Finite Group Databasebeta

← #16956058

Subgroups — #16956058

Order 4352.

2574 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D17C211yesmaximal, characteristic
2C2×C4×#63225C211yesmaximal, characteristic, complemented
3C2×C4×#63227C211yesmaximal, characteristic, complemented
4C2×C4×#63227C211yesmaximal, characteristic, complemented
5C2×C4×C22⋊Dic17C211yesmaximal, characteristic, complemented
6C2×#11762655C211yesmaximal, characteristic, complemented
7#14527050C212yesmaximal, complemented
8#14527028C212yesmaximal, complemented
9#14527027C212yesmaximal, complemented
10#14527023C212yesmaximal
11C2×C4×C22⋊C4×C17C211yesmaximal, characteristic, complemented
12C23×C22⋊D17C2211yescharacteristic
13C23×C4×D17C2211yescharacteristic
14C2×C4×C22⋊D17—24no—
15C2×C4×C22⋊D17—24no—
16C2×C4×C22⋊D17C418yescomplemented
17C22×#63225C2212yes—
18C22×#63225C2211yescharacteristic
19C22×C22⋊Dic17C2212yes—
20C22×C22⋊Dic17C2211yescharacteristic
21C22×#63227C2212yes—
22C22×#63227C2212yes—
23C22×#63227C2211yescharacteristic
24C22×C4×Dic17C2211yescharacteristic
25C22×C4×Dic17C2211yescharacteristic
26C22×C4×Dic17C2211yescharacteristic
27C4×#63225—24no—
28C4×#63227—24no—
29C4×#63227—24no—
30C4×C22⋊Dic17—24no—
31#11762655—24no—
32C2×#10587502C2212yes—
33C2×#10587502C2212yes—
34C2×#10587502C2212yes—
35C2×#10587502C2212yes—
36C2×#10587502C2212yes—
37C2×#10587502C2212yes—
38C24×C4×C17C2211yescharacteristic
39C22×C22⋊C4×C17C2212yes—
40C22×C42×C17C2211yescharacteristic
41C22×C42×C17C2211yescharacteristic
42C4×C22⋊C4×C17—24no—
43C2×C17×#95C2212yes—
44C25×C17C2311yescharacteristic
45C24×D17C2311yescharacteristic
46C23×C4×C17—22no—
47C23×C4×C17—22no—
48C23×C4×C17—22no—
49C23×C4×C17—22no—
50C23×C4×C17—22no—
51C23×C4×C17—22no—
52C23×C4×C17C2×C414yes—
53C23×C4×C17C2311yescharacteristic
54C23×C4×C17C2312yes—
55C23×C4×C17C2312yes—
56C23×C4×C17C2311yescharacteristic
57C22×C22⋊D17—24no—
58C22×C22⋊D17—24no—
59C22×C22⋊D17—22no—
60C22×C22⋊D17—22no—
61C22×C22⋊D17C2×C414yes—
62C23×Dic17C2311yescharacteristic
63C23×Dic17C2312yes—
64C23×Dic17C2312yes—
65C23×Dic17C2311yescharacteristic
66C23×Dic17C2311yescharacteristic
67C22×C4×D17—22no—
68C22×C4×D17—22no—
69C22×C4×D17—22no—
70C22×C4×D17—22no—
71C22×C4×D17—22no—
72C22×C4×D17—22no—
73C22×C4×D17C2×C414yes—
74C2×C22⋊C4×C17—24no—
75C2×C22⋊C4×C17—24no—
76C2×C22⋊C4×C17—24no—
77C2×C42×C17—22no—
78C2×C42×C17—22no—
79C2×C42×C17—22no—
80C2×C42×C17—22no—
81C2×C42×C17—22no—
82C2×C42×C17D414yescomplemented
83C2×C22⋊Dic17—24no—
84C2×C22⋊Dic17—22no—
85C2×C22⋊Dic17—22no—
86C2×C22⋊Dic17—24no—
87C2×C22⋊Dic17—24no—
88C2×C22⋊Dic17C2×C414yes—
89C4×C22⋊D17—232no—
90C2×#63227—24no—
91C2×#63227—24no—
92C2×#63227—24no—
93C2×#63227—24no—
94C2×#63227—22no—
95C2×#63227—22no—
96C2×#63227—24no—
97C2×#63227—24no—
98C2×#63227C2×C414yes—
99C2×#63225—24no—
100C2×#63225—22no—
101C2×#63225—22no—
102C2×#63225—24no—
103C2×#63225—24no—
104C2×#63225C2×C414yes—
105C2×C4×Dic17—22no—
106C2×C4×Dic17—22no—
107C2×C4×Dic17—22no—
108C2×C4×Dic17—22no—
109C2×C4×Dic17—22no—
110C2×C4×Dic17C2×C414yes—
111C2×C4×Dic17D414yes—
112C2×C4×Dic17D414yes—
113C2×C4×Dic17D414yescomplemented
114C17×#95—24no—
115#10587502—24no—
116#10587502—24no—
117#10587502—24no—
118#10587502—24no—
119#10587502—24no—
120#10587502—24no—
121C24×C17—21no—
122C24×C17—21no—
123C24×C17—21no—
124C24×C17—21no—
125C24×C17—22no—
126C24×C17—21no—
127C24×C17—21no—
128C24×C17—22no—
129C24×C17—22no—
130C24×C17C22×C412yes—
131C24×C17#4114yes—
132C24×C17C2411yescharacteristic
133C23×D17—21no—
134C23×D17—21no—
135C23×D17—21no—
136C23×D17—21no—
137C23×D17—21no—
138C23×D17—21no—
139C23×D17—22no—
140C23×D17—22no—
141C23×D17—22no—
142C23×D17C22×C412yes—
143C23×D17#4114yes—
144C22×C4×C17—21no—
145C22×C4×C17—21no—
146C22×C4×C17—21no—
147C22×C4×C17—21no—
148C22×C4×C17—22no—
149C22×C4×C17—22no—
150C22×C4×C17—22no—
151C22×C4×C17—22no—
152C22×C4×C17—21no—
153C22×C4×C17—21no—
154C22×C4×C17—22no—
155C22×C4×C17—22no—
156C22×C4×C17—22no—
157C22×C4×C17—22no—
158C22×C4×C17—22no—
159C22×C4×C17—22no—
160C22×C4×C17—22no—
161C22×C4×C17—22no—
162C22×C4×C17—28no—
163C22×C4×C17—28no—
164C22×C4×C17—28no—
165C22×C4×C17—44no—
166C22×C4×C17—44no—
167C22×C4×C17—44no—
168C22×C4×C17—44no—
169C22×C4×C17C22×C412yes—
170C22×C4×C17C22×C412yes—
171C22×C4×C17C2×D412yes—
172C22×C4×C17C2×D412yes—
173C22×C4×C17C2×D412yes—
174C22×C4×C17C2×D414yes—
175C22×C4×C17C2×D412yes—
176C22×C4×C17#4114yes—
177C22×C4×C17#4112yes—
178C22×C4×C17#4112yes—
179C2×C22⋊D17—216no—
180C2×C22⋊D17—216no—
181C2×C22⋊D17—28no—
182C2×C22⋊D17—28no—
183C2×C22⋊D17—28no—
184C22×Dic17—22no—
185C22×Dic17—22no—
186C22×Dic17—22no—
187C22×Dic17—22no—
188C22×Dic17—21no—
189C22×Dic17—21no—
190C22×Dic17—21no—
191C22×Dic17—21no—
192C22×Dic17—22no—
193C22×Dic17—22no—
194C22×Dic17—22no—
195C22×Dic17—22no—
196C22×Dic17—21no—
197C22×Dic17—21no—
198C22×Dic17—22no—
199C22×Dic17—22no—
200C22×Dic17—22no—
201C22×Dic17—22no—
202C22×Dic17—22no—
203C22×Dic17—22no—
204C22×Dic17—22no—
205C22×Dic17—22no—
206C22×Dic17C22×C412yes—
207C22×Dic17C22×C412yes—
208C22×Dic17C22×C412yes—
209C22×Dic17C2×D414yes—
210C22×Dic17C2×D412yes—
211C22×Dic17C2×D412yes—
212C22×Dic17C2×D412yes—
213C22×Dic17C2×D412yes—
214C22×Dic17#4114yes—
215C2×C4×D17—28no—
216C2×C4×D17—28no—
217C2×C4×D17—28no—
218C2×C4×D17—44no—
219C2×C4×D17—44no—
220C2×C4×D17—44no—
221C2×C4×D17—44no—
222C22⋊C4×C17—216no—
223C42×C17—28no—
224C42×C17—44no—
225C22⋊Dic17—216no—
226C22⋊Dic17—28no—
227#63227—216no—
228#63227—216no—
229#63227—28no—
230#63225—216no—
231#63225—28no—
232C4×Dic17—28no—
233C4×Dic17—44no—
234C4×Dic17C22⋊C4116yescomplemented
235#13847—171nomaximal, Sylow
236C23×C17—22no—
237C23×C17—22no—
238C23×C17—22no—
239C23×C17—22no—
240C23×C17—22no—
241C23×C17—22no—
242C23×C17—24no—
243C23×C17—24no—
244C23×C17—24no—
245C23×C17—24no—
246C23×C17—24no—
247C23×C17—24no—
248C23×C17—41no—
249C23×C17—41no—
250C23×C17—42no—
251C23×C17—42no—
252C23×C17—42no—
253C23×C17—41no—
254C23×C17—42no—
255C23×C17—42no—
256C23×C17—41no—
257C23×C17—42no—
258C23×C17#11714yes—
259C23×C17C23×C411yescharacteristic
260C23×C17C22×D411yescharacteristic
261C23×C17C22×D411yescharacteristic
262C23×C17C22×D411yescharacteristic
263C23×C17C22×D411yescharacteristic
264C23×C17C2×#4112yes—
265C23×C17C2×#4111yescharacteristic
266C23×C17C2×#4112yes—
267C23×C17C2×#4111yescharacteristic
268C23×C17C2×#4112yes—
269C23×C17C2×#4112yes—
270C22×D17—22no—
271C22×D17—22no—
272C22×D17—22no—
273C22×D17—22no—
274C22×D17—22no—
275C22×D17—22no—
276C22×D17—24no—
277C22×D17—24no—
278C22×D17—24no—
279C22×D17—24no—
280C22×D17—24no—
281C22×D17—24no—
282C22×D17—41no—
283C22×D17—41no—
284C22×D17—42no—
285C22×D17—42no—
286C22×D17—42no—
287C22×D17—41no—
288C22×D17—42no—
289C22×D17—42no—
290C22×D17—41no—
291C22×D17—42no—
292C22×D17#11714yes—
293C2×C4×C17—22no—
294C2×C4×C17—22no—
295C2×C4×C17—22no—
296C2×C4×C17—24no—
297C2×C4×C17—24no—
298C2×C4×C17—24no—
299C2×C4×C17—24no—
300C2×C4×C17—24no—
301C2×C4×C17—24no—
302C2×C4×C17—41no—
303C2×C4×C17—41no—
304C2×C4×C17—42no—
305C2×C4×C17—42no—
306C2×C4×C17—42no—
307C2×C4×C17—42no—
308C2×C4×C17—41no—
309C2×C4×C17—42no—
310C2×C4×C17—42no—
311C2×C4×C17—42no—
312C2×C4×C17—41no—
313C2×C4×C17—42no—
314C2×C4×C17—416no—
315C2×C4×C17C2×C22⋊C414yes—
316C2×C4×C17C4×D414yes—
317C2×C4×C17C4×D414yes—
318C2×C4×C17#12114yes—
319C2×C4×C17#12114yes—
320C2×C4×C17#12414yes—
321C2×C4×C17#12714yes—
322C22⋊D17—232no—
323C2×Dic17—22no—
324C2×Dic17—22no—
325C2×Dic17—22no—
326C2×Dic17—22no—
327C2×Dic17—24no—
328C2×Dic17—24no—
329C2×Dic17—24no—
330C2×Dic17—24no—
331C2×Dic17—22no—
332C2×Dic17—22no—
333C2×Dic17—22no—
334C2×Dic17—24no—
335C2×Dic17—24no—
336C2×Dic17—24no—
337C2×Dic17—24no—
338C2×Dic17—24no—
339C2×Dic17—24no—
340C2×Dic17—41no—
341C2×Dic17—41no—
342C2×Dic17—42no—
343C2×Dic17—42no—
344C2×Dic17—42no—
345C2×Dic17—42no—
346C2×Dic17—41no—
347C2×Dic17—42no—
348C2×Dic17—42no—
349C2×Dic17—41no—
350C2×Dic17—42no—
351C2×Dic17—42no—
352C2×Dic17C2×C22⋊C414yes—
353C2×Dic17C2×C22⋊C414yes—
354C4×D17—416no—
355C22×C4×D4—171no—
356C2×C4×C4⋊C4—171no—
357C2×C4×C22⋊C4—171no—
358C2×C4×C22⋊C4—171no—
359C2×C4×C22⋊C4—171no—
360C2×C4×C22⋊C4D1711yescharacteristic, complemented
361C2×#376—171no—
362#1445—172no—
363#1439—172no—
364#1439—172no—
365#1438—172no—
366C22×C17—24no—
367C22×C17—24no—
368C22×C17—24no—
369C22×C17—44no—
370C22×C17—44no—
371C22×C17—44no—
372C22×C17—44no—
373C22×C17—42no—
374C22×C17—42no—
375C22×C17—42no—
376C22×C17—42no—
377C22×C17C22×C22⋊C411yescharacteristic
378C22×C17C2×#11711yescharacteristic
379C22×C17C2×#11711yescharacteristic
380C22×C17C2×C4×D411yescharacteristic
381C22×C17C2×C4×D411yescharacteristic
382C22×C17C4×#4111yescharacteristic
383C22×C17C4×#4111yescharacteristic
384C22×C17C2×#12111yescharacteristic
385C22×C17C2×#12111yescharacteristic
386C22×C17#52512yes—
387C22×C17#52512yes—
388C22×C17#52512yes—
389C22×C17#52512yes—
390C22×C17#52512yes—
391C22×C17#52512yes—
392C22×C17#52512yes—
393C22×C17C2×#12411yescharacteristic
394C22×C17#52912yes—
395C22×C17#52912yes—
396C22×C17#52912yes—
397C22×C17#52912yes—
398C22×C17C2×#12711yescharacteristic
399C22×C17#53212yes—
400C2×D17—24no—
401C2×D17—24no—
402C2×D17—24no—
403C2×D17—44no—
404C2×D17—44no—
405C2×D17—44no—
406C2×D17—44no—
407C2×D17—42no—
408C2×D17—42no—
409C2×D17—42no—
410C2×D17—42no—
411C4×C17—44no—
412C4×C17—44no—
413C4×C17—42no—
414C4×C17#39018yes—
415Dic17—24no—
416Dic17—24no—
417Dic17—44no—
418Dic17—44no—
419Dic17—42no—
420C23×D4—171no—
421C24×C4—171no—
422C24×C4C2×D1711yescharacteristic
423C2×C4×D4—178no—
424C2×C4×D4—344no—
425C2×C4×D4—344no—
426C22×C4⋊C4—171no—
427C22×C4⋊C4—172no—
428C22×C22⋊C4—171no—
429C22×C22⋊C4—171no—
430C22×C22⋊C4—172no—
431C22×C22⋊C4—172no—
432C22×C22⋊C4—172no—
433C22×C22⋊C4C2×D1712yes—
434C22×C42—171no—
435C22×C42—171no—
436C22×C42—171no—
437C22×C42C2×D1711yescharacteristic
438C22×C42C2×D1711yescharacteristic
439C4×C4⋊C4—344no—
440C4×C22⋊C4—24no—
441C4×C22⋊C4—344no—
442C4×C22⋊C4—344no—
443C4×C22⋊C4—344no—
444#376—344no—
445C2×#95—172no—
446C2×#95—172no—
447C2×#95—172no—
448C2×#95—172no—
449C2×#95—172no—
450C2×#95—172no—
451C2×#95C2×D1712yes—
452C2×C17—44no—
453C2×C17#228011yescharacteristic
454C2×C17#229011yescharacteristic
455C2×C17#229011yescharacteristic
456C2×C17#229011yescharacteristic
457C2×C17#229011yescharacteristic
458C2×C17C2×#39011yescharacteristic
459C2×C17#229711yescharacteristic
460C2×C17#239212yes—
461C2×C17#239212yes—
462C2×C17#239712yes—
463C2×C17#239812yes—
464D17—44no—
465C25—171no—
466C25C22×D1711yescharacteristic
467C22×D4—174no—
468C22×D4—342no—
469C22×D4—342no—
470C22×D4—344no—
471C22×D4—344no—
472C23×C4—22no—
473C23×C4—22no—
474C23×C4—22no—
475C23×C4—22no—
476C23×C4—22no—
477C23×C4—22no—
478C23×C4—171no—
479C23×C4—171no—
480C23×C4—172no—
481C23×C4—172no—
482C23×C4—171no—
483C23×C4—174no—
484C23×C4—342no—
485C23×C4—342no—
486C23×C4—342no—
487C23×C4—342no—
488C23×C4—342no—
489C23×C4—342no—
490C23×C4C4×D1714yes—
491C23×C4C22×D1711yescharacteristic
492C23×C4C22×D1712yes—
493C23×C4C22×D1712yes—
494C23×C4C22×D1711yescharacteristic
495C4×D4—3432no—
496C2×C4⋊C4—174no—
497C2×C4⋊C4—342no—
498C2×C4⋊C4—342no—
499C2×C4⋊C4—344no—
500C2×C4⋊C4—344no—
501C2×C4⋊C4—344no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—174no—
506C2×C22⋊C4—174no—
507C2×C22⋊C4—342no—
508C2×C22⋊C4—342no—
509C2×C22⋊C4—344no—
510C2×C22⋊C4—344no—
511C2×C22⋊C4—344no—
512C2×C22⋊C4—344no—
513C2×C22⋊C4—342no—
514C2×C22⋊C4—342no—
515C2×C22⋊C4—344no—
516C2×C22⋊C4—344no—
517C2×C22⋊C4—344no—
518C2×C22⋊C4—344no—
519C2×C22⋊C4—344no—
520C2×C42—22no—
521C2×C42—22no—
522C2×C42—22no—
523C2×C42—22no—
524C2×C42—22no—
525C2×C42—174no—
526C2×C42—174no—
527C2×C42—174no—
528C2×C42—174no—
529C2×C42—342no—
530C2×C42—342no—
531C2×C42—342no—
532C2×C42—342no—
533C2×C42—342no—
534C2×C42C22⋊D1714yescomplemented
535#95—24no—
536#95—344no—
537#95—344no—
538#95—344no—
539#95—344no—
540#95—344no—
541#95—344no—
542C17#1384711yescharacteristic, complemented, Sylow
543C24—22no—
544C24—21no—
545C24—21no—
546C24—21no—
547C24—21no—
548C24—21no—
549C24—22no—
550C24—22no—
551C24—21no—
552C24—172no—
553C24—174no—
554C24—342no—
555C24—341no—
556C24—342no—
557C24—341no—
558C24—341no—
559C24—341no—
560C24—341no—
561C24—342no—
562C24—341no—
563C24C2×C4×D1712yes—
564C24#6325214yes—
565C24C23×D1711yescharacteristic
566C2×D4—348no—
567C2×D4—348no—
568C2×D4—3416no—
569C2×D4—3416no—
570C2×D4—348no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—21no—
588C22×C4—22no—
589C22×C4—28no—
590C22×C4—28no—
591C22×C4—28no—
592C22×C4—44no—
593C22×C4—44no—
594C22×C4—44no—
595C22×C4—44no—
596C22×C4—172no—
597C22×C4—172no—
598C22×C4—172no—
599C22×C4—172no—
600C22×C4—172no—
601C22×C4—172no—
602C22×C4—172no—
603C22×C4—174no—
604C22×C4—174no—
605C22×C4—342no—
606C22×C4—342no—
607C22×C4—342no—
608C22×C4—342no—
609C22×C4—342no—
610C22×C4—342no—
611C22×C4—342no—
612C22×C4—342no—
613C22×C4—342no—
614C22×C4—341no—
615C22×C4—342no—
616C22×C4—341no—
617C22×C4—342no—
618C22×C4—342no—
619C22×C4—341no—
620C22×C4—341no—
621C22×C4—341no—
622C22×C4—342no—
623C22×C4—342no—
624C22×C4—342no—
625C22×C4—341no—
626C22×C4—342no—
627C22×C4—348no—
628C22×C4—348no—
629C22×C4—348no—
630C22×C4—684no—
631C22×C4—684no—
632C22×C4—684no—
633C22×C4—684no—
634C22×C4C2×C4×D1712yes—
635C22×C4C2×C4×D1712yes—
636C22×C4#6325214yes—
637C22×C4#6325212yes—
638C22×C4D4×D1712yes—
639C22×C4D4×D1712yes—
640C22×C4D4×D1712yes—
641C22×C4#6325412yes—
642C22×C4C2×C22⋊D1714yes—
643C22×C4C2×C22⋊D1712yes—
644C4⋊C4—348no—
645C4⋊C4—3416no—
646C22⋊C4—216no—
647C22⋊C4—348no—
648C22⋊C4—3416no—
649C22⋊C4—3416no—
650C22⋊C4—348no—
651C22⋊C4—3416no—
652C42—28no—
653C42—44no—
654C42—1716no—
655C42—348no—
656C42—684no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—41no—
670C23—41no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—41no—
675C23—42no—
676C23—42no—
677C23—41no—
678C23—42no—
679C23—174no—
680C23—342no—
681C23—342no—
682C23—342no—
683C23—342no—
684C23—342no—
685C23—342no—
686C23—344no—
687C23—344no—
688C23—344no—
689C23—344no—
690C23—344no—
691C23—344no—
692C23—681no—
693C23—681no—
694C23—682no—
695C23—682no—
696C23—682no—
697C23—681no—
698C23—682no—
699C23—682no—
700C23—681no—
701C23—682no—
702C23#1058755814yes—
703C23C22×C4×D1711yescharacteristic
704C23C2×#6325212yes—
705C23C2×#6325211yescharacteristic
706C23C2×#6325212yes—
707C23C2×D4×D1711yescharacteristic
708C23C2×D4×D1711yescharacteristic
709C23C2×D4×D1711yescharacteristic
710C23C2×#6325411yescharacteristic
711C23#41×D1712yes—
712C23#41×D1712yes—
713C23C22×C22⋊D1711yescharacteristic
714D4—3432no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—41no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—41no—
735C2×C4—42no—
736C2×C4—416no—
737C2×C4—174no—
738C2×C4—174no—
739C2×C4—342no—
740C2×C4—342no—
741C2×C4—342no—
742C2×C4—342no—
743C2×C4—344no—
744C2×C4—344no—
745C2×C4—344no—
746C2×C4—344no—
747C2×C4—342no—
748C2×C4—342no—
749C2×C4—342no—
750C2×C4—344no—
751C2×C4—344no—
752C2×C4—344no—
753C2×C4—344no—
754C2×C4—344no—
755C2×C4—344no—
756C2×C4—681no—
757C2×C4—681no—
758C2×C4—682no—
759C2×C4—682no—
760C2×C4—682no—
761C2×C4—682no—
762C2×C4—681no—
763C2×C4—682no—
764C2×C4—682no—
765C2×C4—682no—
766C2×C4—681no—
767C2×C4—682no—
768C2×C4—6816no—
769C2×C4C22⋊C4×D1714yes—
770C2×C4#1058756714yes—
771C2×C4#1058757014yes—
772C2×C4#1058757114yes—
773C2×C4C4×C22⋊D1714yes—
774C2×C4#1058762514yes—
775C2×C4#1058762614yes—
776C22—24no—
777C22—24no—
778C22—24no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—44no—
783C22—44no—
784C22—42no—
785C22—44no—
786C22—44no—
787C22—344no—
788C22—344no—
789C22—344no—
790C22—682no—
791C22—682no—
792C22—682no—
793C22—684no—
794C22—684no—
795C22—682no—
796C22—684no—
797C22—684no—
798C22C2×C22⋊C4×D1711yescharacteristic
799C22#117×D1711yescharacteristic
800C22C2×#1058755811yescharacteristic
801C22C2×#1058756711yescharacteristic
802C22C2×C4×C22⋊D1711yescharacteristic
803C22#1176327711yescharacteristic
804C22C4×#6325211yescharacteristic
805C22C2×#1058762511yescharacteristic
806C22C2×#1058757011yescharacteristic
807C22#1176331612yes—
808C22#1176331812yes—
809C22#1176331812yes—
810C22#1176331812yes—
811C22#1176331812yes—
812C22#1176331812yes—
813C22#1176332012yes—
814C22C2×#1058757111yescharacteristic
815C22#1176333712yes—
816C22#1176333912yes—
817C22#1176334112yes—
818C22#1176334312yes—
819C22C2×#1058762611yescharacteristic
820C22#1176335612yes—
821C4—42no—
822C4—44no—
823C4—44no—
824C4—344no—
825C4—344no—
826C4—682no—
827C4—684no—
828C4—684no—
829C4#1176270918yes—
830C2—44no—
831C2—684no—
832C2#1453116511yescharacteristic
833C2#1453122111yescharacteristic
834C2#1453122311yescharacteristic
835C2#1453122711yescharacteristic
836C2#1453123011yescharacteristic
837C2C2×#1176270911yescharacteristic
838C2#1453127011yescharacteristic
839C2#1453202612yes—
840C2#1453202812yes—
841C2#1453206312yes—
842C2#1453207112yes—
subgroupG/H
centerC23×C4C22×D17
commutatorC23×C17C23×C4
FrattiniC24C23×D17
FittingC2×C4×C22⋊C4×C17C2
socle, cosocleC24×C17C24
prime radicalC23×C22⋊D17C22
hypercenterC2×C4×C22⋊C4D17
hypocenterC17#13847
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×#63225C2semidirect
3. C2×C4×#63227C2semidirect
4. C2×C4×#63227C2semidirect
5. C2×C4×C22⋊Dic17C2semidirect
6. C2×#11762655C2semidirect
7. #14527050C2semidirect
8. #14527028C2semidirect
9. #14527027C2semidirect
11. C2×C4×C22⋊C4×C17C2semidirect
16. C2×C4×C22⋊D17C4semidirect
82. C2×C42×C17D4semidirect
113. C2×C4×Dic17D4semidirect
234. C4×Dic17C22⋊C4semidirect
360. C2×C4×C22⋊C4D17semidirect
534. C2×C42C22⋊D17semidirect
542. C17#13847semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D172
C2×C4×#632252
C2×C4×#632272
C2×C4×C22⋊Dic172
C2×#117626552
#145270502
#145270282
#145270272
#145270232
C2×C4×C22⋊C4×C172
#1384717