Finite Group Databasebeta

← C2×#13118497 #16030342

Subgroups — C2×#13118497 #16030342

Order 3328.

4926 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88178C211yesmaximal, characteristic, complemented
2C22×#88132C211yesmaximal, characteristic, complemented
3C23×C22⋊Dic13C211yesmaximal, characteristic
4#13118497C2116yesmaximal, direct product factor
5C2×#11718610C211yesmaximal, characteristic, complemented
6C2×#11718609C211yesmaximal, characteristic, complemented
7C2×#11718609C211yesmaximal, characteristic, complemented
8C2×#11718608C211yesmaximal, characteristic, complemented
9C2×#11718611C211yesmaximal, characteristic, complemented
10C2×#11718871C211yesmaximal, characteristic, complemented
11C2×#11718871C211yesmaximal, characteristic, complemented
12C2×#11718607C211yesmaximal, characteristic, complemented
13C2×#11718873C211yesmaximal, characteristic, complemented
14C2×#11718603C211yesmaximal, characteristic, complemented
15C2×#11718908C211yesmaximal, characteristic
16C23×C13×C22⋊C4C211yesmaximal, characteristic
17C26×C13C2211yescharacteristic
18C24×C4×C13C2211yescharacteristic
19C24×C4×C13C2211yescharacteristic
20C24×Dic13C2211yescharacteristic
21C24×Dic13C2211yescharacteristic
22C23×Dic26C2211yescharacteristic, complemented
23C22×C13×C22⋊C4—28no—
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C13×C22⋊C4C2218yes—
26C22×C13×C22⋊C4C2211yescharacteristic
27C22×C13×C22⋊C4C2211yescharacteristic
28C22×C13×C22⋊C4C2211yescharacteristic
29C22×C22⋊Dic13—28no—
30C22×C22⋊Dic13C2211yescharacteristic
31C22×C22⋊Dic13C2211yescharacteristic
32C22×C22⋊Dic13C2211yescharacteristic
33C22×C22⋊Dic13C2211yescharacteristic
34C22×C22⋊Dic13C2211yescharacteristic
35C22×C22⋊Dic13C2218yes—
36C22×C22⋊Dic13C2211yescharacteristic
37C22×C22⋊Dic13C2211yescharacteristic
38C22×C22⋊Dic13C2211yescharacteristic
39C22×C22⋊Dic13C2211yescharacteristic
40C22×C22⋊Dic13C2211yescharacteristic
41C22×C4⋊Dic13C2211yescharacteristic, complemented
42C22×C4⋊Dic13C2211yescharacteristic, complemented
43C22×C4⋊Dic13C2211yescharacteristic, complemented
44C2×#88178—28no—
45C2×#88178C2218yescomplemented
46C22×#6101C2211yescharacteristic, complemented
47C22×#6101C2211yescharacteristic, complemented
48C22×#6101C2211yescharacteristic, complemented
49C22×#6101C2211yescharacteristic, complemented
50C22×#6101C2211yescharacteristic, complemented
51C22×#6101C2211yescharacteristic, complemented
52C2×#88132—28no—
53C2×#88132C2218yescomplemented
54#11718908C2218yes—
55#11718873C2218yescomplemented
56#11718871C2218yescomplemented
57#11718871C2218yescomplemented
58C2×#88071C2211yescharacteristic, complemented
59C2×#88071C2211yescharacteristic, complemented
60C2×#88071C2211yescharacteristic, complemented
61C2×#88071C2211yescharacteristic, complemented
62C2×#88071C2211yescharacteristic, complemented
63C2×#88071C2211yescharacteristic, complemented
64#11718611C2218yescomplemented
65#11718610C2218yescomplemented
66#11718609C2218yescomplemented
67#11718609C2218yescomplemented
68#11718608C2218yescomplemented
69#11718607C2218yescomplemented
70#11718603C2218yescomplemented
71C25×C13—24no—
72C25×C13—24no—
73C25×C13—24no—
74C25×C13—24no—
75C25×C13—42no—
76C25×C13—42no—
77C25×C13Q818yescomplemented
78C25×C13C2311yescharacteristic
79C25×C13C2314yes—
80C25×C13C2311yescharacteristic
81C25×C13C2311yescharacteristic
82C23×C4×C13—24no—
83C23×C4×C13—24no—
84C23×C4×C13—24no—
85C23×C4×C13—24no—
86C23×C4×C13—42no—
87C23×C4×C13—42no—
88C23×C4×C13C2311yescharacteristic
89C23×C4×C13C2311yescharacteristic
90C23×C4×C13C2314yes—
91C23×C4×C13C2314yes—
92C23×C4×C13C2311yescharacteristic
93C23×C4×C13C2311yescharacteristic
94C23×Dic13—24no—
95C23×Dic13—24no—
96C23×Dic13—24no—
97C23×Dic13—24no—
98C23×Dic13—42no—
99C23×Dic13—42no—
100C23×Dic13C2311yescharacteristic
101C23×Dic13C2311yescharacteristic
102C23×Dic13C2311yescharacteristic
103C23×Dic13C2311yescharacteristic
104C23×Dic13C2311yescharacteristic
105C23×Dic13C2311yescharacteristic
106C23×Dic13C2314yes—
107C23×Dic13C2314yes—
108C23×Dic13C2311yescharacteristic
109C23×Dic13C2311yescharacteristic
110C22×Dic26—24no—
111C22×Dic26—24no—
112C22×Dic26—42no—
113C22×Dic26C2314yescomplemented
114C2×C13×C22⋊C4—24no—
115C2×C13×C22⋊C4—24no—
116C2×C13×C22⋊C4—24no—
117C2×C13×C22⋊C4—232no—
118C2×C13×C22⋊C4D418yes—
119C2×C13×C22⋊C4C2314yes—
120C2×C13×C22⋊C4C2314yes—
121C2×C13×C22⋊C4C2314yes—
122C2×C13×C22⋊C4C2314yes—
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—24no—
130C2×C22⋊Dic13—232no—
131C2×C22⋊Dic13—42no—
132C2×C22⋊Dic13—42no—
133C2×C22⋊Dic13D418yes—
134C2×C22⋊Dic13C2314yes—
135C2×C22⋊Dic13C2314yes—
136C2×C22⋊Dic13C2314yes—
137C2×C22⋊Dic13C2314yes—
138C2×C22⋊Dic13C2314yes—
139C2×C22⋊Dic13C2314yes—
140C2×C22⋊Dic13C2314yes—
141C2×C22⋊Dic13C2314yes—
142C2×C22⋊Dic13C2314yes—
143C2×C22⋊Dic13C2314yes—
144C2×C4⋊Dic13—24no—
145C2×C4⋊Dic13—24no—
146C2×C4⋊Dic13—42no—
147C2×C4⋊Dic13C2314yescomplemented
148C2×C4⋊Dic13C2314yescomplemented
149C2×C4⋊Dic13C2314yescomplemented
150#88178—232no—
151C2×#6101—24no—
152C2×#6101—24no—
153C2×#6101—24no—
154C2×#6101—24no—
155C2×#6101—42no—
156C2×#6101—42no—
157C2×#6101C2314yescomplemented
158C2×#6101C2314yescomplemented
159C2×#6101C2314yescomplemented
160C2×#6101C2314yescomplemented
161C2×#6101C2314yescomplemented
162C2×#6101C2314yescomplemented
163#88132—232no—
164#88071C2314yescomplemented
165#88071C2314yescomplemented
166#88071C2314yescomplemented
167#88071C2314yescomplemented
168#88071C2314yescomplemented
169#88071C2314yescomplemented
170C2×#2437—131nomaximal, Sylow
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—232no—
180C24×C13—232no—
181C24×C13—28no—
182C24×C13—22no—
183C24×C13—28no—
184C24×C13—22no—
185C24×C13—28no—
186C24×C13—22no—
187C24×C13—28no—
188C24×C13—22no—
189C24×C13—22no—
190C24×C13—22no—
191C24×C13—416no—
192C24×C13—44no—
193C24×C13—44no—
194C24×C13—416no—
195C24×C13—416no—
196C24×C13—416no—
197C24×C13—416no—
198C24×C13C2×D414yes—
199C24×C13C2×D414yes—
200C24×C13C2×Q814yes—
201C24×C13C2×Q814yes—
202C24×C13C2×Q814yes—
203C24×C13C2×Q8116yescomplemented
204C24×C13#4114yes—
205C24×C13#4114yes—
206C24×C13C2412yes—
207C24×C13C2412yes—
208C24×C13C2412yes—
209C24×C13C2411yescharacteristic
210C22×C4×C13—22no—
211C22×C4×C13—22no—
212C22×C4×C13—22no—
213C22×C4×C13—22no—
214C22×C4×C13—22no—
215C22×C4×C13—28no—
216C22×C4×C13—22no—
217C22×C4×C13—22no—
218C22×C4×C13—28no—
219C22×C4×C13—22no—
220C22×C4×C13—22no—
221C22×C4×C13—22no—
222C22×C4×C13—28no—
223C22×C4×C13—28no—
224C22×C4×C13—44no—
225C22×C4×C13—44no—
226C22×C4×C13—416no—
227C22×C4×C13—416no—
228C22×C4×C13C2×D414yes—
229C22×C4×C13C2×D414yes—
230C22×C4×C13C2412yes—
231C22×C4×C13C2412yes—
232C22×C4×C13C2412yes—
233C22×C4×C13C2412yes—
234C22×Dic13—22no—
235C22×Dic13—22no—
236C22×Dic13—22no—
237C22×Dic13—22no—
238C22×Dic13—28no—
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×Dic13—28no—
251C22×Dic13—22no—
252C22×Dic13—22no—
253C22×Dic13—22no—
254C22×Dic13—22no—
255C22×Dic13—22no—
256C22×Dic13—22no—
257C22×Dic13—22no—
258C22×Dic13—28no—
259C22×Dic13—28no—
260C22×Dic13—44no—
261C22×Dic13—44no—
262C22×Dic13—416no—
263C22×Dic13—416no—
264C22×Dic13C2×D414yes—
265C22×Dic13C2×D414yes—
266C22×Dic13C2412yes—
267C22×Dic13C2412yes—
268C22×Dic13C2412yes—
269C22×Dic13C2412yes—
270C22×Dic13C2412yes—
271C22×Dic13C2412yes—
272C22×Dic13C2412yes—
273C22×Dic13C2412yes—
274C2×Dic26—28no—
275C2×Dic26—28no—
276C2×Dic26—44no—
277C2×Dic26—416no—
278C13×C22⋊C4—28no—
279C13×C22⋊C4—28no—
280C13×C22⋊C4—28no—
281C13×C22⋊C4C2×D4116yes—
282C22⋊Dic13—28no—
283C22⋊Dic13—28no—
284C22⋊Dic13—28no—
285C22⋊Dic13—28no—
286C22⋊Dic13—28no—
287C22⋊Dic13—28no—
288C22⋊Dic13—28no—
289C22⋊Dic13—44no—
290C22⋊Dic13—44no—
291C22⋊Dic13C2×D4116yes—
292C4⋊Dic13—28no—
293C4⋊Dic13—28no—
294C4⋊Dic13—44no—
295#6101—28no—
296#6101—28no—
297#6101—28no—
298#6101—28no—
299#6101—44no—
300#6101—44no—
301C22×C22⋊Q8—131no—
302C22×C22⋊Q8—131no—
303C23×C22⋊C4—131no—
304C23×C22⋊C4D1311yescharacteristic
305#2437—1316no—
306C2×#399—131no—
307C2×#396—131no—
308C2×#396—131no—
309C2×#393—131no—
310C2×#385—131no—
311C2×#385—131no—
312C2×#385—131no—
313C2×#385—131no—
314C2×#380—131no—
315C2×#380—131no—
316C2×#379—131no—
317C23×C13—28no—
318C23×C13—28no—
319C23×C13—28no—
320C23×C13—28no—
321C23×C13—28no—
322C23×C13—28no—
323C23×C13—28no—
324C23×C13—28no—
325C23×C13—28no—
326C23×C13—28no—
327C23×C13—28no—
328C23×C13—28no—
329C23×C13—22no—
330C23×C13—22no—
331C23×C13—22no—
332C23×C13—22no—
333C23×C13—22no—
334C23×C13—22no—
335C23×C13—22no—
336C23×C13—22no—
337C23×C13—28no—
338C23×C13—28no—
339C23×C13—232no—
340C23×C13—232no—
341C23×C13—28no—
342C23×C13—22no—
343C23×C13—22no—
344C23×C13—22no—
345C23×C13—22no—
346C23×C13—22no—
347C23×C13—22no—
348C23×C13—416no—
349C23×C13—4128no—
350C23×C13—416no—
351C23×C13—416no—
352C23×C13—416no—
353C23×C13—416no—
354C23×C13—44no—
355C23×C13—44no—
356C23×C13—44no—
357C23×C13—44no—
358C23×C13C22⋊Q8116yescomplemented
359C23×C13C22⋊Q8116yescomplemented
360C23×C13C22×D414yes—
361C23×C13C22×D414yes—
362C23×C13C22×D412yes—
363C23×C13C22×D412yes—
364C23×C13C22×Q814yes—
365C23×C13C22×Q814yes—
366C23×C13C22×Q814yes—
367C23×C13C22×Q812yes—
368C23×C13C2×#4114yes—
369C23×C13C2×#4114yes—
370C23×C13C2×#4112yes—
371C23×C13C2×#4112yes—
372C23×C13H(5,𝔽2)12yes—
373C23×C13H(5,𝔽2)12yes—
374C23×C13C2511yescharacteristic
375C2×C4×C13—28no—
376C2×C4×C13—28no—
377C2×C4×C13—22no—
378C2×C4×C13—22no—
379C2×C4×C13—22no—
380C2×C4×C13—22no—
381C2×C4×C13—22no—
382C2×C4×C13—22no—
383C2×C4×C13—22no—
384C2×C4×C13—22no—
385C2×C4×C13—22no—
386C2×C4×C13—22no—
387C2×C4×C13—416no—
388C2×C4×C13—416no—
389C2×C4×C13—44no—
390C2×C4×C13—44no—
391C2×C4×C13C22×D414yes—
392C2×C4×C13C22×D414yes—
393C2×Dic13—28no—
394C2×Dic13—28no—
395C2×Dic13—22no—
396C2×Dic13—22no—
397C2×Dic13—22no—
398C2×Dic13—22no—
399C2×Dic13—22no—
400C2×Dic13—22no—
401C2×Dic13—22no—
402C2×Dic13—22no—
403C2×Dic13—22no—
404C2×Dic13—22no—
405C2×Dic13—22no—
406C2×Dic13—22no—
407C2×Dic13—22no—
408C2×Dic13—22no—
409C2×Dic13—22no—
410C2×Dic13—22no—
411C2×Dic13—22no—
412C2×Dic13—22no—
413C2×Dic13—22no—
414C2×Dic13—22no—
415C2×Dic13—22no—
416C2×Dic13—22no—
417C2×Dic13—416no—
418C2×Dic13—416no—
419C2×Dic13—44no—
420C2×Dic13—44no—
421C2×Dic13—44no—
422C2×Dic13—44no—
423C2×Dic13—44no—
424C2×Dic13—44no—
425C2×Dic13C22×D414yes—
426C2×Dic13C22×D414yes—
427Dic26—416no—
428C26C2×D1311yescharacteristic
429C23×Q8—131no—
430C24×C4—131no—
431C24×C4—131no—
432C24×C4C2×D1311yescharacteristic
433C24×C4C2×D1311yescharacteristic
434C2×C22⋊Q8—138no—
435C2×C22⋊Q8—138no—
436C2×C22⋊Q8—268no—
437C2×C22⋊Q8—268no—
438C22×C4⋊C4—131no—
439C22×C4⋊C4—131no—
440C22×C4⋊C4—131no—
441C22×C4⋊C4—131no—
442C22×C4⋊C4—131no—
443C22×C4⋊C4—131no—
444C22×C4⋊C4—131no—
445C22×C4⋊C4—131no—
446C22×C4⋊C4—131no—
447C22×C22⋊C4—28no—
448C22×C22⋊C4—131no—
449C22×C22⋊C4—131no—
450C22×C22⋊C4—131no—
451C22×C22⋊C4—138no—
452C22×C22⋊C4—131no—
453C22×C22⋊C4—131no—
454C22×C22⋊C4—131no—
455C22×C22⋊C4—131no—
456C22×C22⋊C4—131no—
457C22×C22⋊C4—131no—
458C22×C22⋊C4—131no—
459C22×C22⋊C4—268no—
460C22×C22⋊C4C2×D1311yescharacteristic
461C22×C22⋊C4C2×D1311yescharacteristic
462C22×C22⋊C4C2×D1318yes—
463C22×C22⋊C4C2×D1311yescharacteristic
464C22×C22⋊C4C2×D1311yescharacteristic
465#399—138no—
466#396—138no—
467#396—138no—
468#393—138no—
469#385—138no—
470#385—138no—
471#385—138no—
472#385—138no—
473#380—138no—
474#380—138no—
475#379—138no—
476C2×#95—131no—
477C2×#95—131no—
478C2×#95—131no—
479C2×#95—131no—
480C2×#95—131no—
481C2×#95—131no—
482C22×C13—24no—
483C22×C13—24no—
484C22×C13—24no—
485C22×C13—24no—
486C22×C13—232no—
487C22×C13—232no—
488C22×C13—24no—
489C22×C13—24no—
490C22×C13—24no—
491C22×C13—24no—
492C22×C13—24no—
493C22×C13—24no—
494C22×C13—24no—
495C22×C13—24no—
496C22×C13—24no—
497C22×C13—24no—
498C22×C13—24no—
499C22×C13—464no—
500C22×C13—416no—
501C22×C13—42no—
502C22×C13—42no—
503C22×C13—42no—
504C22×C13—42no—
505C22×C13C2×C22⋊Q814yes—
506C22×C13C2×C22⋊Q814yes—
507C22×C13C2×C22⋊Q818yescomplemented
508C22×C13C2×C22⋊Q818yescomplemented
509C22×C13#54314yes—
510C22×C13D4214yes—
511C22×C13#54614yes—
512C22×C13#54614yes—
513C22×C13#55114yes—
514C22×C13C23×D411yescharacteristic
515C22×C13C23×D411yescharacteristic
516C22×C13C23×Q811yescharacteristic
517C22×C13C22×#4111yescharacteristic
518C22×C13C22×#4111yescharacteristic
519C22×C13C2×H(5,𝔽2)11yescharacteristic
520C22×C13C2×H(5,𝔽2)11yescharacteristic
521C4×C13—24no—
522C4×C13—24no—
523C4×C13—42no—
524C4×C13—42no—
525Dic13—24no—
526Dic13—24no—
527Dic13—42no—
528Dic13—42no—
529Dic13—42no—
530Dic13—42no—
531Dic13—42no—
532Dic13—42no—
533C25—24no—
534C25—24no—
535C25—24no—
536C25—24no—
537C25—42no—
538C25—42no—
539C25Dic2618yescomplemented
540C25C22×D1311yescharacteristic
541C25C22×D1314yes—
542C25C22×D1311yescharacteristic
543C25C22×D1311yescharacteristic
544C22×Q8—134no—
545C22×Q8—264no—
546C22×Q8—264no—
547C22×Q8—522no—
548C23×C4—24no—
549C23×C4—24no—
550C23×C4—24no—
551C23×C4—24no—
552C23×C4—42no—
553C23×C4—42no—
554C23×C4—131no—
555C23×C4—131no—
556C23×C4—131no—
557C23×C4—131no—
558C23×C4—131no—
559C23×C4—131no—
560C23×C4—131no—
561C23×C4—131no—
562C23×C4—134no—
563C23×C4—134no—
564C23×C4—264no—
565C23×C4—264no—
566C23×C4—264no—
567C23×C4—264no—
568C23×C4—522no—
569C23×C4—522no—
570C23×C4C22×D1311yescharacteristic
571C23×C4C22×D1311yescharacteristic
572C23×C4C22×D1314yes—
573C23×C4C22×D1314yes—
574C23×C4C22×D1311yescharacteristic
575C23×C4C22×D1311yescharacteristic
576C22⋊Q8—2632no—
577C22⋊Q8—2632no—
578C2×C4⋊C4—134no—
579C2×C4⋊C4—134no—
580C2×C4⋊C4—134no—
581C2×C4⋊C4—134no—
582C2×C4⋊C4—134no—
583C2×C4⋊C4—134no—
584C2×C4⋊C4—134no—
585C2×C4⋊C4—134no—
586C2×C4⋊C4—134no—
587C2×C4⋊C4—264no—
588C2×C4⋊C4—264no—
589C2×C4⋊C4—264no—
590C2×C4⋊C4—264no—
591C2×C4⋊C4—264no—
592C2×C4⋊C4—264no—
593C2×C4⋊C4—522no—
594C2×C4⋊C4—522no—
595C2×C4⋊C4—522no—
596C2×C22⋊C4—24no—
597C2×C22⋊C4—24no—
598C2×C22⋊C4—24no—
599C2×C22⋊C4—232no—
600C2×C22⋊C4—138no—
601C2×C22⋊C4—134no—
602C2×C22⋊C4—134no—
603C2×C22⋊C4—134no—
604C2×C22⋊C4—134no—
605C2×C22⋊C4—134no—
606C2×C22⋊C4—134no—
607C2×C22⋊C4—134no—
608C2×C22⋊C4—134no—
609C2×C22⋊C4—134no—
610C2×C22⋊C4—134no—
611C2×C22⋊C4—2632no—
612C2×C22⋊C4—264no—
613C2×C22⋊C4—264no—
614C2×C22⋊C4—264no—
615C2×C22⋊C4—264no—
616C2×C22⋊C4—264no—
617C2×C22⋊C4—264no—
618C2×C22⋊C4—264no—
619C2×C22⋊C4—522no—
620C2×C22⋊C4—522no—
621C2×C22⋊C4C22⋊D1318yes—
622C2×C22⋊C4C22×D1314yes—
623C2×C22⋊C4C22×D1314yes—
624C2×C22⋊C4C22×D1314yes—
625C2×C22⋊C4C22×D1314yes—
626#95—134no—
627#95—134no—
628#95—134no—
629#95—134no—
630#95—134no—
631#95—134no—
632C2×C13—28no—
633C2×C13—28no—
634C2×C13—44no—
635C2×C13#243718yescomplemented
636C2×C13C22×C22⋊Q811yescharacteristic
637C2×C13C22×C22⋊Q811yescharacteristic
638C2×C13C2×#54311yescharacteristic
639C2×C13C2×D4211yescharacteristic
640C2×C13C2×#54611yescharacteristic
641C2×C13C2×#54611yescharacteristic
642C2×C13C2×#55111yescharacteristic
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—232no—
652C24—232no—
653C24—28no—
654C24—22no—
655C24—28no—
656C24—22no—
657C24—28no—
658C24—22no—
659C24—22no—
660C24—22no—
661C24—28no—
662C24—22no—
663C24—416no—
664C24—44no—
665C24—44no—
666C24—416no—
667C24—416no—
668C24—416no—
669C24—416no—
670C24C2×Dic2614yes—
671C24C2×Dic2614yes—
672C24C2×Dic2614yes—
673C24C2×Dic26116yescomplemented
674C24#612714yes—
675C24D4×D1314yes—
676C24#612914yes—
677C24C2×C22⋊D1314yes—
678C24C23×D1312yes—
679C24C23×D1312yes—
680C24C23×D1312yes—
681C24C23×D1311yescharacteristic
682C2×Q8—268no—
683C2×Q8—268no—
684C2×Q8—524no—
685C2×Q8—5216no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—28no—
692C22×C4—28no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—28no—
699C22×C4—28no—
700C22×C4—44no—
701C22×C4—44no—
702C22×C4—416no—
703C22×C4—416no—
704C22×C4—134no—
705C22×C4—134no—
706C22×C4—132no—
707C22×C4—132no—
708C22×C4—132no—
709C22×C4—132no—
710C22×C4—132no—
711C22×C4—132no—
712C22×C4—132no—
713C22×C4—132no—
714C22×C4—268no—
715C22×C4—268no—
716C22×C4—262no—
717C22×C4—262no—
718C22×C4—262no—
719C22×C4—262no—
720C22×C4—262no—
721C22×C4—262no—
722C22×C4—268no—
723C22×C4—262no—
724C22×C4—262no—
725C22×C4—262no—
726C22×C4—262no—
727C22×C4—262no—
728C22×C4—262no—
729C22×C4—262no—
730C22×C4—262no—
731C22×C4—262no—
732C22×C4—262no—
733C22×C4—262no—
734C22×C4—262no—
735C22×C4—262no—
736C22×C4—262no—
737C22×C4—262no—
738C22×C4—262no—
739C22×C4—268no—
740C22×C4—524no—
741C22×C4—524no—
742C22×C4—5216no—
743C22×C4—5216no—
744C22×C4C2×C22⋊D1314yes—
745C22×C4C2×C22⋊D1314yes—
746C22×C4C23×D1312yes—
747C22×C4C23×D1312yes—
748C22×C4C23×D1312yes—
749C22×C4C23×D1312yes—
750C4⋊C4—268no—
751C4⋊C4—268no—
752C4⋊C4—268no—
753C4⋊C4—268no—
754C4⋊C4—268no—
755C4⋊C4—268no—
756C4⋊C4—524no—
757C4⋊C4—524no—
758C4⋊C4—524no—
759C22⋊C4—28no—
760C22⋊C4—28no—
761C22⋊C4—28no—
762C22⋊C4—1316no—
763C22⋊C4—268no—
764C22⋊C4—268no—
765C22⋊C4—268no—
766C22⋊C4—268no—
767C22⋊C4—268no—
768C22⋊C4—268no—
769C22⋊C4—268no—
770C22⋊C4—524no—
771C22⋊C4—524no—
772C22⋊C4C2×C22⋊D13116yes—
773C13C2×#243711yescharacteristic, complemented, Sylow
774C23—28no—
775C23—28no—
776C23—28no—
777C23—28no—
778C23—28no—
779C23—28no—
780C23—28no—
781C23—28no—
782C23—28no—
783C23—28no—
784C23—28no—
785C23—28no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—28no—
795C23—232no—
796C23—28no—
797C23—28no—
798C23—232no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—416no—
806C23—4128no—
807C23—416no—
808C23—416no—
809C23—416no—
810C23—416no—
811C23—44no—
812C23—44no—
813C23—44no—
814C23—44no—
815C23#88132116yescomplemented
816C23#88178116yescomplemented
817C23C22×Dic2614yes—
818C23C22×Dic2614yes—
819C23C22×Dic2614yes—
820C23C22×Dic2612yes—
821C23C2×#612714yes—
822C23C2×#612712yes—
823C23C2×D4×D1314yes—
824C23C2×D4×D1312yes—
825C23C2×#612914yes—
826C23C2×#612912yes—
827C23#8825112yes—
828C23#8825112yes—
829C23C22×C22⋊D1314yes—
830C23C22×C22⋊D1312yes—
831C23C24×D1311yescharacteristic
832Q8—5216no—
833C2×C4—28no—
834C2×C4—28no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—416no—
846C2×C4—416no—
847C2×C4—44no—
848C2×C4—44no—
849C2×C4—134no—
850C2×C4—134no—
851C2×C4—268no—
852C2×C4—268no—
853C2×C4—262no—
854C2×C4—262no—
855C2×C4—262no—
856C2×C4—262no—
857C2×C4—262no—
858C2×C4—262no—
859C2×C4—262no—
860C2×C4—262no—
861C2×C4—262no—
862C2×C4—262no—
863C2×C4—262no—
864C2×C4—262no—
865C2×C4—262no—
866C2×C4—262no—
867C2×C4—262no—
868C2×C4—262no—
869C2×C4—262no—
870C2×C4—262no—
871C2×C4—262no—
872C2×C4—262no—
873C2×C4—262no—
874C2×C4—262no—
875C2×C4—5216no—
876C2×C4—5216no—
877C2×C4—524no—
878C2×C4—524no—
879C2×C4—524no—
880C2×C4—524no—
881C2×C4—524no—
882C2×C4—524no—
883C2×C4C22×C22⋊D1314yes—
884C2×C4C22×C22⋊D1314yes—
885C22—232no—
886C22—232no—
887C22—24no—
888C22—24no—
889C22—24no—
890C22—24no—
891C22—24no—
892C22—24no—
893C22—24no—
894C22—24no—
895C22—24no—
896C22—24no—
897C22—24no—
898C22—24no—
899C22—24no—
900C22—24no—
901C22—24no—
902C22—464no—
903C22—416no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22C2×#8813214yes—
909C22C2×#8813218yescomplemented
910C22#1171918814yes—
911C22#1171919514yes—
912C22#1171920014yes—
913C22C2×#8817814yes—
914C22C2×#8817818yescomplemented
915C22D4×C22⋊D1314yes—
916C22#1171951114yes—
917C22C23×Dic2611yescharacteristic
918C22C22×#612711yescharacteristic
919C22C22×D4×D1311yescharacteristic
920C22C22×#612911yescharacteristic
921C22C2×#8825111yescharacteristic
922C22C2×#8825111yescharacteristic
923C22C23×C22⋊D1311yescharacteristic
924C4—24no—
925C4—24no—
926C4—42no—
927C4—42no—
928C4—264no—
929C4—264no—
930C4—522no—
931C4—522no—
932C4—522no—
933C4—522no—
934C4—522no—
935C4—522no—
936C2—28no—
937C2—28no—
938C2—44no—
939C2#1311849718yesdirect product factor
940C2C22×#8813211yescharacteristic
941C2C22×#8817811yescharacteristic
942C2C2×#1171918811yescharacteristic
943C2C2×D4×C22⋊D1311yescharacteristic
944C2C2×#1171919511yescharacteristic
945C2C2×#1171951111yescharacteristic
946C2C2×#1171920011yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC23×C13×C22⋊C4C2
socleC24×C13C24
prime radicalC26×C13C22
hypercenterC23×C22⋊C4D13
hypocenterC13C2×#2437
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C23×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#88178C2semidirect
2. C22×#88132C2semidirect
4. #13118497C2direct (N × H)
5. C2×#11718610C2semidirect
6. C2×#11718609C2semidirect
7. C2×#11718609C2semidirect
8. C2×#11718608C2semidirect
9. C2×#11718611C2semidirect
10. C2×#11718871C2semidirect
11. C2×#11718871C2semidirect
12. C2×#11718607C2semidirect
13. C2×#11718873C2semidirect
14. C2×#11718603C2semidirect
22. C23×Dic26C22semidirect
41. C22×C4⋊Dic13C22semidirect
42. C22×C4⋊Dic13C22semidirect
43. C22×C4⋊Dic13C22semidirect
45. C2×#88178C22semidirect
46. C22×#6101C22semidirect
47. C22×#6101C22semidirect
48. C22×#6101C22semidirect
49. C22×#6101C22semidirect
50. C22×#6101C22semidirect
51. C22×#6101C22semidirect
53. C2×#88132C22semidirect
55. #11718873C22semidirect
56. #11718871C22semidirect
57. #11718871C22semidirect
58. C2×#88071C22semidirect
59. C2×#88071C22semidirect
60. C2×#88071C22semidirect
61. C2×#88071C22semidirect
62. C2×#88071C22semidirect
63. C2×#88071C22semidirect
64. #11718611C22semidirect
65. #11718610C22semidirect
66. #11718609C22semidirect
67. #11718609C22semidirect
68. #11718608C22semidirect
69. #11718607C22semidirect
70. #11718603C22semidirect
77. C25×C13Q8semidirect
113. C22×Dic26C23semidirect
147. C2×C4⋊Dic13C23semidirect
148. C2×C4⋊Dic13C23semidirect
149. C2×C4⋊Dic13C23semidirect
157. C2×#6101C23semidirect
158. C2×#6101C23semidirect
159. C2×#6101C23semidirect
160. C2×#6101C23semidirect
161. C2×#6101C23semidirect
162. C2×#6101C23semidirect
164. #88071C23semidirect
165. #88071C23semidirect
166. #88071C23semidirect
167. #88071C23semidirect
168. #88071C23semidirect
169. #88071C23semidirect
203. C24×C13C2×Q8semidirect
358. C23×C13C22⋊Q8semidirect
359. C23×C13C22⋊Q8semidirect
507. C22×C13C2×C22⋊Q8semidirect
508. C22×C13C2×C22⋊Q8semidirect
539. C25Dic26semidirect
635. C2×C13#2437semidirect
673. C24C2×Dic26semidirect
773. C13C2×#2437semidirect
815. C23#88132semidirect
816. C23#88178semidirect
909. C22C2×#88132semidirect
914. C22C2×#88178semidirect
939. C2#13118497direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881782
C22×#881322
C23×C22⋊Dic132
#131184972
C2×#117186102
C2×#117186092
C2×#117186082
C2×#117186112
C2×#117188712
C2×#117186072
C2×#117188732
C2×#117186032
C2×#117189082
C23×C13×C22⋊C42
C2×#243713