Finite Group Databasebeta

← C2×#13119162 #16031849

Subgroups — C2×#13119162 #16031849

Order 3328.

3114 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88183C211yesmaximal, characteristic
2C22×#88178C211yesmaximal, characteristic, complemented
3#13119162C2116yesmaximal, direct product factor
4C2×#11718321C211yesmaximal, characteristic, complemented
5C2×#11718319C211yesmaximal, characteristic, complemented
6C2×#11718336C211yesmaximal, characteristic, complemented
7C2×#11718334C211yesmaximal, characteristic, complemented
8C2×#11718307C211yesmaximal, characteristic, complemented
9C2×#11718331C211yesmaximal, characteristic, complemented
10C2×#11718330C211yesmaximal, characteristic, complemented
11C2×#11718874C211yesmaximal, characteristic
12C2×#11718874C211yesmaximal, characteristic
13C2×#11718311C211yesmaximal, characteristic, complemented
14C2×#11718872C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊Dic13C211yesmaximal, characteristic, complemented
16C22×C13×#95C211yesmaximal, characteristic, complemented
17C24×C4×C13C2211yescharacteristic
18C24×C4×C13C2211yescharacteristic
19C24×C4×C13C2211yescharacteristic
20C23×C22⋊D13C2211yescharacteristic
21C23×Dic26C2211yescharacteristic
22C22×C22⋊Dic13C2211yescharacteristic
23C22×C22⋊Dic13C2211yescharacteristic
24C22×C22⋊Dic13C2211yescharacteristic
25C2×#88183—28no—
26C2×#88183C2218yes—
27C22×#6103C2211yescharacteristic
28C22×#6103C2211yescharacteristic
29C22×#6103C2211yescharacteristic
30C22×#6103C2211yescharacteristic
31C22×#6103C2211yescharacteristic
32C22×#6103C2211yescharacteristic
33C22×C4⋊Dic13C2211yescharacteristic
34C2×#88178—28no—
35C2×#88178C2218yescomplemented
36C22×#6101C2211yescharacteristic
37C22×#6101C2211yescharacteristic
38C22×#6101C2211yescharacteristic
39C22×#6101C2211yescharacteristic
40C22×C4×Dic13C2211yescharacteristic
41C22×C4×Dic13C2211yescharacteristic
42C2×C13×#95C2211yescharacteristic
43C2×C13×#95C2211yescharacteristic
44C2×C13×#95C2211yescharacteristic
45C2×C13×#95C2211yescharacteristic
46C2×C13×#95C2218yescomplemented
47#11718874C2218yes—
48#11718874C2218yes—
49#11718872C2218yescomplemented
50C4×C22⋊Dic13C2218yescomplemented
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57C2×#88071C2211yescharacteristic
58C2×#88071C2211yescharacteristic
59C2×#88071C2211yescharacteristic
60C2×#88071C2211yescharacteristic
61#11718336C2218yescomplemented
62#11718334C2218yescomplemented
63#11718331C2218yescomplemented
64#11718330C2218yescomplemented
65#11718321C2218yescomplemented
66#11718319C2218yescomplemented
67#11718311C2218yescomplemented
68#11718307C2218yescomplemented
69C25×C13C2311yescharacteristic
70C24×D13C2311yescharacteristic
71C23×C4×C13—24no—
72C23×C4×C13—24no—
73C23×C4×C13—24no—
74C23×C4×C13—24no—
75C23×C4×C13—24no—
76C23×C4×C13—24no—
77C23×C4×C13—24no—
78C23×C4×C13—42no—
79C23×C4×C13—42no—
80C23×C4×C13C2311yescharacteristic
81C23×C4×C13C2311yescharacteristic
82C23×C4×C13C2311yescharacteristic
83C23×C4×C13C2311yescharacteristic
84C23×C4×C13C2314yes—
85C23×C4×C13C2314yes—
86C23×C4×C13C2314yes—
87C23×C4×C13C2311yescharacteristic
88C23×C4×C13C2311yescharacteristic
89C22×C22⋊D13—24no—
90C22×C22⋊D13—24no—
91C22×C22⋊D13—24no—
92C22×C22⋊D13C2314yes—
93C23×Dic13C2311yescharacteristic
94C23×Dic13C2311yescharacteristic
95C23×Dic13C2311yescharacteristic
96C23×Dic13C2311yescharacteristic
97C23×Dic13C2311yescharacteristic
98C23×Dic13C2311yescharacteristic
99C23×Dic13C2311yescharacteristic
100C22×Dic26—24no—
101C22×Dic26—24no—
102C22×Dic26—42no—
103C22×Dic26C2314yes—
104C2×C22⋊Dic13—24no—
105C2×C22⋊Dic13—24no—
106C2×C22⋊Dic13D418yes—
107C2×C22⋊Dic13C2314yes—
108C2×C22⋊Dic13C2314yes—
109C2×C22⋊Dic13C2314yes—
110#88183—232no—
111C2×#6103—24no—
112C2×#6103—24no—
113C2×#6103—24no—
114C2×#6103—24no—
115C2×#6103—42no—
116C2×#6103—42no—
117C2×#6103C2314yes—
118C2×#6103C2314yes—
119C2×#6103C2314yes—
120C2×#6103C2314yes—
121C2×#6103C2314yes—
122C2×#6103C2314yes—
123C2×C4⋊Dic13—24no—
124C2×C4⋊Dic13C2314yes—
125#88178—232no—
126C2×#6101—24no—
127C2×#6101—24no—
128C2×#6101—24no—
129C2×#6101—24no—
130C2×#6101C2314yes—
131C2×#6101C2314yes—
132C2×#6101C2314yes—
133C2×#6101C2314yes—
134C2×C4×Dic13—24no—
135C2×C4×Dic13—42no—
136C2×C4×Dic13C2314yes—
137C2×C4×Dic13C2314yes—
138C13×#95C2314yes—
139C13×#95C2314yes—
140C13×#95C2314yes—
141C13×#95C2314yes—
142#88071C2314yes—
143#88071C2314yes—
144#88071C2314yes—
145#88071C2314yes—
146#88071C2314yes—
147#88071C2314yes—
148#88071C2314yes—
149#88071C2314yes—
150#88071C2314yes—
151#88071C2314yes—
152C2×#2488—131nomaximal, Sylow
153C24×C13—22no—
154C24×C13—22no—
155C24×C13—22no—
156C24×C13—22no—
157C24×C13C2×D414yes—
158C24×C13#4114yes—
159C24×C13#4114yes—
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—28no—
178C22×C4×C13—28no—
179C22×C4×C13—28no—
180C22×C4×C13—22no—
181C22×C4×C13—22no—
182C22×C4×C13—22no—
183C22×C4×C13—22no—
184C22×C4×C13—28no—
185C22×C4×C13—28no—
186C22×C4×C13—22no—
187C22×C4×C13—22no—
188C22×C4×C13—22no—
189C22×C4×C13—22no—
190C22×C4×C13—22no—
191C22×C4×C13—28no—
192C22×C4×C13—28no—
193C22×C4×C13—44no—
194C22×C4×C13—44no—
195C22×C4×C13—416no—
196C22×C4×C13—416no—
197C22×C4×C13—416no—
198C22×C4×C13#4114yes—
199C22×C4×C13#4114yes—
200C22×C4×C13C2412yes—
201C22×C4×C13C2412yes—
202C22×C4×C13C2412yes—
203C22×C4×C13C2412yes—
204C22×C4×C13C2412yes—
205C22×C4×C13C2412yes—
206C2×C22⋊D13—28no—
207C2×C22⋊D13—28no—
208C2×C22⋊D13—28no—
209C2×C22⋊D13—416no—
210C22×Dic13—22no—
211C22×Dic13—22no—
212C22×Dic13—22no—
213C22×Dic13—22no—
214C22×Dic13—22no—
215C22×Dic13—22no—
216C22×Dic13—22no—
217C22×Dic13—22no—
218C22×Dic13—22no—
219C22×Dic13—22no—
220C22×Dic13—22no—
221C22×Dic13—22no—
222C22×Dic13—22no—
223C22×Dic13—22no—
224C22×Dic13—22no—
225C22×Dic13—22no—
226C22×Dic13—22no—
227C22×Dic13—22no—
228C22×Dic13—22no—
229C22×Dic13C2×D414yes—
230C22×Dic13C2×D414yes—
231C22×Dic13C2412yes—
232C22×Dic13C2412yes—
233C22×Dic13C2412yes—
234C22×Dic13C2412yes—
235C22×Dic13C2412yes—
236C22×Dic13C2412yes—
237C22×Dic13C2412yes—
238C2×Dic26—28no—
239C2×Dic26—28no—
240C2×Dic26—44no—
241C2×Dic26—416no—
242C22⋊Dic13—28no—
243C22⋊Dic13—28no—
244C22⋊Dic13C2×D4116yes—
245#6103—28no—
246#6103—28no—
247#6103—28no—
248#6103—28no—
249#6103—44no—
250#6103—44no—
251C4⋊Dic13—28no—
252#6101—28no—
253#6101—28no—
254#6101—28no—
255#6101—28no—
256C4×Dic13—28no—
257C4×Dic13—44no—
258C22×#123—131no—
259C22×C22⋊Q8—131no—
260#2488—1316no—
261C2×#400—131no—
262C2×#400—131no—
263C2×#397—131no—
264C2×#393—131no—
265C2×#391—131no—
266C2×#388—131no—
267C2×#388—131no—
268C2×#386—131no—
269C2×#386—131no—
270C2×#382—131no—
271C2×#381—131no—
272C2×C4×C22⋊C4—131no—
273C22×#95D1311yescharacteristic, complemented
274C23×C13—28no—
275C23×C13—28no—
276C23×C13—28no—
277C23×C13—28no—
278C23×C13—28no—
279C23×C13—28no—
280C23×C13—22no—
281C23×C13—22no—
282C23×C13—22no—
283C23×C13—22no—
284C23×C13#124116yes—
285C23×C13C22×D414yes—
286C23×C13C22×D412yes—
287C23×C13C2×#4114yes—
288C23×C13C2×#4114yes—
289C23×C13C2×#4112yes—
290C23×C13C2×#4112yes—
291C23×C13C2×#4112yes—
292C23×C13C2×#4112yes—
293C23×C13H(5,𝔽2)12yes—
294C23×C132−1+412yes—
295C23×C13C2511yescharacteristic
296C22×D13—22no—
297C22×D13—22no—
298C22×D13—22no—
299C22×D13—22no—
300C22×D13—22no—
301C22×D13—22no—
302C22×D13—22no—
303C22×D13—44no—
304C22×D13—44no—
305C22×D13—44no—
306C22×D13—44no—
307C22×D13—44no—
308C22×D13—44no—
309C22×D13—44no—
310C2×C4×C13—28no—
311C2×C4×C13—28no—
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—416no—
329C2×C4×C13—416no—
330C2×C4×C13—416no—
331C2×C4×C13—44no—
332C2×C4×C13—44no—
333C2×C4×C13—44no—
334C2×C4×C13—44no—
335C2×C4×C13C2×#4114yes—
336C2×C4×C13C2×#4114yes—
337C22⋊D13—416no—
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—22no—
355C2×Dic13—22no—
356C2×Dic13—22no—
357C2×Dic13—22no—
358C2×Dic13—22no—
359C2×Dic13—44no—
360C2×Dic13—44no—
361C2×Dic13—44no—
362C2×Dic13—44no—
363C2×Dic13—44no—
364C2×Dic13C22×D414yes—
365C2×Dic13C22×D414yes—
366Dic26—416no—
367C23×Q8—131no—
368C23×D4—131no—
369C24×C4C2×D1311yescharacteristic
370C24×C4C2×D1311yescharacteristic
371C24×C4C2×D1311yescharacteristic
372C2×#123—138no—
373C2×#123—268no—
374C2×C22⋊Q8—138no—
375C2×C22⋊Q8—268no—
376C22×C4⋊C4—131no—
377C22×C4⋊C4—131no—
378C22×C4⋊C4—131no—
379C22×C4⋊C4—131no—
380C22×C4⋊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⋊C4—131no—
389C22×C22⋊C4—131no—
390C22×C42—131no—
391C22×C42—131no—
392#400—138no—
393#400—138no—
394#397—138no—
395#393—138no—
396#391—138no—
397#388—138no—
398#388—138no—
399#386—138no—
400#386—138no—
401#382—138no—
402#381—138no—
403C4×C22⋊C4—138no—
404C2×#95—131no—
405C2×#95—131no—
406C2×#95—131no—
407C2×#95—131no—
408C2×#95—131no—
409C2×#95—131no—
410C2×#95—131no—
411C2×#95—131no—
412C2×#95—131no—
413C2×#95—131no—
414C2×#95C2×D1311yescharacteristic
415C2×#95C2×D1311yescharacteristic
416C2×#95C2×D1311yescharacteristic
417C2×#95C2×D1311yescharacteristic
418C2×#95C2×D1318yescomplemented
419C22×C13—24no—
420C22×C13—24no—
421C22×C13—24no—
422C22×C13—24no—
423C22×C13—24no—
424C22×C13—24no—
425C22×C13—232no—
426C22×C13C2×#12418yes—
427C22×C13C2×#12414yes—
428C22×C13#52914yes—
429C22×C13#53914yes—
430C22×C13#54614yes—
431C22×C13#54714yes—
432C22×C13#55114yes—
433C22×C13#55214yes—
434C22×C13C23×D411yescharacteristic
435C22×C13C22×#4111yescharacteristic
436C22×C13C22×#4111yescharacteristic
437C22×C13C22×#4111yescharacteristic
438C22×C13C22×#4111yescharacteristic
439C22×C13C2×H(5,𝔽2)11yescharacteristic
440C22×C13C2×2−1+411yescharacteristic
441C2×D13—42no—
442C2×D13—42no—
443C2×D13—42no—
444C2×D13—42no—
445C2×D13—42no—
446C2×D13—42no—
447C2×D13—42no—
448C2×D13—88no—
449C4×C13—24no—
450C4×C13—24no—
451C4×C13—42no—
452C4×C13—42no—
453C4×C13—42no—
454C4×C13—42no—
455Dic13—24no—
456Dic13—24no—
457Dic13—42no—
458Dic13—42no—
459Dic13—42no—
460Dic13—42no—
461Dic13—42no—
462C25—131no—
463C25C22×D1311yescharacteristic
464C22×Q8—134no—
465C22×Q8—264no—
466C22×Q8—264no—
467C22×Q8—522no—
468C22×D4—134no—
469C22×D4—264no—
470C22×D4—264no—
471C22×D4—264no—
472C23×C4—24no—
473C23×C4—24no—
474C23×C4—24no—
475C23×C4—24no—
476C23×C4—24no—
477C23×C4—24no—
478C23×C4—24no—
479C23×C4—42no—
480C23×C4—42no—
481C23×C4—131no—
482C23×C4—131no—
483C23×C4—131no—
484C23×C4—131no—
485C23×C4—131no—
486C23×C4—131no—
487C23×C4—131no—
488C23×C4C22×D1314yes—
489C23×C4C22×D1311yescharacteristic
490C23×C4C22×D1311yescharacteristic
491C23×C4C22×D1311yescharacteristic
492C23×C4C22×D1311yescharacteristic
493C23×C4C22×D1314yes—
494C23×C4C22×D1314yes—
495C23×C4C22×D1311yescharacteristic
496C23×C4C22×D1311yescharacteristic
497#123—2632no—
498C22⋊Q8—2632no—
499C2×C4⋊C4—134no—
500C2×C4⋊C4—134no—
501C2×C4⋊C4—134no—
502C2×C4⋊C4—134no—
503C2×C4⋊C4—134no—
504C2×C4⋊C4—264no—
505C2×C4⋊C4—264no—
506C2×C4⋊C4—264no—
507C2×C4⋊C4—264no—
508C2×C4⋊C4—264no—
509C2×C22⋊C4—138no—
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—134no—
518C2×C22⋊C4—134no—
519C2×C22⋊C4—264no—
520C2×C22⋊C4—264no—
521C2×C22⋊C4—264no—
522C2×C22⋊C4—264no—
523C2×C22⋊C4—264no—
524C2×C22⋊C4—264no—
525C2×C22⋊C4—522no—
526C2×C22⋊C4—522no—
527C2×C42—134no—
528C2×C42—134no—
529C2×C42—264no—
530C2×C42—522no—
531#95—134no—
532#95—134no—
533#95—134no—
534#95—134no—
535#95—134no—
536#95—134no—
537#95—134no—
538#95—134no—
539#95—134no—
540#95—134no—
541#95C22×D1314yes—
542#95C22×D1314yes—
543#95C22×D1314yes—
544#95C22×D1314yes—
545C2×C13—28no—
546C2×C13#248818yescomplemented
547C2×C13C22×#12411yescharacteristic
548C2×C13C2×#52911yescharacteristic
549C2×C13C2×#53911yescharacteristic
550C2×C13C2×#54611yescharacteristic
551C2×C13C2×#54711yescharacteristic
552C2×C13C2×#55111yescharacteristic
553C2×C13C2×#55211yescharacteristic
554D13—82no—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—132no—
560C24—262no—
561C24—262no—
562C24—262no—
563C24—262no—
564C24—262no—
565C24—262no—
566C24—262no—
567C24#612714yes—
568C24D4×D1314yes—
569C24#612914yes—
570C24C23×D1312yes—
571C24C23×D1311yescharacteristic
572C2×Q8—268no—
573C2×Q8—268no—
574C2×Q8—524no—
575C2×Q8—5216no—
576C2×D4—268no—
577C2×D4—268no—
578C2×D4—268no—
579C2×D4—5216no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—28no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—28no—
593C22×C4—28no—
594C22×C4—28no—
595C22×C4—28no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—28no—
602C22×C4—28no—
603C22×C4—44no—
604C22×C4—44no—
605C22×C4—416no—
606C22×C4—416no—
607C22×C4—416no—
608C22×C4—134no—
609C22×C4—134no—
610C22×C4—132no—
611C22×C4—132no—
612C22×C4—132no—
613C22×C4—132no—
614C22×C4—132no—
615C22×C4—132no—
616C22×C4—132no—
617C22×C4—262no—
618C22×C4—262no—
619C22×C4—262no—
620C22×C4—262no—
621C22×C4—262no—
622C22×C4—262no—
623C22×C4—262no—
624C22×C4—262no—
625C22×C4—262no—
626C22×C4—262no—
627C22×C4—262no—
628C22×C4—262no—
629C22×C4—262no—
630C22×C4—262no—
631C22×C4—262no—
632C22×C4—262no—
633C22×C4—262no—
634C22×C4—262no—
635C22×C4—262no—
636C22×C4#612714yes—
637C22×C4#612714yes—
638C22×C4C23×D1312yes—
639C22×C4C23×D1312yes—
640C22×C4C23×D1312yes—
641C22×C4C23×D1312yes—
642C22×C4C23×D1312yes—
643C22×C4C23×D1312yes—
644C4⋊C4—268no—
645C4⋊C4—268no—
646C4⋊C4—268no—
647C4⋊C4—268no—
648C4⋊C4—268no—
649C22⋊C4—1316no—
650C22⋊C4—268no—
651C22⋊C4—268no—
652C22⋊C4—268no—
653C22⋊C4—268no—
654C22⋊C4—268no—
655C22⋊C4—268no—
656C22⋊C4—524no—
657C22⋊C4—524no—
658C42—268no—
659C42—524no—
660C13C2×#248811yescharacteristic, complemented, Sylow
661C23—28no—
662C23—28no—
663C23—28no—
664C23—28no—
665C23—28no—
666C23—28no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—262no—
672C23—262no—
673C23—262no—
674C23—262no—
675C23—262no—
676C23—262no—
677C23—262no—
678C23—524no—
679C23—524no—
680C23—524no—
681C23—524no—
682C23—524no—
683C23—524no—
684C23—524no—
685C23#88139116yes—
686C23C2×#612714yes—
687C23C2×#612712yes—
688C23C2×#612712yes—
689C23C2×#612712yes—
690C23C2×D4×D1314yes—
691C23C2×D4×D1312yes—
692C23C2×#612914yes—
693C23C2×#612912yes—
694C23#8825112yes—
695C23#8825412yes—
696C23C24×D1311yescharacteristic
697Q8—5216no—
698D4—5216no—
699C2×C4—28no—
700C2×C4—28no—
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—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—416no—
718C2×C4—416no—
719C2×C4—44no—
720C2×C4—416no—
721C2×C4—44no—
722C2×C4—44no—
723C2×C4—44no—
724C2×C4—134no—
725C2×C4—134no—
726C2×C4—268no—
727C2×C4—268no—
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—262no—
737C2×C4—262no—
738C2×C4—262no—
739C2×C4—262no—
740C2×C4—262no—
741C2×C4—262no—
742C2×C4—262no—
743C2×C4—262no—
744C2×C4—262no—
745C2×C4—262no—
746C2×C4—262no—
747C2×C4—524no—
748C2×C4—524no—
749C2×C4—524no—
750C2×C4—524no—
751C2×C4—524no—
752C2×C4C2×#612714yes—
753C2×C4C2×#612714yes—
754C22—24no—
755C22—24no—
756C22—24no—
757C22—24no—
758C22—24no—
759C22—232no—
760C22—24no—
761C22—522no—
762C22—522no—
763C22—522no—
764C22—522no—
765C22—522no—
766C22—522no—
767C22—522no—
768C22—1048no—
769C22#1171918414yes—
770C22#1171919514yes—
771C22C2×#8813918yes—
772C22C2×#8813914yes—
773C22#1171920014yes—
774C22#1171921214yes—
775C22#1171921814yes—
776C22#1171922014yes—
777C22C22×#612711yescharacteristic
778C22C22×#612711yescharacteristic
779C22C22×#612711yescharacteristic
780C22C22×D4×D1311yescharacteristic
781C22C22×#612911yescharacteristic
782C22C2×#8825111yescharacteristic
783C22C2×#8825411yescharacteristic
784C4—24no—
785C4—24no—
786C4—42no—
787C4—42no—
788C4—42no—
789C4—42no—
790C4—264no—
791C4—264no—
792C4—522no—
793C4—522no—
794C4—522no—
795C4—522no—
796C4—522no—
797C2—28no—
798C2—1042no—
799C2#1311916218yesdirect product factor
800C2C22×#8813911yescharacteristic
801C2C2×#1171918411yescharacteristic
802C2C2×#1171922011yescharacteristic
803C2C2×#1171919511yescharacteristic
804C2C2×#1171921211yescharacteristic
805C2C2×#1171920011yescharacteristic
806C2C2×#1171921811yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC22×C13×#95C2
socleC24×C13C24
prime radicalC23×C22⋊D13C22
hypercenterC22×#95D13
hypocenterC13C2×#2488
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×#95

Complements

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

NH ≅ G/Ntype
2. C22×#88178C2semidirect
3. #13119162C2direct (N × H)
4. C2×#11718321C2semidirect
5. C2×#11718319C2semidirect
6. C2×#11718336C2semidirect
7. C2×#11718334C2semidirect
8. C2×#11718307C2semidirect
9. C2×#11718331C2semidirect
10. C2×#11718330C2semidirect
13. C2×#11718311C2semidirect
14. C2×#11718872C2semidirect
15. C2×C4×C22⋊Dic13C2semidirect
16. C22×C13×#95C2semidirect
35. C2×#88178C22semidirect
46. C2×C13×#95C22semidirect
49. #11718872C22semidirect
50. C4×C22⋊Dic13C22semidirect
61. #11718336C22semidirect
62. #11718334C22semidirect
63. #11718331C22semidirect
64. #11718330C22semidirect
65. #11718321C22semidirect
66. #11718319C22semidirect
67. #11718311C22semidirect
68. #11718307C22semidirect
273. C22×#95D13semidirect
418. C2×#95C2×D13semidirect
546. C2×C13#2488semidirect
660. C13C2×#2488semidirect
799. C2#13119162direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881832
C22×#881782
#131191622
C2×#117183212
C2×#117183192
C2×#117183362
C2×#117183342
C2×#117183072
C2×#117183312
C2×#117183302
C2×#117188742
C2×#117183112
C2×#117188722
C2×C4×C22⋊Dic132
C22×C13×#952
C2×#248813