Finite Group Databasebeta

← C2×#13117742 #16022211

Subgroups — C2×#13117742 #16022211

Order 3328.

4198 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D13C211yesmaximal, characteristic
2C22×#88135C211yesmaximal, characteristic
3C22×#88135C211yesmaximal, characteristic
4#13117742C2116yesmaximal, direct product factor
5C2×#11718308C211yesmaximal, characteristic, complemented
6C2×#11718633C211yesmaximal, characteristic, complemented
7C2×#11718611C211yesmaximal, characteristic, complemented
8C2×#11718329C211yesmaximal, characteristic, complemented
9C2×#11718650C211yesmaximal, characteristic, complemented
10C2×#11718311C211yesmaximal, characteristic, complemented
11C2×#11718603C211yesmaximal, characteristic, complemented
12C2×#11718648C211yesmaximal, characteristic, complemented
13C2×C4⋊C4×Dic13C211yesmaximal, characteristic, complemented
14C22×#88071C211yesmaximal, characteristic, complemented
15C2×D13×#95C211yesmaximal, characteristic, complemented
16C2×C13×#385C211yesmaximal, characteristic, complemented
17C24×C4×C13C2211yescharacteristic
18C23×C22⋊D13C2211yescharacteristic
19C24×Dic13C2211yescharacteristic
20C24×Dic13C2211yescharacteristic
21C23×C4×D13C2211yescharacteristic
22C23×C4×D13C2211yescharacteristic
23C23×C4×D13C2211yescharacteristic
24C22×C13×C4⋊C4C2211yescharacteristic
25C22×C13×C4⋊C4C2211yescharacteristic
26C22×C13×C22⋊C4C2211yescharacteristic
27C22×C13×C22⋊C4C2211yescharacteristic
28C22×C22⋊Dic13C2211yescharacteristic
29C2×C4×C22⋊D13—28no—
30C2×C4×C22⋊D13C2218yes—
31C22×#6103C2211yescharacteristic
32C22×#6103C2211yescharacteristic
33C22×#6103C2211yescharacteristic
34C22×C4⋊Dic13C2211yescharacteristic
35C22×C4⋊Dic13C2211yescharacteristic
36C22×#6101C2211yescharacteristic
37C22×#6101C2211yescharacteristic
38C22×#6101C2211yescharacteristic
39C22×#6101C2211yescharacteristic
40C22×#6101C2211yescharacteristic
41C22×C4×Dic13C2211yescharacteristic
42C22×C4×Dic13C2211yescharacteristic
43C22×C4×Dic13C2211yescharacteristic
44C2×#88135—28no—
45C2×#88135C4116yescomplemented
46C2×#88135C2218yes—
47C2×#88135C2218yes—
48C13×#385C2218yescomplemented
49C2×C13×#95C2211yescharacteristic
50C2×C13×#95C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57C2×#88071C2211yescharacteristic
58C2×#88071C2211yescharacteristic
59C2×#88071C2218yescomplemented
60#11718650C2218yescomplemented
61#11718648C2218yescomplemented
62C4⋊C4×Dic13C2218yescomplemented
63#11718633C2218yescomplemented
64#11718611C2218yescomplemented
65#11718603C2218yescomplemented
66#11718329C2218yescomplemented
67D13×#95C2218yescomplemented
68#11718311C2218yescomplemented
69#11718308C2218yescomplemented
70C25×C13C2311yescharacteristic
71C24×D13C2311yescharacteristic
72C23×C4×C13—24no—
73C23×C4×C13—24no—
74C23×C4×C13—42no—
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C23×C4×C13C2311yescharacteristic
78C23×C4×C13C2314yes—
79C23×C4×C13C2311yescharacteristic
80C23×C4×C13C2311yescharacteristic
81C23×C4×C13C2311yescharacteristic
82C22×C22⋊D13C2×C418yes—
83C22×C22⋊D13D418yes—
84C22×C22⋊D13Q818yes—
85C22×C22⋊D13C2314yes—
86C23×Dic13—24no—
87C23×Dic13—24no—
88C23×Dic13—42no—
89C23×Dic13—42no—
90C23×Dic13—42no—
91C23×Dic13C2×C418yescomplemented
92C23×Dic13C2311yescharacteristic
93C23×Dic13C2311yescharacteristic
94C23×Dic13C2311yescharacteristic
95C23×Dic13C2314yes—
96C23×Dic13C2311yescharacteristic
97C23×Dic13C2311yescharacteristic
98C23×Dic13C2311yescharacteristic
99C23×Dic13C2314yes—
100C23×Dic13C2311yescharacteristic
101C22×C4×D13—24no—
102C22×C4×D13—24no—
103C22×C4×D13—24no—
104C22×C4×D13—24no—
105C22×C4×D13—42no—
106C22×C4×D13—42no—
107C22×C4×D13—42no—
108C22×C4×D13—42no—
109C22×C4×D13C2×C418yescomplemented
110C22×C4×D13C2314yes—
111C22×C4×D13C2314yes—
112C22×C4×D13C2314yes—
113C2×C13×C4⋊C4—24no—
114C2×C13×C4⋊C4—42no—
115C2×C13×C4⋊C4C2314yes—
116C2×C13×C4⋊C4C2314yes—
117C2×C13×C22⋊C4—24no—
118C2×C13×C22⋊C4C2×C418yescomplemented
119C2×C13×C22⋊C4C2314yes—
120C2×C13×C22⋊C4C2314yes—
121C2×C22⋊Dic13—24no—
122C2×C22⋊Dic13C2314yes—
123C4×C22⋊D13—232no—
124C2×#6103—24no—
125C2×#6103—24no—
126C2×#6103C2×C418yescomplemented
127C2×#6103C2314yes—
128C2×#6103C2314yes—
129C2×#6103C2314yes—
130C2×C4⋊Dic13—24no—
131C2×C4⋊Dic13—42no—
132C2×C4⋊Dic13C2314yes—
133C2×C4⋊Dic13C2314yes—
134C2×#6101—24no—
135C2×#6101—24no—
136C2×#6101—42no—
137C2×#6101—42no—
138C2×#6101C2×C418yescomplemented
139C2×#6101C2314yes—
140C2×#6101C2314yes—
141C2×#6101C2314yes—
142C2×#6101C2314yes—
143C2×#6101C2314yes—
144C2×C4×Dic13—24no—
145C2×C4×Dic13—24no—
146C2×C4×Dic13C2×C418yescomplemented
147C2×C4×Dic13C2314yes—
148C2×C4×Dic13C2314yes—
149C2×C4×Dic13C2314yes—
150#88135—232no—
151#88135C2×C4164yescomplemented
152C13×#95C2314yes—
153C13×#95C2314yes—
154#88071C2314yes—
155#88071C2314yes—
156#88071C2314yes—
157#88071C2314yes—
158#88071C2314yes—
159#88071C2314yes—
160#88071C2314yes—
161#88071C2314yes—
162C2×#2349—131nomaximal, Sylow
163C24×C13—22no—
164C24×C13—22no—
165C24×C13—22no—
166C24×C13—22no—
167C24×C13C22×C414yes—
168C24×C13C2×D414yes—
169C24×C13C2×Q814yes—
170C24×C13C2412yes—
171C24×C13C2411yescharacteristic
172C23×D13—22no—
173C23×D13—22no—
174C23×D13—22no—
175C23×D13—22no—
176C23×D13C22×C414yes—
177C23×D13C2×D414yes—
178C23×D13C2×Q814yes—
179C23×D13C2412yes—
180C22×C4×C13—22no—
181C22×C4×C13—22no—
182C22×C4×C13—22no—
183C22×C4×C13—22no—
184C22×C4×C13—22no—
185C22×C4×C13—22no—
186C22×C4×C13—22no—
187C22×C4×C13—22no—
188C22×C4×C13—22no—
189C22×C4×C13—28no—
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—28no—
197C22×C4×C13—44no—
198C22×C4×C13—416no—
199C22×C4×C13C22×C414yes—
200C22×C4×C13C22×C414yes—
201C22×C4×C13#4114yes—
202C22×C4×C13C2412yes—
203C22×C4×C13C2412yes—
204C22×C4×C13C2412yes—
205C22×C4×C13C2412yes—
206C22×C4×C13C2412yes—
207C22×C4×C13C2412yes—
208C2×C22⋊D13C4⋊C4164yescomplemented
209C2×C22⋊D13C22×C4116yes—
210C2×C22⋊D13C2×D4116yes—
211C2×C22⋊D13C2×Q8116yes—
212C22×Dic13—22no—
213C22×Dic13—22no—
214C22×Dic13—22no—
215C22×Dic13—22no—
216C22×Dic13—22no—
217C22×Dic13—22no—
218C22×Dic13—28no—
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—28no—
229C22×Dic13—416no—
230C22×Dic13—44no—
231C22×Dic13—44no—
232C22×Dic13—44no—
233C22×Dic13—416no—
234C22×Dic13C22×C414yes—
235C22×Dic13C22×C414yes—
236C22×Dic13C22×C414yes—
237C22×Dic13C22×C4116yescomplemented
238C22×Dic13C2×D414yes—
239C22×Dic13C2×Q814yes—
240C22×Dic13#4114yes—
241C22×Dic13C2412yes—
242C22×Dic13C2412yes—
243C22×Dic13C2412yes—
244C22×Dic13C2412yes—
245C22×Dic13C2412yes—
246C22×Dic13C2412yes—
247C22×Dic13C2412yes—
248C2×C4×D13—28no—
249C2×C4×D13—28no—
250C2×C4×D13—28no—
251C2×C4×D13—28no—
252C2×C4×D13—416no—
253C2×C4×D13—44no—
254C2×C4×D13—44no—
255C2×C4×D13—44no—
256C2×C4×D13—44no—
257C2×C4×D13—416no—
258C2×C4×D13—416no—
259C2×C4×D13C22×C4116yescomplemented
260C13×C4⋊C4—28no—
261C13×C4⋊C4—44no—
262C13×C22⋊C4—28no—
263C13×C22⋊C4C22×C4116yescomplemented
264C22⋊Dic13—28no—
265#6103—28no—
266#6103—28no—
267#6103C22×C4116yescomplemented
268C4⋊Dic13—28no—
269C4⋊Dic13—44no—
270#6101—28no—
271#6101—28no—
272#6101—44no—
273#6101—44no—
274#6101C22×C4116yescomplemented
275C4×Dic13—28no—
276C4×Dic13—28no—
277C4×Dic13C22×C4116yescomplemented
278C22×C4×D4—131no—
279C22×C4×D4—131no—
280C22×C4×D4—131no—
281#2349—1316no—
282C2×#389—131no—
283C2×#389—131no—
284C2×#385—131no—
285C2×#385—131no—
286C2×#385—131no—
287C2×#385D1311yescharacteristic, complemented
288C2×#382—131no—
289C2×#380—131no—
290C2×#380—131no—
291C2×C4×C4⋊C4—131no—
292C22×#95—131no—
293C22×#95—131no—
294C23×C13—28no—
295C23×C13—28no—
296C23×C13—28no—
297C23×C13—28no—
298C23×C13—28no—
299C23×C13—28no—
300C23×C13—22no—
301C23×C13—22no—
302C23×C13—22no—
303C23×C13—22no—
304C23×C13C2×C4⋊C4116yes—
305C23×C13C23×C414yes—
306C23×C13C23×C412yes—
307C23×C13C22×D414yes—
308C23×C13C22×D412yes—
309C23×C13C22×Q814yes—
310C23×C13C22×Q812yes—
311C23×C13C2×#4112yes—
312C23×C13C2×#4112yes—
313C23×C13H(5,𝔽2)12yes—
314C23×C13H(5,𝔽2)12yes—
315C23×C13C2511yescharacteristic
316C22×D13—28no—
317C22×D13—28no—
318C22×D13—28no—
319C22×D13—28no—
320C22×D13—28no—
321C22×D13—28no—
322C22×D13—22no—
323C22×D13—22no—
324C22×D13—22no—
325C22×D13—22no—
326C22×D13C2×C4⋊C4116yes—
327C22×D13C23×C414yes—
328C22×D13C22×D414yes—
329C22×D13C22×Q814yes—
330C2×C4×C13—28no—
331C2×C4×C13—28no—
332C2×C4×C13—28no—
333C2×C4×C13—22no—
334C2×C4×C13—22no—
335C2×C4×C13—22no—
336C2×C4×C13—22no—
337C2×C4×C13—22no—
338C2×C4×C13—22no—
339C2×C4×C13—22no—
340C2×C4×C13—22no—
341C2×C4×C13—22no—
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—416no—
349C2×C4×C13—44no—
350C2×C4×C13—44no—
351C2×C4×C13—44no—
352C2×C4×C13C23×C414yes—
353C2×C4×C13C23×C414yes—
354C2×C4×C13C2×#4114yes—
355C22⋊D13C2×C4⋊C4164yescomplemented
356C2×Dic13—28no—
357C2×Dic13—28no—
358C2×Dic13—28no—
359C2×Dic13—22no—
360C2×Dic13—22no—
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—416no—
375C2×Dic13—416no—
376C2×Dic13—44no—
377C2×Dic13—44no—
378C2×Dic13—44no—
379C2×Dic13C2×C4⋊C4116yes—
380C2×Dic13C23×C414yes—
381C2×Dic13C23×C414yes—
382C2×Dic13C23×C414yes—
383C2×Dic13C22×D414yes—
384C2×Dic13C22×Q814yes—
385C2×Dic13C2×#4114yes—
386C4×D13—416no—
387C4×D13—416no—
388C4×D13—416no—
389C23×D4—131no—
390C24×C4—131no—
391C24×C4—131no—
392C24×C4—131no—
393C24×C4—131no—
394C24×C4—131no—
395C24×C4C2×D1311yescharacteristic
396C2×C4×D4—138no—
397C2×C4×D4—1316no—
398C2×C4×D4—138no—
399C2×C4×D4—138no—
400C2×C4×D4—268no—
401C2×C4×D4—268no—
402C22×C4⋊C4—131no—
403C22×C4⋊C4—131no—
404C22×C4⋊C4—131no—
405C22×C4⋊C4—131no—
406C22×C4⋊C4—131no—
407C22×C4⋊C4—131no—
408C22×C4⋊C4—131no—
409C22×C4⋊C4C2×D1311yescharacteristic
410C22×C4⋊C4C2×D1311yescharacteristic
411C22×C22⋊C4—131no—
412C22×C22⋊C4—131no—
413C22×C22⋊C4—131no—
414C22×C22⋊C4—131no—
415C22×C22⋊C4C2×D1311yescharacteristic
416C22×C22⋊C4C2×D1311yescharacteristic
417C22×C42—131no—
418C22×C42—131no—
419C22×C42—131no—
420#389—138no—
421#389—138no—
422#385—138no—
423#385—138no—
424#385—138no—
425#385C2×D1318yescomplemented
426#382—138no—
427#380—138no—
428#380—138no—
429C4×C4⋊C4—138no—
430C2×#95—138no—
431C2×#95—131no—
432C2×#95—131no—
433C2×#95—131no—
434C2×#95—131no—
435C2×#95—131no—
436C2×#95—131no—
437C2×#95—131no—
438C2×#95—131no—
439C2×#95—138no—
440C2×#95C2×D1311yescharacteristic
441C2×#95C2×D1311yescharacteristic
442C22×C13—232no—
443C22×C13—24no—
444C22×C13—24no—
445C22×C13—24no—
446C22×C13—24no—
447C22×C13—24no—
448C22×C13—24no—
449C22×C13C22×C4⋊C418yes—
450C22×C13C22×C4⋊C414yes—
451C22×C13C4×#4114yes—
452C22×C13#51814yes—
453C22×C13#54614yes—
454C22×C13#54614yes—
455C22×C13#55414yes—
456C22×C13#55414yes—
457C22×C13C24×C411yescharacteristic
458C22×C13C23×D411yescharacteristic
459C22×C13C23×Q811yescharacteristic
460C22×C13C22×#4111yescharacteristic
461C22×C13C22×#4111yescharacteristic
462C22×C13C2×H(5,𝔽2)11yescharacteristic
463C22×C13C2×H(5,𝔽2)11yescharacteristic
464C2×D13—232no—
465C2×D13—24no—
466C2×D13—24no—
467C2×D13—24no—
468C2×D13—24no—
469C2×D13—24no—
470C2×D13—24no—
471C2×D13C22×C4⋊C418yes—
472C4×C13—24no—
473C4×C13—24no—
474C4×C13—24no—
475C4×C13—42no—
476C4×C13—42no—
477C4×C13—42no—
478Dic13—24no—
479Dic13—24no—
480Dic13—24no—
481Dic13—42no—
482Dic13—42no—
483Dic13—42no—
484Dic13C22×C4⋊C418yes—
485C25—131no—
486C25C22×D1311yescharacteristic
487C22×D4—138no—
488C22×D4—138no—
489C22×D4—138no—
490C22×D4—134no—
491C23×C4—24no—
492C23×C4—24no—
493C23×C4—42no—
494C23×C4—131no—
495C23×C4—131no—
496C23×C4—131no—
497C23×C4—131no—
498C23×C4—138no—
499C23×C4—134no—
500C23×C4—138no—
501C23×C4—134no—
502C23×C4—131no—
503C23×C4—131no—
504C23×C4—131no—
505C23×C4—134no—
506C23×C4—134no—
507C23×C4—134no—
508C23×C4—264no—
509C23×C4—264no—
510C23×C4—264no—
511C23×C4—264no—
512C23×C4—264no—
513C23×C4—264no—
514C23×C4—522no—
515C23×C4—522no—
516C23×C4—522no—
517C23×C4—522no—
518C23×C4—522no—
519C23×C4—522no—
520C23×C4—522no—
521C23×C4C22×D1311yescharacteristic
522C23×C4C22×D1311yescharacteristic
523C23×C4C22×D1311yescharacteristic
524C23×C4C22×D1314yes—
525C23×C4C22×D1311yescharacteristic
526C23×C4C22×D1311yescharacteristic
527C23×C4C22×D1311yescharacteristic
528C4×D4—1364no—
529C4×D4—2632no—
530C4×D4—2632no—
531C2×C4⋊C4—24no—
532C2×C4⋊C4—42no—
533C2×C4⋊C4—138no—
534C2×C4⋊C4—134no—
535C2×C4⋊C4—134no—
536C2×C4⋊C4—134no—
537C2×C4⋊C4—134no—
538C2×C4⋊C4—134no—
539C2×C4⋊C4—134no—
540C2×C4⋊C4—134no—
541C2×C4⋊C4—264no—
542C2×C4⋊C4—264no—
543C2×C4⋊C4—264no—
544C2×C4⋊C4—522no—
545C2×C4⋊C4—522no—
546C2×C4⋊C4—522no—
547C2×C4⋊C4C22×D1314yes—
548C2×C4⋊C4C22×D1314yes—
549C2×C22⋊C4—24no—
550C2×C22⋊C4—138no—
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⋊C4C4×D1318yescomplemented
559C2×C22⋊C4C22×D1314yes—
560C2×C22⋊C4C22×D1314yes—
561C2×C42—138no—
562C2×C42—134no—
563C2×C42—134no—
564C2×C42—134no—
565C2×C42—264no—
566C2×C42—264no—
567#95—134no—
568#95—134no—
569#95—134no—
570#95—134no—
571#95—134no—
572#95—134no—
573#95—134no—
574#95—134no—
575#95C22×D1314yes—
576#95C22×D1314yes—
577C2×C13—28no—
578C2×C13#234918yescomplemented
579C2×C13C23×C4⋊C411yescharacteristic
580C2×C13C2×C4×#4111yescharacteristic
581C2×C13C2×#51811yescharacteristic
582C2×C13C2×#54611yescharacteristic
583C2×C13C2×#54611yescharacteristic
584C2×C13C2×#55411yescharacteristic
585C2×C13C2×#55411yescharacteristic
586D13—28no—
587C24—22no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—134no—
592C24—134no—
593C24—134no—
594C24—132no—
595C24—262no—
596C24—262no—
597C24—262no—
598C24—262no—
599C24C2×C4×D1314yes—
600C24D4×D1314yes—
601C24Q8×D1314yes—
602C24C23×D1312yes—
603C24C23×D1311yescharacteristic
604C2×D4—1364no—
605C2×D4—1316no—
606C2×D4—1316no—
607C2×D4—1316no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—28no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—28no—
625C22×C4—44no—
626C22×C4—416no—
627C22×C4—134no—
628C22×C4—134no—
629C22×C4—134no—
630C22×C4—132no—
631C22×C4—134no—
632C22×C4—134no—
633C22×C4—134no—
634C22×C4—132no—
635C22×C4—132no—
636C22×C4—132no—
637C22×C4—1316no—
638C22×C4—1316no—
639C22×C4—132no—
640C22×C4—132no—
641C22×C4—132no—
642C22×C4—268no—
643C22×C4—268no—
644C22×C4—268no—
645C22×C4—268no—
646C22×C4—262no—
647C22×C4—262no—
648C22×C4—262no—
649C22×C4—262no—
650C22×C4—262no—
651C22×C4—262no—
652C22×C4—262no—
653C22×C4—262no—
654C22×C4—262no—
655C22×C4—268no—
656C22×C4—262no—
657C22×C4—262no—
658C22×C4—262no—
659C22×C4—262no—
660C22×C4—262no—
661C22×C4—262no—
662C22×C4—268no—
663C22×C4—5216no—
664C22×C4—524no—
665C22×C4—524no—
666C22×C4—524no—
667C22×C4—524no—
668C22×C4—5216no—
669C22×C4—5216no—
670C22×C4—5216no—
671C22×C4—524no—
672C22×C4—524no—
673C22×C4—524no—
674C22×C4—5216no—
675C22×C4C2×C4×D1314yes—
676C22×C4C2×C4×D1314yes—
677C22×C4#612914yes—
678C22×C4C23×D1312yes—
679C22×C4C23×D1312yes—
680C22×C4C23×D1312yes—
681C22×C4C23×D1312yes—
682C22×C4C23×D1312yes—
683C22×C4C23×D1312yes—
684C4⋊C4—28no—
685C4⋊C4—44no—
686C4⋊C4—1316no—
687C4⋊C4—268no—
688C4⋊C4—268no—
689C4⋊C4—268no—
690C4⋊C4—524no—
691C4⋊C4—524no—
692C4⋊C4—524no—
693C22⋊C4—28no—
694C22⋊C4—1316no—
695C22⋊C4—268no—
696C22⋊C4—268no—
697C22⋊C4—268no—
698C22⋊C4C2×C4×D13116yescomplemented
699C42—1316no—
700C42—268no—
701C42—268no—
702C13C2×#234911yescharacteristic, complemented, Sylow
703C23—28no—
704C23—28no—
705C23—28no—
706C23—28no—
707C23—28no—
708C23—28no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—1316no—
714C23—134no—
715C23—134no—
716C23—134no—
717C23—268no—
718C23—268no—
719C23—268no—
720C23—268no—
721C23—268no—
722C23—268no—
723C23—262no—
724C23—262no—
725C23—262no—
726C23—262no—
727C23C4⋊C4×D13116yes—
728C23C22×C4×D1314yes—
729C23C22×C4×D1312yes—
730C23C2×D4×D1314yes—
731C23C2×D4×D1312yes—
732C23C2×#612912yes—
733C23#8825112yes—
734C23C2×Q8×D1314yes—
735C23C2×Q8×D1312yes—
736C23#41×D1312yes—
737C23#8825612yes—
738C23C24×D1311yescharacteristic
739D4—1364no—
740C2×C4—28no—
741C2×C4—28no—
742C2×C4—28no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—416no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—44no—
762C2×C4—1316no—
763C2×C4—134no—
764C2×C4—134no—
765C2×C4—134no—
766C2×C4—134no—
767C2×C4—134no—
768C2×C4—134no—
769C2×C4—268no—
770C2×C4—268no—
771C2×C4—268no—
772C2×C4—262no—
773C2×C4—262no—
774C2×C4—262no—
775C2×C4—262no—
776C2×C4—262no—
777C2×C4—262no—
778C2×C4—262no—
779C2×C4—262no—
780C2×C4—262no—
781C2×C4—262no—
782C2×C4—262no—
783C2×C4—262no—
784C2×C4—262no—
785C2×C4—262no—
786C2×C4—262no—
787C2×C4—5216no—
788C2×C4—5216no—
789C2×C4—5216no—
790C2×C4—5216no—
791C2×C4—5216no—
792C2×C4—524no—
793C2×C4—524no—
794C2×C4—524no—
795C2×C4C22×C4×D1314yes—
796C2×C4C22×C4×D1314yes—
797C2×C4C2×#612914yes—
798C22—232no—
799C22—24no—
800C22—24no—
801C22—24no—
802C22—24no—
803C22—24no—
804C22—24no—
805C22—138no—
806C22—2632no—
807C22—264no—
808C22—264no—
809C22—264no—
810C22—264no—
811C22—264no—
812C22—264no—
813C22C2×C4⋊C4×D1318yes—
814C22C2×C4⋊C4×D1314yes—
815C22C4×#612914yes—
816C22#1171925014yes—
817C22#1171929614yes—
818C22#1171934014yes—
819C22#1171934114yes—
820C22#1171935914yes—
821C22C23×C4×D1311yescharacteristic
822C22C22×D4×D1311yescharacteristic
823C22C22×#612911yescharacteristic
824C22C2×#8825111yescharacteristic
825C22C22×Q8×D1311yescharacteristic
826C22C2×#41×D1311yescharacteristic
827C22C2×#8825611yescharacteristic
828C4—24no—
829C4—24no—
830C4—24no—
831C4—42no—
832C4—42no—
833C4—42no—
834C4—138no—
835C4—264no—
836C4—264no—
837C4—264no—
838C4—522no—
839C4—522no—
840C4—522no—
841C2—28no—
842C2—268no—
843C2#1311774218yesdirect product factor
844C2C22×C4⋊C4×D1311yescharacteristic
845C2C2×C4×#612911yescharacteristic
846C2C2×#1171925011yescharacteristic
847C2C2×#1171929611yescharacteristic
848C2C2×#1171935911yescharacteristic
849C2C2×#1171934111yescharacteristic
850C2C2×#1171934011yescharacteristic
subgroupG/H
centerC24C23×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC2×C13×#385C2
socleC24×C13C24
prime radicalC23×C22⋊D13C22
cosocleC23×C13C25
hypercenterC2×#385D13
hypocenterC13C2×#2349
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
4. #13117742C2direct (N × H)
5. C2×#11718308C2semidirect
6. C2×#11718633C2semidirect
7. C2×#11718611C2semidirect
8. C2×#11718329C2semidirect
9. C2×#11718650C2semidirect
10. C2×#11718311C2semidirect
11. C2×#11718603C2semidirect
12. C2×#11718648C2semidirect
13. C2×C4⋊C4×Dic13C2semidirect
14. C22×#88071C2semidirect
15. C2×D13×#95C2semidirect
16. C2×C13×#385C2semidirect
45. C2×#88135C4semidirect
48. C13×#385C22semidirect
59. C2×#88071C22semidirect
60. #11718650C22semidirect
61. #11718648C22semidirect
62. C4⋊C4×Dic13C22semidirect
63. #11718633C22semidirect
64. #11718611C22semidirect
65. #11718603C22semidirect
66. #11718329C22semidirect
67. D13×#95C22semidirect
68. #11718311C22semidirect
69. #11718308C22semidirect
91. C23×Dic13C2×C4semidirect
109. C22×C4×D13C2×C4semidirect
118. C2×C13×C22⋊C4C2×C4semidirect
126. C2×#6103C2×C4semidirect
138. C2×#6101C2×C4semidirect
146. C2×C4×Dic13C2×C4semidirect
151. #88135C2×C4semidirect
208. C2×C22⋊D13C4⋊C4semidirect
237. C22×Dic13C22×C4semidirect
259. C2×C4×D13C22×C4semidirect
263. C13×C22⋊C4C22×C4semidirect
267. #6103C22×C4semidirect
274. #6101C22×C4semidirect
277. C4×Dic13C22×C4semidirect
287. C2×#385D13semidirect
355. C22⋊D13C2×C4⋊C4semidirect
425. #385C2×D13semidirect
558. C2×C22⋊C4C4×D13semidirect
578. C2×C13#2349semidirect
698. C22⋊C4C2×C4×D13semidirect
702. C13C2×#2349semidirect
843. C2#13117742direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D132
C22×#881352
#131177422
C2×#117183082
C2×#117186332
C2×#117186112
C2×#117183292
C2×#117186502
C2×#117183112
C2×#117186032
C2×#117186482
C2×C4⋊C4×Dic132
C22×#880712
C2×D13×#952
C2×C13×#3852
C2×#234913