Finite Group Databasebeta

← C2×#14540910 #17911042

Subgroups — C2×#14540910 #17911042

Order 4352.

2178 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763499C211yesmaximal, characteristic, complemented
2#14540910C2116yesmaximal, direct product factor
3C2×#11763173C211yesmaximal, characteristic, complemented
4C2×#11763125C211yesmaximal, characteristic, complemented
5C2×#11763130C211yesmaximal, characteristic, complemented
6C2×#11763116C211yesmaximal, characteristic, complemented
7C2×#11763053C211yesmaximal, characteristic, complemented
8C2×#11763036C211yesmaximal, characteristic, complemented
9C2×#11763006C211yesmaximal, characteristic, complemented
10C2×#11762971C211yesmaximal, characteristic, complemented
11C2×#11762971C211yesmaximal, characteristic, complemented
12C2×#11762914C211yesmaximal, characteristic, complemented
13C2×#11762881C211yesmaximal, characteristic, complemented
14C2×#11762810C211yesmaximal, characteristic, complemented
15C2×#11762805C211yesmaximal, characteristic, complemented
16C2×C17×#550C211yesmaximal, characteristic
17C22×#63231C2211yescharacteristic
18C22×#63229C2211yescharacteristic
19C22×#63229C2211yescharacteristic
20C22×#63223C2211yescharacteristic
21C23×#3622C2211yescharacteristic
22#11763499—24no—
23#11763499C2218yescomplemented
24C2×#10587565—21no—
25C2×#10587556C2211yescharacteristic
26C2×#10587575—21no—
27C2×#10587621—21no—
28C2×#10587610C2211yescharacteristic
29C2×#10587610C2211yescharacteristic
30C2×C4×Dic34C2211yescharacteristic
31C2×#10587612C2211yescharacteristic
32C2×#10587563—21no—
33C22×C4⋊Dic17C2211yescharacteristic
34#11763173C2218yescomplemented
35#11763130C2218yescomplemented
36#11763125C2218yescomplemented
37#11763116C2218yescomplemented
38#11763053C2218yescomplemented
39#11763036C2218yescomplemented
40#11763006C2218yescomplemented
41#11762971C2218yescomplemented
42#11762971C2218yescomplemented
43#11762914C2218yescomplemented
44#11762881C2218yescomplemented
45C2×#10587478C2211yescharacteristic
46C2×#10587479C2211yescharacteristic
47C2×#10587479C2211yescharacteristic
48C2×C4⋊#3622C2211yescharacteristic
49#11762810C2218yescomplemented
50#11762805C2218yescomplemented
51C2×#10587506C2211yescharacteristic
52C2×#10587506C2211yescharacteristic
53C2×#10587506C2211yescharacteristic
54C2×#10587481C2211yescharacteristic
55C2×#10587503C2211yescharacteristic
56C2×#10587503C2211yescharacteristic
57C2×#10587503C2211yescharacteristic
58C2×#10587503C2211yescharacteristic
59C2×#10587503C2211yescharacteristic
60C2×#10587503C2211yescharacteristic
61C2×C22⋊#3622C2211yescharacteristic
62C2×C22⋊#3622C2211yescharacteristic
63C2×#10587474C2211yescharacteristic
64C22×#41×C17C2211yescharacteristic
65C22×#41×C17C2211yescharacteristic
66C17×#550—24no—
67C17×#550C2218yes—
68C2×C17×#127—21no—
69C2×C17×#127C2211yescharacteristic
70C2×C17×#121—21no—
71C2×C17×#121—21no—
72C2×C17×#121C2211yescharacteristic
73C2×C17×#121C2211yescharacteristic
74C2×C4×Q8×C17C2211yescharacteristic
75C2×C4×D4×C17—21no—
76C2×C4×D4×C17C2211yescharacteristic
77C2×#41×C17—22no—
78C2×#41×C17—22no—
79C2×#41×C17—24no—
80C2×#41×C17—24no—
81C2×#41×C17—42no—
82C2×#41×C17—42no—
83C2×#41×C17C2314yes—
84C2×#41×C17C2314yes—
85C22×Q8×C17C2311yescharacteristic
86C22×D4×C17—21no—
87C22×D4×C17—21no—
88C22×D4×C17—21no—
89C22×D4×C17—21no—
90C22×D4×C17—21no—
91C22×D4×C17—21no—
92C22×D4×C17D411yescharacteristic
93C22×D4×C17C2311yescharacteristic
94C22×D4×C17C2311yescharacteristic
95C23×C4×C17—21no—
96C23×C4×C17—21no—
97C23×C4×C17C2311yescharacteristic
98C23×C4×C17C2311yescharacteristic
99C23×Dic17—21no—
100C22×Dic34C2311yescharacteristic
101C17×#127—28no—
102C17×#127—22no—
103C17×#127C2314yes—
104C17×#121—22no—
105C17×#121—22no—
106C17×#121—28no—
107C17×#121—28no—
108C17×#121C2314yes—
109C17×#121C2314yes—
110C4×Q8×C17—22no—
111C4×Q8×C17C2314yes—
112C4×D4×C17—28no—
113C4×D4×C17D414yes—
114C4×D4×C17C2314yes—
115C2×C4⋊C4×C17—21no—
116C2×C4⋊C4×C17D411yescharacteristic
117C2×C4⋊C4×C17C2311yescharacteristic
118C2×C22⋊C4×C17—21no—
119C2×C22⋊C4×C17—21no—
120C2×C22⋊C4×C17D411yescharacteristic
121C2×C22⋊C4×C17D411yescharacteristic
122C2×C42×C17—21no—
123C2×C42×C17C2311yescharacteristic
124C2×C22⋊Dic17—21no—
125C2×C22⋊Dic17—21no—
126C2×C22⋊Dic17—21no—
127C2×#63231—24no—
128C2×#63231C2314yes—
129#10587621—28no—
130C2×#63229—42no—
131C2×#63229—42no—
132C2×#63229C2314yes—
133C2×#63229C2314yes—
134#10587612—22no—
135#10587612C2314yes—
136C2×C4⋊Dic17—22no—
137C2×C4⋊Dic17—21no—
138C2×C4⋊Dic17C2314yes—
139C2×C4⋊Dic17C2311yescharacteristic
140C2×C4⋊Dic17C2311yescharacteristic
141C2×C4⋊Dic17C2311yescharacteristic
142#10587610—22no—
143#10587610—22no—
144#10587610C2314yes—
145#10587610C2314yes—
146C2×#63225—21no—
147C2×#63225—21no—
148C2×#63225—21no—
149C2×#63225—21no—
150C2×#63225—21no—
151C2×C4×Dic17—21no—
152C2×C4×Dic17—21no—
153C2×#63223—42no—
154C2×#63223C2314yes—
155C22×#3622—42no—
156C22×#3622C2311yescharacteristic
157C22×#3622C2311yescharacteristic
158C22×#3622C2311yescharacteristic
159C22×#3622C2311yescharacteristic
160C22×#3622C2314yes—
161#10587575—28no—
162#10587565—28no—
163#10587563—28no—
164#10587556—22no—
165#10587556C2314yes—
166C4×Dic34—22no—
167C4×Dic34C2314yes—
168#10587506C2314yes—
169#10587506C2314yes—
170#10587506C2314yes—
171#10587503C2314yes—
172#10587503C2314yes—
173#10587503C2314yes—
174#10587503C2314yes—
175#10587503C2314yes—
176#10587503C2314yes—
177C22⋊#3622C2314yes—
178C22⋊#3622C2314yes—
179#10587481C2314yes—
180#10587479C2314yes—
181#10587479C2314yes—
182#10587478C2314yes—
183C4⋊#3622C2314yes—
184#10587474C2314yes—
185C24×C17—21no—
186C24×C17—21no—
187C24×C17C2×D411yescharacteristic
188C24×C17C2×D411yescharacteristic
189#41×C17—28no—
190#41×C17—28no—
191#41×C17—44no—
192#41×C17—44no—
193#41×C17—48no—
194#41×C17—48no—
195C2×Q8×C17—21no—
196C2×Q8×C17—22no—
197C2×Q8×C17#4114yes—
198C2×Q8×C17C2412yes—
199C2×D4×C17—24no—
200C2×D4×C17—24no—
201C2×D4×C17—24no—
202C2×D4×C17—24no—
203C2×D4×C17—24no—
204C2×D4×C17—21no—
205C2×D4×C17—21no—
206C2×D4×C17—24no—
207C2×D4×C17—22no—
208C2×D4×C17—22no—
209C2×D4×C17—22no—
210C2×D4×C17—22no—
211C2×D4×C17—42no—
212C2×D4×C17—44no—
213C2×D4×C17—44no—
214C2×D4×C17—44no—
215C2×D4×C17—82no—
216C2×D4×C17—82no—
217C2×D4×C17—82no—
218C2×D4×C17C2×D414yes—
219C2×D4×C17C2412yes—
220C2×D4×C17C2412yes—
221C22×C4×C17—21no—
222C22×C4×C17—22no—
223C22×C4×C17—22no—
224C22×C4×C17—22no—
225C22×C4×C17—22no—
226C22×C4×C17—21no—
227C22×C4×C17—24no—
228C22×C4×C17—24no—
229C22×C4×C17—44no—
230C22×C4×C17—44no—
231C22×C4×C17C2×D411yescharacteristic
232C22×C4×C17C2×D411yescharacteristic
233C22×C4×C17C2×D412yes—
234C22×C4×C17C2×D412yes—
235C22×C4×C17C2×D411yescharacteristic
236C22×C4×C17C2×D411yescharacteristic
237C22×C4×C17C2412yes—
238C22×C4×C17C2412yes—
239C22×C4×C17C2411yescharacteristic
240C22×Dic17—21no—
241C22×Dic17—24no—
242C22×Dic17—21no—
243C22×Dic17—21no—
244C22×Dic17—21no—
245C22×Dic17—44no—
246C2×Dic34—22no—
247C2×Dic34—22no—
248C2×Dic34—21no—
249C2×Dic34C2412yes—
250C4⋊C4×C17—24no—
251C4⋊C4×C17—21no—
252C4⋊C4×C17C2×D414yes—
253C4⋊C4×C17C2412yes—
254C22⋊C4×C17—24no—
255C22⋊C4×C17—24no—
256C22⋊C4×C17C2×D414yes—
257C22⋊C4×C17C2×D414yes—
258C42×C17—24no—
259C42×C17C2×D412yes—
260C42×C17C2412yes—
261C22⋊Dic17—24no—
262C22⋊Dic17—24no—
263C22⋊Dic17—24no—
264#63231—28no—
265#63229—44no—
266#63229—44no—
267C4⋊Dic17—21no—
268C4⋊Dic17—21no—
269C4⋊Dic17—21no—
270C4⋊Dic17—24no—
271C4⋊Dic17C2412yes—
272C4⋊Dic17C2412yes—
273C4⋊Dic17C2412yes—
274#63225—24no—
275#63225—24no—
276#63225—24no—
277#63225—24no—
278#63225—24no—
279C4×Dic17—24no—
280C4×Dic17—24no—
281#63223—44no—
282C2×#3622—22no—
283C2×#3622—22no—
284C2×#3622—22no—
285C2×#3622—22no—
286C2×#3622—44no—
287C2×#3622C2412yes—
288C2×#3622C2412yes—
289C2×#3622C2412yes—
290C2×#3622C2412yes—
291C2×#3317—171nomaximal, Sylow
292C23×C17—22no—
293C23×C17—22no—
294C23×C17—22no—
295C23×C17—22no—
296C23×C17—22no—
297C23×C17—22no—
298C23×C17—22no—
299C23×C17—22no—
300C23×C17—42no—
301C23×C17—42no—
302C23×C17—42no—
303C23×C17—42no—
304C23×C17—42no—
305C23×C17—42no—
306C23×C17C22×D412yes—
307C23×C17C22×D412yes—
308C23×C17C22×D411yescharacteristic
309Q8×C17—24no—
310Q8×C17—22no—
311Q8×C17C2×#4114yes—
312D4×C17—22no—
313D4×C17—22no—
314D4×C17—22no—
315D4×C17—22no—
316D4×C17—44no—
317D4×C17—48no—
318D4×C17—48no—
319D4×C17—48no—
320D4×C17—42no—
321D4×C17—42no—
322D4×C17—84no—
323D4×C17—84no—
324D4×C17—84no—
325C2×C4×C17—22no—
326C2×C4×C17—22no—
327C2×C4×C17—24no—
328C2×C4×C17—22no—
329C2×C4×C17—22no—
330C2×C4×C17—22no—
331C2×C4×C17—24no—
332C2×C4×C17—24no—
333C2×C4×C17—22no—
334C2×C4×C17—22no—
335C2×C4×C17—22no—
336C2×C4×C17—22no—
337C2×C4×C17—22no—
338C2×C4×C17—48no—
339C2×C4×C17—48no—
340C2×C4×C17—42no—
341C2×C4×C17C22×D412yes—
342C2×C4×C17C22×D412yes—
343C2×C4×C17C22×D412yes—
344C2×C4×C17C22×D412yes—
345C2×C4×C17C22×D411yescharacteristic
346C2×C4×C17C2×#4112yes—
347C2×C4×C17H(5,𝔽2)12yes—
348C2×C4×C17C2511yescharacteristic
349C2×Dic17—22no—
350C2×Dic17—22no—
351C2×Dic17—22no—
352C2×Dic17—22no—
353C2×Dic17—48no—
354C2×Dic17—42no—
355C2×Dic17—42no—
356C2×Dic17—42no—
357C2×Dic17—42no—
358Dic34—22no—
359Dic34—22no—
360Dic34—42no—
361#3622—22no—
362#3622—22no—
363#3622—22no—
364#3622—22no—
365C2×#552—171no—
366C2×#550D1711yescharacteristic
367#3317—1716no—
368C2×#490—171no—
369C2×#481—171no—
370C2×#482—171no—
371C2×#479—171no—
372C2×#468—171no—
373C2×#465—171no—
374C2×#460—171no—
375C2×#452—171no—
376C2×#452—171no—
377C2×#441—171no—
378C2×#435—171no—
379C2×#417—171no—
380C2×#416—171no—
381C22×C17—22no—
382C22×C17—22no—
383C22×C17—22no—
384C22×C17—22no—
385C22×C17—22no—
386C22×C17—22no—
387C22×C17—44no—
388C22×C17—44no—
389C22×C17—42no—
390C22×C17—42no—
391C22×C17—42no—
392C22×C17—42no—
393C22×C17—42no—
394C22×C17—42no—
395C22×C17—84no—
396C22×C17—84no—
397C22×C17#54612yes—
398C22×C17#57512yes—
399C22×C17#57712yes—
400C22×C17C23×D411yescharacteristic
401C4×C17—22no—
402C4×C17—22no—
403C4×C17—24no—
404C4×C17—22no—
405C4×C17—22no—
406C4×C17—42no—
407C4×C17#54612yes—
408C4×C17C22×#4111yescharacteristic
409C4×C17C2×H(5,𝔽2)11yescharacteristic
410Dic17—42no—
411Dic17—42no—
412Dic17—42no—
413Dic17—42no—
414C22×#41C2×D1711yescharacteristic
415C22×#41C2×D1711yescharacteristic
416C22×Q16—171no—
417C22×SD16—171no—
418C22×SD16—171no—
419C22×M16—171no—
420C23×C8—171no—
421#552—178no—
422#552—344no—
423#550—24no—
424#550C2×D1718yes—
425C2×#127—21no—
426C2×#127C2×D1711yescharacteristic
427C2×#126—341no—
428C2×#125—171no—
429C2×#125—341no—
430C2×#123—341no—
431C2×C22⋊Q8—171no—
432C2×C22⋊Q8—171no—
433C2×#121—21no—
434C2×#121—21no—
435C2×#121C2×D1711yescharacteristic
436C2×#121C2×D1711yescharacteristic
437C2×C4×Q8—171no—
438C2×C4×Q8C2×D1711yescharacteristic
439C2×C4×D4—21no—
440C2×C4×D4C2×D1711yescharacteristic
441C2×#117—171no—
442C2×#117—341no—
443C22×C4⋊C4—171no—
444#490—178no—
445#482—178no—
446#481—178no—
447#479—178no—
448#468—178no—
449#465—178no—
450#460—178no—
451#452—178no—
452#452—178no—
453#441—178no—
454#435—178no—
455C2×#107—171no—
456C2×#106—171no—
457C2×#106—171no—
458C2×C4⋊C8—171no—
459#417—178no—
460#416—178no—
461C2×#103—171no—
462C2×#103—171no—
463C2×#103—171no—
464C2×#103—171no—
465C2×#102—171no—
466C2×#102—171no—
467C2×#102—171no—
468C2×#102—171no—
469C2×#102—171no—
470C2×#102—171no—
471C2×C22⋊C8—171no—
472C2×C22⋊C8—171no—
473C2×#97—171no—
474C2×C17—42no—
475C2×C17—42no—
476C2×C17—82no—
477C2×C17—82no—
478C2×C17#331714yescomplemented
479C2×C17C2×#54611yescharacteristic
480C2×C17C2×#57511yescharacteristic
481C2×C17C2×#57711yescharacteristic
482C2×#41—22no—
483C2×#41—22no—
484C2×#41—24no—
485C2×#41—24no—
486C2×#41—42no—
487C2×#41—42no—
488C2×#41C22×D1714yes—
489C2×#41C22×D1714yes—
490C22×Q8—171no—
491C22×Q8C22×D1711yescharacteristic
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4C22⋊D1711yescharacteristic
499C22×D4C22×D1711yescharacteristic
500C22×D4C22×D1711yescharacteristic
501C23×C4—21no—
502C23×C4—21no—
503C23×C4—341no—
504C23×C4C22×D1711yescharacteristic
505C23×C4C22×D1711yescharacteristic
506C2×Q16—174no—
507C2×Q16—344no—
508C2×SD16—174no—
509C2×SD16—174no—
510C2×SD16—682no—
511C2×SD16—682no—
512C2×M16—174no—
513C2×M16—682no—
514C22×C8—171no—
515C22×C8—171no—
516C22×C8—171no—
517C22×C8—171no—
518C22×C8—174no—
519C22×C8—682no—
520#127—28no—
521#127—22no—
522#127C22×D1714yes—
523#126—348no—
524#125—174no—
525#125—348no—
526#125—342no—
527#123—348no—
528C22⋊Q8—174no—
529C22⋊Q8—174no—
530C22⋊Q8—342no—
531C22⋊Q8—342no—
532#121—22no—
533#121—22no—
534#121—28no—
535#121—28no—
536#121C22×D1714yes—
537#121C22×D1714yes—
538C4×Q8—22no—
539C4×Q8—174no—
540C4×Q8—342no—
541C4×Q8C22×D1714yes—
542C4×D4—28no—
543C4×D4C22⋊D1714yes—
544C4×D4C22×D1714yes—
545#117—174no—
546#117—342no—
547#117—348no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—171no—
550C2×C4⋊C4—171no—
551C2×C4⋊C4—174no—
552C2×C4⋊C4—171no—
553C2×C4⋊C4—341no—
554C2×C4⋊C4—342no—
555C2×C4⋊C4—341no—
556C2×C4⋊C4—341no—
557C2×C4⋊C4—341no—
558C2×C4⋊C4—341no—
559C2×C4⋊C4—341no—
560C2×C4⋊C4C22⋊D1711yescharacteristic
561C2×C4⋊C4C22×D1711yescharacteristic
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—341no—
565C2×C22⋊C4—341no—
566C2×C22⋊C4—341no—
567C2×C22⋊C4C22⋊D1711yescharacteristic
568C2×C22⋊C4C22⋊D1711yescharacteristic
569C2×C42—21no—
570C2×C42—341no—
571C2×C42—341no—
572C2×C42C22×D1711yescharacteristic
573#107—174no—
574#106—174no—
575#106—174no—
576C4⋊C8—174no—
577#103—174no—
578#103—174no—
579#103—174no—
580#103—174no—
581#102—174no—
582#102—174no—
583#102—174no—
584#102—174no—
585#102—174no—
586#102—174no—
587C22⋊C8—174no—
588C22⋊C8—174no—
589#97—174no—
590C17C2×#331711yescharacteristic, complemented, Sylow
591C24—21no—
592C24—21no—
593C24C2×C22⋊D1711yescharacteristic
594C24C2×C22⋊D1711yescharacteristic
595#41—28no—
596#41—28no—
597#41—44no—
598#41—44no—
599#41—48no—
600#41—48no—
601C2×Q8—22no—
602C2×Q8—21no—
603C2×Q8—172no—
604C2×Q8—341no—
605C2×Q8—342no—
606C2×Q8—342no—
607C2×Q8#6325414yes—
608C2×Q8C23×D1712yes—
609C2×D4—24no—
610C2×D4—24no—
611C2×D4—24no—
612C2×D4—24no—
613C2×D4—22no—
614C2×D4—22no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—24no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—24no—
621C2×D4—42no—
622C2×D4—44no—
623C2×D4—44no—
624C2×D4—44no—
625C2×D4—82no—
626C2×D4—82no—
627C2×D4—82no—
628C2×D4C2×C22⋊D1714yes—
629C2×D4C23×D1712yes—
630C2×D4C23×D1712yes—
631C22×C4—21no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—21no—
637C22×C4—24no—
638C22×C4—24no—
639C22×C4—44no—
640C22×C4—44no—
641C22×C4—344no—
642C22×C4—341no—
643C22×C4—341no—
644C22×C4—341no—
645C22×C4—341no—
646C22×C4—684no—
647C22×C4C2×C22⋊D1712yes—
648C22×C4C2×C22⋊D1712yes—
649C22×C4C2×C22⋊D1711yescharacteristic
650C22×C4C2×C22⋊D1711yescharacteristic
651C22×C4C2×C22⋊D1711yescharacteristic
652C22×C4C2×C22⋊D1711yescharacteristic
653C22×C4C23×D1712yes—
654C22×C4C23×D1712yes—
655C22×C4C23×D1711yescharacteristic
656Q16—348no—
657SD16—684no—
658SD16—684no—
659M16—684no—
660C2×C8—172no—
661C2×C8—172no—
662C2×C8—172no—
663C2×C8—172no—
664C2×C8—342no—
665C2×C8—342no—
666C2×C8—342no—
667C2×C8—342no—
668C2×C8—684no—
669C4⋊C4—24no—
670C4⋊C4—21no—
671C4⋊C4—172no—
672C4⋊C4—172no—
673C4⋊C4—172no—
674C4⋊C4—341no—
675C4⋊C4—341no—
676C4⋊C4—344no—
677C4⋊C4—341no—
678C4⋊C4—344no—
679C4⋊C4—344no—
680C4⋊C4—344no—
681C4⋊C4—344no—
682C4⋊C4—344no—
683C4⋊C4C2×C22⋊D1714yes—
684C4⋊C4C23×D1712yes—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—344no—
688C22⋊C4—344no—
689C22⋊C4—344no—
690C22⋊C4C2×C22⋊D1714yes—
691C22⋊C4C2×C22⋊D1714yes—
692C42—24no—
693C42—344no—
694C42—344no—
695C42C2×C22⋊D1712yes—
696C42C23×D1712yes—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23C22×C22⋊D1712yes—
712C23C22×C22⋊D1712yes—
713C23C22×C22⋊D1711yescharacteristic
714Q8—22no—
715Q8—24no—
716Q8—342no—
717Q8—342no—
718Q8—682no—
719Q8C2×#6325414yes—
720D4—22no—
721D4—22no—
722D4—22no—
723D4—22no—
724D4—44no—
725D4—48no—
726D4—48no—
727D4—48no—
728D4—42no—
729D4—42no—
730D4—84no—
731D4—84no—
732D4—84no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—22no—
746C2×C4—48no—
747C2×C4—48no—
748C2×C4—42no—
749C2×C4—342no—
750C2×C4—342no—
751C2×C4—342no—
752C2×C4—342no—
753C2×C4—688no—
754C2×C4—682no—
755C2×C4—682no—
756C2×C4—682no—
757C2×C4—682no—
758C2×C4C2×#6325412yes—
759C2×C4#1058769112yes—
760C2×C4C22×C22⋊D1712yes—
761C2×C4C22×C22⋊D1712yes—
762C2×C4C22×C22⋊D1712yes—
763C2×C4C22×C22⋊D1712yes—
764C2×C4C22×C22⋊D1711yescharacteristic
765C2×C4C24×D1711yescharacteristic
766C8—342no—
767C8—342no—
768C8—342no—
769C8—342no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—44no—
777C22—44no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—84no—
785C22—84no—
786C22#1176345312yes—
787C22#1176360712yes—
788C22#1176362012yes—
789C22C23×C22⋊D1711yescharacteristic
790C4—22no—
791C4—22no—
792C4—24no—
793C4—22no—
794C4—22no—
795C4—42no—
796C4—682no—
797C4—682no—
798C4—682no—
799C4—682no—
800C4#1176345312yes—
801C4C22×#6325411yescharacteristic
802C4C2×#1058769111yescharacteristic
803C2—42no—
804C2—42no—
805C2—82no—
806C2—82no—
807C2#1454091014yesdirect product factor
808C2C2×#1176345311yescharacteristic
809C2C2×#1176360711yescharacteristic
810C2C2×#1176362011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
Fitting, prime radicalC2×C17×#550C2
socleC23×C17C22×D4
hypercenterC2×#550D17
hypocenterC17C2×#3317
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C2×#11763499C2semidirect
2. #14540910C2direct (N × H)
3. C2×#11763173C2semidirect
4. C2×#11763125C2semidirect
5. C2×#11763130C2semidirect
6. C2×#11763116C2semidirect
7. C2×#11763053C2semidirect
8. C2×#11763036C2semidirect
9. C2×#11763006C2semidirect
10. C2×#11762971C2semidirect
11. C2×#11762971C2semidirect
12. C2×#11762914C2semidirect
13. C2×#11762881C2semidirect
14. C2×#11762810C2semidirect
15. C2×#11762805C2semidirect
23. #11763499C22semidirect
34. #11763173C22semidirect
35. #11763130C22semidirect
36. #11763125C22semidirect
37. #11763116C22semidirect
38. #11763053C22semidirect
39. #11763036C22semidirect
40. #11763006C22semidirect
41. #11762971C22semidirect
42. #11762971C22semidirect
43. #11762914C22semidirect
44. #11762881C22semidirect
49. #11762810C22semidirect
50. #11762805C22semidirect
478. C2×C17#3317semidirect
590. C17C2×#3317semidirect
807. C2#14540910direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117634992
#145409102
C2×#117631732
C2×#117631252
C2×#117631302
C2×#117631162
C2×#117630532
C2×#117630362
C2×#117630062
C2×#117629712
C2×#117629142
C2×#117628812
C2×#117628102
C2×#117628052
C2×C17×#5502
C2×#331717