Finite Group Databasebeta

← #16958689

Subgroups — #16958689

Order 4352.

1390 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762716C211yesmaximal, characteristic
2C2×#11762655C211yesmaximal, characteristic
3#14527055C211yesmaximal, characteristic
4#14527046C211yesmaximal, characteristic
5#14527041C211yesmaximal, characteristic
6#14527037C211yesmaximal, characteristic
7#14527018C211yesmaximal, characteristic
8#14527018C211yesmaximal, characteristic
9#14527018C211yesmaximal, characteristic
10#14527016C211yesmaximal, characteristic
11#14527011C211yesmaximal, characteristic
12#14527009C211yesmaximal, characteristic
13#14527009C211yesmaximal, characteristic
14#95×Dic17C211yesmaximal, characteristic
15C2×C17×#391C211yesmaximal, characteristic
16C22×C4⋊Dic17C2211yescharacteristic
17C22×C4⋊Dic17C2211yescharacteristic
18C22×C4×Dic17C2211yescharacteristic
19C22×C4×Dic17C2211yescharacteristic
20C22×C4×Dic17C2211yescharacteristic
21C22×C4×Dic17C2211yescharacteristic
22#11762716—24no—
23#11762655—24no—
24C2×#10587502C2211yescharacteristic
25C2×#10587502C2211yescharacteristic
26C2×#10587502C2211yescharacteristic
27C2×#10587502C2211yescharacteristic
28C2×#10587502C2211yescharacteristic
29C2×#10587502C2211yescharacteristic
30C2×#10587502C2211yescharacteristic
31C2×#10587502C2211yescharacteristic
32C2×#10587502C2211yescharacteristic
33C2×#10587502C2211yescharacteristic
34C2×#10587502C2211yescharacteristic
35C2×#10587502C2211yescharacteristic
36C2×#10587502C2211yescharacteristic
37C2×#10587502C2211yescharacteristic
38C2×#10587502C2211yescharacteristic
39C2×#10587502C2211yescharacteristic
40C2×#10587502C2211yescharacteristic
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C23×Q8×C17C2211yescharacteristic
47C22×C4⋊C4×C17C2211yescharacteristic
48C22×C42×C17C2211yescharacteristic
49C17×#391C418yescomplemented
50C2×C17×#95C2211yescharacteristic
51C2×C17×#95C2211yescharacteristic
52C2×C17×#95C2211yescharacteristic
53C2×C17×#95C2211yescharacteristic
54C22×Q8×C17—22no—
55C22×Q8×C17—22no—
56C22×Q8×C17—22no—
57C22×Q8×C17—22no—
58C22×Q8×C17—41no—
59C22×Q8×C17—41no—
60C22×Q8×C17C2×C414yes—
61C23×C4×C17C2311yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C23×C4×C17C2311yescharacteristic
64C23×C4×C17C2311yescharacteristic
65C23×C4×C17C2311yescharacteristic
66C23×C4×C17C2311yescharacteristic
67C23×C4×C17C2311yescharacteristic
68C23×Dic17C2311yescharacteristic
69C23×Dic17C2311yescharacteristic
70C23×Dic17C2311yescharacteristic
71C23×Dic17C2311yescharacteristic
72C23×Dic17C2311yescharacteristic
73C23×Dic17C2311yescharacteristic
74C23×Dic17C2311yescharacteristic
75C23×Dic17C2311yescharacteristic
76C2×C4⋊C4×C17—41no—
77C2×C4⋊C4×C17—41no—
78C2×C4⋊C4×C17C2×C414yes—
79C2×C42×C17—22no—
80C2×C42×C17—22no—
81C2×C42×C17C2×C414yes—
82C2×C4⋊Dic17—22no—
83C2×C4⋊Dic17—22no—
84C2×C4⋊Dic17—22no—
85C2×C4⋊Dic17—22no—
86C2×C4⋊Dic17—41no—
87C2×C4⋊Dic17—41no—
88C2×C4×Dic17—22no—
89C2×C4×Dic17—22no—
90C2×C4×Dic17—22no—
91C2×C4×Dic17—22no—
92C2×C4×Dic17—22no—
93C2×C4×Dic17—22no—
94C2×C4×Dic17—22no—
95C2×C4×Dic17—22no—
96C2×C4×Dic17—22no—
97C2×C4×Dic17—41no—
98C2×C4×Dic17—41no—
99C2×C4×Dic17Q814yescomplemented
100C17×#95C2×C414yes—
101C17×#95C2×C414yes—
102C17×#95C2×C414yes—
103C17×#95C2×C414yes—
104#10587502—22no—
105#10587502—22no—
106#10587502—22no—
107#10587502—22no—
108#10587502—22no—
109#10587502—22no—
110#10587502—22no—
111#10587502—22no—
112#10587502—22no—
113#10587502—22no—
114#10587502—22no—
115#10587502—22no—
116#10587502—22no—
117#10587502—22no—
118#10587502—22no—
119#10587502—22no—
120#10587502—22no—
121#10587502—41no—
122#10587502—41no—
123#10587502—41no—
124#10587502—41no—
125#10587502D414yes—
126C24×C17C2411yescharacteristic
127C2×Q8×C17—28no—
128C2×Q8×C17—28no—
129C2×Q8×C17—44no—
130C2×Q8×C17—44no—
131C2×Q8×C17—44no—
132C2×Q8×C17—44no—
133C2×Q8×C17—44no—
134C22×C4×C17—21no—
135C22×C4×C17—21no—
136C22×C4×C17—21no—
137C22×C4×C17—21no—
138C22×C4×C17—21no—
139C22×C4×C17—21no—
140C22×C4×C17—21no—
141C22×C4×C17—21no—
142C22×C4×C17—21no—
143C22×C4×C17—21no—
144C22×C4×C17—21no—
145C22×C4×C17—21no—
146C22×C4×C17—21no—
147C22×C4×C17—21no—
148C22×C4×C17—21no—
149C22×C4×C17—21no—
150C22×C4×C17—21no—
151C22×C4×C17—21no—
152C22×C4×C17—21no—
153C22×C4×C17—21no—
154C22×C4×C17—21no—
155C22×C4×C17—21no—
156C22×C4×C17—21no—
157C22×C4×C17—21no—
158C22×C4×C17—21no—
159C22×C4×C17—21no—
160C22×C4×C17—21no—
161C22×C4×C17—21no—
162C22×C4×C17—21no—
163C22×C4×C17—21no—
164C22×C4×C17—21no—
165C22×C4×C17—21no—
166C22×C4×C17—21no—
167C22×C4×C17—21no—
168C22×C4×C17—21no—
169C22×C4×C17—21no—
170C22×C4×C17C22×C412yes—
171C22×C4×C17C22×C412yes—
172C22×C4×C17C22×C412yes—
173C22×C4×C17C22×C412yes—
174C22×C4×C17C22×C412yes—
175C22×C4×C17C22×C412yes—
176C22×C4×C17C22×C412yes—
177C22×C4×C17C2×D412yes—
178C22×C4×C17C2×Q812yes—
179C22×C4×C17#4112yes—
180C22×C4×C17#4112yes—
181C22×C4×C17#4112yes—
182C22×C4×C17#4112yes—
183C22×Dic17—21no—
184C22×Dic17—21no—
185C22×Dic17—21no—
186C22×Dic17—21no—
187C22×Dic17—21no—
188C22×Dic17—21no—
189C22×Dic17—21no—
190C22×Dic17—21no—
191C22×Dic17—21no—
192C22×Dic17—21no—
193C22×Dic17—21no—
194C22×Dic17—21no—
195C22×Dic17—21no—
196C22×Dic17—21no—
197C22×Dic17—21no—
198C22×Dic17—21no—
199C22×Dic17—21no—
200C22×Dic17—21no—
201C22×Dic17—21no—
202C22×Dic17—21no—
203C22×Dic17—21no—
204C22×Dic17—21no—
205C22×Dic17—21no—
206C22×Dic17—21no—
207C22×Dic17—21no—
208C22×Dic17—21no—
209C22×Dic17—21no—
210C22×Dic17—21no—
211C22×Dic17—21no—
212C22×Dic17—21no—
213C22×Dic17—21no—
214C22×Dic17—21no—
215C22×Dic17—21no—
216C22×Dic17—21no—
217C22×Dic17—21no—
218C22×Dic17—21no—
219C22×Dic17—21no—
220C22×Dic17—21no—
221C22×Dic17—21no—
222C22×Dic17—21no—
223C22×Dic17—21no—
224C22×Dic17—21no—
225C22×Dic17—21no—
226C22×Dic17—21no—
227C22×Dic17—21no—
228C22×Dic17—21no—
229C22×Dic17—21no—
230C22×Dic17—21no—
231C22×Dic17C2×D412yes—
232C22×Dic17C2×D412yes—
233C22×Dic17C2×Q812yes—
234C22×Dic17C2×Q812yes—
235C22×Dic17#4112yes—
236C22×Dic17#4112yes—
237C22×Dic17#4112yes—
238C22×Dic17#4112yes—
239C4⋊C4×C17—44no—
240C42×C17—28no—
241C4⋊Dic17—44no—
242C4⋊Dic17—44no—
243C4×Dic17—28no—
244C4×Dic17—28no—
245C4×Dic17—44no—
246C4×Dic17—44no—
247#14090—171nomaximal, Sylow
248C23×C17C23×C411yescharacteristic
249C23×C17C22×D411yescharacteristic
250C23×C17C22×Q811yescharacteristic
251C23×C17C2×#4111yescharacteristic
252C23×C17C2×#4111yescharacteristic
253C23×C17C2×#4111yescharacteristic
254C23×C17C2×#4111yescharacteristic
255C23×C17C2×#4111yescharacteristic
256C23×C17C2×#4111yescharacteristic
257C23×C17C2×#4111yescharacteristic
258C23×C17C2×#4111yescharacteristic
259C23×C17H(5,𝔽2)11yescharacteristic
260C23×C17H(5,𝔽2)11yescharacteristic
261C23×C172−1+411yescharacteristic
262C23×C172−1+411yescharacteristic
263Q8×C17—416no—
264C2×C4×C17—22no—
265C2×C4×C17—22no—
266C2×C4×C17—22no—
267C2×C4×C17—22no—
268C2×C4×C17—22no—
269C2×C4×C17—22no—
270C2×C4×C17—22no—
271C2×C4×C17—22no—
272C2×C4×C17—22no—
273C2×C4×C17—22no—
274C2×C4×C17—22no—
275C2×C4×C17—22no—
276C2×C4×C17—22no—
277C2×C4×C17—22no—
278C2×C4×C17—22no—
279C2×C4×C17—22no—
280C2×C4×C17—22no—
281C2×C4×C17—22no—
282C2×C4×C17—22no—
283C2×C4×C17—22no—
284C2×C4×C17—22no—
285C2×C4×C17—22no—
286C2×C4×C17—22no—
287C2×C4×C17—22no—
288C2×C4×C17—22no—
289C2×C4×C17—22no—
290C2×C4×C17—22no—
291C2×C4×C17—22no—
292C2×C4×C17—22no—
293C2×C4×C17—22no—
294C2×C4×C17—41no—
295C2×C4×C17—41no—
296C2×C4×C17—41no—
297C2×C4×C17—41no—
298C2×C4×C17—41no—
299C2×C4×C17—41no—
300C2×C4×C17—41no—
301C2×C4×C17—41no—
302C2×C4×C17—41no—
303C2×C4×C17—41no—
304C2×C4×C17—41no—
305C2×C4×C17—41no—
306C2×C4×C17—41no—
307C2×C4×C17—41no—
308C2×C4×C17—41no—
309C2×C4×C17—41no—
310C2×C4×C17#11714yes—
311C2×C4×C17C4×D414yes—
312C2×C4×C17C4×Q814yes—
313C2×Dic17—22no—
314C2×Dic17—22no—
315C2×Dic17—22no—
316C2×Dic17—22no—
317C2×Dic17—22no—
318C2×Dic17—22no—
319C2×Dic17—22no—
320C2×Dic17—22no—
321C2×Dic17—22no—
322C2×Dic17—22no—
323C2×Dic17—22no—
324C2×Dic17—22no—
325C2×Dic17—22no—
326C2×Dic17—22no—
327C2×Dic17—22no—
328C2×Dic17—22no—
329C2×Dic17—22no—
330C2×Dic17—22no—
331C2×Dic17—22no—
332C2×Dic17—22no—
333C2×Dic17—22no—
334C2×Dic17—41no—
335C2×Dic17—41no—
336C2×Dic17—41no—
337C2×Dic17—41no—
338C2×Dic17—41no—
339C2×Dic17—41no—
340C2×Dic17—41no—
341C2×Dic17—41no—
342C2×Dic17—41no—
343C2×Dic17—41no—
344C2×Dic17—41no—
345C2×Dic17—41no—
346C2×Dic17—41no—
347C2×Dic17—41no—
348C2×Dic17—41no—
349C2×Dic17—41no—
350C2×Dic17—41no—
351C2×Dic17—41no—
352C2×Dic17—41no—
353C2×Dic17—41no—
354C2×Dic17—41no—
355C2×Dic17—41no—
356C2×Dic17—41no—
357C2×Dic17—41no—
358C2×Dic17—41no—
359C2×Dic17—41no—
360C2×Dic17—41no—
361C2×Dic17—41no—
362C2×Dic17—41no—
363C2×Dic17—41no—
364C2×Dic17—41no—
365C2×Dic17—41no—
366C2×Dic17—41no—
367C2×Dic17—41no—
368C2×Dic17C22⋊Q814yes—
369C2×#391—171no—
370C2×#391D1711yescharacteristic
371C2×#376—171no—
372#1446—171no—
373#1443—171no—
374#1442—171no—
375#1441—171no—
376#1436—171no—
377#1436—171no—
378#1436—171no—
379#1436—171no—
380#1434—171no—
381#1434—171no—
382#1434—171no—
383C4×#95—171no—
384C22×C17C2×#11711yescharacteristic
385C22×C17C2×C4×D411yescharacteristic
386C22×C17C2×C4×Q811yescharacteristic
387C22×C17C4×#4111yescharacteristic
388C22×C17C4×#4111yescharacteristic
389C22×C17#51811yescharacteristic
390C22×C17#51911yescharacteristic
391C22×C17C2×C22⋊Q811yescharacteristic
392C22×C17#52511yescharacteristic
393C22×C17#52911yescharacteristic
394C22×C17#52911yescharacteristic
395C22×C17#52911yescharacteristic
396C22×C17#53311yescharacteristic
397C22×C17#53311yescharacteristic
398C22×C17#53311yescharacteristic
399C22×C17#54211yescharacteristic
400C22×C17#54211yescharacteristic
401C22×C17#54411yescharacteristic
402C22×C17#54411yescharacteristic
403C22×C17#54611yescharacteristic
404C22×C17#54611yescharacteristic
405C22×C17#54711yescharacteristic
406C22×C17#54811yescharacteristic
407C22×C17#55111yescharacteristic
408C22×C17#55111yescharacteristic
409C22×C17#55111yescharacteristic
410C22×C17#55111yescharacteristic
411C22×C17#55211yescharacteristic
412C22×C17#55211yescharacteristic
413C22×C17#55211yescharacteristic
414C22×C17#55511yescharacteristic
415C22×C17#55511yescharacteristic
416C22×C17#55611yescharacteristic
417C22×C17#55611yescharacteristic
418C22×C17#55611yescharacteristic
419C4×C17—24no—
420C4×C17—24no—
421C4×C17—24no—
422C4×C17—42no—
423C4×C17—42no—
424C4×C17—42no—
425C4×C17—42no—
426Dic17—24no—
427Dic17—42no—
428Dic17—42no—
429Dic17—42no—
430Dic17—42no—
431Dic17—42no—
432Dic17—81no—
433Dic17—81no—
434C23×Q8C2×D1711yescharacteristic
435C22×C4⋊C4—171no—
436C22×C4⋊C4—171no—
437C22×C4⋊C4C2×D1711yescharacteristic
438C22×C42—171no—
439C22×C42—171no—
440C22×C42—171no—
441C22×C42—171no—
442C22×C42C2×D1711yescharacteristic
443#391—344no—
444#391Dic1718yescomplemented
445#376—344no—
446C2×#95—171no—
447C2×#95—171no—
448C2×#95—171no—
449C2×#95—171no—
450C2×#95—171no—
451C2×#95—171no—
452C2×#95—171no—
453C2×#95—171no—
454C2×#95—171no—
455C2×#95—171no—
456C2×#95—171no—
457C2×#95—171no—
458C2×#95—171no—
459C2×#95—171no—
460C2×#95—171no—
461C2×#95—171no—
462C2×#95—171no—
463C2×#95—171no—
464C2×#95—171no—
465C2×#95—171no—
466C2×#95—171no—
467C2×#95—171no—
468C2×#95C2×D1711yescharacteristic
469C2×#95C2×D1711yescharacteristic
470C2×#95C2×D1711yescharacteristic
471C2×#95C2×D1711yescharacteristic
472C2×C17#229511yescharacteristic
473C2×C17C4×C22⋊Q811yescharacteristic
474C2×C17#233111yescharacteristic
475C2×C17#234211yescharacteristic
476C2×C17#235611yescharacteristic
477C2×C17#236211yescharacteristic
478C2×C17#237211yescharacteristic
479C2×C17#243811yescharacteristic
480C2×C17#243911yescharacteristic
481C2×C17#247411yescharacteristic
482C2×C17#247711yescharacteristic
483C2×C17#252711yescharacteristic
484C2×C17#253211yescharacteristic
485C2×C17#260511yescharacteristic
486C2×C17#261211yescharacteristic
487C22×Q8—22no—
488C22×Q8—22no—
489C22×Q8—22no—
490C22×Q8—22no—
491C22×Q8—41no—
492C22×Q8—41no—
493C22×Q8C2×Dic1714yes—
494C23×C4—171no—
495C23×C4—171no—
496C23×C4—171no—
497C23×C4—171no—
498C23×C4—171no—
499C23×C4—171no—
500C23×C4—171no—
501C23×C4—171no—
502C23×C4C22×D1711yescharacteristic
503C23×C4C22×D1711yescharacteristic
504C23×C4C22×D1711yescharacteristic
505C23×C4C22×D1711yescharacteristic
506C23×C4C22×D1711yescharacteristic
507C23×C4C22×D1711yescharacteristic
508C23×C4C22×D1711yescharacteristic
509C2×C4⋊C4—41no—
510C2×C4⋊C4—41no—
511C2×C4⋊C4—342no—
512C2×C4⋊C4—342no—
513C2×C4⋊C4—342no—
514C2×C4⋊C4—342no—
515C2×C4⋊C4—681no—
516C2×C4⋊C4—681no—
517C2×C4⋊C4C2×Dic1714yes—
518C2×C42—22no—
519C2×C42—22no—
520C2×C42—174no—
521C2×C42—342no—
522C2×C42—342no—
523C2×C42—342no—
524C2×C42—342no—
525C2×C42—342no—
526C2×C42—342no—
527C2×C42—342no—
528C2×C42—342no—
529C2×C42—342no—
530C2×C42—681no—
531C2×C42—681no—
532C2×C42C2×Dic1714yes—
533#95—174no—
534#95—342no—
535#95—342no—
536#95—342no—
537#95—342no—
538#95—342no—
539#95—342no—
540#95—342no—
541#95—342no—
542#95—342no—
543#95—342no—
544#95—342no—
545#95—342no—
546#95—342no—
547#95—342no—
548#95—342no—
549#95—342no—
550#95—342no—
551#95—681no—
552#95—681no—
553#95—681no—
554#95—681no—
555#95C2×Dic1714yes—
556#95C2×Dic1714yes—
557#95C2×Dic1714yes—
558#95C2×Dic1714yes—
559C17#1409011yescharacteristic, complemented, Sylow
560C24C23×D1711yescharacteristic
561C2×Q8—28no—
562C2×Q8—28no—
563C2×Q8—44no—
564C2×Q8—44no—
565C2×Q8—44no—
566C2×Q8—44no—
567C2×Q8—44no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—172no—
605C22×C4—172no—
606C22×C4—172no—
607C22×C4—172no—
608C22×C4—172no—
609C22×C4—172no—
610C22×C4—172no—
611C22×C4—172no—
612C22×C4—341no—
613C22×C4—341no—
614C22×C4—341no—
615C22×C4—341no—
616C22×C4—341no—
617C22×C4—341no—
618C22×C4—341no—
619C22×C4—341no—
620C22×C4—341no—
621C22×C4—341no—
622C22×C4—341no—
623C22×C4—341no—
624C22×C4—341no—
625C22×C4—341no—
626C22×C4—341no—
627C22×C4—341no—
628C22×C4—341no—
629C22×C4—341no—
630C22×C4—341no—
631C22×C4—341no—
632C22×C4—341no—
633C22×C4—341no—
634C22×C4—341no—
635C22×C4—341no—
636C22×C4—341no—
637C22×C4—341no—
638C22×C4—341no—
639C22×C4—341no—
640C22×C4—341no—
641C22×C4—341no—
642C22×C4—341no—
643C22×C4—341no—
644C22×C4—341no—
645C22×C4—341no—
646C22×C4—341no—
647C22×C4—341no—
648C22×C4—341no—
649C22×C4—341no—
650C22×C4—341no—
651C22×C4—341no—
652C22×C4—341no—
653C22×C4—341no—
654C22×C4—341no—
655C22×C4—341no—
656C22×C4—341no—
657C22×C4—341no—
658C22×C4—341no—
659C22×C4—341no—
660C22×C4#6325212yes—
661C22×C4#6325212yes—
662C22×C4D4×D1712yes—
663C22×C4#6325412yes—
664C22×C4Q8×D1712yes—
665C22×C4#6325612yes—
666C22×C4C22×Dic1712yes—
667C22×C4C22×Dic1712yes—
668C22×C4C22×Dic1712yes—
669C22×C4C22×Dic1712yes—
670C22×C4C22×Dic1712yes—
671C22×C4C22×Dic1712yes—
672C22×C4C22×Dic1712yes—
673C4⋊C4—44no—
674C4⋊C4—684no—
675C4⋊C4—684no—
676C42—28no—
677C42—348no—
678C42—348no—
679C42—684no—
680C42—684no—
681C23C2×#6325211yescharacteristic
682C23C2×#6325211yescharacteristic
683C23C2×D4×D1711yescharacteristic
684C23C2×#6325411yescharacteristic
685C23#1058769111yescharacteristic
686C23#1058769111yescharacteristic
687C23C2×Q8×D1711yescharacteristic
688C23C2×#6325611yescharacteristic
689C23#1058769411yescharacteristic
690C23#1058769411yescharacteristic
691C23#41×D1711yescharacteristic
692C23#41×D1711yescharacteristic
693C23#41×D1711yescharacteristic
694C23#41×D1711yescharacteristic
695C23C23×Dic1711yescharacteristic
696Q8—416no—
697C2×C4—22no—
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—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—174no—
744C2×C4—342no—
745C2×C4—342no—
746C2×C4—342no—
747C2×C4—342no—
748C2×C4—342no—
749C2×C4—342no—
750C2×C4—342no—
751C2×C4—342no—
752C2×C4—342no—
753C2×C4—342no—
754C2×C4—342no—
755C2×C4—342no—
756C2×C4—342no—
757C2×C4—342no—
758C2×C4—342no—
759C2×C4—342no—
760C2×C4—342no—
761C2×C4—342no—
762C2×C4—342no—
763C2×C4—342no—
764C2×C4—342no—
765C2×C4—681no—
766C2×C4—681no—
767C2×C4—681no—
768C2×C4—681no—
769C2×C4—681no—
770C2×C4—681no—
771C2×C4—681no—
772C2×C4—681no—
773C2×C4—681no—
774C2×C4—681no—
775C2×C4—681no—
776C2×C4—681no—
777C2×C4—681no—
778C2×C4—681no—
779C2×C4—681no—
780C2×C4—681no—
781C2×C4—681no—
782C2×C4—681no—
783C2×C4—681no—
784C2×C4—681no—
785C2×C4—681no—
786C2×C4—681no—
787C2×C4—681no—
788C2×C4—681no—
789C2×C4—681no—
790C2×C4—681no—
791C2×C4—681no—
792C2×C4—681no—
793C2×C4—681no—
794C2×C4—681no—
795C2×C4—681no—
796C2×C4—681no—
797C2×C4—681no—
798C2×C4—681no—
799C2×C4#1058761214yes—
800C2×C4D4×Dic1714yes—
801C2×C4Q8×Dic1714yes—
802C22C2×#1058761211yescharacteristic
803C22C2×D4×Dic1711yescharacteristic
804C22C2×Q8×Dic1711yescharacteristic
805C22#41×Dic1711yescharacteristic
806C22#41×Dic1711yescharacteristic
807C22#1176328411yescharacteristic
808C22#1176328711yescharacteristic
809C22C22⋊Q8×D1711yescharacteristic
810C22#1176332211yescharacteristic
811C22#1176334511yescharacteristic
812C22#1176334611yescharacteristic
813C22#1176334611yescharacteristic
814C22#1176336111yescharacteristic
815C22#1176336311yescharacteristic
816C22#1176336311yescharacteristic
817C22#1176343311yescharacteristic
818C22#1176343311yescharacteristic
819C22#1176343611yescharacteristic
820C22#1176343611yescharacteristic
821C22#1176344911yescharacteristic
822C22#1176344911yescharacteristic
823C22#1176346111yescharacteristic
824C22#1176346911yescharacteristic
825C22#1176348511yescharacteristic
826C22#1176348511yescharacteristic
827C22#1176348911yescharacteristic
828C22#1176348911yescharacteristic
829C22#1176349311yescharacteristic
830C22#1176350011yescharacteristic
831C22#1176350011yescharacteristic
832C22#1176352111yescharacteristic
833C22#1176352111yescharacteristic
834C22#1176353011yescharacteristic
835C22#1176353111yescharacteristic
836C22#1176353111yescharacteristic
837C4—24no—
838C4—24no—
839C4—24no—
840C4—42no—
841C4—42no—
842C4—42no—
843C4—42no—
844C4—344no—
845C4—682no—
846C4—682no—
847C4—682no—
848C4—682no—
849C4—682no—
850C4—1361no—
851C4—1361no—
852C2#1453126211yescharacteristic
853C2C22⋊Q8×Dic1711yescharacteristic
854C2#1453153311yescharacteristic
855C2#1453163311yescharacteristic
856C2#1453174911yescharacteristic
857C2#1453181511yescharacteristic
858C2#1453189611yescharacteristic
859C2#1453245711yescharacteristic
860C2#1453247211yescharacteristic
861C2#1453294711yescharacteristic
862C2#1453299211yescharacteristic
863C2#1453357811yescharacteristic
864C2#1453365311yescharacteristic
865C2#1453442911yescharacteristic
866C2#1453448911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC2×C17×#391C2
socle, prime radical, cosocleC24×C17C24
hypercenterC2×#391D17
hypocenterC17#14090
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
49. C17×#391C4semidirect
99. C2×C4×Dic17Q8semidirect
444. #391Dic17semidirect
559. C17#14090semidirect

Maximal subgroups

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

subgroupindex
C2×#117627162
C2×#117626552
#145270552
#145270462
#145270412
#145270372
#145270182
#145270162
#145270112
#145270092
#95×Dic172
C2×C17×#3912
#1409017