Q8×C13—21no—
187C2×Q8×C13—24no—
188C2×Q8×C13—22no—
189C2×Q8×C13—22no—
190C2×Q8×C13—82no—
191C2×Q8×C13C2412yes—
192C2×D4×C13—24no—
193C2×D4×C13—21no—
194C2×D4×C13—22no—
195C2×D4×C13—22no—
196C2×D4×C13—82no—
197C2×D4×C13C2412yes—
198C22×C4×C13—22no—
199C22×C4×C13—22no—
200C22×C4×C13—21no—
201C22×C4×C13—21no—
202C22×C4×C13—21no—
203C22×C4×C13—24no—
204C22×C4×C13—82no—
205C22×C4×C13C2×D411yescharacteristic
206C22×C4×C13C2×D411yescharacteristic
207C22×C4×C13C2×D411yescharacteristic
208C22×C4×C13C2×D412yes—
209C22×C4×C13C2×D411yescharacteristic
210C22×C4×C13C2×D411yescharacteristic
211C22×C4×C13C2412yes—
212C22×C4×C13C2411yescharacteristic
213C2×C22⋊D13—24no—
214C2×C22⋊D13—82no—
215C22×Dic13—21no—
216C22×Dic13—21no—
217C22×Dic13—21no—
218C2×D52—22no—
219C2×D52—22no—
220C2×D52—21no—
221C2×D52C2412yes—
222C2×C4×D13—24no—
223C2×C4×D13—82no—
224C2×Dic26—22no—
225C2×Dic26—22no—
226C2×Dic26—21no—
227C2×Dic26—24no—
228C2×Dic26—82no—
229C2×Dic26C2412yes—
230C13×C4⋊C4—24no—
231C13×C4⋊C4—24no—
232C13×C4⋊C4—24no—
233C13×C4⋊C4—21no—
234C13×C4⋊C4—21no—
235C13×C4⋊C4C2×D414yes—
236C13×C4⋊C4C2×D414yes—
237C13×C4⋊C4C2412yes—
238C13×C4⋊C4C2412yes—
239C13×C22⋊C4—24no—
240C13×C22⋊C4—24no—
241C13×C22⋊C4—24no—
242C13×C22⋊C4—24no—
243C13×C22⋊C4—24no—
244C13×C22⋊C4C2×D414yes—
245C13×C22⋊C4C2×D414yes—
246C42×C13—24no—
247C42×C13C2×D412yes—
248C42×C13C2×D412yes—
249C42×C13C2412yes—
250C42×C13C2412yes—
251C22⋊Dic13—24no—
252#6107—28no—
253#6106—28no—
254#6105—28no—
255#6104—28no—
256#6103—24no—
257#6103—24no—
258#6103—24no—
259#6103—24no—
260C4⋊Dic13—21no—
261C4⋊Dic13—21no—
262C4⋊Dic13—24no—
263C4⋊Dic13C2412yes—
264C4⋊Dic13C2412yes—
265#6101—24no—
266#6101—24no—
267C4×Dic13—24no—
268#6099—28no—
269C2×#1055—22no—
270C2×#1055—22no—
271C2×#1055—28no—
272C2×#1055#4114yes—
273C2×#1055#4114yes—
274C2×#1055C2412yes—
275C2×#1055C2412yes—
276C2×#1055C2412yes—
277C2×#1055C2412yes—
278C2×#542—131no—
279C2×#542D1311yescharacteristic, complemented
280#3173—1316no—
281C2×#498—131no—
282C2×#495—131no—
283C2×#489—131no—
284C2×#489—131no—
285C2×#470—131no—
286C2×#469—131no—
287C2×#465—131no—
288C2×#465—131no—
289C2×#442—131no—
290C2×#441—131no—
291C2×C4×SD16—131no—
292C2×C4×SD16—131no—
293C2×#405—131no—
294C23×C13—22no—
295C23×C13—22no—
296C23×C13—22no—
297C23×C13—22no—
298C23×C13—42no—
299C23×C13—42no—
300C23×C13—42no—
301C23×C13C22×D412yes—
302C23×C13C22×D411yescharacteristic
303C22×D13—22no—
304C22×D13—42no—
305C22×D13—42no—
306C22×D13—42no—
307Q8×C13—22no—
308Q8×C13—22no—
309Q8×C13—42no—
310Q8×C13—84no—
311D4×C13—22no—
312D4×C13—22no—
313D4×C13—42no—
314D4×C13—84no—
315C2×C4×C13—22no—
316C2×C4×C13—22no—
317C2×C4×C13—22no—
318C2×C4×C13—22no—
319C2×C4×C13—22no—
320C2×C4×C13—24no—
321C2×C4×C13—22no—
322C2×C4×C13—22no—
323C2×C4×C13—22no—
324C2×C4×C13—22no—
325C2×C4×C13—22no—
326C2×C4×C13—42no—
327C2×C4×C13—42no—
328C2×C4×C13—42no—
329C2×C4×C13—84no—
330C2×C4×C13C22×D412yes—
331C2×C4×C13C22×D412yes—
332C2×C4×C13C22×D412yes—
333C2×C4×C13C22×D412yes—
334C2×C4×C13C22×D412yes—
335C2×C4×C13C22×D411yescharacteristic
336C2×C4×C13C2×#4112yes—
337C2×C4×C13C2×#4112yes—
338C2×C4×C13C2511yescharacteristic
339C22⋊D13—84no—
340C2×Dic13—22no—
341C2×Dic13—22no—
342C2×Dic13—22no—
343C2×Dic13—42no—
344C2×Dic13—42no—
345C2×Dic13—42no—
346D52—22no—
347D52—22no—
348D52—42no—
349C4×D13—84no—
350Dic26—22no—
351Dic26—22no—
352Dic26—42no—
353Dic26—84no—
354#1055—22no—
355#1055—22no—
356#1055C2×#4114yes—
357#1055C2×#4114yes—
358C22×Q16—131no—
359C22×SD16—131no—
360C22×SD16—131no—
361C22×D8—131no—
362C22×M16—131no—
363C23×C8—131no—
364#542—24no—
365#542—138no—
366#542—264no—
367#542C2×D1318yescomplemented
368C2×C4⋊Q8—131no—
369C2×C4⋊Q8C2×D1311yescharacteristic
370C2×#126—21no—
371C2×#126—261no—
372C2×#124—21no—
373C2×#124—131no—
374C2×#124—261no—
375C2×#124C2×D1311yescharacteristic
376C2×#123—21no—
377C2×#123—261no—
378C2×C22⋊Q8—21no—
379C2×C22⋊Q8—131no—
380C2×C22⋊Q8—261no—
381C2×C22⋊Q8C2×D1311yescharacteristic
382C2×#121—131no—
383C2×#121C2×D1311yescharacteristic
384C2×C4×Q8—131no—
385C2×C4×Q8C2×D1311yescharacteristic
386C2×C4×D4—131no—
387C2×C4×D4C2×D1311yescharacteristic
388C2×#117C2×D1311yescharacteristic
389#498—138no—
390#495—138no—
391#489—138no—
392#489—138no—
393#470—138no—
394#469—138no—
395#465—138no—
396#465—138no—
397#442—138no—
398#441—138no—
399C4×SD16—138no—
400C4×SD16—138no—
401C2×#106—131no—
402C2×#106—131no—
403C2×#106—131no—
404C2×#106—131no—
405C2×#103—131no—
406C2×#103—131no—
407C2×#103—131no—
408C2×#103—131no—
409C2×#102—131no—
410C2×#102—131no—
411C2×#102—131no—
412C2×#102—131no—
413#405—138no—
414C2×#97—131no—
415C2×#97—131no—
416C2×C4×C8—131no—
417C2×C4×C8—131no—
418C22×C13—22no—
419C22×C13—22no—
420C22×C13—22no—
421C22×C13—44no—
422C22×C13—42no—
423C22×C13—42no—
424C22×C13—42no—
425C22×C13—84no—
426C22×C13#53212yes—
427C22×C13#57712yes—
428C22×C13#57712yes—
429C22×C13C23×D411yescharacteristic
430C2×D13—42no—
431C2×D13—42no—
432C2×D13—42no—
433C2×D13—84no—
434C4×C13—22no—
435C4×C13—22no—
436C4×C13—22no—
437C4×C13—22no—
438C4×C13—22no—
439C4×C13—42no—
440C4×C13—42no—
441C4×C13—42no—
442C4×C13#53212yes—
443C4×C13C22×#4111yescharacteristic
444C4×C13C22×#4111yescharacteristic
445Dic13—42no—
446Dic13—42no—
447Dic13—42no—
448C22×Q8—21no—
449C22×Q8—131no—
450C22×Q8—261no—
451C22×Q8C22×D1311yescharacteristic
452C22×D4—21no—
453C22×D4—131no—
454C22×D4—261no—
455C22×D4C22×D1311yescharacteristic
456C23×C4—21no—
457C23×C4—261no—
458C23×C4C22×D1311yescharacteristic
459C2×Q16—134no—
460C2×Q16—264no—
461C2×SD16—134no—
462C2×SD16—134no—
463C2×SD16—264no—
464C2×SD16—264no—
465C2×D8—134no—
466C2×D8—264no—
467C2×M16—134no—
468C2×M16—264no—
469C22×C8—131no—
470C22×C8—131no—
471C22×C8—131no—
472C22×C8—134no—
473C22×C8—131no—
474C22×C8—264no—
475C4⋊Q8—22no—
476C4⋊Q8—134no—
477C4⋊Q8—262no—
478C4⋊Q8C22×D1314yes—
479#126—28no—
480#126—268no—
481#124—28no—
482#124—22no—
483#124—134no—
484#124—268no—
485#124—262no—
486#124C22×D1314yes—
487#123—28no—
488#123—268no—
489C22⋊Q8—22no—
490C22⋊Q8—28no—
491C22⋊Q8—134no—
492C22⋊Q8—262no—
493C22⋊Q8—268no—
494C22⋊Q8C22×D1314yes—
495#121—22no—
496#121—134no—
497#121—262no—
498#121C22×D1314yes—
499C4×Q8—22no—
500C4×Q8—134no—
501C4×Q8—262no—
502C4×Q8C22×D1314yes—
503C4×D4—22no—
504C4×D4—134no—
505C4×D4—262no—
506C4×D4C22×D1314yes—
507#117C22⋊D1314yes—
508#117C22×D1314yes—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—131no—
513C2×C4⋊C4—131no—
514C2×C4⋊C4—261no—
515C2×C4⋊C4—261no—
516C2×C4⋊C4—261no—
517C2×C4⋊C4C22⋊D1311yescharacteristic
518C2×C4⋊C4C22⋊D1311yescharacteristic
519C2×C4⋊C4C22×D1311yescharacteristic
520C2×C4⋊C4C22×D1311yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—261no—
527C2×C22⋊C4—261no—
528C2×C22⋊C4—261no—
529C2×C22⋊C4—261no—
530C2×C22⋊C4—261no—
531C2×C22⋊C4C22⋊D1311yescharacteristic
532C2×C22⋊C4C22⋊D1311yescharacteristic
533C2×C42—21no—
534C2×C42—261no—
535C2×C42C22×D1311yescharacteristic
536C2×C42C22×D1311yescharacteristic
537#106—134no—
538#106—134no—
539#106—134no—
540#106—134no—
541#103—134no—
542#103—134no—
543#103—134no—
544#103—134no—
545#102—134no—
546#102—134no—
547#102—134no—
548#102—134no—
549#97—134no—
550#97—134no—
551C4×C8—134no—
552C4×C8—134no—
553C2×C13—42no—
554C2×C13—82no—
555C2×C13#317314yescomplemented
556C2×C13C2×#53211yescharacteristic
557C2×C13C2×#57711yescharacteristic
558C2×C13C2×#57711yescharacteristic
559D13—82no—
560C24—21no—
561C24—261no—
562C24C2×C22⋊D1311yescharacteristic
563C2×Q8—21no—
564C2×Q8—24no—
565C2×Q8—22no—
566C2×Q8—22no—
567C2×Q8—82no—
568C2×Q8—132no—
569C2×Q8—261no—
570C2×Q8—264no—
571C2×Q8—262no—
572C2×Q8—262no—
573C2×Q8—1042no—
574C2×Q8C23×D1312yes—
575C2×D4—24no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—21no—
579C2×D4—82no—
580C2×D4—132no—
581C2×D4—264no—
582C2×D4—262no—
583C2×D4—262no—
584C2×D4—261no—
585C2×D4—1042no—
586C2×D4C23×D1312yes—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—24no—
593C22×C4—82no—
594C22×C4—261no—
595C22×C4—261no—
596C22×C4—261no—
597C22×C4—264no—
598C22×C4—1042no—
599C22×C4C2×C22⋊D1312yes—
600C22×C4C2×C22⋊D1311yescharacteristic
601C22×C4C2×C22⋊D1311yescharacteristic
602C22×C4C2×C22⋊D1311yescharacteristic
603C22×C4C2×C22⋊D1311yescharacteristic
604C22×C4C2×C22⋊D1311yescharacteristic
605C22×C4C23×D1312yes—
606C22×C4C23×D1311yescharacteristic
607Q16—268no—
608SD16—268no—
609SD16—268no—
610D8—268no—
611M16—268no—
612C2×C8—134no—
613C2×C8—134no—
614C2×C8—132no—
615C2×C8—132no—
616C2×C8—132no—
617C2×C8—132no—
618C2×C8—268no—
619C2×C8—262no—
620C2×C8—262no—
621C4⋊C4—24no—
622C4⋊C4—24no—
623C4⋊C4—24no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—132no—
627C4⋊C4—132no—
628C4⋊C4—261no—
629C4⋊C4—261no—
630C4⋊C4—264no—
631C4⋊C4—264no—
632C4⋊C4—264no—
633C4⋊C4C2×C22⋊D1314yes—
634C4⋊C4C2×C22⋊D1314yes—
635C4⋊C4C23×D1312yes—
636C4⋊C4C23×D1312yes—
637C22⋊C4—24no—
638C22⋊C4—24no—
639C22⋊C4—24no—
640C22⋊C4—24no—
641C22⋊C4—24no—
642C22⋊C4—264no—
643C22⋊C4—264no—
644C22⋊C4—264no—
645C22⋊C4—264no—
646C22⋊C4—264no—
647C22⋊C4C2×C22⋊D1314yes—
648C22⋊C4C2×C22⋊D1314yes—
649C42—24no—
650C42—264no—
651C42C2×C22⋊D1312yes—
652C42C2×C22⋊D1312yes—
653C42C23×D1312yes—
654C42C23×D1312yes—
655C13C2×#317311yescharacteristic, complemented, Sylow
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—262no—
664C23—522no—
665C23—522no—
666C23—522no—
667C23C22×C22⋊D1312yes—
668C23C22×C22⋊D1311yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—42no—
672Q8—84no—
673Q8—262no—
674Q8—262no—
675Q8—522no—
676Q8—1044no—
677D4—22no—
678D4—22no—
679D4—42no—
680D4—84no—
681D4—262no—
682D4—262no—
683D4—522no—
684D4—1044no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—24no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—84no—
700C2×C4—262no—
701C2×C4—262no—
702C2×C4—262no—
703C2×C4—522no—
704C2×C4—522no—
705C2×C4—522no—
706C2×C4—1044no—
707C2×C4#41×D1312yes—
708C2×C4#41×D1312yes—
709C2×C4C22×C22⋊D1312yes—
710C2×C4C22×C22⋊D1312yes—
711C2×C4C22×C22⋊D1312yes—
712C2×C4C22×C22⋊D1312yes—
713C2×C4C22×C22⋊D1312yes—
714C2×C4C22×C22⋊D1311yescharacteristic
715C2×C4C24×D1311yescharacteristic
716C8—134no—
717C8—134no—
718C8—262no—
719C8—262no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—44no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—84no—
728C22—522no—
729C22—522no—
730C22—522no—
731C22—1044no—
732C22#1171953712yes—
733C22#1171954112yes—
734C22#1171954212yes—
735C22C23×C22⋊D1311yescharacteristic
736C4—22no—
737C4—22no—
738C4—22no—
739C4—22no—
740C4—22no—
741C4—42no—
742C4—42no—
743C4—42no—
744C4—522no—
745C4—522no—
746C4—522no—
747C4#1171953712yes—
748C4C2×#41×D1311yescharacteristic
749C4C2×#41×D1311yescharacteristic
750C2—42no—
751C2—82no—
752C2—1042no—
753C2#1312544714yesdirect product factor
754C2C2×#1171953711yescharacteristic
755C2C2×#1171954211yescharacteristic
756C2C2×#1171954111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#542C2
socleC23×C13C22×D4
prime radicalC2×#11718700C2
hypercenterC2×#542D13
hypocenterC13C2×#3173
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#11719239C2semidirect
2. #13125447C2direct (N × H)
3. C2×#11718740C2semidirect
4. C2×#11718720C2semidirect
5. C2×#11718750C2semidirect
6. C2×#11718716C2semidirect
7. C2×#11718713C2semidirect
9. C2×#11718709C2semidirect
10. C2×#11718702C2semidirect
11. C2×#11718675C2semidirect
12. C2×#11718691C2semidirect
13. C2×C4×#6106C2semidirect
14. C2×C4×#6105C2semidirect
15. C2×#11718658C2semidirect
16. C2×C13×#542C2semidirect
18. C13×#542C22semidirect
39. #11719239C22semidirect
52. #11718750C22semidirect
53. #11718740C22semidirect
54. #11718720C22semidirect
55. #11718716C22semidirect
56. #11718713C22semidirect
57. #11718709C22semidirect
58. #11718702C22semidirect
60. #11718691C22semidirect
61. C4×#6106C22semidirect
62. C4×#6105C22semidirect
63. #11718675C22semidirect
64. #11718658C22semidirect
279. C2×#542D13semidirect
367. #542C2×D13semidirect
555. C2×C13#3173semidirect
655. C13C2×#3173semidirect
753. C2#13125447direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192392
#131254472
C2×#117187402
C2×#117187202
C2×#117187502
C2×#117187162
C2×#117187132
C2×#117187002
C2×#117187092
C2×#117187022
C2×#117186752
C2×#117186912
C2×C4×#61062
C2×C4×#61052
C2×#117186582
C2×C13×#5422
C2×#317313