Finite Group Databasebeta

← #385×#595 #17962946

Subgroups — #385×#595 #17962946

Order 4352.

2782 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4×#595C211yesmaximal, characteristic
2C2×#11763756C211yesmaximal, characteristic
3C2×C4⋊C4×#595C212yesmaximal, complemented
4C2×C22⋊C4×#595C211yesmaximal, characteristic
5C2×C22⋊C4×#595C211yesmaximal, characteristic
6#14543964C212yesmaximal, complemented
7#14543963C212yesmaximal, complemented
8#14543958C211yesmaximal, characteristic
9#14543957C211yesmaximal, characteristic
10#95×#595C212yesmaximal, complemented
11D17×#385C211yesmaximal, characteristic
12C24×#595C2211yescharacteristic
13C24×#595C2211yescharacteristic
14C22×C4⋊#595C2212yes—
15C22×C22⋊#595C2211yescharacteristic
16C22×C22⋊#595C2211yescharacteristic
17C22×C4×#595—24no—
18C22×C4×#595—28no—
19C22×C4×#595C2211yescharacteristic
20C22×C4×#595C2211yescharacteristic
21C22×C4×#595C2212yes—
22C22×C4×#595C2212yes—
23C22×C4×#595C2212yes—
24#11763756C418yescomplemented
25C4⋊C4×#595—28no—
26C22⋊C4×#595—24no—
27C22⋊C4×#595C418yescomplemented
28C2×(C2×#595)⋊C4C2211yescharacteristic
29C2×(C2×#595)⋊C4C2211yescharacteristic
30C2×(C2×#595)⋊C4C2212yes—
31C2×(C2×#595)⋊C4C2212yes—
32C2×(C2×#595)⋊C4C2212yes—
33C2×(C2×#595)⋊C4C2212yes—
34C2×(C2×#595)⋊C4C2212yes—
35C2×(C2×#595)⋊C4C2212yes—
36C23×C4×D17C2211yescharacteristic
37C2×C4⋊C4×D17C2212yes—
38C2×C22⋊C4×D17C2211yescharacteristic
39C2×C22⋊C4×D17C2211yescharacteristic
40#11762684C411yescharacteristic, complemented
41#11762683C412yescomplemented
42#11762682C411yescharacteristic, complemented
43#11762681C411yescharacteristic, complemented
44#11762680C412yescomplemented
45#95×D17C2212yes—
46C17×#385C411yescharacteristic, complemented
47C24×D17C2311yescharacteristic
48C23×#595—22no—
49C23×#595—22no—
50C23×#595—24no—
51C23×#595—24no—
52C23×#595—24no—
53C23×#595—24no—
54C23×#595C2×C414yes—
55C23×#595C2×C414yes—
56C23×#595D414yes—
57C23×#595Q814yes—
58C23×#595C2311yescharacteristic
59C23×#595C2312yes—
60C23×#595C2311yescharacteristic
61C23×#595C2311yescharacteristic
62C23×#595C2312yes—
63C23×#595C2311yescharacteristic
64C23×C4×C17C2×C411yescharacteristic
65C23×Dic17C2×C411yescharacteristic
66C22×C4×D17—22no—
67C22×C4×D17—22no—
68C22×C4×D17—24no—
69C22×C4×D17—24no—
70C22×C4×D17C2×C412yes—
71C22×C4×D17C2311yescharacteristic
72C22×C4×D17C2311yescharacteristic
73C22×C4×D17C2312yes—
74C22×C4×D17C2312yes—
75C2×C22⋊#595—22no—
76C2×C22⋊#595—22no—
77C2×C22⋊#595—22no—
78C2×C22⋊#595—22no—
79C2×C22⋊#595C2×C414yes—
80C2×C22⋊#595C2×C414yes—
81C2×C4⋊#595—24no—
82C2×C4⋊#595—24no—
83C2×C4⋊#595C2×C418yescomplemented
84C2×C4×#595—232no—
85C2×C4×#595—24no—
86C2×C4×#595—24no—
87C2×C4×#595—24no—
88C2×C4×#595—24no—
89C2×C4×#595—24no—
90C2×C4×#595—24no—
91C2×C4×#595—24no—
92C2×C4×#595—22no—
93C2×C4×#595—22no—
94C2×C4×#595—24no—
95C2×C4×#595—24no—
96C2×C4×#595C2×C418yescomplemented
97C2×C4×#595D418yes—
98C2×C4⋊C4×C17C2×C412yescomplemented
99C2×C22⋊C4×C17C2×C411yescharacteristic
100C2×C22⋊C4×C17C2×C411yescharacteristic
101C2×C22⋊Dic17C2×C411yescharacteristic
102C2×C22⋊Dic17C2×C411yescharacteristic
103C2×#63227C2×C411yescharacteristic
104C2×#63227C2×C411yescharacteristic
105C2×#63227C2×C412yes—
106C2×C4⋊Dic17C2×C412yescomplemented
107C2×#63225C2×C412yescomplemented
108C2×#63225C2×C412yescomplemented
109C4⋊C4×D17—24no—
110C4⋊C4×D17—24no—
111C22⋊C4×D17—22no—
112C22⋊C4×D17—22no—
113C22⋊C4×D17C2×C414yes—
114C22⋊C4×D17C2×C414yes—
115(C2×#595)⋊C4—22no—
116(C2×#595)⋊C4—22no—
117(C2×#595)⋊C4—24no—
118(C2×#595)⋊C4—24no—
119(C2×#595)⋊C4—24no—
120(C2×#595)⋊C4—24no—
121(C2×#595)⋊C4C2×C418yescomplemented
122(C2×#595)⋊C4C2×C418yescomplemented
123C17×#95C2×C412yescomplemented
124#10587502C2×C412yescomplemented
125#10587502C2×C412yescomplemented
126#10587502C2×C412yescomplemented
127C24×C17C22×C411yescharacteristic
128C23×D17—22no—
129C23×D17—22no—
130C23×D17—22no—
131C23×D17—22no—
132C23×D17C22×C411yescharacteristic
133C23×D17C22×C412yes—
134C23×D17C22×C412yes—
135C23×D17C2×D412yes—
136C23×D17C2×Q812yes—
137C23×D17#4112yes—
138C23×D17#4112yes—
139C23×D17C2411yescharacteristic
140C22×#595—28no—
141C22×#595—216no—
142C22×#595—28no—
143C22×#595—28no—
144C22×#595—22no—
145C22×#595—22no—
146C22×#595—22no—
147C22×#595—22no—
148C22×#595—22no—
149C22×#595—22no—
150C22×#595—216no—
151C22×#595—216no—
152C22×#595—28no—
153C22×#595—216no—
154C22×#595—28no—
155C22×#595—22no—
156C22×#595—21no—
157C22×#595—21no—
158C22×#595—22no—
159C22×#595—22no—
160C22×#595—22no—
161C22×#595—22no—
162C22×#595—22no—
163C22×#595—22no—
164C22×#595—21no—
165C22×#595—21no—
166C22×#595—22no—
167C22×#595—22no—
168C22×#595—22no—
169C22×#595C4⋊C4116yescomplemented
170C22×#595C22×C414yes—
171C22×#595C22×C412yes—
172C22×#595C22×C412yes—
173C22×#595C22×C412yes—
174C22×#595C22×C414yes—
175C22×#595C22×C412yes—
176C22×#595C2×D412yes—
177C22×#595C2×D414yes—
178C22×#595C2×D412yes—
179C22×#595C2×D414yes—
180C22×#595C2×Q812yes—
181C22×#595C2×Q812yes—
182C22×#595#4114yes—
183C22×#595#4114yes—
184C22×C4×C17—22no—
185C22×C4×C17—24no—
186C22×C4×C17C22×C411yescharacteristic
187C22×C4×C17C22×C411yescharacteristic
188C22×C4×C17C22×C412yes—
189C22×C4×C17C22×C412yes—
190C22×Dic17—22no—
191C22×Dic17—24no—
192C22×Dic17C22×C411yescharacteristic
193C22×Dic17C22×C411yescharacteristic
194C22×Dic17C22×C412yes—
195C22×Dic17C22×C412yes—
196C2×C4×D17—28no—
197C2×C4×D17—216no—
198C2×C4×D17—28no—
199C2×C4×D17—24no—
200C2×C4×D17—22no—
201C2×C4×D17—22no—
202C2×C4×D17—22no—
203C2×C4×D17—22no—
204C2×C4×D17—22no—
205C2×C4×D17—22no—
206C2×C4×D17—22no—
207C2×C4×D17—22no—
208C2×C4×D17—24no—
209C2×C4×D17—24no—
210C2×C4×D17—21no—
211C2×C4×D17—21no—
212C2×C4×D17—22no—
213C2×C4×D17—22no—
214C2×C4×D17—22no—
215C2×C4×D17—21no—
216C2×C4×D17—21no—
217C2×C4×D17—22no—
218C2×C4×D17C22×C414yes—
219C2×C4×D17C22×C414yes—
220C2×C4×D17C2×D414yes—
221C2×C4×D17#4114yes—
222C22⋊#595—28no—
223C22⋊#595—28no—
224C4⋊#595—216no—
225C4×#595—216no—
226C4×#595—216no—
227C4×#595—216no—
228C4×#595—44no—
229C4×#595—44no—
230C4⋊C4×C17—24no—
231C22⋊C4×C17—22no—
232C22⋊C4×C17C4214yescomplemented
233C22⋊Dic17—22no—
234C22⋊Dic17C4214yescomplemented
235#63227—22no—
236#63227—22no—
237#63227C4218yescomplemented
238C4⋊Dic17—24no—
239#63225—24no—
240#63225—24no—
241C4×#385—171nomaximal, Sylow
242C23×C17—22no—
243C23×C17—22no—
244C23×C17C2×C4212yes—
245C23×C17C4×D412yes—
246C23×C17C4×Q812yes—
247C23×C17C23×C411yescharacteristic
248C22×D17—22no—
249C22×D17—22no—
250C22×D17—24no—
251C22×D17—24no—
252C22×D17—24no—
253C22×D17—24no—
254C22×D17—22no—
255C22×D17—24no—
256C22×D17—22no—
257C22×D17—22no—
258C22×D17—24no—
259C22×D17—22no—
260C22×D17—24no—
261C22×D17—24no—
262C22×D17—24no—
263C22×D17—24no—
264C22×D17C2×C4212yes—
265C22×D17C2×C4⋊C414yes—
266C22×D17#11714yes—
267C22×D17C4×D414yes—
268C22×D17C4×D412yes—
269C22×D17C4×Q814yes—
270C22×D17C4×Q812yes—
271C22×D17C23×C411yescharacteristic
272C22×D17C23×C411yescharacteristic
273C22×D17C22×D411yescharacteristic
274C22×D17C22×D412yes—
275C22×D17C22×Q811yescharacteristic
276C22×D17C2×#4111yescharacteristic
277C22×D17C2×#4111yescharacteristic
278C22×D17C2×#4112yes—
279C22×D17C2×#4112yes—
280C22×D17C2×#4112yes—
281C2×#595—232no—
282C2×#595—24no—
283C2×#595—24no—
284C2×#595—24no—
285C2×#595—22no—
286C2×#595—24no—
287C2×#595—24no—
288C2×#595—22no—
289C2×#595—24no—
290C2×#595—24no—
291C2×#595—24no—
292C2×#595—232no—
293C2×#595—24no—
294C2×#595—24no—
295C2×#595—24no—
296C2×#595—22no—
297C2×#595—22no—
298C2×#595—24no—
299C2×#595—24no—
300C2×#595—41no—
301C2×#595—41no—
302C2×#595—42no—
303C2×#595—42no—
304C2×#595—42no—
305C2×#595—41no—
306C2×#595—41no—
307C2×#595—42no—
308C2×#595—42no—
309C2×#595—42no—
310C2×#595C2×C4⋊C414yes—
311C2×#595C2×C4⋊C414yes—
312C2×#595C4×D418yes—
313C2×#595C4×D418yes—
314C2×#595#12014yes—
315C2×#595C22⋊Q818yes—
316C2×#595#12314yes—
317C2×C4×C17—28no—
318C2×C4×C17—22no—
319C2×C4×C17—22no—
320C2×C4×C17—22no—
321C2×C4×C17—22no—
322C2×C4×C17—21no—
323C2×C4×C17—21no—
324C2×C4×C17—22no—
325C2×C4×C17—22no—
326C2×C4×C17C2×C4214yescomplemented
327C2×C4×C17C4×D414yes—
328C2×Dic17—28no—
329C2×Dic17—22no—
330C2×Dic17—22no—
331C2×Dic17—22no—
332C2×Dic17—22no—
333C2×Dic17—21no—
334C2×Dic17—21no—
335C2×Dic17—22no—
336C2×Dic17—22no—
337C2×Dic17C2×C4214yescomplemented
338C2×Dic17C4×D414yes—
339C4×D17—216no—
340C4×D17—24no—
341C4×D17—24no—
342C4×D17—24no—
343C4×D17—24no—
344C4×D17—24no—
345C4×D17—24no—
346C4×D17—24no—
347C4×D17—24no—
348C4×D17—41no—
349C4×D17—41no—
350C4×D17—42no—
351C4×D17—41no—
352C4×D17—41no—
353C4×D17—42no—
354C23×C42—171no—
355C2×#385—171no—
356C2×#385—171no—
357C2×C4×C4⋊C4—172no—
358C2×C4×C22⋊C4—171no—
359C2×C4×C22⋊C4—171no—
360#1436—172no—
361#1436—172no—
362C22⋊#95—171no—
363C22⋊#95—171no—
364C4×#95—172no—
365C22×C17—24no—
366C22×C17—22no—
367C22×C17—22no—
368C22×C17—24no—
369C22×C17C4×C4⋊C414yescomplemented
370C22×C17C22×C4211yescharacteristic
371C22×C17C2×C4×D411yescharacteristic
372C22×C17C2×C4×D412yes—
373C22×C17C2×C4×Q811yescharacteristic
374C22×C17C4×#4112yes—
375C2×D17—24no—
376C2×D17—22no—
377C2×D17—22no—
378C2×D17—24no—
379C2×D17—24no—
380C2×D17—28no—
381C2×D17—24no—
382C2×D17—24no—
383C2×D17—24no—
384C2×D17—28no—
385C2×D17C4×C4⋊C414yescomplemented
386C2×D17C22×C4⋊C411yescharacteristic
387C2×D17C2×#11711yescharacteristic
388C2×D17C2×C4×D412yes—
389C2×D17C2×C4×D411yescharacteristic
390C2×D17C2×C4×D412yes—
391C2×D17C2×C4×Q811yescharacteristic
392C2×D17C4×#4112yes—
393C2×D17C4×#4112yes—
394C2×D17C2×#12011yescharacteristic
395C2×D17C2×C22⋊Q812yes—
396C2×D17C2×#12311yescharacteristic
397C2×D17#52512yes—
398C2×D17#52512yes—
399C2×D17#52511yescharacteristic
400C2×D17#52511yescharacteristic
401C2×D17#52912yes—
402C2×D17#52912yes—
403C2×D17#53312yes—
404#595—24no—
405#595—28no—
406#595—44no—
407#595—42no—
408#595—42no—
409#595#38518yesdirect product factor
410C4×C17—24no—
411C4×C17—24no—
412C4×C17—41no—
413C4×C17—41no—
414Dic17—24no—
415Dic17—24no—
416Dic17—41no—
417Dic17—41no—
418C24×C4—171no—
419C24×C4—171no—
420C24×C4—171no—
421C22×C4⋊C4—172no—
422C22×C4⋊C4—172no—
423C22×C22⋊C4—171no—
424C22×C22⋊C4—171no—
425C22×C22⋊C4—171no—
426C22×C22⋊C4—171no—
427C22×C42—172no—
428C22×C42—172no—
429C22×C42—172no—
430C22×C42—171no—
431C22×C42—171no—
432C22×C42—348no—
433C22×C42—344no—
434#385—178no—
435#385—171no—
436#385—172no—
437#385—171no—
438#385—171no—
439#385—172no—
440#385#59511yescharacteristic, direct product factor
441C4×C4⋊C4—348no—
442C4×C22⋊C4—178no—
443C4×C22⋊C4—344no—
444C2×#95—172no—
445C2×#95—172no—
446C2×#95—172no—
447C2×#95—172no—
448C2×#95—172no—
449C2×#95—172no—
450C2×#95—172no—
451C2×#95—171no—
452C2×#95—171no—
453C2×C17—24no—
454C2×C17C2×C4×C4⋊C411yescharacteristic
455C2×C17C42×D412yes—
456C2×C17C4×#12011yescharacteristic
457C2×C17C4×#12311yescharacteristic
458C2×C17C4×C22⋊Q812yes—
459D17—24no—
460D17C2×#38511yescharacteristic
461D17#229012yes—
462D17#229611yescharacteristic
463D17C4×#12011yescharacteristic
464D17C4×#12311yescharacteristic
465D17C4×C22⋊Q812yes—
466C25—171no—
467C23×C4—171no—
468C23×C4—172no—
469C23×C4—174no—
470C23×C4—174no—
471C23×C4—174no—
472C23×C4—171no—
473C23×C4—172no—
474C23×C4—172no—
475C23×C4—171no—
476C23×C4—171no—
477C23×C4—172no—
478C23×C4—174no—
479C23×C4—171no—
480C23×C4—171no—
481C23×C4—171no—
482C23×C4—172no—
483C23×C4—344no—
484C23×C4—344no—
485C23×C4—342no—
486C23×C4—342no—
487C23×C4—344no—
488C23×C4—344no—
489C23×C4—344no—
490C23×C4—344no—
491C23×C4—342no—
492C23×C4—342no—
493C23×C4C2×#59511yescharacteristic
494C2×C4⋊C4—178no—
495C2×C4⋊C4—172no—
496C2×C4⋊C4—172no—
497C2×C4⋊C4—172no—
498C2×C4⋊C4—344no—
499C2×C4⋊C4—344no—
500C2×C4⋊C4—344no—
501C2×C4⋊C4—344no—
502C2×C4⋊C4C2×#59512yescomplemented
503C2×C22⋊C4—171no—
504C2×C22⋊C4—172no—
505C2×C22⋊C4—174no—
506C2×C22⋊C4—174no—
507C2×C22⋊C4—174no—
508C2×C22⋊C4—174no—
509C2×C22⋊C4—171no—
510C2×C22⋊C4—171no—
511C2×C22⋊C4—171no—
512C2×C22⋊C4—342no—
513C2×C22⋊C4—342no—
514C2×C22⋊C4—342no—
515C2×C22⋊C4—342no—
516C2×C22⋊C4—342no—
517C2×C22⋊C4—342no—
518C2×C22⋊C4C2×#59511yescharacteristic
519C2×C22⋊C4C2×#59511yescharacteristic
520C2×C42—178no—
521C2×C42—178no—
522C2×C42—344no—
523C2×C42—344no—
524C2×C42—344no—
525C2×C42—344no—
526C2×C42—344no—
527C2×C42—344no—
528C2×C42—344no—
529C2×C42—3432no—
530C2×C42—342no—
531C2×C42—342no—
532C2×C42—344no—
533C2×C42—344no—
534#95—178no—
535#95—178no—
536#95—172no—
537#95—172no—
538#95—172no—
539#95—342no—
540#95—342no—
541#95—344no—
542#95—344no—
543#95—344no—
544#95—344no—
545#95C2×#59512yescomplemented
546C17C4×#38511yescharacteristic, complemented, Sylow
547C24—171no—
548C24—172no—
549C24—172no—
550C24—172no—
551C24—172no—
552C24—172no—
553C24—172no—
554C24—171no—
555C24—342no—
556C24—342no—
557C24—342no—
558C24—342no—
559C24C22×#59511yescharacteristic
560C22×C4—22no—
561C22×C4—24no—
562C22×C4—172no—
563C22×C4—174no—
564C22×C4—172no—
565C22×C4—172no—
566C22×C4—174no—
567C22×C4—1716no—
568C22×C4—172no—
569C22×C4—174no—
570C22×C4—172no—
571C22×C4—174no—
572C22×C4—172no—
573C22×C4—174no—
574C22×C4—172no—
575C22×C4—172no—
576C22×C4—174no—
577C22×C4—174no—
578C22×C4—174no—
579C22×C4—174no—
580C22×C4—172no—
581C22×C4—174no—
582C22×C4—172no—
583C22×C4—171no—
584C22×C4—171no—
585C22×C4—344no—
586C22×C4—342no—
587C22×C4—342no—
588C22×C4—342no—
589C22×C4—342no—
590C22×C4—342no—
591C22×C4—342no—
592C22×C4—342no—
593C22×C4—342no—
594C22×C4—344no—
595C22×C4—348no—
596C22×C4—348no—
597C22×C4—3416no—
598C22×C4—341no—
599C22×C4—341no—
600C22×C4—342no—
601C22×C4—342no—
602C22×C4—342no—
603C22×C4—341no—
604C22×C4—341no—
605C22×C4—342no—
606C22×C4—344no—
607C22×C4—348no—
608C22×C4—3416no—
609C22×C4—348no—
610C22×C4—3416no—
611C22×C4—3416no—
612C22×C4—342no—
613C22×C4—342no—
614C22×C4—342no—
615C22×C4—342no—
616C22×C4—342no—
617C22×C4—342no—
618C22×C4—348no—
619C22×C4—348no—
620C22×C4—348no—
621C22×C4—3416no—
622C22×C4—342no—
623C22×C4—344no—
624C22×C4—342no—
625C22×C4—341no—
626C22×C4—341no—
627C22×C4—342no—
628C22×C4—342no—
629C22×C4—342no—
630C22×C4—342no—
631C22×C4—342no—
632C22×C4—342no—
633C22×C4—342no—
634C22×C4—341no—
635C22×C4—341no—
636C22×C4—342no—
637C22×C4—342no—
638C22×C4C22×#59511yescharacteristic
639C22×C4C22×#59511yescharacteristic
640C22×C4C22×#59512yes—
641C22×C4C22×#59512yes—
642C4⋊C4—24no—
643C4⋊C4—344no—
644C4⋊C4—344no—
645C4⋊C4—3416no—
646C4⋊C4—344no—
647C22⋊C4—22no—
648C22⋊C4—174no—
649C22⋊C4—178no—
650C22⋊C4—342no—
651C22⋊C4—342no—
652C22⋊C4—348no—
653C22⋊C4—348no—
654C22⋊C4—342no—
655C22⋊C4C4×#59514yescomplemented
656C42—3416no—
657C42—3416no—
658C42—3416no—
659C42—684no—
660C42—684no—
661C23—22no—
662C23—22no—
663C23—171no—
664C23—171no—
665C23—172no—
666C23—171no—
667C23—172no—
668C23—171no—
669C23—171no—
670C23—171no—
671C23—172no—
672C23—172no—
673C23—174no—
674C23—174no—
675C23—174no—
676C23—174no—
677C23—172no—
678C23—172no—
679C23—172no—
680C23—342no—
681C23—344no—
682C23—344no—
683C23—342no—
684C23—344no—
685C23—342no—
686C23—342no—
687C23—344no—
688C23—344no—
689C23—344no—
690C23—344no—
691C23—344no—
692C23—344no—
693C23—344no—
694C23—342no—
695C23—342no—
696C23C2×C4×#59512yes—
697C23D4×#59512yes—
698C23Q8×#59512yes—
699C23C23×#59511yescharacteristic
700C2×C4—28no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—174no—
710C2×C4—178no—
711C2×C4—174no—
712C2×C4—174no—
713C2×C4—178no—
714C2×C4—178no—
715C2×C4—174no—
716C2×C4—174no—
717C2×C4—174no—
718C2×C4—344no—
719C2×C4—344no—
720C2×C4—344no—
721C2×C4—344no—
722C2×C4—344no—
723C2×C4—344no—
724C2×C4—344no—
725C2×C4—344no—
726C2×C4—3416no—
727C2×C4—3432no—
728C2×C4—348no—
729C2×C4—344no—
730C2×C4—342no—
731C2×C4—344no—
732C2×C4—344no—
733C2×C4—344no—
734C2×C4—342no—
735C2×C4—344no—
736C2×C4—344no—
737C2×C4—344no—
738C2×C4—344no—
739C2×C4—3432no—
740C2×C4—342no—
741C2×C4—342no—
742C2×C4—342no—
743C2×C4—342no—
744C2×C4—344no—
745C2×C4—342no—
746C2×C4—342no—
747C2×C4—344no—
748C2×C4—344no—
749C2×C4—344no—
750C2×C4—344no—
751C2×C4—341no—
752C2×C4—341no—
753C2×C4—342no—
754C2×C4—342no—
755C2×C4—681no—
756C2×C4—681no—
757C2×C4—681no—
758C2×C4—682no—
759C2×C4—681no—
760C2×C4—682no—
761C2×C4—681no—
762C2×C4—681no—
763C2×C4—682no—
764C2×C4—681no—
765C2×C4—681no—
766C2×C4—682no—
767C2×C4—682no—
768C2×C4—682no—
769C2×C4—682no—
770C2×C4—682no—
771C2×C4C2×C4×#59514yescomplemented
772C2×C4D4×#59514yes—
773C22—24no—
774C22—22no—
775C22—22no—
776C22—24no—
777C22—171no—
778C22—171no—
779C22—171no—
780C22—171no—
781C22—172no—
782C22—172no—
783C22—172no—
784C22—172no—
785C22—171no—
786C22—172no—
787C22—171no—
788C22—171no—
789C22—171no—
790C22—172no—
791C22—172no—
792C22—172no—
793C22—172no—
794C22—172no—
795C22—174no—
796C22—344no—
797C22—344no—
798C22—348no—
799C22—344no—
800C22—344no—
801C22—348no—
802C22—344no—
803C22—342no—
804C22—342no—
805C22—344no—
806C22C4⋊C4×#59514yescomplemented
807C22C22×C4×#59511yescharacteristic
808C22C2×D4×#59511yescharacteristic
809C22C2×D4×#59512yes—
810C22C2×Q8×#59511yescharacteristic
811C22#41×#59512yes—
812C4—24no—
813C4—24no—
814C4—41no—
815C4—41no—
816C4—178no—
817C4—344no—
818C4—348no—
819C4—344no—
820C4—344no—
821C4—682no—
822C4—684no—
823C4—682no—
824C4—681no—
825C4—681no—
826C2—24no—
827C2—171no—
828C2—171no—
829C2—172no—
830C2—171no—
831C2—171no—
832C2—172no—
833C2—344no—
834C2C2×C4⋊C4×#59511yescharacteristic
835C2C4×D4×#59512yes—
836C2#120×#59511yescharacteristic
837C2#123×#59511yescharacteristic
838C2C22⋊Q8×#59512yes—
subgroupG/H
center, FrattiniC23C23×#595
commutatorC22×C17C22×C42
FittingC17×#385C4
socleC23×C17C23×C4
prime radicalC24×D17C23
cosocleC23×D17C24
hypercenter#385#595
hypocenterC17C4×#385
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
3. C2×C4⋊C4×#595C2semidirect
6. #14543964C2semidirect
7. #14543963C2semidirect
10. #95×#595C2semidirect
24. #11763756C4semidirect
27. C22⋊C4×#595C4semidirect
40. #11762684C4semidirect
41. #11762683C4semidirect
42. #11762682C4semidirect
43. #11762681C4semidirect
44. #11762680C4semidirect
46. C17×#385C4semidirect
83. C2×C4⋊#595C2×C4semidirect
96. C2×C4×#595C2×C4semidirect
98. C2×C4⋊C4×C17C2×C4semidirect
106. C2×C4⋊Dic17C2×C4semidirect
107. C2×#63225C2×C4semidirect
108. C2×#63225C2×C4semidirect
121. (C2×#595)⋊C4C2×C4semidirect
122. (C2×#595)⋊C4C2×C4semidirect
123. C17×#95C2×C4semidirect
124. #10587502C2×C4semidirect
125. #10587502C2×C4semidirect
126. #10587502C2×C4semidirect
169. C22×#595C4⋊C4semidirect
232. C22⋊C4×C17C42semidirect
234. C22⋊Dic17C42semidirect
237. #63227C42semidirect
326. C2×C4×C17C2×C42semidirect
337. C2×Dic17C2×C42semidirect
369. C22×C17C4×C4⋊C4semidirect
385. C2×D17C4×C4⋊C4semidirect
409. #595#385direct (N × H)
440. #385#595direct (N × H)
502. C2×C4⋊C4C2×#595semidirect
545. #95C2×#595semidirect
546. C17C4×#385semidirect
655. C22⋊C4C4×#595semidirect
771. C2×C4C2×C4×#595semidirect
806. C22C4⋊C4×#595semidirect

Maximal subgroups

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

subgroupindex
C23×C4×#5952
C2×#117637562
C2×C4⋊C4×#5952
C2×C22⋊C4×#5952
#145439642
#145439632
#145439582
#145439572
#95×#5952
D17×#3852
C4×#38517