Finite Group Databasebeta

← #17067518

Subgroups — #17067518

Order 4352.

1284 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×#11763147C211yesmaximal, characteristic, complemented
2C2×#11762818C211yesmaximal, characteristic, complemented
3#14533081C211yesmaximal, characteristic
4#14530027C211yesmaximal, characteristic, complemented
5#14530027C211yesmaximal, characteristic, complemented
6#14529984C211yesmaximal, characteristic, complemented
7#14529977C211yesmaximal, characteristic, complemented
8#14529218C211yesmaximal, characteristic, complemented
9#14529082C211yesmaximal, characteristic
10#14529052C211yesmaximal, characteristic, complemented
11#14529038C211yesmaximal, characteristic, complemented
12#14528719C211yesmaximal, characteristic, complemented
13#14528719C211yesmaximal, characteristic, complemented
14#14528719C211yesmaximal, characteristic, complemented
15C2×D4×Q8×C17C211yesmaximal, characteristic
16C22×#63223C2211yescharacteristic
17C2×#10587612C2211yescharacteristic
18#11763147—24no—
19C2×#10587478C2211yescharacteristic
20C2×#10587479C2211yescharacteristic
21#11762818—24no—
22C2×#10587506C2211yescharacteristic
23C2×#10587506C2211yescharacteristic
24C2×#10587506C2211yescharacteristic
25C2×#10587506C2211yescharacteristic
26C2×#10587506C2211yescharacteristic
27C2×#10587506C2211yescharacteristic
28C2×#10587506C2211yescharacteristic
29C2×#10587506C2211yescharacteristic
30C2×#10587506C2211yescharacteristic
31C2×#10587506C2211yescharacteristic
32C2×#10587506C2211yescharacteristic
33C2×#10587506C2211yescharacteristic
34C2×C22⋊#3622C2211yescharacteristic
35C2×C22⋊#3622C2211yescharacteristic
36C2×C22⋊#3622C2211yescharacteristic
37#11762737—21no—
38#11762723—21no—
39#11762707C2211yescharacteristic
40#11762707C2211yescharacteristic
41#11762697—21no—
42#11762690—21no—
43#11762669C2211yescharacteristic
44#11762669C2211yescharacteristic
45#11762669C2211yescharacteristic
46#11762571C2211yescharacteristic
47#11762571C2211yescharacteristic
48#11762564C2211yescharacteristic
49#11762564C2211yescharacteristic
50C23×Q8×C17C2211yescharacteristic
51C23×Q8×C17C2211yescharacteristic
52D4×Q8×C17—24no—
53D4×Q8×C17—24no—
54C2×C17×C4⋊Q8—21no—
55C2×C17×C4⋊Q8C2211yescharacteristic
56C2×C17×C22⋊Q8—21no—
57C2×C17×C22⋊Q8—21no—
58C2×C17×C22⋊Q8C2211yescharacteristic
59C2×C17×C22⋊Q8C2211yescharacteristic
60C2×C4×Q8×C17C2211yescharacteristic
61C2×C4×D4×C17—21no—
62C2×C4×D4×C17C2211yescharacteristic
63C22×Q8×C17—22no—
64C22×Q8×C17—22no—
65C22×Q8×C17—21no—
66C22×Q8×C17—21no—
67C22×Q8×C17—22no—
68C22×Q8×C17—22no—
69C22×Q8×C17—22no—
70C22×Q8×C17—22no—
71C22×Q8×C17—22no—
72C22×Q8×C17—41no—
73C22×Q8×C17—41no—
74C22×Q8×C17—41no—
75C22×Q8×C17—41no—
76C22×Q8×C17D414yes—
77C22×Q8×C17C2311yescharacteristic
78C22×Q8×C17C2311yescharacteristic
79C22×Q8×C17C2311yescharacteristic
80C22×D4×C17D411yescharacteristic
81C23×C4×C17—21no—
82C23×C4×C17—21no—
83C23×C4×C17C2311yescharacteristic
84C23×C4×C17C2311yescharacteristic
85C17×C4⋊Q8—28no—
86C17×C4⋊Q8—22no—
87C17×C4⋊Q8—22no—
88C17×C22⋊Q8—28no—
89C17×C22⋊Q8—28no—
90C17×C22⋊Q8—22no—
91C17×C22⋊Q8—22no—
92C17×C22⋊Q8—22no—
93C17×C22⋊Q8D414yes—
94C4×Q8×C17—22no—
95C4×Q8×C17—22no—
96C4×D4×C17—28no—
97C4×D4×C17—22no—
98C4×D4×C17—22no—
99C2×C4⋊C4×C17—21no—
100C2×C4⋊C4×C17—21no—
101C2×C4⋊C4×C17—21no—
102C2×C4⋊C4×C17—21no—
103C2×C4⋊C4×C17—21no—
104C2×C4⋊C4×C17D411yescharacteristic
105C2×C4⋊C4×C17C2311yescharacteristic
106C2×C22⋊C4×C17—21no—
107C2×C22⋊C4×C17—21no—
108C2×C22⋊C4×C17D411yescharacteristic
109C2×C22⋊C4×C17D411yescharacteristic
110C2×C42×C17—21no—
111C2×C42×C17C2311yescharacteristic
112C2×C22⋊Dic17—21no—
113C2×C22⋊Dic17—21no—
114C2×C22⋊Dic17—21no—
115C2×C22⋊Dic17—21no—
116#10587612—22no—
117#10587612—22no—
118C2×C4⋊Dic17C2311yescharacteristic
119C2×C4⋊Dic17C2311yescharacteristic
120C2×C4⋊Dic17C2311yescharacteristic
121C2×C4⋊Dic17C2311yescharacteristic
122C2×#63225—21no—
123C2×#63225—21no—
124C2×C4×Dic17—21no—
125C2×#63223—22no—
126C2×#63223—41no—
127C2×#63223—41no—
128C22×#3622C2311yescharacteristic
129C22×#3622C2311yescharacteristic
130C22×#3622C2311yescharacteristic
131C22×#3622C2311yescharacteristic
132#10587506—22no—
133#10587506—22no—
134#10587506—22no—
135#10587506—22no—
136#10587506—22no—
137#10587506—22no—
138#10587506—22no—
139#10587506—22no—
140#10587506—41no—
141#10587506—41no—
142#10587506—41no—
143#10587506—41no—
144#10587502—21no—
145#10587502—21no—
146#10587502—21no—
147#10587502—21no—
148#10587502—21no—
149C22⋊#3622—22no—
150C22⋊#3622—41no—
151C22⋊#3622—41no—
152#10587479—22no—
153#10587478—22no—
154C24×C17C2×D411yescharacteristic
155C24×C17C2×D411yescharacteristic
156C2×Q8×C17—24no—
157C2×Q8×C17—24no—
158C2×Q8×C17—21no—
159C2×Q8×C17—21no—
160C2×Q8×C17—21no—
161C2×Q8×C17—21no—
162C2×Q8×C17—21no—
163C2×Q8×C17—28no—
164C2×Q8×C17—21no—
165C2×Q8×C17—21no—
166C2×Q8×C17—21no—
167C2×Q8×C17—21no—
168C2×Q8×C17—21no—
169C2×Q8×C17—21no—
170C2×Q8×C17—21no—
171C2×Q8×C17—21no—
172C2×Q8×C17—42no—
173C2×Q8×C17—42no—
174C2×Q8×C17—42no—
175C2×Q8×C17—42no—
176C2×Q8×C17—44no—
177C2×Q8×C17—44no—
178C2×Q8×C17—44no—
179C2×Q8×C17—44no—
180C2×Q8×C17—44no—
181C2×Q8×C17—44no—
182C2×Q8×C17—44no—
183C2×Q8×C17C2×D412yes—
184C2×Q8×C17C2×D412yes—
185C2×Q8×C17C2×D412yes—
186C2×Q8×C17#4112yes—
187C2×Q8×C17#4112yes—
188C2×D4×C17—22no—
189C2×D4×C17—22no—
190C2×D4×C17—22no—
191C22×C4×C17—21no—
192C22×C4×C17—21no—
193C22×C4×C17—21no—
194C22×C4×C17—21no—
195C22×C4×C17—21no—
196C22×C4×C17—24no—
197C22×C4×C17—24no—
198C22×C4×C17—21no—
199C22×C4×C17—21no—
200C22×C4×C17—21no—
201C22×C4×C17—21no—
202C22×C4×C17—21no—
203C22×C4×C17—21no—
204C22×C4×C17—21no—
205C22×C4×C17—21no—
206C22×C4×C17—21no—
207C22×C4×C17—42no—
208C22×C4×C17—42no—
209C22×C4×C17—42no—
210C22×C4×C17—42no—
211C22×C4×C17C2×D411yescharacteristic
212C22×C4×C17C2×D411yescharacteristic
213C22×C4×C17C2×D411yescharacteristic
214C22×C4×C17C2×D412yes—
215C22×C4×C17C2×D412yes—
216C22×C4×C17C2×D411yescharacteristic
217C22×C4×C17C2411yescharacteristic
218C22×Dic17—21no—
219C22×Dic17—21no—
220C22×Dic17—21no—
221C22×Dic17—21no—
222C4⋊C4×C17—24no—
223C4⋊C4×C17—24no—
224C4⋊C4×C17—24no—
225C4⋊C4×C17—24no—
226C4⋊C4×C17—24no—
227C4⋊C4×C17—22no—
228C4⋊C4×C17—21no—
229C4⋊C4×C17C2×D412yes—
230C22⋊C4×C17—24no—
231C22⋊C4×C17—22no—
232C22⋊C4×C17—24no—
233C22⋊C4×C17—22no—
234C42×C17—24no—
235C42×C17—21no—
236C42×C17—21no—
237C22⋊Dic17—42no—
238C22⋊Dic17—42no—
239C22⋊Dic17—81no—
240C22⋊Dic17—81no—
241C4⋊Dic17—21no—
242C4⋊Dic17—21no—
243C4⋊Dic17—21no—
244C4⋊Dic17—21no—
245C4⋊Dic17—21no—
246C4⋊Dic17—21no—
247C4⋊Dic17—21no—
248C4⋊Dic17—21no—
249#63225—42no—
250#63225—81no—
251C4×Dic17—42no—
252#63223—44no—
253C2×#3622—21no—
254C2×#3622—21no—
255C2×#3622—21no—
256C2×#3622—21no—
257C2×#3622—21no—
258C2×#3622—21no—
259C2×#3622—21no—
260C2×#3622—21no—
261C2×#3622—21no—
262C2×#3622—21no—
263C2×#3622—21no—
264C2×#3622—21no—
265#24053—171nomaximal, Sylow
266C23×C17—21no—
267C23×C17—21no—
268C23×C17—21no—
269C23×C17—21no—
270C23×C17—21no—
271C23×C17—21no—
272C23×C17—21no—
273C23×C17—21no—
274C23×C17—21no—
275C23×C17—21no—
276C23×C17—21no—
277C23×C17—21no—
278C23×C17#12012yes—
279C23×C17#13712yes—
280C23×C17C22×D411yescharacteristic
281Q8×C17—22no—
282Q8×C17—22no—
283Q8×C17—22no—
284Q8×C17—22no—
285Q8×C17—22no—
286Q8×C17—22no—
287Q8×C17—22no—
288Q8×C17—48no—
289Q8×C17—48no—
290Q8×C17—41no—
291Q8×C17—41no—
292Q8×C17—41no—
293Q8×C17—41no—
294Q8×C17#12314yes—
295D4×C17—28no—
296C2×C4×C17—21no—
297C2×C4×C17—22no—
298C2×C4×C17—21no—
299C2×C4×C17—21no—
300C2×C4×C17—22no—
301C2×C4×C17—22no—
302C2×C4×C17—21no—
303C2×C4×C17—22no—
304C2×C4×C17—22no—
305C2×C4×C17—22no—
306C2×C4×C17—22no—
307C2×C4×C17—21no—
308C2×C4×C17—22no—
309C2×C4×C17—22no—
310C2×C4×C17—22no—
311C2×C4×C17—21no—
312C2×C4×C17—21no—
313C2×C4×C17—21no—
314C2×C4×C17—21no—
315C2×C4×C17—21no—
316C2×C4×C17—48no—
317C2×C4×C17—48no—
318C2×C4×C17—41no—
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—41no—
326C2×C4×C17—41no—
327C2×C4×C17—41no—
328C2×C4×C17#12012yes—
329C2×C4×C17#13712yes—
330C2×C4×C17C22×D411yescharacteristic
331C2×C4×C17C22×D411yescharacteristic
332C2×C4×C17C2×#4111yescharacteristic
333C2×C4×C17C2×#4111yescharacteristic
334C2×C4×C17H(5,𝔽2)11yescharacteristic
335C2×C4×C17H(5,𝔽2)11yescharacteristic
336C2×Dic17—41no—
337C2×Dic17—41no—
338C2×Dic17—41no—
339C2×Dic17—41no—
340C2×Dic17—41no—
341C2×Dic17—41no—
342C2×Dic17—41no—
343C2×Dic17—41no—
344C2×Dic17—41no—
345C2×Dic17—41no—
346C2×Dic17—41no—
347C2×Dic17—41no—
348#3622—41no—
349#3622—41no—
350#3622—41no—
351#3622—41no—
352C2×D4×Q8D1711yescharacteristic
353C2×#485—171no—
354C2×#419—171no—
355#2485—171no—
356#2043—171no—
357#2043—171no—
358#2036—171no—
359#2035—171no—
360#1894—171no—
361#1870—171no—
362#1865—171no—
363#1863—171no—
364#1787—171no—
365#1787—171no—
366#1787—171no—
367C22×C17—22no—
368C22×C17—22no—
369C22×C17—22no—
370C22×C17—22no—
371C22×C17—22no—
372C22×C17—22no—
373C22×C17—41no—
374C22×C17—41no—
375C22×C17—41no—
376C22×C17—41no—
377C22×C17—41no—
378C22×C17—41no—
379C22×C17—41no—
380C22×C17—41no—
381C22×C17C2×#12011yescharacteristic
382C22×C17#54611yescharacteristic
383C22×C17#54611yescharacteristic
384C22×C17C2×#13711yescharacteristic
385C22×C17C2×#13711yescharacteristic
386C22×C17#57711yescharacteristic
387C22×C17#57811yescharacteristic
388C4×C17—22no—
389C4×C17—24no—
390C4×C17—22no—
391C4×C17—41no—
392C4×C17—42no—
393C4×C17—42no—
394C4×C17—41no—
395C4×C17—42no—
396C4×C17C2×#12311yescharacteristic
397C4×C17#53411yescharacteristic
398C4×C17#54611yescharacteristic
399C4×C17#54611yescharacteristic
400Dic17—81no—
401Dic17—81no—
402Dic17—81no—
403Dic17—81no—
404C23×Q8C2×D1711yescharacteristic
405C23×Q8C2×D1711yescharacteristic
406C22×M16—171no—
407D4×Q8—24no—
408D4×Q8—24no—
409C2×C4⋊Q8—21no—
410C2×C4⋊Q8C2×D1711yescharacteristic
411C2×C22⋊Q8—21no—
412C2×C22⋊Q8—21no—
413C2×C22⋊Q8C2×D1711yescharacteristic
414C2×C22⋊Q8C2×D1711yescharacteristic
415C2×C4×Q8C2×D1711yescharacteristic
416C2×C4×D4—21no—
417C2×C4×D4C2×D1711yescharacteristic
418C2×#117—171no—
419#485—344no—
420C2×#107—171no—
421C2×#106—171no—
422#419—344no—
423C2×#103—171no—
424C2×#103—171no—
425C2×#103—171no—
426C2×#103—171no—
427C2×#103—171no—
428C2×#103—171no—
429C2×#103—171no—
430C2×#103—171no—
431C2×#103—171no—
432C2×#103—171no—
433C2×#103—171no—
434C2×#103—171no—
435C2×C22⋊C8—171no—
436C2×C22⋊C8—171no—
437C2×C22⋊C8—171no—
438#397—341no—
439#394—341no—
440#389—171no—
441#389—171no—
442#388—341no—
443#387—341no—
444#380—171no—
445#380—171no—
446#380—171no—
447#340—171no—
448#340—171no—
449#336—171no—
450#336—171no—
451C2×C17—42no—
452C2×C17—42no—
453C2×C17#240511yescharacteristic
454C2×C17#300411yescharacteristic
455C2×C17#301311yescharacteristic
456C2×C17#331211yescharacteristic
457C2×C17#332011yescharacteristic
458C2×C17#332811yescharacteristic
459C2×C17#332911yescharacteristic
460C22×Q8—22no—
461C22×Q8—22no—
462C22×Q8—21no—
463C22×Q8—21no—
464C22×Q8—22no—
465C22×Q8—22no—
466C22×Q8—22no—
467C22×Q8—22no—
468C22×Q8—22no—
469C22×Q8—41no—
470C22×Q8—41no—
471C22×Q8—41no—
472C22×Q8—41no—
473C22×Q8C22⋊D1714yes—
474C22×Q8C22×D1711yescharacteristic
475C22×Q8C22×D1711yescharacteristic
476C22×Q8C22×D1711yescharacteristic
477C22×D4C22⋊D1711yescharacteristic
478C23×C4—21no—
479C23×C4—21no—
480C23×C4C22×D1711yescharacteristic
481C23×C4C22×D1711yescharacteristic
482C2×M16—342no—
483C2×M16—681no—
484C2×M16—681no—
485C22×C8—171no—
486C22×C8—171no—
487C22×C8—171no—
488C22×C8—171no—
489C4⋊Q8—28no—
490C4⋊Q8—22no—
491C4⋊Q8—22no—
492C22⋊Q8—28no—
493C22⋊Q8—28no—
494C22⋊Q8—22no—
495C22⋊Q8—22no—
496C22⋊Q8—22no—
497C22⋊Q8C22⋊D1714yes—
498C4×Q8—22no—
499C4×Q8—22no—
500C4×D4—28no—
501C4×D4—22no—
502C4×D4—22no—
503#117—342no—
504#117—342no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—171no—
511C2×C4⋊C4—171no—
512C2×C4⋊C4—171no—
513C2×C4⋊C4—171no—
514C2×C4⋊C4—341no—
515C2×C4⋊C4—341no—
516C2×C4⋊C4C22⋊D1711yescharacteristic
517C2×C4⋊C4C22×D1711yescharacteristic
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—341no—
521C2×C22⋊C4—341no—
522C2×C22⋊C4—341no—
523C2×C22⋊C4—341no—
524C2×C22⋊C4C22⋊D1711yescharacteristic
525C2×C22⋊C4C22⋊D1711yescharacteristic
526C2×C42—21no—
527C2×C42—341no—
528C2×C42C22×D1711yescharacteristic
529#107—342no—
530#106—342no—
531#103—342no—
532#103—342no—
533#103—342no—
534#103—342no—
535#103—342no—
536#103—342no—
537#103—342no—
538#103—342no—
539#103—681no—
540#103—681no—
541#103—681no—
542#103—681no—
543C22⋊C8—342no—
544C22⋊C8—681no—
545C22⋊C8—681no—
546#95—341no—
547#95—341no—
548#95—341no—
549#95—341no—
550#95—341no—
551C17#2405311yescharacteristic, complemented, Sylow
552C24C2×C22⋊D1711yescharacteristic
553C24C2×C22⋊D1711yescharacteristic
554C2×Q8—24no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—24no—
561C2×Q8—28no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—42no—
571C2×Q8—42no—
572C2×Q8—42no—
573C2×Q8—42no—
574C2×Q8—44no—
575C2×Q8—44no—
576C2×Q8—44no—
577C2×Q8—44no—
578C2×Q8—44no—
579C2×Q8—44no—
580C2×Q8—44no—
581C2×Q8#6325412yes—
582C2×Q8#6325412yes—
583C2×Q8C2×C22⋊D1712yes—
584C2×Q8C2×C22⋊D1712yes—
585C2×Q8C2×C22⋊D1712yes—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—22no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—24no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—24no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—341no—
610C22×C4—341no—
611C22×C4—341no—
612C22×C4—341no—
613C22×C4C2×C22⋊D1711yescharacteristic
614C22×C4C2×C22⋊D1711yescharacteristic
615C22×C4C2×C22⋊D1712yes—
616C22×C4C2×C22⋊D1712yes—
617C22×C4C2×C22⋊D1711yescharacteristic
618C22×C4C2×C22⋊D1711yescharacteristic
619C22×C4C23×D1711yescharacteristic
620M16—684no—
621C2×C8—341no—
622C2×C8—341no—
623C2×C8—341no—
624C2×C8—341no—
625C2×C8—341no—
626C2×C8—341no—
627C2×C8—341no—
628C2×C8—341no—
629C2×C8—341no—
630C2×C8—341no—
631C2×C8—341no—
632C2×C8—341no—
633C4⋊C4—24no—
634C4⋊C4—24no—
635C4⋊C4—24no—
636C4⋊C4—24no—
637C4⋊C4—21no—
638C4⋊C4—24no—
639C4⋊C4—22no—
640C4⋊C4—341no—
641C4⋊C4—341no—
642C4⋊C4—341no—
643C4⋊C4—341no—
644C4⋊C4—341no—
645C4⋊C4—341no—
646C4⋊C4—341no—
647C4⋊C4—341no—
648C4⋊C4—682no—
649C4⋊C4—1361no—
650C4⋊C4C2×C22⋊D1712yes—
651C22⋊C4—24no—
652C22⋊C4—24no—
653C22⋊C4—22no—
654C22⋊C4—22no—
655C22⋊C4—682no—
656C22⋊C4—682no—
657C22⋊C4—1361no—
658C22⋊C4—1361no—
659C42—24no—
660C42—21no—
661C42—21no—
662C42—682no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23#1058762812yes—
676C23#1058763912yes—
677C23C22×C22⋊D1711yescharacteristic
678Q8—22no—
679Q8—22no—
680Q8—22no—
681Q8—22no—
682Q8—22no—
683Q8—22no—
684Q8—22no—
685Q8—48no—
686Q8—48no—
687Q8—41no—
688Q8—41no—
689Q8—41no—
690Q8—41no—
691Q8#1058762114yes—
692D4—28no—
693C2×C4—21no—
694C2×C4—22no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—21no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—48no—
714C2×C4—48no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—681no—
726C2×C4—681no—
727C2×C4—681no—
728C2×C4—681no—
729C2×C4—681no—
730C2×C4—681no—
731C2×C4—681no—
732C2×C4—681no—
733C2×C4—681no—
734C2×C4—681no—
735C2×C4—681no—
736C2×C4—681no—
737C2×C4#1058762812yes—
738C2×C4#1058763912yes—
739C2×C4C2×#6325411yescharacteristic
740C2×C4C2×#6325411yescharacteristic
741C2×C4#1058769111yescharacteristic
742C2×C4#1058769111yescharacteristic
743C2×C4C22×C22⋊D1711yescharacteristic
744C2×C4C22×C22⋊D1711yescharacteristic
745C8—681no—
746C8—681no—
747C8—681no—
748C8—681no—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22C2×#1058763911yescharacteristic
764C22#1176345311yescharacteristic
765C22#1176345311yescharacteristic
766C22C2×#1058762811yescharacteristic
767C22C2×#1058762811yescharacteristic
768C22#1176361711yescharacteristic
769C22#1176362411yescharacteristic
770C4—22no—
771C4—24no—
772C4—22no—
773C4—41no—
774C4—42no—
775C4—42no—
776C4—41no—
777C4—42no—
778C4—1361no—
779C4—1361no—
780C4—1361no—
781C4—1361no—
782C4C2×#1058762111yescharacteristic
783C4#1176336811yescharacteristic
784C4#1176345311yescharacteristic
785C4#1176345311yescharacteristic
786C2—42no—
787C2—42no—
788C2#1453210711yescharacteristic
789C2#1453801811yescharacteristic
790C2#1453809911yescharacteristic
791C2#1454083511yescharacteristic
792C2#1454095511yescharacteristic
793C2#1454106711yescharacteristic
794C2#1454107811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutator, cosocleC22×C4×C17C24
FrattiniC22×C4C23×D17
FittingC2×D4×Q8×C17C2
socleC23×C17C22×D4
prime radicalC22×D4×C17D4
hypercenterC2×D4×Q8D17
hypocenterC17#24053
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#11763147C2semidirect
2. C2×#11762818C2semidirect
4. #14530027C2semidirect
5. #14530027C2semidirect
6. #14529984C2semidirect
7. #14529977C2semidirect
8. #14529218C2semidirect
10. #14529052C2semidirect
11. #14529038C2semidirect
12. #14528719C2semidirect
13. #14528719C2semidirect
14. #14528719C2semidirect
551. C17#24053semidirect

Maximal subgroups

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

subgroupindex
C2×#117631472
C2×#117628182
#145330812
#145300272
#145299842
#145299772
#145292182
#145290822
#145290522
#145290382
#145287192
C2×D4×Q8×C172
#2405317