Finite Group Databasebeta

← C2×#13119897 #16032993

Subgroups — C2×#13119897 #16032993

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×#88133C211yesmaximal, characteristic, complemented
2C22×#88189C211yesmaximal, characteristic, complemented
3#13119897C2116yesmaximal, direct product factor
4C2×#11718322C211yesmaximal, characteristic, complemented
5C2×#11718609C211yesmaximal, characteristic, complemented
6C2×#11718883C211yesmaximal, characteristic, complemented
7C2×#11718882C211yesmaximal, characteristic, complemented
8C2×#11718882C211yesmaximal, characteristic, complemented
9C2×#11718882C211yesmaximal, characteristic, complemented
10C2×#11718606C211yesmaximal, characteristic, complemented
11C2×#11718612C211yesmaximal, characteristic, complemented
12C2×#11718605C211yesmaximal, characteristic, complemented
13C2×#11718881C211yesmaximal, characteristic, complemented
14C2×#11718310C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×Dic13C211yesmaximal, characteristic, complemented
16C2×C13×#392C211yesmaximal, characteristic
17C23×D4×C13C2211yescharacteristic
18C23×D4×C13C2211yescharacteristic
19C23×D4×C13C2211yescharacteristic
20C24×Dic13C2211yescharacteristic
21C22×C13×C22⋊C4C2211yescharacteristic
22C22×C13×C22⋊C4C2211yescharacteristic
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C22⋊Dic13C2211yescharacteristic
25C22×C22⋊Dic13C2211yescharacteristic
26C22×C22⋊Dic13C2211yescharacteristic
27C22×C22⋊Dic13C2211yescharacteristic
28C22×C22⋊Dic13C2211yescharacteristic
29C22×C22⋊Dic13C2211yescharacteristic
30C22×C22⋊Dic13C2211yescharacteristic
31C22×C22⋊Dic13C2211yescharacteristic
32C22×C22⋊Dic13C2211yescharacteristic
33C22×C22⋊Dic13C2211yescharacteristic
34C22×C22⋊Dic13C2211yescharacteristic
35C2×#88189—28no—
36C2×#88189C2218yescomplemented
37C22×C4⋊Dic13C2211yescharacteristic
38C22×C4⋊Dic13C2211yescharacteristic
39C22×C4⋊Dic13C2211yescharacteristic
40C22×#6101C2211yescharacteristic
41C22×#6101C2211yescharacteristic
42C22×#6101C2211yescharacteristic
43C22×#6101C2211yescharacteristic
44C22×C4×Dic13C2211yescharacteristic
45C22×C4×Dic13C2211yescharacteristic
46C22×C4×Dic13C2211yescharacteristic
47C22×C4×Dic13C2211yescharacteristic
48C2×#88133—28no—
49C2×#88133C2218yescomplemented
50C13×#392C2218yes—
51C2×C13×#95C2211yescharacteristic
52#11718883C2218yescomplemented
53#11718882C2218yescomplemented
54#11718882C2218yescomplemented
55#11718882C2218yescomplemented
56#11718881C2218yescomplemented
57C2×#88071C2211yescharacteristic
58C2×#88071C2211yescharacteristic
59C2×#88071C2211yescharacteristic
60C2×#88071C2211yescharacteristic
61C2×#88071C2211yescharacteristic
62#11718612C2218yescomplemented
63#11718609C2218yescomplemented
64#11718606C2218yescomplemented
65#11718605C2218yescomplemented
66C22⋊C4×Dic13C2218yescomplemented
67#11718322C2218yescomplemented
68#11718310C2218yescomplemented
69C25×C13C2311yescharacteristic
70C25×C13C2311yescharacteristic
71C25×C13C2311yescharacteristic
72C22×D4×C13—24no—
73C22×D4×C13—24no—
74C22×D4×C13—24no—
75C22×D4×C13—24no—
76C22×D4×C13—24no—
77C22×D4×C13—42no—
78C22×D4×C13—42no—
79C22×D4×C13—42no—
80C22×D4×C13—42no—
81C22×D4×C13C2314yes—
82C22×D4×C13C2314yes—
83C22×D4×C13C2314yes—
84C23×C4×C13C2311yescharacteristic
85C23×C4×C13C2311yescharacteristic
86C23×C4×C13C2311yescharacteristic
87C23×C4×C13C2311yescharacteristic
88C23×Dic13—24no—
89C23×Dic13—24no—
90C23×Dic13—42no—
91C23×Dic13C2311yescharacteristic
92C23×Dic13C2311yescharacteristic
93C23×Dic13C2311yescharacteristic
94C23×Dic13C2311yescharacteristic
95C23×Dic13C2311yescharacteristic
96C23×Dic13C2314yes—
97C23×Dic13C2311yescharacteristic
98C23×Dic13C2311yescharacteristic
99C23×Dic13C2311yescharacteristic
100C2×C13×C22⋊C4—24no—
101C2×C13×C22⋊C4—24no—
102C2×C13×C22⋊C4—24no—
103C2×C13×C22⋊C4C2314yes—
104C2×C13×C22⋊C4C2314yes—
105C2×C13×C22⋊C4C2314yes—
106C2×C22⋊Dic13—24no—
107C2×C22⋊Dic13—24no—
108C2×C22⋊Dic13—24no—
109C2×C22⋊Dic13—24no—
110C2×C22⋊Dic13—24no—
111C2×C22⋊Dic13—24no—
112C2×C22⋊Dic13—24no—
113C2×C22⋊Dic13—24no—
114C2×C22⋊Dic13—42no—
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×C22⋊Dic13C2314yes—
124C2×C22⋊Dic13C2314yes—
125C2×C22⋊Dic13C2314yes—
126C2×C22⋊Dic13C2314yes—
127C2×C22⋊Dic13C2314yes—
128#88189—232no—
129C2×C4⋊Dic13—24no—
130C2×C4⋊Dic13—42no—
131C2×C4⋊Dic13—42no—
132C2×C4⋊Dic13C2314yes—
133C2×C4⋊Dic13C2314yes—
134C2×C4⋊Dic13C2314yes—
135C2×#6101—24no—
136C2×#6101—24no—
137C2×#6101—24no—
138C2×#6101D418yescomplemented
139C2×#6101C2314yes—
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#88133—232no—
152C13×#95C2314yes—
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—22no—
173C24×C13—22no—
174C24×C13—22no—
175C24×C13—22no—
176C24×C13—22no—
177C24×C13—22no—
178C24×C13—22no—
179C24×C13#4114yes—
180C24×C13C2412yes—
181C24×C13C2412yes—
182C24×C13C2412yes—
183C24×C13C2411yescharacteristic
184C2×D4×C13—28no—
185C2×D4×C13—28no—
186C2×D4×C13—28no—
187C2×D4×C13—28no—
188C2×D4×C13—28no—
189C2×D4×C13—44no—
190C2×D4×C13—44no—
191C2×D4×C13—44no—
192C2×D4×C13—44no—
193C2×D4×C13—416no—
194C2×D4×C13—416no—
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—22no—
203C22×C4×C13—22no—
204C22×C4×C13—22no—
205C22×C4×C13C2×D414yes—
206C22×C4×C13#4114yes—
207C22×C4×C13#4114yes—
208C22×C4×C13C2412yes—
209C22×C4×C13C2412yes—
210C22×C4×C13C2412yes—
211C22×C4×C13C2412yes—
212C22×Dic13—22no—
213C22×Dic13—22no—
214C22×Dic13—22no—
215C22×Dic13—22no—
216C22×Dic13—22no—
217C22×Dic13—22no—
218C22×Dic13—22no—
219C22×Dic13—22no—
220C22×Dic13—22no—
221C22×Dic13—22no—
222C22×Dic13—22no—
223C22×Dic13—22no—
224C22×Dic13—22no—
225C22×Dic13—22no—
226C22×Dic13—28no—
227C22×Dic13—22no—
228C22×Dic13—22no—
229C22×Dic13—22no—
230C22×Dic13—22no—
231C22×Dic13—22no—
232C22×Dic13—22no—
233C22×Dic13—22no—
234C22×Dic13—28no—
235C22×Dic13—44no—
236C22×Dic13—416no—
237C22×Dic13C2×D414yes—
238C22×Dic13C2×D414yes—
239C22×Dic13#4114yes—
240C22×Dic13C2412yes—
241C22×Dic13C2412yes—
242C22×Dic13C2412yes—
243C22×Dic13C2412yes—
244C22×Dic13C2412yes—
245C22×Dic13C2412yes—
246C22×Dic13C2412yes—
247C22×Dic13C2412yes—
248C13×C22⋊C4—28no—
249C13×C22⋊C4—28no—
250C13×C22⋊C4—28no—
251C22⋊Dic13—28no—
252C22⋊Dic13—28no—
253C22⋊Dic13—28no—
254C22⋊Dic13—28no—
255C22⋊Dic13—28no—
256C22⋊Dic13—28no—
257C22⋊Dic13—28no—
258C22⋊Dic13—28no—
259C22⋊Dic13—44no—
260C22⋊Dic13—44no—
261C22⋊Dic13—44no—
262C4⋊Dic13—28no—
263C4⋊Dic13—44no—
264C4⋊Dic13—44no—
265#6101—28no—
266#6101—28no—
267#6101—28no—
268#6101C2×D4116yescomplemented
269C4×Dic13—28no—
270C4×Dic13—28no—
271C4×Dic13—44no—
272C4×Dic13—44no—
273C22×#126—131no—
274C22×#123—131no—
275#2554—1316no—
276C2×#398—131no—
277C2×#396—131no—
278C2×#394—131no—
279C2×#392D1311yescharacteristic
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—22no—
306C23×C13—22no—
307C23×C13—22no—
308C23×C13—22no—
309C23×C13—22no—
310C23×C13—22no—
311C23×C13—22no—
312C23×C13—44no—
313C23×C13—44no—
314C23×C13—44no—
315C23×C13—44no—
316C23×C13—44no—
317C23×C13—44no—
318C23×C13—44no—
319C23×C13—44no—
320C23×C13—44no—
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×C13—44no—
330C23×C13C22×D412yes—
331C23×C13C2×#4114yes—
332C23×C13C2×#4112yes—
333C23×C13C2×#4112yes—
334C23×C13C2×#4112yes—
335C23×C13C2×#4112yes—
336C23×C13H(5,𝔽2)12yes—
337C23×C13H(5,𝔽2)12yes—
338C23×C13C2511yescharacteristic
339D4×C13—416no—
340D4×C13—416no—
341D4×C13—416no—
342C2×C4×C13—28no—
343C2×C4×C13—28no—
344C2×C4×C13—28no—
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—44no—
355C2×C4×C13C22×D414yes—
356C2×C4×C13C2×#4114yes—
357C2×C4×C13C2×#4114yes—
358C2×Dic13—28no—
359C2×Dic13—28no—
360C2×Dic13—28no—
361C2×Dic13—22no—
362C2×Dic13—22no—
363C2×Dic13—22no—
364C2×Dic13—22no—
365C2×Dic13—22no—
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—416no—
383C2×Dic13—44no—
384C2×Dic13—44no—
385C2×Dic13—44no—
386C2×Dic13—44no—
387C2×Dic13—44no—
388C2×Dic13C22×D414yes—
389C2×Dic13C22×D414yes—
390C2×Dic13C2×#4114yes—
391C23×D4C2×D1311yescharacteristic
392C23×D4C2×D1311yescharacteristic
393C23×D4C2×D1311yescharacteristic
394C24×C4—131no—
395C2×#126—138no—
396C2×#126—268no—
397C2×#123—138no—
398C2×#123—268no—
399C22×C4⋊C4—131no—
400C22×C4⋊C4—131no—
401C22×C4⋊C4—131no—
402C22×C4⋊C4—131no—
403C22×C4⋊C4—131no—
404C22×C4⋊C4—131no—
405C22×C4⋊C4—131no—
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#392C2×D1318yes—
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×#95C2×D1311yescharacteristic
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—42no—
459C22×C13—42no—
460C22×C13—42no—
461C22×C13—42no—
462C22×C13—42no—
463C22×C13—42no—
464C22×C13—42no—
465C22×C13—88no—
466C22×C13—88no—
467C22×C13#52914yes—
468C22×C13#53214yes—
469C22×C13#53814yes—
470C22×C13#54614yes—
471C22×C13#55014yes—
472C22×C13#55114yes—
473C22×C13#55314yes—
474C22×C13C23×D411yescharacteristic
475C22×C13C22×#4111yescharacteristic
476C22×C13C22×#4111yescharacteristic
477C22×C13C22×#4111yescharacteristic
478C22×C13C22×#4111yescharacteristic
479C22×C13C2×H(5,𝔽2)11yescharacteristic
480C22×C13C2×H(5,𝔽2)11yescharacteristic
481C4×C13—24no—
482C4×C13—24no—
483C4×C13—24no—
484C4×C13—42no—
485Dic13—24no—
486Dic13—24no—
487Dic13—24no—
488Dic13—42no—
489Dic13—42no—
490Dic13—42no—
491Dic13—42no—
492Dic13—42no—
493C25C22×D1311yescharacteristic
494C25C22×D1311yescharacteristic
495C25C22×D1311yescharacteristic
496C22×D4—24no—
497C22×D4—24no—
498C22×D4—24no—
499C22×D4—24no—
500C22×D4—24no—
501C22×D4—42no—
502C22×D4—42no—
503C22×D4—42no—
504C22×D4—42no—
505C22×D4C22×D1314yes—
506C22×D4C22×D1314yes—
507C22×D4C22×D1314yes—
508C23×C4—131no—
509C23×C4—131no—
510C23×C4—131no—
511C23×C4—131no—
512C23×C4—131no—
513C23×C4—131no—
514C23×C4—131no—
515C23×C4—131no—
516C23×C4—134no—
517C23×C4—264no—
518C23×C4—264no—
519C23×C4—522no—
520C23×C4C22×D1311yescharacteristic
521C23×C4C22×D1311yescharacteristic
522C23×C4C22×D1311yescharacteristic
523C23×C4C22×D1311yescharacteristic
524#126—2632no—
525#123—2632no—
526C2×C4⋊C4—138no—
527C2×C4⋊C4—134no—
528C2×C4⋊C4—134no—
529C2×C4⋊C4—134no—
530C2×C4⋊C4—134no—
531C2×C4⋊C4—134no—
532C2×C4⋊C4—134no—
533C2×C4⋊C4—134no—
534C2×C4⋊C4—264no—
535C2×C4⋊C4—264no—
536C2×C4⋊C4—264no—
537C2×C4⋊C4—264no—
538C2×C4⋊C4—522no—
539C2×C4⋊C4—522no—
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#95C22×D1314yes—
582C2×C13—44no—
583C2×C13—82no—
584C2×C13—82no—
585C2×C13#255418yescomplemented
586C2×C13C2×#52911yescharacteristic
587C2×C13C2×#53211yescharacteristic
588C2×C13C2×#53811yescharacteristic
589C2×C13C2×#54611yescharacteristic
590C2×C13C2×#55011yescharacteristic
591C2×C13C2×#55111yescharacteristic
592C2×C13C2×#55311yescharacteristic
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—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24#612914yes—
614C24C23×D1312yes—
615C24C23×D1312yes—
616C24C23×D1312yes—
617C24C23×D1311yescharacteristic
618C2×D4—28no—
619C2×D4—28no—
620C2×D4—28no—
621C2×D4—28no—
622C2×D4—28no—
623C2×D4—44no—
624C2×D4—44no—
625C2×D4—44no—
626C2×D4—44no—
627C2×D4—416no—
628C2×D4—416no—
629C2×D4—416no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—134no—
640C22×C4—134no—
641C22×C4—134no—
642C22×C4—132no—
643C22×C4—132no—
644C22×C4—132no—
645C22×C4—132no—
646C22×C4—132no—
647C22×C4—132no—
648C22×C4—132no—
649C22×C4—132no—
650C22×C4—268no—
651C22×C4—262no—
652C22×C4—262no—
653C22×C4—262no—
654C22×C4—262no—
655C22×C4—262no—
656C22×C4—262no—
657C22×C4—262no—
658C22×C4—262no—
659C22×C4—262no—
660C22×C4—262no—
661C22×C4—262no—
662C22×C4—268no—
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—524no—
674C22×C4—5216no—
675C22×C4D4×D1314yes—
676C22×C4#612914yes—
677C22×C4#612914yes—
678C22×C4C23×D1312yes—
679C22×C4C23×D1312yes—
680C22×C4C23×D1312yes—
681C22×C4C23×D1312yes—
682C4⋊C4—1316no—
683C4⋊C4—268no—
684C4⋊C4—268no—
685C4⋊C4—268no—
686C4⋊C4—268no—
687C4⋊C4—524no—
688C4⋊C4—524no—
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—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—44no—
739C23—44no—
740C23—44no—
741C23—44no—
742C23—44no—
743C23—44no—
744C23—44no—
745C23—44no—
746C23—44no—
747C23—44no—
748C23—44no—
749C23C2×D4×D1312yes—
750C23C2×#612914yes—
751C23C2×#612912yes—
752C23C2×#612912yes—
753C23C2×#612912yes—
754C23#8825112yes—
755C23#8825112yes—
756C23#41×D1312yes—
757C23C24×D1311yescharacteristic
758D4—416no—
759D4—416no—
760D4—416no—
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—44no—
774C2×C4—134no—
775C2×C4—134no—
776C2×C4—134no—
777C2×C4—268no—
778C2×C4—268no—
779C2×C4—262no—
780C2×C4—262no—
781C2×C4—262no—
782C2×C4—262no—
783C2×C4—262no—
784C2×C4—262no—
785C2×C4—268no—
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—5216no—
802C2×C4—524no—
803C2×C4—524no—
804C2×C4—524no—
805C2×C4—524no—
806C2×C4—524no—
807C2×C4C2×D4×D1314yes—
808C2×C4C2×#612914yes—
809C2×C4C2×#612914yes—
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—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—88no—
833C22—88no—
834C22#1171929214yes—
835C22#1171929614yes—
836C22#1171929814yes—
837C22#1171930414yes—
838C22#1171930514yes—
839C22#1171931914yes—
840C22#1171942114yes—
841C22C22×D4×D1311yescharacteristic
842C22C22×#612911yescharacteristic
843C22C22×#612911yescharacteristic
844C22C22×#612911yescharacteristic
845C22C2×#8825111yescharacteristic
846C22C2×#8825111yescharacteristic
847C22C2×#41×D1311yescharacteristic
848C4—24no—
849C4—24no—
850C4—24no—
851C4—42no—
852C4—264no—
853C4—264no—
854C4—264no—
855C4—522no—
856C4—522no—
857C4—522no—
858C4—522no—
859C4—522no—
860C2—44no—
861C2—82no—
862C2—82no—
863C2#1311989718yesdirect product factor
864C2C2×#1171930511yescharacteristic
865C2C2×#1171942111yescharacteristic
866C2C2×#1171929811yescharacteristic
867C2C2×#1171929611yescharacteristic
868C2C2×#1171930411yescharacteristic
869C2C2×#1171929211yescharacteristic
870C2C2×#1171931911yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
Fitting, prime radicalC2×C13×#392C2
socleC24×C13C24
hypercenterC2×#392D13
hypocenterC13C2×#2554
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C22×#88133C2semidirect
2. C22×#88189C2semidirect
3. #13119897C2direct (N × H)
4. C2×#11718322C2semidirect
5. C2×#11718609C2semidirect
6. C2×#11718883C2semidirect
7. C2×#11718882C2semidirect
8. C2×#11718882C2semidirect
9. C2×#11718882C2semidirect
10. C2×#11718606C2semidirect
11. C2×#11718612C2semidirect
12. C2×#11718605C2semidirect
13. C2×#11718881C2semidirect
14. C2×#11718310C2semidirect
15. C2×C22⋊C4×Dic13C2semidirect
36. C2×#88189C22semidirect
49. C2×#88133C22semidirect
52. #11718883C22semidirect
53. #11718882C22semidirect
54. #11718882C22semidirect
55. #11718882C22semidirect
56. #11718881C22semidirect
62. #11718612C22semidirect
63. #11718609C22semidirect
64. #11718606C22semidirect
65. #11718605C22semidirect
66. C22⋊C4×Dic13C22semidirect
67. #11718322C22semidirect
68. #11718310C22semidirect
138. C2×#6101D4semidirect
268. #6101C2×D4semidirect
585. C2×C13#2554semidirect
707. C13C2×#2554semidirect
863. C2#13119897direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881332
C22×#881892
#131198972
C2×#117183222
C2×#117186092
C2×#117188832
C2×#117188822
C2×#117186062
C2×#117186122
C2×#117186052
C2×#117188812
C2×#117183102
C2×C22⋊C4×Dic132
C2×C13×#3922
C2×#255413