Finite Group Databasebeta

← C2×#13120977 #16029648

Subgroups — C2×#13120977 #16029648

Order 3328.

3002 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×#88139C211yesmaximal, characteristic, complemented
3#13120977C2116yesmaximal, direct product factor
4C2×#11718609C211yesmaximal, characteristic, complemented
5C2×#11718655C211yesmaximal, characteristic, complemented
6C2×#11718640C211yesmaximal, characteristic, complemented
7C2×#11718620C211yesmaximal, characteristic, complemented
8C2×#11718620C211yesmaximal, characteristic, complemented
9C2×#11718883C211yesmaximal, characteristic, complemented
10C2×#11718608C211yesmaximal, characteristic, complemented
11C2×#11718884C211yesmaximal, characteristic
12C2×#11718618C211yesmaximal, characteristic, complemented
13C2×#11718606C211yesmaximal, characteristic, complemented
14C2×#11718601C211yesmaximal, characteristic, complemented
15C2×C4×#6101C211yesmaximal, characteristic, complemented
16C2×C13×#390C211yesmaximal, characteristic, complemented
17C23×D4×C13C2211yescharacteristic
18C23×C22⋊D13C2211yescharacteristic
19C23×C22⋊D13C2211yescharacteristic
20C23×Dic26C2211yescharacteristic
21C22×C13×C4⋊C4C2211yescharacteristic
22C22×C13×C22⋊C4C2211yescharacteristic
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C13×C22⋊C4C2211yescharacteristic
26C22×C42×C13C2211yescharacteristic
27C22×C22⋊Dic13C2211yescharacteristic
28C22×C22⋊Dic13C2211yescharacteristic
29C22×C22⋊Dic13C2211yescharacteristic
30C22×C22⋊Dic13C2211yescharacteristic
31C22×C22⋊Dic13C2211yescharacteristic
32C22×C22⋊Dic13C2211yescharacteristic
33C22×#6103C2211yescharacteristic
34C22×#6103C2211yescharacteristic
35C22×#6103C2211yescharacteristic
36C22×#6103C2211yescharacteristic
37C22×#6103C2211yescharacteristic
38C22×C4⋊Dic13C2211yescharacteristic
39C22×#6101C2211yescharacteristic
40C22×#6101C2211yescharacteristic
41C22×#6101C2211yescharacteristic
42C22×#6101C2211yescharacteristic
43C22×#6101C2211yescharacteristic
44C22×C4×Dic13C2211yescharacteristic
45C22×C4×Dic13C2211yescharacteristic
46C2×#88139—28no—
47C2×#88139C2218yescomplemented
48C2×#88133—28no—
49C2×#88133C2218yescomplemented
50C13×#390C2218yescomplemented
51#11718884C2218yes—
52#11718883C2218yescomplemented
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57C2×#88071C2211yescharacteristic
58C2×#88071C2211yescharacteristic
59#11718655C2218yescomplemented
60#11718640C2218yescomplemented
61#11718620C2218yescomplemented
62#11718620C2218yescomplemented
63#11718618C2218yescomplemented
64#11718609C2218yescomplemented
65#11718608C2218yescomplemented
66#11718606C2218yescomplemented
67#11718601C2218yescomplemented
68C4×#6101C2218yescomplemented
69C25×C13C2311yescharacteristic
70C25×C13C2311yescharacteristic
71C24×D13C2311yescharacteristic
72C22×D4×C13—24no—
73C22×D4×C13—42no—
74C22×D4×C13—42no—
75C22×D4×C13C2314yes—
76C23×C4×C13C2311yescharacteristic
77C23×C4×C13C2311yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C23×C4×C13C2311yescharacteristic
80C23×C4×C13C2311yescharacteristic
81C22×C22⋊D13—24no—
82C22×C22⋊D13—24no—
83C22×C22⋊D13—42no—
84C22×C22⋊D13—42no—
85C22×C22⋊D13—42no—
86C22×C22⋊D13—42no—
87C22×C22⋊D13C2314yes—
88C22×C22⋊D13C2314yes—
89C23×Dic13C2311yescharacteristic
90C23×Dic13C2311yescharacteristic
91C23×Dic13C2311yescharacteristic
92C23×Dic13C2311yescharacteristic
93C23×Dic13C2311yescharacteristic
94C23×Dic13C2311yescharacteristic
95C23×Dic13C2311yescharacteristic
96C22×Dic26—24no—
97C22×Dic26—42no—
98C22×Dic26—42no—
99C22×Dic26C2314yes—
100C2×C13×C4⋊C4—42no—
101C2×C13×C4⋊C4C2314yes—
102C2×C13×C22⋊C4—24no—
103C2×C13×C22⋊C4—24no—
104C2×C13×C22⋊C4—42no—
105C2×C13×C22⋊C4—42no—
106C2×C13×C22⋊C4C2314yes—
107C2×C13×C22⋊C4C2314yes—
108C2×C13×C22⋊C4C2314yes—
109C2×C13×C22⋊C4C2314yes—
110C2×C42×C13—42no—
111C2×C42×C13C2314yes—
112C2×C22⋊Dic13—24no—
113C2×C22⋊Dic13—24no—
114C2×C22⋊Dic13—24no—
115C2×C22⋊Dic13—24no—
116C2×C22⋊Dic13—42no—
117C2×C22⋊Dic13—42no—
118C2×C22⋊Dic13C2314yes—
119C2×C22⋊Dic13C2314yes—
120C2×C22⋊Dic13C2314yes—
121C2×C22⋊Dic13C2314yes—
122C2×C22⋊Dic13C2314yes—
123C2×C22⋊Dic13C2314yes—
124C2×#6103—24no—
125C2×#6103—24no—
126C2×#6103—24no—
127C2×#6103—42no—
128C2×#6103—42no—
129C2×#6103C2314yes—
130C2×#6103C2314yes—
131C2×#6103C2314yes—
132C2×#6103C2314yes—
133C2×#6103C2314yes—
134C2×C4⋊Dic13—24no—
135C2×C4⋊Dic13C2314yes—
136C2×#6101—24no—
137C2×#6101—24no—
138C2×#6101—24no—
139C2×#6101—24no—
140C2×#6101—42no—
141C2×#6101C2314yes—
142C2×#6101C2314yes—
143C2×#6101C2314yes—
144C2×#6101C2314yes—
145C2×#6101C2314yes—
146C2×C4×Dic13—42no—
147C2×C4×Dic13D418yescomplemented
148C2×C4×Dic13C2314yes—
149C2×C4×Dic13C2314yes—
150#88139—232no—
151#88133—232no—
152#88071C2314yes—
153#88071C2314yes—
154#88071C2314yes—
155#88071C2314yes—
156#88071C2314yes—
157#88071C2314yes—
158C2×#2662—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×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—44no—
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—22no—
198C22×C4×C13—22no—
199C22×C4×C13—22no—
200C22×C4×C13—22no—
201C22×C4×C13C2×D414yes—
202C22×C4×C13#4114yes—
203C22×C4×C13C2412yes—
204C22×C4×C13C2412yes—
205C22×C4×C13C2412yes—
206C22×C4×C13C2412yes—
207C22×C4×C13C2412yes—
208C2×C22⋊D13—28no—
209C2×C22⋊D13—28no—
210C2×C22⋊D13—44no—
211C2×C22⋊D13—44no—
212C2×C22⋊D13—44no—
213C2×C22⋊D13—44no—
214C2×C22⋊D13—416no—
215C2×C22⋊D13—416no—
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—22no—
227C22×Dic13—22no—
228C22×Dic13—22no—
229C22×Dic13—22no—
230C22×Dic13—22no—
231C22×Dic13—22no—
232C22×Dic13—22no—
233C22×Dic13—22no—
234C22×Dic13C2×D414yes—
235C22×Dic13C2×D414yes—
236C22×Dic13#4114yes—
237C22×Dic13C2412yes—
238C22×Dic13C2412yes—
239C22×Dic13C2412yes—
240C22×Dic13C2412yes—
241C22×Dic13C2412yes—
242C22×Dic13C2412yes—
243C22×Dic13C2412yes—
244C2×Dic26—28no—
245C2×Dic26—44no—
246C2×Dic26—44no—
247C2×Dic26—416no—
248C13×C4⋊C4—44no—
249C13×C22⋊C4—28no—
250C13×C22⋊C4—28no—
251C13×C22⋊C4—44no—
252C13×C22⋊C4—44no—
253C42×C13—44no—
254C22⋊Dic13—28no—
255C22⋊Dic13—28no—
256C22⋊Dic13—28no—
257C22⋊Dic13—28no—
258C22⋊Dic13—44no—
259C22⋊Dic13—44no—
260#6103—28no—
261#6103—28no—
262#6103—28no—
263#6103—44no—
264#6103—44no—
265C4⋊Dic13—28no—
266#6101—28no—
267#6101—28no—
268#6101—28no—
269#6101—28no—
270#6101—44no—
271C4×Dic13—44no—
272C4×Dic13C2×D4116yescomplemented
273C22×#126—131no—
274C22×#124—131no—
275#2662—1316no—
276C2×#396—131no—
277C2×#396—131no—
278C2×#395—131no—
279C2×#394—131no—
280C2×#394—131no—
281C2×#394—131no—
282C2×#393—131no—
283C2×#392—131no—
284C2×#390—131no—
285C2×#390D1311yescharacteristic, complemented
286C2×#388—131no—
287C2×#388—131no—
288C2×C4×C4⋊C4—131no—
289C23×C13—22no—
290C23×C13—22no—
291C23×C13—22no—
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—44no—
304C23×C13—44no—
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×C13—44no—
317C23×C13C22×D412yes—
318C23×C13C2×#4112yes—
319C23×C13C2×#4112yes—
320C23×C13H(5,𝔽2)12yes—
321C23×C13H(5,𝔽2)12yes—
322C23×C13H(5,𝔽2)12yes—
323C23×C132−1+412yes—
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—22no—
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—44no—
356C2×C4×C13—44no—
357C2×C4×C13—44no—
358C2×C4×C13C22×D414yes—
359C2×C4×C13C2×#4114yes—
360C22⋊D13—416no—
361C22⋊D13—416no—
362C2×Dic13—28no—
363C2×Dic13—28no—
364C2×Dic13—28no—
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—22no—
383C2×Dic13—44no—
384C2×Dic13—44no—
385C2×Dic13—44no—
386C2×Dic13—44no—
387C2×Dic13C22×D414yes—
388C2×Dic13C22×D414yes—
389C2×Dic13C2×#4114yes—
390Dic26—416no—
391C23×Q8—131no—
392C23×D4—131no—
393C23×D4—131no—
394C23×D4C2×D1311yescharacteristic
395C2×#126—138no—
396C2×#126—268no—
397C2×#124—138no—
398C2×#124—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⋊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×C22⋊C4C2×D1311yescharacteristic
421C22×C42—131no—
422C22×C42—131no—
423C22×C42C2×D1311yescharacteristic
424#396—138no—
425#396—138no—
426#395—138no—
427#394—138no—
428#394—138no—
429#394—138no—
430#393—138no—
431#392—138no—
432#390—138no—
433#390C2×D1318yescomplemented
434#388—138no—
435#388—138no—
436C4×C4⋊C4—138no—
437C2×#95—131no—
438C2×#95—131no—
439C2×#95—131no—
440C2×#95—131no—
441C2×#95—131no—
442C2×#95—131no—
443C22×C13—42no—
444C22×C13—42no—
445C22×C13—42no—
446C22×C13—42no—
447C22×C13—42no—
448C22×C13—42no—
449C22×C13—42no—
450C22×C13—42no—
451C22×C13—42no—
452C22×C13—42no—
453C22×C13—42no—
454C22×C13—42no—
455C22×C13—42no—
456C22×C13—42no—
457C22×C13—88no—
458C22×C13—88no—
459C22×C13#53214yes—
460C22×C13#53514yes—
461C22×C13#53714yes—
462C22×C13#53814yes—
463C22×C13#53814yes—
464C22×C13#54214yes—
465C22×C13#54214yes—
466C22×C13C23×D411yescharacteristic
467C22×C13C22×#4111yescharacteristic
468C22×C13C22×#4111yescharacteristic
469C22×C13C2×H(5,𝔽2)11yescharacteristic
470C22×C13C2×H(5,𝔽2)11yescharacteristic
471C22×C13C2×H(5,𝔽2)11yescharacteristic
472C22×C13C2×2−1+411yescharacteristic
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—42no—
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×Q8—134no—
497C22×Q8—264no—
498C22×Q8—522no—
499C22×Q8—522no—
500C22×D4—24no—
501C22×D4—42no—
502C22×D4—42no—
503C22×D4—134no—
504C22×D4—134no—
505C22×D4—264no—
506C22×D4—264no—
507C22×D4—522no—
508C22×D4—522no—
509C22×D4—522no—
510C22×D4—522no—
511C22×D4C22×D1314yes—
512C23×C4—131no—
513C23×C4—131no—
514C23×C4—131no—
515C23×C4—131no—
516C23×C4—131no—
517C23×C4—131no—
518C23×C4—131no—
519C23×C4C22×D1311yescharacteristic
520C23×C4C22×D1311yescharacteristic
521C23×C4C22×D1311yescharacteristic
522C23×C4C22×D1311yescharacteristic
523C23×C4C22×D1311yescharacteristic
524#126—2632no—
525#124—2632no—
526C2×C4⋊C4—42no—
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—264no—
534C2×C4⋊C4—264no—
535C2×C4⋊C4—264no—
536C2×C4⋊C4—264no—
537C2×C4⋊C4—264no—
538C2×C4⋊C4—522no—
539C2×C4⋊C4C22×D1314yes—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—24no—
542C2×C22⋊C4—42no—
543C2×C22⋊C4—42no—
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—134no—
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⋊C4—522no—
566C2×C22⋊C4C22×D1314yes—
567C2×C22⋊C4C22×D1314yes—
568C2×C22⋊C4C22×D1314yes—
569C2×C22⋊C4C22×D1314yes—
570C2×C42—42no—
571C2×C42—138no—
572C2×C42—134no—
573C2×C42—134no—
574C2×C42—522no—
575C2×C42C22×D1314yes—
576#95—134no—
577#95—134no—
578#95—134no—
579#95—134no—
580#95—134no—
581#95—134no—
582C2×C13—82no—
583C2×C13—82no—
584C2×C13#266218yescomplemented
585C2×C13C2×#53211yescharacteristic
586C2×C13C2×#53511yescharacteristic
587C2×C13C2×#53711yescharacteristic
588C2×C13C2×#53811yescharacteristic
589C2×C13C2×#53811yescharacteristic
590C2×C13C2×#54211yescharacteristic
591C2×C13C2×#54211yescharacteristic
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—22no—
607C24—132no—
608C24—262no—
609C24—262no—
610C24—262no—
611C24—262no—
612C24—262no—
613C24—262no—
614C24—262no—
615C24C23×D1312yes—
616C24C23×D1312yes—
617C24C23×D1311yescharacteristic
618C2×Q8—268no—
619C2×Q8—524no—
620C2×Q8—524no—
621C2×Q8—5216no—
622C2×D4—28no—
623C2×D4—44no—
624C2×D4—44no—
625C2×D4—416no—
626C2×D4—268no—
627C2×D4—268no—
628C2×D4—524no—
629C2×D4—524no—
630C2×D4—524no—
631C2×D4—524no—
632C2×D4—5216no—
633C2×D4—5216no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—134no—
648C22×C4—134no—
649C22×C4—134no—
650C22×C4—132no—
651C22×C4—132no—
652C22×C4—132no—
653C22×C4—132no—
654C22×C4—132no—
655C22×C4—132no—
656C22×C4—132no—
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×C4—262no—
675C22×C4#612714yes—
676C22×C4D4×D1314yes—
677C22×C4C23×D1312yes—
678C22×C4C23×D1312yes—
679C22×C4C23×D1312yes—
680C22×C4C23×D1312yes—
681C22×C4C23×D1312yes—
682C4⋊C4—44no—
683C4⋊C4—268no—
684C4⋊C4—268no—
685C4⋊C4—268no—
686C4⋊C4—268no—
687C4⋊C4—268no—
688C4⋊C4—524no—
689C22⋊C4—28no—
690C22⋊C4—28no—
691C22⋊C4—44no—
692C22⋊C4—44no—
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—
703C22⋊C4—524no—
704C42—44no—
705C42—1316no—
706C42—524no—
707C13C2×#266211yescharacteristic, complemented, Sylow
708C23—22no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—44no—
723C23—44no—
724C23—44no—
725C23—44no—
726C23—44no—
727C23—44no—
728C23—44no—
729C23—44no—
730C23—44no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—262no—
737C23—262no—
738C23—262no—
739C23—262no—
740C23—262no—
741C23—262no—
742C23—262no—
743C23—524no—
744C23—524no—
745C23—524no—
746C23—524no—
747C23—524no—
748C23—524no—
749C23—524no—
750C23C2×#612712yes—
751C23C2×D4×D1312yes—
752C23#8825112yes—
753C23#8825112yes—
754C23#8825112yes—
755C23#41×D1312yes—
756C23#8825712yes—
757C23C24×D1311yescharacteristic
758Q8—5216no—
759D4—416no—
760D4—5216no—
761D4—5216no—
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—22no—
777C2×C4—44no—
778C2×C4—44no—
779C2×C4—44no—
780C2×C4—134no—
781C2×C4—134no—
782C2×C4—134no—
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—268no—
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—262no—
804C2×C4—524no—
805C2×C4—524no—
806C2×C4—524no—
807C2×C4—524no—
808C2×C4C2×#612714yes—
809C2×C4C2×D4×D1314yes—
810C22—42no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—88no—
825C22—88no—
826C22—522no—
827C22—522no—
828C22—522no—
829C22—522no—
830C22—522no—
831C22—522no—
832C22—522no—
833C22—1048no—
834C22#1171919914yes—
835C22#1171925314yes—
836C22#1171926614yes—
837C22#1171930214yes—
838C22#1171931814yes—
839C22#1171937414yes—
840C22#1171942014yes—
841C22C22×#612711yescharacteristic
842C22C22×D4×D1311yescharacteristic
843C22C2×#8825111yescharacteristic
844C22C2×#8825111yescharacteristic
845C22C2×#8825111yescharacteristic
846C22C2×#41×D1311yescharacteristic
847C22C2×#8825711yescharacteristic
848C4—24no—
849C4—24no—
850C4—42no—
851C4—42no—
852C4—42no—
853C4—264no—
854C4—264no—
855C4—264no—
856C4—522no—
857C4—522no—
858C4—522no—
859C4—522no—
860C2—82no—
861C2—82no—
862C2—1042no—
863C2#1312097718yesdirect product factor
864C2C2×#1171925311yescharacteristic
865C2C2×#1171942011yescharacteristic
866C2C2×#1171930211yescharacteristic
867C2C2×#1171931811yescharacteristic
868C2C2×#1171919911yescharacteristic
869C2C2×#1171937411yescharacteristic
870C2C2×#1171926611yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#390C2
socleC24×C13C24
prime radicalC2×#11718884C2
hypercenterC2×#390D13
hypocenterC13C2×#2662
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
1. C22×#88133C2semidirect
2. C22×#88139C2semidirect
3. #13120977C2direct (N × H)
4. C2×#11718609C2semidirect
5. C2×#11718655C2semidirect
6. C2×#11718640C2semidirect
7. C2×#11718620C2semidirect
8. C2×#11718620C2semidirect
9. C2×#11718883C2semidirect
10. C2×#11718608C2semidirect
12. C2×#11718618C2semidirect
13. C2×#11718606C2semidirect
14. C2×#11718601C2semidirect
15. C2×C4×#6101C2semidirect
16. C2×C13×#390C2semidirect
47. C2×#88139C22semidirect
49. C2×#88133C22semidirect
50. C13×#390C22semidirect
52. #11718883C22semidirect
59. #11718655C22semidirect
60. #11718640C22semidirect
61. #11718620C22semidirect
62. #11718620C22semidirect
63. #11718618C22semidirect
64. #11718609C22semidirect
65. #11718608C22semidirect
66. #11718606C22semidirect
67. #11718601C22semidirect
68. C4×#6101C22semidirect
147. C2×C4×Dic13D4semidirect
272. C4×Dic13C2×D4semidirect
285. C2×#390D13semidirect
433. #390C2×D13semidirect
584. C2×C13#2662semidirect
707. C13C2×#2662semidirect
863. C2#13120977direct (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×#881392
#131209772
C2×#117186092
C2×#117186552
C2×#117186402
C2×#117186202
C2×#117188832
C2×#117186082
C2×#117188842
C2×#117186182
C2×#117186062
C2×#117186012
C2×C4×#61012
C2×C13×#3902
C2×#266213