Finite Group Databasebeta

← C2×#14545516 #17979685

Subgroups — C2×#14545516 #17979685

Order 4352.

2926 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587678C211yesmaximal, characteristic, complemented
2C23×#63247C211yesmaximal, characteristic, complemented
3#14545516C2116yesmaximal, direct product factor
4C2×#11763844C211yesmaximal, characteristic, complemented
5C2×#11763842C211yesmaximal, characteristic, complemented
6C2×#11763841C211yesmaximal, characteristic, complemented
7C2×#11763840C211yesmaximal, characteristic, complemented
8C2×#11763840C211yesmaximal, characteristic, complemented
9C2×#11763838C211yesmaximal, characteristic, complemented
10C2×#11763836C211yesmaximal, characteristic, complemented
11C2×D4×#3624C211yesmaximal, characteristic, complemented
12C2×#11763815C211yesmaximal, characteristic, complemented
13C2×#11763782C211yesmaximal, characteristic, complemented
14C22×C22⋊#3624C211yesmaximal, characteristic, complemented
15C2×#11763773C211yesmaximal, characteristic, complemented
16C2×#11763315C211yesmaximal, characteristic
17C2×#10587678—28no—
18C2×#10587678C2218yescomplemented
19C22×#63243C2211yescharacteristic, complemented
20C22×#63247—28no—
21C22×#63247C2211yescharacteristic
22C22×#63247C2211yescharacteristic
23C22×#63247C2211yescharacteristic
24C22×#63247C2211yescharacteristic
25C22×#63247C2218yescomplemented
26C22×#63247C2211yescharacteristic, complemented
27C22×#63242C2211yescharacteristic, complemented
28C23×#3624C2211yescharacteristic
29C23×#3624C2211yescharacteristic
30C23×#3624C2211yescharacteristic
31C23×#3624C2211yescharacteristic
32C23×#3624C2211yescharacteristic, complemented
33#11763844C2218yescomplemented
34#11763842C2218yescomplemented
35#11763841C2218yescomplemented
36#11763840C2218yescomplemented
37#11763840C2218yescomplemented
38#11763838C2218yescomplemented
39#11763836C2218yescomplemented
40D4×#3624C2218yescomplemented
41#11763815C2218yescomplemented
42C2×#10587544C2211yescharacteristic, complemented
43C2×#10587544C2211yescharacteristic, complemented
44C2×C4⋊#3624C2211yescharacteristic, complemented
45C2×C4⋊#3624C2211yescharacteristic, complemented
46#11763782C2218yescomplemented
47C2×#10587543C2211yescharacteristic, complemented
48C2×#10587543C2211yescharacteristic, complemented
49C2×C22⋊#3624C2211yescharacteristic
50C2×C22⋊#3624C2211yescharacteristic
51C2×C22⋊#3624C2211yescharacteristic
52C2×C22⋊#3624C2211yescharacteristic
53C2×C22⋊#3624C2218yescomplemented
54C2×C22⋊#3624C2211yescharacteristic, complemented
55C2×C22⋊#3624C2211yescharacteristic, complemented
56#11763773C2218yescomplemented
57C2×#10587542C2211yescharacteristic, complemented
58C2×#10587542C2211yescharacteristic, complemented
59C2×C4×#3624C2211yescharacteristic, complemented
60C2×C4×#3624C2211yescharacteristic, complemented
61C22×#63254C2211yescharacteristic
62C24×Dic17C2211yescharacteristic
63#11763315C418yes—
64#11763315C2218yes—
65C2×#10587572C411yescharacteristic
66C2×#10587621C411yescharacteristic
67C2×#10587564C411yescharacteristic
68C2×#10587564C411yescharacteristic
69C2×#10587625C411yescharacteristic
70C2×#10587625C411yescharacteristic
71C2×#10587639C411yescharacteristic
72C2×D4×Dic17C2211yescharacteristic
73C2×D4×Dic17C2211yescharacteristic
74C2×#10587567C2211yescharacteristic
75C2×#10587567C2211yescharacteristic
76C2×#10587563C2211yescharacteristic
77C2×C17×#120C411yescharacteristic
78C25×C17C2×C411yescharacteristic
79C22×D4×C17C2×C411yescharacteristic
80C22×D4×C17C2×C411yescharacteristic
81C22×D4×C17C2×C411yescharacteristic
82C22×C22⋊D17C2×C411yescharacteristic
83C22×C22⋊D17C2×C411yescharacteristic
84C22×C22⋊D17C2×C411yescharacteristic
85C22×C22⋊D17C2×C411yescharacteristic
86C23×Dic17—24no—
87C23×Dic17—24no—
88C23×Dic17C2×C411yescharacteristic
89C23×Dic17C2×C411yescharacteristic
90C23×Dic17C2×C411yescharacteristic
91C23×Dic17C2×C414yes—
92C23×Dic17C2311yescharacteristic
93C23×Dic17C2311yescharacteristic
94C23×Dic17C2311yescharacteristic
95C23×Dic17C2314yes—
96C23×Dic17C2311yescharacteristic
97C2×#63254—24no—
98C2×#63254—24no—
99C2×#63254C2×C414yes—
100C2×#63254C2314yes—
101C22×C4×D17C2311yescharacteristic
102C22×Dic34C2×C411yescharacteristic
103C2×#63247—24no—
104C2×#63247—232no—
105C2×#63247—24no—
106C2×#63247—24no—
107C2×#63247—24no—
108C2×#63247D418yescomplemented
109C2×#63247C2314yes—
110C2×#63247C2314yes—
111C2×#63247C2314yes—
112C2×#63247C2314yes—
113C2×#63247C2314yescomplemented
114C22×#3624—24no—
115C22×#3624—24no—
116C22×#3624—24no—
117C22×#3624—24no—
118C22×#3624—24no—
119C22×#3624C2311yescharacteristic
120C22×#3624C2311yescharacteristic
121C22×#3624C2314yes—
122C22×#3624C2311yescharacteristic
123C22×#3624C2311yescharacteristic
124C22×#3624C2314yes—
125C22×#3624C2311yescharacteristic
126C22×#3624C2311yescharacteristic
127C22×#3624C2314yes—
128C22×#3624C2314yes—
129C22×#3624C2311yescharacteristic
130C22×#3624C2311yescharacteristic
131C22×#3624C2314yescomplemented
132#10587678—232no—
133C2×#63243—24no—
134C2×#63243C2314yescomplemented
135C2×#63242—24no—
136C2×#63242C2314yescomplemented
137C17×#120C2×C418yes—
138C2×C22⋊C4×C17C2×C411yescharacteristic
139C2×C22⋊C4×C17C2×C411yescharacteristic
140C2×C22⋊C4×C17C2×C411yescharacteristic
141#10587639C2×C418yes—
142C2×C22⋊Dic17C2×C411yescharacteristic
143C2×C22⋊Dic17C2×C411yescharacteristic
144C2×C22⋊Dic17C2×C411yescharacteristic
145C2×C22⋊Dic17C2×C411yescharacteristic
146C2×C22⋊Dic17C2×C411yescharacteristic
147#10587625C2×C418yes—
148#10587625C2×C418yes—
149#10587621C2×C418yes—
150D4×Dic17C2×C414yes—
151D4×Dic17C2×C414yes—
152D4×Dic17C2314yes—
153D4×Dic17C2314yes—
154C2×#63227C2×C411yescharacteristic
155C2×#63227C2×C411yescharacteristic
156C2×C4⋊Dic17C2×C411yescharacteristic
157C2×C4⋊Dic17C2×C411yescharacteristic
158C2×#63225C2×C411yescharacteristic
159C2×#63225C2×C411yescharacteristic
160C2×#63225C2×C411yescharacteristic
161C2×#63225C2×C411yescharacteristic
162C2×C4×Dic17C2311yescharacteristic
163C2×C4×Dic17C2311yescharacteristic
164#10587572C2×C418yes—
165#10587567C2×C414yes—
166#10587567C2×C414yes—
167#10587567C2314yes—
168#10587567C2314yes—
169#10587564C2×C418yes—
170#10587564C2×C418yes—
171#10587563C2×C414yes—
172#10587563C2314yes—
173C22⋊#3624C2314yes—
174C22⋊#3624C2314yes—
175C22⋊#3624C2314yes—
176C22⋊#3624C2314yes—
177C22⋊#3624C2314yescomplemented
178C22⋊#3624C2314yescomplemented
179#10587544C2314yescomplemented
180#10587544C2314yescomplemented
181#10587543C2314yescomplemented
182#10587543C2314yescomplemented
183#10587542C2314yescomplemented
184#10587542C2314yescomplemented
185C4⋊#3624C2314yescomplemented
186C4⋊#3624C2314yescomplemented
187C4×#3624C2314yescomplemented
188C4×#3624C2314yescomplemented
189C24×C17—24no—
190C24×C17—24no—
191C24×C17—42no—
192C24×C17C22×C411yescharacteristic
193C24×C17C22×C411yescharacteristic
194C24×C17C22×C414yes—
195C24×C17C22×C411yescharacteristic
196C24×C17C22×C411yescharacteristic
197C23×D17C22×C411yescharacteristic
198C2×D4×C17—24no—
199C2×D4×C17—24no—
200C2×D4×C17—42no—
201C2×D4×C17C22×C414yes—
202C2×D4×C17C22×C414yes—
203C2×D4×C17C22×C414yes—
204C22×C4×C17C22×C411yescharacteristic
205C22×C4×C17C22×C411yescharacteristic
206C22×C4×C17C22×C411yescharacteristic
207C2×C22⋊D17—24no—
208C2×C22⋊D17—24no—
209C2×C22⋊D17—24no—
210C2×C22⋊D17—42no—
211C2×C22⋊D17C22×C414yes—
212C2×C22⋊D17C22×C414yes—
213C2×C22⋊D17C22×C414yes—
214C2×C22⋊D17C22×C414yes—
215C22×Dic17—24no—
216C22×Dic17—24no—
217C22×Dic17—24no—
218C22×Dic17—216no—
219C22×Dic17—22no—
220C22×Dic17—22no—
221C22×Dic17—28no—
222C22×Dic17—22no—
223C22×Dic17—22no—
224C22×Dic17—22no—
225C22×Dic17—22no—
226C22×Dic17—28no—
227C22×Dic17C22×C411yescharacteristic
228C22×Dic17C22×C412yes—
229C22×Dic17C22×C414yes—
230C22×Dic17C22×C414yes—
231C22×Dic17C22×C412yes—
232C22×Dic17C22×C412yes—
233C22×Dic17C22×C414yes—
234C22×Dic17C22×C411yescharacteristic
235C22×Dic17C22×C411yescharacteristic
236C22×Dic17C22×C411yescharacteristic
237C22×Dic17C22×C411yescharacteristic
238C22×Dic17C22×C411yescharacteristic
239C22×Dic17C22×C412yes—
240C22×Dic17C2×D414yes—
241C22×Dic17#4114yes—
242C22×Dic17C2412yes—
243C22×Dic17C2412yes—
244C22×Dic17C2412yes—
245C22×Dic17C2411yescharacteristic
246C22×Dic17C2412yes—
247#63254—216no—
248#63254—28no—
249#63254—28no—
250C2×C4×D17—22no—
251C2×C4×D17—22no—
252C2×C4×D17C22×C412yes—
253C2×C4×D17C2412yes—
254C2×Dic34—24no—
255C2×Dic34C22×C414yes—
256#63247—28no—
257#63247—28no—
258#63247—28no—
259#63247—28no—
260#63247C2×D4116yescomplemented
261C2×#3624—22no—
262C2×#3624—22no—
263C2×#3624—28no—
264C2×#3624—22no—
265C2×#3624—22no—
266C2×#3624—22no—
267C2×#3624—22no—
268C2×#3624—28no—
269C2×#3624—28no—
270C2×#3624—28no—
271C2×#3624—28no—
272C2×#3624C2×D414yes—
273C2×#3624C2×D414yes—
274C2×#3624C2412yes—
275C2×#3624C2412yes—
276C2×#3624C2412yes—
277C2×#3624C2412yes—
278C2×#3624C2412yes—
279C2×#3624C2412yes—
280C2×#3624C2412yes—
281C2×#3624C2412yes—
282#63243—28no—
283#63242—28no—
284C22⋊C4×C17C22×C414yes—
285C22⋊C4×C17C22×C414yes—
286C22⋊C4×C17C22×C414yes—
287C22⋊Dic17C22×C414yes—
288C22⋊Dic17C22×C414yes—
289C22⋊Dic17C22×C414yes—
290C22⋊Dic17C22×C414yes—
291C22⋊Dic17C22×C414yes—
292#63227C22×C414yes—
293#63227C22×C414yes—
294C4⋊Dic17C22×C414yes—
295C4⋊Dic17C22×C414yes—
296#63225C22×C414yes—
297#63225C22×C414yes—
298#63225C22×C414yes—
299#63225C22×C414yes—
300C4×Dic17C22×C412yes—
301C4×Dic17C22×C412yes—
302C4×Dic17C2412yes—
303C4×Dic17C2412yes—
304C2×#2933—171nomaximal, Sylow
305C23×C17—22no—
306C23×C17—22no—
307C23×C17—22no—
308C23×C17—22no—
309C23×C17—28no—
310C23×C17—22no—
311C23×C17—22no—
312C23×C17—22no—
313C23×C17—22no—
314C23×C17—28no—
315C23×C17—22no—
316C23×C17—22no—
317C23×C17—44no—
318C23×C17—416no—
319C23×C17C4×D414yes—
320C23×C17#13114yescomplemented
321C23×C17C23×C412yes—
322C23×C17C23×C412yes—
323C23×C17C23×C412yes—
324C23×C17C23×C412yes—
325C23×C17C23×C411yescharacteristic
326C22×D17—22no—
327C22×D17—22no—
328C22×D17—22no—
329C22×D17C23×C412yes—
330D4×C17—28no—
331D4×C17—28no—
332D4×C17—44no—
333C2×C4×C17—22no—
334C2×C4×C17—22no—
335C2×C4×C17—22no—
336C2×C4×C17C23×C412yes—
337C2×C4×C17C23×C412yes—
338C2×C4×C17C23×C412yes—
339C22⋊D17—28no—
340C22⋊D17—28no—
341C22⋊D17—28no—
342C22⋊D17—44no—
343C2×Dic17—22no—
344C2×Dic17—28no—
345C2×Dic17—22no—
346C2×Dic17—22no—
347C2×Dic17—22no—
348C2×Dic17—22no—
349C2×Dic17—24no—
350C2×Dic17—28no—
351C2×Dic17—28no—
352C2×Dic17—24no—
353C2×Dic17—24no—
354C2×Dic17—22no—
355C2×Dic17—22no—
356C2×Dic17—22no—
357C2×Dic17—22no—
358C2×Dic17—22no—
359C2×Dic17—22no—
360C2×Dic17C4×D414yes—
361C2×Dic17C4×D418yes—
362C2×Dic17C23×C412yes—
363C2×Dic17C23×C412yes—
364C2×Dic17C23×C412yes—
365C2×Dic17C23×C412yes—
366C2×Dic17C23×C412yes—
367C2×Dic17C23×C412yes—
368C2×Dic17C23×C411yescharacteristic
369C2×Dic17C22×D412yes—
370C2×Dic17C22×D414yes—
371C2×Dic17C2×#4112yes—
372C2×Dic17C2×#4114yes—
373C2×Dic17C2511yescharacteristic
374C4×D17—24no—
375C4×D17—22no—
376C4×D17—22no—
377Dic34—28no—
378#3624—22no—
379#3624—22no—
380#3624—22no—
381#3624—22no—
382#3624—22no—
383#3624—22no—
384#3624C22×D414yes—
385#3624C22×D414yes—
386C22×#131—171no—
387C23×M16—171no—
388C2×#525—171no—
389#2933—1716no—
390C2×#436—171no—
391C2×#436—171no—
392C2×#435—171no—
393C2×#435—171no—
394C2×#435—171no—
395C2×#435—171no—
396C2×C8×D4—171no—
397C2×C8×D4—171no—
398C2×#424—171no—
399C2×#408—171no—
400C22×C22⋊C8—171no—
401C2×#405—171no—
402C22×C17—22no—
403C22×C17—28no—
404C22×C17—28no—
405C22×C17—22no—
406C22×C17—22no—
407C22×C17—22no—
408C22×C17—22no—
409C22×C17—22no—
410C22×C17—22no—
411C22×C17—22no—
412C22×C17—22no—
413C22×C17—22no—
414C22×C17—416no—
415C22×C17—44no—
416C22×C17—44no—
417C22×C17C2×C4×D414yes—
418C22×C17C2×C4×D412yes—
419C22×C17C2×#13112yes—
420C22×C17C2×#13114yescomplemented
421C22×C17#56812yes—
422C22×C17C24×C411yescharacteristic
423C2×D17—22no—
424C2×D17—22no—
425C2×D17—22no—
426C2×D17—44no—
427C4×C17—22no—
428C4×C17—22no—
429C4×C17—22no—
430Dic17—22no—
431Dic17—22no—
432Dic17—22no—
433Dic17—22no—
434Dic17—22no—
435Dic17C2×C4×D414yes—
436Dic17C2×C4×D412yes—
437Dic17C23×D411yescharacteristic
438Dic17C22×#4111yescharacteristic
439C22×#41—171no—
440C24×C4—171no—
441C2×#131—178no—
442C2×#131—348no—
443C22×M16—171no—
444C22×M16—171no—
445C22×M16—171no—
446C22×M16—171no—
447C22×M16—171no—
448C22×M16—171no—
449C22×M16—178no—
450C22×M16—348no—
451C23×C8—171no—
452C23×C8—171no—
453C23×C8—171no—
454C23×C8—171no—
455C23×C8—171no—
456C23×C8—171no—
457#525—178no—
458#525—178no—
459C2×#123—171no—
460C2×#123—171no—
461C2×C22⋊Q8—171no—
462C2×C22⋊Q8—171no—
463C2×#121—171no—
464C2×#121—171no—
465C2×#120—171no—
466C2×#120#59511yescharacteristic
467C2×C4×D4—171no—
468C2×C4×D4—171no—
469C2×C4×D4—171no—
470C2×C4×D4—171no—
471C2×#117—171no—
472#436—178no—
473#436—178no—
474#435—178no—
475#435—178no—
476#435—178no—
477#435—178no—
478C8×D4—178no—
479C8×D4—178no—
480#424—178no—
481C2×C4⋊C8—171no—
482C2×C4⋊C8—171no—
483C2×C4⋊C8—171no—
484C2×C4⋊C8—171no—
485#408—178no—
486C2×C22⋊C8—171no—
487C2×C22⋊C8—171no—
488C2×C22⋊C8—171no—
489C2×C22⋊C8—171no—
490C2×C22⋊C8—178no—
491C2×C22⋊C8—171no—
492C2×C22⋊C8—171no—
493C2×C22⋊C8—171no—
494C2×C22⋊C8—171no—
495#405—178no—
496C2×#97—171no—
497C2×#97—171no—
498C2×C4×C8—171no—
499C2×C4×C8—171no—
500C2×C17—24no—
501C2×C17—24no—
502C2×C17—42no—
503C2×C17—42no—
504C2×C17#293314yescomplemented
505C2×C17C22×C4×D411yescharacteristic
506C2×C17C22×#13111yescharacteristic
507C2×C17C2×#56811yescharacteristic
508D17—42no—
509C25C2×#59511yescharacteristic
510C2×#41—174no—
511C2×#41—174no—
512C2×#41—344no—
513C2×#41—344no—
514C22×Q8—171no—
515C22×D4—171no—
516C22×D4—171no—
517C22×D4—171no—
518C22×D4—171no—
519C22×D4C2×#59511yescharacteristic
520C22×D4C2×#59511yescharacteristic
521C22×D4C2×#59511yescharacteristic
522C23×C4—171no—
523C23×C4—171no—
524C23×C4—171no—
525C23×C4—171no—
526C23×C4—171no—
527C23×C4—171no—
528C23×C4—171no—
529C23×C4—174no—
530C23×C4—174no—
531C23×C4—171no—
532C23×C4—344no—
533C23×C4—344no—
534#131—3432no—
535C2×M16—178no—
536C2×M16—174no—
537C2×M16—174no—
538C2×M16—174no—
539C2×M16—174no—
540C2×M16—174no—
541C2×M16—174no—
542C2×M16—344no—
543C2×M16—344no—
544C2×M16—344no—
545C2×M16—344no—
546C2×M16—3432no—
547C2×M16—344no—
548C22×C8—171no—
549C22×C8—171no—
550C22×C8—174no—
551C22×C8—171no—
552C22×C8—171no—
553C22×C8—171no—
554C22×C8—171no—
555C22×C8—174no—
556C22×C8—174no—
557C22×C8—174no—
558C22×C8—171no—
559C22×C8—171no—
560C22×C8—174no—
561C22×C8—174no—
562C22×C8—344no—
563C22×C8—344no—
564C22×C8—344no—
565C22×C8—344no—
566C22×C8—344no—
567C22×C8—344no—
568#123—178no—
569#123—178no—
570C22⋊Q8—178no—
571C22⋊Q8—178no—
572#121—178no—
573#121—178no—
574#120—178no—
575#120C2×#59518yes—
576C4×D4—174no—
577C4×D4—174no—
578C4×D4—174no—
579C4×D4—174no—
580C4×D4—174no—
581C4×D4—174no—
582C4×D4—174no—
583C4×D4—174no—
584#117—174no—
585#117—174no—
586C2×C4⋊C4—171no—
587C2×C4⋊C4—171no—
588C2×C4⋊C4—171no—
589C2×C4⋊C4—171no—
590C2×C4⋊C4—171no—
591C2×C4⋊C4—171no—
592C2×C22⋊C4—171no—
593C2×C22⋊C4—171no—
594C2×C22⋊C4—171no—
595C2×C22⋊C4—171no—
596C2×C22⋊C4—171no—
597C2×C22⋊C4—171no—
598C2×C22⋊C4—171no—
599C2×C22⋊C4C2×#59511yescharacteristic
600C2×C22⋊C4C2×#59511yescharacteristic
601C2×C22⋊C4C2×#59511yescharacteristic
602C2×C42—171no—
603C2×C42—171no—
604C4⋊C8—174no—
605C4⋊C8—174no—
606C4⋊C8—174no—
607C4⋊C8—174no—
608C22⋊C8—174no—
609C22⋊C8—174no—
610C22⋊C8—174no—
611C22⋊C8—174no—
612C22⋊C8—174no—
613C22⋊C8—174no—
614C22⋊C8—174no—
615C22⋊C8—174no—
616#97—174no—
617#97—174no—
618C4×C8—174no—
619C4×C8—174no—
620C17C2×#293311yescharacteristic, complemented, Sylow
621C24—24no—
622C24—24no—
623C24—42no—
624C24—171no—
625C24C22×#59511yescharacteristic
626C24C22×#59511yescharacteristic
627C24C22×#59514yes—
628C24C22×#59511yescharacteristic
629C24C22×#59511yescharacteristic
630#41—348no—
631#41—348no—
632#41—3416no—
633C2×Q8—174no—
634C2×Q8—344no—
635C2×D4—24no—
636C2×D4—24no—
637C2×D4—42no—
638C2×D4—174no—
639C2×D4—174no—
640C2×D4—174no—
641C2×D4—174no—
642C2×D4—344no—
643C2×D4—344no—
644C2×D4—344no—
645C2×D4—682no—
646C2×D4C22×#59514yes—
647C2×D4C22×#59514yes—
648C2×D4C22×#59514yes—
649C22×C4—174no—
650C22×C4—174no—
651C22×C4—172no—
652C22×C4—172no—
653C22×C4—171no—
654C22×C4—171no—
655C22×C4—172no—
656C22×C4—172no—
657C22×C4—172no—
658C22×C4—174no—
659C22×C4—174no—
660C22×C4—174no—
661C22×C4—172no—
662C22×C4—172no—
663C22×C4—172no—
664C22×C4—171no—
665C22×C4—171no—
666C22×C4—171no—
667C22×C4—171no—
668C22×C4—171no—
669C22×C4—172no—
670C22×C4—172no—
671C22×C4—342no—
672C22×C4—342no—
673C22×C4—342no—
674C22×C4—342no—
675C22×C4—342no—
676C22×C4—348no—
677C22×C4—342no—
678C22×C4—342no—
679C22×C4—348no—
680C22×C4—344no—
681C22×C4—344no—
682C22×C4—3416no—
683C22×C4—342no—
684C22×C4—344no—
685C22×C4C22×#59511yescharacteristic
686C22×C4C22×#59511yescharacteristic
687C22×C4C22×#59511yescharacteristic
688M16—1716no—
689M16—348no—
690M16—348no—
691M16—348no—
692M16—348no—
693M16—348no—
694C2×C8—174no—
695C2×C8—174no—
696C2×C8—172no—
697C2×C8—172no—
698C2×C8—172no—
699C2×C8—172no—
700C2×C8—172no—
701C2×C8—172no—
702C2×C8—172no—
703C2×C8—172no—
704C2×C8—348no—
705C2×C8—348no—
706C2×C8—348no—
707C2×C8—348no—
708C2×C8—342no—
709C2×C8—342no—
710C2×C8—348no—
711C2×C8—342no—
712C2×C8—342no—
713C2×C8—342no—
714C2×C8—342no—
715C2×C8—348no—
716C4⋊C4—174no—
717C4⋊C4—174no—
718C4⋊C4—174no—
719C4⋊C4—174no—
720C4⋊C4—174no—
721C4⋊C4—174no—
722C22⋊C4—174no—
723C22⋊C4—174no—
724C22⋊C4—174no—
725C22⋊C4—174no—
726C22⋊C4—174no—
727C22⋊C4—174no—
728C22⋊C4—174no—
729C22⋊C4C22×#59514yes—
730C22⋊C4C22×#59514yes—
731C22⋊C4C22×#59514yes—
732C42—172no—
733C42—172no—
734C42—172no—
735C42—172no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—28no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—28no—
746C23—22no—
747C23—22no—
748C23—44no—
749C23—416no—
750C23—172no—
751C23—342no—
752C23—342no—
753C23—342no—
754C23#1058767814yescomplemented
755C23D4×#59514yes—
756C23C23×#59512yes—
757C23C23×#59512yes—
758C23C23×#59512yes—
759C23C23×#59512yes—
760C23C23×#59511yescharacteristic
761Q8—348no—
762D4—28no—
763D4—28no—
764D4—44no—
765D4—348no—
766D4—348no—
767D4—348no—
768D4—684no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—172no—
773C2×C4—174no—
774C2×C4—172no—
775C2×C4—174no—
776C2×C4—174no—
777C2×C4—178no—
778C2×C4—171no—
779C2×C4—171no—
780C2×C4—172no—
781C2×C4—172no—
782C2×C4—172no—
783C2×C4—172no—
784C2×C4—172no—
785C2×C4—172no—
786C2×C4—342no—
787C2×C4—342no—
788C2×C4—344no—
789C2×C4—342no—
790C2×C4—342no—
791C2×C4—342no—
792C2×C4—342no—
793C2×C4—342no—
794C2×C4—344no—
795C2×C4—344no—
796C2×C4—348no—
797C2×C4—348no—
798C2×C4—342no—
799C2×C4—344no—
800C2×C4—348no—
801C2×C4—342no—
802C2×C4—342no—
803C2×C4—342no—
804C2×C4—342no—
805C2×C4—342no—
806C2×C4C23×#59512yes—
807C2×C4C23×#59512yes—
808C2×C4C23×#59512yes—
809C8—174no—
810C8—174no—
811C8—342no—
812C8—342no—
813C8—342no—
814C8—342no—
815C8—342no—
816C8—342no—
817C22—22no—
818C22—28no—
819C22—28no—
820C22—22no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—22no—
828C22—22no—
829C22—416no—
830C22—44no—
831C22—44no—
832C22—342no—
833C22—342no—
834C22—342no—
835C22—684no—
836C22C2×D4×#59514yes—
837C22C2×D4×#59512yes—
838C22C2×#1058767812yes—
839C22C2×#1058767814yescomplemented
840C22#1176388712yes—
841C22C24×#59511yescharacteristic
842C4—22no—
843C4—22no—
844C4—22no—
845C4—171no—
846C4—171no—
847C4—172no—
848C4—174no—
849C4—342no—
850C4—342no—
851C4—342no—
852C4—342no—
853C4—342no—
854C2—24no—
855C2—24no—
856C2—42no—
857C2—42no—
858C2—682no—
859C2#1454551614yesdirect product factor
860C2C22×D4×#59511yescharacteristic
861C2C22×#1058767811yescharacteristic
862C2C2×#1176388711yescharacteristic
subgroupG/H
centerC23C23×#595
commutatorC22×C17C24×C4
FrattiniC22C24×#595
FittingC2×C17×#120C4
socleC23×C17C23×C4
prime radicalC2×#11763315C2
cosocleC2×Dic17C25
hypercenterC2×#120#595
hypocenterC17C2×#2933
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. C22×#10587678C2semidirect
2. C23×#63247C2semidirect
3. #14545516C2direct (N × H)
4. C2×#11763844C2semidirect
5. C2×#11763842C2semidirect
6. C2×#11763841C2semidirect
7. C2×#11763840C2semidirect
8. C2×#11763840C2semidirect
9. C2×#11763838C2semidirect
10. C2×#11763836C2semidirect
11. C2×D4×#3624C2semidirect
12. C2×#11763815C2semidirect
13. C2×#11763782C2semidirect
14. C22×C22⋊#3624C2semidirect
15. C2×#11763773C2semidirect
18. C2×#10587678C22semidirect
19. C22×#63243C22semidirect
25. C22×#63247C22semidirect
26. C22×#63247C22semidirect
27. C22×#63242C22semidirect
32. C23×#3624C22semidirect
33. #11763844C22semidirect
34. #11763842C22semidirect
35. #11763841C22semidirect
36. #11763840C22semidirect
37. #11763840C22semidirect
38. #11763838C22semidirect
39. #11763836C22semidirect
40. D4×#3624C22semidirect
41. #11763815C22semidirect
42. C2×#10587544C22semidirect
43. C2×#10587544C22semidirect
44. C2×C4⋊#3624C22semidirect
45. C2×C4⋊#3624C22semidirect
46. #11763782C22semidirect
47. C2×#10587543C22semidirect
48. C2×#10587543C22semidirect
53. C2×C22⋊#3624C22semidirect
54. C2×C22⋊#3624C22semidirect
55. C2×C22⋊#3624C22semidirect
56. #11763773C22semidirect
57. C2×#10587542C22semidirect
58. C2×#10587542C22semidirect
59. C2×C4×#3624C22semidirect
60. C2×C4×#3624C22semidirect
108. C2×#63247D4semidirect
113. C2×#63247C23semidirect
131. C22×#3624C23semidirect
134. C2×#63243C23semidirect
136. C2×#63242C23semidirect
177. C22⋊#3624C23semidirect
178. C22⋊#3624C23semidirect
179. #10587544C23semidirect
180. #10587544C23semidirect
181. #10587543C23semidirect
182. #10587543C23semidirect
183. #10587542C23semidirect
184. #10587542C23semidirect
185. C4⋊#3624C23semidirect
186. C4⋊#3624C23semidirect
187. C4×#3624C23semidirect
188. C4×#3624C23semidirect
260. #63247C2×D4semidirect
320. C23×C17#131semidirect
420. C22×C17C2×#131semidirect
504. C2×C17#2933semidirect
620. C17C2×#2933semidirect
754. C23#10587678semidirect
839. C22C2×#10587678semidirect
859. C2#14545516direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105876782
C23×#632472
#145455162
C2×#117638442
C2×#117638422
C2×#117638412
C2×#117638402
C2×#117638382
C2×#117638362
C2×D4×#36242
C2×#117638152
C2×#117637822
C22×C22⋊#36242
C2×#117637732
C2×#117633152
C2×#293317