Finite Group Databasebeta

← C2×#13119986 #16033086

Subgroups — C2×#13119986 #16033086

Order 3328.

2898 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88130C211yesmaximal, characteristic, complemented
2C22×#88150C211yesmaximal, characteristic, complemented
3#13119986C2116yesmaximal, direct product factor
4C2×#11718641C211yesmaximal, characteristic, complemented
5C2×#11718336C211yesmaximal, characteristic, complemented
6C2×#11718333C211yesmaximal, characteristic
7C2×#11718334C211yesmaximal, characteristic, complemented
8C2×#11718307C211yesmaximal, characteristic, complemented
9C2×#11718649C211yesmaximal, characteristic
10C2×#11718651C211yesmaximal, characteristic, complemented
11C2×#11718330C211yesmaximal, characteristic, complemented
12C2×#11718330C211yesmaximal, characteristic, complemented
13C2×#11718326C211yesmaximal, characteristic
14C2×#11718310C211yesmaximal, characteristic, complemented
15C2×C4×#6103C211yesmaximal, characteristic, complemented
16C2×C13×#387C211yesmaximal, characteristic, complemented
17C23×D52C2211yescharacteristic
18C23×C4×D13C2211yescharacteristic
19C23×Dic26C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C13×C4⋊C4C2211yescharacteristic
22C22×C42×C13C2211yescharacteristic
23C22×#6103C2211yescharacteristic
24C22×#6103C2211yescharacteristic
25C22×#6103C2211yescharacteristic
26C22×#6103C2211yescharacteristic
27C22×#6103C2211yescharacteristic
28C22×#6103C2211yescharacteristic
29C22×#6103C2211yescharacteristic
30C22×#6103C2211yescharacteristic
31C22×#6103C2211yescharacteristic
32C22×#6103C2211yescharacteristic
33C22×#6103C2211yescharacteristic
34C22×#6101C2211yescharacteristic
35C22×#6101C2211yescharacteristic
36C22×#6101C2211yescharacteristic
37C22×#6101C2211yescharacteristic
38C22×#6101C2211yescharacteristic
39C22×C4×Dic13C2211yescharacteristic
40C22×C4×Dic13C2211yescharacteristic
41C22×C4×Dic13C2211yescharacteristic
42C2×#88150—28no—
43C2×#88150C2218yescomplemented
44C2×#88130—28no—
45C2×#88130C2218yescomplemented
46C13×#387C2218yescomplemented
47C2×C13×#95C2211yescharacteristic
48C2×C13×#95C2211yescharacteristic
49C2×C13×#95C2211yescharacteristic
50C2×C13×#95C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57#11718651C2218yescomplemented
58#11718649C2218yes—
59#11718641C2218yescomplemented
60C4×#6103C2218yescomplemented
61#11718336C2218yescomplemented
62#11718334C2218yescomplemented
63#11718333C2218yes—
64#11718330C2218yescomplemented
65#11718330C2218yescomplemented
66#11718326C2218yes—
67#11718310C2218yescomplemented
68#11718307C2218yescomplemented
69C24×D13C2311yescharacteristic
70C24×D13C2311yescharacteristic
71C23×C4×C13C2311yescharacteristic
72C23×C4×C13C2311yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C23×C4×C13C2311yescharacteristic
78C23×Dic13C2311yescharacteristic
79C23×Dic13C2311yescharacteristic
80C23×Dic13C2311yescharacteristic
81C23×Dic13C2311yescharacteristic
82C23×Dic13C2311yescharacteristic
83C23×Dic13C2311yescharacteristic
84C22×D52—24no—
85C22×D52—24no—
86C22×D52—42no—
87C22×D52C2314yes—
88C22×C4×D13—24no—
89C22×C4×D13—24no—
90C22×C4×D13—42no—
91C22×C4×D13C2314yes—
92C22×Dic26—24no—
93C22×Dic26—24no—
94C22×Dic26—42no—
95C22×Dic26C2314yes—
96C2×C13×C4⋊C4—24no—
97C2×C13×C4⋊C4—24no—
98C2×C13×C4⋊C4C2314yes—
99C2×C13×C4⋊C4C2314yes—
100C2×C42×C13—24no—
101C2×C42×C13C2314yes—
102C2×#6103—24no—
103C2×#6103—24no—
104C2×#6103—24no—
105C2×#6103—24no—
106C2×#6103—24no—
107C2×#6103—24no—
108C2×#6103—24no—
109C2×#6103—24no—
110C2×#6103—24no—
111C2×#6103—24no—
112C2×#6103—42no—
113C2×#6103C2314yes—
114C2×#6103C2314yes—
115C2×#6103C2314yes—
116C2×#6103C2314yes—
117C2×#6103C2314yes—
118C2×#6103C2314yes—
119C2×#6103C2314yes—
120C2×#6103C2314yes—
121C2×#6103C2314yes—
122C2×#6103C2314yes—
123C2×#6103C2314yes—
124C2×#6101—24no—
125C2×#6101—24no—
126C2×#6101—24no—
127C2×#6101—24no—
128C2×#6101D418yescomplemented
129C2×#6101C2314yes—
130C2×#6101C2314yes—
131C2×#6101C2314yes—
132C2×#6101C2314yes—
133C2×#6101C2314yes—
134C2×C4×Dic13—24no—
135C2×C4×Dic13—42no—
136C2×C4×Dic13—42no—
137C2×C4×Dic13C2314yes—
138C2×C4×Dic13C2314yes—
139C2×C4×Dic13C2314yes—
140#88150—232no—
141#88130—232no—
142C13×#95C2314yes—
143C13×#95C2314yes—
144C13×#95C2314yes—
145C13×#95C2314yes—
146#88071C2314yes—
147#88071C2314yes—
148#88071C2314yes—
149#88071C2314yes—
150#88071C2314yes—
151#88071C2314yes—
152C2×#2560—131nomaximal, Sylow
153C24×C13C2411yescharacteristic
154C23×D13—22no—
155C23×D13—22no—
156C23×D13—22no—
157C23×D13—22no—
158C23×D13—22no—
159C23×D13—22no—
160C23×D13—22no—
161C23×D13—22no—
162C23×D13—22no—
163C23×D13—22no—
164C23×D13—22no—
165C23×D13—22no—
166C23×D13—22no—
167C23×D13#4114yes—
168C23×D13C2412yes—
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×C13—22no—
188C22×C4×C13—22no—
189C22×C4×C13C2×D414yes—
190C22×C4×C13#4114yes—
191C22×C4×C13C2412yes—
192C22×C4×C13C2412yes—
193C22×C4×C13C2412yes—
194C22×C4×C13C2412yes—
195C22×C4×C13C2412yes—
196C22×C4×C13C2412yes—
197C22×C4×C13C2412yes—
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×Dic13C2×D414yes—
213C22×Dic13C2×D414yes—
214C22×Dic13#4114yes—
215C22×Dic13#4114yes—
216C22×Dic13C2412yes—
217C22×Dic13C2412yes—
218C22×Dic13C2412yes—
219C22×Dic13C2412yes—
220C22×Dic13C2412yes—
221C22×Dic13C2412yes—
222C2×D52—28no—
223C2×D52—28no—
224C2×D52—44no—
225C2×D52—416no—
226C2×C4×D13—28no—
227C2×C4×D13—28no—
228C2×C4×D13—44no—
229C2×C4×D13—416no—
230C2×Dic26—28no—
231C2×Dic26—28no—
232C2×Dic26—44no—
233C2×Dic26—416no—
234C13×C4⋊C4—28no—
235C13×C4⋊C4—28no—
236C42×C13—28no—
237#6103—28no—
238#6103—28no—
239#6103—28no—
240#6103—28no—
241#6103—28no—
242#6103—28no—
243#6103—28no—
244#6103—28no—
245#6103—28no—
246#6103—28no—
247#6103—44no—
248#6101—28no—
249#6101—28no—
250#6101—28no—
251#6101—28no—
252#6101C2×D4116yescomplemented
253C4×Dic13—28no—
254C4×Dic13—44no—
255C4×Dic13—44no—
256C22×#126—131no—
257C22×C22⋊Q8—131no—
258#2560—1316no—
259C2×#398—131no—
260C2×#397—131no—
261C2×#394—131no—
262C2×#393—131no—
263C2×#391—131no—
264C2×#390—131no—
265C2×#388—131no—
266C2×#388—131no—
267C2×#388—131no—
268C2×#387D1311yescharacteristic, complemented
269C2×#386—131no—
270C2×C4×C4⋊C4—131no—
271C2×C4×C22⋊C4—131no—
272C23×C13C22×D412yes—
273C23×C13C2×#4112yes—
274C23×C13C2×#4112yes—
275C23×C13C2×#4112yes—
276C23×C13C2×#4112yes—
277C23×C13H(5,𝔽2)12yes—
278C23×C132−1+412yes—
279C23×C13C2511yescharacteristic
280C22×D13—28no—
281C22×D13—28no—
282C22×D13—28no—
283C22×D13—22no—
284C22×D13—22no—
285C22×D13—22no—
286C22×D13—22no—
287C22×D13—22no—
288C22×D13—22no—
289C22×D13—22no—
290C22×D13—22no—
291C22×D13—22no—
292C22×D13—22no—
293C22×D13—22no—
294C22×D13—22no—
295C22×D13—22no—
296C22×D13—44no—
297C22×D13—44no—
298C22×D13—44no—
299C22×D13—44no—
300C22×D13—44no—
301C22×D13—44no—
302C22×D13—44no—
303C22×D13—44no—
304C22×D13—44no—
305C22×D13—44no—
306C22×D13—44no—
307C22×D13C2×#4114yes—
308C2×C4×C13—28no—
309C2×C4×C13—28no—
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—22no—
326C2×C4×C13—22no—
327C2×C4×C13—22no—
328C2×C4×C13—22no—
329C2×C4×C13—44no—
330C2×C4×C13—44no—
331C2×C4×C13—44no—
332C2×C4×C13—44no—
333C2×C4×C13—44no—
334C2×C4×C13C22×D414yes—
335C2×C4×C13C2×#4114yes—
336C2×Dic13—28no—
337C2×Dic13—28no—
338C2×Dic13—28no—
339C2×Dic13—28no—
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—22no—
354C2×Dic13—44no—
355C2×Dic13—44no—
356C2×Dic13C22×D414yes—
357C2×Dic13C22×D414yes—
358C2×Dic13C2×#4114yes—
359C2×Dic13C2×#4114yes—
360D52—416no—
361C4×D13—416no—
362Dic26—416no—
363C23×Q8—131no—
364C23×D4—131no—
365C24×C4—131no—
366C2×#126—138no—
367C2×#126—268no—
368C2×C22⋊Q8—138no—
369C2×C22⋊Q8—268no—
370C22×C4⋊C4—131no—
371C22×C4⋊C4—131no—
372C22×C4⋊C4—131no—
373C22×C4⋊C4—131no—
374C22×C4⋊C4—131no—
375C22×C4⋊C4C2×D1311yescharacteristic
376C22×C4⋊C4C2×D1311yescharacteristic
377C22×C22⋊C4—131no—
378C22×C22⋊C4—131no—
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×C42—131no—
389C22×C42—131no—
390C22×C42—131no—
391C22×C42C2×D1311yescharacteristic
392#398—138no—
393#397—138no—
394#394—138no—
395#393—138no—
396#391—138no—
397#390—138no—
398#388—138no—
399#388—138no—
400#388—138no—
401#387C2×D1318yescomplemented
402#386—138no—
403C4×C4⋊C4—138no—
404C4×C22⋊C4—138no—
405C2×#95—131no—
406C2×#95—131no—
407C2×#95—131no—
408C2×#95—131no—
409C2×#95—131no—
410C2×#95—131no—
411C2×#95C2×D1311yescharacteristic
412C2×#95C2×D1311yescharacteristic
413C2×#95C2×D1311yescharacteristic
414C2×#95C2×D1311yescharacteristic
415C22×C13#52914yes—
416C22×C13#53214yes—
417C22×C13#53914yes—
418C22×C13#54614yes—
419C22×C13#54814yes—
420C22×C13#55114yes—
421C22×C13#55614yes—
422C22×C13C23×D411yescharacteristic
423C22×C13C22×#4111yescharacteristic
424C22×C13C22×#4111yescharacteristic
425C22×C13C22×#4111yescharacteristic
426C22×C13C22×#4111yescharacteristic
427C22×C13C2×H(5,𝔽2)11yescharacteristic
428C22×C13C2×2−1+411yescharacteristic
429C2×D13—24no—
430C2×D13—24no—
431C2×D13—24no—
432C2×D13—416no—
433C2×D13—42no—
434C2×D13—42no—
435C2×D13—42no—
436C2×D13—42no—
437C2×D13—42no—
438C2×D13—42no—
439C2×D13—42no—
440C2×D13—42no—
441C2×D13—42no—
442C2×D13—42no—
443C2×D13—42no—
444C2×D13—88no—
445C4×C13—24no—
446C4×C13—24no—
447C4×C13—42no—
448C4×C13—42no—
449C4×C13—42no—
450C4×C13—42no—
451C4×C13—42no—
452Dic13—24no—
453Dic13—24no—
454Dic13—24no—
455Dic13—24no—
456Dic13—42no—
457Dic13—42no—
458C25—131no—
459C25—131no—
460C22×Q8—134no—
461C22×Q8—264no—
462C22×Q8—264no—
463C22×Q8—522no—
464C22×D4—134no—
465C22×D4—264no—
466C22×D4—264no—
467C22×D4—522no—
468C23×C4—131no—
469C23×C4—131no—
470C23×C4—131no—
471C23×C4—131no—
472C23×C4—131no—
473C23×C4—131no—
474C23×C4—134no—
475C23×C4—264no—
476C23×C4—264no—
477C23×C4—522no—
478C23×C4C22×D1311yescharacteristic
479C23×C4C22×D1311yescharacteristic
480C23×C4C22×D1311yescharacteristic
481C23×C4C22×D1311yescharacteristic
482C23×C4C22×D1311yescharacteristic
483C23×C4C22×D1311yescharacteristic
484C23×C4C22×D1311yescharacteristic
485#126—2632no—
486C22⋊Q8—2632no—
487C2×C4⋊C4—24no—
488C2×C4⋊C4—24no—
489C2×C4⋊C4—138no—
490C2×C4⋊C4—134no—
491C2×C4⋊C4—134no—
492C2×C4⋊C4—134no—
493C2×C4⋊C4—134no—
494C2×C4⋊C4—134no—
495C2×C4⋊C4—264no—
496C2×C4⋊C4—264no—
497C2×C4⋊C4—264no—
498C2×C4⋊C4—264no—
499C2×C4⋊C4C22×D1314yes—
500C2×C4⋊C4C22×D1314yes—
501C2×C22⋊C4—134no—
502C2×C22⋊C4—134no—
503C2×C22⋊C4—134no—
504C2×C22⋊C4—134no—
505C2×C22⋊C4—134no—
506C2×C22⋊C4—134no—
507C2×C22⋊C4—134no—
508C2×C22⋊C4—134no—
509C2×C22⋊C4—134no—
510C2×C22⋊C4—134no—
511C2×C22⋊C4—134no—
512C2×C22⋊C4—264no—
513C2×C22⋊C4—264no—
514C2×C22⋊C4—264no—
515C2×C22⋊C4—264no—
516C2×C22⋊C4—264no—
517C2×C22⋊C4—264no—
518C2×C22⋊C4—264no—
519C2×C22⋊C4—264no—
520C2×C22⋊C4—264no—
521C2×C22⋊C4—264no—
522C2×C22⋊C4—522no—
523C2×C42—24no—
524C2×C42—134no—
525C2×C42—134no—
526C2×C42—134no—
527C2×C42—264no—
528C2×C42—522no—
529C2×C42—522no—
530C2×C42C22×D1314yes—
531#95—134no—
532#95—134no—
533#95—134no—
534#95—134no—
535#95—134no—
536#95—134no—
537#95C22×D1314yes—
538#95C22×D1314yes—
539#95C22×D1314yes—
540#95C22×D1314yes—
541C2×C13#256018yescomplemented
542C2×C13C2×#52911yescharacteristic
543C2×C13C2×#53211yescharacteristic
544C2×C13C2×#53911yescharacteristic
545C2×C13C2×#54611yescharacteristic
546C2×C13C2×#54811yescharacteristic
547C2×C13C2×#55111yescharacteristic
548C2×C13C2×#55611yescharacteristic
549D13—44no—
550D13—82no—
551C24—134no—
552C24—132no—
553C24—132no—
554C24—262no—
555C24—262no—
556C24—262no—
557C24—262no—
558C24—262no—
559C24—262no—
560C24—262no—
561C24—262no—
562C24—262no—
563C24—262no—
564C24—262no—
565C24—262no—
566C24—262no—
567C24C23×D1311yescharacteristic
568C2×Q8—268no—
569C2×Q8—268no—
570C2×Q8—524no—
571C2×Q8—5216no—
572C2×D4—268no—
573C2×D4—268no—
574C2×D4—524no—
575C2×D4—5216no—
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—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—134no—
596C22×C4—134no—
597C22×C4—134no—
598C22×C4—134no—
599C22×C4—132no—
600C22×C4—132no—
601C22×C4—132no—
602C22×C4—132no—
603C22×C4—132no—
604C22×C4—132no—
605C22×C4—268no—
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×C4—262no—
620C22×C4—268no—
621C22×C4—524no—
622C22×C4—5216no—
623C22×C4#612714yes—
624C22×C4D4×D1314yes—
625C22×C4C23×D1312yes—
626C22×C4C23×D1312yes—
627C22×C4C23×D1312yes—
628C22×C4C23×D1312yes—
629C22×C4C23×D1312yes—
630C22×C4C23×D1312yes—
631C22×C4C23×D1312yes—
632C4⋊C4—28no—
633C4⋊C4—28no—
634C4⋊C4—1316no—
635C4⋊C4—268no—
636C4⋊C4—268no—
637C4⋊C4—268no—
638C4⋊C4—268no—
639C22⋊C4—268no—
640C22⋊C4—268no—
641C22⋊C4—268no—
642C22⋊C4—268no—
643C22⋊C4—268no—
644C22⋊C4—268no—
645C22⋊C4—268no—
646C22⋊C4—268no—
647C22⋊C4—268no—
648C22⋊C4—268no—
649C22⋊C4—524no—
650C42—28no—
651C42—268no—
652C42—524no—
653C42—524no—
654C13C2×#256011yescharacteristic, complemented, Sylow
655C23—134no—
656C23—268no—
657C23—268no—
658C23—262no—
659C23—262no—
660C23—262no—
661C23—262no—
662C23—262no—
663C23—262no—
664C23—268no—
665C23—262no—
666C23—262no—
667C23—262no—
668C23—262no—
669C23—262no—
670C23—262no—
671C23—262no—
672C23—524no—
673C23—524no—
674C23—524no—
675C23—524no—
676C23—524no—
677C23—524no—
678C23—524no—
679C23—524no—
680C23—524no—
681C23—524no—
682C23—524no—
683C23C2×#612712yes—
684C23C2×D4×D1312yes—
685C23#8825412yes—
686C23#41×D1312yes—
687C23#41×D1312yes—
688C23#41×D1312yes—
689C23#8825612yes—
690C23C24×D1311yescharacteristic
691Q8—5216no—
692D4—5216no—
693C2×C4—28no—
694C2×C4—28no—
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—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—134no—
720C2×C4—134no—
721C2×C4—134no—
722C2×C4—134no—
723C2×C4—268no—
724C2×C4—268no—
725C2×C4—268no—
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—268no—
735C2×C4—262no—
736C2×C4—262no—
737C2×C4—262no—
738C2×C4—262no—
739C2×C4—262no—
740C2×C4—262no—
741C2×C4—5216no—
742C2×C4—524no—
743C2×C4—524no—
744C2×C4C2×#612714yes—
745C2×C4C2×D4×D1314yes—
746C22—264no—
747C22—264no—
748C22—264no—
749C22—522no—
750C22—522no—
751C22—522no—
752C22—5216no—
753C22—522no—
754C22—522no—
755C22—522no—
756C22—522no—
757C22—522no—
758C22—522no—
759C22—522no—
760C22—522no—
761C22—1048no—
762C22#1171923214yes—
763C22#1171925314yes—
764C22#1171927314yes—
765C22#1171933814yes—
766C22#1171935914yes—
767C22#1171939714yes—
768C22#1171941114yes—
769C22C22×#612711yescharacteristic
770C22C22×D4×D1311yescharacteristic
771C22C2×#8825411yescharacteristic
772C22C2×#41×D1311yescharacteristic
773C22C2×#41×D1311yescharacteristic
774C22C2×#41×D1311yescharacteristic
775C22C2×#8825611yescharacteristic
776C4—24no—
777C4—24no—
778C4—42no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—42no—
783C4—264no—
784C4—264no—
785C4—264no—
786C4—264no—
787C4—522no—
788C4—522no—
789C2—524no—
790C2—1042no—
791C2#1311998618yesdirect product factor
792C2C2×#1171941111yescharacteristic
793C2C2×#1171925311yescharacteristic
794C2C2×#1171939711yescharacteristic
795C2C2×#1171935911yescharacteristic
796C2C2×#1171933811yescharacteristic
797C2C2×#1171923211yescharacteristic
798C2C2×#1171927311yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#387C2
socleC24×C13C24
prime radicalC23×D52C22
hypercenterC2×#387D13
hypocenterC13C2×#2560
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
1. C22×#88130C2semidirect
2. C22×#88150C2semidirect
3. #13119986C2direct (N × H)
4. C2×#11718641C2semidirect
5. C2×#11718336C2semidirect
7. C2×#11718334C2semidirect
8. C2×#11718307C2semidirect
10. C2×#11718651C2semidirect
11. C2×#11718330C2semidirect
12. C2×#11718330C2semidirect
14. C2×#11718310C2semidirect
15. C2×C4×#6103C2semidirect
16. C2×C13×#387C2semidirect
43. C2×#88150C22semidirect
45. C2×#88130C22semidirect
46. C13×#387C22semidirect
57. #11718651C22semidirect
59. #11718641C22semidirect
60. C4×#6103C22semidirect
61. #11718336C22semidirect
62. #11718334C22semidirect
64. #11718330C22semidirect
65. #11718330C22semidirect
67. #11718310C22semidirect
68. #11718307C22semidirect
128. C2×#6101D4semidirect
252. #6101C2×D4semidirect
268. C2×#387D13semidirect
401. #387C2×D13semidirect
541. C2×C13#2560semidirect
654. C13C2×#2560semidirect
791. C2#13119986direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881302
C22×#881502
#131199862
C2×#117186412
C2×#117183362
C2×#117183332
C2×#117183342
C2×#117183072
C2×#117186492
C2×#117186512
C2×#117183302
C2×#117183262
C2×#117183102
C2×C4×#61032
C2×C13×#3872
C2×#256013