Finite Group Databasebeta

← C2×#13122885 #16069444

Subgroups — C2×#13122885 #16069444

Order 3328.

2566 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88143C211yesmaximal, characteristic, complemented
2C22×#88139C211yesmaximal, characteristic
3#13122885C2116yesmaximal, direct product factor
4C2×#11718610C211yesmaximal, characteristic, complemented
5C2×#11718653C211yesmaximal, characteristic, complemented
6C2×#11718336C211yesmaximal, characteristic, complemented
7C2×#11718613C211yesmaximal, characteristic, complemented
8C2×#11718609C211yesmaximal, characteristic, complemented
9C2×#11718655C211yesmaximal, characteristic, complemented
10C2×#11718655C211yesmaximal, characteristic, complemented
11C2×#11718317C211yesmaximal, characteristic, complemented
12C2×#11718640C211yesmaximal, characteristic, complemented
13C2×#11718622C211yesmaximal, characteristic
14C2×#11718620C211yesmaximal, characteristic
15C2×#11718638C211yesmaximal, characteristic, complemented
16C2×C13×#396C211yesmaximal, characteristic, complemented
17C23×C22⋊D13C2211yescharacteristic
18C23×Dic26C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C13×C4⋊C4C2211yescharacteristic
22C22×C13×C22⋊C4C2211yescharacteristic
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C22⋊Dic13C2211yescharacteristic
26C22×C22⋊Dic13C2211yescharacteristic
27C22×C22⋊Dic13C2211yescharacteristic
28C22×#6103C2211yescharacteristic
29C22×#6103C2211yescharacteristic
30C22×#6103C2211yescharacteristic
31C22×#6103C2211yescharacteristic
32C22×#6103C2211yescharacteristic
33C22×#6103C2211yescharacteristic
34C22×C4⋊Dic13C2211yescharacteristic
35C22×C4⋊Dic13C2211yescharacteristic
36C22×C4⋊Dic13C2211yescharacteristic
37C22×#6101C2211yescharacteristic
38C22×#6101C2211yescharacteristic
39C22×#6101C2211yescharacteristic
40C22×#6101C2211yescharacteristic
41C22×#6101C2211yescharacteristic
42C22×#6101C2211yescharacteristic
43C22×C4×Dic13C2211yescharacteristic
44C2×#88143—28no—
45C2×#88143C2218yescomplemented
46C2×#88139—28no—
47C2×#88139C2218yes—
48C13×#396C2218yescomplemented
49C2×C13×#95C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57#11718655C2218yescomplemented
58#11718655C2218yescomplemented
59#11718653C2218yescomplemented
60#11718640C2218yescomplemented
61#11718638C2218yescomplemented
62#11718622C2218yes—
63#11718620C2218yes—
64#11718613C2218yescomplemented
65#11718610C2218yescomplemented
66#11718609C2218yescomplemented
67#11718336C2218yescomplemented
68#11718317C2218yescomplemented
69C25×C13C2311yescharacteristic
70C24×D13C2311yescharacteristic
71C23×C4×C13C2311yescharacteristic
72C23×C4×C13C2311yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C22×C22⋊D13—24no—
78C22×C22⋊D13—42no—
79C22×C22⋊D13—42no—
80C22×C22⋊D13C2314yes—
81C23×Dic13C2311yescharacteristic
82C23×Dic13C2311yescharacteristic
83C23×Dic13C2311yescharacteristic
84C23×Dic13C2311yescharacteristic
85C23×Dic13C2311yescharacteristic
86C23×Dic13C2311yescharacteristic
87C23×Dic13C2311yescharacteristic
88C22×Dic26—24no—
89C22×Dic26—42no—
90C22×Dic26—42no—
91C22×Dic26C2314yes—
92C2×C13×C4⋊C4—24no—
93C2×C13×C4⋊C4—42no—
94C2×C13×C4⋊C4—42no—
95C2×C13×C4⋊C4C2314yes—
96C2×C13×C4⋊C4C2314yes—
97C2×C13×C4⋊C4C2314yes—
98C2×C13×C22⋊C4—24no—
99C2×C13×C22⋊C4—42no—
100C2×C13×C22⋊C4—42no—
101C2×C13×C22⋊C4C2314yes—
102C2×C13×C22⋊C4C2314yes—
103C2×C13×C22⋊C4C2314yes—
104C2×C22⋊Dic13—24no—
105C2×C22⋊Dic13—42no—
106C2×C22⋊Dic13—42no—
107C2×C22⋊Dic13C2314yes—
108C2×C22⋊Dic13C2314yes—
109C2×C22⋊Dic13C2314yes—
110C2×#6103—24no—
111C2×#6103—24no—
112C2×#6103—42no—
113C2×#6103—42no—
114C2×#6103—42no—
115C2×#6103—42no—
116C2×#6103C2314yes—
117C2×#6103C2314yes—
118C2×#6103C2314yes—
119C2×#6103C2314yes—
120C2×#6103C2314yes—
121C2×#6103C2314yes—
122C2×C4⋊Dic13—24no—
123C2×C4⋊Dic13—42no—
124C2×C4⋊Dic13—42no—
125C2×C4⋊Dic13C2314yes—
126C2×C4⋊Dic13C2314yes—
127C2×C4⋊Dic13C2314yes—
128C2×#6101—24no—
129C2×#6101—24no—
130C2×#6101—24no—
131C2×#6101—24no—
132C2×#6101—42no—
133C2×#6101—42no—
134C2×#6101C2314yes—
135C2×#6101C2314yes—
136C2×#6101C2314yes—
137C2×#6101C2314yes—
138C2×#6101C2314yes—
139C2×#6101C2314yes—
140C2×C4×Dic13D418yes—
141C2×C4×Dic13C2314yes—
142#88143—232no—
143#88139—232no—
144C13×#95C2314yes—
145#88071C2314yes—
146#88071C2314yes—
147#88071C2314yes—
148#88071C2314yes—
149#88071C2314yes—
150#88071C2314yes—
151#88071C2314yes—
152C2×#2820—131nomaximal, Sylow
153C24×C13—22no—
154C24×C13—22no—
155C24×C13—22no—
156C24×C13—22no—
157C24×C13—22no—
158C24×C13—22no—
159C24×C13—22no—
160C24×C13C2412yes—
161C24×C13C2411yescharacteristic
162C23×D13—22no—
163C23×D13—22no—
164C23×D13—22no—
165C23×D13—22no—
166C23×D13—22no—
167C23×D13—22no—
168C23×D13—22no—
169C23×D13C2412yes—
170C22×C4×C13—22no—
171C22×C4×C13—22no—
172C22×C4×C13—22no—
173C22×C4×C13—22no—
174C22×C4×C13—22no—
175C22×C4×C13—22no—
176C22×C4×C13—22no—
177C22×C4×C13—22no—
178C22×C4×C13—22no—
179C22×C4×C13—22no—
180C22×C4×C13—22no—
181C22×C4×C13—22no—
182C22×C4×C13—22no—
183C22×C4×C13—22no—
184C22×C4×C13—22no—
185C22×C4×C13—22no—
186C22×C4×C13—22no—
187C22×C4×C13C2×D414yes—
188C22×C4×C13C2412yes—
189C22×C4×C13C2412yes—
190C22×C4×C13C2412yes—
191C22×C4×C13C2412yes—
192C22×C4×C13C2412yes—
193C22×C4×C13C2412yes—
194C2×C22⋊D13—28no—
195C2×C22⋊D13—44no—
196C2×C22⋊D13—44no—
197C2×C22⋊D13—416no—
198C22×Dic13—22no—
199C22×Dic13—22no—
200C22×Dic13—22no—
201C22×Dic13—22no—
202C22×Dic13—22no—
203C22×Dic13—22no—
204C22×Dic13—22no—
205C22×Dic13—22no—
206C22×Dic13—22no—
207C22×Dic13—22no—
208C22×Dic13—22no—
209C22×Dic13—22no—
210C22×Dic13—22no—
211C22×Dic13—22no—
212C22×Dic13—22no—
213C22×Dic13—22no—
214C22×Dic13—22no—
215C22×Dic13—22no—
216C22×Dic13—22no—
217C22×Dic13C2×D414yes—
218C22×Dic13C2×D414yes—
219C22×Dic13C2412yes—
220C22×Dic13C2412yes—
221C22×Dic13C2412yes—
222C22×Dic13C2412yes—
223C22×Dic13C2412yes—
224C22×Dic13C2412yes—
225C22×Dic13C2412yes—
226C2×Dic26—28no—
227C2×Dic26—44no—
228C2×Dic26—44no—
229C2×Dic26—416no—
230C13×C4⋊C4—28no—
231C13×C4⋊C4—44no—
232C13×C4⋊C4—44no—
233C13×C22⋊C4—28no—
234C13×C22⋊C4—44no—
235C13×C22⋊C4—44no—
236C22⋊Dic13—28no—
237C22⋊Dic13—44no—
238C22⋊Dic13—44no—
239#6103—28no—
240#6103—28no—
241#6103—44no—
242#6103—44no—
243#6103—44no—
244#6103—44no—
245C4⋊Dic13—28no—
246C4⋊Dic13—44no—
247C4⋊Dic13—44no—
248#6101—28no—
249#6101—28no—
250#6101—28no—
251#6101—28no—
252#6101—44no—
253#6101—44no—
254C4×Dic13C2×D4116yes—
255C22×#125—131no—
256C22×#124—131no—
257#2820—1316no—
258C2×#399—131no—
259C2×#399—131no—
260C2×#397—131no—
261C2×#397—131no—
262C2×#396—131no—
263C2×#396—131no—
264C2×#396—131no—
265C2×#396D1311yescharacteristic, complemented
266C2×#395—131no—
267C2×#395—131no—
268C2×#394—131no—
269C2×#394—131no—
270C2×#382—131no—
271C23×C13—22no—
272C23×C13—22no—
273C23×C13—22no—
274C23×C13—22no—
275C23×C13—22no—
276C23×C13—22no—
277C23×C13—22no—
278C23×C13—44no—
279C23×C13—44no—
280C23×C13—44no—
281C23×C13—44no—
282C23×C13—44no—
283C23×C13—44no—
284C23×C13—44no—
285C23×C13C22×D412yes—
286C23×C13H(5,𝔽2)12yes—
287C23×C13H(5,𝔽2)12yes—
288C23×C13H(5,𝔽2)12yes—
289C23×C132−1+412yes—
290C23×C132−1+412yes—
291C23×C132−1+412yes—
292C23×C13C2511yescharacteristic
293C22×D13—22no—
294C22×D13—22no—
295C22×D13—22no—
296C22×D13—22no—
297C22×D13—22no—
298C22×D13—22no—
299C22×D13—22no—
300C22×D13—44no—
301C22×D13—44no—
302C22×D13—44no—
303C22×D13—44no—
304C22×D13—44no—
305C22×D13—44no—
306C22×D13—44no—
307C2×C4×C13—28no—
308C2×C4×C13—22no—
309C2×C4×C13—22no—
310C2×C4×C13—22no—
311C2×C4×C13—22no—
312C2×C4×C13—22no—
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—22no—
321C2×C4×C13—22no—
322C2×C4×C13—22no—
323C2×C4×C13—22no—
324C2×C4×C13—22no—
325C2×C4×C13—44no—
326C2×C4×C13—44no—
327C2×C4×C13—44no—
328C2×C4×C13—44no—
329C2×C4×C13—44no—
330C2×C4×C13C22×D414yes—
331C22⋊D13—416no—
332C2×Dic13—28no—
333C2×Dic13—28no—
334C2×Dic13—22no—
335C2×Dic13—22no—
336C2×Dic13—22no—
337C2×Dic13—22no—
338C2×Dic13—22no—
339C2×Dic13—22no—
340C2×Dic13—22no—
341C2×Dic13—22no—
342C2×Dic13—22no—
343C2×Dic13—22no—
344C2×Dic13—22no—
345C2×Dic13—22no—
346C2×Dic13—22no—
347C2×Dic13—22no—
348C2×Dic13—22no—
349C2×Dic13—22no—
350C2×Dic13—22no—
351C2×Dic13—22no—
352C2×Dic13—22no—
353C2×Dic13—44no—
354C2×Dic13—44no—
355C2×Dic13—44no—
356C2×Dic13—44no—
357C2×Dic13—44no—
358C2×Dic13C22×D414yes—
359C2×Dic13C22×D414yes—
360Dic26—416no—
361C23×Q8—131no—
362C23×D4—131no—
363C2×#125—138no—
364C2×#125—268no—
365C2×#124—138no—
366C2×#124—268no—
367C22×C4⋊C4—131no—
368C22×C4⋊C4—131no—
369C22×C4⋊C4—131no—
370C22×C4⋊C4—131no—
371C22×C4⋊C4—131no—
372C22×C4⋊C4—131no—
373C22×C4⋊C4—131no—
374C22×C4⋊C4—131no—
375C22×C4⋊C4—131no—
376C22×C4⋊C4C2×D1311yescharacteristic
377C22×C4⋊C4C2×D1311yescharacteristic
378C22×C4⋊C4C2×D1311yescharacteristic
379C22×C22⋊C4—131no—
380C22×C22⋊C4—131no—
381C22×C22⋊C4—131no—
382C22×C22⋊C4—131no—
383C22×C22⋊C4—131no—
384C22×C22⋊C4—131no—
385C22×C22⋊C4—131no—
386C22×C22⋊C4—131no—
387C22×C22⋊C4—131no—
388C22×C22⋊C4C2×D1311yescharacteristic
389C22×C22⋊C4C2×D1311yescharacteristic
390C22×C22⋊C4C2×D1311yescharacteristic
391C22×C42—131no—
392#399—138no—
393#399—138no—
394#397—138no—
395#397—138no—
396#396—138no—
397#396—138no—
398#396—138no—
399#396C2×D1318yescomplemented
400#395—138no—
401#395—138no—
402#394—138no—
403#394—138no—
404#382—138no—
405C2×#95—131no—
406C2×#95—131no—
407C2×#95—131no—
408C2×#95—131no—
409C2×#95—131no—
410C2×#95—131no—
411C2×#95—131no—
412C2×#95C2×D1311yescharacteristic
413C22×C13—42no—
414C22×C13—42no—
415C22×C13—42no—
416C22×C13—42no—
417C22×C13—42no—
418C22×C13—42no—
419C22×C13—42no—
420C22×C13—88no—
421C22×C13#53514yes—
422C22×C13#53614yes—
423C22×C13#53714yes—
424C22×C13#56214yes—
425C22×C13#56214yes—
426C22×C13#56314yes—
427C22×C13#56314yes—
428C22×C13C23×D411yescharacteristic
429C22×C13C2×H(5,𝔽2)11yescharacteristic
430C22×C13C2×H(5,𝔽2)11yescharacteristic
431C22×C13C2×H(5,𝔽2)11yescharacteristic
432C22×C13C2×2−1+411yescharacteristic
433C22×C13C2×2−1+411yescharacteristic
434C22×C13C2×2−1+411yescharacteristic
435C2×D13—42no—
436C2×D13—42no—
437C2×D13—42no—
438C2×D13—42no—
439C2×D13—42no—
440C2×D13—42no—
441C2×D13—42no—
442C2×D13—88no—
443C4×C13—24no—
444C4×C13—42no—
445C4×C13—42no—
446C4×C13—42no—
447C4×C13—42no—
448C4×C13—42no—
449Dic13—24no—
450Dic13—24no—
451Dic13—42no—
452Dic13—42no—
453Dic13—42no—
454Dic13—42no—
455Dic13—42no—
456C25—131no—
457C25C22×D1311yescharacteristic
458C22×Q8—134no—
459C22×Q8—264no—
460C22×Q8—522no—
461C22×Q8—522no—
462C22×D4—134no—
463C22×D4—264no—
464C22×D4—522no—
465C22×D4—522no—
466C23×C4—131no—
467C23×C4—131no—
468C23×C4—131no—
469C23×C4—131no—
470C23×C4—131no—
471C23×C4—131no—
472C23×C4—131no—
473C23×C4C22×D1311yescharacteristic
474C23×C4C22×D1311yescharacteristic
475C23×C4C22×D1311yescharacteristic
476C23×C4C22×D1311yescharacteristic
477C23×C4C22×D1311yescharacteristic
478C23×C4C22×D1311yescharacteristic
479#125—2632no—
480#124—2632no—
481C2×C4⋊C4—24no—
482C2×C4⋊C4—42no—
483C2×C4⋊C4—42no—
484C2×C4⋊C4—134no—
485C2×C4⋊C4—134no—
486C2×C4⋊C4—134no—
487C2×C4⋊C4—134no—
488C2×C4⋊C4—134no—
489C2×C4⋊C4—134no—
490C2×C4⋊C4—134no—
491C2×C4⋊C4—134no—
492C2×C4⋊C4—134no—
493C2×C4⋊C4—264no—
494C2×C4⋊C4—264no—
495C2×C4⋊C4—264no—
496C2×C4⋊C4—264no—
497C2×C4⋊C4—264no—
498C2×C4⋊C4—522no—
499C2×C4⋊C4—522no—
500C2×C4⋊C4—522no—
501C2×C4⋊C4—522no—
502C2×C4⋊C4C22×D1314yes—
503C2×C4⋊C4C22×D1314yes—
504C2×C4⋊C4C22×D1314yes—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—42no—
507C2×C22⋊C4—42no—
508C2×C22⋊C4—134no—
509C2×C22⋊C4—134no—
510C2×C22⋊C4—134no—
511C2×C22⋊C4—134no—
512C2×C22⋊C4—134no—
513C2×C22⋊C4—134no—
514C2×C22⋊C4—134no—
515C2×C22⋊C4—134no—
516C2×C22⋊C4—134no—
517C2×C22⋊C4—264no—
518C2×C22⋊C4—264no—
519C2×C22⋊C4—264no—
520C2×C22⋊C4—522no—
521C2×C22⋊C4—522no—
522C2×C22⋊C4—522no—
523C2×C22⋊C4—522no—
524C2×C22⋊C4—522no—
525C2×C22⋊C4—522no—
526C2×C22⋊C4C22×D1314yes—
527C2×C22⋊C4C22×D1314yes—
528C2×C22⋊C4C22×D1314yes—
529C2×C42—138no—
530C2×C42—134no—
531#95—134no—
532#95—134no—
533#95—134no—
534#95—134no—
535#95—134no—
536#95—134no—
537#95—134no—
538#95C22×D1314yes—
539C2×C13—82no—
540C2×C13#282018yescomplemented
541C2×C13C2×#53511yescharacteristic
542C2×C13C2×#53611yescharacteristic
543C2×C13C2×#53711yescharacteristic
544C2×C13C2×#56211yescharacteristic
545C2×C13C2×#56211yescharacteristic
546C2×C13C2×#56311yescharacteristic
547C2×C13C2×#56311yescharacteristic
548D13—82no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—132no—
557C24—262no—
558C24—262no—
559C24—262no—
560C24—262no—
561C24—262no—
562C24—262no—
563C24—262no—
564C24C23×D1312yes—
565C24C23×D1311yescharacteristic
566C2×Q8—268no—
567C2×Q8—524no—
568C2×Q8—524no—
569C2×Q8—5216no—
570C2×D4—268no—
571C2×D4—524no—
572C2×D4—524no—
573C2×D4—5216no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—134no—
592C22×C4—134no—
593C22×C4—132no—
594C22×C4—132no—
595C22×C4—132no—
596C22×C4—132no—
597C22×C4—132no—
598C22×C4—132no—
599C22×C4—132no—
600C22×C4—262no—
601C22×C4—262no—
602C22×C4—262no—
603C22×C4—262no—
604C22×C4—262no—
605C22×C4—262no—
606C22×C4—262no—
607C22×C4—262no—
608C22×C4—262no—
609C22×C4—262no—
610C22×C4—262no—
611C22×C4—262no—
612C22×C4—262no—
613C22×C4—262no—
614C22×C4—262no—
615C22×C4—262no—
616C22×C4—262no—
617C22×C4—262no—
618C22×C4—262no—
619C22×C4D4×D1314yes—
620C22×C4C23×D1312yes—
621C22×C4C23×D1312yes—
622C22×C4C23×D1312yes—
623C22×C4C23×D1312yes—
624C22×C4C23×D1312yes—
625C22×C4C23×D1312yes—
626C4⋊C4—28no—
627C4⋊C4—44no—
628C4⋊C4—44no—
629C4⋊C4—268no—
630C4⋊C4—268no—
631C4⋊C4—268no—
632C4⋊C4—268no—
633C4⋊C4—268no—
634C4⋊C4—524no—
635C4⋊C4—524no—
636C4⋊C4—524no—
637C4⋊C4—524no—
638C22⋊C4—28no—
639C22⋊C4—44no—
640C22⋊C4—44no—
641C22⋊C4—268no—
642C22⋊C4—268no—
643C22⋊C4—268no—
644C22⋊C4—524no—
645C22⋊C4—524no—
646C22⋊C4—524no—
647C22⋊C4—524no—
648C22⋊C4—524no—
649C22⋊C4—524no—
650C42—1316no—
651C13C2×#282011yescharacteristic, complemented, Sylow
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—44no—
665C23—44no—
666C23—262no—
667C23—262no—
668C23—262no—
669C23—262no—
670C23—262no—
671C23—262no—
672C23—262no—
673C23—524no—
674C23—524no—
675C23—524no—
676C23—524no—
677C23—524no—
678C23—524no—
679C23—524no—
680C23C2×D4×D1312yes—
681C23#8825112yes—
682C23#8825112yes—
683C23#8825412yes—
684C23#8825612yes—
685C23#8825712yes—
686C23#8825712yes—
687C23C24×D1311yescharacteristic
688Q8—5216no—
689D4—5216no—
690C2×C4—28no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—44no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—134no—
714C2×C4—134no—
715C2×C4—268no—
716C2×C4—268no—
717C2×C4—262no—
718C2×C4—262no—
719C2×C4—262no—
720C2×C4—262no—
721C2×C4—262no—
722C2×C4—262no—
723C2×C4—262no—
724C2×C4—262no—
725C2×C4—262no—
726C2×C4—262no—
727C2×C4—262no—
728C2×C4—262no—
729C2×C4—262no—
730C2×C4—262no—
731C2×C4—262no—
732C2×C4—262no—
733C2×C4—262no—
734C2×C4—262no—
735C2×C4—262no—
736C2×C4—524no—
737C2×C4—524no—
738C2×C4—524no—
739C2×C4—524no—
740C2×C4—524no—
741C2×C4C2×D4×D1314yes—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—88no—
750C22—522no—
751C22—522no—
752C22—522no—
753C22—522no—
754C22—522no—
755C22—522no—
756C22—522no—
757C22—1048no—
758C22#1171930214yes—
759C22#1171931214yes—
760C22#1171932614yes—
761C22#1171933314yes—
762C22#1171935114yes—
763C22#1171935214yes—
764C22#1171941714yes—
765C22C22×D4×D1311yescharacteristic
766C22C2×#8825111yescharacteristic
767C22C2×#8825111yescharacteristic
768C22C2×#8825411yescharacteristic
769C22C2×#8825611yescharacteristic
770C22C2×#8825711yescharacteristic
771C22C2×#8825711yescharacteristic
772C4—24no—
773C4—42no—
774C4—42no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—264no—
779C4—264no—
780C4—522no—
781C4—522no—
782C4—522no—
783C4—522no—
784C4—522no—
785C2—82no—
786C2—1042no—
787C2#1312288518yesdirect product factor
788C2C2×#1171931211yescharacteristic
789C2C2×#1171933311yescharacteristic
790C2C2×#1171930211yescharacteristic
791C2C2×#1171932611yescharacteristic
792C2C2×#1171935211yescharacteristic
793C2C2×#1171935111yescharacteristic
794C2C2×#1171941711yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#396C2
socleC24×C13C24
prime radicalC23×C22⋊D13C22
hypercenterC2×#396D13
hypocenterC13C2×#2820
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×#88143C2semidirect
3. #13122885C2direct (N × H)
4. C2×#11718610C2semidirect
5. C2×#11718653C2semidirect
6. C2×#11718336C2semidirect
7. C2×#11718613C2semidirect
8. C2×#11718609C2semidirect
9. C2×#11718655C2semidirect
10. C2×#11718655C2semidirect
11. C2×#11718317C2semidirect
12. C2×#11718640C2semidirect
15. C2×#11718638C2semidirect
16. C2×C13×#396C2semidirect
45. C2×#88143C22semidirect
48. C13×#396C22semidirect
57. #11718655C22semidirect
58. #11718655C22semidirect
59. #11718653C22semidirect
60. #11718640C22semidirect
61. #11718638C22semidirect
64. #11718613C22semidirect
65. #11718610C22semidirect
66. #11718609C22semidirect
67. #11718336C22semidirect
68. #11718317C22semidirect
265. C2×#396D13semidirect
399. #396C2×D13semidirect
540. C2×C13#2820semidirect
651. C13C2×#2820semidirect
787. C2#13122885direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881432
C22×#881392
#131228852
C2×#117186102
C2×#117186532
C2×#117183362
C2×#117186132
C2×#117186092
C2×#117186552
C2×#117183172
C2×#117186402
C2×#117186222
C2×#117186202
C2×#117186382
C2×C13×#3962
C2×#282013