Finite Group Databasebeta

← C2×C4×#88170 #16726940

Subgroups — C2×C4×#88170 #16726940

Order 3328.

2894 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88170C211yesmaximal, characteristic
2C2×C4×#6131C211yesmaximal, characteristic, complemented
3C2×C4×#6129C211yesmaximal, characteristic, complemented
4C4×#88170C2116yesmaximal, direct product factor
5C2×C4×#6107C211yesmaximal, characteristic, complemented
6C2×#11718451C211yesmaximal, characteristic, complemented
7C2×C4×#6095C211yesmaximal, characteristic, complemented
8C2×SD16×Dic13C211yesmaximal, characteristic, complemented
9C2×#11718513C211yesmaximal, characteristic, complemented
10C2×C4×#6104C211yesmaximal, characteristic, complemented
11C2×#11718417C211yesmaximal, characteristic, complemented
12C2×#11718521C211yesmaximal, characteristic, complemented
13C2×#11718465C211yesmaximal, characteristic, complemented
14C2×#11718433C211yesmaximal, characteristic, complemented
15C2×C4×C8×D13C211yesmaximal, characteristic, complemented
16C2×C4×C13×SD16C211yesmaximal, characteristic, complemented
17C22×#6131C2211yescharacteristic
18C22×#6129C2211yescharacteristic
19C22×C13×SD16C2211yescharacteristic
20C2×C4×Q8×C13C2211yescharacteristic
21C2×C4×D4×C13C2211yescharacteristic
22C2×Q8×Dic13C2211yescharacteristic
23C22×#6107C2211yescharacteristic
24C2×D4×Dic13C2211yescharacteristic
25C22×#6104C2211yescharacteristic
26C2×C4×C22⋊D13—21no—
27C22×C4×Dic13—21no—
28C2×#88170C4116yesdirect product factor
29C2×#88170C2218yes—
30C22×#6095C2211yescharacteristic
31C22×C8×D13C2211yescharacteristic
32C22×C8×D13C2211yescharacteristic
33C4×#6131—24no—
34C4×#6131C2218yescomplemented
35C4×#6129—24no—
36C4×#6129C2218yescomplemented
37C2×#88147—21no—
38C2×#88147C2211yescharacteristic
39C2×#88146—21no—
40C2×#88146C2211yescharacteristic
41C2×#88146C2211yescharacteristic
42C2×#88141C2211yescharacteristic
43C2×#88135—21no—
44C2×#88131—21no—
45C2×C4×D52—21no—
46C2×C4×D52C2211yescharacteristic
47C2×C42×D13—21no—
48C2×C42×D13C2211yescharacteristic
49C2×C4×Dic26C2211yescharacteristic
50C4×C13×SD16C2218yescomplemented
51C2×C13×#106C2211yescharacteristic
52C2×C13×#103C2211yescharacteristic
53C2×C13×#102C2211yescharacteristic
54C2×C4×C8×C13C2211yescharacteristic
55C2×#88075C2211yescharacteristic
56C2×#88072C2211yescharacteristic
57SD16×Dic13C2218yescomplemented
58C2×#88061C2211yescharacteristic
59C2×#88057C2211yescharacteristic
60C2×#88056C2211yescharacteristic
61C2×C8×Dic13C2211yescharacteristic
62C2×C8×Dic13C2211yescharacteristic
63C4×#6107C2218yescomplemented
64C4×#6104C2218yescomplemented
65C2×#88050C2211yescharacteristic
66C2×#88049C2211yescharacteristic
67C2×#88047C2211yescharacteristic
68C2×#88047C2211yescharacteristic
69C2×C4×#1055C2211yescharacteristic
70#11718521C2218yescomplemented
71#11718513C2218yescomplemented
72#11718465C2218yescomplemented
73#11718451C2218yescomplemented
74#11718433C2218yescomplemented
75#11718417C2218yescomplemented
76C4×#6095C2218yescomplemented
77C4×C8×D13C2218yescomplemented
78C22×Q8×C13C2311yescharacteristic
79C22×D4×C13C2311yescharacteristic
80C23×C4×C13—21no—
81C22×C22⋊D13—21no—
82C23×Dic13—21no—
83C23×Dic13—21no—
84C2×#6131—22no—
85C2×#6131—24no—
86C2×#6131C2×C418yescomplemented
87C2×#6131C2314yes—
88C2×#6129—22no—
89C2×#6129—24no—
90C2×#6129C2×C418yescomplemented
91C2×#6129C2314yes—
92C22×D52—21no—
93C22×D52C2311yescharacteristic
94C22×C4×D13—21no—
95C22×C4×D13—21no—
96C22×C4×D13—21no—
97C22×C4×D13D411yescharacteristic
98C22×C4×D13D411yescharacteristic
99C22×C4×D13C2311yescharacteristic
100C22×Dic26C2311yescharacteristic
101C2×C13×SD16C2×C418yescomplemented
102C2×C13×SD16C2314yes—
103C22×C8×C13C2311yescharacteristic
104C22×C8×C13C2311yescharacteristic
105C4×Q8×C13—22no—
106C4×Q8×C13C2314yes—
107C4×D4×C13—22no—
108C4×D4×C13C2314yes—
109C2×C13×C4⋊C4—21no—
110C2×C13×C4⋊C4C2311yescharacteristic
111C2×C13×C4⋊C4C2311yescharacteristic
112C2×C13×C22⋊C4—21no—
113C2×C42×C13—21no—
114C2×C42×C13C2311yescharacteristic
115C2×C22⋊Dic13—21no—
116Q8×Dic13—22no—
117Q8×Dic13C2314yes—
118C2×#6107C2×C418yescomplemented
119C2×#6107C2314yes—
120D4×Dic13—22no—
121D4×Dic13C2314yes—
122C2×#6104C2×C418yescomplemented
123C2×#6104C2314yes—
124C4×C22⋊D13—28no—
125C2×#6103—21no—
126C2×#6103—21no—
127C2×#6103—21no—
128C2×#6103—21no—
129C2×C4⋊Dic13—21no—
130C2×C4⋊Dic13C2311yescharacteristic
131C2×C4⋊Dic13C2311yescharacteristic
132C2×#6101—21no—
133C2×#6101—21no—
134C2×C4×Dic13—21no—
135C2×C4×Dic13—21no—
136C2×C4×Dic13—21no—
137C2×C4×Dic13—21no—
138C2×C4×Dic13—21no—
139C2×C4×Dic13—28no—
140C2×C4×Dic13D411yescharacteristic
141C2×C4×Dic13D411yescharacteristic
142C2×C4×Dic13C2311yescharacteristic
143C22×#1055C2311yescharacteristic
144C22×#1055C2311yescharacteristic
145#88170C2×C4164yesdirect product factor
146C2×#6095C2×C418yescomplemented
147C2×#6095C2314yes—
148C2×C8×D13—24no—
149C2×C8×D13C2×C418yescomplemented
150C2×C8×D13C2314yes—
151C2×C8×D13C2314yes—
152#88147—28no—
153#88147—22no—
154#88147C2314yes—
155#88146—22no—
156#88146—22no—
157#88146—28no—
158#88146C2314yes—
159#88146C2314yes—
160#88141—22no—
161#88141C2314yes—
162#88135—28no—
163#88131—28no—
164C4×D52—28no—
165C4×D52—22no—
166C4×D52C2314yes—
167C42×D13—28no—
168C42×D13D414yes—
169C42×D13C2314yes—
170C4×Dic26—22no—
171C4×Dic26C2314yes—
172C13×#106C2314yes—
173C13×#103C2314yes—
174C13×#102C2314yes—
175C4×C8×C13C2314yes—
176#88075C2314yes—
177#88072C2314yes—
178#88061C2314yes—
179#88057C2314yes—
180#88056C2314yes—
181C8×Dic13C2314yes—
182C8×Dic13C2314yes—
183#88050C2314yes—
184#88049C2314yes—
185#88047C2314yes—
186#88047C2314yes—
187C4×#1055C2314yes—
188C2×C4×#135—131nomaximal, Sylow
189C24×C13—21no—
190C23×D13—21no—
191C23×D13C2×D411yescharacteristic
192C2×Q8×C13—21no—
193C2×Q8×C13—22no—
194C2×Q8×C13C22×C414yes—
195C2×Q8×C13C2412yes—
196C2×D4×C13—21no—
197C2×D4×C13—22no—
198C2×D4×C13C22×C414yes—
199C2×D4×C13C2412yes—
200C22×C4×C13—21no—
201C22×C4×C13—21no—
202C22×C4×C13—21no—
203C22×C4×C13—24no—
204C22×C4×C13—44no—
205C22×C4×C13C2×D411yescharacteristic
206C22×C4×C13C2×D411yescharacteristic
207C22×C4×C13C2411yescharacteristic
208C2×C22⋊D13—28no—
209C2×C22⋊D13—24no—
210C22×Dic13—21no—
211C22×Dic13—28no—
212C22×Dic13—24no—
213C22×Dic13—21no—
214C22×Dic13—21no—
215C22×Dic13—24no—
216C22×Dic13—44no—
217C22×Dic13C2×D411yescharacteristic
218C22×Dic13C2×D411yescharacteristic
219C22×Dic13C2×D411yescharacteristic
220#6131—216no—
221#6131—28no—
222#6131C22×C4116yescomplemented
223#6129—216no—
224#6129—28no—
225#6129C22×C4116yescomplemented
226C2×D52—28no—
227C2×D52—24no—
228C2×D52—21no—
229C2×D52—22no—
230C2×D52C22×C414yes—
231C2×D52C2412yes—
232C2×C4×D13—24no—
233C2×C4×D13—28no—
234C2×C4×D13—24no—
235C2×C4×D13—24no—
236C2×C4×D13—24no—
237C2×C4×D13—24no—
238C2×C4×D13—44no—
239C2×C4×D13—44no—
240C2×C4×D13C22×C414yes—
241C2×C4×D13C2×D414yes—
242C2×C4×D13C2×D414yes—
243C2×C4×D13C2×D412yes—
244C2×C4×D13#4114yes—
245C2×C4×D13C2412yes—
246C2×Dic26—21no—
247C2×Dic26—22no—
248C2×Dic26C22×C414yes—
249C2×Dic26C2412yes—
250C13×SD16C22×C4116yescomplemented
251C2×C8×C13—22no—
252C2×C8×C13C22×C414yes—
253C2×C8×C13C2412yes—
254C2×C8×C13C2412yes—
255C13×C4⋊C4—21no—
256C13×C4⋊C4—24no—
257C13×C4⋊C4—21no—
258C13×C4⋊C4C2412yes—
259C13×C4⋊C4C2412yes—
260C13×C22⋊C4—24no—
261C42×C13—24no—
262C42×C13C2×D412yes—
263C42×C13C2412yes—
264C22⋊Dic13—24no—
265#6107C22×C4116yescomplemented
266#6104C22×C4116yescomplemented
267#6103—24no—
268#6103—24no—
269#6103—24no—
270#6103—24no—
271C4⋊Dic13—21no—
272C4⋊Dic13—21no—
273C4⋊Dic13—24no—
274C4⋊Dic13C2412yes—
275C4⋊Dic13C2412yes—
276#6101—24no—
277#6101—24no—
278C4×Dic13—24no—
279C4×Dic13—24no—
280C4×Dic13—24no—
281C4×Dic13—24no—
282C4×Dic13—24no—
283C4×Dic13C2×D414yes—
284C4×Dic13C2×D412yes—
285C4×Dic13C2×D414yes—
286C4×Dic13C2412yes—
287C2×#1055—22no—
288C2×#1055C22×C414yes—
289C2×#1055C2412yes—
290C2×#1055C2412yes—
291#6095C22×C4116yescomplemented
292C8×D13—28no—
293C8×D13C22×C4116yescomplemented
294C22×#135—131no—
295C2×C4×#41—131no—
296C2×C4×#41—131no—
297C4×#135—1316no—
298C2×C4×Q16—131no—
299C2×C4×Q16—131no—
300C2×C4×SD16—131no—
301C2×C4×SD16—131no—
302C2×C4×SD16—131no—
303C2×C4×SD16D1311yescharacteristic, complemented
304C2×C4×D8—131no—
305C2×C4×D8—131no—
306C2×#427—131no—
307C2×#416—131no—
308C2×#416—131no—
309C22×C4×C8—131no—
310C23×C13—24no—
311C23×C13—22no—
312C23×C13—42no—
313C23×C13—42no—
314C23×C13C22×D411yescharacteristic
315C22×D13—22no—
316C22×D13—22no—
317C22×D13—24no—
318C22×D13—22no—
319C22×D13—42no—
320C22×D13—42no—
321C22×D13C4×D414yes—
322C22×D13C22×D412yes—
323Q8×C13—24no—
324Q8×C13—22no—
325Q8×C13C23×C414yes—
326D4×C13—24no—
327D4×C13—22no—
328D4×C13C23×C414yes—
329C2×C4×C13—24no—
330C2×C4×C13—22no—
331C2×C4×C13—22no—
332C2×C4×C13—22no—
333C2×C4×C13—22no—
334C2×C4×C13—42no—
335C2×C4×C13—42no—
336C2×C4×C13—48no—
337C2×C4×C13#13514yescomplemented
338C2×C4×C13C23×C412yes—
339C2×C4×C13C22×D412yes—
340C2×C4×C13C22×D411yescharacteristic
341C2×C4×C13C22×D412yes—
342C2×C4×C13C2×#4112yes—
343C2×C4×C13C2511yescharacteristic
344C22⋊D13—216no—
345C2×Dic13—24no—
346C2×Dic13—22no—
347C2×Dic13—22no—
348C2×Dic13—216no—
349C2×Dic13—22no—
350C2×Dic13—22no—
351C2×Dic13—42no—
352C2×Dic13—42no—
353C2×Dic13—48no—
354C2×Dic13C4×D414yes—
355C2×Dic13#13514yescomplemented
356C2×Dic13C22×D412yes—
357C2×Dic13C22×D412yes—
358C2×Dic13C22×D412yes—
359D52—216no—
360D52—24no—
361D52—22no—
362D52C23×C414yes—
363C4×D13—28no—
364C4×D13—216no—
365C4×D13—28no—
366C4×D13—48no—
367C4×D13—48no—
368C4×D13C4×D418yes—
369C4×D13C23×C414yes—
370C4×D13C2×#4114yes—
371Dic26—24no—
372Dic26—22no—
373Dic26C23×C414yes—
374C8×C13—22no—
375C8×C13C23×C414yes—
376#1055—22no—
377#1055C23×C414yes—
378C22×#41—131no—
379C22×#41—131no—
380C2×#135—1316no—
381C2×#135—138no—
382C22×Q16—131no—
383C22×SD16—131no—
384C22×SD16C2×D1311yescharacteristic
385C22×D8—131no—
386C23×C8—131no—
387C23×C8—131no—
388C4×#41—138no—
389C4×#41—138no—
390C4×#41—264no—
391C4×#41—264no—
392C2×C4×Q8—131no—
393C2×C4×Q8—131no—
394C2×C4×Q8—131no—
395C2×C4×Q8C2×D1311yescharacteristic
396C2×C4×D4—131no—
397C2×C4×D4—131no—
398C2×C4×D4—131no—
399C2×C4×D4—261no—
400C2×C4×D4—261no—
401C2×C4×D4—261no—
402C2×C4×D4—261no—
403C2×C4×D4C2×D1311yescharacteristic
404C2×#117—131no—
405C2×#117—131no—
406C2×#117—261no—
407C2×#117—261no—
408C22×C42—131no—
409C22×C42—261no—
410C22×C42—261no—
411C4×Q16—138no—
412C4×Q16—138no—
413C4×SD16—138no—
414C4×SD16—138no—
415C4×SD16—138no—
416C4×SD16C2×D1318yescomplemented
417C4×D8—138no—
418C4×D8—138no—
419#427—138no—
420C2×#107—131no—
421C2×#107—131no—
422C2×#106—131no—
423C2×#106C2×D1311yescharacteristic
424#416—138no—
425#416—138no—
426C2×#103—131no—
427C2×#103—131no—
428C2×#103—131no—
429C2×#103C2×D1311yescharacteristic
430C2×#102—131no—
431C2×#102—131no—
432C2×#102—131no—
433C2×#102C2×D1311yescharacteristic
434C2×C4×C8—131no—
435C2×C4×C8—131no—
436C2×C4×C8—131no—
437C2×C4×C8—138no—
438C2×C4×C8C2×D1311yescharacteristic
439C22×C13—24no—
440C22×C13—48no—
441C22×C13—42no—
442C22×C13—42no—
443C22×C13C2×C4×D412yes—
444C22×C13C2×#13512yes—
445C22×C13C2×#13512yes—
446C22×C13C23×D411yescharacteristic
447C2×D13—28no—
448C2×D13—22no—
449C2×D13—22no—
450C2×D13—24no—
451C2×D13—48no—
452C2×D13—42no—
453C2×D13—42no—
454C2×D13C2×C4×D414yes—
455C4×C13—24no—
456C4×C13—22no—
457C4×C13—42no—
458C4×C13—42no—
459C4×C13C2×C4×D412yes—
460C4×C13C2×#13514yescomplemented
461C4×C13C24×C411yescharacteristic
462C4×C13C22×#4111yescharacteristic
463Dic13—24no—
464Dic13—22no—
465Dic13—42no—
466Dic13—42no—
467Dic13C2×C4×D414yes—
468Dic13C2×#13514yescomplemented
469C2×#41—138no—
470C2×#41—134no—
471C2×#41—138no—
472C2×#41—134no—
473C2×#41—262no—
474C2×#41—264no—
475C2×#41—262no—
476C2×#41—264no—
477C22×Q8—131no—
478C22×Q8C22×D1311yescharacteristic
479C22×D4—131no—
480C22×D4—261no—
481C22×D4—261no—
482C22×D4C22×D1311yescharacteristic
483C23×C4—21no—
484C23×C4—131no—
485C23×C4—131no—
486C23×C4—131no—
487C23×C4—261no—
488C23×C4—261no—
489C23×C4—261no—
490C23×C4—261no—
491C23×C4—261no—
492#135—1364no—
493C2×Q16—138no—
494C2×Q16—134no—
495C2×SD16—138no—
496C2×SD16—134no—
497C2×SD16C4×D1318yescomplemented
498C2×SD16C22×D1314yes—
499C2×D8—138no—
500C2×D8—134no—
501C22×C8—131no—
502C22×C8—138no—
503C22×C8—134no—
504C22×C8—131no—
505C22×C8—134no—
506C22×C8—264no—
507C22×C8C22×D1311yescharacteristic
508C22×C8C22×D1311yescharacteristic
509C4×Q8—22no—
510C4×Q8—134no—
511C4×Q8—134no—
512C4×Q8—134no—
513C4×Q8—262no—
514C4×Q8—262no—
515C4×Q8—262no—
516C4×Q8C22×D1314yes—
517C4×D4—22no—
518C4×D4—134no—
519C4×D4—134no—
520C4×D4—134no—
521C4×D4—268no—
522C4×D4—262no—
523C4×D4—262no—
524C4×D4—268no—
525C4×D4—268no—
526C4×D4—268no—
527C4×D4—262no—
528C4×D4C22×D1314yes—
529#117—134no—
530#117—134no—
531#117—268no—
532#117—268no—
533#117—262no—
534#117—262no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—131no—
537C2×C4⋊C4—131no—
538C2×C4⋊C4—261no—
539C2×C4⋊C4—261no—
540C2×C4⋊C4—261no—
541C2×C4⋊C4C22×D1311yescharacteristic
542C2×C4⋊C4C22×D1311yescharacteristic
543C2×C22⋊C4—21no—
544C2×C22⋊C4—261no—
545C2×C22⋊C4—261no—
546C2×C22⋊C4—261no—
547C2×C22⋊C4—261no—
548C2×C22⋊C4—261no—
549C2×C42—21no—
550C2×C42—131no—
551C2×C42—131no—
552C2×C42—131no—
553C2×C42—134no—
554C2×C42—134no—
555C2×C42—268no—
556C2×C42—268no—
557C2×C42—261no—
558C2×C42—261no—
559C2×C42—261no—
560C2×C42—261no—
561C2×C42—261no—
562C2×C42C22×D1311yescharacteristic
563#107—134no—
564#107—134no—
565#106—134no—
566#106C22×D1314yes—
567#103—134no—
568#103—134no—
569#103—134no—
570#103C22×D1314yes—
571#102—134no—
572#102—134no—
573#102—134no—
574#102C22×D1314yes—
575C4×C8—134no—
576C4×C8—134no—
577C4×C8—134no—
578C4×C8C22×D1314yes—
579C2×C13—44no—
580C2×C13C4×#13514yescomplemented
581C2×C13C22×C4×D411yescharacteristic
582C2×C13C22×#13511yescharacteristic
583C2×C13C22×#13511yescharacteristic
584D13—24no—
585D13—44no—
586C24—21no—
587C24—131no—
588C24—261no—
589#41—1316no—
590#41—1316no—
591#41—2616no—
592#41—268no—
593#41—2616no—
594#41—268no—
595C2×Q8—21no—
596C2×Q8—22no—
597C2×Q8—134no—
598C2×Q8—132no—
599C2×Q8—261no—
600C2×Q8—262no—
601C2×Q8C2×C4×D1314yes—
602C2×Q8C23×D1312yes—
603C2×D4—21no—
604C2×D4—22no—
605C2×D4—134no—
606C2×D4—132no—
607C2×D4—264no—
608C2×D4—268no—
609C2×D4—264no—
610C2×D4—268no—
611C2×D4—261no—
612C2×D4—262no—
613C2×D4C2×C4×D1314yes—
614C2×D4C23×D1312yes—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—24no—
619C22×C4—44no—
620C22×C4—131no—
621C22×C4—131no—
622C22×C4—134no—
623C22×C4—132no—
624C22×C4—134no—
625C22×C4—132no—
626C22×C4—131no—
627C22×C4—134no—
628C22×C4—134no—
629C22×C4—264no—
630C22×C4—264no—
631C22×C4—268no—
632C22×C4—264no—
633C22×C4—264no—
634C22×C4—268no—
635C22×C4—264no—
636C22×C4—261no—
637C22×C4—264no—
638C22×C4—261no—
639C22×C4—261no—
640C22×C4—264no—
641C22×C4—524no—
642C22×C4—524no—
643C22×C4—524no—
644C22×C4D4×D1311yescharacteristic
645C22×C4D4×D1311yescharacteristic
646C22×C4C23×D1311yescharacteristic
647Q16—1316no—
648SD16—1316no—
649SD16C2×C4×D13116yescomplemented
650D8—1316no—
651C2×C8—22no—
652C2×C8—134no—
653C2×C8—132no—
654C2×C8—1316no—
655C2×C8—132no—
656C2×C8—268no—
657C2×C8—262no—
658C2×C8C2×C4×D1314yes—
659C2×C8C23×D1312yes—
660C2×C8C23×D1312yes—
661C4⋊C4—24no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—132no—
665C4⋊C4—132no—
666C4⋊C4—264no—
667C4⋊C4—264no—
668C4⋊C4—261no—
669C4⋊C4—261no—
670C4⋊C4—264no—
671C4⋊C4C23×D1312yes—
672C4⋊C4C23×D1312yes—
673C22⋊C4—24no—
674C22⋊C4—264no—
675C22⋊C4—264no—
676C22⋊C4—264no—
677C22⋊C4—264no—
678C22⋊C4—264no—
679C42—24no—
680C42—134no—
681C42—134no—
682C42—132no—
683C42—132no—
684C42—264no—
685C42—264no—
686C42—264no—
687C42—264no—
688C42—264no—
689C42D4×D1312yes—
690C42C23×D1312yes—
691C13C2×C4×#13511yescharacteristic, complemented, Sylow
692C23—24no—
693C23—22no—
694C23—42no—
695C23—42no—
696C23—134no—
697C23—132no—
698C23—262no—
699C23—262no—
700C23—264no—
701C23—262no—
702C23—522no—
703C23—522no—
704C23C2×D4×D1311yescharacteristic
705Q8—24no—
706Q8—22no—
707Q8—134no—
708Q8—264no—
709Q8—262no—
710Q8C22×C4×D1314yes—
711D4—24no—
712D4—22no—
713D4—134no—
714D4—2616no—
715D4—2616no—
716D4—264no—
717D4—262no—
718D4C22×C4×D1314yes—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—48no—
727C2×C4—134no—
728C2×C4—134no—
729C2×C4—132no—
730C2×C4—132no—
731C2×C4—138no—
732C2×C4—134no—
733C2×C4—134no—
734C2×C4—132no—
735C2×C4—268no—
736C2×C4—2616no—
737C2×C4—2616no—
738C2×C4—262no—
739C2×C4—264no—
740C2×C4—262no—
741C2×C4—268no—
742C2×C4—262no—
743C2×C4—262no—
744C2×C4—528no—
745C2×C4—528no—
746C2×C4—522no—
747C2×C4—522no—
748C2×C4—528no—
749C2×C4#8817014yesdirect product factor
750C2×C4C22×C4×D1312yes—
751C2×C4C2×D4×D1312yes—
752C2×C4C2×D4×D1312yes—
753C2×C4C2×D4×D1311yescharacteristic
754C2×C4#41×D1312yes—
755C2×C4C24×D1311yescharacteristic
756C8—22no—
757C8—134no—
758C8—262no—
759C8C22×C4×D1314yes—
760C22—24no—
761C22—48no—
762C22—42no—
763C22—42no—
764C22—134no—
765C22—268no—
766C22—262no—
767C22—262no—
768C22—264no—
769C22—528no—
770C22—522no—
771C22—522no—
772C22C4×D4×D1312yes—
773C22C2×#8817012yes—
774C22D13×#13512yes—
775C22C22×D4×D1311yescharacteristic
776C4—24no—
777C4—22no—
778C4—42no—
779C4—42no—
780C4—134no—
781C4—134no—
782C4—264no—
783C4—262no—
784C4—522no—
785C4—522no—
786C4C4×D4×D1312yes—
787C4C2×#8817014yesdirect product factor
788C4C23×C4×D1311yescharacteristic
789C4C2×#41×D1311yescharacteristic
790C2—44no—
791C2—264no—
792C2—524no—
793C2C4×#8817014yesdirect product factor
794C2C2×C4×D4×D1311yescharacteristic
795C2C2×D13×#13511yescharacteristic
796C2C22×#8817011yescharacteristic
subgroupG/H
centerC22×C4D4×D13
commutatorC4×C13C24×C4
FrattiniC2×C4C24×D13
FittingC2×C4×C13×SD16C2
socleC23×C13C22×D4
prime radicalC22×#88170C2
cosocleC2×C4×C13C25
hypercenterC2×C4×SD16D13
hypocenterC13C2×C4×#135
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
2. C2×C4×#6131C2semidirect
3. C2×C4×#6129C2semidirect
4. C4×#88170C2direct (N × H)
5. C2×C4×#6107C2semidirect
6. C2×#11718451C2semidirect
7. C2×C4×#6095C2semidirect
8. C2×SD16×Dic13C2semidirect
9. C2×#11718513C2semidirect
10. C2×C4×#6104C2semidirect
11. C2×#11718417C2semidirect
12. C2×#11718521C2semidirect
13. C2×#11718465C2semidirect
14. C2×#11718433C2semidirect
15. C2×C4×C8×D13C2semidirect
16. C2×C4×C13×SD16C2semidirect
28. C2×#88170C4direct (N × H)
34. C4×#6131C22semidirect
36. C4×#6129C22semidirect
50. C4×C13×SD16C22semidirect
57. SD16×Dic13C22semidirect
63. C4×#6107C22semidirect
64. C4×#6104C22semidirect
70. #11718521C22semidirect
71. #11718513C22semidirect
72. #11718465C22semidirect
73. #11718451C22semidirect
74. #11718433C22semidirect
75. #11718417C22semidirect
76. C4×#6095C22semidirect
77. C4×C8×D13C22semidirect
86. C2×#6131C2×C4semidirect
90. C2×#6129C2×C4semidirect
101. C2×C13×SD16C2×C4semidirect
118. C2×#6107C2×C4semidirect
122. C2×#6104C2×C4semidirect
145. #88170C2×C4direct (N × H)
146. C2×#6095C2×C4semidirect
149. C2×C8×D13C2×C4semidirect
222. #6131C22×C4semidirect
225. #6129C22×C4semidirect
250. C13×SD16C22×C4semidirect
265. #6107C22×C4semidirect
266. #6104C22×C4semidirect
291. #6095C22×C4semidirect
293. C8×D13C22×C4semidirect
303. C2×C4×SD16D13semidirect
337. C2×C4×C13#135semidirect
355. C2×Dic13#135semidirect
416. C4×SD16C2×D13semidirect
460. C4×C13C2×#135semidirect
468. Dic13C2×#135semidirect
497. C2×SD16C4×D13semidirect
580. C2×C13C4×#135semidirect
649. SD16C2×C4×D13semidirect
691. C13C2×C4×#135semidirect
749. C2×C4#88170direct (N × H)
787. C4C2×#88170direct (N × H)
793. C2C4×#88170direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881702
C2×C4×#61312
C2×C4×#61292
C4×#881702
C2×C4×#61072
C2×#117184512
C2×C4×#60952
C2×SD16×Dic132
C2×#117185132
C2×C4×#61042
C2×#117184172
C2×#117185212
C2×#117184652
C2×#117184332
C2×C4×C8×D132
C2×C4×C13×SD162
C2×C4×#13513