Finite Group Databasebeta

← C2×#13118567 #16030367

Subgroups — C2×#13118567 #16030367

Order 3328.

4002 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88189C211yesmaximal, characteristic, complemented
2C22×D4×Dic13C211yesmaximal, characteristic, complemented
3C23×#6101C211yesmaximal, characteristic, complemented
4#13118567C2116yesmaximal, direct product factor
5C2×#11718610C211yesmaximal, characteristic, complemented
6C2×#11718644C211yesmaximal, characteristic, complemented
7C2×#11718613C211yesmaximal, characteristic, complemented
8C2×#11718883C211yesmaximal, characteristic, complemented
9C2×#11718605C211yesmaximal, characteristic, complemented
10C2×#11718639C211yesmaximal, characteristic, complemented
11C2×#11718881C211yesmaximal, characteristic, complemented
12C2×#11718881C211yesmaximal, characteristic, complemented
13C2×#11718881C211yesmaximal, characteristic, complemented
14C2×#11718871C211yesmaximal, characteristic, complemented
15C2×#11718607C211yesmaximal, characteristic, complemented
16C22×C13×#121C211yesmaximal, characteristic
17C23×D4×C13C2211yescharacteristic
18C23×D4×C13C2211yescharacteristic
19C23×D4×C13C2211yescharacteristic
20C24×C4×C13C2211yescharacteristic
21C24×Dic13C2211yescharacteristic
22C24×Dic13C2211yescharacteristic
23C24×Dic13C2211yescharacteristic
24C2×C13×#121—28no—
25C2×C13×#121C2218yes—
26C22×C13×C4⋊C4C2211yescharacteristic
27C22×C13×C22⋊C4C2211yescharacteristic
28C22×C13×C22⋊C4C2211yescharacteristic
29C22×C22⋊Dic13C2211yescharacteristic
30C22×C22⋊Dic13C2211yescharacteristic
31C22×C22⋊Dic13C2211yescharacteristic
32C22×C22⋊Dic13C2211yescharacteristic
33C22×C22⋊Dic13C2211yescharacteristic
34C22×C22⋊Dic13C2211yescharacteristic
35C22×C22⋊Dic13C2211yescharacteristic
36C22×C22⋊Dic13C2211yescharacteristic
37C22×C22⋊Dic13C2211yescharacteristic
38C2×#88189—28no—
39C2×#88189C2218yescomplemented
40C2×D4×Dic13—28no—
41C2×D4×Dic13C2218yescomplemented
42C22×C4⋊Dic13C2211yescharacteristic
43C22×#6101—28no—
44C22×#6101C2211yescharacteristic
45C22×#6101C2211yescharacteristic
46C22×#6101C2211yescharacteristic
47C22×#6101C2211yescharacteristic
48C22×#6101C2211yescharacteristic
49C22×#6101C2211yescharacteristic
50C22×#6101C2218yescomplemented
51C22×C4×Dic13C2211yescharacteristic
52#11718883C2218yescomplemented
53#11718881C2218yescomplemented
54#11718881C2218yescomplemented
55#11718881C2218yescomplemented
56#11718871C2218yescomplemented
57C2×#88071C2211yescharacteristic
58C2×#88071C2211yescharacteristic
59C2×#88071C2211yescharacteristic
60C2×#88071C2211yescharacteristic
61C2×#88071C2211yescharacteristic
62C2×#88071C2211yescharacteristic
63C2×#88071C2211yescharacteristic
64C2×#88071C2211yescharacteristic
65#11718644C2218yescomplemented
66#11718639C2218yescomplemented
67#11718613C2218yescomplemented
68#11718610C2218yescomplemented
69#11718607C2218yescomplemented
70#11718605C2218yescomplemented
71C25×C13C2311yescharacteristic
72C25×C13C2311yescharacteristic
73C25×C13C2311yescharacteristic
74C22×D4×C13—24no—
75C22×D4×C13—24no—
76C22×D4×C13—24no—
77C22×D4×C13—24no—
78C22×D4×C13—24no—
79C22×D4×C13—24no—
80C22×D4×C13—24no—
81C22×D4×C13—42no—
82C22×D4×C13D418yes—
83C22×D4×C13C2314yes—
84C22×D4×C13C2314yes—
85C22×D4×C13C2314yes—
86C23×C4×C13—24no—
87C23×C4×C13—24no—
88C23×C4×C13—42no—
89C23×C4×C13C2311yescharacteristic
90C23×C4×C13C2311yescharacteristic
91C23×C4×C13C2314yes—
92C23×C4×C13C2311yescharacteristic
93C23×C4×C13C2311yescharacteristic
94C23×Dic13—24no—
95C23×Dic13—24no—
96C23×Dic13—24no—
97C23×Dic13—24no—
98C23×Dic13—24no—
99C23×Dic13—24no—
100C23×Dic13—24no—
101C23×Dic13—42no—
102C23×Dic13—42no—
103C23×Dic13C2311yescharacteristic
104C23×Dic13C2311yescharacteristic
105C23×Dic13C2311yescharacteristic
106C23×Dic13C2311yescharacteristic
107C23×Dic13C2311yescharacteristic
108C23×Dic13C2314yes—
109C23×Dic13C2314yes—
110C23×Dic13C2314yes—
111C23×Dic13C2311yescharacteristic
112C23×Dic13C2311yescharacteristic
113C23×Dic13C2311yescharacteristic
114C13×#121—232no—
115C2×C13×C4⋊C4—24no—
116C2×C13×C4⋊C4C2314yes—
117C2×C13×C22⋊C4—24no—
118C2×C13×C22⋊C4—24no—
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⋊Dic13—24no—
127C2×C22⋊Dic13—24no—
128C2×C22⋊Dic13—24no—
129C2×C22⋊Dic13—42no—
130C2×C22⋊Dic13C2314yes—
131C2×C22⋊Dic13C2314yes—
132C2×C22⋊Dic13C2314yes—
133C2×C22⋊Dic13C2314yes—
134C2×C22⋊Dic13C2314yes—
135C2×C22⋊Dic13C2314yes—
136C2×C22⋊Dic13C2314yes—
137C2×C22⋊Dic13C2314yes—
138C2×C22⋊Dic13C2314yes—
139#88189—232no—
140D4×Dic13—232no—
141C2×C4⋊Dic13—24no—
142C2×C4⋊Dic13C2314yes—
143C2×#6101—24no—
144C2×#6101—24no—
145C2×#6101—24no—
146C2×#6101—24no—
147C2×#6101—232no—
148C2×#6101—42no—
149C2×#6101D418yescomplemented
150C2×#6101C2314yes—
151C2×#6101C2314yes—
152C2×#6101C2314yes—
153C2×#6101C2314yes—
154C2×#6101C2314yes—
155C2×#6101C2314yes—
156C2×C4×Dic13—24no—
157C2×C4×Dic13C2314yes—
158#88071C2314yes—
159#88071C2314yes—
160#88071C2314yes—
161#88071C2314yes—
162#88071C2314yes—
163#88071C2314yes—
164#88071C2314yes—
165#88071C2314yes—
166C2×#2443—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×C13—22no—
180C24×C13—22no—
181C24×C13—22no—
182C24×C13—22no—
183C24×C13—22no—
184C24×C13C2×D414yes—
185C24×C13C2×D414yes—
186C24×C13#4114yes—
187C24×C13#4114yes—
188C24×C13C2412yes—
189C24×C13C2412yes—
190C24×C13C2412yes—
191C24×C13C2411yescharacteristic
192C2×D4×C13—232no—
193C2×D4×C13—28no—
194C2×D4×C13—28no—
195C2×D4×C13—28no—
196C2×D4×C13—28no—
197C2×D4×C13—28no—
198C2×D4×C13—28no—
199C2×D4×C13—28no—
200C2×D4×C13—44no—
201C2×D4×C13—416no—
202C2×D4×C13—416no—
203C2×D4×C13C2×D4116yes—
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—22no—
211C22×C4×C13—28no—
212C22×C4×C13—22no—
213C22×C4×C13—22no—
214C22×C4×C13—22no—
215C22×C4×C13—28no—
216C22×C4×C13—44no—
217C22×C4×C13—416no—
218C22×C4×C13C2×D414yes—
219C22×C4×C13C2×D414yes—
220C22×C4×C13C2412yes—
221C22×C4×C13C2412yes—
222C22×C4×C13C2412yes—
223C22×C4×C13C2412yes—
224C22×Dic13—232no—
225C22×Dic13—22no—
226C22×Dic13—22no—
227C22×Dic13—28no—
228C22×Dic13—22no—
229C22×Dic13—22no—
230C22×Dic13—22no—
231C22×Dic13—22no—
232C22×Dic13—28no—
233C22×Dic13—28no—
234C22×Dic13—22no—
235C22×Dic13—22no—
236C22×Dic13—22no—
237C22×Dic13—22no—
238C22×Dic13—22no—
239C22×Dic13—22no—
240C22×Dic13—28no—
241C22×Dic13—28no—
242C22×Dic13—22no—
243C22×Dic13—22no—
244C22×Dic13—22no—
245C22×Dic13—22no—
246C22×Dic13—22no—
247C22×Dic13—22no—
248C22×Dic13—22no—
249C22×Dic13—22no—
250C22×Dic13—22no—
251C22×Dic13—28no—
252C22×Dic13—28no—
253C22×Dic13—44no—
254C22×Dic13—44no—
255C22×Dic13—416no—
256C22×Dic13—416no—
257C22×Dic13C2×D414yes—
258C22×Dic13C2×D414yes—
259C22×Dic13#4114yes—
260C22×Dic13C2412yes—
261C22×Dic13C2412yes—
262C22×Dic13C2412yes—
263C22×Dic13C2412yes—
264C22×Dic13C2412yes—
265C22×Dic13C2412yes—
266C22×Dic13C2412yes—
267C22×Dic13C2412yes—
268C13×C4⋊C4—28no—
269C13×C22⋊C4—28no—
270C13×C22⋊C4—28no—
271C22⋊Dic13—28no—
272C22⋊Dic13—28no—
273C22⋊Dic13—28no—
274C22⋊Dic13—28no—
275C22⋊Dic13—28no—
276C22⋊Dic13—28no—
277C22⋊Dic13—28no—
278C22⋊Dic13—28no—
279C22⋊Dic13—44no—
280C4⋊Dic13—28no—
281#6101—28no—
282#6101—28no—
283#6101—28no—
284#6101—28no—
285#6101—44no—
286#6101C2×D4116yescomplemented
287C4×Dic13—28no—
288C22×#123—131no—
289C22×#121D1311yescharacteristic
290C22×C4×D4—131no—
291C23×C4⋊C4—131no—
292#2443—1316no—
293C2×#399—131no—
294C2×#398—131no—
295C2×#397—131no—
296C2×#394—131no—
297C2×#388—131no—
298C2×#387—131no—
299C2×#386—131no—
300C2×#386—131no—
301C2×#386—131no—
302C2×#385—131no—
303C2×#385—131no—
304C23×C13—28no—
305C23×C13—28no—
306C23×C13—28no—
307C23×C13—28no—
308C23×C13—28no—
309C23×C13—28no—
310C23×C13—22no—
311C23×C13—22no—
312C23×C13—22no—
313C23×C13—22no—
314C23×C13—28no—
315C23×C13—28no—
316C23×C13—28no—
317C23×C13—22no—
318C23×C13—22no—
319C23×C13—22no—
320C23×C13—22no—
321C23×C13—22no—
322C23×C13—22no—
323C23×C13—22no—
324C23×C13—22no—
325C23×C13—22no—
326C23×C13—22no—
327C23×C13—22no—
328C23×C13—22no—
329C23×C13—22no—
330C23×C13—44no—
331C23×C13—44no—
332C23×C13—44no—
333C23×C13—44no—
334C23×C13—44no—
335C23×C13—44no—
336C23×C13—44no—
337C23×C13—44no—
338C23×C13—44no—
339C23×C13—44no—
340C23×C13—44no—
341C23×C13#123116yescomplemented
342C23×C13C22×D414yes—
343C23×C13C22×D414yes—
344C23×C13C22×D412yes—
345C23×C13C22×D412yes—
346C23×C13C2×#4114yes—
347C23×C13C2×#4114yes—
348C23×C13C2×#4112yes—
349C23×C13C2×#4112yes—
350C23×C13C2×#4112yes—
351C23×C13H(5,𝔽2)12yes—
352C23×C132−1+412yes—
353C23×C13C2511yescharacteristic
354D4×C13—232no—
355D4×C13—416no—
356D4×C13—416no—
357C2×C4×C13—28no—
358C2×C4×C13—28no—
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×C13C22×D414yes—
373C2×C4×C13C22×D414yes—
374C2×Dic13—232no—
375C2×Dic13—28no—
376C2×Dic13—28no—
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—22no—
396C2×Dic13—22no—
397C2×Dic13—22no—
398C2×Dic13—22no—
399C2×Dic13—416no—
400C2×Dic13—416no—
401C2×Dic13—44no—
402C2×Dic13—44no—
403C2×Dic13—44no—
404C2×Dic13—44no—
405C2×Dic13—44no—
406C2×Dic13C22×D414yes—
407C2×Dic13C22×D414yes—
408C2×Dic13C2×#4114yes—
409C23×D4C2×D1311yescharacteristic
410C23×D4C2×D1311yescharacteristic
411C23×D4C2×D1311yescharacteristic
412C24×C4—131no—
413C24×C4—131no—
414C24×C4—131no—
415C24×C4C2×D1311yescharacteristic
416C2×#123—138no—
417C2×#123—268no—
418C2×#121—28no—
419C2×#121C2×D1318yes—
420C2×C4×D4—138no—
421C2×C4×D4—268no—
422C22×C4⋊C4—131no—
423C22×C4⋊C4—131no—
424C22×C4⋊C4—131no—
425C22×C4⋊C4—131no—
426C22×C4⋊C4—131no—
427C22×C4⋊C4—138no—
428C22×C4⋊C4—131no—
429C22×C4⋊C4—131no—
430C22×C4⋊C4—268no—
431C22×C4⋊C4C2×D1311yescharacteristic
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⋊C4—131no—
440C22×C22⋊C4—131no—
441C22×C22⋊C4C2×D1311yescharacteristic
442C22×C22⋊C4C2×D1311yescharacteristic
443C22×C42—131no—
444#399—138no—
445#398—138no—
446#397—138no—
447#394—138no—
448#388—138no—
449#387—138no—
450#386—138no—
451#386—138no—
452#386—138no—
453#385—138no—
454#385—138no—
455C2×#95—131no—
456C2×#95—131no—
457C2×#95—131no—
458C2×#95—131no—
459C2×#95—131no—
460C2×#95—131no—
461C2×#95—131no—
462C2×#95—131no—
463C22×C13—24no—
464C22×C13—24no—
465C22×C13—24no—
466C22×C13—24no—
467C22×C13—24no—
468C22×C13—232no—
469C22×C13—24no—
470C22×C13—24no—
471C22×C13—24no—
472C22×C13—24no—
473C22×C13—42no—
474C22×C13—42no—
475C22×C13—42no—
476C22×C13—416no—
477C22×C13—42no—
478C22×C13—42no—
479C22×C13—42no—
480C22×C13—42no—
481C22×C13—42no—
482C22×C13—42no—
483C22×C13—42no—
484C22×C13—42no—
485C22×C13—88no—
486C22×C13C2×#12314yes—
487C22×C13C2×#12318yescomplemented
488C22×C13#52514yes—
489C22×C13#53914yes—
490C22×C13D4214yes—
491C22×C13#54714yes—
492C22×C13#54814yes—
493C22×C13#55314yes—
494C22×C13C23×D411yescharacteristic
495C22×C13C23×D411yescharacteristic
496C22×C13C22×#4111yescharacteristic
497C22×C13C22×#4111yescharacteristic
498C22×C13C22×#4111yescharacteristic
499C22×C13C2×H(5,𝔽2)11yescharacteristic
500C22×C13C2×2−1+411yescharacteristic
501C4×C13—24no—
502C4×C13—24no—
503C4×C13—42no—
504C4×C13—42no—
505Dic13—24no—
506Dic13—24no—
507Dic13—24no—
508Dic13—42no—
509Dic13—42no—
510Dic13—42no—
511Dic13—42no—
512Dic13—42no—
513C25C22×D1311yescharacteristic
514C25C22×D1311yescharacteristic
515C25C22×D1311yescharacteristic
516C22×D4—24no—
517C22×D4—24no—
518C22×D4—24no—
519C22×D4—24no—
520C22×D4—24no—
521C22×D4—24no—
522C22×D4—24no—
523C22×D4—42no—
524C22×D4C22⋊D1318yes—
525C22×D4C22×D1314yes—
526C22×D4C22×D1314yes—
527C22×D4C22×D1314yes—
528C23×C4—24no—
529C23×C4—24no—
530C23×C4—42no—
531C23×C4—131no—
532C23×C4—131no—
533C23×C4—131no—
534C23×C4—134no—
535C23×C4—131no—
536C23×C4—131no—
537C23×C4—131no—
538C23×C4—131no—
539C23×C4—131no—
540C23×C4—134no—
541C23×C4—134no—
542C23×C4—264no—
543C23×C4—264no—
544C23×C4—264no—
545C23×C4—264no—
546C23×C4—264no—
547C23×C4—264no—
548C23×C4—264no—
549C23×C4—522no—
550C23×C4—522no—
551C23×C4C22×D1311yescharacteristic
552C23×C4C22×D1311yescharacteristic
553C23×C4C22×D1314yes—
554C23×C4C22×D1311yescharacteristic
555C23×C4C22×D1311yescharacteristic
556#123—2632no—
557#121—232no—
558C4×D4—2632no—
559C2×C4⋊C4—24no—
560C2×C4⋊C4—138no—
561C2×C4⋊C4—134no—
562C2×C4⋊C4—134no—
563C2×C4⋊C4—134no—
564C2×C4⋊C4—134no—
565C2×C4⋊C4—134no—
566C2×C4⋊C4—134no—
567C2×C4⋊C4—134no—
568C2×C4⋊C4—2632no—
569C2×C4⋊C4—264no—
570C2×C4⋊C4—264no—
571C2×C4⋊C4—264no—
572C2×C4⋊C4—264no—
573C2×C4⋊C4—264no—
574C2×C4⋊C4—522no—
575C2×C4⋊C4C22×D1314yes—
576C2×C22⋊C4—24no—
577C2×C22⋊C4—24no—
578C2×C22⋊C4—134no—
579C2×C22⋊C4—134no—
580C2×C22⋊C4—134no—
581C2×C22⋊C4—134no—
582C2×C22⋊C4—134no—
583C2×C22⋊C4—134no—
584C2×C22⋊C4—134no—
585C2×C22⋊C4—134no—
586C2×C22⋊C4—134no—
587C2×C22⋊C4—264no—
588C2×C22⋊C4—264no—
589C2×C22⋊C4—264no—
590C2×C22⋊C4—264no—
591C2×C22⋊C4—264no—
592C2×C22⋊C4—264no—
593C2×C22⋊C4—264no—
594C2×C22⋊C4—264no—
595C2×C22⋊C4—522no—
596C2×C22⋊C4C22×D1314yes—
597C2×C22⋊C4C22×D1314yes—
598C2×C42—134no—
599C2×C42—264no—
600#95—134no—
601#95—134no—
602#95—134no—
603#95—134no—
604#95—134no—
605#95—134no—
606#95—134no—
607#95—134no—
608C2×C13—28no—
609C2×C13—44no—
610C2×C13—82no—
611C2×C13#244318yescomplemented
612C2×C13C22×#12311yescharacteristic
613C2×C13C2×#52511yescharacteristic
614C2×C13C2×#53911yescharacteristic
615C2×C13C2×D4211yescharacteristic
616C2×C13C2×#54711yescharacteristic
617C2×C13C2×#54811yescharacteristic
618C2×C13C2×#55311yescharacteristic
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—22no—
627C24—22no—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—22no—
632C24—22no—
633C24—22no—
634C24—22no—
635C24—22no—
636C24#612914yes—
637C24#612914yes—
638C24C2×C22⋊D1314yes—
639C24C2×C22⋊D1314yes—
640C24C23×D1312yes—
641C24C23×D1312yes—
642C24C23×D1312yes—
643C24C23×D1311yescharacteristic
644C2×D4—232no—
645C2×D4—28no—
646C2×D4—28no—
647C2×D4—28no—
648C2×D4—28no—
649C2×D4—28no—
650C2×D4—28no—
651C2×D4—28no—
652C2×D4—44no—
653C2×D4—416no—
654C2×D4—416no—
655C2×D4C2×C22⋊D13116yes—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—28no—
667C22×C4—28no—
668C22×C4—44no—
669C22×C4—416no—
670C22×C4—134no—
671C22×C4—134no—
672C22×C4—134no—
673C22×C4—132no—
674C22×C4—132no—
675C22×C4—132no—
676C22×C4—132no—
677C22×C4—132no—
678C22×C4—132no—
679C22×C4—132no—
680C22×C4—132no—
681C22×C4—268no—
682C22×C4—268no—
683C22×C4—268no—
684C22×C4—268no—
685C22×C4—2632no—
686C22×C4—262no—
687C22×C4—268no—
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—262no—
704C22×C4—262no—
705C22×C4—262no—
706C22×C4—262no—
707C22×C4—262no—
708C22×C4—268no—
709C22×C4—268no—
710C22×C4—524no—
711C22×C4—524no—
712C22×C4—5216no—
713C22×C4—5216no—
714C22×C4D4×D1314yes—
715C22×C4C2×C22⋊D1314yes—
716C22×C4C23×D1312yes—
717C22×C4C23×D1312yes—
718C22×C4C23×D1312yes—
719C22×C4C23×D1312yes—
720C4⋊C4—28no—
721C4⋊C4—1316no—
722C4⋊C4—268no—
723C4⋊C4—268no—
724C4⋊C4—268no—
725C4⋊C4—268no—
726C4⋊C4—268no—
727C4⋊C4—524no—
728C22⋊C4—28no—
729C22⋊C4—28no—
730C22⋊C4—268no—
731C22⋊C4—268no—
732C22⋊C4—268no—
733C22⋊C4—268no—
734C22⋊C4—268no—
735C22⋊C4—268no—
736C22⋊C4—268no—
737C22⋊C4—268no—
738C22⋊C4—524no—
739C42—268no—
740C13C2×#244311yescharacteristic, complemented, Sylow
741C23—28no—
742C23—28no—
743C23—28no—
744C23—28no—
745C23—28no—
746C23—28no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—28no—
752C23—28no—
753C23—28no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—44no—
768C23—44no—
769C23—44no—
770C23—44no—
771C23—44no—
772C23—44no—
773C23—44no—
774C23—44no—
775C23—44no—
776C23—44no—
777C23—44no—
778C23#88189116yescomplemented
779C23C2×D4×D1312yes—
780C23C2×#612914yes—
781C23C2×#612914yes—
782C23C2×#612912yes—
783C23C2×#612912yes—
784C23#8825112yes—
785C23#41×D1312yes—
786C23#8825712yes—
787C23C22×C22⋊D1314yes—
788C23C22×C22⋊D1314yes—
789C23C22×C22⋊D1312yes—
790C23C24×D1311yescharacteristic
791D4—232no—
792D4—416no—
793D4—416no—
794C2×C4—28no—
795C2×C4—28no—
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—134no—
810C2×C4—134no—
811C2×C4—134no—
812C2×C4—2632no—
813C2×C4—268no—
814C2×C4—268no—
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—262no—
834C2×C4—262no—
835C2×C4—262no—
836C2×C4—262no—
837C2×C4—5216no—
838C2×C4—5216no—
839C2×C4—524no—
840C2×C4—524no—
841C2×C4—524no—
842C2×C4—524no—
843C2×C4—524no—
844C2×C4C2×D4×D1314yes—
845C2×C4C22×C22⋊D1314yes—
846C22—24no—
847C22—24no—
848C22—232no—
849C22—24no—
850C22—24no—
851C22—24no—
852C22—24no—
853C22—24no—
854C22—24no—
855C22—24no—
856C22—416no—
857C22—42no—
858C22—42no—
859C22—42no—
860C22—42no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22—42no—
866C22—42no—
867C22—42no—
868C22—88no—
869C22#1171930314yes—
870C22#1171930614yes—
871C22#1171930714yes—
872C22#1171931114yes—
873C22C2×#8818914yes—
874C22C2×#8818918yescomplemented
875C22D4×C22⋊D1314yes—
876C22#1171952914yes—
877C22C22×D4×D1311yescharacteristic
878C22C22×#612911yescharacteristic
879C22C22×#612911yescharacteristic
880C22C2×#8825111yescharacteristic
881C22C2×#41×D1311yescharacteristic
882C22C2×#8825711yescharacteristic
883C22C23×C22⋊D1311yescharacteristic
884C4—24no—
885C4—24no—
886C4—42no—
887C4—42no—
888C4—264no—
889C4—264no—
890C4—264no—
891C4—522no—
892C4—522no—
893C4—522no—
894C4—522no—
895C4—522no—
896C2—28no—
897C2—44no—
898C2—82no—
899C2#1311856718yesdirect product factor
900C2C22×#8818911yescharacteristic
901C2C2×#1171931111yescharacteristic
902C2C2×#1171930711yescharacteristic
903C2C2×D4×C22⋊D1311yescharacteristic
904C2C2×#1171952911yescharacteristic
905C2C2×#1171930311yescharacteristic
906C2C2×#1171930611yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
Fitting, prime radicalC22×C13×#121C2
socleC24×C13C24
hypercenterC22×#121D13
hypocenterC13C2×#2443
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C22×#88189C2semidirect
2. C22×D4×Dic13C2semidirect
3. C23×#6101C2semidirect
4. #13118567C2direct (N × H)
5. C2×#11718610C2semidirect
6. C2×#11718644C2semidirect
7. C2×#11718613C2semidirect
8. C2×#11718883C2semidirect
9. C2×#11718605C2semidirect
10. C2×#11718639C2semidirect
11. C2×#11718881C2semidirect
12. C2×#11718881C2semidirect
13. C2×#11718881C2semidirect
14. C2×#11718871C2semidirect
15. C2×#11718607C2semidirect
39. C2×#88189C22semidirect
41. C2×D4×Dic13C22semidirect
50. C22×#6101C22semidirect
52. #11718883C22semidirect
53. #11718881C22semidirect
54. #11718881C22semidirect
55. #11718881C22semidirect
56. #11718871C22semidirect
65. #11718644C22semidirect
66. #11718639C22semidirect
67. #11718613C22semidirect
68. #11718610C22semidirect
69. #11718607C22semidirect
70. #11718605C22semidirect
149. C2×#6101D4semidirect
286. #6101C2×D4semidirect
341. C23×C13#123semidirect
487. C22×C13C2×#123semidirect
611. C2×C13#2443semidirect
740. C13C2×#2443semidirect
778. C23#88189semidirect
874. C22C2×#88189semidirect
899. C2#13118567direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881892
C22×D4×Dic132
C23×#61012
#131185672
C2×#117186102
C2×#117186442
C2×#117186132
C2×#117188832
C2×#117186052
C2×#117186392
C2×#117188812
C2×#117188712
C2×#117186072
C22×C13×#1212
C2×#244313