Finite Group Databasebeta

← C2×#13118347 #16030788

Subgroups — C2×#13118347 #16030788

Order 3328.

3830 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88137C211yesmaximal, characteristic, complemented
2C22×#88193C211yesmaximal, characteristic
3C22×C4×C22⋊D13C211yesmaximal, characteristic, complemented
4#13118347C2116yesmaximal, direct product factor
5C2×#11718654C211yesmaximal, characteristic, complemented
6C2×#11718614C211yesmaximal, characteristic, complemented
7C2×#11718620C211yesmaximal, characteristic, complemented
8C2×#11718883C211yesmaximal, characteristic, complemented
9C2×#11718618C211yesmaximal, characteristic, complemented
10C2×#11718633C211yesmaximal, characteristic, complemented
11C2×#11718871C211yesmaximal, characteristic, complemented
12C2×#11718650C211yesmaximal, characteristic, complemented
13C2×#11718637C211yesmaximal, characteristic, complemented
14C2×#11718603C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×Dic13C211yesmaximal, characteristic, complemented
16C22×C13×#123C211yesmaximal, characteristic, complemented
17C23×D4×C13C2211yescharacteristic
18C24×C4×C13C2211yescharacteristic
19C23×C22⋊D13C2211yescharacteristic
20C23×C22⋊D13C2211yescharacteristic
21C24×Dic13C2211yescharacteristic
22C23×C4×D13C2211yescharacteristic
23C2×C13×#123—28no—
24C2×C13×#123C2218yescomplemented
25C22×C13×C4⋊C4C2211yescharacteristic
26C22×C13×C4⋊C4C2211yescharacteristic
27C22×C13×C22⋊C4C2211yescharacteristic
28C22×C13×C22⋊C4C2211yescharacteristic
29C22×C13×C22⋊C4C2211yescharacteristic
30C22×C22⋊Dic13C2211yescharacteristic
31C22×C22⋊Dic13C2211yescharacteristic
32C22×C22⋊Dic13C2211yescharacteristic
33C22×C22⋊Dic13C2211yescharacteristic
34C22×C22⋊Dic13C2211yescharacteristic
35C2×#88193—28no—
36C2×#88193C2218yes—
37C2×C4×C22⋊D13—28no—
38C2×C4×C22⋊D13C2218yescomplemented
39C22×#6103C2211yescharacteristic
40C22×#6103C2211yescharacteristic
41C22×#6103C2211yescharacteristic
42C22×#6103C2211yescharacteristic
43C22×C4⋊Dic13C2211yescharacteristic
44C22×#6101C2211yescharacteristic
45C22×#6101C2211yescharacteristic
46C22×#6101C2211yescharacteristic
47C22×#6101C2211yescharacteristic
48C22×#6101C2211yescharacteristic
49C22×#6101C2211yescharacteristic
50C22×C4×Dic13C2211yescharacteristic
51C22×C4×Dic13C2211yescharacteristic
52C2×#88137—28no—
53C2×#88137C2218yescomplemented
54#11718883C2218yescomplemented
55#11718871C2218yescomplemented
56C2×#88071C2211yescharacteristic
57C2×#88071C2211yescharacteristic
58C2×#88071C2211yescharacteristic
59C2×#88071C2211yescharacteristic
60C2×#88071C2211yescharacteristic
61C2×#88071C2211yescharacteristic
62#11718654C2218yescomplemented
63#11718650C2218yescomplemented
64#11718637C2218yescomplemented
65#11718633C2218yescomplemented
66#11718620C2218yescomplemented
67#11718618C2218yescomplemented
68#11718614C2218yescomplemented
69#11718603C2218yescomplemented
70C22⋊C4×Dic13C2218yescomplemented
71C25×C13C2311yescharacteristic
72C25×C13C2311yescharacteristic
73C24×D13C2311yescharacteristic
74C22×D4×C13—24no—
75C22×D4×C13—24no—
76C22×D4×C13—42no—
77C22×D4×C13C2314yes—
78C23×C4×C13—24no—
79C23×C4×C13—24no—
80C23×C4×C13—42no—
81C23×C4×C13C2311yescharacteristic
82C23×C4×C13C2311yescharacteristic
83C23×C4×C13C2311yescharacteristic
84C23×C4×C13C2314yes—
85C23×C4×C13C2311yescharacteristic
86C23×C4×C13C2311yescharacteristic
87C22×C22⋊D13—24no—
88C22×C22⋊D13—24no—
89C22×C22⋊D13—24no—
90C22×C22⋊D13—24no—
91C22×C22⋊D13—42no—
92C22×C22⋊D13D418yes—
93C22×C22⋊D13C2314yes—
94C22×C22⋊D13C2314yes—
95C23×Dic13—24no—
96C23×Dic13—24no—
97C23×Dic13—24no—
98C23×Dic13C2311yescharacteristic
99C23×Dic13C2311yescharacteristic
100C23×Dic13C2311yescharacteristic
101C23×Dic13C2311yescharacteristic
102C23×Dic13C2311yescharacteristic
103C23×Dic13C2314yes—
104C23×Dic13C2311yescharacteristic
105C23×Dic13C2311yescharacteristic
106C22×C4×D13—24no—
107C22×C4×D13—24no—
108C22×C4×D13—42no—
109C22×C4×D13C2314yes—
110C13×#123—232no—
111C2×C13×C4⋊C4—24no—
112C2×C13×C4⋊C4—24no—
113C2×C13×C4⋊C4C2314yes—
114C2×C13×C4⋊C4C2314yes—
115C2×C13×C22⋊C4—24no—
116C2×C13×C22⋊C4—24no—
117C2×C13×C22⋊C4D418yescomplemented
118C2×C13×C22⋊C4C2314yes—
119C2×C13×C22⋊C4C2314yes—
120C2×C13×C22⋊C4C2314yes—
121C2×C22⋊Dic13—24no—
122C2×C22⋊Dic13—24no—
123C2×C22⋊Dic13—24no—
124C2×C22⋊Dic13—24no—
125C2×C22⋊Dic13—24no—
126C2×C22⋊Dic13C2314yes—
127C2×C22⋊Dic13C2314yes—
128C2×C22⋊Dic13C2314yes—
129C2×C22⋊Dic13C2314yes—
130C2×C22⋊Dic13C2314yes—
131#88193—232no—
132C4×C22⋊D13—232no—
133C2×#6103—24no—
134C2×#6103—24no—
135C2×#6103—24no—
136C2×#6103—24no—
137C2×#6103C2314yes—
138C2×#6103C2314yes—
139C2×#6103C2314yes—
140C2×#6103C2314yes—
141C2×C4⋊Dic13—24no—
142C2×C4⋊Dic13C2314yes—
143C2×#6101—24no—
144C2×#6101—24no—
145C2×#6101—24no—
146C2×#6101—24no—
147C2×#6101—42no—
148C2×#6101—42no—
149C2×#6101C2314yes—
150C2×#6101C2314yes—
151C2×#6101C2314yes—
152C2×#6101C2314yes—
153C2×#6101C2314yes—
154C2×#6101C2314yes—
155C2×C4×Dic13—24no—
156C2×C4×Dic13—24no—
157C2×C4×Dic13C2314yes—
158C2×C4×Dic13C2314yes—
159#88137—232no—
160#88071C2314yes—
161#88071C2314yes—
162#88071C2314yes—
163#88071C2314yes—
164#88071C2314yes—
165#88071C2314yes—
166C2×#2422—131nomaximal, Sylow
167C24×C13—22no—
168C24×C13—22no—
169C24×C13—22no—
170C24×C13—22no—
171C24×C13—22no—
172C24×C13—22no—
173C24×C13—22no—
174C24×C13—22no—
175C24×C13—22no—
176C24×C13—22no—
177C24×C13—22no—
178C24×C13—22no—
179C24×C13C2×D414yes—
180C24×C13C2×D414yes—
181C24×C13C2412yes—
182C24×C13C2412yes—
183C24×C13C2411yescharacteristic
184C23×D13—22no—
185C23×D13—22no—
186C23×D13—22no—
187C23×D13—22no—
188C23×D13—22no—
189C23×D13—22no—
190C23×D13C2×D414yes—
191C23×D13C2412yes—
192C2×D4×C13—28no—
193C2×D4×C13—28no—
194C2×D4×C13—44no—
195C2×D4×C13—416no—
196C22×C4×C13—22no—
197C22×C4×C13—22no—
198C22×C4×C13—22no—
199C22×C4×C13—22no—
200C22×C4×C13—22no—
201C22×C4×C13—22no—
202C22×C4×C13—28no—
203C22×C4×C13—22no—
204C22×C4×C13—22no—
205C22×C4×C13—22no—
206C22×C4×C13—22no—
207C22×C4×C13—22no—
208C22×C4×C13—22no—
209C22×C4×C13—22no—
210C22×C4×C13—28no—
211C22×C4×C13—44no—
212C22×C4×C13—416no—
213C22×C4×C13C2×D414yes—
214C22×C4×C13C2×D414yes—
215C22×C4×C13C2412yes—
216C22×C4×C13C2412yes—
217C22×C4×C13C2412yes—
218C22×C4×C13C2412yes—
219C22×C4×C13C2412yes—
220C2×C22⋊D13—28no—
221C2×C22⋊D13—28no—
222C2×C22⋊D13—232no—
223C2×C22⋊D13—28no—
224C2×C22⋊D13—28no—
225C2×C22⋊D13—44no—
226C2×C22⋊D13—416no—
227C2×C22⋊D13C2×D4116yes—
228C22×Dic13—22no—
229C22×Dic13—22no—
230C22×Dic13—22no—
231C22×Dic13—22no—
232C22×Dic13—22no—
233C22×Dic13—22no—
234C22×Dic13—22no—
235C22×Dic13—22no—
236C22×Dic13—22no—
237C22×Dic13—22no—
238C22×Dic13—22no—
239C22×Dic13—22no—
240C22×Dic13—22no—
241C22×Dic13—22no—
242C22×Dic13—22no—
243C22×Dic13—22no—
244C22×Dic13—22no—
245C22×Dic13—28no—
246C22×Dic13—28no—
247C22×Dic13—28no—
248C22×Dic13—416no—
249C22×Dic13C2×D414yes—
250C22×Dic13#4114yes—
251C22×Dic13#4114yes—
252C22×Dic13#4114yes—
253C22×Dic13C2412yes—
254C22×Dic13C2412yes—
255C22×Dic13C2412yes—
256C22×Dic13C2412yes—
257C22×Dic13C2412yes—
258C22×Dic13C2412yes—
259C22×Dic13C2412yes—
260C2×C4×D13—28no—
261C2×C4×D13—28no—
262C2×C4×D13—44no—
263C2×C4×D13—416no—
264C13×C4⋊C4—28no—
265C13×C4⋊C4—28no—
266C13×C22⋊C4—28no—
267C13×C22⋊C4—28no—
268C13×C22⋊C4C2×D4116yescomplemented
269C22⋊Dic13—28no—
270C22⋊Dic13—28no—
271C22⋊Dic13—28no—
272C22⋊Dic13—28no—
273C22⋊Dic13—28no—
274#6103—28no—
275#6103—28no—
276#6103—28no—
277#6103—28no—
278C4⋊Dic13—28no—
279#6101—28no—
280#6101—28no—
281#6101—28no—
282#6101—28no—
283#6101—44no—
284#6101—44no—
285C4×Dic13—28no—
286C4×Dic13—28no—
287C22×#123—131no—
288C22×#123D1311yescharacteristic, complemented
289C22×#121—131no—
290C22×C4×D4—131no—
291#2422—1316no—
292C2×#397—131no—
293C2×#397—131no—
294C2×#394—131no—
295C2×#394—131no—
296C2×#390—131no—
297C2×#389—131no—
298C2×#385—131no—
299C2×#385—131no—
300C2×#384—131no—
301C2×#380—131no—
302C2×C4×C22⋊C4—131no—
303C23×C13—28no—
304C23×C13—28no—
305C23×C13—28no—
306C23×C13—28no—
307C23×C13—28no—
308C23×C13—28no—
309C23×C13—22no—
310C23×C13—22no—
311C23×C13—22no—
312C23×C13—22no—
313C23×C13—22no—
314C23×C13—22no—
315C23×C13—22no—
316C23×C13—22no—
317C23×C13—22no—
318C23×C13—22no—
319C23×C13—22no—
320C23×C13—22no—
321C23×C13—44no—
322C23×C13—44no—
323C23×C13—44no—
324C23×C13—44no—
325C23×C13—44no—
326C23×C13—44no—
327C23×C13—44no—
328C23×C13—44no—
329C23×C13C22×D414yes—
330C23×C13C22×D414yes—
331C23×C13C22×D412yes—
332C23×C13C22×D412yes—
333C23×C13C2×#4112yes—
334C23×C13C2×#4112yes—
335C23×C13C2×#4112yes—
336C23×C13H(5,𝔽2)12yes—
337C23×C132−1+412yes—
338C23×C13C2511yescharacteristic
339C22×D13—28no—
340C22×D13—28no—
341C22×D13—28no—
342C22×D13—22no—
343C22×D13—22no—
344C22×D13—22no—
345C22×D13—22no—
346C22×D13—22no—
347C22×D13—22no—
348C22×D13—44no—
349C22×D13—44no—
350C22×D13—44no—
351C22×D13—44no—
352C22×D13C22×D414yes—
353D4×C13—416no—
354C2×C4×C13—28no—
355C2×C4×C13—28no—
356C2×C4×C13—22no—
357C2×C4×C13—22no—
358C2×C4×C13—22no—
359C2×C4×C13—22no—
360C2×C4×C13—22no—
361C2×C4×C13—22no—
362C2×C4×C13—22no—
363C2×C4×C13—22no—
364C2×C4×C13—22no—
365C2×C4×C13—22no—
366C2×C4×C13—22no—
367C2×C4×C13—22no—
368C2×C4×C13—22no—
369C2×C4×C13—416no—
370C2×C4×C13—44no—
371C2×C4×C13—44no—
372C2×C4×C13—44no—
373C2×C4×C13C22×D414yes—
374C2×C4×C13C22×D414yes—
375C22⋊D13—232no—
376C22⋊D13—416no—
377C2×Dic13—28no—
378C2×Dic13—22no—
379C2×Dic13—22no—
380C2×Dic13—22no—
381C2×Dic13—22no—
382C2×Dic13—22no—
383C2×Dic13—22no—
384C2×Dic13—22no—
385C2×Dic13—22no—
386C2×Dic13—22no—
387C2×Dic13—22no—
388C2×Dic13—22no—
389C2×Dic13—22no—
390C2×Dic13—22no—
391C2×Dic13—22no—
392C2×Dic13—22no—
393C2×Dic13—22no—
394C2×Dic13—22no—
395C2×Dic13—44no—
396C2×Dic13—44no—
397C2×Dic13—44no—
398C2×Dic13—44no—
399C2×Dic13—44no—
400C2×Dic13—416no—
401C2×Dic13#123116yescomplemented
402C2×Dic13C22×D414yes—
403C2×Dic13C2×#4114yes—
404C2×Dic13C2×#4114yes—
405C2×Dic13C2×#4114yes—
406C4×D13—416no—
407C23×D4—131no—
408C23×D4—131no—
409C23×D4C2×D1311yescharacteristic
410C24×C4—131no—
411C24×C4—131no—
412C24×C4C2×D1311yescharacteristic
413C2×#123—28no—
414C2×#123—138no—
415C2×#123—268no—
416C2×#123C2×D1318yescomplemented
417C2×#121—138no—
418C2×#121—268no—
419C2×C4×D4—138no—
420C2×C4×D4—268no—
421C22×C4⋊C4—131no—
422C22×C4⋊C4—131no—
423C22×C4⋊C4—131no—
424C22×C4⋊C4—131no—
425C22×C4⋊C4—131no—
426C22×C4⋊C4—131no—
427C22×C4⋊C4—131no—
428C22×C4⋊C4C2×D1311yescharacteristic
429C22×C4⋊C4C2×D1311yescharacteristic
430C22×C22⋊C4—131no—
431C22×C22⋊C4—131no—
432C22×C22⋊C4—131no—
433C22×C22⋊C4—131no—
434C22×C22⋊C4—131no—
435C22×C22⋊C4—131no—
436C22×C22⋊C4—131no—
437C22×C22⋊C4—131no—
438C22×C22⋊C4—131no—
439C22×C22⋊C4C2×D1311yescharacteristic
440C22×C22⋊C4C2×D1311yescharacteristic
441C22×C22⋊C4C2×D1311yescharacteristic
442C22×C42—131no—
443C22×C42—131no—
444#397—138no—
445#397—138no—
446#394—138no—
447#394—138no—
448#390—138no—
449#389—138no—
450#385—138no—
451#385—138no—
452#384—138no—
453#380—138no—
454C4×C22⋊C4—138no—
455C2×#95—131no—
456C2×#95—131no—
457C2×#95—131no—
458C2×#95—131no—
459C2×#95—131no—
460C2×#95—131no—
461C22×C13—24no—
462C22×C13—24no—
463C22×C13—24no—
464C22×C13—24no—
465C22×C13—24no—
466C22×C13—24no—
467C22×C13—42no—
468C22×C13—42no—
469C22×C13—416no—
470C22×C13—416no—
471C22×C13—42no—
472C22×C13—42no—
473C22×C13—42no—
474C22×C13—42no—
475C22×C13—42no—
476C22×C13—42no—
477C22×C13C2×#12314yes—
478C22×C13#53214yes—
479C22×C13#54214yes—
480C22×C13D4214yes—
481C22×C13#54714yes—
482C22×C13#54714yes—
483C22×C13#55314yes—
484C22×C13C23×D411yescharacteristic
485C22×C13C23×D411yescharacteristic
486C22×C13C22×#4111yescharacteristic
487C22×C13C22×#4111yescharacteristic
488C22×C13C22×#4111yescharacteristic
489C22×C13C2×H(5,𝔽2)11yescharacteristic
490C22×C13C2×2−1+411yescharacteristic
491C2×D13—24no—
492C2×D13—24no—
493C2×D13—24no—
494C2×D13—42no—
495C2×D13—416no—
496C2×D13—42no—
497C2×D13—42no—
498C2×D13—42no—
499C4×C13—24no—
500C4×C13—24no—
501C4×C13—42no—
502C4×C13—42no—
503C4×C13—42no—
504Dic13—24no—
505Dic13—42no—
506Dic13—42no—
507Dic13—42no—
508Dic13—42no—
509Dic13—42no—
510Dic13C2×#12318yescomplemented
511C25—131no—
512C25C22×D1311yescharacteristic
513C25C22×D1311yescharacteristic
514C22×D4—24no—
515C22×D4—24no—
516C22×D4—42no—
517C22×D4—138no—
518C22×D4—134no—
519C22×D4—134no—
520C22×D4—264no—
521C22×D4—264no—
522C22×D4—264no—
523C22×D4—264no—
524C22×D4—522no—
525C22×D4C22×D1314yes—
526C23×C4—24no—
527C23×C4—24no—
528C23×C4—42no—
529C23×C4—131no—
530C23×C4—131no—
531C23×C4—134no—
532C23×C4—131no—
533C23×C4—131no—
534C23×C4—131no—
535C23×C4—131no—
536C23×C4—131no—
537C23×C4—134no—
538C23×C4—264no—
539C23×C4—264no—
540C23×C4—264no—
541C23×C4—264no—
542C23×C4—264no—
543C23×C4—522no—
544C23×C4C22×D1311yescharacteristic
545C23×C4C22×D1311yescharacteristic
546C23×C4C22×D1311yescharacteristic
547C23×C4C22×D1314yes—
548C23×C4C22×D1311yescharacteristic
549C23×C4C22×D1311yescharacteristic
550#123—232no—
551#123—2632no—
552#121—2632no—
553C4×D4—2632no—
554C2×C4⋊C4—24no—
555C2×C4⋊C4—24no—
556C2×C4⋊C4—134no—
557C2×C4⋊C4—134no—
558C2×C4⋊C4—134no—
559C2×C4⋊C4—134no—
560C2×C4⋊C4—134no—
561C2×C4⋊C4—134no—
562C2×C4⋊C4—134no—
563C2×C4⋊C4—264no—
564C2×C4⋊C4—264no—
565C2×C4⋊C4—264no—
566C2×C4⋊C4—264no—
567C2×C4⋊C4—264no—
568C2×C4⋊C4—522no—
569C2×C4⋊C4—522no—
570C2×C4⋊C4C22×D1314yes—
571C2×C4⋊C4C22×D1314yes—
572C2×C22⋊C4—24no—
573C2×C22⋊C4—24no—
574C2×C22⋊C4—134no—
575C2×C22⋊C4—134no—
576C2×C22⋊C4—134no—
577C2×C22⋊C4—134no—
578C2×C22⋊C4—134no—
579C2×C22⋊C4—134no—
580C2×C22⋊C4—134no—
581C2×C22⋊C4—134no—
582C2×C22⋊C4—134no—
583C2×C22⋊C4—264no—
584C2×C22⋊C4—264no—
585C2×C22⋊C4—264no—
586C2×C22⋊C4—264no—
587C2×C22⋊C4—264no—
588C2×C22⋊C4—264no—
589C2×C22⋊C4—264no—
590C2×C22⋊C4—264no—
591C2×C22⋊C4—264no—
592C2×C22⋊C4C22⋊D1318yescomplemented
593C2×C22⋊C4C22×D1314yes—
594C2×C22⋊C4C22×D1314yes—
595C2×C22⋊C4C22×D1314yes—
596C2×C42—134no—
597C2×C42—134no—
598C2×C42—264no—
599C2×C42—264no—
600#95—134no—
601#95—134no—
602#95—134no—
603#95—134no—
604#95—134no—
605#95—134no—
606C2×C13—44no—
607C2×C13—44no—
608C2×C13#242218yescomplemented
609C2×C13C22×#12311yescharacteristic
610C2×C13C2×#53211yescharacteristic
611C2×C13C2×#54211yescharacteristic
612C2×C13C2×D4211yescharacteristic
613C2×C13C2×#54711yescharacteristic
614C2×C13C2×#54711yescharacteristic
615C2×C13C2×#55311yescharacteristic
616D13—44no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—22no—
627C24—22no—
628C24—22no—
629C24—134no—
630C24—132no—
631C24—262no—
632C24—262no—
633C24—262no—
634C24—262no—
635C24—262no—
636C24—262no—
637C24D4×D1314yes—
638C24C2×C22⋊D1314yes—
639C24C23×D1312yes—
640C24C23×D1312yes—
641C24C23×D1311yescharacteristic
642C2×D4—28no—
643C2×D4—28no—
644C2×D4—44no—
645C2×D4—416no—
646C2×D4—1316no—
647C2×D4—2632no—
648C2×D4—268no—
649C2×D4—268no—
650C2×D4—268no—
651C2×D4—268no—
652C2×D4—524no—
653C2×D4—5216no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—28no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—28no—
669C22×C4—44no—
670C22×C4—416no—
671C22×C4—134no—
672C22×C4—134no—
673C22×C4—134no—
674C22×C4—132no—
675C22×C4—134no—
676C22×C4—132no—
677C22×C4—132no—
678C22×C4—132no—
679C22×C4—132no—
680C22×C4—132no—
681C22×C4—132no—
682C22×C4—268no—
683C22×C4—268no—
684C22×C4—268no—
685C22×C4—268no—
686C22×C4—262no—
687C22×C4—262no—
688C22×C4—262no—
689C22×C4—262no—
690C22×C4—262no—
691C22×C4—262no—
692C22×C4—262no—
693C22×C4—262no—
694C22×C4—262no—
695C22×C4—262no—
696C22×C4—262no—
697C22×C4—262no—
698C22×C4—262no—
699C22×C4—262no—
700C22×C4—262no—
701C22×C4—262no—
702C22×C4—262no—
703C22×C4—268no—
704C22×C4—524no—
705C22×C4—5216no—
706C22×C4—5216no—
707C22×C4C2×C22⋊D1314yes—
708C22×C4C2×C22⋊D1314yes—
709C22×C4C23×D1312yes—
710C22×C4C23×D1312yes—
711C22×C4C23×D1312yes—
712C22×C4C23×D1312yes—
713C22×C4C23×D1312yes—
714C4⋊C4—28no—
715C4⋊C4—28no—
716C4⋊C4—268no—
717C4⋊C4—268no—
718C4⋊C4—268no—
719C4⋊C4—268no—
720C4⋊C4—268no—
721C4⋊C4—524no—
722C4⋊C4—524no—
723C22⋊C4—28no—
724C22⋊C4—28no—
725C22⋊C4—268no—
726C22⋊C4—268no—
727C22⋊C4—268no—
728C22⋊C4—268no—
729C22⋊C4—268no—
730C22⋊C4—268no—
731C22⋊C4—268no—
732C22⋊C4—268no—
733C22⋊C4—268no—
734C22⋊C4C2×C22⋊D13116yescomplemented
735C42—268no—
736C42—268no—
737C13C2×#242211yescharacteristic, complemented, Sylow
738C23—28no—
739C23—28no—
740C23—28no—
741C23—28no—
742C23—28no—
743C23—28no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—44no—
757C23—44no—
758C23—44no—
759C23—44no—
760C23—44no—
761C23—44no—
762C23—44no—
763C23—44no—
764C23—134no—
765C23—268no—
766C23—268no—
767C23—268no—
768C23—262no—
769C23—262no—
770C23—262no—
771C23—262no—
772C23—262no—
773C23—262no—
774C23—524no—
775C23—524no—
776C23—524no—
777C23—524no—
778C23C2×D4×D1314yes—
779C23C2×D4×D1312yes—
780C23#8825112yes—
781C23#41×D1312yes—
782C23#41×D1312yes—
783C23#41×D1312yes—
784C23#8825712yes—
785C23C22×C22⋊D1314yes—
786C23C22×C22⋊D1312yes—
787C23C24×D1311yescharacteristic
788D4—416no—
789D4—2632no—
790D4—5216no—
791C2×C4—28no—
792C2×C4—28no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—416no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—44no—
810C2×C4—1316no—
811C2×C4—134no—
812C2×C4—134no—
813C2×C4—134no—
814C2×C4—134no—
815C2×C4—268no—
816C2×C4—262no—
817C2×C4—262no—
818C2×C4—262no—
819C2×C4—262no—
820C2×C4—262no—
821C2×C4—262no—
822C2×C4—262no—
823C2×C4—262no—
824C2×C4—262no—
825C2×C4—262no—
826C2×C4—262no—
827C2×C4—262no—
828C2×C4—262no—
829C2×C4—262no—
830C2×C4—262no—
831C2×C4—262no—
832C2×C4—262no—
833C2×C4—5216no—
834C2×C4—5216no—
835C2×C4—524no—
836C2×C4—524no—
837C2×C4—524no—
838C2×C4—524no—
839C2×C4—524no—
840C2×C4C22×C22⋊D1314yes—
841C2×C4C22×C22⋊D1314yes—
842C22—24no—
843C22—24no—
844C22—24no—
845C22—24no—
846C22—24no—
847C22—24no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—416no—
854C22—416no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—264no—
859C22—264no—
860C22—264no—
861C22—522no—
862C22—522no—
863C22—5216no—
864C22—522no—
865C22—522no—
866C22D13×#12314yes—
867C22#1171936014yes—
868C22#1171936614yes—
869C22#1171936714yes—
870C22D4×C22⋊D1314yes—
871C22#1171952914yes—
872C22#1171953714yes—
873C22C22×D4×D1311yescharacteristic
874C22C2×#8825111yescharacteristic
875C22C2×#41×D1311yescharacteristic
876C22C2×#41×D1311yescharacteristic
877C22C2×#41×D1311yescharacteristic
878C22C2×#8825711yescharacteristic
879C22C23×C22⋊D1311yescharacteristic
880C4—24no—
881C4—24no—
882C4—42no—
883C4—42no—
884C4—42no—
885C4—138no—
886C4—264no—
887C4—522no—
888C4—522no—
889C4—522no—
890C4—522no—
891C4—522no—
892C2—44no—
893C2—44no—
894C2—524no—
895C2#1311834718yesdirect product factor
896C2C2×D13×#12311yescharacteristic
897C2C2×#1171953711yescharacteristic
898C2C2×#1171936711yescharacteristic
899C2C2×D4×C22⋊D1311yescharacteristic
900C2C2×#1171936011yescharacteristic
901C2C2×#1171952911yescharacteristic
902C2C2×#1171936611yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC22×C13×#123C2
socleC24×C13C24
prime radicalC22×#88193C2
hypercenterC22×#123D13
hypocenterC13C2×#2422
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. C22×#88137C2semidirect
3. C22×C4×C22⋊D13C2semidirect
4. #13118347C2direct (N × H)
5. C2×#11718654C2semidirect
6. C2×#11718614C2semidirect
7. C2×#11718620C2semidirect
8. C2×#11718883C2semidirect
9. C2×#11718618C2semidirect
10. C2×#11718633C2semidirect
11. C2×#11718871C2semidirect
12. C2×#11718650C2semidirect
13. C2×#11718637C2semidirect
14. C2×#11718603C2semidirect
15. C2×C22⋊C4×Dic13C2semidirect
16. C22×C13×#123C2semidirect
24. C2×C13×#123C22semidirect
38. C2×C4×C22⋊D13C22semidirect
53. C2×#88137C22semidirect
54. #11718883C22semidirect
55. #11718871C22semidirect
62. #11718654C22semidirect
63. #11718650C22semidirect
64. #11718637C22semidirect
65. #11718633C22semidirect
66. #11718620C22semidirect
67. #11718618C22semidirect
68. #11718614C22semidirect
69. #11718603C22semidirect
70. C22⋊C4×Dic13C22semidirect
117. C2×C13×C22⋊C4D4semidirect
268. C13×C22⋊C4C2×D4semidirect
288. C22×#123D13semidirect
401. C2×Dic13#123semidirect
416. C2×#123C2×D13semidirect
510. Dic13C2×#123semidirect
592. C2×C22⋊C4C22⋊D13semidirect
608. C2×C13#2422semidirect
734. C22⋊C4C2×C22⋊D13semidirect
737. C13C2×#2422semidirect
895. C2#13118347direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881372
C22×#881932
C22×C4×C22⋊D132
#131183472
C2×#117186542
C2×#117186142
C2×#117186202
C2×#117188832
C2×#117186182
C2×#117186332
C2×#117188712
C2×#117186502
C2×#117186372
C2×#117186032
C2×C22⋊C4×Dic132
C22×C13×#1232
C2×#242213