Finite Group Databasebeta

← C2×#13118797 #16030774

Subgroups — C2×#13118797 #16030774

Order 3328.

3786 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×#88139C211yesmaximal, characteristic, complemented
2C22×#88183C211yesmaximal, characteristic, complemented
3C22×#88178C211yesmaximal, characteristic, complemented
4#13118797C2116yesmaximal, direct product factor
5C2×#11718655C211yesmaximal, characteristic, complemented
6C2×#11718640C211yesmaximal, characteristic, complemented
7C2×#11718883C211yesmaximal, characteristic, complemented
8C2×#11718884C211yesmaximal, characteristic
9C2×#11718618C211yesmaximal, characteristic, complemented
10C2×#11718612C211yesmaximal, characteristic, complemented
11C2×#11718601C211yesmaximal, characteristic, complemented
12C2×#11718605C211yesmaximal, characteristic, complemented
13C2×#11718874C211yesmaximal, characteristic, complemented
14C2×#11718871C211yesmaximal, characteristic, complemented
15C2×C4×#6101C211yesmaximal, characteristic, complemented
16C22×C4×D4×C13C211yesmaximal, characteristic, complemented
17C23×D4×C13C2211yescharacteristic
18C24×C4×C13C2211yescharacteristic
19C24×C4×C13C2211yescharacteristic
20C23×C22⋊D13C2211yescharacteristic
21C23×C22⋊D13C2211yescharacteristic
22C23×Dic26C2211yescharacteristic
23C2×C4×D4×C13—28no—
24C2×C4×D4×C13C2218yescomplemented
25C22×C13×C4⋊C4C2211yescharacteristic
26C22×C13×C22⋊C4C2211yescharacteristic
27C22×C13×C22⋊C4C2211yescharacteristic
28C22×C42×C13C2211yescharacteristic
29C22×C22⋊Dic13C2211yescharacteristic
30C22×C22⋊Dic13C2211yescharacteristic
31C22×C22⋊Dic13C2211yescharacteristic
32C22×C22⋊Dic13C2211yescharacteristic
33C22×C22⋊Dic13C2211yescharacteristic
34C22×C22⋊Dic13C2211yescharacteristic
35C2×#88183—28no—
36C2×#88183C2218yescomplemented
37C22×#6103C2211yescharacteristic
38C22×#6103C2211yescharacteristic
39C22×#6103C2211yescharacteristic
40C22×#6103C2211yescharacteristic
41C22×#6103C2211yescharacteristic
42C22×C4⋊Dic13C2211yescharacteristic
43C2×#88178—28no—
44C2×#88178C2218yescomplemented
45C22×#6101C2211yescharacteristic
46C22×#6101C2211yescharacteristic
47C22×#6101C2211yescharacteristic
48C22×#6101C2211yescharacteristic
49C22×#6101C2211yescharacteristic
50C22×C4×Dic13C2211yescharacteristic
51C22×C4×Dic13C2211yescharacteristic
52C2×#88139—28no—
53C2×#88139C2218yescomplemented
54#11718884C2218yes—
55#11718883C2218yescomplemented
56#11718874C2218yescomplemented
57#11718871C2218yescomplemented
58C2×#88071C2211yescharacteristic
59C2×#88071C2211yescharacteristic
60C2×#88071C2211yescharacteristic
61C2×#88071C2211yescharacteristic
62C2×#88071C2211yescharacteristic
63C2×#88071C2211yescharacteristic
64#11718655C2218yescomplemented
65#11718640C2218yescomplemented
66#11718618C2218yescomplemented
67#11718612C2218yescomplemented
68#11718605C2218yescomplemented
69#11718601C2218yescomplemented
70C4×#6101C2218yescomplemented
71C25×C13C2311yescharacteristic
72C25×C13C2311yescharacteristic
73C24×D13C2311yescharacteristic
74C22×D4×C13—24no—
75C22×D4×C13—24no—
76C22×D4×C13—24no—
77C22×D4×C13C2314yes—
78C23×C4×C13—24no—
79C23×C4×C13—24no—
80C23×C4×C13—24no—
81C23×C4×C13—24no—
82C23×C4×C13—42no—
83C23×C4×C13—42no—
84C23×C4×C13C2311yescharacteristic
85C23×C4×C13C2314yes—
86C23×C4×C13C2314yes—
87C23×C4×C13C2311yescharacteristic
88C23×C4×C13C2311yescharacteristic
89C23×C4×C13C2311yescharacteristic
90C23×C4×C13C2311yescharacteristic
91C22×C22⋊D13—24no—
92C22×C22⋊D13—24no—
93C22×C22⋊D13—24no—
94C22×C22⋊D13—24no—
95C22×C22⋊D13—42no—
96C22×C22⋊D13—42no—
97C22×C22⋊D13C2314yes—
98C22×C22⋊D13C2314yes—
99C23×Dic13C2311yescharacteristic
100C23×Dic13C2311yescharacteristic
101C23×Dic13C2311yescharacteristic
102C23×Dic13C2311yescharacteristic
103C23×Dic13C2311yescharacteristic
104C23×Dic13C2311yescharacteristic
105C23×Dic13C2311yescharacteristic
106C22×Dic26—24no—
107C22×Dic26—24no—
108C22×Dic26—42no—
109C22×Dic26C2314yes—
110C4×D4×C13—232no—
111C2×C13×C4⋊C4—24no—
112C2×C13×C4⋊C4C2314yes—
113C2×C13×C22⋊C4—24no—
114C2×C13×C22⋊C4D418yescomplemented
115C2×C13×C22⋊C4C2314yes—
116C2×C13×C22⋊C4C2314yes—
117C2×C42×C13—24no—
118C2×C42×C13C2314yes—
119C2×C22⋊Dic13—24no—
120C2×C22⋊Dic13—24no—
121C2×C22⋊Dic13—24no—
122C2×C22⋊Dic13—24no—
123C2×C22⋊Dic13—24no—
124C2×C22⋊Dic13—24no—
125C2×C22⋊Dic13C2314yes—
126C2×C22⋊Dic13C2314yes—
127C2×C22⋊Dic13C2314yes—
128C2×C22⋊Dic13C2314yes—
129C2×C22⋊Dic13C2314yes—
130C2×C22⋊Dic13C2314yes—
131#88183—232no—
132C2×#6103—24no—
133C2×#6103—24no—
134C2×#6103—24no—
135C2×#6103—24no—
136C2×#6103—24no—
137C2×#6103C2314yes—
138C2×#6103C2314yes—
139C2×#6103C2314yes—
140C2×#6103C2314yes—
141C2×#6103C2314yes—
142C2×C4⋊Dic13—24no—
143C2×C4⋊Dic13C2314yes—
144#88178—232no—
145C2×#6101—24no—
146C2×#6101—24no—
147C2×#6101—24no—
148C2×#6101—42no—
149C2×#6101D418yescomplemented
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#88139—232no—
160#88071C2314yes—
161#88071C2314yes—
162#88071C2314yes—
163#88071C2314yes—
164#88071C2314yes—
165#88071C2314yes—
166C2×#2461—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×C13#4114yes—
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×D13—22no—
191C23×D13C2412yes—
192C2×D4×C13—232no—
193C2×D4×C13—28no—
194C2×D4×C13—28no—
195C2×D4×C13—28no—
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—22no—
203C22×C4×C13—22no—
204C22×C4×C13—22no—
205C22×C4×C13—22no—
206C22×C4×C13—28no—
207C22×C4×C13—22no—
208C22×C4×C13—28no—
209C22×C4×C13—28no—
210C22×C4×C13—28no—
211C22×C4×C13—44no—
212C22×C4×C13—44no—
213C22×C4×C13—416no—
214C22×C4×C13—416no—
215C22×C4×C13C2×D414yes—
216C22×C4×C13C2×D414yes—
217C22×C4×C13C2×D414yes—
218C22×C4×C13#4114yes—
219C22×C4×C13C2412yes—
220C22×C4×C13C2412yes—
221C22×C4×C13C2412yes—
222C22×C4×C13C2412yes—
223C22×C4×C13C2412yes—
224C2×C22⋊D13—28no—
225C2×C22⋊D13—28no—
226C2×C22⋊D13—28no—
227C2×C22⋊D13—28no—
228C2×C22⋊D13—44no—
229C2×C22⋊D13—44no—
230C2×C22⋊D13—416no—
231C2×C22⋊D13—416no—
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—22no—
246C22×Dic13—22no—
247C22×Dic13—22no—
248C22×Dic13—22no—
249C22×Dic13—22no—
250C22×Dic13C2×D414yes—
251C22×Dic13C2×D414yes—
252C22×Dic13#4114yes—
253C22×Dic13C2412yes—
254C22×Dic13C2412yes—
255C22×Dic13C2412yes—
256C22×Dic13C2412yes—
257C22×Dic13C2412yes—
258C22×Dic13C2412yes—
259C22×Dic13C2412yes—
260C2×Dic26—28no—
261C2×Dic26—28no—
262C2×Dic26—44no—
263C2×Dic26—416no—
264C13×C4⋊C4—28no—
265C13×C22⋊C4—28no—
266C13×C22⋊C4C2×D4116yescomplemented
267C42×C13—28no—
268C22⋊Dic13—28no—
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—
278#6103—28no—
279C4⋊Dic13—28no—
280#6101—28no—
281#6101—28no—
282#6101—28no—
283#6101—44no—
284#6101C2×D4116yescomplemented
285C4×Dic13—28no—
286C4×Dic13—28no—
287C22×#124—131no—
288C22×#123—131no—
289C22×C22⋊Q8—131no—
290C22×C4×D4D1311yescharacteristic, complemented
291#2461—1316no—
292C2×#396—131no—
293C2×#395—131no—
294C2×#394—131no—
295C2×#392—131no—
296C2×#390—131no—
297C2×#388—131no—
298C2×#388—131no—
299C2×#388—131no—
300C2×#386—131no—
301C2×#385—131no—
302C2×C4×C4⋊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×D412yes—
331C23×C13C22×D412yes—
332C23×C13C2×#4114yes—
333C23×C13C2×#4112yes—
334C23×C13C2×#4112yes—
335C23×C13C2×#4112yes—
336C23×C13H(5,𝔽2)12yes—
337C23×C132−1+412yes—
338C23×C13C2511yescharacteristic
339C22×D13—22no—
340C22×D13—22no—
341C22×D13—22no—
342C22×D13—22no—
343C22×D13—22no—
344C22×D13—22no—
345C22×D13—22no—
346C22×D13—44no—
347C22×D13—44no—
348C22×D13—44no—
349C22×D13—44no—
350C22×D13—44no—
351C22×D13—44no—
352C22×D13—44no—
353D4×C13—232no—
354C2×C4×C13—28no—
355C2×C4×C13—28no—
356C2×C4×C13—28no—
357C2×C4×C13—28no—
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—416no—
371C2×C4×C13—44no—
372C2×C4×C13C22×D414yes—
373C2×C4×C13C22×D414yes—
374C2×C4×C13C22×D414yes—
375C2×C4×C13C2×#4114yes—
376C22⋊D13—416no—
377C22⋊D13—416no—
378C2×Dic13—28no—
379C2×Dic13—28no—
380C2×Dic13—28no—
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—44no—
400C2×Dic13—44no—
401C2×Dic13—44no—
402C2×Dic13—44no—
403C2×Dic13C22×D414yes—
404C2×Dic13C22×D414yes—
405C2×Dic13C2×#4114yes—
406Dic26—416no—
407C23×Q8—131no—
408C23×D4—131no—
409C23×D4—131no—
410C23×D4C2×D1311yescharacteristic
411C24×C4C2×D1311yescharacteristic
412C24×C4C2×D1311yescharacteristic
413C2×#124—138no—
414C2×#124—268no—
415C2×#123—138no—
416C2×#123—268no—
417C2×C22⋊Q8—138no—
418C2×C22⋊Q8—268no—
419C2×C4×D4—28no—
420C2×C4×D4C2×D1318yescomplemented
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⋊C4C2×D1311yescharacteristic
428C22×C22⋊C4—131no—
429C22×C22⋊C4—131no—
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×C42—131no—
442C22×C42—131no—
443C22×C42C2×D1311yescharacteristic
444#396—138no—
445#395—138no—
446#394—138no—
447#392—138no—
448#390—138no—
449#388—138no—
450#388—138no—
451#388—138no—
452#386—138no—
453#385—138no—
454C4×C4⋊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—42no—
470C22×C13—42no—
471C22×C13—42no—
472C22×C13—42no—
473C22×C13—42no—
474C22×C13—42no—
475C22×C13—416no—
476C22×C13—416no—
477C22×C13#52514yes—
478C22×C13#53214yes—
479C22×C13#54214yes—
480C22×C13D4214yes—
481C22×C13#54714yes—
482C22×C13#54814yes—
483C22×C13#55114yes—
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—42no—
492C2×D13—42no—
493C2×D13—42no—
494C2×D13—42no—
495C2×D13—42no—
496C2×D13—42no—
497C2×D13—42no—
498C2×D13—88no—
499C4×C13—24no—
500C4×C13—24no—
501C4×C13—24no—
502C4×C13—24no—
503C4×C13—42no—
504Dic13—24no—
505Dic13—24no—
506Dic13—24no—
507Dic13—42no—
508Dic13—42no—
509Dic13—42no—
510Dic13—42no—
511C25—131no—
512C25C22×D1311yescharacteristic
513C25C22×D1311yescharacteristic
514C22×Q8—134no—
515C22×Q8—264no—
516C22×Q8—264no—
517C22×Q8—522no—
518C22×D4—24no—
519C22×D4—24no—
520C22×D4—24no—
521C22×D4—134no—
522C22×D4—134no—
523C22×D4—264no—
524C22×D4—264no—
525C22×D4—264no—
526C22×D4—264no—
527C22×D4—522no—
528C22×D4—522no—
529C22×D4C22×D1314yes—
530C23×C4—24no—
531C23×C4—24no—
532C23×C4—24no—
533C23×C4—24no—
534C23×C4—42no—
535C23×C4—42no—
536C23×C4—131no—
537C23×C4—131no—
538C23×C4—131no—
539C23×C4—131no—
540C23×C4—131no—
541C23×C4—131no—
542C23×C4—131no—
543C23×C4C22×D1311yescharacteristic
544C23×C4C22×D1314yes—
545C23×C4C22×D1314yes—
546C23×C4C22×D1311yescharacteristic
547C23×C4C22×D1311yescharacteristic
548C23×C4C22×D1311yescharacteristic
549C23×C4C22×D1311yescharacteristic
550#124—2632no—
551#123—2632no—
552C22⋊Q8—2632no—
553C4×D4—232no—
554C2×C4⋊C4—24no—
555C2×C4⋊C4—138no—
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—264no—
563C2×C4⋊C4—264no—
564C2×C4⋊C4—264no—
565C2×C4⋊C4—264no—
566C2×C4⋊C4—522no—
567C2×C4⋊C4C22×D1314yes—
568C2×C22⋊C4—24no—
569C2×C22⋊C4—134no—
570C2×C22⋊C4—134no—
571C2×C22⋊C4—134no—
572C2×C22⋊C4—134no—
573C2×C22⋊C4—134no—
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—264no—
581C2×C22⋊C4—264no—
582C2×C22⋊C4—264no—
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⋊C4C22⋊D1318yescomplemented
592C2×C22⋊C4C22×D1314yes—
593C2×C22⋊C4C22×D1314yes—
594C2×C42—24no—
595C2×C42—134no—
596C2×C42—134no—
597C2×C42—264no—
598C2×C42—264no—
599C2×C42C22×D1314yes—
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#246118yescomplemented
609C2×C13C2×#52511yescharacteristic
610C2×C13C2×#53211yescharacteristic
611C2×C13C2×#54211yescharacteristic
612C2×C13C2×D4211yescharacteristic
613C2×C13C2×#54711yescharacteristic
614C2×C13C2×#54811yescharacteristic
615C2×C13C2×#55111yescharacteristic
616D13—82no—
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—132no—
630C24—262no—
631C24—262no—
632C24—262no—
633C24—262no—
634C24—262no—
635C24—262no—
636C24—262no—
637C24#612714yes—
638C24C2×C22⋊D1314yes—
639C24C23×D1312yes—
640C24C23×D1312yes—
641C24C23×D1311yescharacteristic
642C2×Q8—268no—
643C2×Q8—268no—
644C2×Q8—524no—
645C2×Q8—5216no—
646C2×D4—232no—
647C2×D4—28no—
648C2×D4—28no—
649C2×D4—28no—
650C2×D4—268no—
651C2×D4—268no—
652C2×D4—268no—
653C2×D4—268no—
654C2×D4—524no—
655C2×D4—524no—
656C2×D4—5216no—
657C2×D4—5216no—
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—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—28no—
670C22×C4—28no—
671C22×C4—28no—
672C22×C4—28no—
673C22×C4—44no—
674C22×C4—44no—
675C22×C4—416no—
676C22×C4—416no—
677C22×C4—134no—
678C22×C4—134no—
679C22×C4—134no—
680C22×C4—132no—
681C22×C4—132no—
682C22×C4—132no—
683C22×C4—132no—
684C22×C4—132no—
685C22×C4—132no—
686C22×C4—132no—
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—262no—
704C22×C4—262no—
705C22×C4#612714yes—
706C22×C4D4×D1314yes—
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—1316no—
716C4⋊C4—268no—
717C4⋊C4—268no—
718C4⋊C4—268no—
719C4⋊C4—268no—
720C4⋊C4—524no—
721C22⋊C4—28no—
722C22⋊C4—268no—
723C22⋊C4—268no—
724C22⋊C4—268no—
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⋊C4C2×C22⋊D13116yescomplemented
734C42—28no—
735C42—268no—
736C42—268no—
737C13C2×#246111yescharacteristic, 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—262no—
765C23—262no—
766C23—262no—
767C23—262no—
768C23—262no—
769C23—262no—
770C23—262no—
771C23—524no—
772C23—524no—
773C23—524no—
774C23—524no—
775C23—524no—
776C23—524no—
777C23—524no—
778C23C2×#612714yes—
779C23C2×#612712yes—
780C23C2×#612712yes—
781C23C2×D4×D1312yes—
782C23#8825112yes—
783C23#41×D1312yes—
784C23#8825712yes—
785C23C22×C22⋊D1314yes—
786C23C22×C22⋊D1312yes—
787C23C24×D1311yescharacteristic
788Q8—5216no—
789D4—232no—
790D4—5216no—
791D4—5216no—
792C2×C4—28no—
793C2×C4—28no—
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—22no—
807C2×C4—416no—
808C2×C4—416no—
809C2×C4—44no—
810C2×C4—134no—
811C2×C4—134no—
812C2×C4—134no—
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—524no—
835C2×C4—524no—
836C2×C4—524no—
837C2×C4—524no—
838C2×C4C2×#612714yes—
839C2×C4C2×D4×D1314yes—
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—416no—
851C22—416no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—522no—
859C22—522no—
860C22—522no—
861C22—522no—
862C22—522no—
863C22—522no—
864C22—522no—
865C22—1048no—
866C22#1171925314yes—
867C22#1171925714yes—
868C22#1171926114yes—
869C22#1171926614yes—
870C22#1171949614yes—
871C22D4×C22⋊D1314yes—
872C22#1171952914yes—
873C22C22×#612711yescharacteristic
874C22C22×#612711yescharacteristic
875C22C22×D4×D1311yescharacteristic
876C22C2×#8825111yescharacteristic
877C22C2×#41×D1311yescharacteristic
878C22C2×#8825711yescharacteristic
879C22C23×C22⋊D1311yescharacteristic
880C4—24no—
881C4—24no—
882C4—24no—
883C4—24no—
884C4—42no—
885C4—264no—
886C4—264no—
887C4—264no—
888C4—522no—
889C4—522no—
890C4—522no—
891C4—522no—
892C2—44no—
893C2—44no—
894C2—1042no—
895C2#1311879718yesdirect product factor
896C2C2×#1171949611yescharacteristic
897C2C2×#1171925311yescharacteristic
898C2C2×#1171926611yescharacteristic
899C2C2×D4×C22⋊D1311yescharacteristic
900C2C2×#1171952911yescharacteristic
901C2C2×#1171925711yescharacteristic
902C2C2×#1171926111yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC22×C4×D4×C13C2
socleC24×C13C24
prime radicalC2×#11718884C2
hypercenterC22×C4×D4D13
hypocenterC13C2×#2461
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×#88139C2semidirect
2. C22×#88183C2semidirect
3. C22×#88178C2semidirect
4. #13118797C2direct (N × H)
5. C2×#11718655C2semidirect
6. C2×#11718640C2semidirect
7. C2×#11718883C2semidirect
9. C2×#11718618C2semidirect
10. C2×#11718612C2semidirect
11. C2×#11718601C2semidirect
12. C2×#11718605C2semidirect
13. C2×#11718874C2semidirect
14. C2×#11718871C2semidirect
15. C2×C4×#6101C2semidirect
16. C22×C4×D4×C13C2semidirect
24. C2×C4×D4×C13C22semidirect
36. C2×#88183C22semidirect
44. C2×#88178C22semidirect
53. C2×#88139C22semidirect
55. #11718883C22semidirect
56. #11718874C22semidirect
57. #11718871C22semidirect
64. #11718655C22semidirect
65. #11718640C22semidirect
66. #11718618C22semidirect
67. #11718612C22semidirect
68. #11718605C22semidirect
69. #11718601C22semidirect
70. C4×#6101C22semidirect
114. C2×C13×C22⋊C4D4semidirect
149. C2×#6101D4semidirect
266. C13×C22⋊C4C2×D4semidirect
284. #6101C2×D4semidirect
290. C22×C4×D4D13semidirect
420. C2×C4×D4C2×D13semidirect
591. C2×C22⋊C4C22⋊D13semidirect
608. C2×C13#2461semidirect
733. C22⋊C4C2×C22⋊D13semidirect
737. C13C2×#2461semidirect
895. C2#13118797direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881392
C22×#881832
C22×#881782
#131187972
C2×#117186552
C2×#117186402
C2×#117188832
C2×#117188842
C2×#117186182
C2×#117186122
C2×#117186012
C2×#117186052
C2×#117188742
C2×#117188712
C2×C4×#61012
C22×C4×D4×C132
C2×#246113