Finite Group Databasebeta

← #17034254

Subgroups — #17034254

Order 4352.

1866 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D17C211yesmaximal, characteristic
2#14531167C211yesmaximal, characteristic, complemented
3#14528856C212yesmaximal, complemented
4#14528769C214yesmaximal, complemented
5#14528698C212yesmaximal
6C4×#10587477C214yesmaximal, complemented
7C17×#2280C211yesmaximal, characteristic, complemented
8C23×C22⋊D17C2211yescharacteristic
9C23×C4×D17C411yescharacteristic, complemented
10C2×C4×C22⋊D17—21no—
11C2×C4×C22⋊D17—21no—
12C2×C4×C22⋊D17—21no—
13C2×C4×C22⋊D17—21no—
14C2×C4×C22⋊D17—21no—
15C2×C4×C22⋊D17—21no—
16C2×C4×C22⋊D17—21no—
17C2×C4×C22⋊D17—21no—
18C2×C4×C22⋊D17C412yescomplemented
19C2×C4×C22⋊D17C412yescomplemented
20C2×C4×C22⋊D17C2212yes—
21C2×C4×C22⋊D17C2212yes—
22C2×#10587612—21no—
23C22×#63225C411yescharacteristic, complemented
24C22×C22⋊Dic17C2211yescharacteristic
25C22×#63227C411yescharacteristic, complemented
26C22×C4×Dic17C411yescharacteristic, complemented
27C2×#10587477C2218yes—
28#11762672—21no—
29#11762669—21no—
30#11762669C2212yescomplemented
31#11762665C2212yes—
32C4×C22⋊Dic17—21no—
33C4×C22⋊Dic17C2212yescomplemented
34#11762575C2218yescomplemented
35C24×C4×C17C2211yescharacteristic
36C2×C17×#117—21no—
37C17×#381—21no—
38C17×#380—21no—
39C17×#380C2212yescomplemented
40C17×#379C2212yes—
41C4×C22⋊C4×C17—21no—
42C4×C22⋊C4×C17C2212yescomplemented
43C25×C17C2311yescharacteristic
44C24×D17C2×C411yescharacteristic
45C23×C4×C17—44no—
46C23×C4×C17C2×C411yescharacteristic
47C23×C4×C17C2×C411yescharacteristic
48C23×C4×C17C2×C411yescharacteristic
49C23×C4×C17C2×C411yescharacteristic
50C23×C4×C17D411yescharacteristic
51C23×C4×C17D411yescharacteristic
52C23×C4×C17D411yescharacteristic
53C23×C4×C17D411yescharacteristic
54C23×C4×C17D411yescharacteristic
55C23×C4×C17D411yescharacteristic
56C23×C4×C17D411yescharacteristic
57C23×C4×C17D411yescharacteristic
58C23×C4×C17C2311yescharacteristic
59C23×C4×C17C2311yescharacteristic
60C22×C22⋊D17—21no—
61C22×C22⋊D17—21no—
62C22×C22⋊D17—21no—
63C22×C22⋊D17—21no—
64C22×C22⋊D17—28no—
65C22×C22⋊D17C2×C412yes—
66C22×C22⋊D17C2312yes—
67C23×Dic17C2×C411yescharacteristic
68C23×Dic17C2×C411yescharacteristic
69C23×Dic17C2×C411yescharacteristic
70C22×C4×D17—21no—
71C22×C4×D17—21no—
72C22×C4×D17—21no—
73C22×C4×D17—21no—
74C22×C4×D17—44no—
75C22×C4×D17C2×C412yes—
76C22×C4×D17C2×C412yes—
77C17×#117—44no—
78C2×C4⋊C4×C17—22no—
79C2×C22⋊C4×C17—22no—
80C2×C22⋊C4×C17—22no—
81C2×C22⋊C4×C17C2314yes—
82C2×C42×C17—22no—
83C2×C22⋊Dic17—21no—
84C2×C22⋊Dic17—21no—
85C2×C22⋊Dic17—21no—
86C2×C22⋊Dic17—21no—
87C2×C22⋊Dic17—22no—
88C2×C22⋊Dic17—22no—
89C2×C22⋊Dic17C2×C412yes—
90C2×C22⋊Dic17C2314yes—
91C2×C22⋊Dic17C2312yes—
92C4×C22⋊D17—22no—
93C4×C22⋊D17—22no—
94C4×C22⋊D17—22no—
95C4×C22⋊D17—22no—
96C4×C22⋊D17—22no—
97C4×C22⋊D17—22no—
98C4×C22⋊D17—22no—
99C4×C22⋊D17—22no—
100C4×C22⋊D17—22no—
101C4×C22⋊D17—22no—
102C4×C22⋊D17—22no—
103C4×C22⋊D17—22no—
104C4×C22⋊D17—22no—
105C4×C22⋊D17—22no—
106C4×C22⋊D17—22no—
107C4×C22⋊D17—22no—
108C2×#63227—21no—
109C2×#63227—21no—
110C2×#63227—21no—
111C2×#63227—21no—
112C2×#63227C2×C412yes—
113C2×#63227C2×C412yes—
114#10587612—44no—
115C2×C4⋊Dic17—22no—
116C2×#63225—21no—
117C2×#63225—21no—
118C2×#63225—21no—
119C2×#63225—21no—
120C2×#63225C2×C412yes—
121C2×#63225C2×C412yes—
122C2×C4×Dic17—21no—
123C2×C4×Dic17—21no—
124C2×C4×Dic17—21no—
125C2×C4×Dic17—21no—
126C2×C4×Dic17—22no—
127C2×C4×Dic17C2×C412yes—
128C2×C4×Dic17C2×C412yes—
129C17×#95—22no—
130C17×#95—22no—
131#10587502—22no—
132#10587502—22no—
133#10587477—216no—
134C24×C17—24no—
135C24×C17—42no—
136C24×C17—42no—
137C24×C17C22×C411yescharacteristic
138C24×C17C22×C411yescharacteristic
139C24×C17C2×D411yescharacteristic
140C24×C17C2×D411yescharacteristic
141C24×C17C2×D411yescharacteristic
142C24×C17C2×D411yescharacteristic
143C24×C17C2411yescharacteristic
144C23×D17—21no—
145C23×D17—21no—
146C23×D17—24no—
147C23×D17—42no—
148C23×D17—42no—
149C23×D17C22×C412yes—
150C22×C4×C17—24no—
151C22×C4×C17—24no—
152C22×C4×C17—24no—
153C22×C4×C17—24no—
154C22×C4×C17—42no—
155C22×C4×C17—42no—
156C22×C4×C17—42no—
157C22×C4×C17—42no—
158C22×C4×C17—42no—
159C22×C4×C17—42no—
160C22×C4×C17—42no—
161C22×C4×C17—42no—
162C22×C4×C17—42no—
163C22×C4×C17—42no—
164C22×C4×C17—42no—
165C22×C4×C17C22⋊C411yescharacteristic
166C22×C4×C17C22⋊C411yescharacteristic
167C22×C4×C17C22⋊C411yescharacteristic
168C22×C4×C17C22⋊C411yescharacteristic
169C22×C4×C17C22⋊C411yescharacteristic
170C22×C4×C17C22⋊C411yescharacteristic
171C22×C4×C17C22⋊C411yescharacteristic
172C22×C4×C17C22⋊C411yescharacteristic
173C22×C4×C17C22⋊C411yescharacteristic
174C22×C4×C17C22⋊C411yescharacteristic
175C22×C4×C17C22⋊C411yescharacteristic
176C22×C4×C17C22⋊C411yescharacteristic
177C22×C4×C17C22⋊C411yescharacteristic
178C22×C4×C17C22⋊C411yescharacteristic
179C22×C4×C17C22⋊C411yescharacteristic
180C22×C4×C17C22⋊C411yescharacteristic
181C22×C4×C17C22×C411yescharacteristic
182C22×C4×C17C22×C411yescharacteristic
183C22×C4×C17C22×C411yescharacteristic
184C22×C4×C17C22×C411yescharacteristic
185C22×C4×C17C2×D411yescharacteristic
186C22×C4×C17C2×D411yescharacteristic
187C22×C4×C17C2×D411yescharacteristic
188C22×C4×C17C2×D411yescharacteristic
189C22×C4×C17C2×D411yescharacteristic
190C22×C4×C17C2×D411yescharacteristic
191C22×C4×C17C2×D411yescharacteristic
192C22×C4×C17C2×D411yescharacteristic
193C2×C22⋊D17—28no—
194C2×C22⋊D17—28no—
195C2×C22⋊D17—28no—
196C2×C22⋊D17—28no—
197C2×C22⋊D17—22no—
198C2×C22⋊D17—22no—
199C2×C22⋊D17—22no—
200C2×C22⋊D17—22no—
201C2×C22⋊D17—24no—
202C2×C22⋊D17—24no—
203C2×C22⋊D17—24no—
204C2×C22⋊D17#4118yes—
205C22×Dic17—21no—
206C22×Dic17—21no—
207C22×Dic17—24no—
208C22×Dic17—21no—
209C22×Dic17—21no—
210C22×Dic17—21no—
211C22×Dic17—21no—
212C22×Dic17—24no—
213C22×Dic17—42no—
214C22×Dic17—42no—
215C22×Dic17C22×C412yes—
216C22×Dic17C22×C412yes—
217C22×Dic17C22×C412yes—
218C2×C4×D17—22no—
219C2×C4×D17—22no—
220C2×C4×D17—22no—
221C2×C4×D17—22no—
222C2×C4×D17—44no—
223C2×C4×D17—44no—
224C2×C4×D17—44no—
225C2×C4×D17—44no—
226C2×C4×D17—44no—
227C2×C4×D17—44no—
228C4⋊C4×C17—44no—
229C22⋊C4×C17—28no—
230C22⋊C4×C17—44no—
231C22⋊C4×C17—44no—
232C42×C17—44no—
233C22⋊Dic17—22no—
234C22⋊Dic17—22no—
235C22⋊Dic17—22no—
236C22⋊Dic17—22no—
237C22⋊Dic17—28no—
238C22⋊Dic17—44no—
239C22⋊Dic17—44no—
240#63227—22no—
241#63227—22no—
242#63227—22no—
243#63227—22no—
244C4⋊Dic17—44no—
245#63225—22no—
246#63225—22no—
247#63225—22no—
248#63225—22no—
249C4×Dic17—22no—
250C4×Dic17—22no—
251C4×Dic17—22no—
252C4×Dic17—22no—
253C4×Dic17—44no—
254#20722—171nomaximal, Sylow
255C23×C17—22no—
256C23×C17—22no—
257C23×C17—22no—
258C23×C17—22no—
259C23×C17—22no—
260C23×C17—22no—
261C23×C17—22no—
262C23×C17—22no—
263C23×C17—22no—
264C23×C17—22no—
265C23×C17—22no—
266C23×C17—22no—
267C23×C17—41no—
268C23×C17—41no—
269C23×C17—41no—
270C23×C17—41no—
271C23×C17—41no—
272C23×C17—41no—
273C23×C17—41no—
274C23×C17—41no—
275C23×C17—416no—
276C23×C17C2×C22⋊C411yescharacteristic
277C23×C17C2×C22⋊C411yescharacteristic
278C23×C17C2×C22⋊C411yescharacteristic
279C23×C17C2×C22⋊C411yescharacteristic
280C23×C17C23×C411yescharacteristic
281C23×C17C22×D411yescharacteristic
282C23×C17C22×D411yescharacteristic
283C23×C17C2×#4114yes—
284C22×D17—24no—
285C22×D17—24no—
286C22×D17—22no—
287C22×D17—22no—
288C22×D17—42no—
289C22×D17—416no—
290C22×D17—42no—
291C22×D17—42no—
292C22×D17—42no—
293C22×D17—42no—
294C22×D17—42no—
295C22×D17#11714yescomplemented
296C2×C4×C17—22no—
297C2×C4×C17—22no—
298C2×C4×C17—22no—
299C2×C4×C17—22no—
300C2×C4×C17—22no—
301C2×C4×C17—22no—
302C2×C4×C17—22no—
303C2×C4×C17—22no—
304C2×C4×C17—22no—
305C2×C4×C17—22no—
306C2×C4×C17—22no—
307C2×C4×C17—22no—
308C2×C4×C17—22no—
309C2×C4×C17—22no—
310C2×C4×C17—22no—
311C2×C4×C17—41no—
312C2×C4×C17—41no—
313C2×C4×C17—41no—
314C2×C4×C17—41no—
315C2×C4×C17—41no—
316C2×C4×C17—41no—
317C2×C4×C17—41no—
318C2×C4×C17—41no—
319C2×C4×C17—41no—
320C2×C4×C17—41no—
321C2×C4×C17—41no—
322C2×C4×C17—41no—
323C2×C4×C17—44no—
324C2×C4×C17—44no—
325C2×C4×C17—44no—
326C2×C4×C17#9914yescomplemented
327C2×C4×C17C2×C22⋊C411yescharacteristic
328C2×C4×C17C2×C22⋊C411yescharacteristic
329C2×C4×C17C2×C22⋊C411yescharacteristic
330C2×C4×C17C2×C22⋊C411yescharacteristic
331C2×C4×C17C2×C22⋊C411yescharacteristic
332C2×C4×C17C2×C22⋊C411yescharacteristic
333C2×C4×C17C2×C22⋊C411yescharacteristic
334C2×C4×C17C2×C22⋊C411yescharacteristic
335C22⋊D17—28no—
336C22⋊D17—28no—
337C22⋊D17—28no—
338C22⋊D17—28no—
339C2×Dic17—24no—
340C2×Dic17—24no—
341C2×Dic17—22no—
342C2×Dic17—22no—
343C2×Dic17—22no—
344C2×Dic17—22no—
345C2×Dic17—42no—
346C2×Dic17—42no—
347C2×Dic17—42no—
348C2×Dic17—42no—
349C2×Dic17—42no—
350C2×Dic17—42no—
351C2×Dic17—44no—
352C2×Dic17—44no—
353C2×Dic17—44no—
354C2×Dic17#11714yescomplemented
355C4×D17—44no—
356C4×D17—44no—
357C4×D17—44no—
358C4×D17—44no—
359C22×C4×D4—171no—
360#2280—171no—
361#2280D1711yescharacteristic, complemented
362#1819—172no—
363#1799—174no—
364#1781—172no—
365C4×#99—174no—
366C22×C17—28no—
367C22×C17—21no—
368C22×C17—21no—
369C22×C17—21no—
370C22×C17—21no—
371C22×C17—21no—
372C22×C17—21no—
373C22×C17—21no—
374C22×C17—21no—
375C22×C17—21no—
376C22×C17—21no—
377C22×C17—21no—
378C22×C17—21no—
379C22×C17—21no—
380C22×C17—21no—
381C22×C17—21no—
382C22×C17—21no—
383C22×C17—44no—
384C22×C17—44no—
385C22×C17—44no—
386C22×C17—44no—
387C22×C17—44no—
388C22×C17—44no—
389C22×C17C2×#9912yes—
390C22×C17#41012yes—
391C22×C17C22×C22⋊C411yescharacteristic
392C22×C17C2×#11712yes—
393C22×C17#52512yes—
394C22×C17#52512yes—
395C2×D17—24no—
396C2×D17—44no—
397C2×D17—48no—
398C2×D17—48no—
399C2×D17—42no—
400C2×D17—42no—
401C2×D17—44no—
402C4×C17—21no—
403C4×C17—21no—
404C4×C17—21no—
405C4×C17—21no—
406C4×C17—21no—
407C4×C17—21no—
408C4×C17—84no—
409C4×C17C2×#9912yes—
410C4×C17C2×#9912yes—
411Dic17—24no—
412Dic17—42no—
413Dic17—42no—
414Dic17—84no—
415C23×D4—171no—
416C24×C4—171no—
417C24×C4C2×D1711yescharacteristic
418C2×C4×D4—172no—
419C2×C4×D4—172no—
420C2×C4×D4—172no—
421C2×C4×D4—172no—
422C2×C4×D4—341no—
423C2×C4×D4—341no—
424C2×C4×D4—341no—
425C2×C4×D4—341no—
426C2×C4×D4—341no—
427C2×C4×D4—341no—
428C2×C4×D4—341no—
429C2×C4×D4—341no—
430C2×#117—21no—
431C2×#117—341no—
432C22×C4⋊C4—171no—
433C22×C22⋊C4—171no—
434C22×C22⋊C4—171no—
435C22×C42—171no—
436C2×#99—178no—
437#381—21no—
438#381—341no—
439#380—21no—
440#380—172no—
441#380—341no—
442#380C2×D1712yescomplemented
443#379—172no—
444#379C2×D1712yes—
445C4×C22⋊C4—21no—
446C4×C22⋊C4—172no—
447C4×C22⋊C4—341no—
448C4×C22⋊C4C2×D1712yescomplemented
449#342—178no—
450C2×C17—22no—
451C2×C17—22no—
452C2×C17—22no—
453C2×C17—22no—
454C2×C17—22no—
455C2×C17—41no—
456C2×C17—41no—
457C2×C17#228011yescharacteristic
458C2×C17C22×#9911yescharacteristic
459C2×C17C2×#41011yescharacteristic
460D17—44no—
461C25—171no—
462C25C22×D1711yescharacteristic
463C22×D4—172no—
464C22×D4—172no—
465C22×D4—348no—
466C22×D4—341no—
467C22×D4—341no—
468C22×D4—341no—
469C22×D4—341no—
470C23×C4—44no—
471C23×C4—171no—
472C23×C4—171no—
473C23×C4—171no—
474C23×C4—172no—
475C23×C4—172no—
476C23×C4—341no—
477C23×C4—341no—
478C23×C4—341no—
479C23×C4—341no—
480C23×C4—684no—
481C23×C4C4×D1711yescharacteristic
482C23×C4C4×D1711yescharacteristic
483C23×C4C4×D1711yescharacteristic
484C23×C4C4×D1711yescharacteristic
485C23×C4D6811yescharacteristic
486C23×C4D6811yescharacteristic
487C23×C4D6811yescharacteristic
488C23×C4D6811yescharacteristic
489C23×C4C22⋊D1711yescharacteristic
490C23×C4C22⋊D1711yescharacteristic
491C23×C4C22⋊D1711yescharacteristic
492C23×C4C22⋊D1711yescharacteristic
493C23×C4C22×D1711yescharacteristic
494C23×C4C22×D1711yescharacteristic
495C4×D4—342no—
496C4×D4—342no—
497C4×D4—342no—
498C4×D4—342no—
499C4×D4—342no—
500C4×D4—342no—
501C4×D4—342no—
502C4×D4—342no—
503C4×D4—342no—
504C4×D4—342no—
505C4×D4—342no—
506C4×D4—342no—
507C4×D4—342no—
508C4×D4—342no—
509C4×D4—342no—
510C4×D4—342no—
511#117—44no—
512#117—684no—
513C2×C4⋊C4—22no—
514C2×C4⋊C4—172no—
515C2×C4⋊C4—172no—
516C2×C4⋊C4—341no—
517C2×C4⋊C4—341no—
518C2×C4⋊C4—341no—
519C2×C4⋊C4—341no—
520C2×C4⋊C4—342no—
521C2×C22⋊C4—22no—
522C2×C22⋊C4—22no—
523C2×C22⋊C4—172no—
524C2×C22⋊C4—172no—
525C2×C22⋊C4—172no—
526C2×C22⋊C4—172no—
527C2×C22⋊C4—174no—
528C2×C22⋊C4—341no—
529C2×C22⋊C4—341no—
530C2×C22⋊C4—341no—
531C2×C22⋊C4—341no—
532C2×C22⋊C4—341no—
533C2×C22⋊C4—341no—
534C2×C22⋊C4—341no—
535C2×C22⋊C4—341no—
536C2×C22⋊C4—342no—
537C2×C22⋊C4—342no—
538C2×C22⋊C4C22×D1714yes—
539C2×C42—22no—
540C2×C42—172no—
541C2×C42—172no—
542C2×C42—341no—
543C2×C42—341no—
544C2×C42—341no—
545C2×C42—341no—
546C2×C42—342no—
547#99—3416no—
548#95—22no—
549#95—22no—
550#95—342no—
551#95—342no—
552C17#2072211yescharacteristic, complemented, Sylow
553C24—24no—
554C24—42no—
555C24—42no—
556C24—172no—
557C24—344no—
558C24—341no—
559C24—341no—
560C24—682no—
561C24—682no—
562C24C2×C4×D1711yescharacteristic
563C24C2×C4×D1711yescharacteristic
564C24C2×D6811yescharacteristic
565C24C2×D6811yescharacteristic
566C24C2×C22⋊D1711yescharacteristic
567C24C2×C22⋊D1711yescharacteristic
568C24C23×D1711yescharacteristic
569C2×D4—178no—
570C2×D4—344no—
571C2×D4—344no—
572C2×D4—348no—
573C2×D4—348no—
574C2×D4—348no—
575C2×D4—348no—
576C2×D4—342no—
577C2×D4—344no—
578C2×D4—342no—
579C2×D4—342no—
580C2×D4—342no—
581C22×C4—24no—
582C22×C4—24no—
583C22×C4—24no—
584C22×C4—24no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—172no—
597C22×C4—172no—
598C22×C4—172no—
599C22×C4—344no—
600C22×C4—341no—
601C22×C4—341no—
602C22×C4—341no—
603C22×C4—341no—
604C22×C4—341no—
605C22×C4—341no—
606C22×C4—342no—
607C22×C4—342no—
608C22×C4—342no—
609C22×C4—342no—
610C22×C4—344no—
611C22×C4—684no—
612C22×C4—684no—
613C22×C4—684no—
614C22×C4—684no—
615C22×C4—684no—
616C22×C4—684no—
617C22×C4—682no—
618C22×C4—682no—
619C22×C4#6322711yescharacteristic
620C22×C4#6322711yescharacteristic
621C22×C4#6322711yescharacteristic
622C22×C4#6322711yescharacteristic
623C22×C4#6322711yescharacteristic
624C22×C4#6322711yescharacteristic
625C22×C4#6322711yescharacteristic
626C22×C4#6322711yescharacteristic
627C22×C4#6322711yescharacteristic
628C22×C4#6322711yescharacteristic
629C22×C4#6322711yescharacteristic
630C22×C4#6322711yescharacteristic
631C22×C4#6322711yescharacteristic
632C22×C4#6322711yescharacteristic
633C22×C4#6322711yescharacteristic
634C22×C4#6322711yescharacteristic
635C22×C4C2×C4×D1711yescharacteristic
636C22×C4C2×C4×D1711yescharacteristic
637C22×C4C2×C4×D1711yescharacteristic
638C22×C4C2×C4×D1711yescharacteristic
639C22×C4C2×D6811yescharacteristic
640C22×C4C2×D6811yescharacteristic
641C22×C4C2×D6811yescharacteristic
642C22×C4C2×D6811yescharacteristic
643C22×C4C2×C22⋊D1711yescharacteristic
644C22×C4C2×C22⋊D1711yescharacteristic
645C22×C4C2×C22⋊D1711yescharacteristic
646C22×C4C2×C22⋊D1711yescharacteristic
647C4⋊C4—44no—
648C4⋊C4—342no—
649C4⋊C4—342no—
650C4⋊C4—342no—
651C4⋊C4—342no—
652C4⋊C4—684no—
653C22⋊C4—28no—
654C22⋊C4—44no—
655C22⋊C4—44no—
656C22⋊C4—342no—
657C22⋊C4—342no—
658C22⋊C4—342no—
659C22⋊C4—342no—
660C22⋊C4—342no—
661C22⋊C4—342no—
662C22⋊C4—342no—
663C22⋊C4—342no—
664C22⋊C4—348no—
665C22⋊C4—684no—
666C22⋊C4—684no—
667C42—44no—
668C42—342no—
669C42—342no—
670C42—342no—
671C42—342no—
672C42—684no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—416no—
694C23—174no—
695C23—344no—
696C23—344no—
697C23—342no—
698C23—342no—
699C23—682no—
700C23—682no—
701C23—682no—
702C23—6816no—
703C23—682no—
704C23—682no—
705C23—682no—
706C23C2×#6322711yescharacteristic
707C23C2×#6322711yescharacteristic
708C23C2×#6322711yescharacteristic
709C23C2×#6322711yescharacteristic
710C23C22×C4×D1711yescharacteristic
711C23C22×D6811yescharacteristic
712C23#41×D1714yes—
713C23C22×C22⋊D1711yescharacteristic
714D4—348no—
715D4—348no—
716D4—348no—
717D4—348no—
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—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
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—41no—
744C2×C4—41no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—174no—
749C2×C4—344no—
750C2×C4—344no—
751C2×C4—342no—
752C2×C4—342no—
753C2×C4—342no—
754C2×C4—342no—
755C2×C4—684no—
756C2×C4—684no—
757C2×C4—682no—
758C2×C4—682no—
759C2×C4—682no—
760C2×C4—682no—
761C2×C4—684no—
762C2×C4—684no—
763C2×C4—682no—
764C2×C4—682no—
765C2×C4—684no—
766C2×C4—684no—
767C2×C4—684no—
768C2×C4#1058747714yescomplemented
769C2×C4C2×#6322711yescharacteristic
770C2×C4C2×#6322711yescharacteristic
771C2×C4C2×#6322711yescharacteristic
772C2×C4C2×#6322711yescharacteristic
773C2×C4C2×#6322711yescharacteristic
774C2×C4C2×#6322711yescharacteristic
775C2×C4C2×#6322711yescharacteristic
776C2×C4C2×#6322711yescharacteristic
777C22—28no—
778C22—21no—
779C22—21no—
780C22—21no—
781C22—21no—
782C22—21no—
783C22—21no—
784C22—21no—
785C22—21no—
786C22—21no—
787C22—21no—
788C22—21no—
789C22—21no—
790C22—21no—
791C22—21no—
792C22—21no—
793C22—21no—
794C22—44no—
795C22—44no—
796C22—44no—
797C22—44no—
798C22—44no—
799C22—44no—
800C22—344no—
801C22—684no—
802C22—684no—
803C22—688no—
804C22—688no—
805C22—682no—
806C22—682no—
807C22C2×#1058747712yes—
808C22#1176278212yes—
809C22C22×#6322711yescharacteristic
810C22#117×D1712yes—
811C22#1176331612yes—
812C22#1176332112yes—
813C4—21no—
814C4—21no—
815C4—21no—
816C4—21no—
817C4—21no—
818C4—21no—
819C4—84no—
820C4—344no—
821C4—682no—
822C4—682no—
823C4—1364no—
824C4C2×#1058747712yes—
825C4C2×#1058747712yes—
826C2—22no—
827C2—22no—
828C2—22no—
829C2—22no—
830C2—22no—
831C2—41no—
832C2—41no—
833C2—684no—
834C2#1453116311yescharacteristic
835C2C22×#1058747711yescharacteristic
836C2C2×#1176278211yescharacteristic
subgroupG/H
centerC2×C4C2×#63227
commutatorC23×C17C23×C4
FrattiniC24C23×D17
FittingC17×#2280C2
socleC22×C17C22×C22⋊C4
prime radicalC23×C22⋊D17C22
cosocleC24×C17C24
hypercenter#2280D17
hypocenterC17#20722
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ #2280

Complements

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

NH ≅ G/Ntype
2. #14531167C2semidirect
3. #14528856C2semidirect
4. #14528769C2semidirect
6. C4×#10587477C2semidirect
7. C17×#2280C2semidirect
9. C23×C4×D17C4semidirect
18. C2×C4×C22⋊D17C4semidirect
19. C2×C4×C22⋊D17C4semidirect
23. C22×#63225C4semidirect
25. C22×#63227C4semidirect
26. C22×C4×Dic17C4semidirect
30. #11762669C22semidirect
33. C4×C22⋊Dic17C22semidirect
34. #11762575C22semidirect
39. C17×#380C22semidirect
42. C4×C22⋊C4×C17C22semidirect
295. C22×D17#117semidirect
326. C2×C4×C17#99semidirect
354. C2×Dic17#117semidirect
361. #2280D17semidirect
442. #380C2×D17semidirect
448. C4×C22⋊C4C2×D17semidirect
552. C17#20722semidirect
768. C2×C4#10587477semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D172
#145311672
#145288562
#145287692
#145286982
C4×#105874772
C17×#22802
#2072217