Finite Group Databasebeta

← C2×#13118792 #16030580

Subgroups — C2×#13118792 #16030580

Order 3328.

3006 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×#88124C211yesmaximal, characteristic, complemented
2C22×#88135C211yesmaximal, characteristic
3#13118792C2116yesmaximal, direct product factor
4C2×#11718336C211yesmaximal, characteristic, complemented
5C2×#11718655C211yesmaximal, characteristic, complemented
6C2×#11718622C211yesmaximal, characteristic
7C2×#11718620C211yesmaximal, characteristic
8C2×#11718606C211yesmaximal, characteristic, complemented
9C2×#11718642C211yesmaximal, characteristic, complemented
10C2×#11718315C211yesmaximal, characteristic, complemented
11C2×#11718313C211yesmaximal, characteristic, complemented
12C2×#11718611C211yesmaximal, characteristic, complemented
13C2×#11718329C211yesmaximal, characteristic, complemented
14C2×#11718603C211yesmaximal, characteristic, complemented
15C2×C4×#6103C211yesmaximal, characteristic, complemented
16C2×C13×#388C211yesmaximal, characteristic, complemented
17C23×C22⋊D13C2211yescharacteristic
18C24×Dic13C2211yescharacteristic
19C23×C4×D13C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C13×C22⋊C4C2211yescharacteristic
22C22×C13×C22⋊C4C2211yescharacteristic
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C42×C13C2211yescharacteristic
25C22×C22⋊Dic13C2211yescharacteristic
26C22×C22⋊Dic13C2211yescharacteristic
27C22×#6103C2211yescharacteristic
28C22×#6103C2211yescharacteristic
29C22×#6103C2211yescharacteristic
30C22×#6103C2211yescharacteristic
31C22×#6103C2211yescharacteristic
32C22×C4⋊Dic13C2211yescharacteristic
33C22×C4⋊Dic13C2211yescharacteristic
34C22×C4⋊Dic13C2211yescharacteristic
35C22×#6101C2211yescharacteristic
36C22×#6101C2211yescharacteristic
37C22×#6101C2211yescharacteristic
38C22×#6101C2211yescharacteristic
39C22×#6101C2211yescharacteristic
40C22×C4×Dic13C2211yescharacteristic
41C22×C4×Dic13C2211yescharacteristic
42C2×#88135—28no—
43C2×#88135C2218yes—
44C2×#88124—28no—
45C2×#88124C2218yescomplemented
46C13×#388C2218yescomplemented
47C2×C13×#95C2211yescharacteristic
48C2×C13×#95C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57#11718655C2218yescomplemented
58#11718642C2218yescomplemented
59#11718622C2218yes—
60#11718620C2218yes—
61#11718611C2218yescomplemented
62#11718606C2218yescomplemented
63#11718603C2218yescomplemented
64C4×#6103C2218yescomplemented
65#11718336C2218yescomplemented
66#11718329C2218yescomplemented
67#11718315C2218yescomplemented
68#11718313C2218yescomplemented
69C25×C13C2311yescharacteristic
70C24×D13C2311yescharacteristic
71C23×C4×C13C2311yescharacteristic
72C23×C4×C13C2311yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C22×C22⋊D13—24no—
78C22×C22⋊D13—24no—
79C22×C22⋊D13—24no—
80C22×C22⋊D13C2314yes—
81C23×Dic13—24no—
82C23×Dic13—24no—
83C23×Dic13—42no—
84C23×Dic13C2311yescharacteristic
85C23×Dic13C2311yescharacteristic
86C23×Dic13C2311yescharacteristic
87C23×Dic13C2311yescharacteristic
88C23×Dic13C2314yes—
89C23×Dic13C2311yescharacteristic
90C23×Dic13C2311yescharacteristic
91C23×Dic13C2311yescharacteristic
92C22×C4×D13—24no—
93C22×C4×D13—24no—
94C22×C4×D13—42no—
95C22×C4×D13C2314yes—
96C2×C13×C4⋊C4—24no—
97C2×C13×C4⋊C4C2314yes—
98C2×C13×C22⋊C4—24no—
99C2×C13×C22⋊C4—24no—
100C2×C13×C22⋊C4—24no—
101C2×C13×C22⋊C4C2314yes—
102C2×C13×C22⋊C4C2314yes—
103C2×C13×C22⋊C4C2314yes—
104C2×C42×C13—24no—
105C2×C42×C13C2314yes—
106C2×C22⋊Dic13—24no—
107C2×C22⋊Dic13—42no—
108C2×C22⋊Dic13C2314yes—
109C2×C22⋊Dic13C2314yes—
110C2×#6103—24no—
111C2×#6103—24no—
112C2×#6103—24no—
113C2×#6103—24no—
114C2×#6103—42no—
115C2×#6103C2314yes—
116C2×#6103C2314yes—
117C2×#6103C2314yes—
118C2×#6103C2314yes—
119C2×#6103C2314yes—
120C2×C4⋊Dic13—24no—
121C2×C4⋊Dic13—24no—
122C2×C4⋊Dic13—24no—
123C2×C4⋊Dic13C2314yes—
124C2×C4⋊Dic13C2314yes—
125C2×C4⋊Dic13C2314yes—
126C2×#6101—24no—
127C2×#6101—24no—
128C2×#6101—24no—
129C2×#6101—42no—
130C2×#6101D418yes—
131C2×#6101C2314yes—
132C2×#6101C2314yes—
133C2×#6101C2314yes—
134C2×#6101C2314yes—
135C2×#6101C2314yes—
136C2×C4×Dic13—24no—
137C2×C4×Dic13—42no—
138C2×C4×Dic13C2314yes—
139C2×C4×Dic13C2314yes—
140#88135—232no—
141#88124—232no—
142C13×#95C2314yes—
143C13×#95C2314yes—
144#88071C2314yes—
145#88071C2314yes—
146#88071C2314yes—
147#88071C2314yes—
148#88071C2314yes—
149#88071C2314yes—
150#88071C2314yes—
151#88071C2314yes—
152C2×#2460—131nomaximal, Sylow
153C24×C13—22no—
154C24×C13—22no—
155C24×C13—22no—
156C24×C13—22no—
157C24×C13—22no—
158C24×C13—22no—
159C24×C13#4114yes—
160C24×C13C2412yes—
161C24×C13C2411yescharacteristic
162C23×D13—22no—
163C23×D13—22no—
164C23×D13—22no—
165C23×D13—22no—
166C23×D13—22no—
167C23×D13—22no—
168C23×D13#4114yes—
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—22no—
184C22×C4×C13—22no—
185C22×C4×C13—22no—
186C22×C4×C13C2×D414yes—
187C22×C4×C13#4114yes—
188C22×C4×C13C2412yes—
189C22×C4×C13C2412yes—
190C22×C4×C13C2412yes—
191C22×C4×C13C2412yes—
192C22×C4×C13C2412yes—
193C22×C4×C13C2412yes—
194C2×C22⋊D13—232no—
195C2×C22⋊D13—28no—
196C2×C22⋊D13—28no—
197C2×C22⋊D13—28no—
198C22×Dic13—22no—
199C22×Dic13—22no—
200C22×Dic13—22no—
201C22×Dic13—22no—
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—28no—
217C22×Dic13—28no—
218C22×Dic13—44no—
219C22×Dic13—416no—
220C22×Dic13C2×D414yes—
221C22×Dic13C2×D414yes—
222C22×Dic13#4114yes—
223C22×Dic13C2412yes—
224C22×Dic13C2412yes—
225C22×Dic13C2412yes—
226C22×Dic13C2412yes—
227C22×Dic13C2412yes—
228C22×Dic13C2412yes—
229C22×Dic13C2412yes—
230C2×C4×D13—28no—
231C2×C4×D13—28no—
232C2×C4×D13—44no—
233C2×C4×D13—416no—
234C13×C4⋊C4—28no—
235C13×C22⋊C4—28no—
236C13×C22⋊C4—28no—
237C13×C22⋊C4—28no—
238C42×C13—28no—
239C22⋊Dic13—28no—
240C22⋊Dic13—44no—
241#6103—28no—
242#6103—28no—
243#6103—28no—
244#6103—28no—
245#6103—44no—
246C4⋊Dic13—28no—
247C4⋊Dic13—28no—
248C4⋊Dic13—28no—
249#6101—28no—
250#6101—28no—
251#6101—28no—
252#6101—44no—
253#6101C2×D4116yes—
254C4×Dic13—28no—
255C4×Dic13—44no—
256C22×#125—131no—
257C22×C4×D4—131no—
258#2460—1316no—
259C2×#397—131no—
260C2×#396—131no—
261C2×#394—131no—
262C2×#394—131no—
263C2×#388—131no—
264C2×#388D1311yescharacteristic, complemented
265C2×#387—131no—
266C2×#387—131no—
267C2×#387—131no—
268C2×#385—131no—
269C2×#385—131no—
270C2×#380—131no—
271C2×C4×C22⋊C4—131no—
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×D412yes—
286C23×C13C2×#4114yes—
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—28no—
295C22×D13—28no—
296C22×D13—28no—
297C22×D13—22no—
298C22×D13—22no—
299C22×D13—22no—
300C22×D13—22no—
301C22×D13—22no—
302C22×D13—22no—
303C22×D13—44no—
304C22×D13—44no—
305C22×D13—44no—
306C22×D13—44no—
307C22×D13C2×#4114yes—
308C2×C4×C13—28no—
309C2×C4×C13—28no—
310C2×C4×C13—22no—
311C2×C4×C13—22no—
312C2×C4×C13—22no—
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—44no—
327C2×C4×C13—44no—
328C2×C4×C13—44no—
329C2×C4×C13—44no—
330C2×C4×C13C22×D414yes—
331C2×C4×C13C2×#4114yes—
332C22⋊D13—232no—
333C2×Dic13—28no—
334C2×Dic13—28no—
335C2×Dic13—28no—
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—416no—
355C2×Dic13—44no—
356C2×Dic13—44no—
357C2×Dic13—44no—
358C2×Dic13—44no—
359C2×Dic13C22×D414yes—
360C2×Dic13C22×D414yes—
361C2×Dic13C2×#4114yes—
362C4×D13—416no—
363C23×D4—131no—
364C24×C4—131no—
365C24×C4—131no—
366C2×#125—138no—
367C2×#125—268no—
368C2×C4×D4—138no—
369C2×C4×D4—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×C4⋊C4—131no—
378C22×C4⋊C4C2×D1311yescharacteristic
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×C22⋊C4C2×D1311yescharacteristic
389C22×C42—131no—
390C22×C42—131no—
391C22×C42C2×D1311yescharacteristic
392#397—138no—
393#396—138no—
394#394—138no—
395#394—138no—
396#388—138no—
397#388C2×D1318yescomplemented
398#387—138no—
399#387—138no—
400#387—138no—
401#385—138no—
402#385—138no—
403#380—138no—
404C4×C22⋊C4—138no—
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#52514yes—
424C22×C13#52914yes—
425C22×C13#53914yes—
426C22×C13#54614yes—
427C22×C13#54814yes—
428C22×C13#55214yes—
429C22×C13#55314yes—
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—24no—
438C2×D13—24no—
439C2×D13—24no—
440C2×D13—42no—
441C2×D13—42no—
442C2×D13—42no—
443C2×D13—42no—
444C2×D13—416no—
445C4×C13—24no—
446C4×C13—24no—
447C4×C13—42no—
448C4×C13—42no—
449C4×C13—42no—
450C4×C13—42no—
451Dic13—24no—
452Dic13—24no—
453Dic13—24no—
454Dic13—42no—
455Dic13—42no—
456Dic13—42no—
457Dic13—42no—
458C25—131no—
459C25C22×D1311yescharacteristic
460C22×D4—134no—
461C22×D4—264no—
462C22×D4—264no—
463C22×D4—264no—
464C23×C4—131no—
465C23×C4—131no—
466C23×C4—131no—
467C23×C4—131no—
468C23×C4—131no—
469C23×C4—131no—
470C23×C4—131no—
471C23×C4—134no—
472C23×C4—134no—
473C23×C4—264no—
474C23×C4—264no—
475C23×C4—264no—
476C23×C4—264no—
477C23×C4—522no—
478C23×C4—522no—
479C23×C4C22×D1311yescharacteristic
480C23×C4C22×D1311yescharacteristic
481C23×C4C22×D1311yescharacteristic
482C23×C4C22×D1311yescharacteristic
483C23×C4C22×D1311yescharacteristic
484C23×C4C22×D1311yescharacteristic
485#125—2632no—
486C4×D4—2632no—
487C2×C4⋊C4—24no—
488C2×C4⋊C4—138no—
489C2×C4⋊C4—134no—
490C2×C4⋊C4—134no—
491C2×C4⋊C4—134no—
492C2×C4⋊C4—134no—
493C2×C4⋊C4—134no—
494C2×C4⋊C4—134no—
495C2×C4⋊C4—134no—
496C2×C4⋊C4—134no—
497C2×C4⋊C4—264no—
498C2×C4⋊C4—264no—
499C2×C4⋊C4—264no—
500C2×C4⋊C4—264no—
501C2×C4⋊C4—264no—
502C2×C4⋊C4—264no—
503C2×C4⋊C4—522no—
504C2×C4⋊C4C22×D1314yes—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—134no—
509C2×C22⋊C4—134no—
510C2×C22⋊C4—134no—
511C2×C22⋊C4—134no—
512C2×C22⋊C4—134no—
513C2×C22⋊C4—134no—
514C2×C22⋊C4—134no—
515C2×C22⋊C4—264no—
516C2×C22⋊C4—264no—
517C2×C22⋊C4—264no—
518C2×C22⋊C4—264no—
519C2×C22⋊C4—264no—
520C2×C22⋊C4—522no—
521C2×C22⋊C4—522no—
522C2×C22⋊C4C22×D1314yes—
523C2×C22⋊C4C22×D1314yes—
524C2×C22⋊C4C22×D1314yes—
525C2×C42—24no—
526C2×C42—134no—
527C2×C42—134no—
528C2×C42—264no—
529C2×C42—522no—
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#246018yescomplemented
543C2×C13C2×#52511yescharacteristic
544C2×C13C2×#52911yescharacteristic
545C2×C13C2×#53911yescharacteristic
546C2×C13C2×#54611yescharacteristic
547C2×C13C2×#54811yescharacteristic
548C2×C13C2×#55211yescharacteristic
549C2×C13C2×#55311yescharacteristic
550D13—44no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—22no—
557C24—134no—
558C24—132no—
559C24—262no—
560C24—262no—
561C24—262no—
562C24—262no—
563C24—262no—
564C24—262no—
565C24#612714yes—
566C24C23×D1312yes—
567C24C23×D1311yescharacteristic
568C2×D4—268no—
569C2×D4—268no—
570C2×D4—2632no—
571C2×D4—268no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
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—134no—
589C22×C4—134no—
590C22×C4—134no—
591C22×C4—132no—
592C22×C4—132no—
593C22×C4—132no—
594C22×C4—132no—
595C22×C4—132no—
596C22×C4—132no—
597C22×C4—132no—
598C22×C4—268no—
599C22×C4—268no—
600C22×C4—268no—
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—268no—
620C22×C4—524no—
621C22×C4—5216no—
622C22×C4—524no—
623C22×C4—5216no—
624C22×C4D4×D1314yes—
625C22×C4#612914yes—
626C22×C4C23×D1312yes—
627C22×C4C23×D1312yes—
628C22×C4C23×D1312yes—
629C22×C4C23×D1312yes—
630C22×C4C23×D1312yes—
631C22×C4C23×D1312yes—
632C4⋊C4—28no—
633C4⋊C4—1316no—
634C4⋊C4—268no—
635C4⋊C4—268no—
636C4⋊C4—268no—
637C4⋊C4—268no—
638C4⋊C4—268no—
639C4⋊C4—268no—
640C4⋊C4—524no—
641C22⋊C4—28no—
642C22⋊C4—28no—
643C22⋊C4—28no—
644C22⋊C4—268no—
645C22⋊C4—268no—
646C22⋊C4—268no—
647C22⋊C4—268no—
648C22⋊C4—268no—
649C22⋊C4—524no—
650C22⋊C4—524no—
651C42—28no—
652C42—268no—
653C42—524no—
654C13C2×#246011yescharacteristic, 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—134no—
669C23—268no—
670C23—262no—
671C23—262no—
672C23—262no—
673C23—268no—
674C23—262no—
675C23—262no—
676C23—262no—
677C23—268no—
678C23—524no—
679C23—524no—
680C23—524no—
681C23—524no—
682C23C2×#612714yes—
683C23C2×#612712yes—
684C23C2×D4×D1312yes—
685C23C2×#612912yes—
686C23#41×D1312yes—
687C23#41×D1312yes—
688C23#8825612yes—
689C23#8825712yes—
690C23C24×D1311yescharacteristic
691D4—2632no—
692C2×C4—28no—
693C2×C4—28no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
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—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—134no—
715C2×C4—134no—
716C2×C4—134no—
717C2×C4—268no—
718C2×C4—268no—
719C2×C4—268no—
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—262no—
736C2×C4—262no—
737C2×C4—262no—
738C2×C4—5216no—
739C2×C4—5216no—
740C2×C4—524no—
741C2×C4—524no—
742C2×C4—524no—
743C2×C4—524no—
744C2×C4C2×D4×D1314yes—
745C2×C4C2×#612914yes—
746C22—24no—
747C22—24no—
748C22—24no—
749C22—416no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—264no—
755C22—264no—
756C22—264no—
757C22—5216no—
758C22—522no—
759C22—522no—
760C22—522no—
761C22—522no—
762C22#1171923614yes—
763C22#1171925214yes—
764C22#1171927014yes—
765C22#1171930314yes—
766C22#1171935914yes—
767C22#1171938514yes—
768C22#1171941214yes—
769C22C22×#612711yescharacteristic
770C22C22×D4×D1311yescharacteristic
771C22C22×#612911yescharacteristic
772C22C2×#41×D1311yescharacteristic
773C22C2×#41×D1311yescharacteristic
774C22C2×#8825611yescharacteristic
775C22C2×#8825711yescharacteristic
776C4—24no—
777C4—24no—
778C4—42no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—264no—
783C4—264no—
784C4—264no—
785C4—522no—
786C4—522no—
787C4—522no—
788C4—522no—
789C2—44no—
790C2—524no—
791C2#1311879218yesdirect product factor
792C2C2×#1171925211yescharacteristic
793C2C2×#1171938511yescharacteristic
794C2C2×#1171941211yescharacteristic
795C2C2×#1171935911yescharacteristic
796C2C2×#1171930311yescharacteristic
797C2C2×#1171923611yescharacteristic
798C2C2×#1171927011yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#388C2
socleC24×C13C24
prime radicalC23×C22⋊D13C22
hypercenterC2×#388D13
hypocenterC13C2×#2460
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×#88124C2semidirect
3. #13118792C2direct (N × H)
4. C2×#11718336C2semidirect
5. C2×#11718655C2semidirect
8. C2×#11718606C2semidirect
9. C2×#11718642C2semidirect
10. C2×#11718315C2semidirect
11. C2×#11718313C2semidirect
12. C2×#11718611C2semidirect
13. C2×#11718329C2semidirect
14. C2×#11718603C2semidirect
15. C2×C4×#6103C2semidirect
16. C2×C13×#388C2semidirect
45. C2×#88124C22semidirect
46. C13×#388C22semidirect
57. #11718655C22semidirect
58. #11718642C22semidirect
61. #11718611C22semidirect
62. #11718606C22semidirect
63. #11718603C22semidirect
64. C4×#6103C22semidirect
65. #11718336C22semidirect
66. #11718329C22semidirect
67. #11718315C22semidirect
68. #11718313C22semidirect
264. C2×#388D13semidirect
397. #388C2×D13semidirect
542. C2×C13#2460semidirect
654. C13C2×#2460semidirect
791. C2#13118792direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881242
C22×#881352
#131187922
C2×#117183362
C2×#117186552
C2×#117186222
C2×#117186202
C2×#117186062
C2×#117186422
C2×#117183152
C2×#117183132
C2×#117186112
C2×#117183292
C2×#117186032
C2×C4×#61032
C2×C13×#3882
C2×#246013