Finite Group Databasebeta

← #17054581

Subgroups — #17054581

Order 4352.

1302 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762960C211yesmaximal, characteristic
2C2×#11762906C211yesmaximal, characteristic, complemented
3#14531789C211yesmaximal, characteristic, complemented
4D4×C22⋊Dic17C211yesmaximal, characteristic
5#14529666C211yesmaximal, characteristic, complemented
6#14529478C211yesmaximal, characteristic, complemented
7#14529407C211yesmaximal, characteristic, complemented
8#14529207C211yesmaximal, characteristic, complemented
9#14529136C211yesmaximal, characteristic, complemented
10#14529116C211yesmaximal, characteristic, complemented
11#14529029C211yesmaximal, characteristic, complemented
12#14528972C211yesmaximal, characteristic, complemented
13#14528611C211yesmaximal, characteristic, complemented
14#14528560C211yesmaximal, characteristic, complemented
15C22×C17×#102C211yesmaximal, characteristic
16C22×#63229C2211yescharacteristic
17C22×#63229C2211yescharacteristic
18C2×#10587610C2211yescharacteristic
19C2×#10587573C2211yescharacteristic, complemented
20C2×D4×Dic17C2211yescharacteristic
21C2×D4×Dic17C2211yescharacteristic
22C22×C22⋊Dic17—21no—
23#11762960C418yescomplemented
24#11762906—24no—
25C2×#10587478C2211yescharacteristic, complemented
26C2×#10587478C2211yescharacteristic, complemented
27C2×#10587487C2211yescharacteristic, complemented
28C2×#10587487C2211yescharacteristic, complemented
29C2×#10587503C2211yescharacteristic
30C2×#10587503C2211yescharacteristic
31C2×C22⋊#3622C2211yescharacteristic
32C2×#10587486C2211yescharacteristic, complemented
33C2×#10587486C2211yescharacteristic, complemented
34#11762714C2211yescharacteristic, complemented
35#11762712C2211yescharacteristic
36#11762712C2211yescharacteristic
37#11762705C2211yescharacteristic, complemented
38#11762704—21no—
39#11762690—21no—
40#11762689—21no—
41#11762689—21no—
42#11762682—21no—
43#11762669C2211yescharacteristic
44#11762665—21no—
45C4⋊C4×Dic17C2211yescharacteristic, complemented
46C4×C22⋊Dic17—21no—
47C4×C22⋊Dic17C2211yescharacteristic
48#11762572C2211yescharacteristic, complemented
49#11762572C2211yescharacteristic, complemented
50#11762571C2211yescharacteristic, complemented
51#11762571C2211yescharacteristic, complemented
52#11762563C2211yescharacteristic, complemented
53#11762563C2211yescharacteristic, complemented
54C23×D4×C17C2211yescharacteristic
55C23×C8×C17C2211yescharacteristic
56C22×C4⋊C4×C17C2211yescharacteristic
57C2×C17×#102—24no—
58C2×C17×#102C2211yescharacteristic
59C2×C17×#102C2211yescharacteristic
60C2×C17×#102C2211yescharacteristic
61C2×C17×#102C2211yescharacteristic
62C25×C17—21no—
63C22×D4×C17—22no—
64C22×D4×C17—22no—
65C22×D4×C17—21no—
66C22×D4×C17—22no—
67C22×D4×C17—41no—
68C22×D4×C17—41no—
69C22×D4×C17C2×C414yes—
70C22×D4×C17C2311yescharacteristic
71C22×D4×C17C2311yescharacteristic
72C23×C4×C17—21no—
73C23×C4×C17C2311yescharacteristic
74C23×Dic17—21no—
75C23×Dic17—21no—
76C22×Dic34C2311yescharacteristic
77C22×C8×C17—22no—
78C22×C8×C17—22no—
79C22×C8×C17—41no—
80C22×C8×C17C2311yescharacteristic
81C22×C8×C17C2311yescharacteristic
82C2×C4⋊C4×C17—22no—
83C2×C4⋊C4×C17—21no—
84C2×C4⋊C4×C17—41no—
85C2×C4⋊C4×C17C2311yescharacteristic
86C2×C4⋊C4×C17C2311yescharacteristic
87C2×C22⋊Dic17—21no—
88C2×C22⋊Dic17—21no—
89C2×C22⋊Dic17—21no—
90C2×C22⋊Dic17—21no—
91C2×C22⋊Dic17—21no—
92C2×C22⋊Dic17—21no—
93C2×C22⋊Dic17—21no—
94C2×C22⋊Dic17—21no—
95C2×C22⋊Dic17—44no—
96C2×C22⋊Dic17D411yescharacteristic
97C2×C22⋊Dic17D411yescharacteristic
98D4×Dic17—22no—
99D4×Dic17—22no—
100D4×Dic17—41no—
101D4×Dic17—41no—
102C2×#63229—22no—
103C2×#63229—22no—
104C2×#63229—41no—
105C2×#63229—41no—
106C2×#63229C2×C414yescomplemented
107C2×#63229C2×C414yescomplemented
108C2×C4⋊Dic17C2311yescharacteristic
109C2×C4⋊Dic17C2311yescharacteristic
110C2×C4⋊Dic17C2311yescharacteristic
111#10587610—22no—
112#10587610C2×C414yescomplemented
113C2×#63225—21no—
114C2×#63225—21no—
115C2×#63225—21no—
116C2×C4×Dic17—21no—
117C2×C4×Dic17—21no—
118C2×C4×Dic17C2311yescharacteristic
119C2×C4×Dic17C2311yescharacteristic
120C22×#3622C2311yescharacteristic
121C22×#3622C2311yescharacteristic
122#10587573—22no—
123#10587573—41no—
124C17×#102—22no—
125C17×#102—22no—
126C17×#102—22no—
127C17×#102D414yes—
128#10587503C2×C414yescomplemented
129#10587503C2×C414yescomplemented
130#10587502—21no—
131#10587502—21no—
132#10587502—21no—
133#10587502—21no—
134#10587502—21no—
135#10587502D411yescharacteristic
136#10587502D411yescharacteristic
137C22⋊#3622C2×C414yescomplemented
138#10587487—22no—
139#10587487—41no—
140#10587486—22no—
141#10587486—41no—
142#10587478—22no—
143#10587478—41no—
144C24×C17—21no—
145C24×C17—21no—
146C24×C17—24no—
147C24×C17—42no—
148C24×C17—42no—
149C24×C17—42no—
150C24×C17—42no—
151C24×C17—81no—
152C24×C17—81no—
153C24×C17C2×D411yescharacteristic
154C2×D4×C17—28no—
155C2×D4×C17—24no—
156C2×D4×C17—21no—
157C2×D4×C17—21no—
158C2×D4×C17—21no—
159C2×D4×C17—21no—
160C2×D4×C17—21no—
161C2×D4×C17—21no—
162C2×D4×C17—21no—
163C2×D4×C17—21no—
164C2×D4×C17—44no—
165C2×D4×C17—44no—
166C2×D4×C17—44no—
167C2×D4×C17—42no—
168C2×D4×C17—42no—
169C2×D4×C17C22×C412yes—
170C2×D4×C17C22×C412yes—
171C2×D4×C17C2×D412yes—
172C2×D4×C17#4112yes—
173C22×C4×C17—21no—
174C22×C4×C17—21no—
175C22×C4×C17—21no—
176C22×C4×C17—21no—
177C22×C4×C17—21no—
178C22×C4×C17—21no—
179C22×C4×C17—42no—
180C22×C4×C17—42no—
181C22×C4×C17—81no—
182C22×C4×C17C22×C412yes—
183C22×C4×C17C2×D411yescharacteristic
184C22×C4×C17#4112yes—
185C22×C4×C17C2411yescharacteristic
186C22×Dic17—21no—
187C22×Dic17—21no—
188C22×Dic17—21no—
189C22×Dic17—21no—
190C22×Dic17—42no—
191C22×Dic17—42no—
192C22×Dic17—42no—
193C22×Dic17—42no—
194C22×Dic17—81no—
195C22×Dic17—81no—
196C22×Dic17C2×D411yescharacteristic
197C22×Dic17C2×D411yescharacteristic
198C22×Dic17C2×D411yescharacteristic
199C22×Dic17C2×D411yescharacteristic
200C2×Dic34—21no—
201C2×Dic34—21no—
202C2×Dic34—21no—
203C2×Dic34—21no—
204C2×Dic34—21no—
205C2×Dic34C22×C412yes—
206C2×C8×C17—21no—
207C2×C8×C17—21no—
208C2×C8×C17—21no—
209C2×C8×C17—21no—
210C2×C8×C17—21no—
211C2×C8×C17—44no—
212C2×C8×C17C2×D412yes—
213C4⋊C4×C17—21no—
214C4⋊C4×C17—21no—
215C4⋊C4×C17—21no—
216C4⋊C4×C17—42no—
217C4⋊C4×C17C2×D412yes—
218C22⋊Dic17—24no—
219C22⋊Dic17—22no—
220C22⋊Dic17—22no—
221C22⋊Dic17—42no—
222C22⋊Dic17—42no—
223C22⋊Dic17—42no—
224C22⋊Dic17—42no—
225C22⋊Dic17—42no—
226C22⋊Dic17—81no—
227C22⋊Dic17—81no—
228#63229—28no—
229#63229—44no—
230C4⋊Dic17—21no—
231C4⋊Dic17—21no—
232C4⋊Dic17—21no—
233C4⋊Dic17—21no—
234C4⋊Dic17—21no—
235C4⋊Dic17C22×C412yes—
236#63225—24no—
237#63225—42no—
238#63225—81no—
239C4×Dic17—21no—
240C4×Dic17—21no—
241C4×Dic17—21no—
242C4×Dic17—21no—
243C4×Dic17—42no—
244C4×Dic17—81no—
245C2×#3622—21no—
246C2×#3622—21no—
247C2×#3622—21no—
248C2×#3622—21no—
249C2×#3622C22×C412yes—
250C2×#3622C22×C412yes—
251#22854—171nomaximal, Sylow
252C23×C17—21no—
253C23×C17—21no—
254C23×C17—21no—
255C23×C17—21no—
256C23×C17—22no—
257C23×C17—22no—
258C23×C17—22no—
259C23×C17—22no—
260C23×C17—48no—
261C23×C17—41no—
262C23×C17—41no—
263C23×C17—41no—
264C23×C17—41no—
265C23×C17—41no—
266C23×C17—41no—
267C23×C17—41no—
268C23×C17—41no—
269C23×C17—41no—
270C23×C17—41no—
271C23×C17—48no—
272C23×C17—84no—
273C23×C17—84no—
274C23×C17—84no—
275C23×C17—84no—
276C23×C17—84no—
277C23×C17C4×D412yes—
278C23×C17AGL(1,ℤ/8)12yes—
279C23×C17#13712yes—
280C23×C17C22×D411yescharacteristic
281D4×C17—22no—
282D4×C17—22no—
283D4×C17—22no—
284D4×C17—22no—
285D4×C17—22no—
286D4×C17—48no—
287D4×C17—41no—
288D4×C17—41no—
289D4×C17C4×D414yes—
290C2×C4×C17—21no—
291C2×C4×C17—21no—
292C2×C4×C17—22no—
293C2×C4×C17—22no—
294C2×C4×C17—22no—
295C2×C4×C17—22no—
296C2×C4×C17—22no—
297C2×C4×C17—41no—
298C2×C4×C17—41no—
299C2×C4×C17—41no—
300C2×C4×C17—41no—
301C2×C4×C17—41no—
302C2×C4×C17—84no—
303C2×C4×C17C4×D412yes—
304C2×C4×C17C23×C411yescharacteristic
305C2×C4×C17C22×D411yescharacteristic
306C2×C4×C17C2×#4111yescharacteristic
307C2×C4×C17C2×#4111yescharacteristic
308C2×C4×C17H(5,𝔽2)11yescharacteristic
309C2×C4×C17H(5,𝔽2)11yescharacteristic
310C2×Dic17—22no—
311C2×Dic17—22no—
312C2×Dic17—21no—
313C2×Dic17—21no—
314C2×Dic17—21no—
315C2×Dic17—21no—
316C2×Dic17—21no—
317C2×Dic17—21no—
318C2×Dic17—21no—
319C2×Dic17—21no—
320C2×Dic17—21no—
321C2×Dic17—21no—
322C2×Dic17—21no—
323C2×Dic17—21no—
324C2×Dic17—41no—
325C2×Dic17—41no—
326C2×Dic17—41no—
327C2×Dic17—41no—
328C2×Dic17—41no—
329C2×Dic17—41no—
330C2×Dic17—41no—
331C2×Dic17—41no—
332C2×Dic17—41no—
333C2×Dic17—41no—
334C2×Dic17—84no—
335C2×Dic17—84no—
336Dic34—22no—
337Dic34—22no—
338Dic34—41no—
339Dic34—41no—
340C8×C17—22no—
341C8×C17—41no—
342#3622—22no—
343#3622—22no—
344C2×#450—171no—
345C2×#440—171no—
346C22×#102D1711yescharacteristic
347#2360—171no—
348D4×C22⋊C4—171no—
349#1973—171no—
350#1936—171no—
351#1925—171no—
352#1892—171no—
353#1880—171no—
354#1877—171no—
355#1862—171no—
356#1852—171no—
357#1762—171no—
358#1752—171no—
359C22×C17—22no—
360C22×C17—22no—
361C22×C17—22no—
362C22×C17—22no—
363C22×C17—22no—
364C22×C17—22no—
365C22×C17—24no—
366C22×C17—42no—
367C22×C17—42no—
368C22×C17—42no—
369C22×C17—42no—
370C22×C17—42no—
371C22×C17—42no—
372C22×C17—42no—
373C22×C17—42no—
374C22×C17—42no—
375C22×C17—816no—
376C22×C17—81no—
377C22×C17—81no—
378C22×C17—81no—
379C22×C17—81no—
380C22×C17#44014yescomplemented
381C22×C17C2×C4×D411yescharacteristic
382C22×C17D4211yescharacteristic
383C22×C17#54611yescharacteristic
384C22×C17C2×AGL(1,ℤ/8)11yescharacteristic
385C22×C17C2×#13711yescharacteristic
386C22×C17#57611yescharacteristic
387C22×C17#57711yescharacteristic
388C4×C17—22no—
389C4×C17—42no—
390C4×C17—81no—
391C4×C17C2×C4×D411yescharacteristic
392C4×C17#51811yescharacteristic
393C4×C17#54611yescharacteristic
394C4×C17#55111yescharacteristic
395Dic17—42no—
396Dic17—42no—
397Dic17—41no—
398Dic17—41no—
399Dic17—41no—
400Dic17—41no—
401Dic17—81no—
402Dic17—81no—
403C23×D4C2×D1711yescharacteristic
404C22×SD16—171no—
405C22×SD16—171no—
406C23×C8C2×D1711yescharacteristic
407C2×C22⋊Q8—171no—
408C2×C4×Q8—171no—
409C2×C4×D4—171no—
410C2×C4×D4—171no—
411C22×C4⋊C4C2×D1711yescharacteristic
412C22×C22⋊C4—341no—
413#450—178no—
414#440—344no—
415C2×#107—171no—
416C2×#107—171no—
417C2×#103—171no—
418C2×#103—171no—
419C2×#102—24no—
420C2×#102—171no—
421C2×#102—171no—
422C2×#102C2×D1711yescharacteristic
423C2×#102C2×D1711yescharacteristic
424C2×#102C2×D1711yescharacteristic
425C2×#102C2×D1711yescharacteristic
426C2×C22⋊C8—171no—
427C2×#97—171no—
428C2×#97—171no—
429#391—171no—
430#390—171no—
431#390—171no—
432#389—171no—
433#389—341no—
434#387—341no—
435#386—341no—
436#386—341no—
437#385—341no—
438#380—171no—
439#379—341no—
440C4×C4⋊C4—171no—
441C4×C22⋊C4—171no—
442C4×C22⋊C4—341no—
443#340—171no—
444#340—171no—
445#340—171no—
446#340—171no—
447#336—171no—
448#336—171no—
449C2×C17—24no—
450C2×C17—44no—
451C2×C17—82no—
452C2×C17#235811yescharacteristic
453C2×C17C2×#44011yescharacteristic
454C2×C17#294611yescharacteristic
455C2×C17#326411yescharacteristic
456C2×C17#326611yescharacteristic
457C2×C17#331011yescharacteristic
458C2×C17#331411yescharacteristic
459C25—21no—
460C22×Q8—171no—
461C22×D4—22no—
462C22×D4—22no—
463C22×D4—21no—
464C22×D4—22no—
465C22×D4—41no—
466C22×D4—41no—
467C22×D4C4×D1714yes—
468C22×D4C22×D1711yescharacteristic
469C22×D4C22×D1711yescharacteristic
470C23×C4—21no—
471C23×C4—341no—
472C23×C4—341no—
473C23×C4C22×D1711yescharacteristic
474C2×SD16—174no—
475C2×SD16—174no—
476C2×SD16—342no—
477C2×SD16—342no—
478C2×SD16—681no—
479C2×SD16—681no—
480C22×C8—22no—
481C22×C8—22no—
482C22×C8—41no—
483C22×C8—171no—
484C22×C8—171no—
485C22×C8C22×D1711yescharacteristic
486C22×C8C22×D1711yescharacteristic
487C22⋊Q8—174no—
488C22⋊Q8—342no—
489C4×Q8—342no—
490C4×Q8—681no—
491C4×D4—342no—
492C4×D4—342no—
493C4×D4—681no—
494C4×D4—681no—
495C2×C4⋊C4—22no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—41no—
498C2×C4⋊C4—171no—
499C2×C4⋊C4—171no—
500C2×C4⋊C4—171no—
501C2×C4⋊C4—341no—
502C2×C4⋊C4—341no—
503C2×C4⋊C4—341no—
504C2×C4⋊C4C22×D1711yescharacteristic
505C2×C4⋊C4C22×D1711yescharacteristic
506C2×C22⋊C4—171no—
507C2×C22⋊C4—171no—
508C2×C22⋊C4—341no—
509C2×C22⋊C4—341no—
510C2×C22⋊C4—341no—
511C2×C22⋊C4—341no—
512C2×C22⋊C4—341no—
513C2×C22⋊C4—341no—
514C2×C22⋊C4—341no—
515C2×C22⋊C4—341no—
516C2×C22⋊C4—684no—
517C2×C42—171no—
518C2×C42—171no—
519C2×C42—341no—
520C2×C42—341no—
521#107—342no—
522#107—681no—
523#103—342no—
524#103—681no—
525#102—22no—
526#102—22no—
527#102—22no—
528#102—174no—
529#102—174no—
530#102C22⋊D1714yes—
531C22⋊C8—174no—
532#97—342no—
533#97—681no—
534#95—171no—
535#95—171no—
536#95—341no—
537#95—341no—
538#95—341no—
539#95—341no—
540#95—341no—
541C17#2285411yescharacteristic, complemented, Sylow
542C24—21no—
543C24—21no—
544C24—24no—
545C24—42no—
546C24—42no—
547C24—42no—
548C24—42no—
549C24—81no—
550C24—81no—
551C24D4×D1711yescharacteristic
552C2×Q8—172no—
553C2×Q8—341no—
554C2×Q8—341no—
555C2×Q8—341no—
556C2×Q8—341no—
557C2×Q8—341no—
558C2×D4—28no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—24no—
568C2×D4—44no—
569C2×D4—44no—
570C2×D4—44no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4C2×C4×D1712yes—
574C2×D4C2×C4×D1712yes—
575C2×D4#6325212yes—
576C2×D4C2×C22⋊D1712yes—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—81no—
586C22×C4—171no—
587C22×C4—171no—
588C22×C4—171no—
589C22×C4—171no—
590C22×C4—341no—
591C22×C4—341no—
592C22×C4—341no—
593C22×C4—341no—
594C22×C4—682no—
595C22×C4—682no—
596C22×C4—682no—
597C22×C4—682no—
598C22×C4—1361no—
599C22×C4—1361no—
600C22×C4C2×C4×D1712yes—
601C22×C4D4×D1711yescharacteristic
602C22×C4#6325412yes—
603C22×C4C23×D1711yescharacteristic
604SD16—348no—
605SD16—684no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—44no—
612C2×C8—172no—
613C2×C8—172no—
614C2×C8—341no—
615C2×C8—341no—
616C2×C8—341no—
617C2×C8—341no—
618C2×C8C2×C22⋊D1712yes—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—42no—
623C4⋊C4—172no—
624C4⋊C4—341no—
625C4⋊C4—344no—
626C4⋊C4—341no—
627C4⋊C4—341no—
628C4⋊C4—341no—
629C4⋊C4—341no—
630C4⋊C4—682no—
631C4⋊C4—1361no—
632C4⋊C4C2×C22⋊D1712yes—
633C22⋊C4—344no—
634C22⋊C4—342no—
635C22⋊C4—342no—
636C22⋊C4—682no—
637C22⋊C4—682no—
638C22⋊C4—682no—
639C22⋊C4—682no—
640C22⋊C4—682no—
641C22⋊C4—1361no—
642C22⋊C4—1361no—
643C42—341no—
644C42—341no—
645C42—341no—
646C42—341no—
647C42—682no—
648C42—1361no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—48no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—48no—
667C23—41no—
668C23—41no—
669C23—84no—
670C23—84no—
671C23—84no—
672C23—84no—
673C23—84no—
674C23#1058756712yes—
675C23#1058759712yes—
676C23#1058760112yes—
677C23C2×D4×D1711yescharacteristic
678Q8—342no—
679Q8—342no—
680Q8—681no—
681Q8—681no—
682D4—22no—
683D4—22no—
684D4—22no—
685D4—22no—
686D4—22no—
687D4—48no—
688D4—41no—
689D4—41no—
690D4C4×C22⋊D1714yes—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—84no—
704C2×C4—342no—
705C2×C4—342no—
706C2×C4—341no—
707C2×C4—341no—
708C2×C4—341no—
709C2×C4—341no—
710C2×C4—341no—
711C2×C4—341no—
712C2×C4—341no—
713C2×C4—341no—
714C2×C4—341no—
715C2×C4—341no—
716C2×C4—341no—
717C2×C4—341no—
718C2×C4—681no—
719C2×C4—681no—
720C2×C4—681no—
721C2×C4—681no—
722C2×C4—681no—
723C2×C4—681no—
724C2×C4—681no—
725C2×C4—681no—
726C2×C4—681no—
727C2×C4—681no—
728C2×C4—1364no—
729C2×C4—1364no—
730C2×C4#1058756712yes—
731C2×C4C22×C4×D1711yescharacteristic
732C2×C4C2×#6325211yescharacteristic
733C2×C4C2×#6325411yescharacteristic
734C2×C4#1058769111yescharacteristic
735C2×C4#1058769111yescharacteristic
736C2×C4C22×C22⋊D1711yescharacteristic
737C8—22no—
738C8—41no—
739C8—342no—
740C8—342no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—24no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—816no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22#1176290614yescomplemented
763C22C2×#1058756711yescharacteristic
764C22D4×C22⋊D1711yescharacteristic
765C22#1176344911yescharacteristic
766C22C2×#1058759711yescharacteristic
767C22C2×#1058760111yescharacteristic
768C22#1176361011yescharacteristic
769C22#1176361511yescharacteristic
770C4—22no—
771C4—42no—
772C4—81no—
773C4—681no—
774C4—681no—
775C4—681no—
776C4—682no—
777C4—682no—
778C4—681no—
779C4—1361no—
780C4—1361no—
781C4C2×C4×C22⋊D1711yescharacteristic
782C4#1176328211yescharacteristic
783C4#1176345311yescharacteristic
784C4#1176348511yescharacteristic
785C2—24no—
786C2—44no—
787C2—82no—
788C2#1453176311yescharacteristic
789C2C2×#1176290611yescharacteristic
790C2#1453761011yescharacteristic
791C2#1454026411yescharacteristic
792C2#1454029411yescharacteristic
793C2#1454080111yescharacteristic
794C2#1454086111yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC22×C17×#102C2
socleC23×C17C22×D4
prime radicalC23×D4×C17C22
cosocleC22×C4×C17C24
hypercenterC22×#102D17
hypocenterC17#22854
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
2. C2×#11762906C2semidirect
3. #14531789C2semidirect
5. #14529666C2semidirect
6. #14529478C2semidirect
7. #14529407C2semidirect
8. #14529207C2semidirect
9. #14529136C2semidirect
10. #14529116C2semidirect
11. #14529029C2semidirect
12. #14528972C2semidirect
13. #14528611C2semidirect
14. #14528560C2semidirect
19. C2×#10587573C22semidirect
23. #11762960C4semidirect
25. C2×#10587478C22semidirect
26. C2×#10587478C22semidirect
27. C2×#10587487C22semidirect
28. C2×#10587487C22semidirect
32. C2×#10587486C22semidirect
33. C2×#10587486C22semidirect
34. #11762714C22semidirect
37. #11762705C22semidirect
45. C4⋊C4×Dic17C22semidirect
48. #11762572C22semidirect
49. #11762572C22semidirect
50. #11762571C22semidirect
51. #11762571C22semidirect
52. #11762563C22semidirect
53. #11762563C22semidirect
106. C2×#63229C2×C4semidirect
107. C2×#63229C2×C4semidirect
112. #10587610C2×C4semidirect
128. #10587503C2×C4semidirect
129. #10587503C2×C4semidirect
137. C22⋊#3622C2×C4semidirect
380. C22×C17#440semidirect
541. C17#22854semidirect
762. C22#11762906semidirect

Maximal subgroups

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

subgroupindex
C2×#117629602
C2×#117629062
#145317892
D4×C22⋊Dic172
#145296662
#145294782
#145294072
#145292072
#145291362
#145291162
#145290292
#145289722
#145286112
#145285602
C22×C17×#1022
#2285417