Finite Group Databasebeta

← #16955894

Subgroups — #16955894

Order 4352.

2666 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D17C211yesmaximal, characteristic
2C2×#11762709C212yesmaximal
3C2×#11762660C212yesmaximal, complemented
4C2×C4×C22⋊Dic17C211yesmaximal, characteristic, complemented
5C2×#11762656C211yesmaximal, characteristic, complemented
6#14527021C212yesmaximal, complemented
7#14527020C212yesmaximal, complemented
8#14527012C211yesmaximal, characteristic, complemented
9#14527005C211yesmaximal, characteristic, complemented
10#95×Dic17C211yesmaximal, characteristic, complemented
11C17×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×C22⋊D17C2211yescharacteristic
13C23×C4×D17C2211yescharacteristic
14C2×C4×C22⋊D17—28no—
15C2×C4×C22⋊D17C418yescomplemented
16C22×#63225C2212yes—
17C22×#63225C2211yescharacteristic
18C22×C22⋊Dic17C2211yescharacteristic
19C22×C22⋊Dic17C2212yes—
20C22×#63227C2211yescharacteristic
21C22×#63227C2212yes—
22C22×#63227C2212yes—
23C22×C4×Dic17C2212yes—
24C22×C4×Dic17C2212yes—
25C22×C4×Dic17C2211yescharacteristic
26C22×C4×Dic17C2212yes—
27#11762709C4116yescomplemented
28#11762660—28no—
29C4×C22⋊Dic17—24no—
30#11762656—24no—
31C2×#10587502C2212yes—
32C2×#10587502C2211yescharacteristic
33C2×#10587502C2212yes—
34C2×#10587502C2212yes—
35C2×#10587502C2211yescharacteristic
36C24×C4×C17C2211yescharacteristic
37C22×C22⋊C4×C17C2212yes—
38C2×C17×#95C2211yescharacteristic
39C2×C17×#95C2211yescharacteristic
40C2×C17×#95C2212yes—
41C25×C17C2311yescharacteristic
42C24×D17C2311yescharacteristic
43C23×C4×C17—24no—
44C23×C4×C17—22no—
45C23×C4×C17—22no—
46C23×C4×C17—42no—
47C23×C4×C17C2×C414yes—
48C23×C4×C17C2312yes—
49C23×C4×C17C2312yes—
50C23×C4×C17C2311yescharacteristic
51C23×C4×C17C2311yescharacteristic
52C22×C22⋊D17—24no—
53C22×C22⋊D17—22no—
54C22×C22⋊D17—22no—
55C22×C22⋊D17C2×C418yes—
56C22×C22⋊D17C2×C414yes—
57C23×Dic17C2312yes—
58C23×Dic17C2311yescharacteristic
59C23×Dic17C2311yescharacteristic
60C23×Dic17C2312yes—
61C23×Dic17C2311yescharacteristic
62C22×C4×D17—22no—
63C22×C4×D17—22no—
64C22×C4×D17—24no—
65C22×C4×D17—42no—
66C22×C4×D17C2×C414yes—
67C2×C22⋊C4×C17—42no—
68C2×C22⋊C4×C17—42no—
69C2×C22⋊C4×C17C2×C418yescomplemented
70C2×C22⋊Dic17—24no—
71C2×C22⋊Dic17—24no—
72C2×C22⋊Dic17—24no—
73C2×C22⋊Dic17C2×C414yes—
74C2×C22⋊Dic17C2×C418yescomplemented
75C4×C22⋊D17—232no—
76C2×#63227—24no—
77C2×#63227—24no—
78C2×#63227—24no—
79C2×#63227—42no—
80C2×#63227—42no—
81C2×#63227C2×C414yes—
82C2×#63227C2×C418yescomplemented
83C2×#63227C2×C418yescomplemented
84C2×#63225—24no—
85C2×#63225—24no—
86C2×#63225C2×C414yes—
87C2×#63225C2×C418yescomplemented
88C2×#63225D418yes—
89C2×C4×Dic17—24no—
90C2×C4×Dic17—24no—
91C2×C4×Dic17—24no—
92C2×C4×Dic17—24no—
93C2×C4×Dic17—24no—
94C2×C4×Dic17—24no—
95C2×C4×Dic17—24no—
96C2×C4×Dic17—42no—
97C2×C4×Dic17—42no—
98C2×C4×Dic17C2×C414yes—
99C2×C4×Dic17C2×C418yescomplemented
100C17×#95—22no—
101C17×#95—24no—
102C17×#95—22no—
103#10587502—22no—
104#10587502—24no—
105#10587502—24no—
106#10587502—42no—
107#10587502D414yescomplemented
108C24×C17—22no—
109C24×C17—21no—
110C24×C17—21no—
111C24×C17—21no—
112C24×C17—21no—
113C24×C17—22no—
114C24×C17—22no—
115C24×C17—21no—
116C24×C17—21no—
117C24×C17C22×C412yes—
118C24×C17C22×C414yes—
119C24×C17C2411yescharacteristic
120C23×D17—22no—
121C23×D17—21no—
122C23×D17—21no—
123C23×D17—21no—
124C23×D17—21no—
125C23×D17—22no—
126C23×D17—22no—
127C23×D17—21no—
128C23×D17—21no—
129C23×D17C22×C412yes—
130C23×D17C22×C414yes—
131C22×C4×C17—22no—
132C22×C4×C17—21no—
133C22×C4×C17—21no—
134C22×C4×C17—22no—
135C22×C4×C17—22no—
136C22×C4×C17—22no—
137C22×C4×C17—22no—
138C22×C4×C17—22no—
139C22×C4×C17—22no—
140C22×C4×C17—22no—
141C22×C4×C17—22no—
142C22×C4×C17—22no—
143C22×C4×C17—22no—
144C22×C4×C17—22no—
145C22×C4×C17—22no—
146C22×C4×C17—22no—
147C22×C4×C17—22no—
148C22×C4×C17—28no—
149C22×C4×C17—28no—
150C22×C4×C17—44no—
151C22×C4×C17—48no—
152C22×C4×C17—48no—
153C22×C4×C17C22×C414yes—
154C22×C4×C17C22×C414yes—
155C22×C4×C17C22×C412yes—
156C22×C4×C17C22×C412yes—
157C22×C4×C17C2×D414yes—
158C22×C4×C17C2×D412yes—
159C22×C4×C17#4112yes—
160C2×C22⋊D17—28no—
161C2×C22⋊D17—28no—
162C2×C22⋊D17—216no—
163C2×C22⋊D17—216no—
164C2×C22⋊D17C42116yescomplemented
165C22×Dic17—21no—
166C22×Dic17—22no—
167C22×Dic17—21no—
168C22×Dic17—22no—
169C22×Dic17—22no—
170C22×Dic17—22no—
171C22×Dic17—22no—
172C22×Dic17—22no—
173C22×Dic17—22no—
174C22×Dic17—22no—
175C22×Dic17—22no—
176C22×Dic17—22no—
177C22×Dic17—22no—
178C22×Dic17—21no—
179C22×Dic17—22no—
180C22×Dic17—22no—
181C22×Dic17—21no—
182C22×Dic17C22×C412yes—
183C22×Dic17C22×C414yes—
184C22×Dic17C22×C412yes—
185C22×Dic17C22×C414yes—
186C22×Dic17C22×C412yes—
187C22×Dic17C22×C414yes—
188C22×Dic17C2×D414yes—
189C22×Dic17C2×D414yes—
190C22×Dic17C2×D414yes—
191C22×Dic17#4114yes—
192C22×Dic17#4112yes—
193C22×Dic17#4112yes—
194C2×C4×D17—28no—
195C2×C4×D17—28no—
196C2×C4×D17—44no—
197C2×C4×D17—48no—
198C2×C4×D17—48no—
199C22⋊C4×C17—48no—
200C22⋊Dic17—28no—
201C22⋊Dic17—216no—
202#63227—28no—
203#63227—216no—
204#63227—48no—
205#63225—216no—
206#63225C22⋊C4116yescomplemented
207C4×Dic17—28no—
208C4×Dic17—216no—
209C4×Dic17—48no—
210C4×Dic17—48no—
211#13820—171nomaximal, Sylow
212C23×C17—22no—
213C23×C17—22no—
214C23×C17—24no—
215C23×C17—24no—
216C23×C17—24no—
217C23×C17—22no—
218C23×C17—24no—
219C23×C17—22no—
220C23×C17—24no—
221C23×C17—22no—
222C23×C17—22no—
223C23×C17—24no—
224C23×C17—42no—
225C23×C17—42no—
226C23×C17—41no—
227C23×C17—42no—
228C23×C17—42no—
229C23×C17—41no—
230C23×C17—42no—
231C23×C17—41no—
232C23×C17—41no—
233C23×C17—42no—
234C23×C17C2×C4214yes—
235C23×C17C23×C411yescharacteristic
236C23×C17C23×C412yes—
237C23×C17C22×D412yes—
238C23×C17C22×D411yescharacteristic
239C23×C17C2×#4111yescharacteristic
240C23×C17C2×#4111yescharacteristic
241C23×C17C2×#4111yescharacteristic
242C23×C17C2×#4112yes—
243C23×C17H(5,𝔽2)12yes—
244C23×C17H(5,𝔽2)11yescharacteristic
245C23×C172−1+411yescharacteristic
246C22×D17—22no—
247C22×D17—22no—
248C22×D17—22no—
249C22×D17—24no—
250C22×D17—24no—
251C22×D17—24no—
252C22×D17—24no—
253C22×D17—22no—
254C22×D17—22no—
255C22×D17—24no—
256C22×D17—22no—
257C22×D17—24no—
258C22×D17—42no—
259C22×D17—42no—
260C22×D17—41no—
261C22×D17—42no—
262C22×D17—42no—
263C22×D17—41no—
264C22×D17—42no—
265C22×D17—41no—
266C22×D17—41no—
267C22×D17—42no—
268C22×D17C2×C4214yes—
269C2×C4×C17—22no—
270C2×C4×C17—22no—
271C2×C4×C17—22no—
272C2×C4×C17—22no—
273C2×C4×C17—24no—
274C2×C4×C17—24no—
275C2×C4×C17—24no—
276C2×C4×C17—24no—
277C2×C4×C17—24no—
278C2×C4×C17—24no—
279C2×C4×C17—24no—
280C2×C4×C17—24no—
281C2×C4×C17—24no—
282C2×C4×C17—24no—
283C2×C4×C17—416no—
284C2×C4×C17—42no—
285C2×C4×C17—42no—
286C2×C4×C17—42no—
287C2×C4×C17—42no—
288C2×C4×C17—42no—
289C2×C4×C17—42no—
290C2×C4×C17—42no—
291C2×C4×C17—42no—
292C2×C4×C17C2×C22⋊C414yes—
293C2×C4×C17C4×D414yes—
294C22⋊D17—232no—
295C2×Dic17—22no—
296C2×Dic17—24no—
297C2×Dic17—22no—
298C2×Dic17—24no—
299C2×Dic17—24no—
300C2×Dic17—24no—
301C2×Dic17—24no—
302C2×Dic17—24no—
303C2×Dic17—24no—
304C2×Dic17—24no—
305C2×Dic17—22no—
306C2×Dic17—24no—
307C2×Dic17—24no—
308C2×Dic17—22no—
309C2×Dic17—24no—
310C2×Dic17—22no—
311C2×Dic17—42no—
312C2×Dic17—42no—
313C2×Dic17—42no—
314C2×Dic17—42no—
315C2×Dic17—42no—
316C2×Dic17—42no—
317C2×Dic17C2×C4214yes—
318C2×Dic17C2×C22⋊C414yes—
319C2×Dic17C2×C22⋊C414yes—
320C2×Dic17#11714yes—
321C2×Dic17C4×D418yes—
322C2×Dic17C4×D418yes—
323C2×Dic17C4×D418yescomplemented
324C4×D17—416no—
325C22×C4×D4—171no—
326C2×#390—172no—
327C2×C4×C4⋊C4—172no—
328C2×C4×C22⋊C4—171no—
329C2×C4×C22⋊C4—171no—
330#1437—172no—
331#1437—172no—
332C4⋊#95—171no—
333C22⋊#95—171no—
334C22⋊#95D1711yescharacteristic, complemented
335C4×#95—171no—
336C22×C17—24no—
337C22×C17—24no—
338C22×C17—24no—
339C22×C17—42no—
340C22×C17—42no—
341C22×C17—42no—
342C22×C17—42no—
343C22×C17—44no—
344C22×C17—44no—
345C22×C17—44no—
346C22×C17—44no—
347C22×C17C22×C4211yescharacteristic
348C22×C17C22×C22⋊C411yescharacteristic
349C22×C17C2×#11711yescharacteristic
350C22×C17C2×C4×D412yes—
351C22×C17C2×C4×D412yes—
352C22×C17C2×C4×D412yes—
353C22×C17C2×C4×D411yescharacteristic
354C22×C17C4×#4112yes—
355C22×C17C4×#4111yescharacteristic
356C22×C17#51811yescharacteristic
357C22×C17#51812yes—
358C22×C17#52011yescharacteristic
359C22×C17#52012yes—
360C22×C17D4212yes—
361C22×C17#54612yes—
362C22×C17#54711yescharacteristic
363C22×C17#54812yes—
364C22×C17#55012yes—
365C22×C17#55011yescharacteristic
366C22×C17#55312yes—
367C22×C17#55511yescharacteristic
368C22×C17#55611yescharacteristic
369C22×C17#55912yes—
370C2×D17—24no—
371C2×D17—24no—
372C2×D17—24no—
373C2×D17—42no—
374C2×D17—42no—
375C2×D17—42no—
376C2×D17—42no—
377C2×D17—44no—
378C2×D17—44no—
379C2×D17—44no—
380C2×D17—44no—
381C4×C17—24no—
382C4×C17—24no—
383C4×C17—44no—
384C4×C17—44no—
385Dic17—24no—
386Dic17—28no—
387Dic17—42no—
388Dic17—44no—
389Dic17C4×C22⋊C418yescomplemented
390C23×D4—171no—
391C24×C4—171no—
392C24×C4C2×D1711yescharacteristic
393C2×C4×D4—178no—
394C2×C4×D4—348no—
395C22×C4⋊C4—171no—
396C22×C4⋊C4—172no—
397C22×C22⋊C4—171no—
398C22×C22⋊C4—172no—
399C22×C22⋊C4—171no—
400C22×C22⋊C4—172no—
401C22×C22⋊C4—172no—
402C22×C22⋊C4C2×D1712yes—
403C22×C42—171no—
404C22×C42—172no—
405C22×C42—172no—
406C22×C42—172no—
407#390—1716no—
408C4×C4⋊C4—348no—
409C4×C22⋊C4—344no—
410C4×C22⋊C4—344no—
411C2×#95—171no—
412C2×#95—172no—
413C2×#95—171no—
414C2×#95—172no—
415C2×#95—172no—
416C2×#95C2×D1711yescharacteristic
417C2×#95C2×D1711yescharacteristic
418C2×#95C2×D1712yes—
419C2×C17—44no—
420C2×C17C2×C4×C22⋊C411yescharacteristic
421C2×C17C42×D411yescharacteristic
422C2×C17#227511yescharacteristic
423C2×C17D4×C22⋊C411yescharacteristic
424C2×C17#234111yescharacteristic
425C2×C17#235411yescharacteristic
426C2×C17#235711yescharacteristic
427C2×C17#236112yes—
428C2×C17#236312yes—
429C2×C17#236612yes—
430C2×C17#236712yes—
431D17—44no—
432C25—171no—
433C25C22×D1711yescharacteristic
434C22×D4—174no—
435C22×D4—178no—
436C22×D4—344no—
437C22×D4—342no—
438C22×D4—342no—
439C23×C4—24no—
440C23×C4—22no—
441C23×C4—22no—
442C23×C4—42no—
443C23×C4—171no—
444C23×C4—172no—
445C23×C4—171no—
446C23×C4—172no—
447C23×C4—171no—
448C23×C4—174no—
449C23×C4—344no—
450C23×C4—342no—
451C23×C4—342no—
452C23×C4—682no—
453C23×C4C4×D1714yes—
454C23×C4C22×D1712yes—
455C23×C4C22×D1712yes—
456C23×C4C22×D1711yescharacteristic
457C23×C4C22×D1711yescharacteristic
458C4×D4—3432no—
459C2×C4⋊C4—174no—
460C2×C4⋊C4—178no—
461C2×C4⋊C4—178no—
462C2×C4⋊C4—344no—
463C2×C4⋊C4—344no—
464C2×C22⋊C4—42no—
465C2×C22⋊C4—42no—
466C2×C22⋊C4—174no—
467C2×C22⋊C4—178no—
468C2×C22⋊C4—174no—
469C2×C22⋊C4—178no—
470C2×C22⋊C4—178no—
471C2×C22⋊C4—344no—
472C2×C22⋊C4—344no—
473C2×C22⋊C4—344no—
474C2×C22⋊C4—344no—
475C2×C22⋊C4—344no—
476C2×C22⋊C4—344no—
477C2×C22⋊C4—682no—
478C2×C22⋊C4—682no—
479C2×C22⋊C4C4×D1718yescomplemented
480C2×C42—174no—
481C2×C42—178no—
482C2×C42—344no—
483C2×C42—344no—
484C2×C42—344no—
485C2×C42—344no—
486C2×C42—344no—
487C2×C42—344no—
488C2×C42—344no—
489C2×C42—682no—
490C2×C42—682no—
491#95—22no—
492#95—24no—
493#95—22no—
494#95—174no—
495#95—344no—
496#95—344no—
497#95—342no—
498#95—682no—
499C17#1382011yescharacteristic, complemented, Sylow
500C24—21no—
501C24—22no—
502C24—21no—
503C24—21no—
504C24—22no—
505C24—21no—
506C24—22no—
507C24—21no—
508C24—21no—
509C24—174no—
510C24—172no—
511C24—341no—
512C24—342no—
513C24—341no—
514C24—341no—
515C24—342no—
516C24—341no—
517C24—342no—
518C24—341no—
519C24—341no—
520C24C2×C4×D1714yes—
521C24C2×C4×D1712yes—
522C24C23×D1711yescharacteristic
523C2×D4—1716no—
524C2×D4—348no—
525C2×D4—348no—
526C2×D4—3416no—
527C2×D4—3416no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—28no—
546C22×C4—28no—
547C22×C4—44no—
548C22×C4—48no—
549C22×C4—48no—
550C22×C4—172no—
551C22×C4—174no—
552C22×C4—174no—
553C22×C4—172no—
554C22×C4—172no—
555C22×C4—174no—
556C22×C4—172no—
557C22×C4—174no—
558C22×C4—174no—
559C22×C4—174no—
560C22×C4—172no—
561C22×C4—174no—
562C22×C4—348no—
563C22×C4—342no—
564C22×C4—341no—
565C22×C4—341no—
566C22×C4—342no—
567C22×C4—342no—
568C22×C4—342no—
569C22×C4—342no—
570C22×C4—342no—
571C22×C4—342no—
572C22×C4—342no—
573C22×C4—341no—
574C22×C4—342no—
575C22×C4—342no—
576C22×C4—341no—
577C22×C4—342no—
578C22×C4—342no—
579C22×C4—342no—
580C22×C4—348no—
581C22×C4—684no—
582C22×C4—688no—
583C22×C4—688no—
584C22×C4C2×C4×D1714yes—
585C22×C4C2×C4×D1714yes—
586C22×C4C2×C4×D1712yes—
587C22×C4C2×C4×D1712yes—
588C22×C4D4×D1714yes—
589C22×C4D4×D1712yes—
590C22×C4#6325412yes—
591C4⋊C4—1716no—
592C4⋊C4—3416no—
593C22⋊C4—48no—
594C22⋊C4—3416no—
595C22⋊C4—3416no—
596C22⋊C4—348no—
597C22⋊C4—348no—
598C22⋊C4—688no—
599C42—348no—
600C42—3416no—
601C42—688no—
602C42—688no—
603C23—22no—
604C23—22no—
605C23—24no—
606C23—24no—
607C23—24no—
608C23—22no—
609C23—24no—
610C23—22no—
611C23—24no—
612C23—22no—
613C23—24no—
614C23—22no—
615C23—41no—
616C23—42no—
617C23—41no—
618C23—42no—
619C23—42no—
620C23—41no—
621C23—41no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—174no—
626C23—342no—
627C23—342no—
628C23—344no—
629C23—344no—
630C23—344no—
631C23—342no—
632C23—344no—
633C23—342no—
634C23—344no—
635C23—342no—
636C23—344no—
637C23—342no—
638C23—681no—
639C23—682no—
640C23—681no—
641C23—682no—
642C23—682no—
643C23—681no—
644C23—681no—
645C23—682no—
646C23—682no—
647C23—682no—
648C23C42×D1714yes—
649C23C22×C4×D1711yescharacteristic
650C23C22×C4×D1712yes—
651C23C2×D4×D1711yescharacteristic
652C23C2×D4×D1712yes—
653C23C2×#6325411yescharacteristic
654C23#1058769111yescharacteristic
655C23#1058769112yes—
656C23#1058769411yescharacteristic
657C23#41×D1711yescharacteristic
658C23#41×D1712yes—
659C23#41×D1711yescharacteristic
660D4—3432no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—416no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—174no—
685C2×C4—174no—
686C2×C4—174no—
687C2×C4—178no—
688C2×C4—178no—
689C2×C4—174no—
690C2×C4—178no—
691C2×C4—344no—
692C2×C4—344no—
693C2×C4—344no—
694C2×C4—344no—
695C2×C4—342no—
696C2×C4—342no—
697C2×C4—344no—
698C2×C4—344no—
699C2×C4—344no—
700C2×C4—344no—
701C2×C4—342no—
702C2×C4—344no—
703C2×C4—344no—
704C2×C4—342no—
705C2×C4—344no—
706C2×C4—342no—
707C2×C4—6816no—
708C2×C4—682no—
709C2×C4—682no—
710C2×C4—682no—
711C2×C4—682no—
712C2×C4—682no—
713C2×C4—682no—
714C2×C4C22⋊C4×D1714yes—
715C2×C4#1058756714yes—
716C22—24no—
717C22—24no—
718C22—24no—
719C22—44no—
720C22—44no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—44no—
726C22—44no—
727C22—344no—
728C22—344no—
729C22—344no—
730C22—684no—
731C22—684no—
732C22—682no—
733C22—682no—
734C22—682no—
735C22—682no—
736C22—684no—
737C22—684no—
738C22C2×C42×D1711yescharacteristic
739C22C2×C22⋊C4×D1711yescharacteristic
740C22#117×D1711yescharacteristic
741C22C4×D4×D1712yes—
742C22C4×D4×D1712yes—
743C22C4×D4×D1712yes—
744C22C2×#1058756711yescharacteristic
745C22C4×#6325412yes—
746C22#1176327711yescharacteristic
747C22#1176328212yes—
748C22#1176328211yescharacteristic
749C22#1176329012yes—
750C22#1176329011yescharacteristic
751C22#1176344112yes—
752C22#1176344612yes—
753C22#1176346111yescharacteristic
754C22#1176346912yes—
755C22#1176347711yescharacteristic
756C22#1176347712yes—
757C22#1176350412yes—
758C22#1176352311yescharacteristic
759C22#1176353011yescharacteristic
760C22#1176354312yes—
761C4—24no—
762C4—24no—
763C4—44no—
764C4—44no—
765C4—178no—
766C4—344no—
767C4—348no—
768C4—684no—
769C4—682no—
770C2—44no—
771C2—684no—
772C2C4×C22⋊C4×D1711yescharacteristic
773C2C4×#1058756711yescharacteristic
774C2#1453114211yescharacteristic
775C2#1453160011yescharacteristic
776C2#1453162111yescharacteristic
777C2#1453172811yescharacteristic
778C2#1453175211yescharacteristic
779C2#1453180312yes—
780C2#1453182512yes—
781C2#1453184712yes—
782C2#1453185212yes—
subgroupG/H
center, FrattiniC24C23×D17
commutatorC22×C17C22×C42
FittingC17×C22⋊#95C2
socle, cosocleC24×C17C24
prime radicalC23×C22⋊D17C22
hypercenterC22⋊#95D17
hypocenterC17#13820
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×#11762660C2semidirect
4. C2×C4×C22⋊Dic17C2semidirect
5. C2×#11762656C2semidirect
6. #14527021C2semidirect
7. #14527020C2semidirect
8. #14527012C2semidirect
9. #14527005C2semidirect
10. #95×Dic17C2semidirect
11. C17×C22⋊#95C2semidirect
15. C2×C4×C22⋊D17C4semidirect
27. #11762709C4semidirect
69. C2×C22⋊C4×C17C2×C4semidirect
74. C2×C22⋊Dic17C2×C4semidirect
82. C2×#63227C2×C4semidirect
83. C2×#63227C2×C4semidirect
87. C2×#63225C2×C4semidirect
99. C2×C4×Dic17C2×C4semidirect
107. #10587502D4semidirect
164. C2×C22⋊D17C42semidirect
206. #63225C22⋊C4semidirect
323. C2×Dic17C4×D4semidirect
334. C22⋊#95D17semidirect
389. Dic17C4×C22⋊C4semidirect
479. C2×C22⋊C4C4×D17semidirect
499. C17#13820semidirect

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×#117627092
C2×#117626602
C2×C4×C22⋊Dic172
C2×#117626562
#145270212
#145270202
#145270122
#145270052
#95×Dic172
C17×C22⋊#952
#1382017