Finite Group Databasebeta

← C2×#14532483 #17202149

Subgroups — C2×#14532483 #17202149

Order 4352.

3550 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
1C22×#10587630C211yesmaximal, characteristic, complemented
2C22×#10587564C211yesmaximal, characteristic
3C23×#63225C211yesmaximal, characteristic
4#14532483C2116yesmaximal, direct product factor
5C2×#11762740C211yesmaximal, characteristic, complemented
6C2×#11762739C211yesmaximal, characteristic, complemented
7C2×#11762729C211yesmaximal, characteristic, complemented
8C2×#11762728C211yesmaximal, characteristic, complemented
9C2×#11762704C211yesmaximal, characteristic, complemented
10C2×#11762704C211yesmaximal, characteristic, complemented
11C2×#11762682C211yesmaximal, characteristic
12C2×#11762681C211yesmaximal, characteristic
13C2×#11762678C211yesmaximal, characteristic, complemented
14C2×#11762667C211yesmaximal, characteristic
15C2×C22⋊C4×Dic17C211yesmaximal, characteristic
16C22×C17×C22⋊Q8C211yesmaximal, characteristic
17C23×Dic34C2211yescharacteristic
18C24×Dic17C2211yescharacteristic
19C24×Dic17C2211yescharacteristic
20C2×#10587630—28no—
21C2×#10587630C2218yescomplemented
22C2×#10587564—28no—
23C2×#10587564C2218yes—
24C22×C4⋊Dic17C2211yescharacteristic
25C22×#63225—28no—
26C22×#63225C2211yescharacteristic
27C22×#63225C2211yescharacteristic
28C22×#63225C2211yescharacteristic
29C22×#63225C2218yes—
30C22×#63225C2211yescharacteristic
31C22×#63225C2211yescharacteristic
32C22×#63225C2211yescharacteristic
33C22×#63225C2211yescharacteristic
34C22×#63225C2211yescharacteristic
35C22×#63225C2211yescharacteristic
36C22×#63225C2211yescharacteristic
37C22×#63225C2211yescharacteristic
38C22×#63225C2211yescharacteristic
39C22×C22⋊Dic17C2211yescharacteristic
40C22×C22⋊Dic17C2211yescharacteristic
41C22×C4×Dic17C2211yescharacteristic
42C22×C4×Dic17C2211yescharacteristic
43#11762740C2218yescomplemented
44#11762739C2218yescomplemented
45#11762729C2218yescomplemented
46#11762728C2218yescomplemented
47#11762704C2218yescomplemented
48#11762704C2218yescomplemented
49#11762682C2218yes—
50#11762681C2218yes—
51#11762678C2218yescomplemented
52#11762667C2218yes—
53C22⋊C4×Dic17C2218yes—
54C2×#10587502C2211yescharacteristic
55C2×#10587502C2211yescharacteristic
56C2×#10587502C2211yescharacteristic
57C2×#10587502C2211yescharacteristic
58C2×#10587502C2211yescharacteristic
59C2×#10587502C2211yescharacteristic
60C2×#10587502C2211yescharacteristic
61C2×#10587502C2211yescharacteristic
62C23×Q8×C17C2211yescharacteristic
63C24×C4×C17C2211yescharacteristic
64C2×C17×C22⋊Q8—28no—
65C2×C17×C22⋊Q8C2218yes—
66C22×C4⋊C4×C17C2211yescharacteristic
67C22×C4⋊C4×C17C2211yescharacteristic
68C22×C4⋊C4×C17C2211yescharacteristic
69C22×C22⋊C4×C17C2211yescharacteristic
70C22×C22⋊C4×C17C2211yescharacteristic
71C25×C17C2311yescharacteristic
72C22×Q8×C17—24no—
73C22×Q8×C17—24no—
74C22×Q8×C17—42no—
75C22×Q8×C17C2314yes—
76C23×C4×C17—24no—
77C23×C4×C17—24no—
78C23×C4×C17—42no—
79C23×C4×C17C2311yescharacteristic
80C23×C4×C17C2311yescharacteristic
81C23×C4×C17C2311yescharacteristic
82C23×C4×C17C2314yes—
83C23×C4×C17C2311yescharacteristic
84C23×C4×C17C2311yescharacteristic
85C23×C4×C17C2311yescharacteristic
86C23×Dic17—24no—
87C23×Dic17—24no—
88C23×Dic17—24no—
89C23×Dic17—24no—
90C23×Dic17—42no—
91C23×Dic17Q818yescomplemented
92C23×Dic17C2311yescharacteristic
93C23×Dic17C2311yescharacteristic
94C23×Dic17C2311yescharacteristic
95C23×Dic17C2314yes—
96C23×Dic17C2311yescharacteristic
97C23×Dic17C2311yescharacteristic
98C23×Dic17C2311yescharacteristic
99C23×Dic17C2311yescharacteristic
100C23×Dic17C2314yes—
101C23×Dic17C2311yescharacteristic
102C22×Dic34—24no—
103C22×Dic34—24no—
104C22×Dic34—42no—
105C22×Dic34C2314yes—
106C17×C22⋊Q8—232no—
107C2×C4⋊C4×C17—24no—
108C2×C4⋊C4×C17—24no—
109C2×C4⋊C4×C17—24no—
110C2×C4⋊C4×C17C2314yes—
111C2×C4⋊C4×C17C2314yes—
112C2×C4⋊C4×C17C2314yes—
113C2×C22⋊C4×C17—24no—
114C2×C22⋊C4×C17D418yes—
115C2×C22⋊C4×C17C2314yes—
116C2×C22⋊C4×C17C2314yes—
117C2×C22⋊Dic17—24no—
118C2×C22⋊Dic17Q818yescomplemented
119C2×C22⋊Dic17C2314yes—
120C2×C22⋊Dic17C2314yes—
121#10587630—232no—
122C2×C4⋊Dic17—24no—
123C2×C4⋊Dic17C2314yes—
124C2×#63225—232no—
125C2×#63225—24no—
126C2×#63225—24no—
127C2×#63225—24no—
128C2×#63225—24no—
129C2×#63225—24no—
130C2×#63225—24no—
131C2×#63225—24no—
132C2×#63225—24no—
133C2×#63225—24no—
134C2×#63225—42no—
135C2×#63225—42no—
136C2×#63225D418yes—
137C2×#63225C2314yes—
138C2×#63225C2314yes—
139C2×#63225C2314yes—
140C2×#63225C2314yes—
141C2×#63225C2314yes—
142C2×#63225C2314yes—
143C2×#63225C2314yes—
144C2×#63225C2314yes—
145C2×#63225C2314yes—
146C2×#63225C2314yes—
147C2×#63225C2314yes—
148C2×#63225C2314yes—
149C2×C4×Dic17—24no—
150C2×C4×Dic17—24no—
151C2×C4×Dic17C2314yes—
152C2×C4×Dic17C2314yes—
153#10587564—232no—
154#10587502C2314yes—
155#10587502C2314yes—
156#10587502C2314yes—
157#10587502C2314yes—
158#10587502C2314yes—
159#10587502C2314yes—
160#10587502C2314yes—
161#10587502C2314yes—
162C24×C17—22no—
163C24×C17—22no—
164C24×C17—22no—
165C24×C17—22no—
166C24×C17C2×D414yes—
167C24×C17C2×Q814yes—
168C24×C17C2×Q814yes—
169C24×C17C2412yes—
170C24×C17C2411yescharacteristic
171C2×Q8×C17—28no—
172C2×Q8×C17—28no—
173C2×Q8×C17—44no—
174C2×Q8×C17—416no—
175C22×C4×C17—22no—
176C22×C4×C17—22no—
177C22×C4×C17—22no—
178C22×C4×C17—22no—
179C22×C4×C17—22no—
180C22×C4×C17—22no—
181C22×C4×C17—28no—
182C22×C4×C17—22no—
183C22×C4×C17—22no—
184C22×C4×C17—22no—
185C22×C4×C17—22no—
186C22×C4×C17—22no—
187C22×C4×C17—22no—
188C22×C4×C17—22no—
189C22×C4×C17—22no—
190C22×C4×C17—22no—
191C22×C4×C17—28no—
192C22×C4×C17—44no—
193C22×C4×C17—416no—
194C22×C4×C17C2×D414yes—
195C22×C4×C17C2×D414yes—
196C22×C4×C17C2×D414yes—
197C22×C4×C17C2412yes—
198C22×C4×C17C2412yes—
199C22×C4×C17C2412yes—
200C22×C4×C17C2412yes—
201C22×C4×C17C2412yes—
202C22×C4×C17C2412yes—
203C22×Dic17—22no—
204C22×Dic17—22no—
205C22×Dic17—22no—
206C22×Dic17—22no—
207C22×Dic17—22no—
208C22×Dic17—22no—
209C22×Dic17—22no—
210C22×Dic17—22no—
211C22×Dic17—232no—
212C22×Dic17—28no—
213C22×Dic17—28no—
214C22×Dic17—22no—
215C22×Dic17—22no—
216C22×Dic17—28no—
217C22×Dic17—22no—
218C22×Dic17—22no—
219C22×Dic17—22no—
220C22×Dic17—22no—
221C22×Dic17—22no—
222C22×Dic17—22no—
223C22×Dic17—22no—
224C22×Dic17—28no—
225C22×Dic17—44no—
226C22×Dic17—416no—
227C22×Dic17C2×D414yes—
228C22×Dic17C2×D414yes—
229C22×Dic17C2×Q814yes—
230C22×Dic17C2×Q814yes—
231C22×Dic17C2×Q814yes—
232C22×Dic17C2×Q814yes—
233C22×Dic17C2×Q8116yescomplemented
234C22×Dic17#4114yes—
235C22×Dic17C2412yes—
236C22×Dic17C2412yes—
237C22×Dic17C2412yes—
238C22×Dic17C2412yes—
239C22×Dic17C2412yes—
240C22×Dic17C2412yes—
241C22×Dic17C2412yes—
242C22×Dic17C2412yes—
243C2×Dic34—28no—
244C2×Dic34—28no—
245C2×Dic34—44no—
246C2×Dic34—416no—
247C4⋊C4×C17—28no—
248C4⋊C4×C17—28no—
249C4⋊C4×C17—28no—
250C22⋊C4×C17—28no—
251C22⋊C4×C17C2×D4116yes—
252C22⋊Dic17—28no—
253C22⋊Dic17C2×Q8116yescomplemented
254C4⋊Dic17—28no—
255#63225—28no—
256#63225—28no—
257#63225—28no—
258#63225—28no—
259#63225—28no—
260#63225—28no—
261#63225—28no—
262#63225—28no—
263#63225—28no—
264#63225—44no—
265#63225—44no—
266#63225C2×D4116yes—
267C4×Dic17—28no—
268C4×Dic17—28no—
269C2×#2440—171nomaximal, Sylow
270C23×C17—28no—
271C23×C17—28no—
272C23×C17—28no—
273C23×C17—28no—
274C23×C17—28no—
275C23×C17—28no—
276C23×C17—22no—
277C23×C17—22no—
278C23×C17—22no—
279C23×C17—22no—
280C23×C17C4⋊Q8116yescomplemented
281C23×C17C22×D412yes—
282C23×C17C22×D414yes—
283C23×C17C22×D412yes—
284C23×C17C22×Q814yes—
285C23×C17C22×Q814yes—
286C23×C17C22×Q812yes—
287C23×C17C22×Q812yes—
288C23×C17C2×#4112yes—
289C23×C17H(5,𝔽2)12yes—
290C23×C172−1+412yes—
291C23×C17C2511yescharacteristic
292Q8×C17—416no—
293C2×C4×C17—28no—
294C2×C4×C17—28no—
295C2×C4×C17—28no—
296C2×C4×C17—22no—
297C2×C4×C17—22no—
298C2×C4×C17—22no—
299C2×C4×C17—22no—
300C2×C4×C17—22no—
301C2×C4×C17—22no—
302C2×C4×C17—22no—
303C2×C4×C17—22no—
304C2×C4×C17—22no—
305C2×C4×C17—22no—
306C2×C4×C17—22no—
307C2×C4×C17—22no—
308C2×C4×C17—22no—
309C2×C4×C17—22no—
310C2×C4×C17—22no—
311C2×C4×C17—416no—
312C2×C4×C17—44no—
313C2×C4×C17—44no—
314C2×C4×C17—44no—
315C2×C4×C17C22×D414yes—
316C2×C4×C17C22×D414yes—
317C2×C4×C17C22×D414yes—
318C2×Dic17—28no—
319C2×Dic17—28no—
320C2×Dic17—28no—
321C2×Dic17—28no—
322C2×Dic17—22no—
323C2×Dic17—22no—
324C2×Dic17—22no—
325C2×Dic17—22no—
326C2×Dic17—22no—
327C2×Dic17—22no—
328C2×Dic17—22no—
329C2×Dic17—22no—
330C2×Dic17—232no—
331C2×Dic17—22no—
332C2×Dic17—22no—
333C2×Dic17—22no—
334C2×Dic17—22no—
335C2×Dic17—22no—
336C2×Dic17—22no—
337C2×Dic17—22no—
338C2×Dic17—22no—
339C2×Dic17—22no—
340C2×Dic17—416no—
341C2×Dic17—44no—
342C2×Dic17—44no—
343C2×Dic17—44no—
344C2×Dic17C22⋊Q8116yescomplemented
345C2×Dic17C22×D414yes—
346C2×Dic17C22×D414yes—
347C2×Dic17C22×Q814yes—
348C2×Dic17C22×Q814yes—
349C2×Dic17C22×Q814yes—
350C2×Dic17C22×Q814yes—
351C2×Dic17C2×#4114yes—
352Dic34—416no—
353C22×C4⋊Q8—171no—
354C22×C22⋊Q8—171no—
355C22×C22⋊Q8D1711yescharacteristic
356C23×C4⋊C4—171no—
357#2440—1716no—
358C2×#398—171no—
359C2×#398—171no—
360C2×#395—171no—
361C2×#395—171no—
362C2×#389—171no—
363C2×#389—171no—
364C2×#385—171no—
365C2×#385—171no—
366C2×#384—171no—
367C2×#380—171no—
368C2×C4×C22⋊C4—171no—
369C22×C17—24no—
370C22×C17—24no—
371C22×C17—24no—
372C22×C17—232no—
373C22×C17—24no—
374C22×C17—24no—
375C22×C17—24no—
376C22×C17C2×C22⋊Q814yes—
377C22×C17C2×C4⋊Q814yes—
378C22×C17C2×C4⋊Q818yescomplemented
379C22×C17#54414yes—
380C22×C17D4214yes—
381C22×C17#54714yes—
382C22×C17D4×Q814yes—
383C22×C17#55414yes—
384C22×C17C23×D411yescharacteristic
385C22×C17C23×D411yescharacteristic
386C22×C17C23×Q811yescharacteristic
387C22×C17C23×Q811yescharacteristic
388C22×C17C22×#4111yescharacteristic
389C22×C17C2×H(5,𝔽2)11yescharacteristic
390C22×C17C2×2−1+411yescharacteristic
391C4×C17—24no—
392C4×C17—24no—
393C4×C17—24no—
394C4×C17—42no—
395C4×C17—42no—
396C4×C17—42no—
397Dic17—24no—
398Dic17—24no—
399Dic17—24no—
400Dic17—24no—
401Dic17—42no—
402Dic17—42no—
403Dic17—42no—
404Dic17C2×C22⋊Q818yescomplemented
405C23×Q8—171no—
406C23×Q8C2×D1711yescharacteristic
407C24×C4—171no—
408C24×C4—171no—
409C24×C4C2×D1711yescharacteristic
410C2×C4⋊Q8—178no—
411C2×C4⋊Q8—348no—
412C2×C22⋊Q8—28no—
413C2×C22⋊Q8—178no—
414C2×C22⋊Q8—348no—
415C2×C22⋊Q8C2×D1718yes—
416C22×C4⋊C4—171no—
417C22×C4⋊C4—171no—
418C22×C4⋊C4—171no—
419C22×C4⋊C4—171no—
420C22×C4⋊C4—171no—
421C22×C4⋊C4—171no—
422C22×C4⋊C4—171no—
423C22×C4⋊C4—178no—
424C22×C4⋊C4—171no—
425C22×C4⋊C4—171no—
426C22×C4⋊C4—171no—
427C22×C4⋊C4—171no—
428C22×C4⋊C4—171no—
429C22×C4⋊C4—171no—
430C22×C4⋊C4—348no—
431C22×C4⋊C4C2×D1711yescharacteristic
432C22×C4⋊C4C2×D1711yescharacteristic
433C22×C4⋊C4C2×D1711yescharacteristic
434C22×C22⋊C4—171no—
435C22×C22⋊C4—171no—
436C22×C22⋊C4C2×D1711yescharacteristic
437C22×C22⋊C4C2×D1711yescharacteristic
438C22×C42—171no—
439C22×C42—171no—
440#398—178no—
441#398—178no—
442#395—178no—
443#395—178no—
444#389—178no—
445#389—178no—
446#385—178no—
447#385—178no—
448#384—178no—
449#380—178no—
450C4×C22⋊C4—178no—
451C2×#95—171no—
452C2×#95—171no—
453C2×#95—171no—
454C2×#95—171no—
455C2×#95—171no—
456C2×#95—171no—
457C2×#95—171no—
458C2×#95—171no—
459C2×C17—28no—
460C2×C17#244018yescomplemented
461C2×C17C22×C22⋊Q811yescharacteristic
462C2×C17C22×C4⋊Q811yescharacteristic
463C2×C17C2×#54411yescharacteristic
464C2×C17C2×D4211yescharacteristic
465C2×C17C2×#54711yescharacteristic
466C2×C17C2×D4×Q811yescharacteristic
467C2×C17C2×#55411yescharacteristic
468C25C22×D1711yescharacteristic
469C22×Q8—24no—
470C22×Q8—24no—
471C22×Q8—42no—
472C22×Q8—174no—
473C22×Q8—344no—
474C22×Q8—344no—
475C22×Q8—682no—
476C22×Q8C22×D1714yes—
477C23×C4—24no—
478C23×C4—24no—
479C23×C4—42no—
480C23×C4—171no—
481C23×C4—178no—
482C23×C4—174no—
483C23×C4—171no—
484C23×C4—171no—
485C23×C4—171no—
486C23×C4—171no—
487C23×C4—171no—
488C23×C4—171no—
489C23×C4—171no—
490C23×C4—174no—
491C23×C4—344no—
492C23×C4—344no—
493C23×C4—344no—
494C23×C4—344no—
495C23×C4—682no—
496C23×C4C22×D1711yescharacteristic
497C23×C4C22×D1711yescharacteristic
498C23×C4C22×D1711yescharacteristic
499C23×C4C22×D1714yes—
500C23×C4C22×D1711yescharacteristic
501C23×C4C22×D1711yescharacteristic
502C23×C4C22×D1711yescharacteristic
503C4⋊Q8—3432no—
504C22⋊Q8—232no—
505C22⋊Q8—3432no—
506C2×C4⋊C4—24no—
507C2×C4⋊C4—24no—
508C2×C4⋊C4—24no—
509C2×C4⋊C4—178no—
510C2×C4⋊C4—174no—
511C2×C4⋊C4—174no—
512C2×C4⋊C4—174no—
513C2×C4⋊C4—174no—
514C2×C4⋊C4—174no—
515C2×C4⋊C4—174no—
516C2×C4⋊C4—174no—
517C2×C4⋊C4—174no—
518C2×C4⋊C4—174no—
519C2×C4⋊C4—174no—
520C2×C4⋊C4—174no—
521C2×C4⋊C4—174no—
522C2×C4⋊C4—174no—
523C2×C4⋊C4—3432no—
524C2×C4⋊C4—344no—
525C2×C4⋊C4—344no—
526C2×C4⋊C4—344no—
527C2×C4⋊C4—344no—
528C2×C4⋊C4—344no—
529C2×C4⋊C4—344no—
530C2×C4⋊C4—344no—
531C2×C4⋊C4—344no—
532C2×C4⋊C4—344no—
533C2×C4⋊C4—344no—
534C2×C4⋊C4—682no—
535C2×C4⋊C4—682no—
536C2×C4⋊C4C22×D1714yes—
537C2×C4⋊C4C22×D1714yes—
538C2×C4⋊C4C22×D1714yes—
539C2×C22⋊C4—24no—
540C2×C22⋊C4—178no—
541C2×C22⋊C4—174no—
542C2×C22⋊C4—174no—
543C2×C22⋊C4—344no—
544C2×C22⋊C4C22⋊D1718yes—
545C2×C22⋊C4C22×D1714yes—
546C2×C22⋊C4C22×D1714yes—
547C2×C42—174no—
548C2×C42—174no—
549C2×C42—344no—
550C2×C42—344no—
551#95—174no—
552#95—174no—
553#95—174no—
554#95—174no—
555#95—174no—
556#95—174no—
557#95—174no—
558#95—174no—
559C17C2×#244011yescharacteristic, complemented, Sylow
560C24—22no—
561C24—22no—
562C24—22no—
563C24—22no—
564C24Q8×D1714yes—
565C24Q8×D1714yes—
566C24C2×C22⋊D1714yes—
567C24C23×D1712yes—
568C24C23×D1711yescharacteristic
569C2×Q8—28no—
570C2×Q8—28no—
571C2×Q8—44no—
572C2×Q8—416no—
573C2×Q8—348no—
574C2×Q8—348no—
575C2×Q8—684no—
576C2×Q8—6816no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—28no—
593C22×C4—28no—
594C22×C4—44no—
595C22×C4—416no—
596C22×C4—174no—
597C22×C4—174no—
598C22×C4—174no—
599C22×C4—172no—
600C22×C4—174no—
601C22×C4—174no—
602C22×C4—174no—
603C22×C4—174no—
604C22×C4—1716no—
605C22×C4—172no—
606C22×C4—172no—
607C22×C4—172no—
608C22×C4—172no—
609C22×C4—172no—
610C22×C4—172no—
611C22×C4—172no—
612C22×C4—348no—
613C22×C4—3432no—
614C22×C4—348no—
615C22×C4—348no—
616C22×C4—342no—
617C22×C4—342no—
618C22×C4—342no—
619C22×C4—342no—
620C22×C4—342no—
621C22×C4—342no—
622C22×C4—342no—
623C22×C4—342no—
624C22×C4—342no—
625C22×C4—342no—
626C22×C4—342no—
627C22×C4—342no—
628C22×C4—342no—
629C22×C4—342no—
630C22×C4—342no—
631C22×C4—342no—
632C22×C4—342no—
633C22×C4—348no—
634C22×C4—684no—
635C22×C4—6816no—
636C22×C4D4×D1714yes—
637C22×C4C2×C22⋊D1714yes—
638C22×C4C2×C22⋊D1714yes—
639C22×C4C23×D1712yes—
640C22×C4C23×D1712yes—
641C22×C4C23×D1712yes—
642C22×C4C23×D1712yes—
643C22×C4C23×D1712yes—
644C22×C4C23×D1712yes—
645C4⋊C4—28no—
646C4⋊C4—28no—
647C4⋊C4—28no—
648C4⋊C4—1716no—
649C4⋊C4—348no—
650C4⋊C4—348no—
651C4⋊C4—348no—
652C4⋊C4—348no—
653C4⋊C4—348no—
654C4⋊C4—348no—
655C4⋊C4—348no—
656C4⋊C4—348no—
657C4⋊C4—348no—
658C4⋊C4—348no—
659C4⋊C4—684no—
660C4⋊C4—684no—
661C22⋊C4—28no—
662C22⋊C4—1716no—
663C22⋊C4—348no—
664C22⋊C4C2×C22⋊D17116yes—
665C42—348no—
666C42—348no—
667C23—28no—
668C23—28no—
669C23—28no—
670C23—28no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—28no—
676C23—28no—
677C23#10587630116yescomplemented
678C23C2×D4×D1712yes—
679C23#1058769112yes—
680C23C2×Q8×D1714yes—
681C23C2×Q8×D1714yes—
682C23C2×Q8×D1712yes—
683C23C2×Q8×D1712yes—
684C23#41×D1712yes—
685C23#1058769712yes—
686C23C22×C22⋊D1714yes—
687C23C22×C22⋊D1712yes—
688C23C24×D1711yescharacteristic
689Q8—416no—
690Q8—6816no—
691C2×C4—28no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—28no—
699C2×C4—28no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—416no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—1716no—
714C2×C4—174no—
715C2×C4—174no—
716C2×C4—174no—
717C2×C4—174no—
718C2×C4—174no—
719C2×C4—174no—
720C2×C4—174no—
721C2×C4—3432no—
722C2×C4—348no—
723C2×C4—348no—
724C2×C4—348no—
725C2×C4—342no—
726C2×C4—342no—
727C2×C4—342no—
728C2×C4—342no—
729C2×C4—342no—
730C2×C4—342no—
731C2×C4—342no—
732C2×C4—342no—
733C2×C4—348no—
734C2×C4—342no—
735C2×C4—342no—
736C2×C4—342no—
737C2×C4—342no—
738C2×C4—342no—
739C2×C4—342no—
740C2×C4—342no—
741C2×C4—342no—
742C2×C4—342no—
743C2×C4—6816no—
744C2×C4—684no—
745C2×C4—684no—
746C2×C4—684no—
747C2×C4C2×D4×D1714yes—
748C2×C4C22×C22⋊D1714yes—
749C2×C4C22×C22⋊D1714yes—
750C22—24no—
751C22—232no—
752C22—24no—
753C22—24no—
754C22—24no—
755C22—24no—
756C22—24no—
757C22C22⋊Q8×D1714yes—
758C22C2×#1058763014yes—
759C22C2×#1058763018yescomplemented
760C22#1176343814yes—
761C22D4×C22⋊D1714yes—
762C22#1176345814yes—
763C22#1176347214yes—
764C22#1176351314yes—
765C22C22×D4×D1711yescharacteristic
766C22C23×C22⋊D1711yescharacteristic
767C22C22×Q8×D1711yescharacteristic
768C22C22×Q8×D1711yescharacteristic
769C22C2×#41×D1711yescharacteristic
770C22C2×#1058769111yescharacteristic
771C22C2×#1058769711yescharacteristic
772C4—24no—
773C4—24no—
774C4—24no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—178no—
779C4—344no—
780C4—344no—
781C4—344no—
782C4—344no—
783C4—682no—
784C4—682no—
785C4—682no—
786C2—28no—
787C2#1453248318yesdirect product factor
788C2C2×C22⋊Q8×D1711yescharacteristic
789C2C22×#1058763011yescharacteristic
790C2C2×#1176343811yescharacteristic
791C2C2×D4×C22⋊D1711yescharacteristic
792C2C2×#1176345811yescharacteristic
793C2C2×#1176347211yescharacteristic
794C2C2×#1176351311yescharacteristic
subgroupG/H
centerC24C23×D17
commutator, cosocleC23×C17C25
FrattiniC23C24×D17
FittingC22×C17×C22⋊Q8C2
socleC24×C17C24
prime radicalC25×C17C23
hypercenterC22×C22⋊Q8D17
hypocenterC17C2×#2440
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×#10587630C2semidirect
4. #14532483C2direct (N × H)
5. C2×#11762740C2semidirect
6. C2×#11762739C2semidirect
7. C2×#11762729C2semidirect
8. C2×#11762728C2semidirect
9. C2×#11762704C2semidirect
10. C2×#11762704C2semidirect
13. C2×#11762678C2semidirect
21. C2×#10587630C22semidirect
43. #11762740C22semidirect
44. #11762739C22semidirect
45. #11762729C22semidirect
46. #11762728C22semidirect
47. #11762704C22semidirect
48. #11762704C22semidirect
51. #11762678C22semidirect
91. C23×Dic17Q8semidirect
118. C2×C22⋊Dic17Q8semidirect
233. C22×Dic17C2×Q8semidirect
253. C22⋊Dic17C2×Q8semidirect
280. C23×C17C4⋊Q8semidirect
344. C2×Dic17C22⋊Q8semidirect
378. C22×C17C2×C4⋊Q8semidirect
404. Dic17C2×C22⋊Q8semidirect
460. C2×C17#2440semidirect
559. C17C2×#2440semidirect
677. C23#10587630semidirect
759. C22C2×#10587630semidirect
787. C2#14532483direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105876302
C22×#105875642
C23×#632252
#145324832
C2×#117627402
C2×#117627392
C2×#117627292
C2×#117627282
C2×#117627042
C2×#117626822
C2×#117626812
C2×#117626782
C2×#117626672
C2×C22⋊C4×Dic172
C22×C17×C22⋊Q82
C2×#244017