Finite Group Databasebeta

← C2×#13117734 #16022202

Subgroups — C2×#13117734 #16022202

Order 3328.

4718 conjugacy classes of subgroups.

The subgroup lattice has 876 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
4C23×#6101C211yesmaximal, characteristic, complemented
5C22×C4⋊C4×D13C211yesmaximal, characteristic, complemented
6#13117734C2116yesmaximal, direct product factor
7C2×#11718308C211yesmaximal, characteristic, complemented
8C2×#11718633C211yesmaximal, characteristic, complemented
9C2×#11718611C211yesmaximal, characteristic, complemented
10C2×#11718329C211yesmaximal, characteristic, complemented
11C2×#11718650C211yesmaximal, characteristic, complemented
12C2×#11718637C211yesmaximal, characteristic, complemented
13C2×#11718328C211yesmaximal, characteristic, complemented
14C2×#11718603C211yesmaximal, characteristic, complemented
15C2×#11718310C211yesmaximal, 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×#6101—28no—
37C22×#6101C2211yescharacteristic
38C22×#6101C2211yescharacteristic
39C22×#6101C2211yescharacteristic
40C22×#6101C2211yescharacteristic
41C22×#6101C2211yescharacteristic
42C22×#6101C2211yescharacteristic
43C22×#6101C2211yescharacteristic
44C22×#6101C2211yescharacteristic
45C22×#6101C2211yescharacteristic
46C22×#6101C2218yescomplemented
47C22×C4×Dic13C2211yescharacteristic
48C22×C4×Dic13C2211yescharacteristic
49C22×C4×Dic13C2211yescharacteristic
50C2×C4⋊C4×D13—28no—
51C2×C4⋊C4×D13C2218yescomplemented
52C2×#88135—28no—
53C2×#88135C4116yescomplemented
54C2×#88135C2218yes—
55C2×#88135C2218yes—
56C13×#385C2218yescomplemented
57C2×C13×#95C2211yescharacteristic
58C2×C13×#95C2211yescharacteristic
59C2×#88071C2211yescharacteristic
60C2×#88071C2211yescharacteristic
61C2×#88071C2211yescharacteristic
62C2×#88071C2211yescharacteristic
63#11718650C2218yescomplemented
64#11718637C2218yescomplemented
65#11718633C2218yescomplemented
66#11718611C2218yescomplemented
67#11718603C2218yescomplemented
68#11718329C2218yescomplemented
69#11718328C2218yescomplemented
70#11718310C2218yescomplemented
71#11718308C2218yescomplemented
72C25×C13C2311yescharacteristic
73C24×D13C2311yescharacteristic
74C23×C4×C13—24no—
75C23×C4×C13—24no—
76C23×C4×C13—42no—
77C23×C4×C13C2311yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C23×C4×C13C2311yescharacteristic
80C23×C4×C13C2314yes—
81C23×C4×C13C2311yescharacteristic
82C23×C4×C13C2311yescharacteristic
83C23×C4×C13C2311yescharacteristic
84C22×C22⋊D13C2×C418yes—
85C22×C22⋊D13D418yes—
86C22×C22⋊D13Q818yes—
87C22×C22⋊D13C2314yes—
88C23×Dic13—24no—
89C23×Dic13—24no—
90C23×Dic13—24no—
91C23×Dic13—24no—
92C23×Dic13—42no—
93C23×Dic13C2×C418yescomplemented
94C23×Dic13C2311yescharacteristic
95C23×Dic13C2311yescharacteristic
96C23×Dic13C2311yescharacteristic
97C23×Dic13C2314yes—
98C23×Dic13C2311yescharacteristic
99C23×Dic13C2314yes—
100C23×Dic13C2311yescharacteristic
101C23×Dic13C2311yescharacteristic
102C23×Dic13C2311yescharacteristic
103C22×C4×D13—24no—
104C22×C4×D13—24no—
105C22×C4×D13—24no—
106C22×C4×D13—24no—
107C22×C4×D13—24no—
108C22×C4×D13—24no—
109C22×C4×D13—42no—
110C22×C4×D13—42no—
111C22×C4×D13C2×C418yescomplemented
112C22×C4×D13C2314yes—
113C22×C4×D13C2314yes—
114C22×C4×D13C2314yes—
115C2×C13×C4⋊C4—24no—
116C2×C13×C4⋊C4—42no—
117C2×C13×C4⋊C4C2314yes—
118C2×C13×C4⋊C4C2314yes—
119C2×C13×C22⋊C4—24no—
120C2×C13×C22⋊C4C2×C418yescomplemented
121C2×C13×C22⋊C4C2314yes—
122C2×C13×C22⋊C4C2314yes—
123C2×C22⋊Dic13—24no—
124C2×C22⋊Dic13C2314yes—
125C4×C22⋊D13—232no—
126C2×#6103—24no—
127C2×#6103—24no—
128C2×#6103C2×C418yescomplemented
129C2×#6103C2314yes—
130C2×#6103C2314yes—
131C2×#6103C2314yes—
132C2×C4⋊Dic13—24no—
133C2×C4⋊Dic13—42no—
134C2×C4⋊Dic13C2314yes—
135C2×C4⋊Dic13C2314yes—
136C2×#6101—24no—
137C2×#6101—24no—
138C2×#6101—24no—
139C2×#6101—24no—
140C2×#6101—24no—
141C2×#6101—24no—
142C2×#6101—24no—
143C2×#6101—232no—
144C2×#6101C2×C418yescomplemented
145C2×#6101D418yescomplemented
146C2×#6101C2314yes—
147C2×#6101C2314yes—
148C2×#6101C2314yes—
149C2×#6101C2314yes—
150C2×#6101C2314yes—
151C2×#6101C2314yes—
152C2×#6101C2314yes—
153C2×#6101C2314yes—
154C2×#6101C2314yes—
155C2×C4×Dic13—24no—
156C2×C4×Dic13—24no—
157C2×C4×Dic13C2×C418yescomplemented
158C2×C4×Dic13C2314yes—
159C2×C4×Dic13C2314yes—
160C2×C4×Dic13C2314yes—
161C4⋊C4×D13—232no—
162#88135—232no—
163#88135C2×C4164yescomplemented
164C13×#95C2314yes—
165C13×#95C2314yes—
166#88071C2314yes—
167#88071C2314yes—
168#88071C2314yes—
169#88071C2314yes—
170C2×D4×C4⋊C4—131nomaximal, Sylow
171C24×C13—22no—
172C24×C13—22no—
173C24×C13—22no—
174C24×C13—22no—
175C24×C13C22×C414yes—
176C24×C13C2×D414yes—
177C24×C13C2×Q814yes—
178C24×C13C2412yes—
179C24×C13C2411yescharacteristic
180C23×D13—22no—
181C23×D13—22no—
182C23×D13—22no—
183C23×D13—22no—
184C23×D13C22×C414yes—
185C23×D13C2×D414yes—
186C23×D13C2×Q814yes—
187C23×D13C2412yes—
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—28no—
200C22×C4×C13—22no—
201C22×C4×C13—22no—
202C22×C4×C13—22no—
203C22×C4×C13—22no—
204C22×C4×C13—28no—
205C22×C4×C13—44no—
206C22×C4×C13—416no—
207C22×C4×C13C22×C414yes—
208C22×C4×C13C22×C414yes—
209C22×C4×C13C2×D414yes—
210C22×C4×C13C2412yes—
211C22×C4×C13C2412yes—
212C22×C4×C13C2412yes—
213C22×C4×C13C2412yes—
214C22×C4×C13C2412yes—
215C22×C4×C13C2412yes—
216C2×C22⋊D13C4⋊C4164yescomplemented
217C2×C22⋊D13C22×C4116yes—
218C2×C22⋊D13C2×D4116yes—
219C2×C22⋊D13C2×Q8116yes—
220C22×Dic13—22no—
221C22×Dic13—22no—
222C22×Dic13—22no—
223C22×Dic13—22no—
224C22×Dic13—232no—
225C22×Dic13—28no—
226C22×Dic13—28no—
227C22×Dic13—28no—
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—28no—
238C22×Dic13—44no—
239C22×Dic13—416no—
240C22×Dic13C22×C414yes—
241C22×Dic13C22×C414yes—
242C22×Dic13C22×C414yes—
243C22×Dic13C22×C4116yescomplemented
244C22×Dic13C2×D414yes—
245C22×Dic13C2×D414yes—
246C22×Dic13C2×D414yes—
247C22×Dic13C2×Q814yes—
248C22×Dic13#4114yes—
249C22×Dic13C2412yes—
250C22×Dic13C2412yes—
251C22×Dic13C2412yes—
252C22×Dic13C2412yes—
253C22×Dic13C2412yes—
254C22×Dic13C2412yes—
255C22×Dic13C2412yes—
256C2×C4×D13—232no—
257C2×C4×D13—28no—
258C2×C4×D13—28no—
259C2×C4×D13—28no—
260C2×C4×D13—28no—
261C2×C4×D13—28no—
262C2×C4×D13—28no—
263C2×C4×D13—44no—
264C2×C4×D13—44no—
265C2×C4×D13—416no—
266C2×C4×D13—416no—
267C2×C4×D13C22×C4116yescomplemented
268C13×C4⋊C4—28no—
269C13×C4⋊C4—44no—
270C13×C22⋊C4—28no—
271C13×C22⋊C4C22×C4116yescomplemented
272C22⋊Dic13—28no—
273#6103—28no—
274#6103—28no—
275#6103C22×C4116yescomplemented
276C4⋊Dic13—28no—
277C4⋊Dic13—44no—
278#6101—28no—
279#6101—28no—
280#6101—28no—
281#6101—28no—
282#6101—28no—
283#6101—28no—
284#6101—28no—
285#6101C22×C4116yescomplemented
286#6101C2×D4116yescomplemented
287C4×Dic13—28no—
288C4×Dic13—28no—
289C4×Dic13C22×C4116yescomplemented
290C22×C4×D4—131no—
291C22×C4×D4—131no—
292C22×C4×D4—131no—
293C23×C4⋊C4—131no—
294C23×C4⋊C4—131no—
295D4×C4⋊C4—1316no—
296C2×#389—131no—
297C2×#389—131no—
298C2×#385—131no—
299C2×#385—131no—
300C2×#385—131no—
301C2×#385D1311yescharacteristic, complemented
302C2×#384—131no—
303C2×#380—131no—
304C2×#380—131no—
305C2×C4×C4⋊C4—131no—
306C23×C13—28no—
307C23×C13—28no—
308C23×C13—28no—
309C23×C13—28no—
310C23×C13—28no—
311C23×C13—28no—
312C23×C13—22no—
313C23×C13—22no—
314C23×C13—22no—
315C23×C13—22no—
316C23×C13C2×C4⋊C4116yescomplemented
317C23×C13C23×C414yes—
318C23×C13C23×C412yes—
319C23×C13C22×D414yes—
320C23×C13C22×D412yes—
321C23×C13C22×D412yes—
322C23×C13C22×Q814yes—
323C23×C13C22×Q812yes—
324C23×C13C2×#4112yes—
325C23×C13H(5,𝔽2)12yes—
326C23×C132−1+412yes—
327C23×C13C2511yescharacteristic
328C22×D13—28no—
329C22×D13—28no—
330C22×D13—28no—
331C22×D13—28no—
332C22×D13—28no—
333C22×D13—28no—
334C22×D13—22no—
335C22×D13—22no—
336C22×D13—22no—
337C22×D13—22no—
338C22×D13C2×C4⋊C4116yescomplemented
339C22×D13C23×C414yes—
340C22×D13C22×D414yes—
341C22×D13C22×Q814yes—
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—22no—
355C2×C4×C13—22no—
356C2×C4×C13—22no—
357C2×C4×C13—22no—
358C2×C4×C13—22no—
359C2×C4×C13—22no—
360C2×C4×C13—416no—
361C2×C4×C13—44no—
362C2×C4×C13—44no—
363C2×C4×C13—44no—
364C2×C4×C13C23×C414yes—
365C2×C4×C13C23×C414yes—
366C2×C4×C13C22×D414yes—
367C22⋊D13C2×C4⋊C4164yescomplemented
368C2×Dic13—28no—
369C2×Dic13—28no—
370C2×Dic13—22no—
371C2×Dic13—22no—
372C2×Dic13—22no—
373C2×Dic13—22no—
374C2×Dic13—232no—
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—416no—
385C2×Dic13—44no—
386C2×Dic13—44no—
387C2×Dic13—44no—
388C2×Dic13C2×C4⋊C4116yescomplemented
389C2×Dic13C4×D4116yescomplemented
390C2×Dic13C23×C414yes—
391C2×Dic13C23×C414yes—
392C2×Dic13C23×C414yes—
393C2×Dic13C22×D414yes—
394C2×Dic13C22×D414yes—
395C2×Dic13C22×D414yes—
396C2×Dic13C22×Q814yes—
397C2×Dic13C2×#4114yes—
398C4×D13—232no—
399C4×D13—416no—
400C4×D13—416no—
401C23×D4—131no—
402C24×C4—131no—
403C24×C4—131no—
404C24×C4—131no—
405C24×C4—131no—
406C24×C4—131no—
407C24×C4C2×D1311yescharacteristic
408C2×C4×D4—138no—
409C2×C4×D4—1316no—
410C2×C4×D4—138no—
411C2×C4×D4—138no—
412C2×C4×D4—268no—
413C2×C4×D4—268no—
414C22×C4⋊C4—131no—
415C22×C4⋊C4—131no—
416C22×C4⋊C4—138no—
417C22×C4⋊C4—131no—
418C22×C4⋊C4—131no—
419C22×C4⋊C4—131no—
420C22×C4⋊C4—131no—
421C22×C4⋊C4—131no—
422C22×C4⋊C4—131no—
423C22×C4⋊C4—131no—
424C22×C4⋊C4—131no—
425C22×C4⋊C4—131no—
426C22×C4⋊C4—138no—
427C22×C4⋊C4—268no—
428C22×C4⋊C4—268no—
429C22×C4⋊C4C2×D1311yescharacteristic
430C22×C4⋊C4C2×D1311yescharacteristic
431C22×C22⋊C4—131no—
432C22×C22⋊C4—131no—
433C22×C22⋊C4—131no—
434C22×C22⋊C4—131no—
435C22×C22⋊C4C2×D1311yescharacteristic
436C22×C22⋊C4C2×D1311yescharacteristic
437C22×C42—131no—
438C22×C42—131no—
439C22×C42—131no—
440#389—138no—
441#389—138no—
442#385—138no—
443#385—138no—
444#385—138no—
445#385C2×D1318yescomplemented
446#384—138no—
447#380—138no—
448#380—138no—
449C4×C4⋊C4—138no—
450C2×#95—131no—
451C2×#95—131no—
452C2×#95—131no—
453C2×#95—131no—
454C2×#95C2×D1311yescharacteristic
455C2×#95C2×D1311yescharacteristic
456C22×C13—232no—
457C22×C13—24no—
458C22×C13—24no—
459C22×C13—24no—
460C22×C13—24no—
461C22×C13—24no—
462C22×C13—24no—
463C22×C13C22×C4⋊C414yes—
464C22×C13C22×C4⋊C418yescomplemented
465C22×C13C2×C4×D414yes—
466C22×C13#52014yes—
467C22×C13D4214yes—
468C22×C13#54714yes—
469C22×C13D4×Q814yes—
470C22×C13#55414yes—
471C22×C13C24×C411yescharacteristic
472C22×C13C23×D411yescharacteristic
473C22×C13C23×D411yescharacteristic
474C22×C13C23×Q811yescharacteristic
475C22×C13C22×#4111yescharacteristic
476C22×C13C2×H(5,𝔽2)11yescharacteristic
477C22×C13C2×2−1+411yescharacteristic
478C2×D13—232no—
479C2×D13—24no—
480C2×D13—24no—
481C2×D13—24no—
482C2×D13—24no—
483C2×D13—24no—
484C2×D13—24no—
485C2×D13C22×C4⋊C418yescomplemented
486C4×C13—24no—
487C4×C13—24no—
488C4×C13—24no—
489C4×C13—42no—
490C4×C13—42no—
491C4×C13—42no—
492Dic13—24no—
493Dic13—24no—
494Dic13—42no—
495Dic13—42no—
496Dic13—42no—
497Dic13C22×C4⋊C418yescomplemented
498Dic13C2×C4×D418yescomplemented
499C25—131no—
500C25C22×D1311yescharacteristic
501C22×D4—138no—
502C22×D4—138no—
503C22×D4—138no—
504C22×D4—134no—
505C23×C4—24no—
506C23×C4—24no—
507C23×C4—42no—
508C23×C4—131no—
509C23×C4—131no—
510C23×C4—138no—
511C23×C4—134no—
512C23×C4—131no—
513C23×C4—131no—
514C23×C4—138no—
515C23×C4—134no—
516C23×C4—131no—
517C23×C4—131no—
518C23×C4—131no—
519C23×C4—134no—
520C23×C4—134no—
521C23×C4—134no—
522C23×C4—264no—
523C23×C4—264no—
524C23×C4—264no—
525C23×C4—264no—
526C23×C4—264no—
527C23×C4—264no—
528C23×C4—264no—
529C23×C4—264no—
530C23×C4—264no—
531C23×C4—264no—
532C23×C4—522no—
533C23×C4—522no—
534C23×C4—522no—
535C23×C4C22×D1311yescharacteristic
536C23×C4C22×D1311yescharacteristic
537C23×C4C22×D1311yescharacteristic
538C23×C4C22×D1314yes—
539C23×C4C22×D1311yescharacteristic
540C23×C4C22×D1311yescharacteristic
541C23×C4C22×D1311yescharacteristic
542C4×D4—1364no—
543C4×D4—2632no—
544C4×D4—2632no—
545C2×C4⋊C4—24no—
546C2×C4⋊C4—42no—
547C2×C4⋊C4—138no—
548C2×C4⋊C4—138no—
549C2×C4⋊C4—134no—
550C2×C4⋊C4—134no—
551C2×C4⋊C4—134no—
552C2×C4⋊C4—134no—
553C2×C4⋊C4—134no—
554C2×C4⋊C4—134no—
555C2×C4⋊C4—134no—
556C2×C4⋊C4—134no—
557C2×C4⋊C4—134no—
558C2×C4⋊C4—134no—
559C2×C4⋊C4—134no—
560C2×C4⋊C4—2632no—
561C2×C4⋊C4—2632no—
562C2×C4⋊C4—264no—
563C2×C4⋊C4—264no—
564C2×C4⋊C4—264no—
565C2×C4⋊C4—264no—
566C2×C4⋊C4—264no—
567C2×C4⋊C4—264no—
568C2×C4⋊C4—264no—
569C2×C4⋊C4—264no—
570C2×C4⋊C4—522no—
571C2×C4⋊C4C22×D1314yes—
572C2×C4⋊C4C22×D1314yes—
573C2×C22⋊C4—24no—
574C2×C22⋊C4—138no—
575C2×C22⋊C4—134no—
576C2×C22⋊C4—134no—
577C2×C22⋊C4—134no—
578C2×C22⋊C4—134no—
579C2×C22⋊C4—264no—
580C2×C22⋊C4—264no—
581C2×C22⋊C4—264no—
582C2×C22⋊C4C4×D1318yescomplemented
583C2×C22⋊C4C22×D1314yes—
584C2×C22⋊C4C22×D1314yes—
585C2×C42—138no—
586C2×C42—134no—
587C2×C42—134no—
588C2×C42—134no—
589C2×C42—264no—
590C2×C42—264no—
591#95—134no—
592#95—134no—
593#95—134no—
594#95—134no—
595#95C22×D1314yes—
596#95C22×D1314yes—
597C2×C13—28no—
598C2×C13D4×C4⋊C418yescomplemented
599C2×C13C23×C4⋊C411yescharacteristic
600C2×C13C22×C4×D411yescharacteristic
601C2×C13C2×#52011yescharacteristic
602C2×C13C2×D4211yescharacteristic
603C2×C13C2×#54711yescharacteristic
604C2×C13C2×D4×Q811yescharacteristic
605C2×C13C2×#55411yescharacteristic
606D13—28no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—134no—
612C24—134no—
613C24—134no—
614C24—132no—
615C24—262no—
616C24—262no—
617C24—262no—
618C24—262no—
619C24C2×C4×D1314yes—
620C24D4×D1314yes—
621C24Q8×D1314yes—
622C24C23×D1312yes—
623C24C23×D1311yescharacteristic
624C2×D4—1364no—
625C2×D4—1316no—
626C2×D4—1316no—
627C2×D4—1316no—
628C22×C4—22no—
629C22×C4—22no—
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—28no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—28no—
645C22×C4—44no—
646C22×C4—416no—
647C22×C4—134no—
648C22×C4—134no—
649C22×C4—134no—
650C22×C4—134no—
651C22×C4—134no—
652C22×C4—134no—
653C22×C4—132no—
654C22×C4—132no—
655C22×C4—134no—
656C22×C4—1316no—
657C22×C4—134no—
658C22×C4—132no—
659C22×C4—132no—
660C22×C4—1316no—
661C22×C4—132no—
662C22×C4—132no—
663C22×C4—132no—
664C22×C4—268no—
665C22×C4—2632no—
666C22×C4—268no—
667C22×C4—268no—
668C22×C4—268no—
669C22×C4—268no—
670C22×C4—268no—
671C22×C4—2632no—
672C22×C4—268no—
673C22×C4—268no—
674C22×C4—262no—
675C22×C4—262no—
676C22×C4—262no—
677C22×C4—262no—
678C22×C4—262no—
679C22×C4—262no—
680C22×C4—262no—
681C22×C4—262no—
682C22×C4—262no—
683C22×C4—268no—
684C22×C4—262no—
685C22×C4—262no—
686C22×C4—262no—
687C22×C4—262no—
688C22×C4—268no—
689C22×C4—524no—
690C22×C4—524no—
691C22×C4—5216no—
692C22×C4—5216no—
693C22×C4—524no—
694C22×C4—5216no—
695C22×C4C2×C4×D1314yes—
696C22×C4C2×C4×D1314yes—
697C22×C4D4×D1314yes—
698C22×C4C23×D1312yes—
699C22×C4C23×D1312yes—
700C22×C4C23×D1312yes—
701C22×C4C23×D1312yes—
702C22×C4C23×D1312yes—
703C22×C4C23×D1312yes—
704C4⋊C4—28no—
705C4⋊C4—44no—
706C4⋊C4—1316no—
707C4⋊C4—1316no—
708C4⋊C4—268no—
709C4⋊C4—268no—
710C4⋊C4—268no—
711C4⋊C4—268no—
712C4⋊C4—268no—
713C4⋊C4—268no—
714C4⋊C4—268no—
715C4⋊C4—268no—
716C4⋊C4—524no—
717C22⋊C4—28no—
718C22⋊C4—1316no—
719C22⋊C4—268no—
720C22⋊C4—268no—
721C22⋊C4—268no—
722C22⋊C4C2×C4×D13116yescomplemented
723C42—1316no—
724C42—268no—
725C42—268no—
726C13C2×D4×C4⋊C411yescharacteristic, complemented, Sylow
727C23—28no—
728C23—28no—
729C23—28no—
730C23—28no—
731C23—28no—
732C23—28no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—1316no—
738C23—134no—
739C23—134no—
740C23—134no—
741C23—268no—
742C23—268no—
743C23—268no—
744C23—268no—
745C23—268no—
746C23—268no—
747C23—262no—
748C23—262no—
749C23—262no—
750C23—262no—
751C23C4⋊C4×D13116yescomplemented
752C23C22×C4×D1314yes—
753C23C22×C4×D1312yes—
754C23C2×D4×D1314yes—
755C23C2×D4×D1312yes—
756C23C2×D4×D1312yes—
757C23#8825112yes—
758C23C2×Q8×D1314yes—
759C23C2×Q8×D1312yes—
760C23#41×D1312yes—
761C23#8825712yes—
762C23C24×D1311yescharacteristic
763D4—1364no—
764C2×C4—28no—
765C2×C4—28no—
766C2×C4—28no—
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—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—416no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—1316no—
787C2×C4—1316no—
788C2×C4—134no—
789C2×C4—134no—
790C2×C4—134no—
791C2×C4—134no—
792C2×C4—134no—
793C2×C4—134no—
794C2×C4—134no—
795C2×C4—134no—
796C2×C4—2632no—
797C2×C4—2632no—
798C2×C4—268no—
799C2×C4—268no—
800C2×C4—262no—
801C2×C4—262no—
802C2×C4—262no—
803C2×C4—262no—
804C2×C4—262no—
805C2×C4—262no—
806C2×C4—262no—
807C2×C4—262no—
808C2×C4—262no—
809C2×C4—262no—
810C2×C4—262no—
811C2×C4—262no—
812C2×C4—262no—
813C2×C4—5216no—
814C2×C4—5216no—
815C2×C4—5216no—
816C2×C4—524no—
817C2×C4—524no—
818C2×C4—524no—
819C2×C4C22×C4×D1314yes—
820C2×C4C22×C4×D1314yes—
821C2×C4C2×D4×D1314yes—
822C22—232no—
823C22—24no—
824C22—24no—
825C22—24no—
826C22—24no—
827C22—24no—
828C22—24no—
829C22—138no—
830C22—2632no—
831C22—264no—
832C22—264no—
833C22—264no—
834C22—264no—
835C22—264no—
836C22—264no—
837C22C2×C4⋊C4×D1314yes—
838C22C2×C4⋊C4×D1318yescomplemented
839C22C4×D4×D1314yes—
840C22#1171925114yes—
841C22#1171929514yes—
842C22#1171933714yes—
843C22#1171934114yes—
844C22#1171936014yes—
845C22C23×C4×D1311yescharacteristic
846C22C22×D4×D1311yescharacteristic
847C22C22×D4×D1311yescharacteristic
848C22C2×#8825111yescharacteristic
849C22C22×Q8×D1311yescharacteristic
850C22C2×#41×D1311yescharacteristic
851C22C2×#8825711yescharacteristic
852C4—24no—
853C4—24no—
854C4—24no—
855C4—42no—
856C4—42no—
857C4—42no—
858C4—138no—
859C4—138no—
860C4—264no—
861C4—264no—
862C4—522no—
863C4—522no—
864C4—522no—
865C2—28no—
866C2—268no—
867C2#1311773418yesdirect product factor
868C2C22×C4⋊C4×D1311yescharacteristic
869C2C2×C4×D4×D1311yescharacteristic
870C2C2×#1171925111yescharacteristic
871C2C2×#1171929511yescharacteristic
872C2C2×#1171936011yescharacteristic
873C2C2×#1171933711yescharacteristic
874C2C2×#1171934111yescharacteristic
subgroupG/H
centerC24C23×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC2×C13×#385C2
socleC24×C13C24
prime radicalC23×C22⋊D13C22
cosocleC23×C13C25
hypercenterC2×#385D13
hypocenterC13C2×D4×C4⋊C4
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
4. C23×#6101C2semidirect
5. C22×C4⋊C4×D13C2semidirect
6. #13117734C2direct (N × H)
7. C2×#11718308C2semidirect
8. C2×#11718633C2semidirect
9. C2×#11718611C2semidirect
10. C2×#11718329C2semidirect
11. C2×#11718650C2semidirect
12. C2×#11718637C2semidirect
13. C2×#11718328C2semidirect
14. C2×#11718603C2semidirect
15. C2×#11718310C2semidirect
16. C2×C13×#385C2semidirect
46. C22×#6101C22semidirect
51. C2×C4⋊C4×D13C22semidirect
53. C2×#88135C4semidirect
56. C13×#385C22semidirect
63. #11718650C22semidirect
64. #11718637C22semidirect
65. #11718633C22semidirect
66. #11718611C22semidirect
67. #11718603C22semidirect
68. #11718329C22semidirect
69. #11718328C22semidirect
70. #11718310C22semidirect
71. #11718308C22semidirect
93. C23×Dic13C2×C4semidirect
111. C22×C4×D13C2×C4semidirect
120. C2×C13×C22⋊C4C2×C4semidirect
128. C2×#6103C2×C4semidirect
144. C2×#6101C2×C4semidirect
145. C2×#6101D4semidirect
157. C2×C4×Dic13C2×C4semidirect
163. #88135C2×C4semidirect
216. C2×C22⋊D13C4⋊C4semidirect
243. C22×Dic13C22×C4semidirect
267. C2×C4×D13C22×C4semidirect
271. C13×C22⋊C4C22×C4semidirect
275. #6103C22×C4semidirect
285. #6101C22×C4semidirect
286. #6101C2×D4semidirect
289. C4×Dic13C22×C4semidirect
301. C2×#385D13semidirect
316. C23×C13C2×C4⋊C4semidirect
338. C22×D13C2×C4⋊C4semidirect
367. C22⋊D13C2×C4⋊C4semidirect
388. C2×Dic13C2×C4⋊C4semidirect
389. C2×Dic13C4×D4semidirect
445. #385C2×D13semidirect
464. C22×C13C22×C4⋊C4semidirect
485. C2×D13C22×C4⋊C4semidirect
497. Dic13C22×C4⋊C4semidirect
498. Dic13C2×C4×D4semidirect
582. C2×C22⋊C4C4×D13semidirect
598. C2×C13D4×C4⋊C4semidirect
722. C22⋊C4C2×C4×D13semidirect
726. C13C2×D4×C4⋊C4semidirect
751. C23C4⋊C4×D13semidirect
838. C22C2×C4⋊C4×D13semidirect
867. C2#13117734direct (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
C23×#61012
C22×C4⋊C4×D132
#131177342
C2×#117183082
C2×#117186332
C2×#117186112
C2×#117183292
C2×#117186502
C2×#117186372
C2×#117183282
C2×#117186032
C2×#117183102
C2×C13×#3852
C2×D4×C4⋊C413