Finite Group Databasebeta

← #16957780

Subgroups — #16957780

Order 4352.

3166 conjugacy classes of subgroups.

The subgroup lattice has 1398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic17C211yesmaximal, characteristic, complemented
2C2×#11762689C211yesmaximal, characteristic, complemented
3C2×#11762689C211yesmaximal, characteristic, complemented
4C2×#11762689C211yesmaximal, characteristic, complemented
5C2×#11762689C211yesmaximal, characteristic, complemented
6C22×#10587502C211yesmaximal, characteristic, complemented
7#14527037C211yesmaximal, characteristic, complemented
8#14527033C211yesmaximal, characteristic, complemented
9#14527029C211yesmaximal, characteristic, complemented
10#14527025C211yesmaximal, characteristic, complemented
11#14527021C211yesmaximal, characteristic, complemented
12#14527016C211yesmaximal, characteristic, complemented
13#14527007C211yesmaximal, characteristic, complemented
14#14527006C211yesmaximal, characteristic, complemented
15C22×C17×#121C211yesmaximal, characteristic
16C24×Dic17C2211yescharacteristic
17C24×Dic17C2211yescharacteristic
18C24×Dic17C2211yescharacteristic
19C2×D4×Dic17—24no—
20C2×D4×Dic17—24no—
21C2×D4×Dic17—24no—
22C22×C4⋊Dic17C2211yescharacteristic
23C22×C22⋊Dic17C2211yescharacteristic
24C22×C22⋊Dic17C2211yescharacteristic
25C22×C22⋊Dic17C2211yescharacteristic
26C22×C22⋊Dic17C2211yescharacteristic
27C22×C22⋊Dic17C2211yescharacteristic
28C22×C22⋊Dic17C2211yescharacteristic
29C22×C22⋊Dic17C2211yescharacteristic
30C22×C22⋊Dic17C2211yescharacteristic
31C22×C22⋊Dic17C2211yescharacteristic
32C22×C4×Dic17C2211yescharacteristic
33#11762689—24no—
34#11762689—24no—
35#11762689—24no—
36#11762689—24no—
37C2×#10587502—24no—
38C2×#10587502C2211yescharacteristic
39C2×#10587502C2211yescharacteristic
40C2×#10587502C2211yescharacteristic
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48C2×#10587502C2211yescharacteristic
49C2×#10587502C2211yescharacteristic
50C2×#10587502C2211yescharacteristic
51C2×#10587502C2211yescharacteristic
52C23×D4×C17C2211yescharacteristic
53C23×D4×C17C2211yescharacteristic
54C23×D4×C17C2211yescharacteristic
55C24×C4×C17C2211yescharacteristic
56C2×C17×#121—24no—
57C2×C17×#121—24no—
58C2×C17×#121C418yescomplemented
59C22×C4⋊C4×C17C2211yescharacteristic
60C22×C22⋊C4×C17C2211yescharacteristic
61C22×C22⋊C4×C17C2211yescharacteristic
62C25×C17C2311yescharacteristic
63C25×C17C2311yescharacteristic
64C25×C17C2311yescharacteristic
65C22×D4×C17—22no—
66C22×D4×C17—22no—
67C22×D4×C17—22no—
68C22×D4×C17—22no—
69C22×D4×C17—22no—
70C22×D4×C17—22no—
71C22×D4×C17—22no—
72C22×D4×C17—22no—
73C22×D4×C17—22no—
74C22×D4×C17—22no—
75C22×D4×C17—22no—
76C22×D4×C17—22no—
77C22×D4×C17—22no—
78C22×D4×C17—22no—
79C22×D4×C17—41no—
80C22×D4×C17—41no—
81C22×D4×C17C2×C414yes—
82C22×D4×C17C2×C414yescomplemented
83C22×D4×C17C2×C414yescomplemented
84C22×D4×C17D414yes—
85C22×D4×C17D414yes—
86C23×C4×C17—22no—
87C23×C4×C17—22no—
88C23×C4×C17—22no—
89C23×C4×C17—22no—
90C23×C4×C17—41no—
91C23×C4×C17—41no—
92C23×C4×C17C2×C414yescomplemented
93C23×C4×C17C2311yescharacteristic
94C23×C4×C17C2311yescharacteristic
95C23×C4×C17C2311yescharacteristic
96C23×C4×C17C2311yescharacteristic
97C23×Dic17—22no—
98C23×Dic17—22no—
99C23×Dic17—22no—
100C23×Dic17—22no—
101C23×Dic17—22no—
102C23×Dic17—22no—
103C23×Dic17—22no—
104C23×Dic17—22no—
105C23×Dic17—22no—
106C23×Dic17—22no—
107C23×Dic17—22no—
108C23×Dic17—22no—
109C23×Dic17—22no—
110C23×Dic17—22no—
111C23×Dic17—41no—
112C23×Dic17—41no—
113C23×Dic17—41no—
114C23×Dic17—41no—
115C23×Dic17—41no—
116C23×Dic17—41no—
117C23×Dic17D414yescomplemented
118C23×Dic17C2311yescharacteristic
119C23×Dic17C2311yescharacteristic
120C23×Dic17C2311yescharacteristic
121C23×Dic17C2311yescharacteristic
122C23×Dic17C2311yescharacteristic
123C23×Dic17C2311yescharacteristic
124C23×Dic17C2311yescharacteristic
125C23×Dic17C2311yescharacteristic
126C17×#121—232no—
127C2×C4⋊C4×C17—22no—
128C2×C4⋊C4×C17—22no—
129C2×C4⋊C4×C17C2×C414yescomplemented
130C2×C22⋊C4×C17—22no—
131C2×C22⋊C4×C17—22no—
132C2×C22⋊C4×C17—22no—
133C2×C22⋊C4×C17—22no—
134C2×C22⋊C4×C17C2×C414yescomplemented
135C2×C22⋊C4×C17C2×C414yescomplemented
136C2×C22⋊Dic17—22no—
137C2×C22⋊Dic17—22no—
138C2×C22⋊Dic17—22no—
139C2×C22⋊Dic17—22no—
140C2×C22⋊Dic17—22no—
141C2×C22⋊Dic17—22no—
142C2×C22⋊Dic17—22no—
143C2×C22⋊Dic17—22no—
144C2×C22⋊Dic17—22no—
145C2×C22⋊Dic17—22no—
146C2×C22⋊Dic17—22no—
147C2×C22⋊Dic17—22no—
148C2×C22⋊Dic17—22no—
149C2×C22⋊Dic17—22no—
150C2×C22⋊Dic17—22no—
151C2×C22⋊Dic17—22no—
152C2×C22⋊Dic17—22no—
153C2×C22⋊Dic17—22no—
154C2×C22⋊Dic17—22no—
155C2×C22⋊Dic17—22no—
156C2×C22⋊Dic17—41no—
157C2×C22⋊Dic17—41no—
158C2×C22⋊Dic17—41no—
159C2×C22⋊Dic17—41no—
160C2×C22⋊Dic17—41no—
161C2×C22⋊Dic17—41no—
162C2×C22⋊Dic17D414yescomplemented
163D4×Dic17—232no—
164C2×C4⋊Dic17—22no—
165C2×C4⋊Dic17—22no—
166C2×C4⋊Dic17—22no—
167C2×C4×Dic17—22no—
168C2×C4×Dic17—22no—
169C2×C4×Dic17—22no—
170#10587502—22no—
171#10587502—22no—
172#10587502—22no—
173#10587502—22no—
174#10587502—22no—
175#10587502—22no—
176#10587502—22no—
177#10587502—22no—
178#10587502—22no—
179#10587502—22no—
180#10587502—22no—
181#10587502—41no—
182#10587502—41no—
183#10587502D414yescomplemented
184C24×C17—21no—
185C24×C17—21no—
186C24×C17—21no—
187C24×C17—21no—
188C24×C17—21no—
189C24×C17—21no—
190C24×C17—21no—
191C24×C17—21no—
192C24×C17—21no—
193C24×C17—21no—
194C24×C17—21no—
195C24×C17—21no—
196C24×C17—21no—
197C24×C17—21no—
198C24×C17—21no—
199C24×C17—21no—
200C24×C17—21no—
201C24×C17—21no—
202C24×C17—21no—
203C24×C17—21no—
204C24×C17—21no—
205C24×C17—21no—
206C24×C17—21no—
207C24×C17—21no—
208C24×C17—21no—
209C24×C17—21no—
210C24×C17—21no—
211C24×C17—21no—
212C24×C17—21no—
213C24×C17—21no—
214C24×C17—21no—
215C24×C17—21no—
216C24×C17—21no—
217C24×C17—21no—
218C24×C17C22×C412yes—
219C24×C17C22×C412yes—
220C24×C17C22×C412yes—
221C24×C17C2×D412yes—
222C24×C17C2×D412yes—
223C24×C17C2×D412yes—
224C24×C17C2×D412yes—
225C24×C17C2×D412yes—
226C24×C17C2×D412yes—
227C24×C17#4112yes—
228C24×C17#4112yes—
229C24×C17C2411yescharacteristic
230C2×D4×C17—28no—
231C2×D4×C17—28no—
232C2×D4×C17—28no—
233C2×D4×C17—28no—
234C2×D4×C17—28no—
235C2×D4×C17—28no—
236C2×D4×C17—28no—
237C2×D4×C17—28no—
238C2×D4×C17—28no—
239C2×D4×C17—28no—
240C2×D4×C17—28no—
241C2×D4×C17—44no—
242C2×D4×C17—44no—
243C2×D4×C17—44no—
244C2×D4×C17—44no—
245C2×D4×C17—44no—
246C2×D4×C17—44no—
247C2×D4×C17—44no—
248C2×D4×C17—44no—
249C2×D4×C17—44no—
250C2×D4×C17C22⋊C4116yescomplemented
251C22×C4×C17—21no—
252C22×C4×C17—21no—
253C22×C4×C17—21no—
254C22×C4×C17—21no—
255C22×C4×C17—21no—
256C22×C4×C17—21no—
257C22×C4×C17—21no—
258C22×C4×C17—21no—
259C22×C4×C17—28no—
260C22×C4×C17—21no—
261C22×C4×C17—21no—
262C22×C4×C17—21no—
263C22×C4×C17—21no—
264C22×C4×C17—21no—
265C22×C4×C17—21no—
266C22×C4×C17—21no—
267C22×C4×C17—21no—
268C22×C4×C17—21no—
269C22×C4×C17—21no—
270C22×C4×C17—21no—
271C22×C4×C17—21no—
272C22×C4×C17—28no—
273C22×C4×C17—44no—
274C22×C4×C17—44no—
275C22×C4×C17—44no—
276C22×C4×C17—44no—
277C22×C4×C17—44no—
278C22×C4×C17C22×C412yes—
279C22×C4×C17C22×C412yes—
280C22×C4×C17C22×C412yes—
281C22×C4×C17C22×C412yes—
282C22×C4×C17C2×D412yes—
283C22×C4×C17C2×D412yes—
284C22×C4×C17C2×D412yes—
285C22×C4×C17#4112yes—
286C22×Dic17—21no—
287C22×Dic17—21no—
288C22×Dic17—21no—
289C22×Dic17—21no—
290C22×Dic17—28no—
291C22×Dic17—28no—
292C22×Dic17—28no—
293C22×Dic17—21no—
294C22×Dic17—21no—
295C22×Dic17—21no—
296C22×Dic17—21no—
297C22×Dic17—21no—
298C22×Dic17—21no—
299C22×Dic17—21no—
300C22×Dic17—21no—
301C22×Dic17—21no—
302C22×Dic17—21no—
303C22×Dic17—21no—
304C22×Dic17—21no—
305C22×Dic17—21no—
306C22×Dic17—21no—
307C22×Dic17—21no—
308C22×Dic17—21no—
309C22×Dic17—21no—
310C22×Dic17—21no—
311C22×Dic17—21no—
312C22×Dic17—21no—
313C22×Dic17—21no—
314C22×Dic17—21no—
315C22×Dic17—21no—
316C22×Dic17—21no—
317C22×Dic17—21no—
318C22×Dic17—21no—
319C22×Dic17—21no—
320C22×Dic17—21no—
321C22×Dic17—21no—
322C22×Dic17—21no—
323C22×Dic17—28no—
324C22×Dic17—21no—
325C22×Dic17—21no—
326C22×Dic17—21no—
327C22×Dic17—21no—
328C22×Dic17—21no—
329C22×Dic17—21no—
330C22×Dic17—21no—
331C22×Dic17—21no—
332C22×Dic17—21no—
333C22×Dic17—21no—
334C22×Dic17—21no—
335C22×Dic17—21no—
336C22×Dic17—21no—
337C22×Dic17—21no—
338C22×Dic17—44no—
339C22×Dic17—44no—
340C22×Dic17—44no—
341C22×Dic17—44no—
342C22×Dic17—44no—
343C22×Dic17—44no—
344C22×Dic17—44no—
345C22×Dic17—44no—
346C22×Dic17—44no—
347C22×Dic17—44no—
348C22×Dic17—44no—
349C22×Dic17—44no—
350C22×Dic17—44no—
351C22×Dic17—44no—
352C22×Dic17—44no—
353C22×Dic17—44no—
354C22×Dic17—44no—
355C22×Dic17C2×D412yes—
356C22×Dic17C2×D412yes—
357C22×Dic17C2×D412yes—
358C22×Dic17C2×D412yes—
359C22×Dic17C2×D412yes—
360C22×Dic17C2×D412yes—
361C22×Dic17#4112yes—
362C22×Dic17#4112yes—
363C4⋊C4×C17—28no—
364C22⋊C4×C17—28no—
365C22⋊C4×C17—28no—
366C22⋊Dic17—28no—
367C22⋊Dic17—28no—
368C22⋊Dic17—44no—
369C22⋊Dic17—44no—
370C22⋊Dic17—44no—
371C22⋊Dic17—44no—
372C22⋊Dic17—44no—
373C22⋊Dic17—44no—
374C22⋊Dic17—44no—
375C4⋊Dic17—28no—
376C4×Dic17—28no—
377#14023—171nomaximal, Sylow
378C23×C17—22no—
379C23×C17—22no—
380C23×C17—22no—
381C23×C17—22no—
382C23×C17—22no—
383C23×C17—22no—
384C23×C17—22no—
385C23×C17—22no—
386C23×C17—22no—
387C23×C17—22no—
388C23×C17—22no—
389C23×C17—22no—
390C23×C17—22no—
391C23×C17—22no—
392C23×C17—22no—
393C23×C17—22no—
394C23×C17—22no—
395C23×C17—22no—
396C23×C17—22no—
397C23×C17—22no—
398C23×C17—22no—
399C23×C17—22no—
400C23×C17—22no—
401C23×C17—22no—
402C23×C17—22no—
403C23×C17—22no—
404C23×C17—22no—
405C23×C17—22no—
406C23×C17—22no—
407C23×C17—22no—
408C23×C17—22no—
409C23×C17—22no—
410C23×C17—22no—
411C23×C17—22no—
412C23×C17—22no—
413C23×C17—22no—
414C23×C17—22no—
415C23×C17—22no—
416C23×C17—22no—
417C23×C17—22no—
418C23×C17—22no—
419C23×C17—22no—
420C23×C17—22no—
421C23×C17—22no—
422C23×C17—22no—
423C23×C17—22no—
424C23×C17—22no—
425C23×C17—22no—
426C23×C17—22no—
427C23×C17—22no—
428C23×C17—22no—
429C23×C17—22no—
430C23×C17—22no—
431C23×C17—41no—
432C23×C17—41no—
433C23×C17—41no—
434C23×C17—41no—
435C23×C17—41no—
436C23×C17—41no—
437C23×C17—41no—
438C23×C17—41no—
439C23×C17—41no—
440C23×C17—41no—
441C23×C17—41no—
442C23×C17—41no—
443C23×C17—41no—
444C23×C17—41no—
445C23×C17—41no—
446C23×C17—41no—
447C23×C17—41no—
448C23×C17—41no—
449C23×C17—41no—
450C23×C17—41no—
451C23×C17—41no—
452C23×C17—41no—
453C23×C17—41no—
454C23×C17—41no—
455C23×C17—41no—
456C23×C17—41no—
457C23×C17—41no—
458C23×C17—41no—
459C23×C17—41no—
460C23×C17—41no—
461C23×C17—41no—
462C23×C17—41no—
463C23×C17—41no—
464C23×C17—41no—
465C23×C17—41no—
466C23×C17—41no—
467C23×C17—41no—
468C23×C17—41no—
469C23×C17—41no—
470C23×C17—41no—
471C23×C17—41no—
472C23×C17—41no—
473C23×C17—41no—
474C23×C17—41no—
475C23×C17C2×C22⋊C414yes—
476C23×C17C2×C22⋊C414yes—
477C23×C17C4×D414yes—
478C23×C17C4×D414yes—
479C23×C17#12014yes—
480C23×C17#12114yes—
481C23×C17#12114yes—
482C23×C17#12314yes—
483C23×C17C23×C411yescharacteristic
484C23×C17C22×D411yescharacteristic
485C23×C17C22×D411yescharacteristic
486C23×C17C22×D411yescharacteristic
487C23×C17C22×D411yescharacteristic
488C23×C17C22×D411yescharacteristic
489C23×C17C2×#4111yescharacteristic
490C23×C17C2×#4111yescharacteristic
491C23×C17C2×#4111yescharacteristic
492C23×C17C2×#4111yescharacteristic
493C23×C17C2×#4111yescharacteristic
494C23×C17H(5,𝔽2)11yescharacteristic
495C23×C17H(5,𝔽2)11yescharacteristic
496C23×C17H(5,𝔽2)11yescharacteristic
497C23×C172−1+411yescharacteristic
498D4×C17—232no—
499D4×C17—416no—
500D4×C17—416no—
501C2×C4×C17—22no—
502C2×C4×C17—22no—
503C2×C4×C17—22no—
504C2×C4×C17—22no—
505C2×C4×C17—22no—
506C2×C4×C17—22no—
507C2×C4×C17—22no—
508C2×C4×C17—22no—
509C2×C4×C17—22no—
510C2×C4×C17—22no—
511C2×C4×C17—22no—
512C2×C4×C17—22no—
513C2×C4×C17—22no—
514C2×C4×C17—22no—
515C2×C4×C17—22no—
516C2×C4×C17—22no—
517C2×C4×C17—22no—
518C2×C4×C17—22no—
519C2×C4×C17—416no—
520C2×C4×C17—41no—
521C2×C4×C17—41no—
522C2×C4×C17—41no—
523C2×C4×C17—41no—
524C2×C4×C17—41no—
525C2×C4×C17—41no—
526C2×C4×C17—41no—
527C2×C4×C17—41no—
528C2×C4×C17C2×C22⋊C414yes—
529C2×C4×C17C4×D414yescomplemented
530C2×Dic17—22no—
531C2×Dic17—22no—
532C2×Dic17—22no—
533C2×Dic17—22no—
534C2×Dic17—22no—
535C2×Dic17—22no—
536C2×Dic17—22no—
537C2×Dic17—22no—
538C2×Dic17—22no—
539C2×Dic17—22no—
540C2×Dic17—22no—
541C2×Dic17—22no—
542C2×Dic17—22no—
543C2×Dic17—22no—
544C2×Dic17—22no—
545C2×Dic17—22no—
546C2×Dic17—22no—
547C2×Dic17—22no—
548C2×Dic17—22no—
549C2×Dic17—22no—
550C2×Dic17—22no—
551C2×Dic17—416no—
552C2×Dic17—416no—
553C2×Dic17—416no—
554C2×Dic17—41no—
555C2×Dic17—41no—
556C2×Dic17—41no—
557C2×Dic17—41no—
558C2×Dic17—41no—
559C2×Dic17—41no—
560C2×Dic17—41no—
561C2×Dic17—41no—
562C2×Dic17—41no—
563C2×Dic17—41no—
564C2×Dic17—41no—
565C2×Dic17—41no—
566C2×Dic17—41no—
567C2×Dic17—41no—
568C2×Dic17—41no—
569C2×Dic17—41no—
570C2×Dic17—41no—
571C2×Dic17—41no—
572C2×Dic17—41no—
573C2×Dic17—41no—
574C2×Dic17—41no—
575C2×Dic17—41no—
576C2×Dic17—41no—
577C2×Dic17—41no—
578C2×Dic17—41no—
579C2×Dic17—41no—
580C2×Dic17—41no—
581C2×Dic17—41no—
582C2×Dic17—41no—
583C2×Dic17—41no—
584C2×Dic17—41no—
585C2×Dic17—41no—
586C2×Dic17—41no—
587C2×Dic17—41no—
588C2×Dic17#12114yescomplemented
589C22×#121D1711yescharacteristic
590C22×C4×D4—171no—
591C2×#386—171no—
592C2×#386—171no—
593C2×#386—171no—
594C2×#386—171no—
595C22×#95—171no—
596#1441—171no—
597#1440—171no—
598#1439—171no—
599#1438—171no—
600#1437—171no—
601#1436—171no—
602C22⋊#95—171no—
603C22⋊#95—171no—
604C22×C17—24no—
605C22×C17—24no—
606C22×C17—24no—
607C22×C17—24no—
608C22×C17—24no—
609C22×C17—24no—
610C22×C17—24no—
611C22×C17—24no—
612C22×C17—24no—
613C22×C17—24no—
614C22×C17—24no—
615C22×C17—24no—
616C22×C17—24no—
617C22×C17—24no—
618C22×C17—24no—
619C22×C17—24no—
620C22×C17—24no—
621C22×C17—42no—
622C22×C17—42no—
623C22×C17—42no—
624C22×C17—42no—
625C22×C17—42no—
626C22×C17—42no—
627C22×C17—42no—
628C22×C17—42no—
629C22×C17—42no—
630C22×C17—42no—
631C22×C17—42no—
632C22×C17—42no—
633C22×C17—42no—
634C22×C17—42no—
635C22×C17—42no—
636C22×C17—42no—
637C22×C17—42no—
638C22×C17—42no—
639C22×C17—42no—
640C22×C17—81no—
641C22×C17—81no—
642C22×C17—81no—
643C22×C17—81no—
644C22×C17—81no—
645C22×C17—81no—
646C22×C17—81no—
647C22×C17—81no—
648C22×C17#38618yescomplemented
649C22×C17C22×C22⋊C411yescharacteristic
650C22×C17C2×C4×D411yescharacteristic
651C22×C17C2×C4×D411yescharacteristic
652C22×C17C2×C4×D411yescharacteristic
653C22×C17C4×#4111yescharacteristic
654C22×C17#51811yescharacteristic
655C22×C17#52011yescharacteristic
656C22×C17C2×#12011yescharacteristic
657C22×C17C2×#12111yescharacteristic
658C22×C17C2×#12111yescharacteristic
659C22×C17C2×#12111yescharacteristic
660C22×C17C2×#12311yescharacteristic
661C22×C17#52511yescharacteristic
662C22×C17#52911yescharacteristic
663C22×C17#53211yescharacteristic
664C22×C17#53411yescharacteristic
665C22×C17#53711yescharacteristic
666C22×C17#53811yescharacteristic
667C22×C17#53911yescharacteristic
668C22×C17D4211yescharacteristic
669C22×C17D4211yescharacteristic
670C22×C17D4211yescharacteristic
671C22×C17#54611yescharacteristic
672C22×C17#54611yescharacteristic
673C22×C17#54611yescharacteristic
674C22×C17#54611yescharacteristic
675C22×C17#54611yescharacteristic
676C22×C17#54611yescharacteristic
677C22×C17#54711yescharacteristic
678C22×C17#54711yescharacteristic
679C22×C17#54711yescharacteristic
680C22×C17#54811yescharacteristic
681C22×C17#55311yescharacteristic
682C22×C17#55311yescharacteristic
683C22×C17#55311yescharacteristic
684C4×C17—24no—
685C4×C17—24no—
686C4×C17—42no—
687C4×C17—42no—
688Dic17—24no—
689Dic17—42no—
690Dic17—42no—
691Dic17—42no—
692Dic17—42no—
693Dic17—42no—
694Dic17—81no—
695Dic17—81no—
696C23×D4C2×D1711yescharacteristic
697C23×D4C2×D1711yescharacteristic
698C23×D4C2×D1711yescharacteristic
699C24×C4—171no—
700C24×C4—171no—
701C24×C4—171no—
702C24×C4C2×D1711yescharacteristic
703C2×#121—24no—
704C2×#121—24no—
705C2×#121Dic1718yescomplemented
706C2×C4×D4—344no—
707C2×C4×D4—344no—
708C2×C4×D4—344no—
709C22×C4⋊C4—171no—
710C22×C4⋊C4C2×D1711yescharacteristic
711C22×C22⋊C4—171no—
712C22×C22⋊C4—171no—
713C22×C22⋊C4—171no—
714C22×C22⋊C4—171no—
715C22×C22⋊C4—171no—
716C22×C22⋊C4—171no—
717C22×C22⋊C4—171no—
718C22×C22⋊C4—171no—
719C22×C22⋊C4—171no—
720C22×C22⋊C4C2×D1711yescharacteristic
721C22×C22⋊C4C2×D1711yescharacteristic
722C22×C42—171no—
723#386—344no—
724#386—344no—
725#386—344no—
726#386—344no—
727C2×#95—171no—
728C2×#95—171no—
729C2×#95—171no—
730C2×#95—171no—
731C2×#95—171no—
732C2×#95—171no—
733C2×#95—171no—
734C2×#95—171no—
735C2×#95—171no—
736C2×#95—171no—
737C2×#95—171no—
738C2×#95—171no—
739C2×#95—171no—
740C2×#95—171no—
741C2×#95—344no—
742C2×C17—28no—
743C2×C17—44no—
744C2×C17—82no—
745C2×C17C2×#38611yescharacteristic
746C2×C17C4×#12111yescharacteristic
747C2×C17#232511yescharacteristic
748C2×C17D4×C22⋊C411yescharacteristic
749C2×C17#233911yescharacteristic
750C2×C17#236111yescharacteristic
751C2×C17#236411yescharacteristic
752C2×C17#241011yescharacteristic
753C2×C17#241611yescharacteristic
754C2×C17#242411yescharacteristic
755C2×C17#242511yescharacteristic
756C2×C17#243011yescharacteristic
757C2×C17#244311yescharacteristic
758C2×C17#244411yescharacteristic
759C2×C17#254311yescharacteristic
760C25C22×D1711yescharacteristic
761C25C22×D1711yescharacteristic
762C25C22×D1711yescharacteristic
763C22×D4—22no—
764C22×D4—22no—
765C22×D4—22no—
766C22×D4—22no—
767C22×D4—22no—
768C22×D4—22no—
769C22×D4—22no—
770C22×D4—22no—
771C22×D4—22no—
772C22×D4—22no—
773C22×D4—22no—
774C22×D4—22no—
775C22×D4—22no—
776C22×D4—22no—
777C22×D4—41no—
778C22×D4—41no—
779C22×D4C2×Dic1714yes—
780C22×D4C2×Dic1714yescomplemented
781C22×D4C2×Dic1714yescomplemented
782C22×D4C22⋊D1714yes—
783C22×D4C22⋊D1714yes—
784C23×C4—22no—
785C23×C4—22no—
786C23×C4—22no—
787C23×C4—22no—
788C23×C4—41no—
789C23×C4—41no—
790C23×C4—171no—
791C23×C4—171no—
792C23×C4—171no—
793C23×C4—171no—
794C23×C4—171no—
795C23×C4—171no—
796C23×C4—174no—
797C23×C4—171no—
798C23×C4—171no—
799C23×C4—342no—
800C23×C4—342no—
801C23×C4—342no—
802C23×C4—342no—
803C23×C4—342no—
804C23×C4—342no—
805C23×C4—342no—
806C23×C4—342no—
807C23×C4—342no—
808C23×C4—342no—
809C23×C4—342no—
810C23×C4—342no—
811C23×C4—342no—
812C23×C4—342no—
813C23×C4—681no—
814C23×C4—681no—
815C23×C4—681no—
816C23×C4—681no—
817C23×C4—681no—
818C23×C4—681no—
819C23×C4C2×Dic1714yescomplemented
820C23×C4C22×D1711yescharacteristic
821C23×C4C22×D1711yescharacteristic
822C23×C4C22×D1711yescharacteristic
823C23×C4C22×D1711yescharacteristic
824#121—232no—
825C4×D4—3432no—
826C2×C4⋊C4—22no—
827C2×C4⋊C4—22no—
828C2×C4⋊C4—342no—
829C2×C4⋊C4—342no—
830C2×C4⋊C4—342no—
831C2×C4⋊C4C2×Dic1714yescomplemented
832C2×C22⋊C4—22no—
833C2×C22⋊C4—22no—
834C2×C22⋊C4—22no—
835C2×C22⋊C4—22no—
836C2×C22⋊C4—174no—
837C2×C22⋊C4—342no—
838C2×C22⋊C4—342no—
839C2×C22⋊C4—342no—
840C2×C22⋊C4—342no—
841C2×C22⋊C4—342no—
842C2×C22⋊C4—342no—
843C2×C22⋊C4—342no—
844C2×C22⋊C4—342no—
845C2×C22⋊C4—342no—
846C2×C22⋊C4—342no—
847C2×C22⋊C4—342no—
848C2×C22⋊C4—342no—
849C2×C22⋊C4—342no—
850C2×C22⋊C4—342no—
851C2×C22⋊C4—342no—
852C2×C22⋊C4—342no—
853C2×C22⋊C4—342no—
854C2×C22⋊C4—342no—
855C2×C22⋊C4—342no—
856C2×C22⋊C4—342no—
857C2×C22⋊C4—681no—
858C2×C22⋊C4—681no—
859C2×C22⋊C4—681no—
860C2×C22⋊C4—681no—
861C2×C22⋊C4—681no—
862C2×C22⋊C4—681no—
863C2×C22⋊C4C2×Dic1714yescomplemented
864C2×C22⋊C4C2×Dic1714yescomplemented
865C2×C42—342no—
866C2×C42—342no—
867C2×C42—342no—
868#95—174no—
869#95—342no—
870#95—342no—
871#95—342no—
872#95—342no—
873#95—342no—
874#95—342no—
875#95—342no—
876#95—342no—
877#95—342no—
878#95—342no—
879#95—342no—
880#95—681no—
881#95—681no—
882C17#1402311yescharacteristic, complemented, Sylow
883C24—21no—
884C24—21no—
885C24—21no—
886C24—21no—
887C24—21no—
888C24—21no—
889C24—21no—
890C24—21no—
891C24—21no—
892C24—21no—
893C24—21no—
894C24—21no—
895C24—21no—
896C24—21no—
897C24—21no—
898C24—21no—
899C24—21no—
900C24—21no—
901C24—21no—
902C24—21no—
903C24—21no—
904C24—21no—
905C24—21no—
906C24—21no—
907C24—21no—
908C24—21no—
909C24—21no—
910C24—21no—
911C24—21no—
912C24—21no—
913C24—21no—
914C24—21no—
915C24—21no—
916C24—21no—
917C24D4×D1712yes—
918C24D4×D1712yes—
919C24#6325412yes—
920C24#6325412yes—
921C24C22×Dic1712yes—
922C24C22×Dic1712yes—
923C24C22×Dic1712yes—
924C24C2×C22⋊D1712yes—
925C24C2×C22⋊D1712yes—
926C24C2×C22⋊D1712yes—
927C24C2×C22⋊D1712yes—
928C24C23×D1711yescharacteristic
929C2×D4—28no—
930C2×D4—28no—
931C2×D4—28no—
932C2×D4—28no—
933C2×D4—28no—
934C2×D4—28no—
935C2×D4—28no—
936C2×D4—28no—
937C2×D4—28no—
938C2×D4—28no—
939C2×D4—28no—
940C2×D4—44no—
941C2×D4—44no—
942C2×D4—44no—
943C2×D4—44no—
944C2×D4—44no—
945C2×D4—44no—
946C2×D4—44no—
947C2×D4—44no—
948C2×D4—44no—
949C2×D4C22⋊Dic17116yescomplemented
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—28no—
971C22×C4—28no—
972C22×C4—44no—
973C22×C4—44no—
974C22×C4—44no—
975C22×C4—44no—
976C22×C4—44no—
977C22×C4—172no—
978C22×C4—172no—
979C22×C4—172no—
980C22×C4—172no—
981C22×C4—172no—
982C22×C4—172no—
983C22×C4—172no—
984C22×C4—172no—
985C22×C4—348no—
986C22×C4—341no—
987C22×C4—341no—
988C22×C4—341no—
989C22×C4—341no—
990C22×C4—348no—
991C22×C4—348no—
992C22×C4—341no—
993C22×C4—341no—
994C22×C4—341no—
995C22×C4—341no—
996C22×C4—341no—
997C22×C4—341no—
998C22×C4—341no—
999C22×C4—341no—
1000C22×C4—341no—
1001C22×C4—341no—
1002C22×C4—341no—
1003C22×C4—341no—
1004C22×C4—341no—
1005C22×C4—341no—
1006C22×C4—341no—
1007C22×C4—341no—
1008C22×C4—341no—
1009C22×C4—341no—
1010C22×C4—341no—
1011C22×C4—341no—
1012C22×C4—341no—
1013C22×C4—341no—
1014C22×C4—341no—
1015C22×C4—341no—
1016C22×C4—341no—
1017C22×C4—341no—
1018C22×C4—341no—
1019C22×C4—341no—
1020C22×C4—341no—
1021C22×C4—341no—
1022C22×C4—348no—
1023C22×C4—341no—
1024C22×C4—341no—
1025C22×C4—341no—
1026C22×C4—341no—
1027C22×C4—341no—
1028C22×C4—341no—
1029C22×C4—341no—
1030C22×C4—341no—
1031C22×C4—341no—
1032C22×C4—341no—
1033C22×C4—341no—
1034C22×C4—341no—
1035C22×C4—341no—
1036C22×C4—341no—
1037C22×C4—684no—
1038C22×C4—684no—
1039C22×C4—684no—
1040C22×C4—684no—
1041C22×C4—684no—
1042C22×C4—684no—
1043C22×C4—684no—
1044C22×C4—684no—
1045C22×C4—684no—
1046C22×C4—684no—
1047C22×C4—684no—
1048C22×C4—684no—
1049C22×C4—684no—
1050C22×C4—684no—
1051C22×C4—684no—
1052C22×C4—684no—
1053C22×C4—684no—
1054C22×C4D4×D1712yes—
1055C22×C4#6325412yes—
1056C22×C4C22×Dic1712yes—
1057C22×C4C22×Dic1712yes—
1058C22×C4C22×Dic1712yes—
1059C22×C4C22×Dic1712yes—
1060C22×C4C2×C22⋊D1712yes—
1061C22×C4C2×C22⋊D1712yes—
1062C4⋊C4—28no—
1063C4⋊C4—348no—
1064C22⋊C4—28no—
1065C22⋊C4—28no—
1066C22⋊C4—348no—
1067C22⋊C4—348no—
1068C22⋊C4—684no—
1069C22⋊C4—684no—
1070C22⋊C4—684no—
1071C22⋊C4—684no—
1072C22⋊C4—684no—
1073C22⋊C4—684no—
1074C22⋊C4—684no—
1075C42—348no—
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—22no—
1084C23—22no—
1085C23—22no—
1086C23—22no—
1087C23—22no—
1088C23—22no—
1089C23—22no—
1090C23—22no—
1091C23—22no—
1092C23—22no—
1093C23—22no—
1094C23—22no—
1095C23—22no—
1096C23—22no—
1097C23—22no—
1098C23—22no—
1099C23—22no—
1100C23—22no—
1101C23—22no—
1102C23—22no—
1103C23—22no—
1104C23—22no—
1105C23—22no—
1106C23—22no—
1107C23—22no—
1108C23—22no—
1109C23—22no—
1110C23—22no—
1111C23—22no—
1112C23—22no—
1113C23—22no—
1114C23—22no—
1115C23—22no—
1116C23—22no—
1117C23—22no—
1118C23—22no—
1119C23—22no—
1120C23—22no—
1121C23—22no—
1122C23—22no—
1123C23—22no—
1124C23—22no—
1125C23—22no—
1126C23—22no—
1127C23—22no—
1128C23—22no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23—41no—
1148C23—41no—
1149C23—41no—
1150C23—41no—
1151C23—41no—
1152C23—41no—
1153C23—41no—
1154C23—41no—
1155C23—41no—
1156C23—41no—
1157C23—41no—
1158C23—41no—
1159C23—41no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—41no—
1164C23—41no—
1165C23—41no—
1166C23—41no—
1167C23—41no—
1168C23—41no—
1169C23—41no—
1170C23—41no—
1171C23—41no—
1172C23—41no—
1173C23D4×Dic1714yes—
1174C23D4×Dic1714yes—
1175C23#1058762114yes—
1176C23#1058762314yes—
1177C23#1058762514yes—
1178C23#1058762514yes—
1179C23C2×C22⋊Dic1714yes—
1180C23C2×C22⋊Dic1714yes—
1181C23C2×D4×D1711yescharacteristic
1182C23C2×D4×D1711yescharacteristic
1183C23C2×D4×D1711yescharacteristic
1184C23C2×#6325411yescharacteristic
1185C23C2×#6325411yescharacteristic
1186C23C2×#6325411yescharacteristic
1187C23#1058769111yescharacteristic
1188C23#1058769111yescharacteristic
1189C23#41×D1711yescharacteristic
1190C23#41×D1711yescharacteristic
1191C23#1058769611yescharacteristic
1192C23#1058769711yescharacteristic
1193C23C23×Dic1711yescharacteristic
1194C23C22×C22⋊D1711yescharacteristic
1195C23C22×C22⋊D1711yescharacteristic
1196D4—232no—
1197D4—416no—
1198D4—416no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—416no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—174no—
1227C2×C4—342no—
1228C2×C4—342no—
1229C2×C4—342no—
1230C2×C4—342no—
1231C2×C4—342no—
1232C2×C4—342no—
1233C2×C4—342no—
1234C2×C4—342no—
1235C2×C4—342no—
1236C2×C4—342no—
1237C2×C4—342no—
1238C2×C4—342no—
1239C2×C4—342no—
1240C2×C4—342no—
1241C2×C4—342no—
1242C2×C4—342no—
1243C2×C4—342no—
1244C2×C4—342no—
1245C2×C4—342no—
1246C2×C4—342no—
1247C2×C4—342no—
1248C2×C4—6816no—
1249C2×C4—6816no—
1250C2×C4—6816no—
1251C2×C4—681no—
1252C2×C4—681no—
1253C2×C4—681no—
1254C2×C4—681no—
1255C2×C4—681no—
1256C2×C4—681no—
1257C2×C4—681no—
1258C2×C4—681no—
1259C2×C4—681no—
1260C2×C4—681no—
1261C2×C4—681no—
1262C2×C4—681no—
1263C2×C4—681no—
1264C2×C4—681no—
1265C2×C4—681no—
1266C2×C4—681no—
1267C2×C4—681no—
1268C2×C4—681no—
1269C2×C4—681no—
1270C2×C4—681no—
1271C2×C4—681no—
1272C2×C4—681no—
1273C2×C4—681no—
1274C2×C4—681no—
1275C2×C4—681no—
1276C2×C4—681no—
1277C2×C4—681no—
1278C2×C4—681no—
1279C2×C4—681no—
1280C2×C4—681no—
1281C2×C4—681no—
1282C2×C4—681no—
1283C2×C4—681no—
1284C2×C4—681no—
1285C2×C4D4×Dic1714yescomplemented
1286C2×C4C2×C22⋊Dic1714yes—
1287C22—24no—
1288C22—24no—
1289C22—24no—
1290C22—24no—
1291C22—24no—
1292C22—24no—
1293C22—24no—
1294C22—24no—
1295C22—24no—
1296C22—24no—
1297C22—24no—
1298C22—24no—
1299C22—24no—
1300C22—24no—
1301C22—24no—
1302C22—24no—
1303C22—24no—
1304C22—42no—
1305C22—42no—
1306C22—42no—
1307C22—42no—
1308C22—42no—
1309C22—42no—
1310C22—42no—
1311C22—42no—
1312C22—42no—
1313C22—42no—
1314C22—42no—
1315C22—42no—
1316C22—42no—
1317C22—42no—
1318C22—42no—
1319C22—42no—
1320C22—42no—
1321C22—42no—
1322C22—42no—
1323C22—81no—
1324C22—81no—
1325C22—81no—
1326C22—81no—
1327C22—81no—
1328C22—81no—
1329C22—81no—
1330C22—81no—
1331C22#1176268918yescomplemented
1332C22C22×C22⋊Dic1711yescharacteristic
1333C22C2×D4×Dic1711yescharacteristic
1334C22C2×D4×Dic1711yescharacteristic
1335C22C2×D4×Dic1711yescharacteristic
1336C22#41×Dic1711yescharacteristic
1337C22#1176328411yescharacteristic
1338C22#1176329211yescharacteristic
1339C22C2×#1058762311yescharacteristic
1340C22#121×D1711yescharacteristic
1341C22C2×#1058762511yescharacteristic
1342C22C2×#1058762511yescharacteristic
1343C22C2×#1058762111yescharacteristic
1344C22#1176331911yescharacteristic
1345C22#1176334011yescharacteristic
1346C22#1176335411yescharacteristic
1347C22#1176336711yescharacteristic
1348C22#1176338611yescharacteristic
1349C22#1176339611yescharacteristic
1350C22#1176340411yescharacteristic
1351C22D4×C22⋊D1711yescharacteristic
1352C22D4×C22⋊D1711yescharacteristic
1353C22#1176344311yescharacteristic
1354C22#1176344711yescharacteristic
1355C22#1176344711yescharacteristic
1356C22#1176344811yescharacteristic
1357C22#1176344811yescharacteristic
1358C22#1176345311yescharacteristic
1359C22#1176345311yescharacteristic
1360C22#1176345811yescharacteristic
1361C22#1176345811yescharacteristic
1362C22#1176345911yescharacteristic
1363C22#1176346511yescharacteristic
1364C22#1176350211yescharacteristic
1365C22#1176350211yescharacteristic
1366C22#1176351111yescharacteristic
1367C4—24no—
1368C4—24no—
1369C4—42no—
1370C4—42no—
1371C4—344no—
1372C4—682no—
1373C4—682no—
1374C4—682no—
1375C4—682no—
1376C4—682no—
1377C4—1361no—
1378C4—1361no—
1379C2—28no—
1380C2—44no—
1381C2—82no—
1382C2C2×#1176268911yescharacteristic
1383C2#121×Dic1711yescharacteristic
1384C2#1453148911yescharacteristic
1385C2D4×C22⋊Dic1711yescharacteristic
1386C2#1453161411yescharacteristic
1387C2#1453180411yescharacteristic
1388C2#1453183611yescharacteristic
1389C2#1453215511yescharacteristic
1390C2#1453222111yescharacteristic
1391C2#1453232611yescharacteristic
1392C2#1453234111yescharacteristic
1393C2#1453239011yescharacteristic
1394C2#1453251511yescharacteristic
1395C2#1453253011yescharacteristic
1396C2#1453374211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
Fitting, prime radicalC22×C17×#121C2
socle, cosocleC24×C17C24
hypercenterC22×#121D17
hypocenterC17#14023
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C22×D4×Dic17C2semidirect
2. C2×#11762689C2semidirect
3. C2×#11762689C2semidirect
4. C2×#11762689C2semidirect
5. C2×#11762689C2semidirect
6. C22×#10587502C2semidirect
7. #14527037C2semidirect
8. #14527033C2semidirect
9. #14527029C2semidirect
10. #14527025C2semidirect
11. #14527021C2semidirect
12. #14527016C2semidirect
13. #14527007C2semidirect
14. #14527006C2semidirect
58. C2×C17×#121C4semidirect
82. C22×D4×C17C2×C4semidirect
83. C22×D4×C17C2×C4semidirect
92. C23×C4×C17C2×C4semidirect
117. C23×Dic17D4semidirect
129. C2×C4⋊C4×C17C2×C4semidirect
134. C2×C22⋊C4×C17C2×C4semidirect
135. C2×C22⋊C4×C17C2×C4semidirect
162. C2×C22⋊Dic17D4semidirect
183. #10587502D4semidirect
250. C2×D4×C17C22⋊C4semidirect
529. C2×C4×C17C4×D4semidirect
588. C2×Dic17#121semidirect
648. C22×C17#386semidirect
705. C2×#121Dic17semidirect
780. C22×D4C2×Dic17semidirect
781. C22×D4C2×Dic17semidirect
819. C23×C4C2×Dic17semidirect
831. C2×C4⋊C4C2×Dic17semidirect
863. C2×C22⋊C4C2×Dic17semidirect
864. C2×C22⋊C4C2×Dic17semidirect
882. C17#14023semidirect
949. C2×D4C22⋊Dic17semidirect
1285. C2×C4D4×Dic17semidirect
1331. C22#11762689semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic172
C2×#117626892
C22×#105875022
#145270372
#145270332
#145270292
#145270252
#145270212
#145270162
#145270072
#145270062
C22×C17×#1212
#1402317