Finite Group Databasebeta

← C2×#13119892 #16032994

Subgroups — C2×#13119892 #16032994

Order 3328.

3158 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88152C211yesmaximal, characteristic, complemented
2#13119892C2116yesmaximal, direct product factor
3C2×#11718644C211yesmaximal, characteristic, complemented
4C2×#11718609C211yesmaximal, characteristic, complemented
5C2×#11718622C211yesmaximal, characteristic, complemented
6C2×#11718884C211yesmaximal, characteristic
7C2×#11718882C211yesmaximal, characteristic, complemented
8C2×#11718618C211yesmaximal, characteristic, complemented
9C2×#11718618C211yesmaximal, characteristic, complemented
10C2×#11718606C211yesmaximal, characteristic, complemented
11C2×#11718651C211yesmaximal, characteristic, complemented
12C2×#11718605C211yesmaximal, characteristic, complemented
13C2×#11718874C211yesmaximal, characteristic, complemented
14C2×C4⋊C4×Dic13C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊Dic13C211yesmaximal, characteristic, complemented
16C22×C13×#123C211yesmaximal, characteristic, complemented
17C23×D4×C13C2211yescharacteristic
18C24×C4×C13C2211yescharacteristic
19C23×C22⋊D13C2211yescharacteristic
20C23×C22⋊D13C2211yescharacteristic
21C2×C13×#123—28no—
22C2×C13×#123C2218yescomplemented
23C22×C13×C4⋊C4C2211yescharacteristic
24C22×C13×C4⋊C4C2211yescharacteristic
25C22×C13×C22⋊C4C2211yescharacteristic
26C22×C13×C22⋊C4C2211yescharacteristic
27C22×C13×C22⋊C4C2211yescharacteristic
28C22×C22⋊Dic13C2211yescharacteristic
29C22×C22⋊Dic13C2211yescharacteristic
30C22×C22⋊Dic13C2211yescharacteristic
31C22×C22⋊Dic13C2211yescharacteristic
32C22×C22⋊Dic13C2211yescharacteristic
33C22×C22⋊Dic13C2211yescharacteristic
34C22×#6103C2211yescharacteristic
35C22×#6103C2211yescharacteristic
36C22×#6103C2211yescharacteristic
37C22×#6103C2211yescharacteristic
38C22×#6103C2211yescharacteristic
39C22×C4⋊Dic13C2211yescharacteristic
40C22×C4⋊Dic13C2211yescharacteristic
41C22×#6101C2211yescharacteristic
42C22×#6101C2211yescharacteristic
43C22×#6101C2211yescharacteristic
44C22×C4×Dic13C2211yescharacteristic
45C22×C4×Dic13C2211yescharacteristic
46C22×C4×Dic13C2211yescharacteristic
47C22×C4×Dic13C2211yescharacteristic
48C2×#88152—28no—
49C2×#88152C2218yescomplemented
50#11718884C2218yes—
51#11718882C2218yescomplemented
52#11718874C2218yescomplemented
53C4×C22⋊Dic13C2218yescomplemented
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57C2×#88071C2211yescharacteristic
58C2×#88071C2211yescharacteristic
59C2×#88071C2211yescharacteristic
60#11718651C2218yescomplemented
61#11718644C2218yescomplemented
62C4⋊C4×Dic13C2218yescomplemented
63#11718622C2218yescomplemented
64#11718618C2218yescomplemented
65#11718618C2218yescomplemented
66#11718609C2218yescomplemented
67#11718606C2218yescomplemented
68#11718605C2218yescomplemented
69C25×C13C2311yescharacteristic
70C25×C13C2311yescharacteristic
71C24×D13C2311yescharacteristic
72C22×D4×C13—24no—
73C22×D4×C13—24no—
74C22×D4×C13—42no—
75C22×D4×C13C2314yes—
76C23×C4×C13—24no—
77C23×C4×C13—24no—
78C23×C4×C13—42no—
79C23×C4×C13C2311yescharacteristic
80C23×C4×C13C2311yescharacteristic
81C23×C4×C13C2314yes—
82C23×C4×C13C2311yescharacteristic
83C23×C4×C13C2311yescharacteristic
84C23×C4×C13C2311yescharacteristic
85C22×C22⋊D13—24no—
86C22×C22⋊D13—24no—
87C22×C22⋊D13—24no—
88C22×C22⋊D13—42no—
89C22×C22⋊D13—42no—
90C22×C22⋊D13—42no—
91C22×C22⋊D13C2314yes—
92C22×C22⋊D13C2314yes—
93C23×Dic13C2311yescharacteristic
94C23×Dic13C2311yescharacteristic
95C23×Dic13C2311yescharacteristic
96C23×Dic13C2311yescharacteristic
97C23×Dic13C2311yescharacteristic
98C23×Dic13C2311yescharacteristic
99C23×Dic13C2311yescharacteristic
100C13×#123—232no—
101C2×C13×C4⋊C4—24no—
102C2×C13×C4⋊C4D418yescomplemented
103C2×C13×C4⋊C4C2314yes—
104C2×C13×C4⋊C4C2314yes—
105C2×C13×C22⋊C4—24no—
106C2×C13×C22⋊C4—24no—
107C2×C13×C22⋊C4—24no—
108C2×C13×C22⋊C4C2314yes—
109C2×C13×C22⋊C4C2314yes—
110C2×C13×C22⋊C4C2314yes—
111C2×C22⋊Dic13—24no—
112C2×C22⋊Dic13—24no—
113C2×C22⋊Dic13—24no—
114C2×C22⋊Dic13—24no—
115C2×C22⋊Dic13—42no—
116C2×C22⋊Dic13—42no—
117C2×C22⋊Dic13C2314yes—
118C2×C22⋊Dic13C2314yes—
119C2×C22⋊Dic13C2314yes—
120C2×C22⋊Dic13C2314yes—
121C2×C22⋊Dic13C2314yes—
122C2×C22⋊Dic13C2314yes—
123C2×#6103—24no—
124C2×#6103—24no—
125C2×#6103—24no—
126C2×#6103—24no—
127C2×#6103—42no—
128C2×#6103C2314yes—
129C2×#6103C2314yes—
130C2×#6103C2314yes—
131C2×#6103C2314yes—
132C2×#6103C2314yes—
133C2×C4⋊Dic13—24no—
134C2×C4⋊Dic13—24no—
135C2×C4⋊Dic13C2314yes—
136C2×C4⋊Dic13C2314yes—
137C2×#6101—24no—
138C2×#6101—42no—
139C2×#6101—42no—
140C2×#6101C2314yes—
141C2×#6101C2314yes—
142C2×#6101C2314yes—
143C2×C4×Dic13—24no—
144C2×C4×Dic13—24no—
145C2×C4×Dic13—42no—
146C2×C4×Dic13—42no—
147C2×C4×Dic13C2314yes—
148C2×C4×Dic13C2314yes—
149C2×C4×Dic13C2314yes—
150C2×C4×Dic13C2314yes—
151#88152—232no—
152#88071C2314yes—
153#88071C2314yes—
154#88071C2314yes—
155#88071C2314yes—
156#88071C2314yes—
157#88071C2314yes—
158C2×#2554—131nomaximal, Sylow
159C24×C13—22no—
160C24×C13—22no—
161C24×C13—22no—
162C24×C13—22no—
163C24×C13—22no—
164C24×C13—22no—
165C24×C13—22no—
166C24×C13—22no—
167C24×C13—22no—
168C24×C13—22no—
169C24×C13—22no—
170C24×C13—22no—
171C24×C13—22no—
172C24×C13#4114yes—
173C24×C13C2412yes—
174C24×C13C2412yes—
175C24×C13C2411yescharacteristic
176C23×D13—22no—
177C23×D13—22no—
178C23×D13—22no—
179C23×D13—22no—
180C23×D13—22no—
181C23×D13—22no—
182C23×D13—22no—
183C23×D13C2412yes—
184C2×D4×C13—28no—
185C2×D4×C13—28no—
186C2×D4×C13—44no—
187C2×D4×C13—416no—
188C22×C4×C13—22no—
189C22×C4×C13—22no—
190C22×C4×C13—22no—
191C22×C4×C13—22no—
192C22×C4×C13—22no—
193C22×C4×C13—22no—
194C22×C4×C13—22no—
195C22×C4×C13—22no—
196C22×C4×C13—22no—
197C22×C4×C13—28no—
198C22×C4×C13—22no—
199C22×C4×C13—22no—
200C22×C4×C13—22no—
201C22×C4×C13—28no—
202C22×C4×C13—44no—
203C22×C4×C13—416no—
204C22×C4×C13C2×D414yes—
205C22×C4×C13C2×D414yes—
206C22×C4×C13C2×D414yes—
207C22×C4×C13C2412yes—
208C22×C4×C13C2412yes—
209C22×C4×C13C2412yes—
210C22×C4×C13C2412yes—
211C22×C4×C13C2412yes—
212C2×C22⋊D13—28no—
213C2×C22⋊D13—28no—
214C2×C22⋊D13—28no—
215C2×C22⋊D13—44no—
216C2×C22⋊D13—44no—
217C2×C22⋊D13—44no—
218C2×C22⋊D13—416no—
219C2×C22⋊D13—416no—
220C22×Dic13—22no—
221C22×Dic13—22no—
222C22×Dic13—22no—
223C22×Dic13—22no—
224C22×Dic13—22no—
225C22×Dic13—22no—
226C22×Dic13—22no—
227C22×Dic13—22no—
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#4114yes—
239C22×Dic13#4114yes—
240C22×Dic13#4114yes—
241C22×Dic13C2412yes—
242C22×Dic13C2412yes—
243C22×Dic13C2412yes—
244C22×Dic13C2412yes—
245C22×Dic13C2412yes—
246C22×Dic13C2412yes—
247C22×Dic13C2412yes—
248C13×C4⋊C4—28no—
249C13×C4⋊C4C2×D4116yescomplemented
250C13×C22⋊C4—28no—
251C13×C22⋊C4—28no—
252C13×C22⋊C4—28no—
253C22⋊Dic13—28no—
254C22⋊Dic13—28no—
255C22⋊Dic13—28no—
256C22⋊Dic13—28no—
257C22⋊Dic13—44no—
258C22⋊Dic13—44no—
259#6103—28no—
260#6103—28no—
261#6103—28no—
262#6103—28no—
263#6103—44no—
264C4⋊Dic13—28no—
265C4⋊Dic13—28no—
266#6101—28no—
267#6101—44no—
268#6101—44no—
269C4×Dic13—28no—
270C4×Dic13—28no—
271C4×Dic13—44no—
272C4×Dic13—44no—
273C22×#126—131no—
274C22×#123D1311yescharacteristic, complemented
275#2554—1316no—
276C2×#398—131no—
277C2×#396—131no—
278C2×#394—131no—
279C2×#392—131no—
280C2×#390—131no—
281C2×#390—131no—
282C2×#390—131no—
283C2×#388—131no—
284C2×#388—131no—
285C2×#388—131no—
286C2×#386—131no—
287C2×C4×C4⋊C4—131no—
288C2×C4×C22⋊C4—131no—
289C23×C13—28no—
290C23×C13—28no—
291C23×C13—28no—
292C23×C13—22no—
293C23×C13—22no—
294C23×C13—22no—
295C23×C13—22no—
296C23×C13—22no—
297C23×C13—22no—
298C23×C13—22no—
299C23×C13—22no—
300C23×C13—22no—
301C23×C13—22no—
302C23×C13—22no—
303C23×C13—22no—
304C23×C13—22no—
305C23×C13—44no—
306C23×C13—44no—
307C23×C13—44no—
308C23×C13—44no—
309C23×C13—44no—
310C23×C13—44no—
311C23×C13—44no—
312C23×C13—44no—
313C23×C13—44no—
314C23×C13—44no—
315C23×C13—44no—
316C23×C13C22×D412yes—
317C23×C13C2×#4114yes—
318C23×C13C2×#4112yes—
319C23×C13C2×#4112yes—
320C23×C13C2×#4112yes—
321C23×C13C2×#4112yes—
322C23×C13H(5,𝔽2)12yes—
323C23×C13H(5,𝔽2)12yes—
324C23×C13C2511yescharacteristic
325C22×D13—22no—
326C22×D13—22no—
327C22×D13—22no—
328C22×D13—22no—
329C22×D13—22no—
330C22×D13—22no—
331C22×D13—22no—
332C22×D13—44no—
333C22×D13—44no—
334C22×D13—44no—
335C22×D13—44no—
336C22×D13—44no—
337C22×D13—44no—
338C22×D13—44no—
339D4×C13—416no—
340C2×C4×C13—28no—
341C2×C4×C13—28no—
342C2×C4×C13—28no—
343C2×C4×C13—22no—
344C2×C4×C13—22no—
345C2×C4×C13—22no—
346C2×C4×C13—22no—
347C2×C4×C13—22no—
348C2×C4×C13—22no—
349C2×C4×C13—22no—
350C2×C4×C13—22no—
351C2×C4×C13—22no—
352C2×C4×C13—22no—
353C2×C4×C13—22no—
354C2×C4×C13—22no—
355C2×C4×C13—416no—
356C2×C4×C13—44no—
357C2×C4×C13—44no—
358C2×C4×C13C22×D414yes—
359C2×C4×C13C22×D414yes—
360C2×C4×C13C22×D414yes—
361C22⋊D13—416no—
362C22⋊D13—416no—
363C2×Dic13—28no—
364C2×Dic13—28no—
365C2×Dic13—28no—
366C2×Dic13—22no—
367C2×Dic13—22no—
368C2×Dic13—22no—
369C2×Dic13—22no—
370C2×Dic13—22no—
371C2×Dic13—22no—
372C2×Dic13—22no—
373C2×Dic13—22no—
374C2×Dic13—22no—
375C2×Dic13—22no—
376C2×Dic13—22no—
377C2×Dic13—22no—
378C2×Dic13—22no—
379C2×Dic13—22no—
380C2×Dic13—22no—
381C2×Dic13—22no—
382C2×Dic13—22no—
383C2×Dic13—22no—
384C2×Dic13—44no—
385C2×Dic13—44no—
386C2×Dic13—44no—
387C2×Dic13—44no—
388C2×Dic13C2×#4114yes—
389C2×Dic13C2×#4114yes—
390C2×Dic13C2×#4114yes—
391C23×D4—131no—
392C23×D4—131no—
393C23×D4C2×D1311yescharacteristic
394C24×C4C2×D1311yescharacteristic
395C2×#126—138no—
396C2×#126—268no—
397C2×#123—28no—
398C2×#123C2×D1318yescomplemented
399C22×C4⋊C4—131no—
400C22×C4⋊C4—131no—
401C22×C4⋊C4—131no—
402C22×C4⋊C4—131no—
403C22×C4⋊C4—131no—
404C22×C4⋊C4C2×D1311yescharacteristic
405C22×C4⋊C4C2×D1311yescharacteristic
406C22×C22⋊C4—131no—
407C22×C22⋊C4—131no—
408C22×C22⋊C4—131no—
409C22×C22⋊C4—131no—
410C22×C22⋊C4—131no—
411C22×C22⋊C4—131no—
412C22×C22⋊C4—131no—
413C22×C22⋊C4—131no—
414C22×C22⋊C4—131no—
415C22×C22⋊C4—131no—
416C22×C22⋊C4—131no—
417C22×C22⋊C4C2×D1311yescharacteristic
418C22×C22⋊C4C2×D1311yescharacteristic
419C22×C22⋊C4C2×D1311yescharacteristic
420C22×C42—131no—
421C22×C42—131no—
422C22×C42—131no—
423C22×C42—131no—
424#398—138no—
425#396—138no—
426#394—138no—
427#392—138no—
428#390—138no—
429#390—138no—
430#390—138no—
431#388—138no—
432#388—138no—
433#388—138no—
434#386—138no—
435C4×C4⋊C4—138no—
436C4×C22⋊C4—138no—
437C2×#95—131no—
438C2×#95—131no—
439C2×#95—131no—
440C2×#95—131no—
441C2×#95—131no—
442C2×#95—131no—
443C22×C13—24no—
444C22×C13—24no—
445C22×C13—24no—
446C22×C13—42no—
447C22×C13—42no—
448C22×C13—42no—
449C22×C13—42no—
450C22×C13—416no—
451C22×C13—42no—
452C22×C13—42no—
453C22×C13—42no—
454C22×C13—42no—
455C22×C13—42no—
456C22×C13—42no—
457C22×C13—42no—
458C22×C13—88no—
459C22×C13#52914yes—
460C22×C13#53214yes—
461C22×C13#53814yes—
462C22×C13#54614yes—
463C22×C13#55014yes—
464C22×C13#55114yes—
465C22×C13#55314yes—
466C22×C13C23×D411yescharacteristic
467C22×C13C22×#4111yescharacteristic
468C22×C13C22×#4111yescharacteristic
469C22×C13C22×#4111yescharacteristic
470C22×C13C22×#4111yescharacteristic
471C22×C13C2×H(5,𝔽2)11yescharacteristic
472C22×C13C2×H(5,𝔽2)11yescharacteristic
473C2×D13—42no—
474C2×D13—42no—
475C2×D13—42no—
476C2×D13—42no—
477C2×D13—42no—
478C2×D13—42no—
479C2×D13—42no—
480C2×D13—88no—
481C4×C13—24no—
482C4×C13—24no—
483C4×C13—24no—
484C4×C13—42no—
485C4×C13—42no—
486Dic13—24no—
487Dic13—24no—
488Dic13—24no—
489Dic13—42no—
490Dic13—42no—
491Dic13—42no—
492Dic13—42no—
493C25—131no—
494C25C22×D1311yescharacteristic
495C25C22×D1311yescharacteristic
496C22×D4—24no—
497C22×D4—24no—
498C22×D4—42no—
499C22×D4—134no—
500C22×D4—134no—
501C22×D4—264no—
502C22×D4—264no—
503C22×D4—264no—
504C22×D4—522no—
505C22×D4—522no—
506C22×D4—522no—
507C22×D4C22×D1314yes—
508C23×C4—24no—
509C23×C4—24no—
510C23×C4—42no—
511C23×C4—131no—
512C23×C4—131no—
513C23×C4—131no—
514C23×C4—131no—
515C23×C4—131no—
516C23×C4—131no—
517C23×C4—131no—
518C23×C4C22×D1311yescharacteristic
519C23×C4C22×D1311yescharacteristic
520C23×C4C22×D1314yes—
521C23×C4C22×D1311yescharacteristic
522C23×C4C22×D1311yescharacteristic
523C23×C4C22×D1311yescharacteristic
524#126—2632no—
525#123—232no—
526C2×C4⋊C4—24no—
527C2×C4⋊C4—134no—
528C2×C4⋊C4—134no—
529C2×C4⋊C4—134no—
530C2×C4⋊C4—134no—
531C2×C4⋊C4—134no—
532C2×C4⋊C4—264no—
533C2×C4⋊C4—264no—
534C2×C4⋊C4—264no—
535C2×C4⋊C4—522no—
536C2×C4⋊C4—522no—
537C2×C4⋊C4C22⋊D1318yescomplemented
538C2×C4⋊C4C22×D1314yes—
539C2×C4⋊C4C22×D1314yes—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—24no—
542C2×C22⋊C4—24no—
543C2×C22⋊C4—134no—
544C2×C22⋊C4—134no—
545C2×C22⋊C4—134no—
546C2×C22⋊C4—134no—
547C2×C22⋊C4—134no—
548C2×C22⋊C4—134no—
549C2×C22⋊C4—134no—
550C2×C22⋊C4—134no—
551C2×C22⋊C4—134no—
552C2×C22⋊C4—134no—
553C2×C22⋊C4—134no—
554C2×C22⋊C4—264no—
555C2×C22⋊C4—264no—
556C2×C22⋊C4—264no—
557C2×C22⋊C4—264no—
558C2×C22⋊C4—264no—
559C2×C22⋊C4—264no—
560C2×C22⋊C4—264no—
561C2×C22⋊C4—264no—
562C2×C22⋊C4—522no—
563C2×C22⋊C4—522no—
564C2×C22⋊C4—522no—
565C2×C22⋊C4C22×D1314yes—
566C2×C22⋊C4C22×D1314yes—
567C2×C22⋊C4C22×D1314yes—
568C2×C42—134no—
569C2×C42—134no—
570C2×C42—134no—
571C2×C42—134no—
572C2×C42—264no—
573C2×C42—264no—
574C2×C42—522no—
575C2×C42—522no—
576#95—134no—
577#95—134no—
578#95—134no—
579#95—134no—
580#95—134no—
581#95—134no—
582C2×C13—44no—
583C2×C13—82no—
584C2×C13#255418yescomplemented
585C2×C13C2×#52911yescharacteristic
586C2×C13C2×#53211yescharacteristic
587C2×C13C2×#53811yescharacteristic
588C2×C13C2×#54611yescharacteristic
589C2×C13C2×#55011yescharacteristic
590C2×C13C2×#55111yescharacteristic
591C2×C13C2×#55311yescharacteristic
592D13—82no—
593C24—22no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24—22no—
603C24—22no—
604C24—22no—
605C24—22no—
606C24—132no—
607C24—262no—
608C24—262no—
609C24—262no—
610C24—262no—
611C24—262no—
612C24—262no—
613C24—262no—
614C24#612914yes—
615C24C23×D1312yes—
616C24C23×D1312yes—
617C24C23×D1311yescharacteristic
618C2×D4—28no—
619C2×D4—28no—
620C2×D4—44no—
621C2×D4—416no—
622C2×D4—268no—
623C2×D4—268no—
624C2×D4—268no—
625C2×D4—524no—
626C2×D4—524no—
627C2×D4—524no—
628C2×D4—5216no—
629C2×D4—5216no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—28no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—28no—
644C22×C4—44no—
645C22×C4—416no—
646C22×C4—134no—
647C22×C4—134no—
648C22×C4—134no—
649C22×C4—132no—
650C22×C4—132no—
651C22×C4—132no—
652C22×C4—132no—
653C22×C4—132no—
654C22×C4—132no—
655C22×C4—132no—
656C22×C4—262no—
657C22×C4—262no—
658C22×C4—262no—
659C22×C4—262no—
660C22×C4—262no—
661C22×C4—262no—
662C22×C4—262no—
663C22×C4—262no—
664C22×C4—262no—
665C22×C4—262no—
666C22×C4—262no—
667C22×C4—262no—
668C22×C4—262no—
669C22×C4—262no—
670C22×C4—262no—
671C22×C4—262no—
672C22×C4—262no—
673C22×C4—262no—
674C22×C4C2×C22⋊D1314yes—
675C22×C4C2×C22⋊D1314yes—
676C22×C4C2×C22⋊D1314yes—
677C22×C4C23×D1312yes—
678C22×C4C23×D1312yes—
679C22×C4C23×D1312yes—
680C22×C4C23×D1312yes—
681C22×C4C23×D1312yes—
682C4⋊C4—28no—
683C4⋊C4—268no—
684C4⋊C4—268no—
685C4⋊C4—268no—
686C4⋊C4—524no—
687C4⋊C4—524no—
688C4⋊C4C2×C22⋊D13116yescomplemented
689C22⋊C4—28no—
690C22⋊C4—28no—
691C22⋊C4—28no—
692C22⋊C4—268no—
693C22⋊C4—268no—
694C22⋊C4—268no—
695C22⋊C4—268no—
696C22⋊C4—268no—
697C22⋊C4—268no—
698C22⋊C4—268no—
699C22⋊C4—268no—
700C22⋊C4—524no—
701C22⋊C4—524no—
702C22⋊C4—524no—
703C42—268no—
704C42—268no—
705C42—524no—
706C42—524no—
707C13C2×#255411yescharacteristic, complemented, Sylow
708C23—28no—
709C23—28no—
710C23—28no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—44no—
725C23—44no—
726C23—44no—
727C23—44no—
728C23—44no—
729C23—44no—
730C23—44no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—262no—
736C23—262no—
737C23—262no—
738C23—262no—
739C23—262no—
740C23—262no—
741C23—262no—
742C23—524no—
743C23—524no—
744C23—524no—
745C23—524no—
746C23—524no—
747C23—524no—
748C23—524no—
749C23C2×#612914yes—
750C23C2×#612912yes—
751C23#8825112yes—
752C23#41×D1312yes—
753C23#41×D1312yes—
754C23#41×D1312yes—
755C23#8825612yes—
756C23C22×C22⋊D1312yes—
757C23C24×D1311yescharacteristic
758D4—416no—
759D4—5216no—
760D4—5216no—
761C2×C4—28no—
762C2×C4—28no—
763C2×C4—28no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—416no—
777C2×C4—44no—
778C2×C4—44no—
779C2×C4—134no—
780C2×C4—134no—
781C2×C4—134no—
782C2×C4—268no—
783C2×C4—268no—
784C2×C4—268no—
785C2×C4—262no—
786C2×C4—262no—
787C2×C4—262no—
788C2×C4—262no—
789C2×C4—262no—
790C2×C4—262no—
791C2×C4—262no—
792C2×C4—262no—
793C2×C4—262no—
794C2×C4—262no—
795C2×C4—262no—
796C2×C4—262no—
797C2×C4—262no—
798C2×C4—262no—
799C2×C4—262no—
800C2×C4—262no—
801C2×C4—262no—
802C2×C4—262no—
803C2×C4—524no—
804C2×C4—524no—
805C2×C4—524no—
806C2×C4—524no—
807C2×C4C22×C22⋊D1314yes—
808C2×C4C22×C22⋊D1314yes—
809C2×C4C22×C22⋊D1314yes—
810C22—24no—
811C22—24no—
812C22—24no—
813C22—42no—
814C22—416no—
815C22—42no—
816C22—42no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—88no—
826C22—522no—
827C22—522no—
828C22—522no—
829C22—522no—
830C22—522no—
831C22—522no—
832C22—522no—
833C22—1048no—
834C22#1171935414yes—
835C22#1171936214yes—
836C22#1171936314yes—
837C22#1171936614yes—
838C22#1171951114yes—
839C22#1171953714yes—
840C22#1171953914yes—
841C22C22×#612911yescharacteristic
842C22C2×#8825111yescharacteristic
843C22C2×#41×D1311yescharacteristic
844C22C2×#41×D1311yescharacteristic
845C22C2×#41×D1311yescharacteristic
846C22C2×#8825611yescharacteristic
847C22C23×C22⋊D1311yescharacteristic
848C4—24no—
849C4—24no—
850C4—24no—
851C4—42no—
852C4—42no—
853C4—264no—
854C4—264no—
855C4—264no—
856C4—522no—
857C4—522no—
858C4—522no—
859C4—522no—
860C2—44no—
861C2—82no—
862C2—1042no—
863C2#1311989218yesdirect product factor
864C2C2×#1171935411yescharacteristic
865C2C2×#1171953711yescharacteristic
866C2C2×#1171936211yescharacteristic
867C2C2×#1171951111yescharacteristic
868C2C2×#1171953911yescharacteristic
869C2C2×#1171936311yescharacteristic
870C2C2×#1171936611yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC22×C13×#123C2
socleC24×C13C24
prime radicalC2×#11718884C2
hypercenterC22×#123D13
hypocenterC13C2×#2554
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. C22×#88152C2semidirect
2. #13119892C2direct (N × H)
3. C2×#11718644C2semidirect
4. C2×#11718609C2semidirect
5. C2×#11718622C2semidirect
7. C2×#11718882C2semidirect
8. C2×#11718618C2semidirect
9. C2×#11718618C2semidirect
10. C2×#11718606C2semidirect
11. C2×#11718651C2semidirect
12. C2×#11718605C2semidirect
13. C2×#11718874C2semidirect
14. C2×C4⋊C4×Dic13C2semidirect
15. C2×C4×C22⋊Dic13C2semidirect
16. C22×C13×#123C2semidirect
22. C2×C13×#123C22semidirect
49. C2×#88152C22semidirect
51. #11718882C22semidirect
52. #11718874C22semidirect
53. C4×C22⋊Dic13C22semidirect
60. #11718651C22semidirect
61. #11718644C22semidirect
62. C4⋊C4×Dic13C22semidirect
63. #11718622C22semidirect
64. #11718618C22semidirect
65. #11718618C22semidirect
66. #11718609C22semidirect
67. #11718606C22semidirect
68. #11718605C22semidirect
102. C2×C13×C4⋊C4D4semidirect
249. C13×C4⋊C4C2×D4semidirect
274. C22×#123D13semidirect
398. C2×#123C2×D13semidirect
537. C2×C4⋊C4C22⋊D13semidirect
584. C2×C13#2554semidirect
688. C4⋊C4C2×C22⋊D13semidirect
707. C13C2×#2554semidirect
863. C2#13119892direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881522
#131198922
C2×#117186442
C2×#117186092
C2×#117186222
C2×#117188842
C2×#117188822
C2×#117186182
C2×#117186062
C2×#117186512
C2×#117186052
C2×#117188742
C2×C4⋊C4×Dic132
C2×C4×C22⋊Dic132
C22×C13×#1232
C2×#255413