Finite Group Databasebeta

← #17050465

Subgroups — #17050465

Order 4352.

1294 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14531633C212yesmaximal, complemented
2#14529770C212yesmaximal, complemented
3#14529243C212yesmaximal, complemented
4#14529238C212yesmaximal
5#14528861C211yesmaximal, characteristic, complemented
6#14528858C211yesmaximal, characteristic, complemented
7#14528772C211yesmaximal, characteristic, complemented
8C4×#10587505C211yesmaximal, characteristic, complemented
9#14528517C211yesmaximal, characteristic, complemented
10C2×#11762576C211yesmaximal, characteristic, complemented
11C2×C17×#551C211yesmaximal, characteristic
12C2×#10587612C2212yes—
13C22×C22⋊Dic17C2212yes—
14C2×#10587505C2212yes—
15C2×#10587505C2212yes—
16#11762702—22no—
17#11762702—22no—
18#11762684—22no—
19#11762672C2212yes—
20#11762669C2212yes—
21#11762665C2212yes—
22C22⋊C4×Dic17—22no—
23C4×C22⋊Dic17C2212yes—
24#11762576C2211yescharacteristic
25#11762576C2211yescharacteristic
26#11762576C2212yes—
27#11762576C2211yescharacteristic
28#11762576C2212yes—
29#11762576C2211yescharacteristic
30#11762576C2212yes—
31#11762576C2212yes—
32C17×#551—22no—
33C17×#551—22no—
34C17×#551—22no—
35C17×#551—22no—
36C2×C17×#126C411yescharacteristic, complemented
37C2×C17×#126C411yescharacteristic, complemented
38C2×C17×#124C411yescharacteristic, complemented
39C2×C17×#123C411yescharacteristic, complemented
40C2×C17×#123C411yescharacteristic, complemented
41C2×C17×#123C2211yescharacteristic
42C2×C17×C22⋊Q8C411yescharacteristic, complemented
43C2×C17×C22⋊Q8C2211yescharacteristic
44C2×C17×#120C2211yescharacteristic
45C2×C4×D4×C17C411yescharacteristic, complemented
46C2×C4×D4×C17C2211yescharacteristic
47C2×C17×#117C411yescharacteristic, complemented
48C2×C17×#117C2211yescharacteristic
49C22×C22⋊C4×C17C2211yescharacteristic
50C22×C22⋊C4×C17C2211yescharacteristic
51C25×C17C2311yescharacteristic
52C22×Q8×C17C2×C411yescharacteristic, complemented
53C22×D4×C17C2×C411yescharacteristic
54C22×D4×C17C2×C411yescharacteristic
55C22×D4×C17C2311yescharacteristic
56C23×C4×C17C2×C411yescharacteristic
57C23×C4×C17C2×C411yescharacteristic
58C23×C4×C17C2×C411yescharacteristic, complemented
59C23×C4×C17C2311yescharacteristic
60C23×C4×C17C2311yescharacteristic
61C23×Dic17—22no—
62C17×#126—22no—
63C17×#126—22no—
64C17×#126—22no—
65C17×#126—22no—
66C17×#124—22no—
67C17×#124—22no—
68C17×#123—22no—
69C17×#123—22no—
70C17×#123—22no—
71C17×#123—22no—
72C17×#123—22no—
73C17×#123—22no—
74C17×C22⋊Q8—22no—
75C17×C22⋊Q8—22no—
76C17×C22⋊Q8—22no—
77C17×C22⋊Q8—22no—
78C17×#120—22no—
79C17×#120—22no—
80C4×D4×C17—22no—
81C4×D4×C17—22no—
82C4×D4×C17—21no—
83C4×D4×C17—21no—
84C4×D4×C17—21no—
85C4×D4×C17—21no—
86C17×#117—22no—
87C17×#117—22no—
88C17×#117—21no—
89C17×#117—21no—
90C17×#117—21no—
91C17×#117—21no—
92C2×C4⋊C4×C17C2×C411yescharacteristic, complemented
93C2×C4⋊C4×C17C2×C411yescharacteristic, complemented
94C2×C4⋊C4×C17C2×C411yescharacteristic, complemented
95C2×C4⋊C4×C17C2×C411yescharacteristic, complemented
96C2×C4⋊C4×C17C2×C411yescharacteristic, complemented
97C2×C4⋊C4×C17C2×C411yescharacteristic, complemented
98C2×C4⋊C4×C17C2×C411yescharacteristic, complemented
99C2×C4⋊C4×C17C2×C411yescharacteristic, complemented
100C2×C22⋊C4×C17—22no—
101C2×C22⋊C4×C17—22no—
102C2×C22⋊C4×C17C2×C411yescharacteristic
103C2×C22⋊C4×C17C2×C411yescharacteristic
104C2×C22⋊C4×C17C2×C411yescharacteristic
105C2×C22⋊C4×C17C2×C411yescharacteristic
106C2×C22⋊C4×C17C2×C411yescharacteristic
107C2×C22⋊C4×C17C2×C411yescharacteristic
108C2×C22⋊C4×C17C2×C411yescharacteristic
109C2×C22⋊C4×C17C2×C411yescharacteristic
110C2×C22⋊C4×C17C2×C411yescharacteristic, complemented
111C2×C22⋊C4×C17C2×C411yescharacteristic, complemented
112C2×C22⋊C4×C17C2×C411yescharacteristic, complemented
113C2×C22⋊C4×C17D412yes—
114C2×C22⋊C4×C17D412yes—
115C2×C22⋊C4×C17D412yes—
116C2×C22⋊C4×C17D412yes—
117C2×C22⋊C4×C17C2311yescharacteristic
118C2×C22⋊C4×C17C2311yescharacteristic
119C2×C22⋊C4×C17C2311yescharacteristic
120C2×C42×C17C2×C411yescharacteristic, complemented
121C2×C42×C17C2×C411yescharacteristic, complemented
122C2×C42×C17C2×C411yescharacteristic, complemented
123C2×C22⋊Dic17—24no—
124C2×C22⋊Dic17—22no—
125C2×C22⋊Dic17—22no—
126C2×C22⋊Dic17—22no—
127C2×C22⋊Dic17—42no—
128C2×C22⋊Dic17C2312yes—
129C2×C22⋊Dic17C2312yes—
130C2×C22⋊Dic17C2312yes—
131C2×C22⋊Dic17C2312yes—
132#10587612—24no—
133#10587612—42no—
134C2×C4⋊Dic17—22no—
135C2×C4⋊Dic17—22no—
136C2×C4×Dic17—22no—
137C2×C4×Dic17—22no—
138#10587505—24no—
139#10587505—42no—
140#10587502—22no—
141#10587502—22no—
142#10587502—22no—
143#10587502—22no—
144C24×C17—22no—
145C24×C17—21no—
146C24×C17—21no—
147C24×C17—42no—
148C24×C17—81no—
149C24×C17C22×C411yescharacteristic
150C24×C17C22×C411yescharacteristic
151C24×C17C22×C411yescharacteristic
152C24×C17C2×D412yes—
153C24×C17C2×D412yes—
154C24×C17C2411yescharacteristic
155C2×Q8×C17—22no—
156C2×Q8×C17—81no—
157C2×D4×C17—21no—
158C2×D4×C17—21no—
159C2×D4×C17—22no—
160C2×D4×C17—22no—
161C2×D4×C17—21no—
162C2×D4×C17—21no—
163C2×D4×C17—22no—
164C2×D4×C17—42no—
165C2×D4×C17—81no—
166C22×C4×C17—22no—
167C22×C4×C17—21no—
168C22×C4×C17—21no—
169C22×C4×C17—21no—
170C22×C4×C17—21no—
171C22×C4×C17—21no—
172C22×C4×C17—21no—
173C22×C4×C17—21no—
174C22×C4×C17—21no—
175C22×C4×C17—42no—
176C22×C4×C17—81no—
177C22×C4×C17—81no—
178C22×C4×C17—81no—
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×C17C22×C411yescharacteristic
186C22×C4×C17C22×C411yescharacteristic
187C22×C4×C17C22×C411yescharacteristic
188C22×C4×C17C22×C411yescharacteristic
189C22×C4×C17C22×C411yescharacteristic
190C22×C4×C17C2×D412yes—
191C22×C4×C17C2×D412yes—
192C22×C4×C17C2×D412yes—
193C22×C4×C17C2×D412yes—
194C22×Dic17—22no—
195C22×Dic17—22no—
196C22×Dic17—22no—
197C22×Dic17—22no—
198C22×Dic17—44no—
199C22×Dic17—44no—
200C22×Dic17—82no—
201C4⋊C4×C17—22no—
202C4⋊C4×C17—22no—
203C4⋊C4×C17—22no—
204C4⋊C4×C17—21no—
205C4⋊C4×C17—21no—
206C4⋊C4×C17—22no—
207C4⋊C4×C17—21no—
208C4⋊C4×C17—21no—
209C4⋊C4×C17—22no—
210C4⋊C4×C17—21no—
211C4⋊C4×C17—21no—
212C22⋊C4×C17—21no—
213C22⋊C4×C17—21no—
214C22⋊C4×C17—22no—
215C22⋊C4×C17—22no—
216C22⋊C4×C17—22no—
217C22⋊C4×C17—22no—
218C22⋊C4×C17—22no—
219C22⋊C4×C17—22no—
220C22⋊C4×C17—22no—
221C22⋊C4×C17—22no—
222C22⋊C4×C17—21no—
223C22⋊C4×C17—21no—
224C22⋊C4×C17C22⋊C412yes—
225C22⋊C4×C17C22⋊C412yes—
226C22⋊C4×C17C22⋊C412yes—
227C22⋊C4×C17C22⋊C412yes—
228C22⋊C4×C17C22⋊C412yes—
229C22⋊C4×C17C22⋊C412yes—
230C22⋊C4×C17C22⋊C411yescharacteristic
231C22⋊C4×C17C22⋊C411yescharacteristic
232C22⋊C4×C17C22⋊C411yescharacteristic
233C22⋊C4×C17C22⋊C411yescharacteristic
234C42×C17—21no—
235C42×C17—21no—
236C42×C17—21no—
237C42×C17—21no—
238C42×C17—21no—
239C42×C17—21no—
240C22⋊Dic17—22no—
241C22⋊Dic17—22no—
242C22⋊Dic17—22no—
243C22⋊Dic17—22no—
244C22⋊Dic17—22no—
245C22⋊Dic17—22no—
246C22⋊Dic17—22no—
247C22⋊Dic17—44no—
248C22⋊Dic17—44no—
249C22⋊Dic17—82no—
250C22⋊Dic17#4114yes—
251C4⋊Dic17—44no—
252C4⋊Dic17—82no—
253C4×Dic17—44no—
254C4×Dic17—82no—
255#22477—171nomaximal, Sylow
256C23×C17—21no—
257C23×C17—21no—
258C23×C17—22no—
259C23×C17—22no—
260C23×C17—24no—
261C23×C17—22no—
262C23×C17—21no—
263C23×C17—21no—
264C23×C17—22no—
265C23×C17—22no—
266C23×C17—21no—
267C23×C17—21no—
268C23×C17—21no—
269C23×C17—42no—
270C23×C17—41no—
271C23×C17—41no—
272C23×C17—41no—
273C23×C17—42no—
274C23×C17—41no—
275C23×C17—41no—
276C23×C17—42no—
277C23×C17—41no—
278C23×C17—41no—
279C23×C17—84no—
280C23×C17—82no—
281C23×C17—82no—
282C23×C17C2×C22⋊C412yes—
283C23×C17C2×C22⋊C411yescharacteristic
284C23×C17C2×C22⋊C411yescharacteristic
285C23×C17C23×C411yescharacteristic
286C23×C17C22×D412yes—
287C23×C17C2×#4112yes—
288C23×C17H(5,𝔽2)11yescharacteristic
289C23×C172−1+411yescharacteristic
290Q8×C17—82no—
291D4×C17—42no—
292D4×C17—42no—
293D4×C17—42no—
294D4×C17—42no—
295D4×C17—82no—
296C2×C4×C17—21no—
297C2×C4×C17—21no—
298C2×C4×C17—21no—
299C2×C4×C17—21no—
300C2×C4×C17—22no—
301C2×C4×C17—22no—
302C2×C4×C17—22no—
303C2×C4×C17—22no—
304C2×C4×C17—21no—
305C2×C4×C17—21no—
306C2×C4×C17—21no—
307C2×C4×C17—21no—
308C2×C4×C17—21no—
309C2×C4×C17—21no—
310C2×C4×C17—21no—
311C2×C4×C17—21no—
312C2×C4×C17—21no—
313C2×C4×C17—41no—
314C2×C4×C17—41no—
315C2×C4×C17—42no—
316C2×C4×C17—42no—
317C2×C4×C17—42no—
318C2×C4×C17—42no—
319C2×C4×C17—41no—
320C2×C4×C17—41no—
321C2×C4×C17—41no—
322C2×C4×C17—41no—
323C2×C4×C17—41no—
324C2×C4×C17—41no—
325C2×C4×C17—81no—
326C2×C4×C17—81no—
327C2×C4×C17—81no—
328C2×C4×C17—81no—
329C2×C4×C17C2×C22⋊C411yescharacteristic
330C2×C4×C17C2×C22⋊C411yescharacteristic
331C2×C4×C17C2×C22⋊C411yescharacteristic
332C2×C4×C17C2×C22⋊C411yescharacteristic
333C2×C4×C17C2×C22⋊C412yes—
334C2×C4×C17C2×C22⋊C412yes—
335C2×Dic17—24no—
336C2×Dic17—42no—
337C2×Dic17—42no—
338C2×Dic17—42no—
339C2×Dic17—42no—
340C2×Dic17—42no—
341C2×Dic17—42no—
342C2×Dic17—42no—
343C2×Dic17—42no—
344C2×Dic17—42no—
345C2×Dic17—42no—
346C2×Dic17—42no—
347C2×Dic17—88no—
348C2×#551D1711yescharacteristic
349#2342—172no—
350#1996—172no—
351#1899—172no—
352#1898—172no—
353#1820—171no—
354#1819—171no—
355#1799—171no—
356C4×#99—171no—
357#1740—171no—
358C2×#342—171no—
359C22×C17—21no—
360C22×C17—22no—
361C22×C17—21no—
362C22×C17—22no—
363C22×C17—21no—
364C22×C17—21no—
365C22×C17—21no—
366C22×C17—22no—
367C22×C17—21no—
368C22×C17—22no—
369C22×C17—21no—
370C22×C17—22no—
371C22×C17—42no—
372C22×C17—41no—
373C22×C17—41no—
374C22×C17—44no—
375C22×C17—44no—
376C22×C17—42no—
377C22×C17—42no—
378C22×C17—41no—
379C22×C17—41no—
380C22×C17—41no—
381C22×C17—82no—
382C22×C17—82no—
383C22×C17—81no—
384C22×C17—81no—
385C22×C17—81no—
386C22×C17—81no—
387C22×C17#41012yes—
388C22×C17C22×C22⋊C411yescharacteristic
389C22×C17C4×#4111yescharacteristic
390C22×C17#52011yescharacteristic
391C22×C17#54612yes—
392C22×C17#54712yes—
393C4×C17—21no—
394C4×C17—22no—
395C4×C17—21no—
396C4×C17—21no—
397C4×C17—21no—
398C4×C17—22no—
399C4×C17—41no—
400C4×C17—41no—
401C4×C17—41no—
402C4×C17—41no—
403C4×C17—41no—
404C4×C17—41no—
405C4×C17—41no—
406Dic17—44no—
407Dic17—82no—
408Dic17—82no—
409Dic17—82no—
410#551—22no—
411#551—22no—
412#551—22no—
413#551—22no—
414C2×#126Dic1711yescharacteristic, complemented
415C2×#126Dic1711yescharacteristic, complemented
416C2×#124Dic1711yescharacteristic, complemented
417C2×#123Dic1711yescharacteristic, complemented
418C2×#123Dic1711yescharacteristic, complemented
419C2×#123C2×D1711yescharacteristic
420C2×C22⋊Q8Dic1711yescharacteristic, complemented
421C2×C22⋊Q8C2×D1711yescharacteristic
422C2×#120C2×D1711yescharacteristic
423C2×C4×D4Dic1711yescharacteristic, complemented
424C2×C4×D4C2×D1711yescharacteristic
425C2×#117—172no—
426C2×#117Dic1711yescharacteristic, complemented
427C2×#117C2×D1711yescharacteristic
428C22×C22⋊C4—172no—
429C22×C22⋊C4C2×D1711yescharacteristic
430C22×C22⋊C4C2×D1711yescharacteristic
431C2×#99—172no—
432C2×#99—172no—
433#388—342no—
434#388—342no—
435#385—342no—
436#381—172no—
437#380—172no—
438#379—172no—
439C4×C22⋊C4—172no—
440C4×C22⋊C4—342no—
441#342—171no—
442#342—171no—
443#342—171no—
444#342—172no—
445#342—172no—
446#342—172no—
447#342—172no—
448#342—171no—
449C2×C17—22no—
450C2×C17—22no—
451C2×C17—22no—
452C2×C17—21no—
453C2×C17—21no—
454C2×C17—41no—
455C2×C17—42no—
456C2×C17—81no—
457C2×C17#233911yescharacteristic
458C2×C17C2×#41011yescharacteristic
459C2×C17#288311yescharacteristic
460C25C22×D1711yescharacteristic
461C22×Q8C2×Dic1711yescharacteristic, complemented
462C22×D4C2×Dic1711yescharacteristic
463C22×D4C2×Dic1711yescharacteristic
464C22×D4C22×D1711yescharacteristic
465C23×C4—342no—
466C23×C4C2×Dic1711yescharacteristic
467C23×C4C2×Dic1711yescharacteristic
468C23×C4C2×Dic1711yescharacteristic, complemented
469C23×C4C22×D1711yescharacteristic
470C23×C4C22×D1711yescharacteristic
471#126—22no—
472#126—22no—
473#126—22no—
474#126—22no—
475#124—22no—
476#124—22no—
477#123—22no—
478#123—22no—
479#123—22no—
480#123—22no—
481#123—22no—
482#123—22no—
483C22⋊Q8—22no—
484C22⋊Q8—22no—
485C22⋊Q8—22no—
486C22⋊Q8—22no—
487#120—22no—
488#120—22no—
489C4×D4—22no—
490C4×D4—22no—
491C4×D4—21no—
492C4×D4—21no—
493C4×D4—21no—
494C4×D4—21no—
495#117—22no—
496#117—22no—
497#117—21no—
498#117—21no—
499#117—21no—
500#117—21no—
501#117—344no—
502#117—682no—
503C2×C4⋊C4—342no—
504C2×C4⋊C4—342no—
505C2×C4⋊C4C2×Dic1711yescharacteristic, complemented
506C2×C4⋊C4C2×Dic1711yescharacteristic, complemented
507C2×C4⋊C4C2×Dic1711yescharacteristic, complemented
508C2×C4⋊C4C2×Dic1711yescharacteristic, complemented
509C2×C4⋊C4C2×Dic1711yescharacteristic, complemented
510C2×C4⋊C4C2×Dic1711yescharacteristic, complemented
511C2×C4⋊C4C2×Dic1711yescharacteristic, complemented
512C2×C4⋊C4C2×Dic1711yescharacteristic, complemented
513C2×C22⋊C4—22no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—172no—
516C2×C22⋊C4—172no—
517C2×C22⋊C4—172no—
518C2×C22⋊C4—172no—
519C2×C22⋊C4—344no—
520C2×C22⋊C4—342no—
521C2×C22⋊C4—342no—
522C2×C22⋊C4—342no—
523C2×C22⋊C4—682no—
524C2×C22⋊C4C2×Dic1711yescharacteristic
525C2×C22⋊C4C2×Dic1711yescharacteristic
526C2×C22⋊C4C2×Dic1711yescharacteristic
527C2×C22⋊C4C2×Dic1711yescharacteristic
528C2×C22⋊C4C2×Dic1711yescharacteristic
529C2×C22⋊C4C2×Dic1711yescharacteristic
530C2×C22⋊C4C2×Dic1711yescharacteristic
531C2×C22⋊C4C2×Dic1711yescharacteristic
532C2×C22⋊C4C2×Dic1711yescharacteristic, complemented
533C2×C22⋊C4C2×Dic1711yescharacteristic, complemented
534C2×C22⋊C4C2×Dic1711yescharacteristic, complemented
535C2×C22⋊C4C22⋊D1712yes—
536C2×C22⋊C4C22⋊D1712yes—
537C2×C22⋊C4C22⋊D1712yes—
538C2×C22⋊C4C22⋊D1712yes—
539C2×C22⋊C4C22×D1711yescharacteristic
540C2×C22⋊C4C22×D1711yescharacteristic
541C2×C22⋊C4C22×D1711yescharacteristic
542C2×C42—342no—
543C2×C42—342no—
544C2×C42C2×Dic1711yescharacteristic, complemented
545C2×C42C2×Dic1711yescharacteristic, complemented
546C2×C42C2×Dic1711yescharacteristic, complemented
547#99—344no—
548#99—682no—
549#95—342no—
550#95—342no—
551#95—342no—
552#95—342no—
553C17#2247711yescharacteristic, complemented, Sylow
554C24—22no—
555C24—21no—
556C24—21no—
557C24—42no—
558C24—81no—
559C24C22×Dic1711yescharacteristic
560C24C22×Dic1711yescharacteristic
561C24C22×Dic1711yescharacteristic
562C24C2×C22⋊D1712yes—
563C24C2×C22⋊D1712yes—
564C24C23×D1711yescharacteristic
565C2×Q8—22no—
566C2×Q8—81no—
567C2×D4—22no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—22no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—22no—
574C2×D4—42no—
575C2×D4—81no—
576C22×C4—22no—
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—42no—
586C22×C4—81no—
587C22×C4—81no—
588C22×C4—81no—
589C22×C4—342no—
590C22×C4—342no—
591C22×C4—342no—
592C22×C4—342no—
593C22×C4—684no—
594C22×C4—684no—
595C22×C4—1362no—
596C22×C4C22×Dic1711yescharacteristic
597C22×C4C22×Dic1711yescharacteristic
598C22×C4C22×Dic1711yescharacteristic
599C22×C4C22×Dic1711yescharacteristic
600C22×C4C22×Dic1711yescharacteristic
601C22×C4C22×Dic1711yescharacteristic
602C22×C4C22×Dic1711yescharacteristic
603C22×C4C22×Dic1711yescharacteristic
604C22×C4C22×Dic1711yescharacteristic
605C22×C4C22×Dic1711yescharacteristic
606C22×C4C22×Dic1711yescharacteristic
607C22×C4C2×C22⋊D1712yes—
608C22×C4C2×C22⋊D1712yes—
609C22×C4C2×C22⋊D1712yes—
610C22×C4C2×C22⋊D1712yes—
611C4⋊C4—22no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—22no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—22no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—22no—
621C4⋊C4—22no—
622C4⋊C4—684no—
623C4⋊C4—1362no—
624C22⋊C4—22no—
625C22⋊C4—22no—
626C22⋊C4—22no—
627C22⋊C4—22no—
628C22⋊C4—22no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—22no—
636C22⋊C4—174no—
637C22⋊C4—342no—
638C22⋊C4—342no—
639C22⋊C4—342no—
640C22⋊C4—342no—
641C22⋊C4—342no—
642C22⋊C4—342no—
643C22⋊C4—342no—
644C22⋊C4—684no—
645C22⋊C4—684no—
646C22⋊C4—1362no—
647C22⋊C4C22⋊Dic1711yescharacteristic
648C22⋊C4C22⋊Dic1711yescharacteristic
649C22⋊C4C22⋊Dic1711yescharacteristic
650C22⋊C4C22⋊Dic1711yescharacteristic
651C22⋊C4C22⋊Dic1712yes—
652C22⋊C4C22⋊Dic1712yes—
653C22⋊C4C22⋊Dic1712yes—
654C22⋊C4C22⋊Dic1712yes—
655C22⋊C4C22⋊Dic1712yes—
656C22⋊C4C22⋊Dic1712yes—
657C42—21no—
658C42—21no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—21no—
663C42—684no—
664C42—1362no—
665C23—22no—
666C23—21no—
667C23—21no—
668C23—24no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—21no—
673C23—21no—
674C23—22no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—41no—
679C23—41no—
680C23—42no—
681C23—41no—
682C23—42no—
683C23—41no—
684C23—41no—
685C23—42no—
686C23—41no—
687C23—41no—
688C23—84no—
689C23—82no—
690C23—82no—
691C23C2×C22⋊Dic1712yes—
692C23C2×C22⋊Dic1711yescharacteristic
693C23C2×C22⋊Dic1711yescharacteristic
694C23#41×D1712yes—
695C23#1058769611yescharacteristic
696C23#1058769711yescharacteristic
697C23C23×Dic1711yescharacteristic
698C23C22×C22⋊D1712yes—
699Q8—82no—
700D4—42no—
701D4—42no—
702D4—42no—
703D4—42no—
704D4—82no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—81no—
735C2×C4—81no—
736C2×C4—81no—
737C2×C4—81no—
738C2×C4—344no—
739C2×C4—682no—
740C2×C4—682no—
741C2×C4—682no—
742C2×C4—682no—
743C2×C4—682no—
744C2×C4—682no—
745C2×C4—682no—
746C2×C4—682no—
747C2×C4—682no—
748C2×C4—682no—
749C2×C4—682no—
750C2×C4—1368no—
751C2×C4C2×C22⋊Dic1711yescharacteristic
752C2×C4C2×C22⋊Dic1711yescharacteristic
753C2×C4C2×C22⋊Dic1711yescharacteristic
754C2×C4C2×C22⋊Dic1711yescharacteristic
755C2×C4C2×C22⋊Dic1712yes—
756C2×C4C2×C22⋊Dic1712yes—
757C22—21no—
758C22—22no—
759C22—21no—
760C22—22no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—22no—
765C22—21no—
766C22—22no—
767C22—22no—
768C22—21no—
769C22—42no—
770C22—41no—
771C22—41no—
772C22—44no—
773C22—44no—
774C22—42no—
775C22—42no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—82no—
780C22—82no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22#1176278312yes—
786C22C22×C22⋊Dic1711yescharacteristic
787C22#41×Dic1711yescharacteristic
788C22#1176329211yescharacteristic
789C22#1176344712yes—
790C22#1176345812yes—
791C4—21no—
792C4—21no—
793C4—22no—
794C4—21no—
795C4—22no—
796C4—21no—
797C4—41no—
798C4—41no—
799C4—41no—
800C4—41no—
801C4—41no—
802C4—41no—
803C4—41no—
804C4—684no—
805C4—1362no—
806C4—1362no—
807C4—1362no—
808C2—22no—
809C2—22no—
810C2—22no—
811C2—21no—
812C2—21no—
813C2—41no—
814C2—42no—
815C2—81no—
816C2#1453161411yescharacteristic
817C2C2×#1176278311yescharacteristic
818C2#1453724511yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic17
commutatorC23×C17C23×C4
FrattiniC24C23×D17
FittingC2×C17×#551C2
socleC22×C17C22×C22⋊C4
prime radicalC2×C17×#120C22
cosocleC24×C17C24
hypercenterC2×#551D17
hypocenterC17#22477
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C22⋊C4 ◁ C2×#551

Complements

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

NH ≅ G/Ntype
1. #14531633C2semidirect
2. #14529770C2semidirect
3. #14529243C2semidirect
5. #14528861C2semidirect
6. #14528858C2semidirect
7. #14528772C2semidirect
8. C4×#10587505C2semidirect
9. #14528517C2semidirect
10. C2×#11762576C2semidirect
36. C2×C17×#126C4semidirect
37. C2×C17×#126C4semidirect
38. C2×C17×#124C4semidirect
39. C2×C17×#123C4semidirect
40. C2×C17×#123C4semidirect
42. C2×C17×C22⋊Q8C4semidirect
45. C2×C4×D4×C17C4semidirect
47. C2×C17×#117C4semidirect
52. C22×Q8×C17C2×C4semidirect
58. C23×C4×C17C2×C4semidirect
92. C2×C4⋊C4×C17C2×C4semidirect
93. C2×C4⋊C4×C17C2×C4semidirect
94. C2×C4⋊C4×C17C2×C4semidirect
95. C2×C4⋊C4×C17C2×C4semidirect
96. C2×C4⋊C4×C17C2×C4semidirect
97. C2×C4⋊C4×C17C2×C4semidirect
98. C2×C4⋊C4×C17C2×C4semidirect
99. C2×C4⋊C4×C17C2×C4semidirect
110. C2×C22⋊C4×C17C2×C4semidirect
111. C2×C22⋊C4×C17C2×C4semidirect
112. C2×C22⋊C4×C17C2×C4semidirect
120. C2×C42×C17C2×C4semidirect
121. C2×C42×C17C2×C4semidirect
122. C2×C42×C17C2×C4semidirect
414. C2×#126Dic17semidirect
415. C2×#126Dic17semidirect
416. C2×#124Dic17semidirect
417. C2×#123Dic17semidirect
418. C2×#123Dic17semidirect
420. C2×C22⋊Q8Dic17semidirect
423. C2×C4×D4Dic17semidirect
426. C2×#117Dic17semidirect
461. C22×Q8C2×Dic17semidirect
468. C23×C4C2×Dic17semidirect
505. C2×C4⋊C4C2×Dic17semidirect
506. C2×C4⋊C4C2×Dic17semidirect
507. C2×C4⋊C4C2×Dic17semidirect
508. C2×C4⋊C4C2×Dic17semidirect
509. C2×C4⋊C4C2×Dic17semidirect
510. C2×C4⋊C4C2×Dic17semidirect
511. C2×C4⋊C4C2×Dic17semidirect
512. C2×C4⋊C4C2×Dic17semidirect
532. C2×C22⋊C4C2×Dic17semidirect
533. C2×C22⋊C4C2×Dic17semidirect
534. C2×C22⋊C4C2×Dic17semidirect
544. C2×C42C2×Dic17semidirect
545. C2×C42C2×Dic17semidirect
546. C2×C42C2×Dic17semidirect
553. C17#22477semidirect

Maximal subgroups

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

subgroupindex
#145316332
#145297702
#145292432
#145292382
#145288612
#145288582
#145287722
C4×#105875052
#145285172
C2×#117625762
C2×C17×#5512
#2247717