Finite Group Databasebeta

← C2×#14545347 #17979413

Subgroups — C2×#14545347 #17979413

Order 4352.

3342 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D17⋊M16C211yesmaximal, characteristic
2C22×#10587677C211yesmaximal, characteristic
3#14545347C2116yesmaximal, direct product factor
4C2×#11763775C214yesmaximal, complemented
5C2×#11763772C214yesmaximal, complemented
6C2×M16×#595C214yesmaximal, complemented
7C22×M16×D17C211yesmaximal, characteristic
8C22×#63243C412yescomplemented
9C2×D17⋊M16C412yescomplemented
10C2×D17⋊M16C418yescomplemented
11C2×D17⋊M16C412yescomplemented
12C2×D17⋊M16C2212yes—
13C2×D17⋊M16C2212yes—
14C2×D17⋊M16C2218yes—
15C22×#63247C412yescomplemented
16C22×#63242C2212yes—
17C2×#10587677C412yes—
18C2×#10587677C412yes—
19C2×#10587677C418yes—
20C2×#10587677C2212yes—
21C2×#10587677C2212yes—
22C2×#10587677C2218yes—
23C22×C4⋊#595C412yes—
24C22×C22⋊#595C412yes—
25C22×C4×#595C2212yes—
26#11763775C22132yescomplemented
27#11763772C22132yescomplemented
28M16×#595C22132yescomplemented
29C2×#10587532C2218yescomplemented
30C2×C8×#595C2218yescomplemented
31C23×C4×D17C2211yescharacteristic
32C22×#63223C411yescharacteristic, complemented
33C22×#63218C412yescomplemented
34C2×M16×D17C412yescomplemented
35C2×M16×D17C412yescomplemented
36C2×M16×D17C418yescomplemented
37C2×M16×D17C2212yes—
38C2×M16×D17C2212yes—
39C2×M16×D17C2218yes—
40C22×C8×D17C2212yes—
41C22×M16×C17C411yescharacteristic, complemented
42C24×D17C2×C411yescharacteristic
43C23×#595C2×C414yes—
44C23×C4×C17C2×C411yescharacteristic
45C23×Dic17C2×C411yescharacteristic
46C22×C4×D17C2×C411yescharacteristic
47C22×C4×D17C2×C411yescharacteristic
48C22×C4×D17C2×C411yescharacteristic
49C22×C4×D17C2×C414yes—
50C22×C4×D17C2×C411yescharacteristic
51C22×C4×D17C2×C414yes—
52C22×C4×D17C2×C411yescharacteristic
53C22×C4×D17C2×C411yescharacteristic
54C22×C4×D17C2×C411yescharacteristic
55C22×C4×D17C2×C414yes—
56C22×C4×D17C2×C411yescharacteristic
57C22×C4×D17C2×C411yescharacteristic
58C22×C4×D17C2311yescharacteristic
59C22×C4×D17C2311yescharacteristic
60C22×C4×D17C2311yescharacteristic
61C22×C4×D17C2314yes—
62C2×C22⋊#595C2×C414yes—
63C2×C22⋊#595C2×C414yes—
64C2×C22⋊#595C2×C4116yes—
65C2×#63247C2×C414yes—
66C2×#63247C2×C414yescomplemented
67C2×#63247C2×C4116yescomplemented
68C22×#3624C2×C414yescomplemented
69#10587677C2×C418yes—
70#10587677C2×C418yes—
71#10587677C2×C4116yes—
72#10587677C2×C4116yes—
73#10587677C2318yes—
74#10587677C2318yes—
75C2×C4⋊#595C2×C414yes—
76C2×C4⋊#595C2×C414yes—
77C2×C4⋊#595C2×C4116yes—
78C2×C4×#595C2×C414yes—
79C2×C4×#595C2×C418yes—
80C2×C4×#595C2314yes—
81C2×C4×#595C2318yes—
82D17⋊M16C2×C418yes—
83D17⋊M16C2×C418yescomplemented
84D17⋊M16C2×C4116yescomplemented
85D17⋊M16C2×C4116yescomplemented
86D17⋊M16C2318yes—
87D17⋊M16C2318yes—
88C2×#63243C2×C414yes—
89C2×#63243C2×C4116yescomplemented
90C2×#63243C2×C414yescomplemented
91C2×#63242C2×C418yescomplemented
92C2×#63242C2×C414yescomplemented
93C2×#63242C2314yes—
94C2×#63242C2318yes—
95C2×M16×C17C2×C412yes—
96C2×M16×C17C2×C412yescomplemented
97C2×M16×C17C2×C418yescomplemented
98C22×C8×C17C2×C412yescomplemented
99C2×#63223C2×C412yes—
100C2×#63223C2×C412yescomplemented
101C2×#63223C2×C418yescomplemented
102C22×#3622C2×C412yescomplemented
103M16×D17C2×C418yes—
104M16×D17C2×C4116yescomplemented
105M16×D17C2×C418yescomplemented
106M16×D17C2×C4116yescomplemented
107M16×D17C2318yes—
108M16×D17C2318yes—
109C2×#63218C2×C414yes—
110C2×#63218C2×C414yescomplemented
111C2×#63218C2×C4116yescomplemented
112C2×C8×D17C2×C414yescomplemented
113C2×C8×D17C2×C418yescomplemented
114C2×C8×D17C2314yes—
115C2×C8×D17C2318yes—
116#10587532C23132yescomplemented
117C8×#595C23132yescomplemented
118C24×C17C4211yescharacteristic
119C23×D17—44no—
120C23×D17C4214yes—
121C23×D17C4211yescharacteristic
122C23×D17C4211yescharacteristic
123C23×D17C4211yescharacteristic
124C23×D17C22×C411yescharacteristic
125C23×D17C22×C411yescharacteristic
126C23×D17C22×C411yescharacteristic
127C23×D17C22×C414yes—
128C22×#595—48no—
129C22×#595C22×C418yes—
130C22×#595C22×C4116yes—
131C22×C4×C17C4211yescharacteristic
132C22×C4×C17C4211yescharacteristic
133C22×C4×C17C4211yescharacteristic
134C22×C4×C17C4214yes—
135C22×C4×C17C22×C411yescharacteristic
136C22×C4×C17C22×C411yescharacteristic
137C22×C4×C17C22×C414yes—
138C22×C4×C17C22×C411yescharacteristic
139C22×Dic17C4211yescharacteristic
140C22×Dic17C4211yescharacteristic
141C22×Dic17C4211yescharacteristic
142C22×Dic17C4214yes—
143C22×Dic17C22×C411yescharacteristic
144C22×Dic17C22×C411yescharacteristic
145C22×Dic17C22×C411yescharacteristic
146C22×Dic17C22×C414yes—
147C2×C4×D17C4214yes—
148C2×C4×D17C4211yescharacteristic
149C2×C4×D17C4211yescharacteristic
150C2×C4×D17C4214yes—
151C2×C4×D17C4214yes—
152C2×C4×D17C4211yescharacteristic
153C2×C4×D17C4211yescharacteristic
154C2×C4×D17C4211yescharacteristic
155C2×C4×D17C4211yescharacteristic
156C2×C4×D17C4214yes—
157C2×C4×D17C4214yes—
158C2×C4×D17C4214yes—
159C2×C4×D17C4214yes—
160C2×C4×D17C4214yes—
161C2×C4×D17C4214yes—
162C2×C4×D17C22×C412yes—
163C2×C4×D17C22×C411yescharacteristic
164C2×C4×D17C22×C414yes—
165C2×C4×D17C22×C411yescharacteristic
166C2×C4×D17C22×C411yescharacteristic
167C2×C4×D17C22×C412yes—
168C2×C4×D17C22×C412yes—
169C2×C4×D17C22×C414yes—
170C2×C4×D17C22×C414yes—
171C2×C4×D17C22×C412yes—
172C2×C4×D17C22×C411yescharacteristic
173C2×C4×D17C22×C411yescharacteristic
174C2×C4×D17C22×C414yes—
175C2×C4×D17C22×C411yescharacteristic
176C2×C4×D17C22×C412yes—
177C2×C4×D17C22×C412yes—
178C2×C4×D17C22×C414yes—
179C2×C4×D17C22×C414yes—
180C2×C4×D17C22×C412yes—
181C2×C4×D17C22×C411yescharacteristic
182C2×C4×D17C22×C411yescharacteristic
183C2×C4×D17C22×C414yes—
184C2×C4×D17C22×C411yescharacteristic
185C2×C4×D17C22×C412yes—
186C2×C4×D17C22×C412yes—
187C2×C4×D17C22×C414yes—
188C2×C4×D17C22×C414yes—
189C2×C4×D17C2411yescharacteristic
190C2×C4×D17C2412yes—
191C2×C4×D17C2412yes—
192C2×C4×D17C2412yes—
193C22⋊#595C22×C4116yes—
194C22⋊#595C22×C4116yes—
195#63247C22×C4116yes—
196#63247C22×C4116yescomplemented
197C2×#3624C22×C418yes—
198C2×#3624C22×C4116yescomplemented
199C4⋊#595C22×C4116yes—
200C4⋊#595C22×C4116yes—
201C4×#595C22×C418yes—
202C4×#595C22×C4116yes—
203C4×#595C2418yes—
204#63243C22×C4116yes—
205#63243C22×C4116yescomplemented
206#63242C22×C418yes—
207#63242C22×C4116yescomplemented
208#63242C2418yes—
209M16×C17C22×C418yes—
210M16×C17C22×C418yescomplemented
211C2×C8×C17C22×C414yes—
212C2×C8×C17C22×C418yescomplemented
213#63223C22×C418yes—
214#63223C22×C418yescomplemented
215C2×#3622C22×C414yes—
216C2×#3622C22×C418yescomplemented
217#63218C22×C4116yes—
218#63218C22×C4116yescomplemented
219C8×D17C22×C418yes—
220C8×D17C22×C4116yescomplemented
221C8×D17C2418yes—
222C2×#2873—171nomaximal, Sylow
223C23×C17—42no—
224C23×C17C2×C4211yescharacteristic
225C23×C17C2×C4211yescharacteristic
226C23×C17C2×C4211yescharacteristic
227C23×C17C2×C4214yes—
228C22×D17—24no—
229C22×D17—24no—
230C22×D17—24no—
231C22×D17—48no—
232C22×D17—48no—
233C22×D17—42no—
234C22×D17—42no—
235C22×D17—42no—
236C22×D17C2×C4211yescharacteristic
237C22×D17C2×C4211yescharacteristic
238C22×D17C2×C4211yescharacteristic
239C22×D17C2×C4212yes—
240C22×D17C2×C4212yes—
241C22×D17C2×C4212yes—
242C22×D17C2×C4214yes—
243C22×D17C2×C4214yes—
244C22×D17C2×C4214yes—
245C22×D17C23×C412yes—
246C22×D17C23×C412yes—
247C22×D17C23×C412yes—
248C22×D17C23×C411yescharacteristic
249C2×#595—216no—
250C2×#595—416no—
251C2×#595C23×C4116yes—
252C2×C4×C17C2×C4212yes—
253C2×C4×C17C2×C4214yes—
254C2×C4×C17C2×C4212yes—
255C2×C4×C17C2×C4214yes—
256C2×C4×C17C2×C4212yes—
257C2×C4×C17C2×C4214yes—
258C2×C4×C17C2×C4211yescharacteristic
259C2×C4×C17C2×C4211yescharacteristic
260C2×C4×C17C2×C4211yescharacteristic
261C2×C4×C17C23×C412yes—
262C2×C4×C17C23×C412yes—
263C2×C4×C17C23×C412yes—
264C2×C4×C17C23×C411yescharacteristic
265C2×Dic17C2×C4212yes—
266C2×Dic17C2×C4214yes—
267C2×Dic17C2×C4212yes—
268C2×Dic17C2×C4214yes—
269C2×Dic17C2×C4212yes—
270C2×Dic17C2×C4214yes—
271C2×Dic17C2×C4211yescharacteristic
272C2×Dic17C2×C4211yescharacteristic
273C2×Dic17C2×C4211yescharacteristic
274C2×Dic17C23×C411yescharacteristic
275C2×Dic17C23×C412yes—
276C2×Dic17C23×C412yes—
277C2×Dic17C23×C412yes—
278C4×D17C2×C4212yes—
279C4×D17C2×C4212yes—
280C4×D17C2×C4214yes—
281C4×D17C2×C4214yes—
282C4×D17C2×C4212yes—
283C4×D17C2×C4212yes—
284C4×D17C2×C4212yes—
285C4×D17C2×C4214yes—
286C4×D17C2×C4212yes—
287C4×D17C2×C4214yes—
288C4×D17C2×C4214yes—
289C4×D17C2×C4214yes—
290C4×D17C2×C4212yes—
291C4×D17C2×C4212yes—
292C4×D17C2×C4212yes—
293C4×D17C23×C411yescharacteristic
294C4×D17C23×C412yes—
295C4×D17C23×C412yes—
296C4×D17C23×C412yes—
297C4×D17C23×C411yescharacteristic
298C4×D17C23×C412yes—
299C4×D17C23×C412yes—
300C4×D17C23×C412yes—
301C4×D17C23×C411yescharacteristic
302C4×D17C23×C412yes—
303C4×D17C23×C412yes—
304C4×D17C23×C412yes—
305C4×D17C2511yescharacteristic
306#3624C23×C4116yes—
307C8×C17C23×C418yes—
308#3622C23×C418yes—
309C23×M16—171no—
310C23×M16—171no—
311C22×#117—171no—
312#2873—1716no—
313C2×#405—174no—
314C2×#405—174no—
315C2×C4×M16—174no—
316C22×C17—22no—
317C22×C17—22no—
318C22×C17—22no—
319C22×C17—44no—
320C22×C17C22×C4212yes—
321C22×C17C22×C4212yes—
322C22×C17C22×C4212yes—
323C22×C17C22×C4211yescharacteristic
324C2×D17—22no—
325C2×D17—22no—
326C2×D17—22no—
327C2×D17—24no—
328C2×D17—24no—
329C2×D17—24no—
330C2×D17—24no—
331C2×D17—24no—
332C2×D17—24no—
333C2×D17—44no—
334C2×D17—44no—
335C2×D17—44no—
336C2×D17C22×C4212yes—
337C2×D17C22×C4212yes—
338C2×D17C22×C4212yes—
339C2×D17C22×C4211yescharacteristic
340C2×D17#56814yes—
341C2×D17C24×C411yescharacteristic
342#595—216no—
343C4×C17C22×C4212yes—
344C4×C17C22×C4212yes—
345C4×C17C22×C4212yes—
346C4×C17C22×C4211yescharacteristic
347C4×C17C24×C411yescharacteristic
348Dic17C22×C4211yescharacteristic
349Dic17C22×C4212yes—
350Dic17C22×C4212yes—
351Dic17C22×C4212yes—
352Dic17C24×C411yescharacteristic
353C24×C4—171no—
354C22×M16—172no—
355C22×M16—172no—
356C22×M16—178no—
357C22×M16—172no—
358C22×M16—172no—
359C22×M16—178no—
360C22×M16—172no—
361C22×M16—172no—
362C22×M16—171no—
363C22×M16—172no—
364C22×M16—172no—
365C22×M16—172no—
366C22×M16—178no—
367C22×M16—172no—
368C22×M16—178no—
369C22×M16—172no—
370C22×M16#59511yescharacteristic, complemented
371C23×C8—172no—
372C23×C8—172no—
373C2×#117—172no—
374C2×#117—172no—
375C2×#117—178no—
376C2×#117—172no—
377C2×#117—172no—
378C2×#117—178no—
379C22×C4⋊C4—172no—
380C22×C22⋊C4—172no—
381C22×C42—172no—
382#405—1732no—
383#405—1732no—
384C4×M16—1732no—
385C2×#97—178no—
386C2×C4×C8—178no—
387C2×C17—22no—
388C2×C17—22no—
389C2×C17—22no—
390C2×C17#287312yescomplemented
391C2×C17C23×C4211yescharacteristic
392D17—22no—
393D17—22no—
394D17—22no—
395D17#287312yescomplemented
396D17C2×#56812yes—
397C25—171no—
398C23×C4—171no—
399C23×C4—171no—
400C23×C4—171no—
401C23×C4—171no—
402C23×C4—174no—
403C23×C4—171no—
404C23×C4—171no—
405C23×C4—171no—
406C23×C4—174no—
407C23×C4—171no—
408C23×C4—171no—
409C23×C4—174no—
410C23×C4—174no—
411C23×C4—171no—
412C23×C4—171no—
413C23×C4—171no—
414C23×C4—171no—
415C23×C4—174no—
416C23×C4C2×#59511yescharacteristic
417C2×M16—174no—
418C2×M16—174no—
419C2×M16—1716no—
420C2×M16—178no—
421C2×M16—178no—
422C2×M16—1716no—
423C2×M16—1716no—
424C2×M16—178no—
425C2×M16—178no—
426C2×M16—174no—
427C2×M16—174no—
428C2×M16—1716no—
429C2×M16—172no—
430C2×M16—178no—
431C2×M16—172no—
432C2×M16—178no—
433C2×M16—178no—
434C2×M16—1716no—
435C2×M16—178no—
436C2×M16—178no—
437C2×M16—1716no—
438C2×M16—174no—
439C2×M16—174no—
440C2×M16—1716no—
441C2×M16C2×#59512yes—
442C2×M16C2×#59512yescomplemented
443C2×M16C2×#59518yescomplemented
444C22×C8—178no—
445C22×C8—174no—
446C22×C8—174no—
447C22×C8—178no—
448C22×C8—174no—
449C22×C8—172no—
450C22×C8—174no—
451C22×C8—174no—
452C22×C8—178no—
453C22×C8—178no—
454C22×C8C2×#59512yescomplemented
455#117—178no—
456#117—178no—
457#117—1716no—
458#117—1716no—
459#117—178no—
460#117—178no—
461C2×C4⋊C4—174no—
462C2×C4⋊C4—174no—
463C2×C4⋊C4—1716no—
464C2×C22⋊C4—174no—
465C2×C22⋊C4—174no—
466C2×C22⋊C4—1716no—
467C2×C42—174no—
468C2×C42—178no—
469C2×C42—174no—
470C2×C42—178no—
471#97—1732no—
472C4×C8—1732no—
473C17C2×#287311yescharacteristic, complemented, Sylow
474C24—171no—
475C24—171no—
476C24—171no—
477C24—174no—
478C24—171no—
479C24—171no—
480C24—171no—
481C24—174no—
482C24—684no—
483C24C4×#59511yescharacteristic
484C22×C4—171no—
485C22×C4—171no—
486C22×C4—171no—
487C22×C4—174no—
488C22×C4—171no—
489C22×C4—171no—
490C22×C4—171no—
491C22×C4—174no—
492C22×C4—174no—
493C22×C4—171no—
494C22×C4—171no—
495C22×C4—174no—
496C22×C4—174no—
497C22×C4—171no—
498C22×C4—171no—
499C22×C4—171no—
500C22×C4—171no—
501C22×C4—174no—
502C22×C4—174no—
503C22×C4—174no—
504C22×C4—174no—
505C22×C4—174no—
506C22×C4—174no—
507C22×C4—171no—
508C22×C4—172no—
509C22×C4—171no—
510C22×C4—171no—
511C22×C4—174no—
512C22×C4—172no—
513C22×C4—172no—
514C22×C4—174no—
515C22×C4—174no—
516C22×C4—172no—
517C22×C4—171no—
518C22×C4—171no—
519C22×C4—171no—
520C22×C4—174no—
521C22×C4—172no—
522C22×C4—172no—
523C22×C4—174no—
524C22×C4—174no—
525C22×C4—172no—
526C22×C4—172no—
527C22×C4—174no—
528C22×C4—172no—
529C22×C4—174no—
530C22×C4—174no—
531C22×C4—172no—
532C22×C4—172no—
533C22×C4—172no—
534C22×C4—171no—
535C22×C4—171no—
536C22×C4—171no—
537C22×C4—171no—
538C22×C4—178no—
539C22×C4—1716no—
540C22×C4—688no—
541C22×C4C4×#59511yescharacteristic
542C22×C4C4×#59511yescharacteristic
543C22×C4C4×#59511yescharacteristic
544C22×C4C4×#59514yes—
545C22×C4C22×#59514yes—
546C22×C4C22×#59511yescharacteristic
547C22×C4C22×#59511yescharacteristic
548C22×C4C22×#59511yescharacteristic
549M16—1716no—
550M16—1716no—
551M16—1716no—
552M16—1716no—
553M16—178no—
554M16—178no—
555M16—1716no—
556M16—1716no—
557M16C22×#59518yes—
558M16C22×#59518yescomplemented
559C2×C8—178no—
560C2×C8—1716no—
561C2×C8—178no—
562C2×C8—178no—
563C2×C8—1716no—
564C2×C8—178no—
565C2×C8—174no—
566C2×C8—178no—
567C2×C8—178no—
568C2×C8—1716no—
569C2×C8C22×#59514yes—
570C2×C8C22×#59518yescomplemented
571C4⋊C4—1716no—
572C4⋊C4—1716no—
573C22⋊C4—1716no—
574C22⋊C4—1716no—
575C42—178no—
576C42—1716no—
577C42—178no—
578C23—42no—
579C23—171no—
580C23—172no—
581C23—172no—
582C23—172no—
583C23—172no—
584C23—172no—
585C23—172no—
586C23—171no—
587C23—171no—
588C23—171no—
589C23—174no—
590C23—174no—
591C23—174no—
592C23—344no—
593C23—344no—
594C23—344no—
595C23—682no—
596C23—682no—
597C23—682no—
598C23—688no—
599C23—688no—
600C23C2×C4×#59511yescharacteristic
601C23C2×C4×#59511yescharacteristic
602C23C2×C4×#59511yescharacteristic
603C23C2×C4×#59514yes—
604C2×C4—172no—
605C2×C4—171no—
606C2×C4—172no—
607C2×C4—172no—
608C2×C4—172no—
609C2×C4—172no—
610C2×C4—174no—
611C2×C4—172no—
612C2×C4—174no—
613C2×C4—174no—
614C2×C4—171no—
615C2×C4—171no—
616C2×C4—171no—
617C2×C4—172no—
618C2×C4—171no—
619C2×C4—172no—
620C2×C4—172no—
621C2×C4—172no—
622C2×C4—171no—
623C2×C4—172no—
624C2×C4—172no—
625C2×C4—172no—
626C2×C4—172no—
627C2×C4—172no—
628C2×C4—172no—
629C2×C4—174no—
630C2×C4—174no—
631C2×C4—172no—
632C2×C4—172no—
633C2×C4—174no—
634C2×C4—174no—
635C2×C4—174no—
636C2×C4—174no—
637C2×C4—172no—
638C2×C4—172no—
639C2×C4—172no—
640C2×C4—171no—
641C2×C4—171no—
642C2×C4—172no—
643C2×C4—172no—
644C2×C4—172no—
645C2×C4—1716no—
646C2×C4—3416no—
647C2×C4—6816no—
648C2×C4C2×C4×#59514yes—
649C2×C4C2×C4×#59514yes—
650C2×C4C2×C4×#59514yes—
651C2×C4C2×C4×#59511yescharacteristic
652C2×C4C2×C4×#59511yescharacteristic
653C2×C4C2×C4×#59511yescharacteristic
654C2×C4C2×C4×#59512yes—
655C2×C4C2×C4×#59512yes—
656C2×C4C2×C4×#59512yes—
657C2×C4C23×#59512yes—
658C2×C4C23×#59512yes—
659C2×C4C23×#59512yes—
660C2×C4C23×#59511yescharacteristic
661C8—1716no—
662C8—178no—
663C8C23×#59518yes—
664C22—22no—
665C22—22no—
666C22—22no—
667C22—44no—
668C22—171no—
669C22—171no—
670C22—174no—
671C22—172no—
672C22—172no—
673C22—172no—
674C22—344no—
675C22—344no—
676C22—344no—
677C22—344no—
678C22—344no—
679C22—344no—
680C22—342no—
681C22—342no—
682C22—342no—
683C22—684no—
684C22—684no—
685C22—684no—
686C22C22×C4×#59512yes—
687C22C22×C4×#59512yes—
688C22C22×C4×#59512yes—
689C22C22×C4×#59511yescharacteristic
690C4—171no—
691C4—171no—
692C4—172no—
693C4—172no—
694C4—172no—
695C4—3416no—
696C4C22×C4×#59512yes—
697C4C22×C4×#59512yes—
698C4C22×C4×#59512yes—
699C4C22×C4×#59511yescharacteristic
700C4C24×#59511yescharacteristic
701C2—22no—
702C2—22no—
703C2—22no—
704C2—172no—
705C2—172no—
706C2—342no—
707C2—342no—
708C2—342no—
709C2#1454534712yesdirect product factor
710C2C23×C4×#59511yescharacteristic
subgroupG/H
centerC2×C4C23×#595
commutatorC2×C17C23×C42
FrattiniC4C24×#595
FittingC22×M16×C17C4
socleC22×C17C22×C42
prime radicalC24×D17C2×C4
cosocleC4×D17C25
hypercenterC22×M16#595
hypocenterC17C2×#2873
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×M16

Complements

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

NH ≅ G/Ntype
3. #14545347C2direct (N × H)
4. C2×#11763775C2semidirect
5. C2×#11763772C2semidirect
6. C2×M16×#595C2semidirect
8. C22×#63243C4semidirect
9. C2×D17⋊M16C4semidirect
10. C2×D17⋊M16C4semidirect
11. C2×D17⋊M16C4semidirect
15. C22×#63247C4semidirect
26. #11763775C22semidirect
27. #11763772C22semidirect
28. M16×#595C22semidirect
29. C2×#10587532C22semidirect
30. C2×C8×#595C22semidirect
32. C22×#63223C4semidirect
33. C22×#63218C4semidirect
34. C2×M16×D17C4semidirect
35. C2×M16×D17C4semidirect
36. C2×M16×D17C4semidirect
41. C22×M16×C17C4semidirect
66. C2×#63247C2×C4semidirect
67. C2×#63247C2×C4semidirect
68. C22×#3624C2×C4semidirect
83. D17⋊M16C2×C4semidirect
84. D17⋊M16C2×C4semidirect
85. D17⋊M16C2×C4semidirect
89. C2×#63243C2×C4semidirect
90. C2×#63243C2×C4semidirect
91. C2×#63242C2×C4semidirect
92. C2×#63242C2×C4semidirect
96. C2×M16×C17C2×C4semidirect
97. C2×M16×C17C2×C4semidirect
98. C22×C8×C17C2×C4semidirect
100. C2×#63223C2×C4semidirect
101. C2×#63223C2×C4semidirect
102. C22×#3622C2×C4semidirect
104. M16×D17C2×C4semidirect
105. M16×D17C2×C4semidirect
106. M16×D17C2×C4semidirect
110. C2×#63218C2×C4semidirect
111. C2×#63218C2×C4semidirect
112. C2×C8×D17C2×C4semidirect
113. C2×C8×D17C2×C4semidirect
116. #10587532C23semidirect
117. C8×#595C23semidirect
196. #63247C22×C4semidirect
198. C2×#3624C22×C4semidirect
205. #63243C22×C4semidirect
207. #63242C22×C4semidirect
210. M16×C17C22×C4semidirect
212. C2×C8×C17C22×C4semidirect
214. #63223C22×C4semidirect
216. C2×#3622C22×C4semidirect
218. #63218C22×C4semidirect
220. C8×D17C22×C4semidirect
370. C22×M16#595semidirect
390. C2×C17#2873semidirect
395. D17#2873semidirect
442. C2×M16C2×#595semidirect
443. C2×M16C2×#595semidirect
454. C22×C8C2×#595semidirect
473. C17C2×#2873semidirect
558. M16C22×#595semidirect
570. C2×C8C22×#595semidirect
709. C2#14545347direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D17⋊M162
C22×#105876772
#145453472
C2×#117637752
C2×#117637722
C2×M16×#5952
C22×M16×D172
C2×#287317