Finite Group Databasebeta

← C2×C4×#10587477 #17031971

Subgroups — C2×C4×#10587477 #17031971

Order 4352.

2242 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D17C211yesmaximal, characteristic
2C22×#10587477C212yesmaximal
3C2×C4×C22⋊Dic17C211yesmaximal, characteristic, complemented
4C4×#10587477C218yesmaximal, direct product factor
5C2×#11762575C212yesmaximal, complemented
6C2×C4×C22⋊C4×C17C211yesmaximal, characteristic, complemented
7C23×C22⋊D17C2211yescharacteristic
8C23×C4×D17C411yescharacteristic, complemented
9C2×C4×C22⋊D17—21no—
10C2×C4×C22⋊D17—21no—
11C2×C4×C22⋊D17—22no—
12C2×C4×C22⋊D17—21no—
13C2×C4×C22⋊D17—21no—
14C2×C4×C22⋊D17—22no—
15C2×C4×C22⋊D17C414yescomplemented
16C2×C4×C22⋊D17C2214yes—
17C22×#63225C411yescharacteristic, complemented
18C22×C22⋊Dic17C2212yes—
19C22×C22⋊Dic17C2211yescharacteristic
20C22×#63227C411yescharacteristic, complemented
21C22×C4×Dic17—21no—
22C22×C4×Dic17C411yescharacteristic, complemented
23C2×#10587477C4116yesdirect product factor
24C2×#10587477C2218yes—
25C4×C22⋊Dic17—22no—
26C4×C22⋊Dic17C2214yescomplemented
27C2×#10587502—21no—
28#11762575C2218yescomplemented
29C24×C4×C17C2211yescharacteristic
30C22×C22⋊C4×C17C2212yes—
31C22×C42×C17—21no—
32C4×C22⋊C4×C17—22no—
33C4×C22⋊C4×C17C2214yescomplemented
34C2×C17×#95—21no—
35C25×C17C2311yescharacteristic
36C24×D17C2×C411yescharacteristic
37C23×C4×C17—22no—
38C23×C4×C17—44no—
39C23×C4×C17C2×C411yescharacteristic
40C23×C4×C17C2×C411yescharacteristic
41C23×C4×C17C2×C412yes—
42C23×C4×C17D411yescharacteristic
43C23×C4×C17D411yescharacteristic
44C23×C4×C17D411yescharacteristic
45C23×C4×C17D412yes—
46C23×C4×C17D411yescharacteristic
47C23×C4×C17D412yes—
48C23×C4×C17C2312yes—
49C22×C22⋊D17—21no—
50C22×C22⋊D17—21no—
51C22×C22⋊D17—21no—
52C22×C22⋊D17—21no—
53C22×C22⋊D17—24no—
54C22×C22⋊D17C2×C418yes—
55C22×C22⋊D17C2×C412yes—
56C22×C22⋊D17C2312yes—
57C23×Dic17—22no—
58C23×Dic17C2×C411yescharacteristic
59C23×Dic17C2×C411yescharacteristic
60C23×Dic17C2×C411yescharacteristic
61C22×C4×D17—21no—
62C22×C4×D17—22no—
63C22×C4×D17—21no—
64C22×C4×D17—44no—
65C22×C4×D17C2×C414yescomplemented
66C2×C22⋊C4×C17—22no—
67C2×C22⋊C4×C17—24no—
68C2×C22⋊C4×C17C2×C418yescomplemented
69C2×C22⋊C4×C17C2314yes—
70C2×C42×C17—24no—
71C2×C42×C17—44no—
72C2×C22⋊Dic17—21no—
73C2×C22⋊Dic17—21no—
74C2×C22⋊Dic17—21no—
75C2×C22⋊Dic17—21no—
76C2×C22⋊Dic17—22no—
77C2×C22⋊Dic17—24no—
78C2×C22⋊Dic17C2×C412yes—
79C2×C22⋊Dic17C2×C418yescomplemented
80C2×C22⋊Dic17C2312yes—
81C2×C22⋊Dic17C2314yes—
82C4×C22⋊D17—24no—
83C4×C22⋊D17—24no—
84C4×C22⋊D17—24no—
85C4×C22⋊D17—24no—
86C4×C22⋊D17—24no—
87C4×C22⋊D17—24no—
88C4×C22⋊D17—24no—
89C4×C22⋊D17—24no—
90C2×#63227—21no—
91C2×#63227—21no—
92C2×#63227—22no—
93C2×#63227C2×C414yescomplemented
94C2×#63225—21no—
95C2×#63225—21no—
96C2×#63225—22no—
97C2×#63225C2×C414yescomplemented
98C2×C4×Dic17—22no—
99C2×C4×Dic17—21no—
100C2×C4×Dic17—21no—
101C2×C4×Dic17—24no—
102C2×C4×Dic17—44no—
103C2×C4×Dic17C2×C414yescomplemented
104C17×#95—24no—
105#10587502—24no—
106#10587477C2×C4132yesdirect product factor
107C24×C17—42no—
108C24×C17—42no—
109C24×C17C22×C411yescharacteristic
110C24×C17C22×C411yescharacteristic
111C24×C17C22×C414yes—
112C24×C17C2×D411yescharacteristic
113C24×C17C2×D411yescharacteristic
114C24×C17C2×D411yescharacteristic
115C24×C17C2×D411yescharacteristic
116C24×C17#4114yes—
117C24×C17C2411yescharacteristic
118C23×D17—21no—
119C23×D17—21no—
120C23×D17—22no—
121C23×D17—42no—
122C23×D17—42no—
123C23×D17C4214yescomplemented
124C23×D17C22×C412yes—
125C22×C4×C17—24no—
126C22×C4×C17—24no—
127C22×C4×C17—24no—
128C22×C4×C17—28no—
129C22×C4×C17—24no—
130C22×C4×C17—44no—
131C22×C4×C17—44no—
132C22×C4×C17—44no—
133C22×C4×C17—44no—
134C22×C4×C17—42no—
135C22×C4×C17—42no—
136C22×C4×C17—42no—
137C22×C4×C17—44no—
138C22×C4×C17—44no—
139C22×C4×C17C22⋊C411yescharacteristic
140C22×C4×C17C22⋊C412yes—
141C22×C4×C17C22⋊C411yescharacteristic
142C22×C4×C17C22⋊C411yescharacteristic
143C22×C4×C17C22⋊C412yes—
144C22×C4×C17C22⋊C412yes—
145C22×C4×C17C22⋊C412yes—
146C22×C4×C17C22⋊C412yes—
147C22×C4×C17C22⋊C412yes—
148C22×C4×C17C22⋊C411yescharacteristic
149C22×C4×C17C22×C412yes—
150C22×C4×C17C22×C412yes—
151C22×C4×C17C2×D412yes—
152C22×C4×C17C2×D412yes—
153C22×C4×C17C2×D412yes—
154C22×C4×C17C2×D412yes—
155C2×C22⋊D17—22no—
156C2×C22⋊D17—22no—
157C2×C22⋊D17—24no—
158C2×C22⋊D17—28no—
159C2×C22⋊D17—28no—
160C2×C22⋊D17—28no—
161C2×C22⋊D17—28no—
162C2×C22⋊D17—22no—
163C2×C22⋊D17—22no—
164C2×C22⋊D17—24no—
165C2×C22⋊D17C4218yescomplemented
166C2×C22⋊D17C22×C418yes—
167C22×Dic17—21no—
168C22×Dic17—21no—
169C22×Dic17—22no—
170C22×Dic17—21no—
171C22×Dic17—21no—
172C22×Dic17—21no—
173C22×Dic17—21no—
174C22×Dic17—28no—
175C22×Dic17—24no—
176C22×Dic17—44no—
177C22×Dic17—44no—
178C22×Dic17—42no—
179C22×Dic17—42no—
180C22×Dic17C4214yescomplemented
181C22×Dic17C22×C412yes—
182C22×Dic17C22×C412yes—
183C22×Dic17C22×C412yes—
184C2×C4×D17—24no—
185C2×C4×D17—24no—
186C2×C4×D17—44no—
187C2×C4×D17—48no—
188C2×C4×D17—44no—
189C2×C4×D17—48no—
190C22⋊C4×C17—28no—
191C22⋊C4×C17—24no—
192C22⋊C4×C17C22×C418yescomplemented
193C42×C17—48no—
194C22⋊Dic17—22no—
195C22⋊Dic17—22no—
196C22⋊Dic17—28no—
197C22⋊Dic17—22no—
198C22⋊Dic17—22no—
199C22⋊Dic17—24no—
200C22⋊Dic17C22×C418yescomplemented
201#63227—24no—
202#63227—24no—
203#63225—24no—
204#63225—24no—
205C4×Dic17—24no—
206C4×Dic17—24no—
207C4×Dic17—48no—
208C2×C4×#99—171nomaximal, Sylow
209C23×C17—22no—
210C23×C17—22no—
211C23×C17—22no—
212C23×C17—22no—
213C23×C17—22no—
214C23×C17—22no—
215C23×C17—41no—
216C23×C17—41no—
217C23×C17—41no—
218C23×C17—41no—
219C23×C17—41no—
220C23×C17—48no—
221C23×C17—41no—
222C23×C17—41no—
223C23×C17—48no—
224C23×C17—41no—
225C23×C17C2×C4212yes—
226C23×C17C2×C4212yes—
227C23×C17C2×C22⋊C411yescharacteristic
228C23×C17C2×C22⋊C411yescharacteristic
229C23×C17C2×C22⋊C411yescharacteristic
230C23×C17C2×C22⋊C411yescharacteristic
231C23×C17#11712yes—
232C23×C17#11712yes—
233C23×C17C4×D414yes—
234C23×C17C4×D414yes—
235C23×C17C4×D414yes—
236C23×C17C4×D414yes—
237C23×C17C23×C411yescharacteristic
238C23×C17C23×C412yes—
239C23×C17C22×D411yescharacteristic
240C23×C17C22×D411yescharacteristic
241C23×C17C2×#4112yes—
242C22×D17—22no—
243C22×D17—22no—
244C22×D17—24no—
245C22×D17—24no—
246C22×D17—42no—
247C22×D17—42no—
248C22×D17—48no—
249C22×D17—42no—
250C22×D17—42no—
251C22×D17—42no—
252C22×D17—48no—
253C22×D17—42no—
254C22×D17C2×C4214yescomplemented
255C2×C4×C17—22no—
256C2×C4×C17—22no—
257C2×C4×C17—22no—
258C2×C4×C17—24no—
259C2×C4×C17—24no—
260C2×C4×C17—24no—
261C2×C4×C17—24no—
262C2×C4×C17—24no—
263C2×C4×C17—24no—
264C2×C4×C17—28no—
265C2×C4×C17—42no—
266C2×C4×C17—42no—
267C2×C4×C17—42no—
268C2×C4×C17—42no—
269C2×C4×C17—42no—
270C2×C4×C17—42no—
271C2×C4×C17—44no—
272C2×C4×C17—44no—
273C2×C4×C17—416no—
274C2×C4×C17#9914yescomplemented
275C2×C4×C17C2×C22⋊C412yes—
276C2×C4×C17C2×C22⋊C412yes—
277C2×C4×C17C2×C22⋊C412yes—
278C2×C4×C17C2×C22⋊C412yes—
279C22⋊D17—28no—
280C22⋊D17—28no—
281C22⋊D17—28no—
282C22⋊D17—28no—
283C2×Dic17—22no—
284C2×Dic17—22no—
285C2×Dic17—24no—
286C2×Dic17—24no—
287C2×Dic17—22no—
288C2×Dic17—22no—
289C2×Dic17—28no—
290C2×Dic17—42no—
291C2×Dic17—44no—
292C2×Dic17—416no—
293C2×Dic17—42no—
294C2×Dic17—44no—
295C2×Dic17—42no—
296C2×Dic17—42no—
297C2×Dic17—42no—
298C2×Dic17—42no—
299C2×Dic17C2×C4214yescomplemented
300C4×D17—48no—
301C4×D17—48no—
302C22×C4×D4—171no—
303C22×#99—172no—
304C2×C4×C22⋊C4—171no—
305C2×C4×C22⋊C4D1711yescharacteristic, complemented
306C4×#99—178no—
307C2×#342—172no—
308C22×C17—21no—
309C22×C17—21no—
310C22×C17—21no—
311C22×C17—21no—
312C22×C17—21no—
313C22×C17—21no—
314C22×C17—21no—
315C22×C17—21no—
316C22×C17—21no—
317C22×C17—21no—
318C22×C17—21no—
319C22×C17—21no—
320C22×C17—28no—
321C22×C17—28no—
322C22×C17—24no—
323C22×C17—24no—
324C22×C17—42no—
325C22×C17—42no—
326C22×C17—44no—
327C22×C17—44no—
328C22×C17—42no—
329C22×C17—42no—
330C22×C17C4×C22⋊C412yes—
331C22×C17C4×C22⋊C412yes—
332C22×C17C4×C22⋊C412yes—
333C22×C17C4×C22⋊C412yes—
334C22×C17C2×#9912yes—
335C22×C17#41012yes—
336C22×C17C22×C4211yescharacteristic
337C22×C17C22×C22⋊C411yescharacteristic
338C22×C17C2×#11711yescharacteristic
339C22×C17C2×C4×D412yes—
340C22×C17C2×C4×D412yes—
341C2×D17—24no—
342C2×D17—44no—
343C2×D17—48no—
344C2×D17—42no—
345C2×D17—42no—
346C2×D17—48no—
347C2×D17—44no—
348C4×C17—22no—
349C4×C17—22no—
350C4×C17—22no—
351C4×C17—48no—
352C4×C17C2×#9914yescomplemented
353Dic17—24no—
354Dic17—48no—
355Dic17—42no—
356Dic17—42no—
357C23×D4—171no—
358C24×C4—171no—
359C24×C4C2×D1711yescharacteristic
360C2×C4×D4—174no—
361C2×C4×D4—174no—
362C2×C4×D4—341no—
363C2×C4×D4—342no—
364C2×C4×D4—341no—
365C2×C4×D4—341no—
366C2×C4×D4—342no—
367C2×C4×D4—341no—
368C22×C4⋊C4—171no—
369C22×C22⋊C4—172no—
370C22×C22⋊C4—171no—
371C22×C22⋊C4—171no—
372C22×C22⋊C4C2×D1712yes—
373C22×C42—21no—
374C22×C42—171no—
375C22×C42—341no—
376C2×#99—1716no—
377C2×#99—178no—
378C4×C22⋊C4—22no—
379C4×C22⋊C4—174no—
380C4×C22⋊C4—342no—
381C4×C22⋊C4C2×D1714yescomplemented
382C2×#95—21no—
383C2×#95—341no—
384#342—178no—
385C2×C17—22no—
386C2×C17—22no—
387C2×C17—21no—
388C2×C17—22no—
389C2×C17—21no—
390C2×C17—22no—
391C2×C17—22no—
392C2×C17C4×#9914yescomplemented
393C2×C17C2×C4×C22⋊C411yescharacteristic
394C2×C17C22×#9911yescharacteristic
395C2×C17C2×#41011yescharacteristic
396D17—44no—
397C25—171no—
398C25C22×D1711yescharacteristic
399C22×D4—172no—
400C22×D4—178no—
401C22×D4—172no—
402C22×D4—341no—
403C22×D4—341no—
404C22×D4—344no—
405C22×D4—341no—
406C22×D4—341no—
407C23×C4—22no—
408C23×C4—44no—
409C23×C4—171no—
410C23×C4—171no—
411C23×C4—171no—
412C23×C4—174no—
413C23×C4—342no—
414C23×C4—342no—
415C23×C4—341no—
416C23×C4—341no—
417C23×C4—684no—
418C23×C4C4×D1711yescharacteristic
419C23×C4C4×D1711yescharacteristic
420C23×C4C4×D1712yes—
421C23×C4D6811yescharacteristic
422C23×C4D6811yescharacteristic
423C23×C4D6812yes—
424C23×C4C22⋊D1711yescharacteristic
425C23×C4C22⋊D1711yescharacteristic
426C23×C4C22⋊D1712yes—
427C23×C4C22×D1712yes—
428C4×D4—344no—
429C4×D4—344no—
430C4×D4—344no—
431C4×D4—344no—
432C4×D4—344no—
433C4×D4—344no—
434C4×D4—344no—
435C4×D4—344no—
436C2×C4⋊C4—174no—
437C2×C4⋊C4—341no—
438C2×C4⋊C4—341no—
439C2×C4⋊C4—342no—
440C2×C22⋊C4—24no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4—178no—
443C2×C22⋊C4—174no—
444C2×C22⋊C4—172no—
445C2×C22⋊C4—172no—
446C2×C22⋊C4—174no—
447C2×C22⋊C4—341no—
448C2×C22⋊C4—341no—
449C2×C22⋊C4—342no—
450C2×C22⋊C4—344no—
451C2×C22⋊C4—341no—
452C2×C22⋊C4—341no—
453C2×C22⋊C4—341no—
454C2×C22⋊C4—341no—
455C2×C22⋊C4—342no—
456C2×C22⋊C4C4×D1718yescomplemented
457C2×C22⋊C4C22×D1714yes—
458C2×C42—24no—
459C2×C42—44no—
460C2×C42—174no—
461C2×C42—341no—
462C2×C42—342no—
463C2×C42—341no—
464C2×C42—344no—
465C2×C42—684no—
466#99—1732no—
467#95—24no—
468#95—344no—
469C17C2×C4×#9911yescharacteristic, complemented, Sylow
470C24—42no—
471C24—42no—
472C24—172no—
473C24—174no—
474C24—342no—
475C24—341no—
476C24—341no—
477C24—682no—
478C24—682no—
479C24C2×C4×D1711yescharacteristic
480C24C2×C4×D1711yescharacteristic
481C24C2×C4×D1714yes—
482C24C2×D6811yescharacteristic
483C24C2×D6811yescharacteristic
484C24#6325214yes—
485C24C2×C22⋊D1711yescharacteristic
486C24C2×C22⋊D1711yescharacteristic
487C24C23×D1711yescharacteristic
488C2×D4—178no—
489C2×D4—178no—
490C2×D4—342no—
491C2×D4—344no—
492C2×D4—342no—
493C2×D4—344no—
494C2×D4—348no—
495C2×D4—348no—
496C2×D4—342no—
497C2×D4—342no—
498C2×D4—348no—
499C2×D4—348no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—28no—
505C22×C4—44no—
506C22×C4—44no—
507C22×C4—44no—
508C22×C4—44no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—44no—
513C22×C4—44no—
514C22×C4—172no—
515C22×C4—174no—
516C22×C4—172no—
517C22×C4—172no—
518C22×C4—342no—
519C22×C4—341no—
520C22×C4—341no—
521C22×C4—344no—
522C22×C4—348no—
523C22×C4—341no—
524C22×C4—341no—
525C22×C4—341no—
526C22×C4—341no—
527C22×C4—344no—
528C22×C4—344no—
529C22×C4—684no—
530C22×C4—688no—
531C22×C4—688no—
532C22×C4—684no—
533C22×C4—684no—
534C22×C4—684no—
535C22×C4—682no—
536C22×C4—682no—
537C22×C4#6322711yescharacteristic
538C22×C4#6322712yes—
539C22×C4#6322711yescharacteristic
540C22×C4#6322711yescharacteristic
541C22×C4#6322712yes—
542C22×C4#6322712yes—
543C22×C4#6322712yes—
544C22×C4#6322712yes—
545C22×C4#6322712yes—
546C22×C4#6322711yescharacteristic
547C22×C4C2×C4×D1712yes—
548C22×C4C2×C4×D1712yes—
549C22×C4C2×D6812yes—
550C22×C4C2×D6812yes—
551C22×C4C2×C22⋊D1712yes—
552C22×C4C2×C22⋊D1712yes—
553C4⋊C4—344no—
554C4⋊C4—344no—
555C22⋊C4—24no—
556C22⋊C4—28no—
557C22⋊C4—178no—
558C22⋊C4—342no—
559C22⋊C4—344no—
560C22⋊C4—342no—
561C22⋊C4—348no—
562C22⋊C4—342no—
563C22⋊C4—342no—
564C22⋊C4—344no—
565C22⋊C4—344no—
566C22⋊C4C2×C4×D1718yescomplemented
567C42—48no—
568C42—344no—
569C42—344no—
570C42—688no—
571C23—22no—
572C23—22no—
573C23—22no—
574C23—22no—
575C23—22no—
576C23—22no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—48no—
583C23—41no—
584C23—48no—
585C23—41no—
586C23—41no—
587C23—174no—
588C23—342no—
589C23—342no—
590C23—344no—
591C23—344no—
592C23—682no—
593C23—682no—
594C23—688no—
595C23—682no—
596C23—682no—
597C23—688no—
598C23—682no—
599C23—682no—
600C23C42×D1712yes—
601C23C42×D1712yes—
602C23#1058755812yes—
603C23#1058755812yes—
604C23C4×D6814yes—
605C23C4×D6814yes—
606C23C2×#6322711yescharacteristic
607C23C2×#6322711yescharacteristic
608C23C2×#6322711yescharacteristic
609C23C2×#6322711yescharacteristic
610C23C4×C22⋊D1714yes—
611C23C4×C22⋊D1714yes—
612C23C22×C4×D1711yescharacteristic
613C23C22×C4×D1712yes—
614C23C22×D6811yescharacteristic
615C23C2×#6325212yes—
616C23C22×C22⋊D1711yescharacteristic
617D4—348no—
618D4—348no—
619D4—348no—
620D4—348no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—24no—
625C2×C4—24no—
626C2×C4—24no—
627C2×C4—24no—
628C2×C4—24no—
629C2×C4—24no—
630C2×C4—28no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—44no—
638C2×C4—44no—
639C2×C4—416no—
640C2×C4—174no—
641C2×C4—342no—
642C2×C4—342no—
643C2×C4—344no—
644C2×C4—344no—
645C2×C4—342no—
646C2×C4—342no—
647C2×C4—348no—
648C2×C4—688no—
649C2×C4—684no—
650C2×C4—682no—
651C2×C4—684no—
652C2×C4—6816no—
653C2×C4—682no—
654C2×C4—682no—
655C2×C4—682no—
656C2×C4—688no—
657C2×C4—682no—
658C2×C4—682no—
659C2×C4#1058747714yesdirect product factor
660C2×C4C2×#6322712yes—
661C2×C4C2×#6322712yes—
662C2×C4C2×#6322712yes—
663C2×C4C2×#6322712yes—
664C22—21no—
665C22—21no—
666C22—21no—
667C22—21no—
668C22—21no—
669C22—21no—
670C22—21no—
671C22—21no—
672C22—21no—
673C22—21no—
674C22—21no—
675C22—21no—
676C22—28no—
677C22—28no—
678C22—24no—
679C22—24no—
680C22—42no—
681C22—42no—
682C22—42no—
683C22—42no—
684C22—44no—
685C22—44no—
686C22—344no—
687C22—684no—
688C22—684no—
689C22—688no—
690C22—682no—
691C22—682no—
692C22—688no—
693C22C4×#6322712yes—
694C22C4×#6322712yes—
695C22C4×#6322712yes—
696C22C4×#6322712yes—
697C22C2×#1058747712yes—
698C22#1176278212yes—
699C22C2×C42×D1711yescharacteristic
700C22C22×#6322711yescharacteristic
701C22C2×#1058755811yescharacteristic
702C22C2×C4×C22⋊D1712yes—
703C22C2×C4×D6812yes—
704C4—22no—
705C4—22no—
706C4—22no—
707C4—48no—
708C4—344no—
709C4—688no—
710C4—682no—
711C4—682no—
712C4C2×#1058747714yesdirect product factor
713C2—22no—
714C2—22no—
715C2—21no—
716C2—21no—
717C2—22no—
718C2—22no—
719C2—22no—
720C2—684no—
721C2C4×#1058747714yesdirect product factor
722C2C2×C4×#6322711yescharacteristic
723C2C22×#1058747711yescharacteristic
724C2C2×#1176278211yescharacteristic
subgroupG/H
centerC22×C4#63227
commutatorC22×C17C22×C42
FrattiniC24C23×D17
FittingC2×C4×C22⋊C4×C17C2
socleC23×C17C2×C22⋊C4
prime radicalC23×C22⋊D17C22
cosocleC24×C17C24
hypercenterC2×C4×C22⋊C4D17
hypocenterC17C2×C4×#99
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×C4×C22⋊Dic17C2semidirect
4. C4×#10587477C2direct (N × H)
5. C2×#11762575C2semidirect
6. C2×C4×C22⋊C4×C17C2semidirect
8. C23×C4×D17C4semidirect
15. C2×C4×C22⋊D17C4semidirect
17. C22×#63225C4semidirect
20. C22×#63227C4semidirect
22. C22×C4×Dic17C4semidirect
23. C2×#10587477C4direct (N × H)
26. C4×C22⋊Dic17C22semidirect
28. #11762575C22semidirect
33. C4×C22⋊C4×C17C22semidirect
65. C22×C4×D17C2×C4semidirect
68. C2×C22⋊C4×C17C2×C4semidirect
79. C2×C22⋊Dic17C2×C4semidirect
93. C2×#63227C2×C4semidirect
97. C2×#63225C2×C4semidirect
103. C2×C4×Dic17C2×C4semidirect
106. #10587477C2×C4direct (N × H)
123. C23×D17C42semidirect
165. C2×C22⋊D17C42semidirect
180. C22×Dic17C42semidirect
192. C22⋊C4×C17C22×C4semidirect
200. C22⋊Dic17C22×C4semidirect
254. C22×D17C2×C42semidirect
274. C2×C4×C17#99semidirect
299. C2×Dic17C2×C42semidirect
305. C2×C4×C22⋊C4D17semidirect
352. C4×C17C2×#99semidirect
381. C4×C22⋊C4C2×D17semidirect
392. C2×C17C4×#99semidirect
456. C2×C22⋊C4C4×D17semidirect
469. C17C2×C4×#99semidirect
566. C22⋊C4C2×C4×D17semidirect
659. C2×C4#10587477direct (N × H)
712. C4C2×#10587477direct (N × H)
721. C2C4×#10587477direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D172
C22×#105874772
C2×C4×C22⋊Dic172
C4×#105874772
C2×#117625752
C2×C4×C22⋊C4×C172
C2×C4×#9917