Finite Group Databasebeta

← C2×#14541859 #17915340

Subgroups — C2×#14541859 #17915340

Order 4352.

1938 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763532C211yesmaximal, characteristic, complemented
2#14541859C2116yesmaximal, direct product factor
3C2×#11763204C211yesmaximal, characteristic, complemented
4C2×#11763201C211yesmaximal, characteristic, complemented
5C2×#11763191C211yesmaximal, characteristic
6C2×#11763031C211yesmaximal, characteristic, complemented
7C2×#11763028C211yesmaximal, characteristic, complemented
8C2×#11763019C211yesmaximal, characteristic, complemented
9C2×#11763016C211yesmaximal, characteristic, complemented
10C2×#11763024C211yesmaximal, characteristic
11C2×#11763021C211yesmaximal, characteristic
12C2×#11762940C211yesmaximal, characteristic, complemented
13C2×#11762909C211yesmaximal, characteristic, complemented
14C2×#11762907C211yesmaximal, characteristic, complemented
15C2×C4×#63231C211yesmaximal, characteristic, complemented
16C2×C17×#556C211yesmaximal, characteristic, complemented
17C22×#63231C2211yescharacteristic
18C22×#63231C2211yescharacteristic
19C22×#63231C2211yescharacteristic
20C22×#63231C2211yescharacteristic
21C22×#63229C2211yescharacteristic
22C22×#63229C2211yescharacteristic
23C22×#63230C2211yescharacteristic
24C22×#63230C2211yescharacteristic
25C22×#63228C2211yescharacteristic
26#11763532—24no—
27#11763532C2218yescomplemented
28C2×#10587555C2211yescharacteristic
29C2×#10587584—21no—
30C2×#10587584—21no—
31C2×#10587561C2211yescharacteristic
32C2×#10587561C2211yescharacteristic
33C2×#10587632—21no—
34C2×C4×Dic34C2211yescharacteristic
35C2×C4×Dic34C2211yescharacteristic
36C2×C4×D68C2211yescharacteristic
37C2×#10587578—21no—
38#11763204C2218yescomplemented
39#11763201C2218yescomplemented
40#11763191C2218yes—
41#11763031C2218yescomplemented
42#11763028C2218yescomplemented
43#11763024C2218yes—
44#11763021C2218yes—
45#11763019C2218yescomplemented
46#11763016C2218yescomplemented
47#11762940C2218yescomplemented
48#11762909C2218yescomplemented
49#11762907C2218yescomplemented
50C4×#63231C2218yescomplemented
51C2×#10587478C2211yescharacteristic
52C2×C4⋊#3622C2211yescharacteristic
53C2×C4⋊#3622C2211yescharacteristic
54C2×C4⋊#3622C2211yescharacteristic
55C2×#10587506C2211yescharacteristic
56C2×#10587506C2211yescharacteristic
57C2×#10587481C2211yescharacteristic
58C2×#10587481C2211yescharacteristic
59C2×#10587503C2211yescharacteristic
60C2×#10587480C2211yescharacteristic
61C2×#10587474C2211yescharacteristic
62C2×#10587474C2211yescharacteristic
63C2×C4×#3622C2211yescharacteristic
64C17×#556—24no—
65C17×#556C2218yescomplemented
66C2×C17×C4⋊Q8C2211yescharacteristic
67C2×C17×#126—21no—
68C2×C17×#126—21no—
69C2×C17×#124C2211yescharacteristic
70C2×C17×#124C2211yescharacteristic
71C2×C17×C22⋊Q8—21no—
72C2×C4×Q8×C17C2211yescharacteristic
73C2×C4×Q8×C17C2211yescharacteristic
74C2×C4×Q8×C17C2211yescharacteristic
75C2×C4×D4×C17C2211yescharacteristic
76C2×C17×#117—21no—
77C22×Q8×C17D411yescharacteristic
78C22×Q8×C17C2311yescharacteristic
79C22×Q8×C17C2311yescharacteristic
80C22×D4×C17C2311yescharacteristic
81C23×C4×C17—21no—
82C22×D68C2311yescharacteristic
83C22×C4×D17—21no—
84C22×Dic34C2311yescharacteristic
85C22×Dic34C2311yescharacteristic
86C17×C4⋊Q8—22no—
87C17×C4⋊Q8C2314yes—
88C17×#126—28no—
89C17×#126—28no—
90C17×#124—22no—
91C17×#124—22no—
92C17×#124C2314yes—
93C17×#124C2314yes—
94C17×C22⋊Q8—28no—
95C4×Q8×C17—22no—
96C4×Q8×C17—22no—
97C4×Q8×C17D414yes—
98C4×Q8×C17C2314yes—
99C4×Q8×C17C2314yes—
100C4×Q8×C17C2314yes—
101C4×D4×C17—22no—
102C4×D4×C17C2314yes—
103C17×#117—28no—
104C2×C4⋊C4×C17—21no—
105C2×C4⋊C4×C17—21no—
106C2×C4⋊C4×C17—21no—
107C2×C4⋊C4×C17—21no—
108C2×C4⋊C4×C17D411yescharacteristic
109C2×C4⋊C4×C17D411yescharacteristic
110C2×C4⋊C4×C17D411yescharacteristic
111C2×C4⋊C4×C17C2311yescharacteristic
112C2×C22⋊C4×C17—21no—
113C2×C22⋊C4×C17—21no—
114C2×C22⋊C4×C17—21no—
115C2×C22⋊C4×C17—21no—
116C2×C22⋊C4×C17—21no—
117C2×C42×C17—21no—
118C2×C42×C17—21no—
119C2×C42×C17C2311yescharacteristic
120C2×C42×C17C2311yescharacteristic
121C2×C42×C17C2311yescharacteristic
122#10587632—28no—
123C2×#63231—24no—
124C2×#63231—42no—
125C2×#63231—42no—
126C2×#63231—42no—
127C2×#63231C2314yes—
128C2×#63231C2314yes—
129C2×#63231C2314yes—
130C2×#63231C2314yes—
131C2×#63230—24no—
132C2×#63230—42no—
133C2×#63230C2314yes—
134C2×#63230C2314yes—
135C2×#63229—24no—
136C2×#63229—42no—
137C2×#63229C2314yes—
138C2×#63229C2314yes—
139C2×#63228—42no—
140C2×#63228C2314yes—
141C2×#63227—21no—
142C2×#63227—21no—
143C2×#63227—21no—
144C2×#63227—21no—
145C2×#63227—21no—
146C2×C4⋊Dic17—21no—
147C2×C4⋊Dic17—21no—
148C2×C4⋊Dic17C2311yescharacteristic
149C2×#63225—21no—
150C2×#63225—21no—
151C2×C4×Dic17—21no—
152C2×C4×Dic17—21no—
153C22×#3622C2311yescharacteristic
154C22×#3622C2311yescharacteristic
155C22×#3622C2311yescharacteristic
156C22×#3622C2311yescharacteristic
157#10587584—28no—
158#10587584—28no—
159#10587578—28no—
160#10587561—22no—
161#10587561—22no—
162#10587561C2314yes—
163#10587561C2314yes—
164C4×D68—22no—
165C4×D68C2314yes—
166#10587555—22no—
167#10587555C2314yes—
168C4×Dic34—22no—
169C4×Dic34—22no—
170C4×Dic34C2314yes—
171C4×Dic34C2314yes—
172#10587506C2314yes—
173#10587506C2314yes—
174#10587503C2314yes—
175#10587481C2314yes—
176#10587481C2314yes—
177#10587480C2314yes—
178#10587478C2314yes—
179C4⋊#3622C2314yes—
180C4⋊#3622C2314yes—
181C4⋊#3622C2314yes—
182#10587474C2314yes—
183#10587474C2314yes—
184C4×#3622C2314yes—
185C24×C17—21no—
186C23×D17—21no—
187C2×Q8×C17—21no—
188C2×Q8×C17—21no—
189C2×Q8×C17—22no—
190C2×Q8×C17—22no—
191C2×Q8×C17—22no—
192C2×Q8×C17—22no—
193C2×Q8×C17—42no—
194C2×Q8×C17C2×D414yes—
195C2×Q8×C17C2412yes—
196C2×Q8×C17C2412yes—
197C2×D4×C17—21no—
198C2×D4×C17—22no—
199C2×D4×C17—22no—
200C2×D4×C17C2412yes—
201C22×C4×C17—21no—
202C22×C4×C17—21no—
203C22×C4×C17—21no—
204C22×C4×C17—24no—
205C22×C4×C17—44no—
206C22×C4×C17C2×D411yescharacteristic
207C22×C4×C17C2×D411yescharacteristic
208C22×C4×C17C2×D411yescharacteristic
209C22×C4×C17C2×D411yescharacteristic
210C22×C4×C17C2×D411yescharacteristic
211C22×C4×C17C2×D411yescharacteristic
212C22×C4×C17C2411yescharacteristic
213C22×Dic17—21no—
214C22×Dic17—21no—
215C22×Dic17—21no—
216C2×D68—22no—
217C2×D68—22no—
218C2×D68—21no—
219C2×D68C2412yes—
220C2×C4×D17—24no—
221C2×C4×D17—44no—
222C2×Dic34—22no—
223C2×Dic34—22no—
224C2×Dic34—22no—
225C2×Dic34—22no—
226C2×Dic34—21no—
227C2×Dic34—21no—
228C2×Dic34C2412yes—
229C2×Dic34C2412yes—
230C4⋊C4×C17—24no—
231C4⋊C4×C17—24no—
232C4⋊C4×C17—24no—
233C4⋊C4×C17—24no—
234C4⋊C4×C17—21no—
235C4⋊C4×C17C2×D414yes—
236C4⋊C4×C17C2×D414yes—
237C4⋊C4×C17C2×D414yes—
238C4⋊C4×C17C2412yes—
239C22⋊C4×C17—24no—
240C22⋊C4×C17—24no—
241C22⋊C4×C17—24no—
242C22⋊C4×C17—24no—
243C22⋊C4×C17—24no—
244C42×C17—24no—
245C42×C17—24no—
246C42×C17C2×D412yes—
247C42×C17C2×D412yes—
248C42×C17C2×D412yes—
249C42×C17C2412yes—
250C42×C17C2412yes—
251C42×C17C2412yes—
252#63231—28no—
253#63231—44no—
254#63231—44no—
255#63231—44no—
256#63230—28no—
257#63230—44no—
258#63229—28no—
259#63229—44no—
260#63228—44no—
261#63227—24no—
262#63227—24no—
263#63227—24no—
264#63227—24no—
265#63227—24no—
266C4⋊Dic17—21no—
267C4⋊Dic17—24no—
268C4⋊Dic17—24no—
269C4⋊Dic17C2412yes—
270#63225—24no—
271#63225—24no—
272C4×Dic17—24no—
273C4×Dic17—24no—
274C2×#3622—22no—
275C2×#3622—22no—
276C2×#3622—22no—
277C2×#3622#4114yes—
278C2×#3622C2412yes—
279C2×#3622C2412yes—
280C2×#3622C2412yes—
281C2×#3622C2412yes—
282C2×#3402—171nomaximal, Sylow
283C23×C17—22no—
284C23×C17—42no—
285C23×C17—42no—
286C23×C17—42no—
287C23×C17C22×D411yescharacteristic
288C22×D17—22no—
289C22×D17—42no—
290C22×D17—42no—
291C22×D17—42no—
292Q8×C17—22no—
293Q8×C17—22no—
294Q8×C17—22no—
295Q8×C17—22no—
296Q8×C17—44no—
297Q8×C17—42no—
298Q8×C17—42no—
299D4×C17—22no—
300D4×C17—22no—
301D4×C17—42no—
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—48no—
312C2×C4×C17—42no—
313C2×C4×C17—42no—
314C2×C4×C17—42no—
315C2×C4×C17C22×D412yes—
316C2×C4×C17C22×D412yes—
317C2×C4×C17C22×D412yes—
318C2×C4×C17C22×D412yes—
319C2×C4×C17C22×D412yes—
320C2×C4×C17C22×D412yes—
321C2×C4×C17C22×D411yescharacteristic
322C2×C4×C17C2×#4112yes—
323C2×C4×C17H(5,𝔽2)12yes—
324C2×C4×C17C2511yescharacteristic
325C2×Dic17—22no—
326C2×Dic17—22no—
327C2×Dic17—22no—
328C2×Dic17—42no—
329C2×Dic17—42no—
330C2×Dic17—42no—
331D68—22no—
332D68—22no—
333D68—42no—
334C4×D17—48no—
335Dic34—22no—
336Dic34—22no—
337Dic34—22no—
338Dic34—22no—
339Dic34—42no—
340Dic34—42no—
341#3622—22no—
342#3622—22no—
343#3622—22no—
344#3622C2×#4114yes—
345C2×#556—171no—
346C2×#556D1711yescharacteristic, complemented
347#3402—1716no—
348C2×#497—171no—
349C2×#497—171no—
350C2×#495—171no—
351C2×#464—171no—
352C2×#464—171no—
353C2×#462—171no—
354C2×#462—171no—
355C2×#463—171no—
356C2×#463—171no—
357C2×#446—171no—
358C2×#440—171no—
359C2×#440—171no—
360C2×C4×Q16—171no—
361C22×C17—42no—
362C22×C17—42no—
363C22×C17—42no—
364C22×C17—84no—
365C22×C17#55012yes—
366C22×C17#57512yes—
367C22×C17#57812yes—
368C22×C17C23×D411yescharacteristic
369C2×D17—42no—
370C2×D17—42no—
371C2×D17—42no—
372C2×D17—84no—
373C4×C17—22no—
374C4×C17—22no—
375C4×C17—22no—
376C4×C17—22no—
377C4×C17—22no—
378C4×C17—22no—
379C4×C17—42no—
380C4×C17—42no—
381C4×C17—42no—
382C4×C17#55012yes—
383C4×C17C22×#4111yescharacteristic
384C4×C17C2×H(5,𝔽2)11yescharacteristic
385Dic17—42no—
386Dic17—42no—
387Dic17—42no—
388C22×Q16—171no—
389C22×Q16—171no—
390C22×Q16—171no—
391C22×Q16—171no—
392C22×SD16—171no—
393C22×SD16—171no—
394C22×SD16—171no—
395C22×SD16—171no—
396C22×D8—171no—
397#556—24no—
398#556—178no—
399#556—344no—
400#556C2×D1718yescomplemented
401C2×C4⋊Q8—171no—
402C2×C4⋊Q8C2×D1711yescharacteristic
403C2×#126—21no—
404C2×#126—21no—
405C2×#126—341no—
406C2×#126—341no—
407C2×#124—171no—
408C2×#124—171no—
409C2×#124C2×D1711yescharacteristic
410C2×#124C2×D1711yescharacteristic
411C2×C22⋊Q8—21no—
412C2×C22⋊Q8—341no—
413C2×C4×Q8—171no—
414C2×C4×Q8—171no—
415C2×C4×Q8C2×D1711yescharacteristic
416C2×C4×Q8C2×D1711yescharacteristic
417C2×C4×Q8C2×D1711yescharacteristic
418C2×C4×D4—171no—
419C2×C4×D4C2×D1711yescharacteristic
420C2×#117—21no—
421C2×#117—341no—
422#497—178no—
423#497—178no—
424#495—178no—
425#464—178no—
426#464—178no—
427#463—178no—
428#463—178no—
429#462—178no—
430#462—178no—
431#446—178no—
432#440—178no—
433#440—178no—
434C4×Q16—178no—
435C2×#107—171no—
436C2×C4⋊C8—171no—
437C2×C4⋊C8—171no—
438C2×C4⋊C8—171no—
439C2×#103—171no—
440C2×#103—171no—
441C2×#103—171no—
442C2×#103—171no—
443C2×#102—171no—
444C2×#102—171no—
445C2×#97—171no—
446C2×#97—171no—
447C2×C4×C8—171no—
448C2×C17—82no—
449C2×C17#340214yescomplemented
450C2×C17C2×#55011yescharacteristic
451C2×C17C2×#57511yescharacteristic
452C2×C17C2×#57811yescharacteristic
453D17—82no—
454C22×Q8—171no—
455C22×Q8—171no—
456C22×Q8C22⋊D1711yescharacteristic
457C22×Q8C22×D1711yescharacteristic
458C22×Q8C22×D1711yescharacteristic
459C22×D4—171no—
460C22×D4C22×D1711yescharacteristic
461C23×C4—21no—
462C23×C4—341no—
463C2×Q16—174no—
464C2×Q16—174no—
465C2×Q16—174no—
466C2×Q16—174no—
467C2×Q16—344no—
468C2×Q16—682no—
469C2×Q16—682no—
470C2×Q16—682no—
471C2×SD16—174no—
472C2×SD16—174no—
473C2×SD16—174no—
474C2×SD16—174no—
475C2×SD16—344no—
476C2×SD16—344no—
477C2×SD16—682no—
478C2×SD16—682no—
479C2×D8—174no—
480C2×D8—682no—
481C22×C8—171no—
482C22×C8—171no—
483C22×C8—171no—
484C22×C8—171no—
485C4⋊Q8—22no—
486C4⋊Q8—174no—
487C4⋊Q8—342no—
488C4⋊Q8C22×D1714yes—
489#126—28no—
490#126—28no—
491#126—348no—
492#126—348no—
493#124—22no—
494#124—22no—
495#124—174no—
496#124—174no—
497#124—342no—
498#124—342no—
499#124C22×D1714yes—
500#124C22×D1714yes—
501C22⋊Q8—28no—
502C22⋊Q8—348no—
503C4×Q8—22no—
504C4×Q8—22no—
505C4×Q8—174no—
506C4×Q8—174no—
507C4×Q8—342no—
508C4×Q8—342no—
509C4×Q8C22⋊D1714yes—
510C4×Q8C22×D1714yes—
511C4×Q8C22×D1714yes—
512C4×Q8C22×D1714yes—
513C4×D4—22no—
514C4×D4—174no—
515C4×D4—342no—
516C4×D4C22×D1714yes—
517#117—28no—
518#117—348no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—171no—
524C2×C4⋊C4—341no—
525C2×C4⋊C4—341no—
526C2×C4⋊C4—341no—
527C2×C4⋊C4—341no—
528C2×C4⋊C4C22⋊D1711yescharacteristic
529C2×C4⋊C4C22⋊D1711yescharacteristic
530C2×C4⋊C4C22⋊D1711yescharacteristic
531C2×C4⋊C4C22×D1711yescharacteristic
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—341no—
538C2×C22⋊C4—341no—
539C2×C22⋊C4—341no—
540C2×C22⋊C4—341no—
541C2×C22⋊C4—341no—
542C2×C42—21no—
543C2×C42—21no—
544C2×C42—341no—
545C2×C42—341no—
546C2×C42C22×D1711yescharacteristic
547C2×C42C22×D1711yescharacteristic
548C2×C42C22×D1711yescharacteristic
549#107—174no—
550C4⋊C8—174no—
551C4⋊C8—174no—
552C4⋊C8—174no—
553#103—174no—
554#103—174no—
555#103—174no—
556#103—174no—
557#102—174no—
558#102—174no—
559#97—174no—
560#97—174no—
561C4×C8—174no—
562C17C2×#340211yescharacteristic, complemented, Sylow
563C24—21no—
564C24—341no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—22no—
568C2×Q8—22no—
569C2×Q8—22no—
570C2×Q8—22no—
571C2×Q8—42no—
572C2×Q8—172no—
573C2×Q8—172no—
574C2×Q8—341no—
575C2×Q8—341no—
576C2×Q8—342no—
577C2×Q8—342no—
578C2×Q8—342no—
579C2×Q8—342no—
580C2×Q8C2×C22⋊D1714yes—
581C2×Q8C23×D1712yes—
582C2×Q8C23×D1712yes—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—21no—
586C2×D4—172no—
587C2×D4—342no—
588C2×D4—342no—
589C2×D4—341no—
590C2×D4C23×D1712yes—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—24no—
595C22×C4—44no—
596C22×C4—341no—
597C22×C4—341no—
598C22×C4—341no—
599C22×C4—344no—
600C22×C4—684no—
601C22×C4C2×C22⋊D1711yescharacteristic
602C22×C4C2×C22⋊D1711yescharacteristic
603C22×C4C2×C22⋊D1711yescharacteristic
604C22×C4C2×C22⋊D1711yescharacteristic
605C22×C4C2×C22⋊D1711yescharacteristic
606C22×C4C2×C22⋊D1711yescharacteristic
607C22×C4C23×D1711yescharacteristic
608Q16—348no—
609Q16—684no—
610Q16—684no—
611Q16—684no—
612SD16—348no—
613SD16—348no—
614SD16—684no—
615SD16—684no—
616D8—684no—
617C2×C8—174no—
618C2×C8—172no—
619C2×C8—172no—
620C2×C8—172no—
621C2×C8—172no—
622C2×C8—342no—
623C2×C8—342no—
624C2×C8—342no—
625C4⋊C4—24no—
626C4⋊C4—24no—
627C4⋊C4—24no—
628C4⋊C4—24no—
629C4⋊C4—21no—
630C4⋊C4—172no—
631C4⋊C4—341no—
632C4⋊C4—344no—
633C4⋊C4—344no—
634C4⋊C4—344no—
635C4⋊C4—344no—
636C4⋊C4C2×C22⋊D1714yes—
637C4⋊C4C2×C22⋊D1714yes—
638C4⋊C4C2×C22⋊D1714yes—
639C4⋊C4C23×D1712yes—
640C22⋊C4—24no—
641C22⋊C4—24no—
642C22⋊C4—24no—
643C22⋊C4—24no—
644C22⋊C4—24no—
645C22⋊C4—344no—
646C22⋊C4—344no—
647C22⋊C4—344no—
648C22⋊C4—344no—
649C22⋊C4—344no—
650C42—24no—
651C42—24no—
652C42—344no—
653C42—344no—
654C42C2×C22⋊D1712yes—
655C42C2×C22⋊D1712yes—
656C42C2×C22⋊D1712yes—
657C42C23×D1712yes—
658C42C23×D1712yes—
659C42C23×D1712yes—
660C23—22no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—342no—
665C23—682no—
666C23—682no—
667C23—682no—
668C23C22×C22⋊D1711yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—22no—
672Q8—22no—
673Q8—44no—
674Q8—42no—
675Q8—42no—
676Q8—342no—
677Q8—342no—
678Q8—342no—
679Q8—342no—
680Q8—682no—
681Q8—682no—
682D4—22no—
683D4—22no—
684D4—42no—
685D4—342no—
686D4—342no—
687D4—682no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—48no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—342no—
702C2×C4—342no—
703C2×C4—342no—
704C2×C4—688no—
705C2×C4—682no—
706C2×C4—682no—
707C2×C4—682no—
708C2×C4#41×D1712yes—
709C2×C4#1058769612yes—
710C2×C4C22×C22⋊D1712yes—
711C2×C4C22×C22⋊D1712yes—
712C2×C4C22×C22⋊D1712yes—
713C2×C4C22×C22⋊D1712yes—
714C2×C4C22×C22⋊D1712yes—
715C2×C4C22×C22⋊D1712yes—
716C2×C4C22×C22⋊D1711yescharacteristic
717C2×C4C24×D1711yescharacteristic
718C8—174no—
719C8—342no—
720C8—342no—
721C8—342no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—84no—
726C22—682no—
727C22—682no—
728C22—682no—
729C22—1364no—
730C22#1176347812yes—
731C22#1176360712yes—
732C22#1176362412yes—
733C22C23×C22⋊D1711yescharacteristic
734C4—22no—
735C4—22no—
736C4—22no—
737C4—22no—
738C4—22no—
739C4—22no—
740C4—42no—
741C4—42no—
742C4—42no—
743C4—682no—
744C4—682no—
745C4—682no—
746C4#1176347812yes—
747C4C2×#41×D1711yescharacteristic
748C4C2×#1058769611yescharacteristic
749C2—82no—
750C2—1362no—
751C2#1454185914yesdirect product factor
752C2C2×#1176347811yescharacteristic
753C2C2×#1176360711yescharacteristic
754C2C2×#1176362411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#556C2
socleC23×C17C22×D4
prime radicalC22×#63228C22
hypercenterC2×#556D17
hypocenterC17C2×#3402
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. C2×#11763532C2semidirect
2. #14541859C2direct (N × H)
3. C2×#11763204C2semidirect
4. C2×#11763201C2semidirect
6. C2×#11763031C2semidirect
7. C2×#11763028C2semidirect
8. C2×#11763019C2semidirect
9. C2×#11763016C2semidirect
12. C2×#11762940C2semidirect
13. C2×#11762909C2semidirect
14. C2×#11762907C2semidirect
15. C2×C4×#63231C2semidirect
16. C2×C17×#556C2semidirect
27. #11763532C22semidirect
38. #11763204C22semidirect
39. #11763201C22semidirect
41. #11763031C22semidirect
42. #11763028C22semidirect
45. #11763019C22semidirect
46. #11763016C22semidirect
47. #11762940C22semidirect
48. #11762909C22semidirect
49. #11762907C22semidirect
50. C4×#63231C22semidirect
65. C17×#556C22semidirect
346. C2×#556D17semidirect
400. #556C2×D17semidirect
449. C2×C17#3402semidirect
562. C17C2×#3402semidirect
751. C2#14541859direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117635322
#145418592
C2×#117632042
C2×#117632012
C2×#117631912
C2×#117630312
C2×#117630282
C2×#117630192
C2×#117630162
C2×#117630242
C2×#117630212
C2×#117629402
C2×#117629092
C2×#117629072
C2×C4×#632312
C2×C17×#5562
C2×#340217