Finite Group Databasebeta

← C2×#13119539 #16031990

Subgroups — C2×#13119539 #16031990

Order 3328.

2898 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88133C211yesmaximal, characteristic, complemented
2C22×#88139C211yesmaximal, characteristic
3#13119539C2116yesmaximal, direct product factor
4C2×#11718338C211yesmaximal, characteristic, complemented
5C2×#11718614C211yesmaximal, characteristic, complemented
6C2×#11718317C211yesmaximal, characteristic, complemented
7C2×#11718622C211yesmaximal, characteristic
8C2×#11718590C211yesmaximal, characteristic, complemented
9C2×#11718331C211yesmaximal, characteristic, complemented
10C2×#11718601C211yesmaximal, characteristic, complemented
11C2×#11718601C211yesmaximal, characteristic, complemented
12C2×#11718314C211yesmaximal, characteristic, complemented
13C2×#11718874C211yesmaximal, characteristic
14C2×#11718873C211yesmaximal, characteristic, complemented
15C2×C4×C4⋊Dic13C211yesmaximal, characteristic, complemented
16C2×C4×C13×C22⋊C4C211yesmaximal, characteristic, complemented
17C24×C4×C13C2211yescharacteristic
18C23×C22⋊D13C2211yescharacteristic
19C23×Dic26C2211yescharacteristic
20C22×C13×C22⋊C4C2211yescharacteristic
21C22×C13×C22⋊C4C2211yescharacteristic
22C22×C42×C13C2211yescharacteristic
23C22×C42×C13C2211yescharacteristic
24C22×C22⋊Dic13C2211yescharacteristic
25C22×C22⋊Dic13C2211yescharacteristic
26C22×C22⋊Dic13C2211yescharacteristic
27C22×#6103C2211yescharacteristic
28C22×#6103C2211yescharacteristic
29C22×#6103C2211yescharacteristic
30C22×#6103C2211yescharacteristic
31C22×#6103C2211yescharacteristic
32C22×#6103C2211yescharacteristic
33C22×C4⋊Dic13C2211yescharacteristic
34C22×C4⋊Dic13C2211yescharacteristic
35C22×C4⋊Dic13C2211yescharacteristic
36C22×C4⋊Dic13C2211yescharacteristic
37C22×C4⋊Dic13C2211yescharacteristic
38C22×#6101C2211yescharacteristic
39C22×#6101C2211yescharacteristic
40C22×C4×Dic13C2211yescharacteristic
41C22×C4×Dic13C2211yescharacteristic
42C2×#88139—28no—
43C2×#88139C2218yes—
44C2×#88133—28no—
45C2×#88133C2218yescomplemented
46C4×C13×C22⋊C4C2218yescomplemented
47C2×C13×#95C2211yescharacteristic
48C2×C13×#95C2211yescharacteristic
49#11718874C2218yes—
50#11718873C2218yescomplemented
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57C2×#88071C2211yescharacteristic
58C2×#88071C2211yescharacteristic
59#11718622C2218yes—
60#11718614C2218yescomplemented
61#11718601C2218yescomplemented
62#11718601C2218yescomplemented
63C4×C4⋊Dic13C2218yescomplemented
64#11718590C2218yescomplemented
65#11718338C2218yescomplemented
66#11718331C2218yescomplemented
67#11718317C2218yescomplemented
68#11718314C2218yescomplemented
69C25×C13C2311yescharacteristic
70C24×D13C2311yescharacteristic
71C23×C4×C13—24no—
72C23×C4×C13—24no—
73C23×C4×C13—42no—
74C23×C4×C13C2311yescharacteristic
75C23×C4×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⋊D13C2314yes—
85C23×Dic13C2311yescharacteristic
86C23×Dic13C2311yescharacteristic
87C23×Dic13C2311yescharacteristic
88C23×Dic13C2311yescharacteristic
89C23×Dic13C2311yescharacteristic
90C23×Dic13C2311yescharacteristic
91C23×Dic13C2311yescharacteristic
92C22×Dic26—24no—
93C22×Dic26—24no—
94C22×Dic26—42no—
95C22×Dic26C2314yes—
96C2×C13×C22⋊C4—24no—
97C2×C13×C22⋊C4D418yes—
98C2×C13×C22⋊C4C2314yes—
99C2×C13×C22⋊C4C2314yes—
100C2×C42×C13—24no—
101C2×C42×C13—42no—
102C2×C42×C13C2314yes—
103C2×C42×C13C2314yes—
104C2×C22⋊Dic13—24no—
105C2×C22⋊Dic13—24no—
106C2×C22⋊Dic13—24no—
107C2×C22⋊Dic13C2314yes—
108C2×C22⋊Dic13C2314yes—
109C2×C22⋊Dic13C2314yes—
110C2×#6103—24no—
111C2×#6103—24no—
112C2×#6103—24no—
113C2×#6103—24no—
114C2×#6103—24no—
115C2×#6103—42no—
116C2×#6103C2314yes—
117C2×#6103C2314yes—
118C2×#6103C2314yes—
119C2×#6103C2314yes—
120C2×#6103C2314yes—
121C2×#6103C2314yes—
122C2×C4⋊Dic13—24no—
123C2×C4⋊Dic13—24no—
124C2×C4⋊Dic13—24no—
125C2×C4⋊Dic13—24no—
126C2×C4⋊Dic13—42no—
127C2×C4⋊Dic13C2314yes—
128C2×C4⋊Dic13C2314yes—
129C2×C4⋊Dic13C2314yes—
130C2×C4⋊Dic13C2314yes—
131C2×C4⋊Dic13C2314yes—
132C2×#6101—24no—
133C2×#6101—24no—
134C2×#6101C2314yes—
135C2×#6101C2314yes—
136C2×C4×Dic13—24no—
137C2×C4×Dic13—24no—
138C2×C4×Dic13C2314yes—
139C2×C4×Dic13C2314yes—
140#88139—232no—
141#88133—232no—
142C13×#95C2314yes—
143C13×#95C2314yes—
144#88071C2314yes—
145#88071C2314yes—
146#88071C2314yes—
147#88071C2314yes—
148#88071C2314yes—
149#88071C2314yes—
150#88071C2314yes—
151#88071C2314yes—
152C2×#2521—131nomaximal, Sylow
153C24×C13—22no—
154C24×C13—22no—
155C24×C13—22no—
156C24×C13—22no—
157C24×C13—22no—
158C24×C13—22no—
159C24×C13C2×D414yes—
160C24×C13C2412yes—
161C24×C13C2411yescharacteristic
162C23×D13—22no—
163C23×D13—22no—
164C23×D13—22no—
165C23×D13—22no—
166C23×D13—22no—
167C23×D13—22no—
168C23×D13—22no—
169C23×D13C2412yes—
170C22×C4×C13—22no—
171C22×C4×C13—22no—
172C22×C4×C13—22no—
173C22×C4×C13—22no—
174C22×C4×C13—22no—
175C22×C4×C13—22no—
176C22×C4×C13—22no—
177C22×C4×C13—22no—
178C22×C4×C13—22no—
179C22×C4×C13—22no—
180C22×C4×C13—22no—
181C22×C4×C13—22no—
182C22×C4×C13—22no—
183C22×C4×C13—28no—
184C22×C4×C13—28no—
185C22×C4×C13—44no—
186C22×C4×C13—416no—
187C22×C4×C13C2×D414yes—
188C22×C4×C13C2×D414yes—
189C22×C4×C13#4114yes—
190C22×C4×C13#4114yes—
191C22×C4×C13#4114yes—
192C22×C4×C13C2412yes—
193C22×C4×C13C2412yes—
194C22×C4×C13C2412yes—
195C22×C4×C13C2412yes—
196C22×C4×C13C2412yes—
197C22×C4×C13C2412yes—
198C2×C22⋊D13—28no—
199C2×C22⋊D13—28no—
200C2×C22⋊D13—44no—
201C2×C22⋊D13—416no—
202C22×Dic13—22no—
203C22×Dic13—22no—
204C22×Dic13—22no—
205C22×Dic13—22no—
206C22×Dic13—22no—
207C22×Dic13—22no—
208C22×Dic13—22no—
209C22×Dic13—22no—
210C22×Dic13—22no—
211C22×Dic13—22no—
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#4114yes—
223C22×Dic13C2412yes—
224C22×Dic13C2412yes—
225C22×Dic13C2412yes—
226C22×Dic13C2412yes—
227C22×Dic13C2412yes—
228C22×Dic13C2412yes—
229C22×Dic13C2412yes—
230C2×Dic26—28no—
231C2×Dic26—28no—
232C2×Dic26—44no—
233C2×Dic26—416no—
234C13×C22⋊C4—28no—
235C13×C22⋊C4C2×D4116yes—
236C42×C13—28no—
237C42×C13—44no—
238C22⋊Dic13—28no—
239C22⋊Dic13—28no—
240C22⋊Dic13—28no—
241#6103—28no—
242#6103—28no—
243#6103—28no—
244#6103—28no—
245#6103—28no—
246#6103—44no—
247C4⋊Dic13—28no—
248C4⋊Dic13—28no—
249C4⋊Dic13—28no—
250C4⋊Dic13—28no—
251C4⋊Dic13—44no—
252#6101—28no—
253#6101—28no—
254C4×Dic13—28no—
255C4×Dic13—28no—
256C22×#126—131no—
257C22×#124—131no—
258#2521—1316no—
259C2×#399—131no—
260C2×#397—131no—
261C2×#395—131no—
262C2×#394—131no—
263C2×#391—131no—
264C2×#388—131no—
265C2×#388—131no—
266C2×#388—131no—
267C2×#387—131no—
268C2×#386—131no—
269C2×#380—131no—
270C2×C4×C4⋊C4—131no—
271C2×C4×C22⋊C4D1311yescharacteristic, complemented
272C23×C13—28no—
273C23×C13—28no—
274C23×C13—28no—
275C23×C13—22no—
276C23×C13—22no—
277C23×C13—22no—
278C23×C13—22no—
279C23×C13—22no—
280C23×C13—22no—
281C23×C13—44no—
282C23×C13—44no—
283C23×C13—44no—
284C23×C13—44no—
285C23×C13C22×D414yes—
286C23×C13C22×D412yes—
287C23×C13C2×#4112yes—
288C23×C13C2×#4112yes—
289C23×C13C2×#4112yes—
290C23×C13C2×#4112yes—
291C23×C13H(5,𝔽2)12yes—
292C23×C132−1+412yes—
293C23×C13C2511yescharacteristic
294C22×D13—22no—
295C22×D13—22no—
296C22×D13—22no—
297C22×D13—22no—
298C22×D13—22no—
299C22×D13—22no—
300C22×D13—22no—
301C22×D13—44no—
302C22×D13—44no—
303C22×D13—44no—
304C22×D13—44no—
305C22×D13—44no—
306C22×D13—44no—
307C22×D13—44no—
308C2×C4×C13—28no—
309C2×C4×C13—28no—
310C2×C4×C13—28no—
311C2×C4×C13—28no—
312C2×C4×C13—28no—
313C2×C4×C13—22no—
314C2×C4×C13—22no—
315C2×C4×C13—22no—
316C2×C4×C13—22no—
317C2×C4×C13—22no—
318C2×C4×C13—22no—
319C2×C4×C13—22no—
320C2×C4×C13—22no—
321C2×C4×C13—22no—
322C2×C4×C13—22no—
323C2×C4×C13—22no—
324C2×C4×C13—22no—
325C2×C4×C13—22no—
326C2×C4×C13—416no—
327C2×C4×C13—44no—
328C2×C4×C13C22×D414yes—
329C2×C4×C13C22×D414yes—
330C2×C4×C13C2×#4114yes—
331C2×C4×C13C2×#4114yes—
332C2×C4×C13C2×#4114yes—
333C22⋊D13—416no—
334C2×Dic13—28no—
335C2×Dic13—22no—
336C2×Dic13—22no—
337C2×Dic13—22no—
338C2×Dic13—22no—
339C2×Dic13—22no—
340C2×Dic13—22no—
341C2×Dic13—22no—
342C2×Dic13—22no—
343C2×Dic13—22no—
344C2×Dic13—22no—
345C2×Dic13—22no—
346C2×Dic13—22no—
347C2×Dic13—22no—
348C2×Dic13—22no—
349C2×Dic13—22no—
350C2×Dic13—22no—
351C2×Dic13—22no—
352C2×Dic13—22no—
353C2×Dic13—22no—
354C2×Dic13—22no—
355C2×Dic13—44no—
356C2×Dic13—44no—
357C2×Dic13—44no—
358C2×Dic13—44no—
359C2×Dic13—44no—
360C2×Dic13—44no—
361C2×Dic13C2×#4114yes—
362Dic26—416no—
363C23×Q8—131no—
364C23×D4—131no—
365C24×C4C2×D1311yescharacteristic
366C2×#126—138no—
367C2×#126—268no—
368C2×#124—138no—
369C2×#124—268no—
370C22×C4⋊C4—131no—
371C22×C4⋊C4—131no—
372C22×C4⋊C4—131no—
373C22×C4⋊C4—131no—
374C22×C4⋊C4—131no—
375C22×C4⋊C4—131no—
376C22×C4⋊C4—131no—
377C22×C22⋊C4—131no—
378C22×C22⋊C4—131no—
379C22×C22⋊C4—131no—
380C22×C22⋊C4—131no—
381C22×C22⋊C4—131no—
382C22×C22⋊C4—131no—
383C22×C22⋊C4—131no—
384C22×C22⋊C4—131no—
385C22×C22⋊C4—131no—
386C22×C22⋊C4C2×D1311yescharacteristic
387C22×C22⋊C4C2×D1311yescharacteristic
388C22×C42—131no—
389C22×C42—131no—
390C22×C42C2×D1311yescharacteristic
391C22×C42C2×D1311yescharacteristic
392#399—138no—
393#397—138no—
394#395—138no—
395#394—138no—
396#391—138no—
397#388—138no—
398#388—138no—
399#388—138no—
400#387—138no—
401#386—138no—
402#380—138no—
403C4×C4⋊C4—138no—
404C4×C22⋊C4C2×D1318yescomplemented
405C2×#95—131no—
406C2×#95—131no—
407C2×#95—131no—
408C2×#95—131no—
409C2×#95—131no—
410C2×#95—131no—
411C2×#95—131no—
412C2×#95—131no—
413C2×#95C2×D1311yescharacteristic
414C2×#95C2×D1311yescharacteristic
415C22×C13—24no—
416C22×C13—24no—
417C22×C13—24no—
418C22×C13—42no—
419C22×C13—42no—
420C22×C13—42no—
421C22×C13—42no—
422C22×C13—416no—
423C22×C13#52914yes—
424C22×C13#53214yes—
425C22×C13#54214yes—
426C22×C13#54614yes—
427C22×C13#54714yes—
428C22×C13#55114yes—
429C22×C13#55614yes—
430C22×C13C23×D411yescharacteristic
431C22×C13C22×#4111yescharacteristic
432C22×C13C22×#4111yescharacteristic
433C22×C13C22×#4111yescharacteristic
434C22×C13C22×#4111yescharacteristic
435C22×C13C2×H(5,𝔽2)11yescharacteristic
436C22×C13C2×2−1+411yescharacteristic
437C2×D13—42no—
438C2×D13—42no—
439C2×D13—42no—
440C2×D13—42no—
441C2×D13—42no—
442C2×D13—42no—
443C2×D13—42no—
444C2×D13—88no—
445C4×C13—24no—
446C4×C13—24no—
447C4×C13—24no—
448C4×C13—24no—
449C4×C13—24no—
450C4×C13—42no—
451Dic13—24no—
452Dic13—42no—
453Dic13—42no—
454Dic13—42no—
455Dic13—42no—
456Dic13—42no—
457Dic13—42no—
458C25—131no—
459C25C22×D1311yescharacteristic
460C22×Q8—134no—
461C22×Q8—264no—
462C22×Q8—264no—
463C22×Q8—522no—
464C22×D4—134no—
465C22×D4—264no—
466C22×D4—264no—
467C22×D4—522no—
468C23×C4—24no—
469C23×C4—24no—
470C23×C4—42no—
471C23×C4—131no—
472C23×C4—131no—
473C23×C4—131no—
474C23×C4—131no—
475C23×C4—131no—
476C23×C4—131no—
477C23×C4—131no—
478C23×C4C22×D1311yescharacteristic
479C23×C4C22×D1314yes—
480C23×C4C22×D1311yescharacteristic
481C23×C4C22×D1311yescharacteristic
482C23×C4C22×D1311yescharacteristic
483C23×C4C22×D1311yescharacteristic
484C23×C4C22×D1311yescharacteristic
485#126—2632no—
486#124—2632no—
487C2×C4⋊C4—134no—
488C2×C4⋊C4—134no—
489C2×C4⋊C4—134no—
490C2×C4⋊C4—134no—
491C2×C4⋊C4—134no—
492C2×C4⋊C4—134no—
493C2×C4⋊C4—134no—
494C2×C4⋊C4—264no—
495C2×C4⋊C4—264no—
496C2×C4⋊C4—264no—
497C2×C4⋊C4—264no—
498C2×C4⋊C4—264no—
499C2×C4⋊C4—264no—
500C2×C4⋊C4—522no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—134no—
503C2×C22⋊C4—134no—
504C2×C22⋊C4—134no—
505C2×C22⋊C4—134no—
506C2×C22⋊C4—134no—
507C2×C22⋊C4—134no—
508C2×C22⋊C4—134no—
509C2×C22⋊C4—134no—
510C2×C22⋊C4—134no—
511C2×C22⋊C4—264no—
512C2×C22⋊C4—264no—
513C2×C22⋊C4—264no—
514C2×C22⋊C4—264no—
515C2×C22⋊C4—264no—
516C2×C22⋊C4—264no—
517C2×C22⋊C4—264no—
518C2×C22⋊C4—264no—
519C2×C22⋊C4—522no—
520C2×C22⋊C4D5218yes—
521C2×C22⋊C4C22×D1314yes—
522C2×C22⋊C4C22×D1314yes—
523C2×C42—24no—
524C2×C42—42no—
525C2×C42—134no—
526C2×C42—134no—
527C2×C42—264no—
528C2×C42—264no—
529C2×C42C22×D1314yes—
530C2×C42C22×D1314yes—
531#95—134no—
532#95—134no—
533#95—134no—
534#95—134no—
535#95—134no—
536#95—134no—
537#95—134no—
538#95—134no—
539#95C22×D1314yes—
540#95C22×D1314yes—
541C2×C13—44no—
542C2×C13#252118yescomplemented
543C2×C13C2×#52911yescharacteristic
544C2×C13C2×#53211yescharacteristic
545C2×C13C2×#54211yescharacteristic
546C2×C13C2×#54611yescharacteristic
547C2×C13C2×#54711yescharacteristic
548C2×C13C2×#55111yescharacteristic
549C2×C13C2×#55611yescharacteristic
550D13—82no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—22no—
557C24—132no—
558C24—262no—
559C24—262no—
560C24—262no—
561C24—262no—
562C24—262no—
563C24—262no—
564C24—262no—
565C24C2×D5214yes—
566C24C23×D1312yes—
567C24C23×D1311yescharacteristic
568C2×Q8—268no—
569C2×Q8—268no—
570C2×Q8—524no—
571C2×Q8—5216no—
572C2×D4—268no—
573C2×D4—268no—
574C2×D4—524no—
575C2×D4—5216no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—28no—
590C22×C4—28no—
591C22×C4—44no—
592C22×C4—416no—
593C22×C4—134no—
594C22×C4—132no—
595C22×C4—132no—
596C22×C4—132no—
597C22×C4—132no—
598C22×C4—132no—
599C22×C4—132no—
600C22×C4—132no—
601C22×C4—262no—
602C22×C4—262no—
603C22×C4—262no—
604C22×C4—262no—
605C22×C4—262no—
606C22×C4—262no—
607C22×C4—262no—
608C22×C4—262no—
609C22×C4—262no—
610C22×C4—262no—
611C22×C4—262no—
612C22×C4—262no—
613C22×C4—262no—
614C22×C4—262no—
615C22×C4—262no—
616C22×C4—262no—
617C22×C4—262no—
618C22×C4—262no—
619C22×C4—262no—
620C22×C4—262no—
621C22×C4C2×D5214yes—
622C22×C4C2×D5214yes—
623C22×C4#612714yes—
624C22×C4#612714yes—
625C22×C4#612914yes—
626C22×C4C23×D1312yes—
627C22×C4C23×D1312yes—
628C22×C4C23×D1312yes—
629C22×C4C23×D1312yes—
630C22×C4C23×D1312yes—
631C22×C4C23×D1312yes—
632C4⋊C4—268no—
633C4⋊C4—268no—
634C4⋊C4—268no—
635C4⋊C4—268no—
636C4⋊C4—268no—
637C4⋊C4—268no—
638C4⋊C4—524no—
639C22⋊C4—28no—
640C22⋊C4—268no—
641C22⋊C4—268no—
642C22⋊C4—268no—
643C22⋊C4—268no—
644C22⋊C4—268no—
645C22⋊C4—268no—
646C22⋊C4—268no—
647C22⋊C4—268no—
648C22⋊C4—524no—
649C22⋊C4C2×D52116yes—
650C42—28no—
651C42—44no—
652C42—268no—
653C42—268no—
654C13C2×#252111yescharacteristic, complemented, Sylow
655C23—28no—
656C23—28no—
657C23—28no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—44no—
668C23—262no—
669C23—262no—
670C23—262no—
671C23—262no—
672C23—262no—
673C23—262no—
674C23—262no—
675C23—524no—
676C23—524no—
677C23—524no—
678C23—524no—
679C23—524no—
680C23—524no—
681C23—524no—
682C23C22×D5214yes—
683C23C22×D5212yes—
684C23C2×#612712yes—
685C23C2×#612712yes—
686C23C2×#612912yes—
687C23#8825112yes—
688C23#41×D1312yes—
689C23#8825712yes—
690C23C24×D1311yescharacteristic
691Q8—5216no—
692D4—5216no—
693C2×C4—28no—
694C2×C4—28no—
695C2×C4—28no—
696C2×C4—28no—
697C2×C4—28no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—416no—
712C2×C4—44no—
713C2×C4—134no—
714C2×C4—268no—
715C2×C4—262no—
716C2×C4—262no—
717C2×C4—262no—
718C2×C4—262no—
719C2×C4—262no—
720C2×C4—262no—
721C2×C4—262no—
722C2×C4—262no—
723C2×C4—262no—
724C2×C4—262no—
725C2×C4—262no—
726C2×C4—262no—
727C2×C4—262no—
728C2×C4—262no—
729C2×C4—262no—
730C2×C4—262no—
731C2×C4—262no—
732C2×C4—262no—
733C2×C4—262no—
734C2×C4—262no—
735C2×C4—524no—
736C2×C4—524no—
737C2×C4—524no—
738C2×C4—524no—
739C2×C4—524no—
740C2×C4—524no—
741C2×C4C22×D5214yes—
742C2×C4C22×D5214yes—
743C2×C4C2×#612714yes—
744C2×C4C2×#612714yes—
745C2×C4C2×#612914yes—
746C22—24no—
747C22—24no—
748C22—24no—
749C22—42no—
750C22—416no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—522no—
755C22—522no—
756C22—522no—
757C22—522no—
758C22—522no—
759C22—522no—
760C22—522no—
761C22—1048no—
762C22#1171918214yes—
763C22#1171920014yes—
764C22#1171923814yes—
765C22#1171924314yes—
766C22#1171925914yes—
767C22#1171926014yes—
768C22#1171926614yes—
769C22C23×D5211yescharacteristic
770C22C22×#612711yescharacteristic
771C22C22×#612711yescharacteristic
772C22C22×#612911yescharacteristic
773C22C2×#8825111yescharacteristic
774C22C2×#41×D1311yescharacteristic
775C22C2×#8825711yescharacteristic
776C4—24no—
777C4—24no—
778C4—24no—
779C4—24no—
780C4—24no—
781C4—42no—
782C4—264no—
783C4—522no—
784C4—522no—
785C4—522no—
786C4—522no—
787C4—522no—
788C4—522no—
789C2—44no—
790C2—1042no—
791C2#1311953918yesdirect product factor
792C2C2×#1171924311yescharacteristic
793C2C2×#1171918211yescharacteristic
794C2C2×#1171926611yescharacteristic
795C2C2×#1171925911yescharacteristic
796C2C2×#1171926011yescharacteristic
797C2C2×#1171920011yescharacteristic
798C2C2×#1171923811yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C4×C13×C22⋊C4C2
socleC24×C13C24
prime radicalC23×C22⋊D13C22
hypercenterC2×C4×C22⋊C4D13
hypocenterC13C2×#2521
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#88133C2semidirect
3. #13119539C2direct (N × H)
4. C2×#11718338C2semidirect
5. C2×#11718614C2semidirect
6. C2×#11718317C2semidirect
8. C2×#11718590C2semidirect
9. C2×#11718331C2semidirect
10. C2×#11718601C2semidirect
11. C2×#11718601C2semidirect
12. C2×#11718314C2semidirect
14. C2×#11718873C2semidirect
15. C2×C4×C4⋊Dic13C2semidirect
16. C2×C4×C13×C22⋊C4C2semidirect
45. C2×#88133C22semidirect
46. C4×C13×C22⋊C4C22semidirect
50. #11718873C22semidirect
60. #11718614C22semidirect
61. #11718601C22semidirect
62. #11718601C22semidirect
63. C4×C4⋊Dic13C22semidirect
64. #11718590C22semidirect
65. #11718338C22semidirect
66. #11718331C22semidirect
67. #11718317C22semidirect
68. #11718314C22semidirect
271. C2×C4×C22⋊C4D13semidirect
404. C4×C22⋊C4C2×D13semidirect
542. C2×C13#2521semidirect
654. C13C2×#2521semidirect
791. C2#13119539direct (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
#131195392
C2×#117183382
C2×#117186142
C2×#117183172
C2×#117186222
C2×#117185902
C2×#117183312
C2×#117186012
C2×#117183142
C2×#117188742
C2×#117188732
C2×C4×C4⋊Dic132
C2×C4×C13×C22⋊C42
C2×#252113