Finite Group Databasebeta

← C2×#13119207 #16032137

Subgroups — C2×#13119207 #16032137

Order 3328.

2854 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88142C211yesmaximal, characteristic, complemented
2C22×#88132C211yesmaximal, characteristic
3#13119207C2116yesmaximal, direct product factor
4C2×#11718321C211yesmaximal, characteristic, complemented
5C2×#11718647C211yesmaximal, characteristic, complemented
6C2×#11718608C211yesmaximal, characteristic
7C2×#11718608C211yesmaximal, characteristic
8C2×#11718590C211yesmaximal, characteristic, complemented
9C2×#11718307C211yesmaximal, characteristic, complemented
10C2×#11718307C211yesmaximal, characteristic, complemented
11C2×#11718307C211yesmaximal, characteristic, complemented
12C2×#11718612C211yesmaximal, characteristic
13C2×#11718603C211yesmaximal, characteristic
14C2×C4×#6101C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×Dic13C211yesmaximal, characteristic
16C2×C13×#388C211yesmaximal, characteristic
17C24×Dic13C2211yescharacteristic
18C23×Dic26C2211yescharacteristic
19C23×Dic26C2211yescharacteristic
20C23×Dic26C2211yescharacteristic
21C22×C13×C4⋊C4C2211yescharacteristic
22C22×C13×C22⋊C4C2211yescharacteristic
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C42×C13C2211yescharacteristic
26C22×C22⋊Dic13C2211yescharacteristic
27C22×C22⋊Dic13C2211yescharacteristic
28C22×C22⋊Dic13C2211yescharacteristic
29C22×C4⋊Dic13C2211yescharacteristic
30C22×C4⋊Dic13C2211yescharacteristic
31C22×#6101C2211yescharacteristic
32C22×#6101C2211yescharacteristic
33C22×#6101C2211yescharacteristic
34C22×#6101C2211yescharacteristic
35C22×C4×Dic13C2211yescharacteristic
36C22×C4×Dic13C2211yescharacteristic
37C22×C4×Dic13C2211yescharacteristic
38C2×#88142—28no—
39C2×#88142C2218yescomplemented
40C2×#88132—28no—
41C2×#88132C2218yes—
42C13×#388C2218yes—
43C2×C13×#95C2211yescharacteristic
44C2×C13×#95C2211yescharacteristic
45C2×#88071C2211yescharacteristic
46C2×#88071C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57#11718647C2218yescomplemented
58#11718612C2218yes—
59#11718608C2218yes—
60#11718608C2218yes—
61#11718603C2218yes—
62C22⋊C4×Dic13C2218yes—
63C4×#6101C2218yescomplemented
64#11718590C2218yescomplemented
65#11718321C2218yescomplemented
66#11718307C2218yescomplemented
67#11718307C2218yescomplemented
68#11718307C2218yescomplemented
69C25×C13C2311yescharacteristic
70C23×C4×C13C2311yescharacteristic
71C23×C4×C13C2311yescharacteristic
72C23×C4×C13C2311yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×Dic13—24no—
77C23×Dic13—24no—
78C23×Dic13—24no—
79C23×Dic13C2314yes—
80C23×Dic13C2311yescharacteristic
81C23×Dic13C2311yescharacteristic
82C23×Dic13C2311yescharacteristic
83C23×Dic13C2311yescharacteristic
84C23×Dic13C2311yescharacteristic
85C23×Dic13C2311yescharacteristic
86C23×Dic13C2311yescharacteristic
87C23×Dic13C2311yescharacteristic
88C22×Dic26—24no—
89C22×Dic26—24no—
90C22×Dic26—24no—
91C22×Dic26—24no—
92C22×Dic26—24no—
93C22×Dic26—24no—
94C22×Dic26—24no—
95C22×Dic26—42no—
96C22×Dic26—42no—
97C22×Dic26C2314yes—
98C22×Dic26C2314yes—
99C22×Dic26C2314yes—
100C2×C13×C4⋊C4—24no—
101C2×C13×C4⋊C4C2314yes—
102C2×C13×C22⋊C4—24no—
103C2×C13×C22⋊C4—42no—
104C2×C13×C22⋊C4Q818yescomplemented
105C2×C13×C22⋊C4C2314yes—
106C2×C13×C22⋊C4C2314yes—
107C2×C13×C22⋊C4C2314yes—
108C2×C42×C13—42no—
109C2×C42×C13C2314yes—
110C2×C22⋊Dic13—24no—
111C2×C22⋊Dic13—24no—
112C2×C22⋊Dic13—42no—
113C2×C22⋊Dic13C2314yes—
114C2×C22⋊Dic13C2314yes—
115C2×C22⋊Dic13C2314yes—
116C2×C4⋊Dic13—24no—
117C2×C4⋊Dic13—24no—
118C2×C4⋊Dic13C2314yes—
119C2×C4⋊Dic13C2314yes—
120C2×#6101—24no—
121C2×#6101—24no—
122C2×#6101—24no—
123C2×#6101D418yes—
124C2×#6101C2314yes—
125C2×#6101C2314yes—
126C2×#6101C2314yes—
127C2×#6101C2314yes—
128C2×C4×Dic13—24no—
129C2×C4×Dic13—24no—
130C2×C4×Dic13—42no—
131C2×C4×Dic13C2314yes—
132C2×C4×Dic13C2314yes—
133C2×C4×Dic13C2314yes—
134#88142—232no—
135#88132—232no—
136C13×#95C2314yes—
137C13×#95C2314yes—
138#88071C2314yes—
139#88071C2314yes—
140#88071C2314yes—
141#88071C2314yes—
142#88071C2314yes—
143#88071C2314yes—
144#88071C2314yes—
145#88071C2314yes—
146#88071C2314yes—
147#88071C2314yes—
148#88071C2314yes—
149#88071C2314yes—
150C2×#2492—131nomaximal, Sylow
151C24×C13—22no—
152C24×C13—22no—
153C24×C13—22no—
154C24×C13—22no—
155C24×C13—22no—
156C24×C13—22no—
157C24×C13C2×Q814yes—
158C24×C13C2412yes—
159C24×C13C2411yescharacteristic
160C22×C4×C13—22no—
161C22×C4×C13—22no—
162C22×C4×C13—22no—
163C22×C4×C13—22no—
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×C13C2×D414yes—
176C22×C4×C13C2×Q814yes—
177C22×C4×C13C2×Q814yes—
178C22×C4×C13C2412yes—
179C22×C4×C13C2412yes—
180C22×C4×C13C2412yes—
181C22×C4×C13C2412yes—
182C22×C4×C13C2412yes—
183C22×C4×C13C2412yes—
184C22×Dic13—22no—
185C22×Dic13—22no—
186C22×Dic13—22no—
187C22×Dic13—22no—
188C22×Dic13—22no—
189C22×Dic13—22no—
190C22×Dic13—22no—
191C22×Dic13—22no—
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—28no—
204C22×Dic13—28no—
205C22×Dic13—28no—
206C22×Dic13—416no—
207C22×Dic13C2×D414yes—
208C22×Dic13C2×D414yes—
209C22×Dic13#4114yes—
210C22×Dic13#4114yes—
211C22×Dic13#4114yes—
212C22×Dic13C2412yes—
213C22×Dic13C2412yes—
214C22×Dic13C2412yes—
215C22×Dic13C2412yes—
216C22×Dic13C2412yes—
217C22×Dic13C2412yes—
218C22×Dic13C2412yes—
219C22×Dic13C2412yes—
220C2×Dic26—28no—
221C2×Dic26—28no—
222C2×Dic26—28no—
223C2×Dic26—28no—
224C2×Dic26—28no—
225C2×Dic26—28no—
226C2×Dic26—28no—
227C2×Dic26—44no—
228C2×Dic26—44no—
229C2×Dic26—416no—
230C2×Dic26—416no—
231C2×Dic26—416no—
232C13×C4⋊C4—28no—
233C13×C22⋊C4—28no—
234C13×C22⋊C4—44no—
235C13×C22⋊C4C2×Q8116yescomplemented
236C42×C13—44no—
237C22⋊Dic13—28no—
238C22⋊Dic13—28no—
239C22⋊Dic13—44no—
240C4⋊Dic13—28no—
241C4⋊Dic13—28no—
242#6101—28no—
243#6101—28no—
244#6101—28no—
245#6101C2×D4116yes—
246C4×Dic13—28no—
247C4×Dic13—28no—
248C4×Dic13—44no—
249C22×C4⋊Q8—131no—
250C22×C22⋊Q8—131no—
251#2492—1316no—
252C2×#400—131no—
253C2×#400—131no—
254C2×#393—131no—
255C2×#393—131no—
256C2×#391—131no—
257C2×#391—131no—
258C2×#391—131no—
259C2×#391—131no—
260C2×#388—131no—
261C2×#388D1311yescharacteristic
262C2×#380—131no—
263C2×C4×C4⋊C4—131no—
264C2×C4×C22⋊C4—131no—
265C23×C13—28no—
266C23×C13—28no—
267C23×C13—28no—
268C23×C13—22no—
269C23×C13—22no—
270C23×C13—22no—
271C23×C13—22no—
272C23×C13—22no—
273C23×C13—22no—
274C23×C13—44no—
275C23×C13—44no—
276C23×C13—44no—
277C23×C13—44no—
278C23×C13C22×D412yes—
279C23×C13C22×Q814yes—
280C23×C13C22×Q812yes—
281C23×C13C2×#4112yes—
282C23×C13C2×#4112yes—
283C23×C13C2×#4112yes—
284C23×C13H(5,𝔽2)12yes—
285C23×C132−1+412yes—
286C23×C13C2511yescharacteristic
287C2×C4×C13—28no—
288C2×C4×C13—28no—
289C2×C4×C13—28no—
290C2×C4×C13—22no—
291C2×C4×C13—22no—
292C2×C4×C13—22no—
293C2×C4×C13—22no—
294C2×C4×C13—22no—
295C2×C4×C13—22no—
296C2×C4×C13—22no—
297C2×C4×C13—22no—
298C2×C4×C13—22no—
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—44no—
306C2×C4×C13—44no—
307C2×C4×C13—44no—
308C2×C4×C13C22×D414yes—
309C2×C4×C13C22×Q814yes—
310C2×C4×C13C22×Q814yes—
311C2×Dic13—28no—
312C2×Dic13—28no—
313C2×Dic13—22no—
314C2×Dic13—22no—
315C2×Dic13—22no—
316C2×Dic13—22no—
317C2×Dic13—22no—
318C2×Dic13—22no—
319C2×Dic13—22no—
320C2×Dic13—22no—
321C2×Dic13—22no—
322C2×Dic13—22no—
323C2×Dic13—22no—
324C2×Dic13—22no—
325C2×Dic13—22no—
326C2×Dic13—22no—
327C2×Dic13—22no—
328C2×Dic13—22no—
329C2×Dic13—22no—
330C2×Dic13—22no—
331C2×Dic13—22no—
332C2×Dic13—44no—
333C2×Dic13—44no—
334C2×Dic13—44no—
335C2×Dic13—44no—
336C2×Dic13—44no—
337C2×Dic13—416no—
338C2×Dic13#124116yes—
339C2×Dic13C22×D414yes—
340C2×Dic13C22×D414yes—
341C2×Dic13C2×#4114yes—
342C2×Dic13C2×#4114yes—
343C2×Dic13C2×#4114yes—
344Dic26—416no—
345Dic26—416no—
346Dic26—416no—
347C23×Q8—131no—
348C23×Q8—131no—
349C23×Q8—131no—
350C24×C4—131no—
351C2×C4⋊Q8—138no—
352C2×C4⋊Q8—268no—
353C2×C22⋊Q8—138no—
354C2×C22⋊Q8—268no—
355C22×C4⋊C4—131no—
356C22×C4⋊C4—131no—
357C22×C4⋊C4—131no—
358C22×C4⋊C4—131no—
359C22×C4⋊C4—131no—
360C22×C4⋊C4—131no—
361C22×C4⋊C4C2×D1311yescharacteristic
362C22×C22⋊C4—131no—
363C22×C22⋊C4—131no—
364C22×C22⋊C4—131no—
365C22×C22⋊C4C2×D1311yescharacteristic
366C22×C22⋊C4C2×D1311yescharacteristic
367C22×C22⋊C4C2×D1311yescharacteristic
368C22×C42—131no—
369C22×C42—131no—
370C22×C42—131no—
371C22×C42C2×D1311yescharacteristic
372#400—138no—
373#400—138no—
374#393—138no—
375#393—138no—
376#391—138no—
377#391—138no—
378#391—138no—
379#391—138no—
380#388—138no—
381#388C2×D1318yes—
382#380—138no—
383C4×C4⋊C4—138no—
384C4×C22⋊C4—138no—
385C2×#95—131no—
386C2×#95—131no—
387C2×#95—131no—
388C2×#95—131no—
389C2×#95—131no—
390C2×#95—131no—
391C2×#95—131no—
392C2×#95—131no—
393C2×#95—131no—
394C2×#95—131no—
395C2×#95—131no—
396C2×#95—131no—
397C2×#95C2×D1311yescharacteristic
398C2×#95C2×D1311yescharacteristic
399C22×C13—24no—
400C22×C13—24no—
401C22×C13—24no—
402C22×C13—42no—
403C22×C13—42no—
404C22×C13—42no—
405C22×C13—42no—
406C22×C13—416no—
407C22×C13C2×#12414yes—
408C22×C13#53314yes—
409C22×C13#54214yes—
410C22×C13#54614yes—
411C22×C13D4×Q814yes—
412C22×C13#55414yes—
413C22×C13#55614yes—
414C22×C13C23×D411yescharacteristic
415C22×C13C23×Q811yescharacteristic
416C22×C13C22×#4111yescharacteristic
417C22×C13C22×#4111yescharacteristic
418C22×C13C22×#4111yescharacteristic
419C22×C13C2×H(5,𝔽2)11yescharacteristic
420C22×C13C2×2−1+411yescharacteristic
421C4×C13—24no—
422C4×C13—24no—
423C4×C13—24no—
424C4×C13—42no—
425C4×C13—42no—
426C4×C13—42no—
427Dic13—24no—
428Dic13—24no—
429Dic13—42no—
430Dic13—42no—
431Dic13—42no—
432Dic13—42no—
433Dic13—42no—
434Dic13C2×#12418yes—
435C25C22×D1311yescharacteristic
436C22×Q8—134no—
437C22×Q8—134no—
438C22×Q8—134no—
439C22×Q8—264no—
440C22×Q8—264no—
441C22×Q8—264no—
442C22×Q8—264no—
443C22×Q8—264no—
444C22×Q8—264no—
445C22×Q8—264no—
446C22×Q8—522no—
447C22×Q8—522no—
448C23×C4—131no—
449C23×C4—131no—
450C23×C4—131no—
451C23×C4—134no—
452C23×C4—131no—
453C23×C4—131no—
454C23×C4—131no—
455C23×C4—131no—
456C23×C4—131no—
457C23×C4—264no—
458C23×C4—264no—
459C23×C4—264no—
460C23×C4C22×D1311yescharacteristic
461C23×C4C22×D1311yescharacteristic
462C23×C4C22×D1311yescharacteristic
463C23×C4C22×D1311yescharacteristic
464C23×C4C22×D1311yescharacteristic
465C23×C4C22×D1311yescharacteristic
466C4⋊Q8—2632no—
467C22⋊Q8—2632no—
468C2×C4⋊C4—24no—
469C2×C4⋊C4—138no—
470C2×C4⋊C4—134no—
471C2×C4⋊C4—134no—
472C2×C4⋊C4—134no—
473C2×C4⋊C4—134no—
474C2×C4⋊C4—134no—
475C2×C4⋊C4—134no—
476C2×C4⋊C4—264no—
477C2×C4⋊C4—264no—
478C2×C4⋊C4—264no—
479C2×C4⋊C4—264no—
480C2×C4⋊C4—264no—
481C2×C4⋊C4C22×D1314yes—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—42no—
484C2×C22⋊C4—134no—
485C2×C22⋊C4—134no—
486C2×C22⋊C4—134no—
487C2×C22⋊C4—264no—
488C2×C22⋊C4—264no—
489C2×C22⋊C4—522no—
490C2×C22⋊C4Dic2618yescomplemented
491C2×C22⋊C4C22×D1314yes—
492C2×C22⋊C4C22×D1314yes—
493C2×C22⋊C4C22×D1314yes—
494C2×C42—42no—
495C2×C42—134no—
496C2×C42—134no—
497C2×C42—134no—
498C2×C42—264no—
499C2×C42—264no—
500C2×C42—522no—
501C2×C42C22×D1314yes—
502#95—134no—
503#95—134no—
504#95—134no—
505#95—134no—
506#95—134no—
507#95—134no—
508#95—134no—
509#95—134no—
510#95—134no—
511#95—134no—
512#95—134no—
513#95—134no—
514#95C22×D1314yes—
515#95C22×D1314yes—
516C2×C13—44no—
517C2×C13#249218yescomplemented
518C2×C13C22×#12411yescharacteristic
519C2×C13C2×#53311yescharacteristic
520C2×C13C2×#54211yescharacteristic
521C2×C13C2×#54611yescharacteristic
522C2×C13C2×D4×Q811yescharacteristic
523C2×C13C2×#55411yescharacteristic
524C2×C13C2×#55611yescharacteristic
525C24—22no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24C2×Dic2614yes—
532C24C23×D1312yes—
533C24C23×D1311yescharacteristic
534C2×Q8—268no—
535C2×Q8—268no—
536C2×Q8—268no—
537C2×Q8—268no—
538C2×Q8—268no—
539C2×Q8—268no—
540C2×Q8—268no—
541C2×Q8—524no—
542C2×Q8—524no—
543C2×Q8—5216no—
544C2×Q8—5216no—
545C2×Q8—5216no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—134no—
562C22×C4—134no—
563C22×C4—134no—
564C22×C4—132no—
565C22×C4—134no—
566C22×C4—134no—
567C22×C4—132no—
568C22×C4—132no—
569C22×C4—132no—
570C22×C4—132no—
571C22×C4—132no—
572C22×C4—132no—
573C22×C4—132no—
574C22×C4—268no—
575C22×C4—268no—
576C22×C4—268no—
577C22×C4—262no—
578C22×C4—262no—
579C22×C4—262no—
580C22×C4—262no—
581C22×C4—262no—
582C22×C4—262no—
583C22×C4—262no—
584C22×C4—262no—
585C22×C4—262no—
586C22×C4—262no—
587C22×C4—262no—
588C22×C4—262no—
589C22×C4—262no—
590C22×C4—262no—
591C22×C4—262no—
592C22×C4—262no—
593C22×C4—262no—
594C22×C4—262no—
595C22×C4—262no—
596C22×C4—5216no—
597C22×C4C2×Dic2614yes—
598C22×C4C2×Dic2614yes—
599C22×C4D4×D1314yes—
600C22×C4C23×D1312yes—
601C22×C4C23×D1312yes—
602C22×C4C23×D1312yes—
603C22×C4C23×D1312yes—
604C22×C4C23×D1312yes—
605C22×C4C23×D1312yes—
606C4⋊C4—28no—
607C4⋊C4—1316no—
608C4⋊C4—268no—
609C4⋊C4—268no—
610C4⋊C4—268no—
611C4⋊C4—268no—
612C4⋊C4—268no—
613C22⋊C4—28no—
614C22⋊C4—44no—
615C22⋊C4—268no—
616C22⋊C4—268no—
617C22⋊C4—524no—
618C22⋊C4C2×Dic26116yescomplemented
619C42—44no—
620C42—268no—
621C42—268no—
622C42—524no—
623C13C2×#249211yescharacteristic, complemented, Sylow
624C23—28no—
625C23—28no—
626C23—28no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—44no—
634C23—44no—
635C23—44no—
636C23—44no—
637C23C22×Dic2614yes—
638C23C22×Dic2612yes—
639C23C2×D4×D1312yes—
640C23#8825112yes—
641C23#41×D1312yes—
642C23#41×D1312yes—
643C23#41×D1312yes—
644C23#8825712yes—
645C23C24×D1311yescharacteristic
646Q8—5216no—
647Q8—5216no—
648Q8—5216no—
649C2×C4—28no—
650C2×C4—28no—
651C2×C4—28no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—44no—
668C2×C4—44no—
669C2×C4—44no—
670C2×C4—1316no—
671C2×C4—134no—
672C2×C4—134no—
673C2×C4—134no—
674C2×C4—134no—
675C2×C4—134no—
676C2×C4—268no—
677C2×C4—268no—
678C2×C4—262no—
679C2×C4—262no—
680C2×C4—262no—
681C2×C4—262no—
682C2×C4—262no—
683C2×C4—262no—
684C2×C4—262no—
685C2×C4—262no—
686C2×C4—262no—
687C2×C4—262no—
688C2×C4—262no—
689C2×C4—262no—
690C2×C4—262no—
691C2×C4—262no—
692C2×C4—262no—
693C2×C4—262no—
694C2×C4—262no—
695C2×C4—262no—
696C2×C4—262no—
697C2×C4—5216no—
698C2×C4—524no—
699C2×C4—524no—
700C2×C4—524no—
701C2×C4—524no—
702C2×C4—524no—
703C2×C4C22×Dic2614yes—
704C2×C4C22×Dic2614yes—
705C2×C4C2×D4×D1314yes—
706C22—24no—
707C22—24no—
708C22—24no—
709C22—42no—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—416no—
714C22#1171922214yes—
715C22D4×Dic2614yes—
716C22#1171924414yes—
717C22#1171931514yes—
718C22#1171936714yes—
719C22D13×#12414yes—
720C22#1171940714yes—
721C22C23×Dic2611yescharacteristic
722C22C22×D4×D1311yescharacteristic
723C22C2×#8825111yescharacteristic
724C22C2×#41×D1311yescharacteristic
725C22C2×#41×D1311yescharacteristic
726C22C2×#41×D1311yescharacteristic
727C22C2×#8825711yescharacteristic
728C4—24no—
729C4—24no—
730C4—24no—
731C4—42no—
732C4—42no—
733C4—42no—
734C4—138no—
735C4—264no—
736C4—264no—
737C4—522no—
738C4—522no—
739C4—522no—
740C4—522no—
741C4—522no—
742C2—44no—
743C2#1311920718yesdirect product factor
744C2C2×D13×#12411yescharacteristic
745C2C2×#1171922211yescharacteristic
746C2C2×#1171936711yescharacteristic
747C2C2×#1171931511yescharacteristic
748C2C2×D4×Dic2611yescharacteristic
749C2C2×#1171924411yescharacteristic
750C2C2×#1171940711yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#388C2
socleC24×C13C24
prime radicalC25×C13C23
hypercenterC2×#388D13
hypocenterC13C2×#2492
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×#88142C2semidirect
3. #13119207C2direct (N × H)
4. C2×#11718321C2semidirect
5. C2×#11718647C2semidirect
8. C2×#11718590C2semidirect
9. C2×#11718307C2semidirect
10. C2×#11718307C2semidirect
11. C2×#11718307C2semidirect
14. C2×C4×#6101C2semidirect
39. C2×#88142C22semidirect
57. #11718647C22semidirect
63. C4×#6101C22semidirect
64. #11718590C22semidirect
65. #11718321C22semidirect
66. #11718307C22semidirect
67. #11718307C22semidirect
68. #11718307C22semidirect
104. C2×C13×C22⋊C4Q8semidirect
235. C13×C22⋊C4C2×Q8semidirect
490. C2×C22⋊C4Dic26semidirect
517. C2×C13#2492semidirect
618. C22⋊C4C2×Dic26semidirect
623. C13C2×#2492semidirect
743. C2#13119207direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881422
C22×#881322
#131192072
C2×#117183212
C2×#117186472
C2×#117186082
C2×#117185902
C2×#117183072
C2×#117186122
C2×#117186032
C2×C4×#61012
C2×C22⋊C4×Dic132
C2×C13×#3882
C2×#249213