Finite Group Databasebeta

← C2×#14542666 #17942765

Subgroups — C2×#14542666 #17942765

Order 4352.

7022 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14542666C2132yesmaximal, direct product factor
2C2×#11763536C214yesmaximal, complemented
3C2×#11763526C214yesmaximal, complemented
4C2×#11763495C214yesmaximal, complemented
5C2×#11763491C214yesmaximal, complemented
6C2×#11763422C211yesmaximal, characteristic, complemented
7C2×#11763421C211yesmaximal, characteristic, complemented
8C2×#11763420C211yesmaximal, characteristic, complemented
9C2×#11763382C212yesmaximal
10C2×#11763365C211yesmaximal, characteristic, complemented
11C2×#11763363C212yesmaximal, complemented
12C2×#11763361C212yesmaximal, complemented
13C2×C4⋊Q8×D17C211yesmaximal, characteristic, complemented
14C2×#11763285C212yesmaximal, complemented
15C2×#11763277C211yesmaximal, characteristic
16C2×C17×#541C211yesmaximal, characteristic, complemented
17C22×#63252C2211yescharacteristic
18C22×Q8×D17C2212yes—
19#11763536C22164yescomplemented
20#11763526C22164yescomplemented
21#11763495C22164yescomplemented
22#11763491C22164yescomplemented
23#11763422C22116yescomplemented
24#11763421C22116yescomplemented
25#11763420C22116yescomplemented
26#11763382C22132yes—
27#11763365C22116yescomplemented
28#11763363C22132yescomplemented
29#11763361C22132yescomplemented
30C2×#10587555C2211yescharacteristic
31C2×#10587574C2214yes—
32C2×#10587574C2214yes—
33C2×#10587574C2212yes—
34C2×#10587630C2212yes—
35C4⋊Q8×D17C22116yescomplemented
36C2×#10587584C2214yes—
37C2×#10587584C2214yes—
38C2×#10587565C2214yes—
39C2×#10587556C2211yescharacteristic
40C2×#10587576C2214yes—
41C2×#10587575C2214yes—
42C2×#10587575C2214yes—
43C2×#10587575C2214yes—
44C2×#10587575C2214yes—
45C2×#10587571C2214yes—
46C2×#10587580C2214yes—
47C2×#10587569C2214yes—
48C2×#10587583C2212yes—
49C2×#10587610C2212yes—
50C2×#10587582C2214yes—
51C2×#10587582C2214yes—
52C2×#10587564C2214yes—
53C2×#10587632C2212yes—
54#11763285C22132yescomplemented
55#11763277C22116yes—
56C2×Q8×Dic17C2212yes—
57C2×C4×Dic34C2214yes—
58C2×C4×Dic34C2214yes—
59C2×C4×Dic34C2212yes—
60C2×#10587573C2212yes—
61C2×#10587573C2214yes—
62C2×#10587573C2214yes—
63C2×#10587573C2214yes—
64C2×#10587573C2212yes—
65C2×#10587579C2212yes—
66C2×#10587567C2212yes—
67C2×#10587567C2212yes—
68C2×#10587578C2212yes—
69C2×#10587578C2214yes—
70C2×#10587558C2211yescharacteristic
71C2×#10587558C2211yescharacteristic
72C2×#10587558C2214yes—
73C2×#10587558C2214yes—
74C2×#10587563C2214yes—
75C2×C4⋊C4×D17C2214yes—
76C22×C4×Dic17C2211yescharacteristic
77C2×C42×D17C2211yescharacteristic
78C2×C42×D17C2211yescharacteristic
79C17×#541C22116yescomplemented
80C2×C17×C4⋊Q8C2211yescharacteristic
81C2×C17×#126C2214yes—
82C2×C17×#125C2214yes—
83C2×C17×#125C2211yescharacteristic
84C2×C17×C22⋊Q8C2212yes—
85C2×C4×Q8×C17C2212yes—
86C2×C17×#117C2211yescharacteristic
87C22×Q8×C17C2312yes—
88C23×C4×C17C2311yescharacteristic
89C22×C22⋊D17C2311yescharacteristic
90C22×C22⋊D17C2311yescharacteristic
91C23×Dic17C2312yes—
92C2×Q8×D17—216no—
93C2×Q8×D17C23116yes—
94C2×#63252—28no—
95C2×#63252C2318yes—
96C22×D68C2311yescharacteristic
97C22×C4×D17C2312yes—
98C22×C4×D17C2312yes—
99C22×C4×D17C2311yescharacteristic
100C22×C4×D17C2314yes—
101C22×C4×D17C2311yescharacteristic
102C22×Dic34C2314yes—
103C22×Dic34C2311yescharacteristic
104C22×Dic34C2312yes—
105C22×Dic34C2314yes—
106C17×C4⋊Q8C2318yes—
107C17×#126C23132yes—
108C17×#125C23132yes—
109C17×#125C2318yes—
110C17×C22⋊Q8C23116yes—
111C4×Q8×C17C23116yes—
112C17×#117C2318yes—
113C2×C4⋊C4×C17C2312yes—
114C2×C4⋊C4×C17C2312yes—
115C2×C4⋊C4×C17C2314yes—
116C2×C4⋊C4×C17C2314yes—
117C2×C4⋊C4×C17C2314yes—
118C2×C4⋊C4×C17C2314yes—
119C2×C22⋊C4×C17C2312yes—
120C2×C22⋊C4×C17C2314yes—
121C2×C42×C17C2311yescharacteristic
122C2×C42×C17C2311yescharacteristic
123C2×C42×C17C2314yes—
124C2×C22⋊Dic17C2314yes—
125#10587632C23116yes—
126Q8×Dic17C23116yes—
127#10587630C23116yes—
128C2×#63227C2312yes—
129C2×#63227C2314yes—
130C2×#63227C2312yes—
131C2×#63227C2314yes—
132C2×#63227C2314yes—
133C2×C4⋊Dic17C2314yes—
134C2×C4⋊Dic17C2312yes—
135C2×C4⋊Dic17C2314yes—
136C2×C4⋊Dic17C2314yes—
137#10587610C23116yes—
138C2×#63225C2314yes—
139C2×#63225C2314yes—
140C2×#63225C2314yes—
141C2×#63225C2312yes—
142C2×#63225C2312yes—
143C2×#63225C2314yes—
144C2×#63225C2314yes—
145C2×#63225C2314yes—
146C2×#63225C2314yes—
147C2×#63225C2314yes—
148C2×C4×Dic17C2311yescharacteristic
149C2×C4×Dic17C2312yes—
150C2×C4×Dic17C2312yes—
151C2×C4×Dic17C2311yescharacteristic
152C2×C4×Dic17C2312yes—
153C2×C4×Dic17C2318yes—
154C2×C4×Dic17C2314yes—
155C2×C4×Dic17C2314yes—
156C2×C4×Dic17C2314yes—
157C2×C4×Dic17C2314yes—
158#10587584C23132yes—
159#10587584C23132yes—
160#10587583C23116yes—
161#10587582C23132yes—
162#10587582C23132yes—
163#10587580C23132yes—
164#10587579C23116yes—
165#10587578C23132yes—
166#10587578C23116yes—
167C4⋊C4×D17C23132yes—
168#10587576C23132yes—
169#10587575C23132yes—
170#10587575C23132yes—
171#10587575C23132yes—
172#10587575C23132yes—
173#10587574C23132yes—
174#10587574C23132yes—
175#10587574C23116yes—
176#10587573C23132yes—
177#10587573C23132yes—
178#10587573C23132yes—
179#10587573C23116yes—
180#10587573C23116yes—
181#10587571C23132yes—
182#10587569C23132yes—
183#10587567C23116yes—
184#10587567C23116yes—
185#10587565C23132yes—
186#10587564C23132yes—
187#10587563C23132yes—
188#10587558C23132yes—
189#10587558C23132yes—
190#10587558C2318yes—
191#10587558C2318yes—
192C42×D17C2318yes—
193C42×D17C2318yes—
194#10587556C2318yes—
195#10587555C2318yes—
196C4×Dic34C23132yes—
197C4×Dic34C23132yes—
198C4×Dic34C23116yes—
199C24×C17C2411yescharacteristic
200C23×D17C2411yescharacteristic
201C23×D17C2411yescharacteristic
202C2×Q8×C17—28no—
203C2×Q8×C17C2418yes—
204C22×C4×C17—24no—
205C22×C4×C17C2414yes—
206C22×C4×C17C2414yes—
207C22×C4×C17C2411yescharacteristic
208C22×C4×C17C2414yes—
209C22×C4×C17C2412yes—
210C22×C4×C17C2412yes—
211C22×C4×C17C2411yescharacteristic
212C2×C22⋊D17—24no—
213C2×C22⋊D17—24no—
214C2×C22⋊D17C2414yes—
215C2×C22⋊D17C2414yes—
216C22×Dic17—28no—
217C22×Dic17C2414yes—
218C22×Dic17C2411yescharacteristic
219C22×Dic17C2414yes—
220C22×Dic17C2418yes—
221C22×Dic17C2412yes—
222C22×Dic17C2411yescharacteristic
223C22×Dic17C2412yes—
224Q8×D17—264no—
225#63252—232no—
226C2×D68—24no—
227C2×D68C2414yes—
228C2×C4×D17—216no—
229C2×C4×D17—24no—
230C2×C4×D17—28no—
231C2×C4×D17—28no—
232C2×C4×D17#4118yes—
233C2×C4×D17C2414yes—
234C2×C4×D17C24116yes—
235C2×C4×D17C2418yes—
236C2×C4×D17C2418yes—
237C2×C4×D17C2414yes—
238C2×Dic34—28no—
239C2×Dic34—24no—
240C2×Dic34—216no—
241C2×Dic34—216no—
242C2×Dic34C2414yes—
243C2×Dic34C2418yes—
244C2×Dic34C24116yes—
245C2×Dic34C24116yes—
246C4⋊C4×C17C24116yes—
247C4⋊C4×C17C2418yes—
248C4⋊C4×C17C24116yes—
249C4⋊C4×C17C2418yes—
250C4⋊C4×C17C24116yes—
251C4⋊C4×C17C24116yes—
252C22⋊C4×C17C24116yes—
253C22⋊C4×C17C2418yes—
254C42×C17C24116yes—
255C42×C17C2414yes—
256C42×C17C2414yes—
257C22⋊Dic17C24116yes—
258#63227C2418yes—
259#63227C2418yes—
260#63227C24116yes—
261#63227C24116yes—
262#63227C24116yes—
263C4⋊Dic17C2418yes—
264C4⋊Dic17C24116yes—
265C4⋊Dic17C24116yes—
266C4⋊Dic17C24116yes—
267#63225C24116yes—
268#63225C2418yes—
269#63225C24116yes—
270#63225C24116yes—
271#63225C24116yes—
272#63225C24116yes—
273#63225C24116yes—
274#63225C24116yes—
275#63225C2418yes—
276#63225C24116yes—
277C4×Dic17C2418yes—
278C4×Dic17C24116yes—
279C4×Dic17C24116yes—
280C4×Dic17C24116yes—
281C4×Dic17C2414yes—
282C4×Dic17C2418yes—
283C4×Dic17C2414yes—
284C4×Dic17C24116yes—
285C4×Dic17C2418yes—
286C2×#3509—171nomaximal, Sylow
287C23×C17—22no—
288C23×C17—24no—
289C23×C17C2512yes—
290C23×C17C2511yescharacteristic
291C22×D17—24no—
292C22×D17—22no—
293C22×D17—24no—
294C22×D17C2×#4114yes—
295C22×D17C2512yes—
296C22×D17C2512yes—
297Q8×C17—216no—
298C2×C4×C17—28no—
299C2×C4×C17—22no—
300C2×C4×C17—28no—
301C2×C4×C17—24no—
302C2×C4×C17—24no—
303C2×C4×C17—28no—
304C2×C4×C17C2×#4114yes—
305C2×C4×C17C2514yes—
306C2×C4×C17C2518yes—
307C2×C4×C17C2514yes—
308C2×C4×C17C2518yes—
309C2×C4×C17C2512yes—
310C2×C4×C17C2512yes—
311C22⋊D17—28no—
312C22⋊D17—28no—
313C2×Dic17—28no—
314C2×Dic17—22no—
315C2×Dic17—28no—
316C2×Dic17—24no—
317C2×Dic17—216no—
318C2×Dic17C2×#4114yes—
319C2×Dic172−1+418yes—
320C2×Dic17C2518yes—
321C2×Dic17C2518yes—
322C2×Dic17C2512yes—
323C2×Dic17C2514yes—
324C2×Dic17C2512yes—
325C2×Dic17C2514yes—
326D68—28no—
327C4×D17—232no—
328C4×D17—28no—
329C4×D17—216no—
330C4×D17—216no—
331C4×D17C2×#41116yes—
332Dic34—216no—
333Dic34—28no—
334Dic34—232no—
335Dic34—232no—
336#3509—1732no—
337C2×#557—174no—
338C2×#556—174no—
339C2×#552—174no—
340C2×#552—174no—
341C2×#541—171no—
342C2×#541—171no—
343C2×#541—171no—
344C2×#541D1711yescharacteristic, complemented
345C2×#536—172no—
346C2×#533—171no—
347C2×#533—172no—
348C2×#533—172no—
349C22×C4⋊Q8—171no—
350C2×#519—172no—
351C2×C4×#41—171no—
352C22×C17—22no—
353C22×C17—24no—
354C22×C17—44no—
355C22×C17C22×#4112yes—
356C22×C17C2×2−1+414yes—
357C22×C17C2611yescharacteristic
358C2×D17—24no—
359C2×D17—28no—
360C2×D17—22no—
361C2×D17—24no—
362C2×D17—44no—
363C2×D17C22×#4114yes—
364C4×C17—28no—
365C4×C17—22no—
366C4×C17—28no—
367C4×C17—24no—
368C4×C17—24no—
369C4×C17C22×#4114yes—
370Dic17—28no—
371Dic17—22no—
372Dic17—28no—
373Dic17—24no—
374Dic17C22×#4114yes—
375Dic17C2×2−1+418yes—
376C22×#41—171no—
377C23×Q8—172no—
378#557—1764no—
379#556—1764no—
380#552—1764no—
381#552—1764no—
382#541—1716no—
383#541—1716no—
384#541—1716no—
385#541C2×D17116yescomplemented
386#536—1732no—
387#533—1716no—
388#533—1732no—
389#533—1732no—
390C2×C4⋊Q8—172no—
391C2×C4⋊Q8—1716no—
392C2×C4⋊Q8—174no—
393C2×C4⋊Q8—172no—
394C2×C4⋊Q8—174no—
395C2×C4⋊Q8—171no—
396C2×C4⋊Q8C2×D1711yescharacteristic
397C2×#126—174no—
398C2×#126—174no—
399C2×#126—174no—
400C2×#126C2×D1714yes—
401C2×#125—174no—
402C2×#125—174no—
403C2×#125—174no—
404C2×#125—174no—
405C2×#125—174no—
406C2×#125—171no—
407C2×#125C2×D1711yescharacteristic
408C2×#125C2×D1714yes—
409C2×#124—174no—
410C2×#123—174no—
411C2×#123—174no—
412C2×C22⋊Q8—172no—
413C2×C22⋊Q8—172no—
414C2×C22⋊Q8—174no—
415C2×C22⋊Q8—174no—
416C2×C22⋊Q8—172no—
417C2×C22⋊Q8—174no—
418C2×C22⋊Q8C2×D1712yes—
419#519—1732no—
420C4×#41—1716no—
421C2×C4×Q8—172no—
422C2×C4×Q8—172no—
423C2×C4×Q8—172no—
424C2×C4×Q8—174no—
425C2×C4×Q8—174no—
426C2×C4×Q8—174no—
427C2×C4×Q8—172no—
428C2×C4×Q8—174no—
429C2×C4×Q8—174no—
430C2×C4×Q8C2×D1712yes—
431C2×C4×D4—172no—
432C2×C4×D4—172no—
433C2×C4×D4—172no—
434C2×#117—172no—
435C2×#117—174no—
436C2×#117—174no—
437C2×#117—171no—
438C2×#117—171no—
439C2×#117—174no—
440C2×#117—174no—
441C2×#117C2×D1711yescharacteristic
442C22×C4⋊C4—174no—
443C22×C42—171no—
444C22×C42—171no—
445C22×C42—171no—
446C2×C17—42no—
447C2×C17#350914yescomplemented
448C2×C17C23×#4111yescharacteristic
449C2×C17C22×2−1+412yes—
450D17—24no—
451D17—42no—
452C2×#41—178no—
453C2×#41—348no—
454C22×Q8—1716no—
455C22×Q8—174no—
456C22×Q8—172no—
457C22×Q8—174no—
458C22×Q8—171no—
459C22×Q8—3416no—
460C22×Q8C22×D1712yes—
461C22×D4—171no—
462C22×D4—171no—
463C22×D4—171no—
464C23×C4—171no—
465C23×C4—172no—
466C23×C4—174no—
467C23×C4—172no—
468C23×C4—172no—
469C23×C4—171no—
470C23×C4C22×D1711yescharacteristic
471C4⋊Q8—1716no—
472C4⋊Q8—1732no—
473C4⋊Q8—1716no—
474C4⋊Q8—1732no—
475C4⋊Q8—178no—
476C4⋊Q8C22×D1718yes—
477#126—1732no—
478#126—1732no—
479#126—1732no—
480#126C22×D17132yes—
481#125—1732no—
482#125—1732no—
483#125—1732no—
484#125—1732no—
485#125—1732no—
486#125—178no—
487#125C22×D1718yes—
488#125C22×D17132yes—
489#124—1732no—
490#123—1732no—
491#123—1732no—
492C22⋊Q8—1716no—
493C22⋊Q8—1716no—
494C22⋊Q8—1716no—
495C22⋊Q8—1732no—
496C22⋊Q8—1732no—
497C22⋊Q8—1732no—
498C22⋊Q8C22×D17116yes—
499C4×Q8—1716no—
500C4×Q8—1716no—
501C4×Q8—1716no—
502C4×Q8—1732no—
503C4×Q8—1732no—
504C4×Q8—1732no—
505C4×Q8—1716no—
506C4×Q8—1732no—
507C4×Q8—1732no—
508C4×Q8C22×D17116yes—
509C4×D4—1716no—
510C4×D4—1716no—
511C4×D4—1716no—
512#117—1716no—
513#117—1732no—
514#117—1732no—
515#117—178no—
516#117—178no—
517#117—1732no—
518#117—1732no—
519#117C22×D1718yes—
520C2×C4⋊C4—174no—
521C2×C4⋊C4—174no—
522C2×C4⋊C4—174no—
523C2×C4⋊C4—174no—
524C2×C4⋊C4—172no—
525C2×C4⋊C4—172no—
526C2×C4⋊C4—172no—
527C2×C4⋊C4—174no—
528C2×C4⋊C4—174no—
529C2×C4⋊C4—174no—
530C2×C4⋊C4—174no—
531C2×C4⋊C4—174no—
532C2×C4⋊C4—174no—
533C2×C4⋊C4—174no—
534C2×C4⋊C4—1732no—
535C2×C4⋊C4C22×D1714yes—
536C2×C4⋊C4C22×D1712yes—
537C2×C4⋊C4C22×D1714yes—
538C2×C4⋊C4C22×D1712yes—
539C2×C4⋊C4C22×D1714yes—
540C2×C4⋊C4C22×D1714yes—
541C2×C22⋊C4—174no—
542C2×C22⋊C4—172no—
543C2×C22⋊C4—174no—
544C2×C22⋊C4—172no—
545C2×C22⋊C4—174no—
546C2×C22⋊C4—174no—
547C2×C22⋊C4C22×D1714yes—
548C2×C22⋊C4C22×D1712yes—
549C2×C42—171no—
550C2×C42—174no—
551C2×C42—174no—
552C2×C42—174no—
553C2×C42—174no—
554C2×C42—172no—
555C2×C42—172no—
556C2×C42—172no—
557C2×C42—178no—
558C2×C42—171no—
559C2×C42—178no—
560C2×C42—178no—
561C2×C42C22×D1714yes—
562C2×C42C22×D1711yescharacteristic
563C2×C42C22×D1711yescharacteristic
564C17C2×#350911yescharacteristic, complemented, Sylow
565C24—171no—
566C24—171no—
567C24C23×D1711yescharacteristic
568#41—3432no—
569C2×Q8—28no—
570C2×Q8—1716no—
571C2×Q8—178no—
572C2×Q8—1716no—
573C2×Q8—174no—
574C2×Q8—3416no—
575C2×Q8—3416no—
576C2×Q8—344no—
577C2×Q8—3464no—
578C2×Q8—348no—
579C2×Q8C23×D1718yes—
580C2×D4—174no—
581C2×D4—174no—
582C2×D4—174no—
583C2×D4—344no—
584C2×D4—344no—
585C2×D4—344no—
586C22×C4—24no—
587C22×C4—171no—
588C22×C4—172no—
589C22×C4—178no—
590C22×C4—174no—
591C22×C4—178no—
592C22×C4—172no—
593C22×C4—174no—
594C22×C4—174no—
595C22×C4—171no—
596C22×C4—178no—
597C22×C4—178no—
598C22×C4—174no—
599C22×C4—1716no—
600C22×C4—348no—
601C22×C4—348no—
602C22×C4—3416no—
603C22×C4—348no—
604C22×C4—344no—
605C22×C4C23×D1714yes—
606C22×C4C23×D1712yes—
607C22×C4C23×D1714yes—
608C22×C4C23×D1711yescharacteristic
609C22×C4C23×D1712yes—
610C22×C4C23×D1714yes—
611C22×C4C23×D1711yescharacteristic
612C4⋊C4—1716no—
613C4⋊C4—1716no—
614C4⋊C4—1716no—
615C4⋊C4—1716no—
616C4⋊C4—178no—
617C4⋊C4—178no—
618C4⋊C4—178no—
619C4⋊C4—1716no—
620C4⋊C4—1716no—
621C4⋊C4—1716no—
622C4⋊C4—1716no—
623C4⋊C4—1716no—
624C4⋊C4—1716no—
625C4⋊C4—1716no—
626C4⋊C4C23×D17116yes—
627C4⋊C4C23×D1718yes—
628C4⋊C4C23×D17116yes—
629C4⋊C4C23×D1718yes—
630C4⋊C4C23×D17116yes—
631C4⋊C4C23×D17116yes—
632C22⋊C4—1716no—
633C22⋊C4—178no—
634C22⋊C4—1716no—
635C22⋊C4—178no—
636C22⋊C4—1716no—
637C22⋊C4—1716no—
638C22⋊C4C23×D17116yes—
639C22⋊C4C23×D1718yes—
640C42—174no—
641C42—174no—
642C42—178no—
643C42—178no—
644C42—178no—
645C42—1716no—
646C42—1716no—
647C42—1716no—
648C42—1716no—
649C42C23×D1714yes—
650C42C23×D1714yes—
651C42C23×D17116yes—
652C23—22no—
653C23—24no—
654C23—174no—
655C23—172no—
656C23—172no—
657C23—344no—
658C23—342no—
659C23—344no—
660C23C24×D1712yes—
661C23C24×D1711yescharacteristic
662Q8—216no—
663Q8—3432no—
664Q8—348no—
665Q8—3432no—
666Q8—3416no—
667D4—348no—
668D4—348no—
669D4—348no—
670C2×C4—22no—
671C2×C4—28no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—28no—
675C2×C4—28no—
676C2×C4—174no—
677C2×C4—178no—
678C2×C4—172no—
679C2×C4—174no—
680C2×C4—1716no—
681C2×C4—174no—
682C2×C4—178no—
683C2×C4—178no—
684C2×C4—172no—
685C2×C4—3416no—
686C2×C4—3416no—
687C2×C4—3432no—
688C2×C4—3416no—
689C2×C4—342no—
690C2×C4—348no—
691C2×C4—344no—
692C2×C4—348no—
693C2×C4—348no—
694C2×C4#41×D1714yes—
695C2×C4C24×D1714yes—
696C2×C4C24×D1718yes—
697C2×C4C24×D1712yes—
698C2×C4C24×D1714yes—
699C2×C4C24×D1718yes—
700C2×C4C24×D1712yes—
701C22—22no—
702C22—24no—
703C22—44no—
704C22—174no—
705C22—348no—
706C22—344no—
707C22—342no—
708C22—344no—
709C22—684no—
710C22C2×#41×D1712yes—
711C222−1+4×D1714yes—
712C22C25×D1711yescharacteristic
713C4—22no—
714C4—28no—
715C4—24no—
716C4—24no—
717C4—28no—
718C4—174no—
719C4—178no—
720C4—342no—
721C4—348no—
722C4—344no—
723C4—348no—
724C4C2×#41×D1714yes—
725C2—42no—
726C2—344no—
727C2—682no—
728C2#1454266614yesdirect product factor
729C2C22×#41×D1711yescharacteristic
730C2C2×2−1+4×D1712yes—
subgroupG/H
centerC23C24×D17
commutator, cosocleC22×C17C26
FrattiniC22C25×D17
FittingC2×C17×#541C2
socleC23×C17C25
prime radicalC22×#63252C22
hypercenterC2×#541D17
hypocenterC17C2×#3509
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#541

Complements

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

NH ≅ G/Ntype
1. #14542666C2direct (N × H)
2. C2×#11763536C2semidirect
3. C2×#11763526C2semidirect
4. C2×#11763495C2semidirect
5. C2×#11763491C2semidirect
6. C2×#11763422C2semidirect
7. C2×#11763421C2semidirect
8. C2×#11763420C2semidirect
10. C2×#11763365C2semidirect
11. C2×#11763363C2semidirect
12. C2×#11763361C2semidirect
13. C2×C4⋊Q8×D17C2semidirect
14. C2×#11763285C2semidirect
16. C2×C17×#541C2semidirect
19. #11763536C22semidirect
20. #11763526C22semidirect
21. #11763495C22semidirect
22. #11763491C22semidirect
23. #11763422C22semidirect
24. #11763421C22semidirect
25. #11763420C22semidirect
27. #11763365C22semidirect
28. #11763363C22semidirect
29. #11763361C22semidirect
35. C4⋊Q8×D17C22semidirect
54. #11763285C22semidirect
79. C17×#541C22semidirect
344. C2×#541D17semidirect
385. #541C2×D17semidirect
447. C2×C17#3509semidirect
564. C17C2×#3509semidirect
728. C2#14542666direct (N × H)

Maximal subgroups

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

subgroupindex
#145426662
C2×#117635362
C2×#117635262
C2×#117634952
C2×#117634912
C2×#117634222
C2×#117634212
C2×#117634202
C2×#117633822
C2×#117633652
C2×#117633632
C2×#117633612
C2×C4⋊Q8×D172
C2×#117632852
C2×#117632772
C2×C17×#5412
C2×#350917