Finite Group Databasebeta

← C2×#13118308 #16030622

Subgroups — C2×#13118308 #16030622

Order 3328.

3222 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88137C211yesmaximal, characteristic
2C22×#88135C211yesmaximal, characteristic
3#13118308C2116yesmaximal, direct product factor
4C2×#11718319C211yesmaximal, characteristic, complemented
5C2×#11718645C211yesmaximal, characteristic, complemented
6C2×#11718613C211yesmaximal, characteristic, complemented
7C2×#11718316C211yesmaximal, characteristic, complemented
8C2×#11718313C211yesmaximal, characteristic, complemented
9C2×#11718617C211yesmaximal, characteristic
10C2×#11718607C211yesmaximal, characteristic, complemented
11C2×#11718650C211yesmaximal, characteristic, complemented
12C2×#11718325C211yesmaximal, characteristic, complemented
13C2×#11718604C211yesmaximal, characteristic, complemented
14C2×#11718328C211yesmaximal, characteristic, complemented
15C2×D13×#95C211yesmaximal, characteristic, complemented
16C2×C13×#397C211yesmaximal, characteristic, complemented
17C23×C22⋊D13C2211yescharacteristic
18C24×Dic13C2211yescharacteristic
19C23×C4×D13C2211yescharacteristic
20C23×C4×D13C2211yescharacteristic
21C23×C4×D13C2211yescharacteristic
22C22×C13×C4⋊C4C2211yescharacteristic
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C13×C22⋊C4C2211yescharacteristic
26C22×C22⋊Dic13C2211yescharacteristic
27C22×C22⋊Dic13C2211yescharacteristic
28C22×#6103C2211yescharacteristic
29C22×#6103C2211yescharacteristic
30C22×#6103C2211yescharacteristic
31C22×C4⋊Dic13C2211yescharacteristic
32C22×#6101C2211yescharacteristic
33C22×#6101C2211yescharacteristic
34C22×#6101C2211yescharacteristic
35C22×#6101C2211yescharacteristic
36C22×#6101C2211yescharacteristic
37C22×C4×Dic13C2211yescharacteristic
38C2×#88137—28no—
39C2×#88137C2218yes—
40C2×#88135—28no—
41C2×#88135C2218yes—
42C13×#397C2218yescomplemented
43C2×C13×#95C2211yescharacteristic
44C2×C13×#95C2211yescharacteristic
45C2×C13×#95C2211yescharacteristic
46C2×#88071C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57#11718650C2218yescomplemented
58#11718645C2218yescomplemented
59#11718617C2218yes—
60#11718613C2218yescomplemented
61#11718607C2218yescomplemented
62#11718604C2218yescomplemented
63#11718328C2218yescomplemented
64#11718325C2218yescomplemented
65D13×#95C2218yescomplemented
66#11718319C2218yescomplemented
67#11718316C2218yescomplemented
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⋊D13D418yes—
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—24no—
95C22×C4×D13—24no—
96C22×C4×D13—24no—
97C22×C4×D13—24no—
98C22×C4×D13—24no—
99C22×C4×D13—42no—
100C22×C4×D13—42no—
101C22×C4×D13C2314yes—
102C22×C4×D13C2314yes—
103C22×C4×D13C2314yes—
104C2×C13×C4⋊C4—42no—
105C2×C13×C4⋊C4C2314yes—
106C2×C13×C22⋊C4—24no—
107C2×C13×C22⋊C4—24no—
108C2×C13×C22⋊C4—42no—
109C2×C13×C22⋊C4C2314yes—
110C2×C13×C22⋊C4C2314yes—
111C2×C13×C22⋊C4C2314yes—
112C2×C22⋊Dic13—24no—
113C2×C22⋊Dic13—24no—
114C2×C22⋊Dic13C2314yes—
115C2×C22⋊Dic13C2314yes—
116C2×#6103—24no—
117C2×#6103—24no—
118C2×#6103—24no—
119C2×#6103C2314yes—
120C2×#6103C2314yes—
121C2×#6103C2314yes—
122C2×C4⋊Dic13—24no—
123C2×C4⋊Dic13C2314yes—
124C2×#6101—24no—
125C2×#6101—24no—
126C2×#6101—24no—
127C2×#6101—24no—
128C2×#6101—42no—
129C2×#6101C2314yes—
130C2×#6101C2314yes—
131C2×#6101C2314yes—
132C2×#6101C2314yes—
133C2×#6101C2314yes—
134C2×C4×Dic13—24no—
135C2×C4×Dic13C2314yes—
136#88137—232no—
137#88135—232no—
138C13×#95C2314yes—
139C13×#95C2314yes—
140C13×#95C2314yes—
141#88071C2314yes—
142#88071C2314yes—
143#88071C2314yes—
144#88071C2314yes—
145#88071C2314yes—
146#88071C2314yes—
147#88071C2314yes—
148#88071C2314yes—
149#88071C2314yes—
150#88071C2314yes—
151#88071C2314yes—
152C2×#2419—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×D13C2×D414yes—
167C23×D13#4114yes—
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×C13—22no—
187C22×C4×C13—22no—
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⋊D13C2×D4116yes—
198C22×Dic13—22no—
199C22×Dic13—22no—
200C22×Dic13—22no—
201C22×Dic13—22no—
202C22×Dic13—22no—
203C22×Dic13—22no—
204C22×Dic13—28no—
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—28no—
218C22×Dic13—44no—
219C22×Dic13—416no—
220C22×Dic13C2×D414yes—
221C22×Dic13#4114yes—
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—28no—
233C2×C4×D13—28no—
234C2×C4×D13—28no—
235C2×C4×D13—28no—
236C2×C4×D13—28no—
237C2×C4×D13—44no—
238C2×C4×D13—44no—
239C2×C4×D13—416no—
240C2×C4×D13—416no—
241C2×C4×D13—416no—
242C13×C4⋊C4—44no—
243C13×C22⋊C4—28no—
244C13×C22⋊C4—28no—
245C13×C22⋊C4—44no—
246C22⋊Dic13—28no—
247C22⋊Dic13—28no—
248#6103—28no—
249#6103—28no—
250#6103—28no—
251C4⋊Dic13—28no—
252#6101—28no—
253#6101—28no—
254#6101—28no—
255#6101—28no—
256#6101—44no—
257C4×Dic13—28no—
258C22×#123—131no—
259C22×C4×D4—131no—
260#2419—1316no—
261C2×#400—131no—
262C2×#398—131no—
263C2×#397—131no—
264C2×#397D1311yescharacteristic, complemented
265C2×#387—131no—
266C2×#387—131no—
267C2×#386—131no—
268C2×#385—131no—
269C2×#385—131no—
270C2×#381—131no—
271C2×#381—131no—
272C2×#380—131no—
273C22×#95—131no—
274C23×C13—28no—
275C23×C13—28no—
276C23×C13—28no—
277C23×C13—22no—
278C23×C13—22no—
279C23×C13—22no—
280C23×C13—22no—
281C23×C13—22no—
282C23×C13—22no—
283C23×C13—44no—
284C23×C13—44no—
285C23×C13—44no—
286C23×C13—44no—
287C23×C13C22×D414yes—
288C23×C13C22×D412yes—
289C23×C13C2×#4112yes—
290C23×C13C2×#4112yes—
291C23×C13C2×#4112yes—
292C23×C13C2×#4112yes—
293C23×C13H(5,𝔽2)12yes—
294C23×C132−1+412yes—
295C23×C13C2511yescharacteristic
296C22×D13—28no—
297C22×D13—28no—
298C22×D13—28no—
299C22×D13—28no—
300C22×D13—28no—
301C22×D13—28no—
302C22×D13—22no—
303C22×D13—22no—
304C22×D13—22no—
305C22×D13—22no—
306C22×D13#123116yes—
307C22×D13C22×D414yes—
308C22×D13C2×#4114yes—
309C22×D13C2×#4114yes—
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—22no—
327C2×C4×C13—22no—
328C2×C4×C13—44no—
329C2×C4×C13—44no—
330C2×C4×C13—44no—
331C2×C4×C13—44no—
332C2×C4×C13—44no—
333C2×C4×C13—44no—
334C22⋊D13—232no—
335C2×Dic13—28no—
336C2×Dic13—28no—
337C2×Dic13—28no—
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—22no—
356C2×Dic13—416no—
357C2×Dic13—44no—
358C2×Dic13—44no—
359C2×Dic13—44no—
360C2×Dic13—44no—
361C2×Dic13C22×D414yes—
362C2×Dic13C2×#4114yes—
363C2×Dic13C2×#4114yes—
364C4×D13—416no—
365C4×D13—416no—
366C4×D13—416no—
367C23×D4—131no—
368C24×C4—131no—
369C24×C4—131no—
370C24×C4—131no—
371C24×C4—131no—
372C2×#123—138no—
373C2×#123—268no—
374C2×C4×D4—138no—
375C2×C4×D4—268no—
376C22×C4⋊C4—131no—
377C22×C4⋊C4—131no—
378C22×C4⋊C4—131no—
379C22×C4⋊C4—131no—
380C22×C4⋊C4—131no—
381C22×C4⋊C4—131no—
382C22×C4⋊C4C2×D1311yescharacteristic
383C22×C22⋊C4—131no—
384C22×C22⋊C4—131no—
385C22×C22⋊C4—131no—
386C22×C22⋊C4—131no—
387C22×C22⋊C4—131no—
388C22×C22⋊C4C2×D1311yescharacteristic
389C22×C22⋊C4C2×D1311yescharacteristic
390C22×C22⋊C4C2×D1311yescharacteristic
391C22×C42—131no—
392#400—138no—
393#398—138no—
394#397—138no—
395#397C2×D1318yescomplemented
396#387—138no—
397#387—138no—
398#386—138no—
399#385—138no—
400#385—138no—
401#381—138no—
402#381—138no—
403#380—138no—
404C2×#95—131no—
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×#95—131no—
414C2×#95—131no—
415C2×#95—138no—
416C2×#95C2×D1311yescharacteristic
417C2×#95C2×D1311yescharacteristic
418C2×#95C2×D1311yescharacteristic
419C22×C13—24no—
420C22×C13—24no—
421C22×C13—24no—
422C22×C13—42no—
423C22×C13—416no—
424C22×C13—42no—
425C22×C13—42no—
426C22×C13—42no—
427C22×C13C2×#12314yes—
428C22×C13#52914yes—
429C22×C13#53914yes—
430C22×C13#54614yes—
431C22×C13#54714yes—
432C22×C13#55114yes—
433C22×C13#55214yes—
434C22×C13C23×D411yescharacteristic
435C22×C13C22×#4111yescharacteristic
436C22×C13C22×#4111yescharacteristic
437C22×C13C22×#4111yescharacteristic
438C22×C13C22×#4111yescharacteristic
439C22×C13C2×H(5,𝔽2)11yescharacteristic
440C22×C13C2×2−1+411yescharacteristic
441C2×D13—24no—
442C2×D13—232no—
443C2×D13—24no—
444C2×D13—24no—
445C2×D13—24no—
446C2×D13—24no—
447C2×D13—24no—
448C2×D13C2×#12318yes—
449C4×C13—42no—
450C4×C13—42no—
451C4×C13—42no—
452C4×C13—42no—
453C4×C13—42no—
454C4×C13—42no—
455Dic13—24no—
456Dic13—24no—
457Dic13—24no—
458Dic13—42no—
459Dic13—42no—
460Dic13—42no—
461Dic13—42no—
462C25—131no—
463C25C22×D1311yescharacteristic
464C22×D4—138no—
465C22×D4—134no—
466C22×D4—264no—
467C22×D4—264no—
468C23×C4—131no—
469C23×C4—131no—
470C23×C4—131no—
471C23×C4—131no—
472C23×C4—131no—
473C23×C4—131no—
474C23×C4—131no—
475C23×C4—134no—
476C23×C4—134no—
477C23×C4—134no—
478C23×C4—134no—
479C23×C4—264no—
480C23×C4—264no—
481C23×C4—264no—
482C23×C4—264no—
483C23×C4—264no—
484C23×C4—264no—
485C23×C4—264no—
486C23×C4—264no—
487C23×C4—264no—
488C23×C4—522no—
489C23×C4—522no—
490C23×C4—522no—
491C23×C4C22×D1311yescharacteristic
492C23×C4C22×D1311yescharacteristic
493C23×C4C22×D1311yescharacteristic
494C23×C4C22×D1311yescharacteristic
495C23×C4C22×D1311yescharacteristic
496C23×C4C22×D1311yescharacteristic
497#123—2632no—
498C4×D4—2632no—
499C2×C4⋊C4—42no—
500C2×C4⋊C4—134no—
501C2×C4⋊C4—134no—
502C2×C4⋊C4—134no—
503C2×C4⋊C4—134no—
504C2×C4⋊C4—134no—
505C2×C4⋊C4—134no—
506C2×C4⋊C4—264no—
507C2×C4⋊C4—264no—
508C2×C4⋊C4—264no—
509C2×C4⋊C4—264no—
510C2×C4⋊C4—264no—
511C2×C4⋊C4—522no—
512C2×C4⋊C4C22×D1314yes—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—42no—
516C2×C22⋊C4—134no—
517C2×C22⋊C4—134no—
518C2×C22⋊C4—134no—
519C2×C22⋊C4—134no—
520C2×C22⋊C4—134no—
521C2×C22⋊C4—264no—
522C2×C22⋊C4—264no—
523C2×C22⋊C4—264no—
524C2×C22⋊C4—264no—
525C2×C22⋊C4—264no—
526C2×C22⋊C4C22×D1314yes—
527C2×C22⋊C4C22×D1314yes—
528C2×C22⋊C4C22×D1314yes—
529C2×C42—134no—
530C2×C42—264no—
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#95—134no—
540#95—134no—
541#95—134no—
542#95C22×D1314yes—
543#95C22×D1314yes—
544#95C22×D1314yes—
545C2×C13—44no—
546C2×C13#241918yescomplemented
547C2×C13C22×#12311yescharacteristic
548C2×C13C2×#52911yescharacteristic
549C2×C13C2×#53911yescharacteristic
550C2×C13C2×#54611yescharacteristic
551C2×C13C2×#54711yescharacteristic
552C2×C13C2×#55111yescharacteristic
553C2×C13C2×#55211yescharacteristic
554D13—28no—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—22no—
560C24—22no—
561C24—134no—
562C24—134no—
563C24—134no—
564C24—132no—
565C24—262no—
566C24—262no—
567C24—262no—
568C24—262no—
569C24D4×D1314yes—
570C24C23×D1312yes—
571C24C23×D1311yescharacteristic
572C2×D4—1316no—
573C2×D4—2632no—
574C2×D4—268no—
575C2×D4—268no—
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—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—134no—
595C22×C4—134no—
596C22×C4—134no—
597C22×C4—132no—
598C22×C4—132no—
599C22×C4—132no—
600C22×C4—132no—
601C22×C4—132no—
602C22×C4—132no—
603C22×C4—132no—
604C22×C4—268no—
605C22×C4—268no—
606C22×C4—268no—
607C22×C4—268no—
608C22×C4—268no—
609C22×C4—268no—
610C22×C4—268no—
611C22×C4—268no—
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×C4—268no—
622C22×C4—262no—
623C22×C4—262no—
624C22×C4—262no—
625C22×C4—262no—
626C22×C4—262no—
627C22×C4—262no—
628C22×C4—262no—
629C22×C4—262no—
630C22×C4—262no—
631C22×C4—524no—
632C22×C4—524no—
633C22×C4—5216no—
634C22×C4—5216no—
635C22×C4—5216no—
636C22×C4—524no—
637C22×C4—5216no—
638C22×C4C23×D1312yes—
639C22×C4C23×D1312yes—
640C22×C4C23×D1312yes—
641C22×C4C23×D1312yes—
642C22×C4C23×D1312yes—
643C22×C4C23×D1312yes—
644C4⋊C4—44no—
645C4⋊C4—268no—
646C4⋊C4—268no—
647C4⋊C4—268no—
648C4⋊C4—268no—
649C4⋊C4—268no—
650C4⋊C4—524no—
651C22⋊C4—28no—
652C22⋊C4—28no—
653C22⋊C4—44no—
654C22⋊C4—268no—
655C22⋊C4—268no—
656C22⋊C4—268no—
657C22⋊C4—268no—
658C22⋊C4—268no—
659C42—268no—
660C13C2×#241911yescharacteristic, complemented, Sylow
661C23—28no—
662C23—28no—
663C23—28no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—44no—
671C23—44no—
672C23—44no—
673C23—44no—
674C23—1316no—
675C23—134no—
676C23—134no—
677C23—134no—
678C23—268no—
679C23—268no—
680C23—268no—
681C23—268no—
682C23—262no—
683C23—262no—
684C23—262no—
685C23—262no—
686C23—268no—
687C23—268no—
688C23C2×D4×D1314yes—
689C23C2×D4×D1312yes—
690C23#8825112yes—
691C23#41×D1312yes—
692C23#41×D1312yes—
693C23#41×D1312yes—
694C23#41×D1312yes—
695C23#8825712yes—
696C23C24×D1311yescharacteristic
697D4—2632no—
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—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—44no—
721C2×C4—44no—
722C2×C4—134no—
723C2×C4—134no—
724C2×C4—134no—
725C2×C4—268no—
726C2×C4—268no—
727C2×C4—262no—
728C2×C4—268no—
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—262no—
739C2×C4—262no—
740C2×C4—262no—
741C2×C4—262no—
742C2×C4—262no—
743C2×C4—262no—
744C2×C4—262no—
745C2×C4—262no—
746C2×C4—5216no—
747C2×C4—5216no—
748C2×C4—5216no—
749C2×C4—5216no—
750C2×C4—524no—
751C2×C4—524no—
752C2×C4—524no—
753C2×C4—524no—
754C22—24no—
755C22—24no—
756C22—24no—
757C22—416no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—138no—
763C22—264no—
764C22—264no—
765C22—2632no—
766C22—264no—
767C22—264no—
768C22—264no—
769C22—264no—
770C22#1171931514yes—
771C22D13×#12314yes—
772C22#1171936014yes—
773C22#1171936514yes—
774C22#1171938414yes—
775C22#1171941114yes—
776C22#1171941314yes—
777C22C22×D4×D1311yescharacteristic
778C22C2×#8825111yescharacteristic
779C22C2×#41×D1311yescharacteristic
780C22C2×#41×D1311yescharacteristic
781C22C2×#41×D1311yescharacteristic
782C22C2×#41×D1311yescharacteristic
783C22C2×#8825711yescharacteristic
784C4—42no—
785C4—42no—
786C4—42no—
787C4—42no—
788C4—42no—
789C4—42no—
790C4—264no—
791C4—264no—
792C4—264no—
793C4—522no—
794C4—522no—
795C4—522no—
796C4—522no—
797C2—44no—
798C2—268no—
799C2#1311830818yesdirect product factor
800C2C2×D13×#12311yescharacteristic
801C2C2×#1171941111yescharacteristic
802C2C2×#1171936511yescharacteristic
803C2C2×#1171931511yescharacteristic
804C2C2×#1171936011yescharacteristic
805C2C2×#1171938411yescharacteristic
806C2C2×#1171941311yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#397C2
socleC24×C13C24
prime radicalC23×C22⋊D13C22
hypercenterC2×#397D13
hypocenterC13C2×#2419
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
3. #13118308C2direct (N × H)
4. C2×#11718319C2semidirect
5. C2×#11718645C2semidirect
6. C2×#11718613C2semidirect
7. C2×#11718316C2semidirect
8. C2×#11718313C2semidirect
10. C2×#11718607C2semidirect
11. C2×#11718650C2semidirect
12. C2×#11718325C2semidirect
13. C2×#11718604C2semidirect
14. C2×#11718328C2semidirect
15. C2×D13×#95C2semidirect
16. C2×C13×#397C2semidirect
42. C13×#397C22semidirect
57. #11718650C22semidirect
58. #11718645C22semidirect
60. #11718613C22semidirect
61. #11718607C22semidirect
62. #11718604C22semidirect
63. #11718328C22semidirect
64. #11718325C22semidirect
65. D13×#95C22semidirect
66. #11718319C22semidirect
67. #11718316C22semidirect
68. #11718313C22semidirect
264. C2×#397D13semidirect
395. #397C2×D13semidirect
546. C2×C13#2419semidirect
660. C13C2×#2419semidirect
799. C2#13118308direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881372
C22×#881352
#131183082
C2×#117183192
C2×#117186452
C2×#117186132
C2×#117183162
C2×#117183132
C2×#117186172
C2×#117186072
C2×#117186502
C2×#117183252
C2×#117186042
C2×#117183282
C2×D13×#952
C2×C13×#3972
C2×#241913