Finite Group Databasebeta

← #16942198

Subgroups — #16942198

Order 4352.

1186 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587491C211yesmaximal, characteristic
2C2×#11762666C211yesmaximal, characteristic
3C2×#11762666C211yesmaximal, characteristic
4C2×#11762572C211yesmaximal, characteristic, complemented
5C2×#11762571C211yesmaximal, characteristic, complemented
6C2×#11762571C211yesmaximal, characteristic, complemented
7C2×C17×#340C211yesmaximal, characteristic, complemented
8C23×C4×D17C2211yescharacteristic
9C23×#3622C2211yescharacteristic
10C22×C4⋊Dic17C2211yescharacteristic
11C22×C4⋊Dic17C2211yescharacteristic
12C22×#63227—21no—
13C22×#63227—21no—
14C2×#10587491—22no—
15C2×#10587491—22no—
16C2×#10587491—22no—
17#11762666—22no—
18#11762666—22no—
19#11762666—22no—
20#11762666C414yescomplemented
21C2×#10587502—21no—
22C2×#10587502—21no—
23#11762572—22no—
24#11762571—22no—
25#11762571—22no—
26C23×C8×C17C2211yescharacteristic
27C22×C4⋊C4×C17C2211yescharacteristic
28C22×C4⋊C4×C17C2211yescharacteristic
29C17×#340—22no—
30C24×D17D411yescharacteristic
31C23×C4×C17—21no—
32C23×C4×C17—21no—
33C23×C4×C17C2311yescharacteristic
34C23×Dic17—21no—
35C23×Dic17—21no—
36C23×Dic17D411yescharacteristic
37C22×C4×D17—21no—
38C22×C4×D17—21no—
39C22×C4×D17—21no—
40C22×C4×D17—21no—
41C22×C4×D17—21no—
42C22×C4×D17—21no—
43C22×C4×D17—21no—
44C22×C4×D17—21no—
45C22×C4×D17—21no—
46C22×C4×D17—21no—
47C22×C4×D17—21no—
48C22×C4×D17—21no—
49C22×C4×D17C2×C412yes—
50C22×C4×D17D412yes—
51C22×C8×C17—21no—
52C22×C8×C17—21no—
53C22×C8×C17—21no—
54C22×C8×C17—21no—
55C22×C8×C17—21no—
56C22×C8×C17—21no—
57C22×C8×C17D412yes—
58C2×C4⋊C4×C17—21no—
59C2×C4⋊C4×C17—21no—
60C2×C4⋊C4×C17—21no—
61C2×C4⋊C4×C17—21no—
62C2×C4⋊C4×C17—21no—
63C2×C4⋊C4×C17—21no—
64C2×C4⋊C4×C17—21no—
65C2×C4⋊C4×C17—21no—
66C2×C4⋊C4×C17—21no—
67C2×C4⋊C4×C17—21no—
68C2×C4⋊C4×C17C2×C412yes—
69C2×C4⋊C4×C17D412yes—
70C2×#63227—24no—
71C2×#63227—24no—
72C2×#63227—42no—
73C2×#63227—42no—
74C2×#63227—42no—
75C2×#63227—42no—
76C2×C4⋊Dic17—21no—
77C2×C4⋊Dic17—21no—
78C2×C4⋊Dic17—21no—
79C2×C4⋊Dic17—21no—
80C2×C4⋊Dic17—21no—
81C2×C4⋊Dic17—21no—
82C2×C4⋊Dic17—21no—
83C2×C4⋊Dic17—21no—
84C2×C4⋊Dic17—21no—
85C2×C4⋊Dic17—21no—
86C2×C4⋊Dic17C2×C412yes—
87C2×C4⋊Dic17D412yes—
88C22×#3622—21no—
89C22×#3622—21no—
90C22×#3622—21no—
91C22×#3622—21no—
92C22×#3622—21no—
93C22×#3622—21no—
94C22×#3622D412yes—
95#10587502—24no—
96#10587502—24no—
97#10587491—28no—
98C24×C17C2×D411yescharacteristic
99C23×D17—21no—
100C23×D17—21no—
101C23×D17—21no—
102C23×D17—21no—
103C23×D17—21no—
104C23×D17—21no—
105C23×D17—21no—
106C23×D17—21no—
107C23×D17—21no—
108C23×D17—21no—
109C23×D17—21no—
110C23×D17—21no—
111C23×D17C22⋊C412yes—
112C23×D17SD1612yes—
113C23×D17Q1612yes—
114C22×C4×C17—22no—
115C22×C4×C17—22no—
116C22×C4×C17—41no—
117C22×C4×C17—41no—
118C22×C4×C17—41no—
119C22×C4×C17—41no—
120C22×C4×C17—41no—
121C22×C4×C17—41no—
122C22×C4×C17—41no—
123C22×C4×C17—41no—
124C22×C4×C17—41no—
125C22×C4×C17—41no—
126C22×C4×C17—41no—
127C22×C4×C17—41no—
128C22×C4×C17C22×C411yescharacteristic
129C22×C4×C17C2×D411yescharacteristic
130C22×C4×C17C2×D411yescharacteristic
131C22×C4×C17C2×D411yescharacteristic
132C22×C4×C17C2×D411yescharacteristic
133C22×C4×C17C2×D411yescharacteristic
134C22×C4×C17#4111yescharacteristic
135C22×C4×C17#4111yescharacteristic
136C22×C4×C17#4111yescharacteristic
137C22×C4×C17#4111yescharacteristic
138C22×C4×C17#4111yescharacteristic
139C22×C4×C17#4111yescharacteristic
140C22×C4×C17#4111yescharacteristic
141C22×C4×C17#4111yescharacteristic
142C22×Dic17—21no—
143C22×Dic17—21no—
144C22×Dic17—21no—
145C22×Dic17—21no—
146C22×Dic17—21no—
147C22×Dic17—21no—
148C22×Dic17—22no—
149C22×Dic17—22no—
150C22×Dic17—41no—
151C22×Dic17—41no—
152C22×Dic17—41no—
153C22×Dic17—41no—
154C22×Dic17—41no—
155C22×Dic17—41no—
156C22×Dic17—41no—
157C22×Dic17—41no—
158C22×Dic17—41no—
159C22×Dic17—41no—
160C22×Dic17—41no—
161C22×Dic17—41no—
162C22×Dic17C22⋊C412yes—
163C2×C4×D17—22no—
164C2×C4×D17—22no—
165C2×C4×D17—22no—
166C2×C4×D17—22no—
167C2×C4×D17—22no—
168C2×C4×D17—22no—
169C2×C4×D17—22no—
170C2×C4×D17—22no—
171C2×C4×D17—22no—
172C2×C4×D17—22no—
173C2×C4×D17—22no—
174C2×C4×D17—22no—
175C2×C4×D17—41no—
176C2×C4×D17—41no—
177C2×C4×D17—41no—
178C2×C4×D17—41no—
179C2×C4×D17—41no—
180C2×C4×D17—41no—
181C2×C4×D17—41no—
182C2×C4×D17—41no—
183C2×C4×D17—41no—
184C2×C4×D17—41no—
185C2×C4×D17—41no—
186C2×C4×D17—41no—
187C2×C4×D17—41no—
188C2×C4×D17—41no—
189C2×C4×D17—41no—
190C2×C4×D17—41no—
191C2×C8×C17—22no—
192C2×C8×C17—22no—
193C2×C8×C17—22no—
194C2×C8×C17—41no—
195C2×C8×C17—41no—
196C2×C8×C17—41no—
197C2×C8×C17—41no—
198C4⋊C4×C17—22no—
199C4⋊C4×C17—22no—
200C4⋊C4×C17—22no—
201C4⋊C4×C17—22no—
202C4⋊C4×C17—41no—
203C4⋊C4×C17—41no—
204C4⋊C4×C17—41no—
205C4⋊C4×C17—41no—
206#63227—48no—
207#63227—48no—
208C4⋊Dic17—22no—
209C4⋊Dic17—22no—
210C4⋊Dic17—22no—
211C4⋊Dic17—22no—
212C4⋊Dic17—41no—
213C4⋊Dic17—41no—
214C4⋊Dic17—41no—
215C4⋊Dic17—41no—
216C2×#3622—22no—
217C2×#3622—22no—
218C2×#3622—22no—
219C2×#3622—41no—
220C2×#3622—41no—
221C2×#3622—41no—
222C2×#3622—41no—
223#11200—171nomaximal, Sylow
224C23×C17C2×C22⋊C411yescharacteristic
225C23×C17#12011yescharacteristic
226C23×C17#12111yescharacteristic
227C23×C17#12111yescharacteristic
228C23×C17#12311yescharacteristic
229C23×C17#12311yescharacteristic
230C23×C17#12311yescharacteristic
231C23×C17C2×SD1611yescharacteristic
232C23×C17C2×Q1611yescharacteristic
233C23×C17#13511yescharacteristic
234C23×C17#13511yescharacteristic
235C23×C17AGL(1,ℤ/8)11yescharacteristic
236C23×C17AGL(1,ℤ/8)11yescharacteristic
237C23×C17AGL(1,ℤ/8)11yescharacteristic
238C23×C17#13711yescharacteristic
239C22×D17—22no—
240C22×D17—22no—
241C22×D17—22no—
242C22×D17—22no—
243C22×D17—22no—
244C22×D17—22no—
245C22×D17—22no—
246C22×D17—22no—
247C22×D17—22no—
248C22×D17—22no—
249C22×D17—22no—
250C22×D17—22no—
251C22×D17—22no—
252C22×D17—22no—
253C22×D17—22no—
254C22×D17—22no—
255C22×D17—22no—
256C22×D17—22no—
257C22×D17—41no—
258C22×D17—41no—
259C22×D17—41no—
260C22×D17—41no—
261C22×D17—41no—
262C22×D17—41no—
263C22×D17—41no—
264C22×D17—41no—
265C22×D17—41no—
266C22×D17—41no—
267C22×D17—41no—
268C22×D17—41no—
269C22×D17—41no—
270C22×D17—41no—
271C22×D17—41no—
272C22×D17—41no—
273C22×D17#10314yes—
274C2×C4×C17—42no—
275C2×C4×C17—42no—
276C2×C4×C17—42no—
277C2×C4×C17—42no—
278C2×C4×C17—42no—
279C2×C4×C17—42no—
280C2×C4×C17—81no—
281C2×C4×C17—81no—
282C2×C4×C17—81no—
283C2×C4×C17—81no—
284C2×C4×C17—81no—
285C2×C4×C17—81no—
286C2×C4×C17—81no—
287C2×C4×C17—81no—
288C2×C4×C17#11711yescharacteristic
289C2×C4×C17#11711yescharacteristic
290C2×C4×C17C4×D411yescharacteristic
291C2×C4×C17C4×D411yescharacteristic
292C2×C4×C17C4×D411yescharacteristic
293C2×C4×C17C4×D411yescharacteristic
294C2×C4×C17#12011yescharacteristic
295C2×C4×C17#12111yescharacteristic
296C2×C4×C17#12111yescharacteristic
297C2×C4×C17#12111yescharacteristic
298C2×C4×C17#12111yescharacteristic
299C2×C4×C17#12111yescharacteristic
300C2×C4×C17#12111yescharacteristic
301C2×C4×C17#12311yescharacteristic
302C2×C4×C17#12311yescharacteristic
303C2×C4×C17#12311yescharacteristic
304C2×C4×C17#12311yescharacteristic
305C2×C4×C17#12311yescharacteristic
306C2×C4×C17#12311yescharacteristic
307C2×C4×C17#12311yescharacteristic
308C2×C4×C17#12411yescharacteristic
309C2×C4×C17#12411yescharacteristic
310C2×C4×C17#12411yescharacteristic
311C2×C4×C17#12411yescharacteristic
312C2×C4×C17#12611yescharacteristic
313C2×C4×C17#12611yescharacteristic
314C2×C4×C17#12611yescharacteristic
315C2×C4×C17#12611yescharacteristic
316C2×Dic17—22no—
317C2×Dic17—22no—
318C2×Dic17—22no—
319C2×Dic17—41no—
320C2×Dic17—41no—
321C2×Dic17—41no—
322C2×Dic17—41no—
323C2×Dic17—42no—
324C2×Dic17—42no—
325C2×Dic17—42no—
326C2×Dic17—42no—
327C2×Dic17—42no—
328C2×Dic17—42no—
329C2×Dic17—81no—
330C2×Dic17—81no—
331C2×Dic17—81no—
332C2×Dic17—81no—
333C2×Dic17—81no—
334C2×Dic17—81no—
335C2×Dic17—81no—
336C2×Dic17—81no—
337C4×D17—42no—
338C4×D17—42no—
339C4×D17—42no—
340C4×D17—42no—
341C4×D17—42no—
342C4×D17—42no—
343C4×D17—42no—
344C4×D17—42no—
345C8×C17—42no—
346#3622—42no—
347C22×C22⋊C8—171no—
348C2×#380—171no—
349C2×#380—171no—
350C2×#340—171no—
351C2×#340—171no—
352C2×#340—171no—
353C2×#340D1711yescharacteristic, complemented
354C22×C17#38111yescharacteristic
355C22×C17#38611yescharacteristic
356C22×C17#38611yescharacteristic
357C22×C17#39411yescharacteristic
358C22×C17#39411yescharacteristic
359C22×C17#39711yescharacteristic
360C22×C17#39711yescharacteristic
361C22×C17C2×#10311yescharacteristic
362C22×C17#41611yescharacteristic
363C22×C17#41711yescharacteristic
364C22×C17#41811yescharacteristic
365C22×C17#44911yescharacteristic
366C22×C17#44911yescharacteristic
367C22×C17#45011yescharacteristic
368C22×C17#45111yescharacteristic
369C22×C17#46511yescharacteristic
370C22×C17#46511yescharacteristic
371C22×C17#46711yescharacteristic
372C22×C17#46711yescharacteristic
373C22×C17#46811yescharacteristic
374C22×C17#46811yescharacteristic
375C22×C17#46911yescharacteristic
376C22×C17#46911yescharacteristic
377C22×C17#48111yescharacteristic
378C22×C17#48111yescharacteristic
379C22×C17#48211yescharacteristic
380C22×C17#48211yescharacteristic
381C22×C17#48211yescharacteristic
382C22×C17#48211yescharacteristic
383C22×C17#48311yescharacteristic
384C22×C17#48411yescharacteristic
385C22×C17#48411yescharacteristic
386C22×C17#48411yescharacteristic
387C22×C17#48511yescharacteristic
388C22×C17#48511yescharacteristic
389C2×D17—24no—
390C2×D17—24no—
391C2×D17—24no—
392C2×D17—42no—
393C2×D17—42no—
394C2×D17—42no—
395C2×D17—42no—
396C2×D17—42no—
397C2×D17—42no—
398C2×D17—42no—
399C2×D17—42no—
400C2×D17—42no—
401C2×D17—42no—
402C2×D17—42no—
403C2×D17—42no—
404C4×C17—82no—
405C4×C17—82no—
406C4×C17#38811yescharacteristic
407C4×C17#38811yescharacteristic
408C4×C17#38811yescharacteristic
409C4×C17#38811yescharacteristic
410C4×C17#39411yescharacteristic
411C4×C17#39411yescharacteristic
412C4×C17#39711yescharacteristic
413C4×C17#39711yescharacteristic
414Dic17—42no—
415Dic17—82no—
416Dic17—82no—
417C24×C4—171no—
418C23×C8—171no—
419C23×C8C2×D1711yescharacteristic
420C22×C4⋊C4—171no—
421C22×C4⋊C4—171no—
422C22×C4⋊C4C2×D1711yescharacteristic
423C22×C4⋊C4C2×D1711yescharacteristic
424C22×C22⋊C4—341no—
425C22×C22⋊C4—341no—
426C2×C22⋊C8—342no—
427C2×C22⋊C8—342no—
428C2×C22⋊C8—342no—
429#380—174no—
430#380—342no—
431#380—342no—
432#380—342no—
433C2×#95—341no—
434C2×#95—341no—
435#340—22no—
436#340—342no—
437#340—342no—
438#340—342no—
439C2×C17#144011yescharacteristic
440C2×C17#182411yescharacteristic
441C2×C17#182511yescharacteristic
442C2×C17#187211yescharacteristic
443C2×C17#187511yescharacteristic
444C2×C17#189211yescharacteristic
445C2×C17#189511yescharacteristic
446C2×C17#203411yescharacteristic
447C2×C17#203411yescharacteristic
448C2×C17#203611yescharacteristic
449C2×C17#203611yescharacteristic
450C2×C17#207611yescharacteristic
451C2×C17#207611yescharacteristic
452C2×C17#207711yescharacteristic
453C2×C17#207711yescharacteristic
454D17—44no—
455C25—171no—
456C23×C4—21no—
457C23×C4—21no—
458C23×C4—171no—
459C23×C4—172no—
460C23×C4—172no—
461C23×C4—341no—
462C23×C4—341no—
463C23×C4—341no—
464C23×C4—341no—
465C23×C4—341no—
466C23×C4—341no—
467C23×C4—341no—
468C23×C4—341no—
469C23×C4—341no—
470C23×C4—341no—
471C23×C4—341no—
472C23×C4—341no—
473C23×C4—341no—
474C23×C4—341no—
475C23×C4C22×D1711yescharacteristic
476C22×C8—21no—
477C22×C8—21no—
478C22×C8—21no—
479C22×C8—21no—
480C22×C8—21no—
481C22×C8—21no—
482C22×C8—172no—
483C22×C8—341no—
484C22×C8—341no—
485C22×C8—341no—
486C22×C8—341no—
487C22×C8—341no—
488C22×C8—341no—
489C22×C8C22⋊D1712yes—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—172no—
501C2×C4⋊C4—172no—
502C2×C4⋊C4—341no—
503C2×C4⋊C4—341no—
504C2×C4⋊C4—341no—
505C2×C4⋊C4—341no—
506C2×C4⋊C4—341no—
507C2×C4⋊C4—341no—
508C2×C4⋊C4—341no—
509C2×C4⋊C4—341no—
510C2×C4⋊C4—341no—
511C2×C4⋊C4—341no—
512C2×C4⋊C4C4×D1712yes—
513C2×C4⋊C4D6812yes—
514C2×C22⋊C4—344no—
515C2×C22⋊C4—344no—
516C2×C22⋊C4—682no—
517C2×C22⋊C4—682no—
518C2×C22⋊C4—682no—
519C2×C22⋊C4—682no—
520C22⋊C8—348no—
521#95—344no—
522#95—344no—
523C17#1120011yescharacteristic, complemented, Sylow
524C24—172no—
525C24—172no—
526C24—172no—
527C24—341no—
528C24—341no—
529C24—341no—
530C24—341no—
531C24—341no—
532C24—341no—
533C24—341no—
534C24—341no—
535C24—341no—
536C24—341no—
537C24—341no—
538C24—341no—
539C24D4×D1711yescharacteristic
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—41no—
543C22×C4—41no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—172no—
555C22×C4—341no—
556C22×C4—341no—
557C22×C4—341no—
558C22×C4—341no—
559C22×C4—341no—
560C22×C4—341no—
561C22×C4—342no—
562C22×C4—342no—
563C22×C4—342no—
564C22×C4—342no—
565C22×C4—342no—
566C22×C4—342no—
567C22×C4—342no—
568C22×C4—342no—
569C22×C4—342no—
570C22×C4—342no—
571C22×C4—342no—
572C22×C4—342no—
573C22×C4—342no—
574C22×C4—342no—
575C22×C4—681no—
576C22×C4—681no—
577C22×C4—681no—
578C22×C4—681no—
579C22×C4—681no—
580C22×C4—681no—
581C22×C4—681no—
582C22×C4—681no—
583C22×C4—681no—
584C22×C4—681no—
585C22×C4—681no—
586C22×C4—681no—
587C22×C4—681no—
588C22×C4—681no—
589C22×C4—681no—
590C22×C4—681no—
591C22×C4—681no—
592C22×C4—681no—
593C22×C4—681no—
594C22×C4—681no—
595C22×C4—681no—
596C22×C4—681no—
597C22×C4—681no—
598C22×C4—681no—
599C22×C4—681no—
600C22×C4—681no—
601C22×C4—681no—
602C22×C4—681no—
603C22×C4C2×C4×D1711yescharacteristic
604C22×C4C2×D6811yescharacteristic
605C22×C4#6325211yescharacteristic
606C22×C4#6325211yescharacteristic
607C22×C4#6325211yescharacteristic
608C22×C4#6325211yescharacteristic
609C22×C4D4×D1711yescharacteristic
610C22×C4D4×D1711yescharacteristic
611C22×C4D4×D1711yescharacteristic
612C22×C4#6325411yescharacteristic
613C22×C4#6325411yescharacteristic
614C22×C4#6325611yescharacteristic
615C22×C4#6325611yescharacteristic
616C22×C4C2×C22⋊D1711yescharacteristic
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8—41no—
621C2×C8—41no—
622C2×C8—41no—
623C2×C8—41no—
624C2×C8—342no—
625C2×C8—342no—
626C2×C8—342no—
627C2×C8—681no—
628C2×C8—681no—
629C2×C8—681no—
630C2×C8—681no—
631C4⋊C4—22no—
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—41no—
636C4⋊C4—41no—
637C4⋊C4—41no—
638C4⋊C4—41no—
639C4⋊C4—342no—
640C4⋊C4—342no—
641C4⋊C4—342no—
642C4⋊C4—342no—
643C4⋊C4—681no—
644C4⋊C4—681no—
645C4⋊C4—681no—
646C4⋊C4—681no—
647C22⋊C4—688no—
648C22⋊C4—688no—
649C23—174no—
650C23—342no—
651C23—342no—
652C23—342no—
653C23—342no—
654C23—342no—
655C23—342no—
656C23—342no—
657C23—342no—
658C23—342no—
659C23—342no—
660C23—342no—
661C23—342no—
662C23—342no—
663C23—342no—
664C23—342no—
665C23—342no—
666C23—342no—
667C23—342no—
668C23—681no—
669C23—681no—
670C23—681no—
671C23—681no—
672C23—681no—
673C23—681no—
674C23—681no—
675C23—681no—
676C23—681no—
677C23—681no—
678C23—681no—
679C23—681no—
680C23—681no—
681C23—681no—
682C23—681no—
683C23—681no—
684C23C22⋊C4×D1711yescharacteristic
685C23#1058756811yescharacteristic
686C23#1058756911yescharacteristic
687C23#1058757011yescharacteristic
688C23#1058758011yescharacteristic
689C23#1058758011yescharacteristic
690C23#1058759711yescharacteristic
691C23#1058759711yescharacteristic
692C23SD16×D1711yescharacteristic
693C23#1058760011yescharacteristic
694C23#1058760111yescharacteristic
695C23#1058760211yescharacteristic
696C23Q16×D1711yescharacteristic
697C23#1058760511yescharacteristic
698C23#1058762411yescharacteristic
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—81no—
706C2×C4—81no—
707C2×C4—81no—
708C2×C4—81no—
709C2×C4—81no—
710C2×C4—81no—
711C2×C4—81no—
712C2×C4—81no—
713C2×C4—342no—
714C2×C4—342no—
715C2×C4—342no—
716C2×C4—681no—
717C2×C4—681no—
718C2×C4—681no—
719C2×C4—681no—
720C2×C4—682no—
721C2×C4—682no—
722C2×C4—682no—
723C2×C4—682no—
724C2×C4—682no—
725C2×C4—682no—
726C2×C4—682no—
727C2×C4—682no—
728C2×C4—682no—
729C2×C4—682no—
730C2×C4—682no—
731C2×C4—682no—
732C2×C4—682no—
733C2×C4—682no—
734C2×C4—1361no—
735C2×C4—1361no—
736C2×C4—1361no—
737C2×C4—1361no—
738C2×C4—1361no—
739C2×C4—1361no—
740C2×C4—1361no—
741C2×C4—1361no—
742C2×C4#1058755811yescharacteristic
743C2×C4C4×D6811yescharacteristic
744C2×C4#1058756111yescharacteristic
745C2×C4#1058756211yescharacteristic
746C2×C4#1058756711yescharacteristic
747C2×C4#1058756911yescharacteristic
748C2×C4#1058756911yescharacteristic
749C2×C4#1058757011yescharacteristic
750C2×C4#1058757011yescharacteristic
751C2×C4#1058757111yescharacteristic
752C2×C4#1058757111yescharacteristic
753C2×C4#1058757211yescharacteristic
754C2×C4#1058757811yescharacteristic
755C2×C4#1058757911yescharacteristic
756C2×C4#1058758011yescharacteristic
757C2×C4#1058758011yescharacteristic
758C2×C4#1058758011yescharacteristic
759C2×C4#1058758111yescharacteristic
760C2×C4#1058758111yescharacteristic
761C2×C4#1058758411yescharacteristic
762C2×C4#1058758411yescharacteristic
763C2×C4#1058758411yescharacteristic
764C2×C4C4×C22⋊D1711yescharacteristic
765C2×C4#1058761511yescharacteristic
766C2×C4#1058761611yescharacteristic
767C2×C4#1058762311yescharacteristic
768C2×C4#1058762511yescharacteristic
769C2×C4#1058763311yescharacteristic
770C8—42no—
771C8—682no—
772C22—344no—
773C22—344no—
774C22—344no—
775C22—682no—
776C22—682no—
777C22—682no—
778C22—682no—
779C22—682no—
780C22—682no—
781C22—682no—
782C22—682no—
783C22—682no—
784C22—682no—
785C22—682no—
786C22—682no—
787C22#1176267111yescharacteristic
788C22#1176268511yescharacteristic
789C22#1176268711yescharacteristic
790C22#1176272511yescharacteristic
791C22#1176272711yescharacteristic
792C22#1176273511yescharacteristic
793C22#1176273811yescharacteristic
794C22#103×D1711yescharacteristic
795C22#1176280411yescharacteristic
796C22#1176280711yescharacteristic
797C22#1176281211yescharacteristic
798C22#1176295511yescharacteristic
799C22#1176295711yescharacteristic
800C22#1176296111yescharacteristic
801C22#1176296611yescharacteristic
802C22#1176303511yescharacteristic
803C22#1176304111yescharacteristic
804C22#1176304711yescharacteristic
805C22#1176304911yescharacteristic
806C22#1176305211yescharacteristic
807C22#1176305411yescharacteristic
808C22#1176305911yescharacteristic
809C22#1176306111yescharacteristic
810C22#1176312611yescharacteristic
811C22#1176312911yescharacteristic
812C22#1176313211yescharacteristic
813C22#1176313511yescharacteristic
814C22#1176313611yescharacteristic
815C22#1176313611yescharacteristic
816C22#1176314111yescharacteristic
817C22#1176314311yescharacteristic
818C22#1176314611yescharacteristic
819C22#1176314611yescharacteristic
820C22#1176314911yescharacteristic
821C22#1176315311yescharacteristic
822C4—82no—
823C4—82no—
824C4—682no—
825C4—1362no—
826C4—1362no—
827C4#1176269811yescharacteristic
828C4#1176269911yescharacteristic
829C4#1176270011yescharacteristic
830C4#1176270111yescharacteristic
831C4#1176272411yescharacteristic
832C4#1176272611yescharacteristic
833C4#1176273611yescharacteristic
834C4#1176273811yescharacteristic
835C2—684no—
836C2#1452703211yescharacteristic
837C2#1452887311yescharacteristic
838C2#1452887811yescharacteristic
839C2#1452909011yescharacteristic
840C2#1452910511yescharacteristic
841C2#1452920411yescharacteristic
842C2#1452921911yescharacteristic
843C2#1452997211yescharacteristic
844C2#1452997611yescharacteristic
845C2#1452998611yescharacteristic
846C2#1452999011yescharacteristic
847C2#1453021311yescharacteristic
848C2#1453021611yescharacteristic
849C2#1453021811yescharacteristic
850C2#1453022311yescharacteristic
subgroupG/H
centerC24D4×D17
commutatorC22×C4×C17C22×C4
FrattiniC23×C4C22×D17
FittingC2×C17×#340C2
socleC24×C17C2×D4
prime radicalC24×D17D4
cosocleC23×C4×C17C23
hypercenterC2×#340D17
hypocenterC17#11200
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
4. C2×#11762572C2semidirect
5. C2×#11762571C2semidirect
6. C2×#11762571C2semidirect
7. C2×C17×#340C2semidirect
20. #11762666C4semidirect
353. C2×#340D17semidirect
523. C17#11200semidirect

Maximal subgroups

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

subgroupindex
C22×#105874912
C2×#117626662
C2×#117625722
C2×#117625712
C2×C17×#3402
#1120017