Finite Group Databasebeta

← C2×#13119843 #16032964

Subgroups — C2×#13119843 #16032964

Order 3328.

3094 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88150C211yesmaximal, characteristic
2C22×#88150C211yesmaximal, characteristic
3#13119843C2116yesmaximal, direct product factor
4C2×#11718318C211yesmaximal, characteristic, complemented
5C2×#11718317C211yesmaximal, characteristic, complemented
6C2×#11718640C211yesmaximal, characteristic, complemented
7C2×#11718635C211yesmaximal, characteristic, complemented
8C2×#11718307C211yesmaximal, characteristic, complemented
9C2×#11718634C211yesmaximal, characteristic, complemented
10C2×#11718633C211yesmaximal, characteristic, complemented
11C2×#11718329C211yesmaximal, characteristic
12C2×#11718650C211yesmaximal, characteristic
13C2×#11718648C211yesmaximal, characteristic
14C2×#11718327C211yesmaximal, characteristic
15C2×D13×#95C211yesmaximal, characteristic
16C2×C13×#398C211yesmaximal, characteristic, complemented
17C23×C4×D13C2211yescharacteristic
18C23×C4×D13C2211yescharacteristic
19C23×C4×D13C2211yescharacteristic
20C23×Dic26C2211yescharacteristic
21C23×Dic26C2211yescharacteristic
22C22×C13×C4⋊C4C2211yescharacteristic
23C22×C13×C4⋊C4C2211yescharacteristic
24C22×C13×C4⋊C4C2211yescharacteristic
25C22×C13×C4⋊C4C2211yescharacteristic
26C22×#6103C2211yescharacteristic
27C22×#6103C2211yescharacteristic
28C22×#6103C2211yescharacteristic
29C22×#6103C2211yescharacteristic
30C22×C4⋊Dic13C2211yescharacteristic
31C22×C4⋊Dic13C2211yescharacteristic
32C22×#6101C2211yescharacteristic
33C22×#6101C2211yescharacteristic
34C22×#6101C2211yescharacteristic
35C22×#6101C2211yescharacteristic
36C22×#6101C2211yescharacteristic
37C22×#6101C2211yescharacteristic
38C22×C4×Dic13C2211yescharacteristic
39C22×C4×Dic13C2211yescharacteristic
40C2×#88150—28no—
41C2×#88150—28no—
42C2×#88150C2218yes—
43C2×#88150C2218yes—
44C13×#398C2218yescomplemented
45C2×C13×#95C2211yescharacteristic
46C2×C13×#95C2211yescharacteristic
47C2×C13×#95C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57#11718650C2218yes—
58#11718648C2218yes—
59#11718640C2218yescomplemented
60#11718635C2218yescomplemented
61#11718634C2218yescomplemented
62#11718633C2218yescomplemented
63#11718329C2218yes—
64#11718327C2218yes—
65D13×#95C2218yes—
66#11718318C2218yescomplemented
67#11718317C2218yescomplemented
68#11718307C2218yescomplemented
69C24×D13C2311yescharacteristic
70C23×C4×C13C2311yescharacteristic
71C23×C4×C13C2311yescharacteristic
72C23×C4×C13C2311yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C23×Dic13C2311yescharacteristic
78C23×Dic13C2311yescharacteristic
79C23×Dic13C2311yescharacteristic
80C23×Dic13C2311yescharacteristic
81C23×Dic13C2311yescharacteristic
82C23×Dic13C2311yescharacteristic
83C23×Dic13C2311yescharacteristic
84C22×C4×D13—24no—
85C22×C4×D13—24no—
86C22×C4×D13—24no—
87C22×C4×D13—24no—
88C22×C4×D13—42no—
89C22×C4×D13—42no—
90C22×C4×D13—42no—
91C22×C4×D13—42no—
92C22×C4×D13Q818yescomplemented
93C22×C4×D13C2314yes—
94C22×C4×D13C2314yes—
95C22×C4×D13C2314yes—
96C22×Dic26—24no—
97C22×Dic26—24no—
98C22×Dic26—24no—
99C22×Dic26—24no—
100C22×Dic26—42no—
101C22×Dic26—42no—
102C22×Dic26C2314yes—
103C22×Dic26C2314yes—
104C2×C13×C4⋊C4—24no—
105C2×C13×C4⋊C4—24no—
106C2×C13×C4⋊C4—42no—
107C2×C13×C4⋊C4—42no—
108C2×C13×C4⋊C4C2314yes—
109C2×C13×C4⋊C4C2314yes—
110C2×C13×C4⋊C4C2314yes—
111C2×C13×C4⋊C4C2314yes—
112C2×#6103—24no—
113C2×#6103—24no—
114C2×#6103D418yes—
115C2×#6103Q818yescomplemented
116C2×#6103C2314yes—
117C2×#6103C2314yes—
118C2×#6103C2314yes—
119C2×#6103C2314yes—
120C2×C4⋊Dic13—24no—
121C2×C4⋊Dic13—42no—
122C2×C4⋊Dic13C2314yes—
123C2×C4⋊Dic13C2314yes—
124C2×#6101—24no—
125C2×#6101—24no—
126C2×#6101—24no—
127C2×#6101—24no—
128C2×#6101—24no—
129C2×#6101—42no—
130C2×#6101C2314yes—
131C2×#6101C2314yes—
132C2×#6101C2314yes—
133C2×#6101C2314yes—
134C2×#6101C2314yes—
135C2×#6101C2314yes—
136C2×C4×Dic13—42no—
137C2×C4×Dic13—42no—
138C2×C4×Dic13C2314yes—
139C2×C4×Dic13C2314yes—
140#88150—232no—
141#88150—232no—
142C13×#95C2314yes—
143C13×#95C2314yes—
144C13×#95C2314yes—
145#88071C2314yes—
146#88071C2314yes—
147#88071C2314yes—
148#88071C2314yes—
149#88071C2314yes—
150#88071C2314yes—
151#88071C2314yes—
152#88071C2314yes—
153#88071C2314yes—
154C2×#2549—131nomaximal, Sylow
155C24×C13C2411yescharacteristic
156C23×D13—22no—
157C23×D13—22no—
158C23×D13—22no—
159C23×D13—22no—
160C23×D13C2×D414yes—
161C23×D13C2×Q814yes—
162C23×D13C2×Q814yes—
163C23×D13C2412yes—
164C22×C4×C13—22no—
165C22×C4×C13—22no—
166C22×C4×C13—22no—
167C22×C4×C13—22no—
168C22×C4×C13—22no—
169C22×C4×C13—22no—
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×C13C2×D414yes—
183C22×C4×C13C2×Q814yes—
184C22×C4×C13C2×Q814yes—
185C22×C4×C13C2412yes—
186C22×C4×C13C2412yes—
187C22×C4×C13C2412yes—
188C22×C4×C13C2412yes—
189C22×C4×C13C2412yes—
190C22×C4×C13C2412yes—
191C22×C4×C13C2412yes—
192C22×Dic13—22no—
193C22×Dic13—22no—
194C22×Dic13—22no—
195C22×Dic13—22no—
196C22×Dic13—22no—
197C22×Dic13—22no—
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×Dic13C2×D414yes—
209C22×Dic13C2×Q814yes—
210C22×Dic13C2×Q814yes—
211C22×Dic13#4114yes—
212C22×Dic13#4114yes—
213C22×Dic13C2412yes—
214C22×Dic13C2412yes—
215C22×Dic13C2412yes—
216C22×Dic13C2412yes—
217C22×Dic13C2412yes—
218C22×Dic13C2412yes—
219C22×Dic13C2412yes—
220C2×C4×D13—28no—
221C2×C4×D13—28no—
222C2×C4×D13—28no—
223C2×C4×D13—28no—
224C2×C4×D13—416no—
225C2×C4×D13—44no—
226C2×C4×D13—44no—
227C2×C4×D13—44no—
228C2×C4×D13—44no—
229C2×C4×D13—416no—
230C2×C4×D13—416no—
231C2×C4×D13C2×Q8116yescomplemented
232C2×Dic26—28no—
233C2×Dic26—28no—
234C2×Dic26—28no—
235C2×Dic26—28no—
236C2×Dic26—44no—
237C2×Dic26—44no—
238C2×Dic26—416no—
239C2×Dic26—416no—
240C13×C4⋊C4—28no—
241C13×C4⋊C4—28no—
242C13×C4⋊C4—44no—
243C13×C4⋊C4—44no—
244#6103—28no—
245#6103—28no—
246#6103C2×D4116yes—
247#6103C2×Q8116yescomplemented
248C4⋊Dic13—28no—
249C4⋊Dic13—44no—
250#6101—28no—
251#6101—28no—
252#6101—28no—
253#6101—28no—
254#6101—28no—
255#6101—44no—
256C4×Dic13—44no—
257C4×Dic13—44no—
258C22×C22⋊Q8—131no—
259C22×C22⋊Q8—131no—
260#2549—1316no—
261C2×#398—131no—
262C2×#398D1311yescharacteristic, complemented
263C2×#395—131no—
264C2×#395—131no—
265C2×#391—131no—
266C2×#391—131no—
267C2×#389—131no—
268C2×#389—131no—
269C2×#385—131no—
270C2×#385—131no—
271C2×#380—131no—
272C2×C4×C22⋊C4—131no—
273C22×#95—131no—
274C23×C13C22×D412yes—
275C23×C13C22×Q812yes—
276C23×C13C22×Q812yes—
277C23×C13C2×#4112yes—
278C23×C13C2×#4112yes—
279C23×C13H(5,𝔽2)12yes—
280C23×C13H(5,𝔽2)12yes—
281C23×C13C2511yescharacteristic
282C22×D13—28no—
283C22×D13—28no—
284C22×D13—28no—
285C22×D13—28no—
286C22×D13—28no—
287C22×D13—28no—
288C22×D13—22no—
289C22×D13—22no—
290C22×D13—22no—
291C22×D13—22no—
292C22×D13C4⋊Q8116yes—
293C22×D13C22×D414yes—
294C22×D13C22×Q814yes—
295C22×D13C22×Q814yes—
296C2×C4×C13—28no—
297C2×C4×C13—28no—
298C2×C4×C13—28no—
299C2×C4×C13—22no—
300C2×C4×C13—22no—
301C2×C4×C13—22no—
302C2×C4×C13—22no—
303C2×C4×C13—22no—
304C2×C4×C13—22no—
305C2×C4×C13—22no—
306C2×C4×C13—22no—
307C2×C4×C13—22no—
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—44no—
318C2×C4×C13—44no—
319C2×C4×C13—44no—
320C2×C4×C13—44no—
321C2×C4×C13C22×D414yes—
322C2×C4×C13C22×Q814yes—
323C2×C4×C13C22×Q814yes—
324C2×Dic13—28no—
325C2×Dic13—28no—
326C2×Dic13—28no—
327C2×Dic13—28no—
328C2×Dic13—28no—
329C2×Dic13—22no—
330C2×Dic13—22no—
331C2×Dic13—22no—
332C2×Dic13—22no—
333C2×Dic13—22no—
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—44no—
346C2×Dic13—44no—
347C2×Dic13C22×D414yes—
348C2×Dic13C22×Q814yes—
349C2×Dic13C22×Q814yes—
350C2×Dic13C2×#4114yes—
351C2×Dic13C2×#4114yes—
352C4×D13—416no—
353C4×D13—416no—
354C4×D13—416no—
355Dic26—416no—
356Dic26—416no—
357C23×Q8—131no—
358C23×Q8—131no—
359C24×C4—131no—
360C24×C4—131no—
361C24×C4—131no—
362C2×C22⋊Q8—138no—
363C2×C22⋊Q8—138no—
364C2×C22⋊Q8—268no—
365C2×C22⋊Q8—268no—
366C22×C4⋊C4—131no—
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⋊C4C2×D1311yescharacteristic
375C22×C4⋊C4C2×D1311yescharacteristic
376C22×C4⋊C4C2×D1311yescharacteristic
377C22×C4⋊C4C2×D1311yescharacteristic
378C22×C22⋊C4—131no—
379C22×C22⋊C4—131no—
380C22×C22⋊C4—131no—
381C22×C22⋊C4—131no—
382C22×C42—131no—
383C22×C42—131no—
384#398—138no—
385#398C2×D1318yescomplemented
386#395—138no—
387#395—138no—
388#391—138no—
389#391—138no—
390#389—138no—
391#389—138no—
392#385—138no—
393#385—138no—
394#380—138no—
395C4×C22⋊C4—138no—
396C2×#95—131no—
397C2×#95—131no—
398C2×#95—131no—
399C2×#95—131no—
400C2×#95—131no—
401C2×#95—131no—
402C2×#95—131no—
403C2×#95—131no—
404C2×#95—131no—
405C2×#95—138no—
406C2×#95C2×D1311yescharacteristic
407C2×#95C2×D1311yescharacteristic
408C2×#95C2×D1311yescharacteristic
409C22×C13C2×C4⋊Q814yes—
410C22×C13#53314yes—
411C22×C13#54314yes—
412C22×C13#54614yes—
413C22×C13#54614yes—
414C22×C13#55414yes—
415C22×C13#55414yes—
416C22×C13C23×D411yescharacteristic
417C22×C13C23×Q811yescharacteristic
418C22×C13C23×Q811yescharacteristic
419C22×C13C22×#4111yescharacteristic
420C22×C13C22×#4111yescharacteristic
421C22×C13C2×H(5,𝔽2)11yescharacteristic
422C22×C13C2×H(5,𝔽2)11yescharacteristic
423C2×D13—24no—
424C2×D13—24no—
425C2×D13—24no—
426C2×D13—24no—
427C2×D13—24no—
428C2×D13—24no—
429C2×D13—232no—
430C2×D13C2×C4⋊Q818yes—
431C4×C13—24no—
432C4×C13—24no—
433C4×C13—24no—
434C4×C13—42no—
435C4×C13—42no—
436C4×C13—42no—
437C4×C13—42no—
438Dic13—24no—
439Dic13—24no—
440Dic13—24no—
441Dic13—24no—
442Dic13—24no—
443Dic13—42no—
444Dic13—42no—
445C25—131no—
446C22×Q8—134no—
447C22×Q8—134no—
448C22×Q8—264no—
449C22×Q8—264no—
450C22×Q8—264no—
451C22×Q8—264no—
452C22×Q8—522no—
453C22×Q8—522no—
454C23×C4—131no—
455C23×C4—131no—
456C23×C4—131no—
457C23×C4—131no—
458C23×C4—131no—
459C23×C4—138no—
460C23×C4—134no—
461C23×C4—131no—
462C23×C4—131no—
463C23×C4—134no—
464C23×C4—134no—
465C23×C4—264no—
466C23×C4—264no—
467C23×C4—264no—
468C23×C4—264no—
469C23×C4—522no—
470C23×C4—522no—
471C23×C4—522no—
472C23×C4—522no—
473C23×C4C22×D1311yescharacteristic
474C23×C4C22×D1311yescharacteristic
475C23×C4C22×D1311yescharacteristic
476C23×C4C22×D1311yescharacteristic
477C23×C4C22×D1311yescharacteristic
478C23×C4C22×D1311yescharacteristic
479C23×C4C22×D1311yescharacteristic
480C22⋊Q8—2632no—
481C22⋊Q8—2632no—
482C2×C4⋊C4—24no—
483C2×C4⋊C4—24no—
484C2×C4⋊C4—42no—
485C2×C4⋊C4—42no—
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—134no—
494C2×C4⋊C4—264no—
495C2×C4⋊C4—264no—
496C2×C4⋊C4—264no—
497C2×C4⋊C4—264no—
498C2×C4⋊C4—264no—
499C2×C4⋊C4—264no—
500C2×C4⋊C4—522no—
501C2×C4⋊C4—522no—
502C2×C4⋊C4C22×D1314yes—
503C2×C4⋊C4C22×D1314yes—
504C2×C4⋊C4C22×D1314yes—
505C2×C4⋊C4C22×D1314yes—
506C2×C22⋊C4—138no—
507C2×C22⋊C4—138no—
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×C42—134no—
515C2×C42—134no—
516C2×C42—522no—
517C2×C42—522no—
518#95—134no—
519#95—134no—
520#95—134no—
521#95—134no—
522#95—134no—
523#95—134no—
524#95—134no—
525#95—134no—
526#95—134no—
527#95C22×D1314yes—
528#95C22×D1314yes—
529#95C22×D1314yes—
530C2×C13#254918yescomplemented
531C2×C13C22×C4⋊Q811yescharacteristic
532C2×C13C2×#53311yescharacteristic
533C2×C13C2×#54311yescharacteristic
534C2×C13C2×#54611yescharacteristic
535C2×C13C2×#54611yescharacteristic
536C2×C13C2×#55411yescharacteristic
537C2×C13C2×#55411yescharacteristic
538D13—28no—
539C24—134no—
540C24—134no—
541C24—134no—
542C24—132no—
543C24—262no—
544C24—262no—
545C24—262no—
546C24—262no—
547C24C23×D1311yescharacteristic
548C2×Q8—268no—
549C2×Q8—268no—
550C2×Q8—268no—
551C2×Q8—268no—
552C2×Q8—524no—
553C2×Q8—524no—
554C2×Q8—5216no—
555C2×Q8—5216no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—134no—
575C22×C4—134no—
576C22×C4—134no—
577C22×C4—134no—
578C22×C4—134no—
579C22×C4—132no—
580C22×C4—132no—
581C22×C4—132no—
582C22×C4—132no—
583C22×C4—132no—
584C22×C4—1316no—
585C22×C4—132no—
586C22×C4—132no—
587C22×C4—268no—
588C22×C4—268no—
589C22×C4—268no—
590C22×C4—268no—
591C22×C4—262no—
592C22×C4—262no—
593C22×C4—262no—
594C22×C4—262no—
595C22×C4—262no—
596C22×C4—262no—
597C22×C4—262no—
598C22×C4—262no—
599C22×C4—262no—
600C22×C4—262no—
601C22×C4—262no—
602C22×C4—262no—
603C22×C4—262no—
604C22×C4—262no—
605C22×C4—262no—
606C22×C4—262no—
607C22×C4—5216no—
608C22×C4—524no—
609C22×C4—524no—
610C22×C4—524no—
611C22×C4—524no—
612C22×C4—5216no—
613C22×C4—5216no—
614C22×C4D4×D1314yes—
615C22×C4Q8×D1314yes—
616C22×C4Q8×D1314yes—
617C22×C4C23×D1312yes—
618C22×C4C23×D1312yes—
619C22×C4C23×D1312yes—
620C22×C4C23×D1312yes—
621C22×C4C23×D1312yes—
622C22×C4C23×D1312yes—
623C22×C4C23×D1312yes—
624C4⋊C4—28no—
625C4⋊C4—28no—
626C4⋊C4—44no—
627C4⋊C4—44no—
628C4⋊C4—268no—
629C4⋊C4—268no—
630C4⋊C4—268no—
631C4⋊C4—268no—
632C4⋊C4—268no—
633C4⋊C4—268no—
634C4⋊C4—524no—
635C4⋊C4—524no—
636C22⋊C4—1316no—
637C22⋊C4—1316no—
638C22⋊C4—268no—
639C22⋊C4—268no—
640C42—524no—
641C42—524no—
642C13C2×#254911yescharacteristic, complemented, Sylow
643C23—1316no—
644C23—134no—
645C23—134no—
646C23—134no—
647C23—268no—
648C23—268no—
649C23—268no—
650C23—268no—
651C23—262no—
652C23—262no—
653C23—262no—
654C23—262no—
655C23—268no—
656C23—268no—
657C23C2×D4×D1312yes—
658C23#8825112yes—
659C23C2×Q8×D1312yes—
660C23C2×Q8×D1312yes—
661C23#41×D1312yes—
662C23#41×D1312yes—
663C23#8825612yes—
664C23C24×D1311yescharacteristic
665Q8—5216no—
666Q8—5216no—
667C2×C4—28no—
668C2×C4—28no—
669C2×C4—28no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—44no—
692C2×C4—134no—
693C2×C4—134no—
694C2×C4—134no—
695C2×C4—134no—
696C2×C4—134no—
697C2×C4—268no—
698C2×C4—268no—
699C2×C4—268no—
700C2×C4—268no—
701C2×C4—262no—
702C2×C4—262no—
703C2×C4—262no—
704C2×C4—262no—
705C2×C4—262no—
706C2×C4—262no—
707C2×C4—262no—
708C2×C4—262no—
709C2×C4—262no—
710C2×C4—262no—
711C2×C4—268no—
712C2×C4—262no—
713C2×C4—262no—
714C2×C4—262no—
715C2×C4—262no—
716C2×C4—262no—
717C2×C4—262no—
718C2×C4—5216no—
719C2×C4—5216no—
720C2×C4—5216no—
721C2×C4—524no—
722C2×C4—524no—
723C2×C4C2×D4×D1314yes—
724C2×C4C2×Q8×D1314yes—
725C2×C4C2×Q8×D1314yes—
726C22—138no—
727C22—264no—
728C22—264no—
729C22—264no—
730C22—2632no—
731C22—264no—
732C22—264no—
733C22—264no—
734C22#1171931714yes—
735C22#1171933914yes—
736C22#1171934114yes—
737C22#1171935914yes—
738C22#1171939314yes—
739C22#1171939514yes—
740C22D13×C4⋊Q814yes—
741C22C22×D4×D1311yescharacteristic
742C22C2×#8825111yescharacteristic
743C22C22×Q8×D1311yescharacteristic
744C22C22×Q8×D1311yescharacteristic
745C22C2×#41×D1311yescharacteristic
746C22C2×#41×D1311yescharacteristic
747C22C2×#8825611yescharacteristic
748C4—24no—
749C4—24no—
750C4—24no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—264no—
756C4—264no—
757C4—264no—
758C4—264no—
759C4—264no—
760C4—522no—
761C4—522no—
762C2—268no—
763C2#1311984318yesdirect product factor
764C2C2×D13×C4⋊Q811yescharacteristic
765C2C2×#1171939311yescharacteristic
766C2C2×#1171933911yescharacteristic
767C2C2×#1171935911yescharacteristic
768C2C2×#1171931711yescharacteristic
769C2C2×#1171934111yescharacteristic
770C2C2×#1171939511yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#398C2
socleC24×C13C24
prime radicalC24×D13C23
hypercenterC2×#398D13
hypocenterC13C2×#2549
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
3. #13119843C2direct (N × H)
4. C2×#11718318C2semidirect
5. C2×#11718317C2semidirect
6. C2×#11718640C2semidirect
7. C2×#11718635C2semidirect
8. C2×#11718307C2semidirect
9. C2×#11718634C2semidirect
10. C2×#11718633C2semidirect
16. C2×C13×#398C2semidirect
44. C13×#398C22semidirect
59. #11718640C22semidirect
60. #11718635C22semidirect
61. #11718634C22semidirect
62. #11718633C22semidirect
66. #11718318C22semidirect
67. #11718317C22semidirect
68. #11718307C22semidirect
92. C22×C4×D13Q8semidirect
115. C2×#6103Q8semidirect
231. C2×C4×D13C2×Q8semidirect
247. #6103C2×Q8semidirect
262. C2×#398D13semidirect
385. #398C2×D13semidirect
530. C2×C13#2549semidirect
642. C13C2×#2549semidirect
763. C2#13119843direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881502
#131198432
C2×#117183182
C2×#117183172
C2×#117186402
C2×#117186352
C2×#117183072
C2×#117186342
C2×#117186332
C2×#117183292
C2×#117186502
C2×#117186482
C2×#117183272
C2×D13×#952
C2×C13×#3982
C2×#254913