Finite Group Databasebeta

← C2×#13117567 #16021739

Subgroups — C2×#13117567 #16021739

Order 3328.

2982 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88132C211yesmaximal, characteristic
2#13117567C2116yesmaximal, direct product factor
3C2×#11718635C211yesmaximal, characteristic, complemented
4C2×#11718307C211yesmaximal, characteristic, complemented
5C2×#11718634C211yesmaximal, characteristic, complemented
6C2×#11718633C211yesmaximal, characteristic, complemented
7C2×#11718314C211yesmaximal, characteristic, complemented
8C2×#11718313C211yesmaximal, characteristic, complemented
9C2×#11718313C211yesmaximal, characteristic, complemented
10C2×#11718639C211yesmaximal, characteristic, complemented
11C2×#11718871C211yesmaximal, characteristic
12C2×#11718603C211yesmaximal, characteristic
13C2×C22⋊C4×Dic13C211yesmaximal, characteristic
14C2×C22⋊C4×Dic13C211yesmaximal, characteristic
15C22×#88071C211yesmaximal, characteristic
16C2×C13×#385C211yesmaximal, characteristic
17C24×C4×C13C2211yescharacteristic
18C24×Dic13C2211yescharacteristic
19C24×Dic13C2211yescharacteristic
20C23×Dic26C2211yescharacteristic
21C22×C13×C4⋊C4C2211yescharacteristic
22C22×C13×C4⋊C4C2211yescharacteristic
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C22⋊Dic13C2211yescharacteristic
26C22×C22⋊Dic13C2211yescharacteristic
27C22×C4⋊Dic13C2211yescharacteristic
28C22×#6101C2211yescharacteristic
29C22×#6101C2211yescharacteristic
30C22×#6101C2211yescharacteristic
31C22×#6101C2211yescharacteristic
32C22×#6101C2211yescharacteristic
33C22×#6101C2211yescharacteristic
34C22×C4×Dic13C2211yescharacteristic
35C22×C4×Dic13C2211yescharacteristic
36C22×C4×Dic13C2211yescharacteristic
37C22×C4×Dic13C2211yescharacteristic
38C2×#88132C4116yescomplemented
39C2×#88132C2218yes—
40C13×#385C2218yes—
41C2×C13×#95C2211yescharacteristic
42C2×C13×#95C2211yescharacteristic
43#11718871C2218yes—
44C2×#88071C2211yescharacteristic
45C2×#88071C2211yescharacteristic
46C2×#88071C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2218yes—
57#11718639C2218yescomplemented
58#11718635C2218yescomplemented
59#11718634C2218yescomplemented
60#11718633C2218yescomplemented
61#11718603C2218yes—
62C22⋊C4×Dic13C2218yes—
63C22⋊C4×Dic13C2218yes—
64#11718314C2218yescomplemented
65#11718313C2218yescomplemented
66#11718313C2218yescomplemented
67#11718307C2218yescomplemented
68C25×C13C2311yescharacteristic
69C23×C4×C13—24no—
70C23×C4×C13—42no—
71C23×C4×C13—42no—
72C23×C4×C13C2311yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C23×C4×C13C2311yescharacteristic
78C23×C4×C13C2314yes—
79C23×Dic13—42no—
80C23×Dic13—42no—
81C23×Dic13—42no—
82C23×Dic13—42no—
83C23×Dic13C2×C418yes—
84C23×Dic13Q818yescomplemented
85C23×Dic13C2311yescharacteristic
86C23×Dic13C2311yescharacteristic
87C23×Dic13C2311yescharacteristic
88C23×Dic13C2311yescharacteristic
89C23×Dic13C2311yescharacteristic
90C23×Dic13C2311yescharacteristic
91C23×Dic13C2311yescharacteristic
92C23×Dic13C2311yescharacteristic
93C23×Dic13C2314yes—
94C23×Dic13C2314yes—
95C22×Dic26—42no—
96C22×Dic26—42no—
97C22×Dic26C2×C418yescomplemented
98C22×Dic26C2314yes—
99C2×C13×C4⋊C4—42no—
100C2×C13×C4⋊C4—42no—
101C2×C13×C4⋊C4C2314yes—
102C2×C13×C4⋊C4C2314yes—
103C2×C13×C22⋊C4—24no—
104C2×C13×C22⋊C4C2×C418yes—
105C2×C13×C22⋊C4C2314yes—
106C2×C13×C22⋊C4C2314yes—
107C2×C22⋊Dic13—24no—
108C2×C22⋊Dic13C2×C418yes—
109C2×C22⋊Dic13C2314yes—
110C2×C22⋊Dic13C2314yes—
111C2×C4⋊Dic13C2×C418yescomplemented
112C2×C4⋊Dic13C2314yes—
113C2×#6101—42no—
114C2×#6101—42no—
115C2×#6101—42no—
116C2×#6101—42no—
117C2×#6101C2×C418yescomplemented
118C2×#6101C2×C418yescomplemented
119C2×#6101C2314yes—
120C2×#6101C2314yes—
121C2×#6101C2314yes—
122C2×#6101C2314yes—
123C2×#6101C2314yes—
124C2×#6101C2314yes—
125C2×C4×Dic13—42no—
126C2×C4×Dic13—42no—
127C2×C4×Dic13—42no—
128C2×C4×Dic13—42no—
129C2×C4×Dic13C2314yes—
130C2×C4×Dic13C2314yes—
131C2×C4×Dic13C2314yes—
132C2×C4×Dic13C2314yes—
133#88132C2×C4164yescomplemented
134C13×#95C2314yes—
135C13×#95C2314yes—
136#88071C2314yes—
137#88071C2314yes—
138#88071C2314yes—
139#88071C2314yes—
140#88071C2314yes—
141#88071C2314yes—
142#88071C2314yes—
143#88071C2314yes—
144#88071C2314yes—
145#88071C2314yes—
146#88071C2314yes—
147#88071C2314yes—
148C2×#2329—131nomaximal, Sylow
149C24×C13—22no—
150C24×C13—22no—
151C24×C13—22no—
152C24×C13—22no—
153C24×C13C22×C414yes—
154C24×C13C2×Q814yes—
155C24×C13#4114yes—
156C24×C13C2412yes—
157C24×C13C2411yescharacteristic
158C22×C4×C13—22no—
159C22×C4×C13—22no—
160C22×C4×C13—22no—
161C22×C4×C13—22no—
162C22×C4×C13—22no—
163C22×C4×C13—22no—
164C22×C4×C13—28no—
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—44no—
176C22×C4×C13—44no—
177C22×C4×C13—416no—
178C22×C4×C13C22×C414yes—
179C22×C4×C13C22×C414yes—
180C22×C4×C13C2412yes—
181C22×C4×C13C2412yes—
182C22×C4×C13C2412yes—
183C22×C4×C13C2412yes—
184C22×C4×C13C2412yes—
185C22×C4×C13C2412yes—
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—22no—
204C22×Dic13—416no—
205C22×Dic13—416no—
206C22×Dic13—44no—
207C22×Dic13—44no—
208C22×Dic13—44no—
209C22×Dic13—44no—
210C22×Dic13C22×C414yes—
211C22×Dic13C22×C414yes—
212C22×Dic13C22×C414yes—
213C22×Dic13C22×C414yes—
214C22×Dic13C22×C4116yes—
215C22×Dic13C2×Q814yes—
216C22×Dic13C2×Q814yes—
217C22×Dic13C2×Q8116yescomplemented
218C22×Dic13C2412yes—
219C22×Dic13C2412yes—
220C22×Dic13C2412yes—
221C22×Dic13C2412yes—
222C22×Dic13C2412yes—
223C22×Dic13C2412yes—
224C22×Dic13C2412yes—
225C22×Dic13C2412yes—
226C2×Dic26—416no—
227C2×Dic26—44no—
228C2×Dic26—44no—
229C2×Dic26C22×C4116yescomplemented
230C13×C4⋊C4—44no—
231C13×C4⋊C4—44no—
232C13×C22⋊C4—28no—
233C13×C22⋊C4C22×C4116yes—
234C22⋊Dic13—28no—
235C22⋊Dic13C22×C4116yes—
236C4⋊Dic13C22×C4116yescomplemented
237#6101—44no—
238#6101—44no—
239#6101—44no—
240#6101—44no—
241#6101C22×C4116yescomplemented
242#6101C22×C4116yescomplemented
243C4×Dic13—44no—
244C4×Dic13—44no—
245C4×Dic13—44no—
246C4×Dic13—44no—
247C22×C22⋊Q8—131no—
248#2329—1316no—
249C2×#391—131no—
250C2×#391—131no—
251C2×#389—131no—
252C2×#389—131no—
253C2×#387—131no—
254C2×#387—131no—
255C2×#387—131no—
256C2×#387—131no—
257C2×#385—131no—
258C2×#385D1311yescharacteristic
259C2×#380—131no—
260C2×C4×C22⋊C4—131no—
261C2×C4×C22⋊C4—131no—
262C22×#95—131no—
263C23×C13—28no—
264C23×C13—28no—
265C23×C13—28no—
266C23×C13—28no—
267C23×C13—28no—
268C23×C13—28no—
269C23×C13—22no—
270C23×C13—22no—
271C23×C13—22no—
272C23×C13—22no—
273C23×C13C4×Q8116yes—
274C23×C13C23×C414yes—
275C23×C13C23×C412yes—
276C23×C13C22×Q814yes—
277C23×C13C22×Q812yes—
278C23×C13C2×#4114yes—
279C23×C13C2×#4112yes—
280C23×C13H(5,𝔽2)12yes—
281C23×C13H(5,𝔽2)12yes—
282C23×C13H(5,𝔽2)12yes—
283C23×C132−1+412yes—
284C23×C13C2511yescharacteristic
285C2×C4×C13—28no—
286C2×C4×C13—28no—
287C2×C4×C13—22no—
288C2×C4×C13—22no—
289C2×C4×C13—22no—
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—416no—
304C2×C4×C13—44no—
305C2×C4×C13—44no—
306C2×C4×C13—44no—
307C2×C4×C13—44no—
308C2×C4×C13C23×C414yes—
309C2×C4×C13C23×C414yes—
310C2×Dic13—28no—
311C2×Dic13—28no—
312C2×Dic13—28no—
313C2×Dic13—28no—
314C2×Dic13—28no—
315C2×Dic13—28no—
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—22no—
333C2×Dic13—22no—
334C2×Dic13—416no—
335C2×Dic13—416no—
336C2×Dic13—44no—
337C2×Dic13—44no—
338C2×Dic13C23×C414yes—
339C2×Dic13C23×C414yes—
340C2×Dic13C23×C414yes—
341C2×Dic13C23×C414yes—
342C2×Dic13C22×Q814yes—
343C2×Dic13C22×Q814yes—
344Dic26—416no—
345C23×Q8—131no—
346C24×C4—131no—
347C24×C4—131no—
348C24×C4C2×D1311yescharacteristic
349C2×C22⋊Q8—1316no—
350C2×C22⋊Q8—138no—
351C22×C4⋊C4—131no—
352C22×C4⋊C4—131no—
353C22×C4⋊C4—131no—
354C22×C4⋊C4—131no—
355C22×C4⋊C4—131no—
356C22×C4⋊C4—131no—
357C22×C4⋊C4—131no—
358C22×C4⋊C4C2×D1311yescharacteristic
359C22×C4⋊C4C2×D1311yescharacteristic
360C22×C22⋊C4—131no—
361C22×C22⋊C4—131no—
362C22×C22⋊C4C2×D1311yescharacteristic
363C22×C22⋊C4C2×D1311yescharacteristic
364C22×C42—131no—
365C22×C42—131no—
366C22×C42—131no—
367C22×C42—131no—
368#391—138no—
369#391—138no—
370#389—138no—
371#389—138no—
372#387—138no—
373#387—138no—
374#387—138no—
375#387—138no—
376#385—138no—
377#385C2×D1318yes—
378#380—138no—
379C4×C22⋊C4—138no—
380C4×C22⋊C4—138no—
381C2×#95—138no—
382C2×#95—131no—
383C2×#95—131no—
384C2×#95—131no—
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×#95C2×D1311yescharacteristic
395C2×#95C2×D1311yescharacteristic
396C22×C13—232no—
397C22×C13—24no—
398C22×C13—24no—
399C22×C13—24no—
400C22×C13—24no—
401C22×C13—24no—
402C22×C13—24no—
403C22×C13C2×C4×Q818yes—
404C22×C13C2×C4×Q814yes—
405C22×C13#51814yes—
406C22×C13#52014yes—
407C22×C13#53814yes—
408C22×C13#53914yes—
409C22×C13#54314yes—
410C22×C13#54414yes—
411C22×C13C24×C411yescharacteristic
412C22×C13C23×Q811yescharacteristic
413C22×C13C22×#4111yescharacteristic
414C22×C13C2×H(5,𝔽2)11yescharacteristic
415C22×C13C2×H(5,𝔽2)11yescharacteristic
416C22×C13C2×H(5,𝔽2)11yescharacteristic
417C22×C13C2×2−1+411yescharacteristic
418C4×C13—24no—
419C4×C13—24no—
420C4×C13—42no—
421C4×C13—42no—
422C4×C13—42no—
423C4×C13—42no—
424Dic13—24no—
425Dic13—24no—
426Dic13—24no—
427Dic13—24no—
428Dic13—24no—
429Dic13—24no—
430Dic13—42no—
431Dic13—42no—
432C25C22×D1311yescharacteristic
433C22×Q8—138no—
434C22×Q8—134no—
435C22×Q8—522no—
436C22×Q8—522no—
437C23×C4—24no—
438C23×C4—42no—
439C23×C4—42no—
440C23×C4—131no—
441C23×C4—131no—
442C23×C4—131no—
443C23×C4—131no—
444C23×C4—131no—
445C23×C4—131no—
446C23×C4—138no—
447C23×C4—138no—
448C23×C4—134no—
449C23×C4—134no—
450C23×C4—131no—
451C23×C4—131no—
452C23×C4—522no—
453C23×C4—522no—
454C23×C4—522no—
455C23×C4—522no—
456C23×C4C22×D1311yescharacteristic
457C23×C4C22×D1311yescharacteristic
458C23×C4C22×D1311yescharacteristic
459C23×C4C22×D1311yescharacteristic
460C23×C4C22×D1311yescharacteristic
461C23×C4C22×D1311yescharacteristic
462C23×C4C22×D1314yes—
463C22⋊Q8—1364no—
464C2×C4⋊C4—42no—
465C2×C4⋊C4—42no—
466C2×C4⋊C4—138no—
467C2×C4⋊C4—138no—
468C2×C4⋊C4—138no—
469C2×C4⋊C4—134no—
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—522no—
477C2×C4⋊C4—522no—
478C2×C4⋊C4—522no—
479C2×C4⋊C4—522no—
480C2×C4⋊C4C22×D1314yes—
481C2×C4⋊C4C22×D1314yes—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—138no—
484C2×C22⋊C4—134no—
485C2×C22⋊C4—134no—
486C2×C22⋊C4—264no—
487C2×C22⋊C4C4×D1318yes—
488C2×C22⋊C4C22×D1314yes—
489C2×C22⋊C4C22×D1314yes—
490C2×C42—134no—
491C2×C42—134no—
492C2×C42—134no—
493C2×C42—134no—
494C2×C42—522no—
495C2×C42—522no—
496C2×C42—522no—
497C2×C42—522no—
498#95—134no—
499#95—134no—
500#95—134no—
501#95—134no—
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#95C22×D1314yes—
511#95C22×D1314yes—
512C2×C13—28no—
513C2×C13#232918yescomplemented
514C2×C13C22×C4×Q811yescharacteristic
515C2×C13C2×#51811yescharacteristic
516C2×C13C2×#52011yescharacteristic
517C2×C13C2×#53811yescharacteristic
518C2×C13C2×#53911yescharacteristic
519C2×C13C2×#54311yescharacteristic
520C2×C13C2×#54411yescharacteristic
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24C2×C4×D1314yes—
526C24#612914yes—
527C24Q8×D1314yes—
528C24C23×D1312yes—
529C24C23×D1311yescharacteristic
530C2×Q8—1316no—
531C2×Q8—5216no—
532C2×Q8—524no—
533C2×Q8—524no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—28no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—44no—
552C22×C4—44no—
553C22×C4—416no—
554C22×C4—134no—
555C22×C4—134no—
556C22×C4—134no—
557C22×C4—134no—
558C22×C4—134no—
559C22×C4—134no—
560C22×C4—132no—
561C22×C4—132no—
562C22×C4—132no—
563C22×C4—132no—
564C22×C4—132no—
565C22×C4—132no—
566C22×C4—1316no—
567C22×C4—1316no—
568C22×C4—132no—
569C22×C4—132no—
570C22×C4—262no—
571C22×C4—262no—
572C22×C4—262no—
573C22×C4—262no—
574C22×C4—262no—
575C22×C4—262no—
576C22×C4—262no—
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—5216no—
589C22×C4—5216no—
590C22×C4—524no—
591C22×C4—524no—
592C22×C4—524no—
593C22×C4—524no—
594C22×C4C2×C4×D1314yes—
595C22×C4C2×C4×D1314yes—
596C22×C4C23×D1312yes—
597C22×C4C23×D1312yes—
598C22×C4C23×D1312yes—
599C22×C4C23×D1312yes—
600C22×C4C23×D1312yes—
601C22×C4C23×D1312yes—
602C4⋊C4—44no—
603C4⋊C4—44no—
604C4⋊C4—1316no—
605C4⋊C4—1316no—
606C4⋊C4—1316no—
607C4⋊C4—524no—
608C4⋊C4—524no—
609C4⋊C4—524no—
610C4⋊C4—524no—
611C22⋊C4—28no—
612C22⋊C4—1316no—
613C22⋊C4—268no—
614C22⋊C4C2×C4×D13116yes—
615C42—524no—
616C42—524no—
617C42—524no—
618C42—524no—
619C13C2×#232911yescharacteristic, complemented, Sylow
620C23—28no—
621C23—28no—
622C23—28no—
623C23—28no—
624C23—28no—
625C23—28no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23#88141116yes—
631C23C22×C4×D1314yes—
632C23C22×C4×D1312yes—
633C23C2×#612914yes—
634C23C2×#612912yes—
635C23#8825112yes—
636C23#8825112yes—
637C23C2×Q8×D1314yes—
638C23C2×Q8×D1312yes—
639C23#8825612yes—
640C23#8825712yes—
641C23C24×D1311yescharacteristic
642Q8—5216no—
643C2×C4—28no—
644C2×C4—28no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
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—416no—
662C2×C4—44no—
663C2×C4—44no—
664C2×C4—44no—
665C2×C4—44no—
666C2×C4—134no—
667C2×C4—134no—
668C2×C4—134no—
669C2×C4—134no—
670C2×C4—134no—
671C2×C4—134no—
672C2×C4—268no—
673C2×C4—268no—
674C2×C4—268no—
675C2×C4—268no—
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—5216no—
697C2×C4—5216no—
698C2×C4—524no—
699C2×C4—524no—
700C2×C4C22×C4×D1314yes—
701C2×C4C22×C4×D1314yes—
702C22—24no—
703C22—24no—
704C22—24no—
705C22—24no—
706C22—232no—
707C22—24no—
708C22—24no—
709C22C2×#8814118yes—
710C22C2×#8814114yes—
711C22#1171925014yes—
712C22#1171925114yes—
713C22#1171929814yes—
714C22#1171932814yes—
715C22#1171933914yes—
716C22#1171937014yes—
717C22C23×C4×D1311yescharacteristic
718C22C22×#612911yescharacteristic
719C22C2×#8825111yescharacteristic
720C22C2×#8825111yescharacteristic
721C22C22×Q8×D1311yescharacteristic
722C22C2×#8825611yescharacteristic
723C22C2×#8825711yescharacteristic
724C4—24no—
725C4—24no—
726C4—42no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—264no—
731C4—264no—
732C4—264no—
733C4—264no—
734C4—264no—
735C4—264no—
736C4—522no—
737C4—522no—
738C2—28no—
739C2#1311756718yesdirect product factor
740C2C22×#8814111yescharacteristic
741C2C2×#1171925011yescharacteristic
742C2C2×#1171925111yescharacteristic
743C2C2×#1171929811yescharacteristic
744C2C2×#1171937011yescharacteristic
745C2C2×#1171933911yescharacteristic
746C2C2×#1171932811yescharacteristic
subgroupG/H
centerC24C23×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC2×C13×#385C2
socleC24×C13C24
prime radicalC25×C13C23
cosocleC23×C13C25
hypercenterC2×#385D13
hypocenterC13C2×#2329
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. #13117567C2direct (N × H)
3. C2×#11718635C2semidirect
4. C2×#11718307C2semidirect
5. C2×#11718634C2semidirect
6. C2×#11718633C2semidirect
7. C2×#11718314C2semidirect
8. C2×#11718313C2semidirect
9. C2×#11718313C2semidirect
10. C2×#11718639C2semidirect
38. C2×#88132C4semidirect
57. #11718639C22semidirect
58. #11718635C22semidirect
59. #11718634C22semidirect
60. #11718633C22semidirect
64. #11718314C22semidirect
65. #11718313C22semidirect
66. #11718313C22semidirect
67. #11718307C22semidirect
84. C23×Dic13Q8semidirect
97. C22×Dic26C2×C4semidirect
111. C2×C4⋊Dic13C2×C4semidirect
117. C2×#6101C2×C4semidirect
118. C2×#6101C2×C4semidirect
133. #88132C2×C4semidirect
217. C22×Dic13C2×Q8semidirect
229. C2×Dic26C22×C4semidirect
236. C4⋊Dic13C22×C4semidirect
241. #6101C22×C4semidirect
242. #6101C22×C4semidirect
513. C2×C13#2329semidirect
619. C13C2×#2329semidirect
739. C2#13117567direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881322
#131175672
C2×#117186352
C2×#117183072
C2×#117186342
C2×#117186332
C2×#117183142
C2×#117183132
C2×#117186392
C2×#117188712
C2×#117186032
C2×C22⋊C4×Dic132
C22×#880712
C2×C13×#3852
C2×#232913