Finite Group Databasebeta

← C2×#14541230 #17912861

Subgroups — C2×#14541230 #17912861

Order 4352.

2094 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763501C211yesmaximal, characteristic, complemented
2C2×#11763459C211yesmaximal, characteristic
3#14541230C2116yesmaximal, direct product factor
4C2×#11763216C211yesmaximal, characteristic, complemented
5C2×#11763143C211yesmaximal, characteristic, complemented
6C2×#11763131C211yesmaximal, characteristic, complemented
7C2×#11763137C211yesmaximal, characteristic, complemented
8C2×#11763120C211yesmaximal, characteristic, complemented
9C2×#11763102C211yesmaximal, characteristic, complemented
10C2×#11763107C211yesmaximal, characteristic, complemented
11C2×#11763052C211yesmaximal, characteristic, complemented
12C2×#11762910C211yesmaximal, characteristic, complemented
13C2×#11762880C211yesmaximal, characteristic, complemented
14C2×#11762848C211yesmaximal, characteristic, complemented
15C22×#10587489C211yesmaximal, characteristic, complemented
16C2×C17×#465C211yesmaximal, characteristic, complemented
17C22×#63254—21no—
18C22×#63218C2211yescharacteristic
19#11763501—24no—
20#11763501C2218yescomplemented
21#11763459—24no—
22#11763459C2218yes—
23C2×#10587574C2211yescharacteristic
24C2×#10587584—21no—
25C2×#10587576—21no—
26C2×#10587576C2211yescharacteristic
27C2×#10587572—21no—
28C2×#10587569—21no—
29C2×#10587621—21no—
30C2×#10587564—21no—
31C2×#10587632C2211yescharacteristic
32C2×#10587624C2211yescharacteristic
33C2×Q8×Dic17C2211yescharacteristic
34C2×D4×Dic17C2211yescharacteristic
35C2×C4×C22⋊D17C2211yescharacteristic
36C2×#10587578C2211yescharacteristic
37C2×#10587563—21no—
38C22×C4⋊Dic17C2211yescharacteristic
39C22×C4⋊Dic17C2211yescharacteristic
40C2×C4⋊C4×D17C2211yescharacteristic
41#11763216C2218yescomplemented
42#11763143C2218yescomplemented
43#11763137C2218yescomplemented
44#11763131C2218yescomplemented
45#11763120C2218yescomplemented
46#11763107C2218yescomplemented
47#11763102C2218yescomplemented
48#11763052C2218yescomplemented
49#11762910C2218yescomplemented
50#11762880C2218yescomplemented
51#11762848C2218yescomplemented
52C2×#10587489C2211yescharacteristic
53C2×#10587489C2211yescharacteristic
54C2×#10587489C2211yescharacteristic
55C2×#10587489C2211yescharacteristic
56C2×#10587489C2218yescomplemented
57C2×#10587478C2211yescharacteristic
58C2×#10587478C2211yescharacteristic
59C2×#10587479C2211yescharacteristic
60C2×#10587479C2211yescharacteristic
61C2×#10587485C2211yescharacteristic
62C2×#10587506C2211yescharacteristic
63C2×#10587506C2211yescharacteristic
64C2×#10587503C2211yescharacteristic
65C2×#10587503C2211yescharacteristic
66C2×C22⋊#3622C2211yescharacteristic
67C2×#10587491C2211yescharacteristic
68C2×#10587486C2211yescharacteristic
69C22×SD16×C17C2211yescharacteristic
70C23×C8×C17C2211yescharacteristic
71C2×C17×C22⋊Q8C2211yescharacteristic
72C2×C17×#121C2211yescharacteristic
73C17×#465C2218yescomplemented
74C2×C17×#106C2211yescharacteristic
75C2×C17×#103C2211yescharacteristic
76C2×C17×#102C2211yescharacteristic
77C22×Q8×C17C2311yescharacteristic
78C22×D4×C17—21no—
79C22×D4×C17C2311yescharacteristic
80C23×C4×C17C2311yescharacteristic
81C22×C22⋊D17—21no—
82C22×C22⋊D17D411yescharacteristic
83C23×Dic17—21no—
84C23×Dic17—21no—
85C23×Dic17—21no—
86C2×#63254—28no—
87C2×#63254—48no—
88C22×C4×D17—21no—
89C22×C4×D17C2311yescharacteristic
90C22×Dic34—21no—
91C2×SD16×C17—24no—
92C2×SD16×C17C2314yes—
93C22×C8×C17—24no—
94C22×C8×C17C2311yescharacteristic
95C22×C8×C17C2314yes—
96C22×C8×C17C2311yescharacteristic
97C17×C22⋊Q8—22no—
98C17×C22⋊Q8C2314yes—
99C17×#121—22no—
100C17×#121C2314yes—
101C2×C4⋊C4×C17—21no—
102C2×C4⋊C4×C17C2311yescharacteristic
103C2×C4⋊C4×C17C2311yescharacteristic
104C2×C22⋊C4×C17—21no—
105C2×C22⋊C4×C17—21no—
106C2×C22⋊Dic17—21no—
107C2×C22⋊Dic17—21no—
108C2×C22⋊Dic17D411yescharacteristic
109#10587632—22no—
110#10587632C2314yes—
111Q8×Dic17—22no—
112Q8×Dic17C2314yes—
113#10587624—22no—
114#10587624C2314yes—
115#10587621—28no—
116D4×Dic17—22no—
117D4×Dic17C2314yes—
118C4×C22⋊D17D414yes—
119C4×C22⋊D17C2314yes—
120C2×#63227—21no—
121C2×#63227—21no—
122C2×#63227D411yescharacteristic
123C2×C4⋊Dic17—22no—
124C2×C4⋊Dic17—22no—
125C2×C4⋊Dic17—21no—
126C2×C4⋊Dic17—21no—
127C2×C4⋊Dic17—21no—
128C2×C4⋊Dic17—21no—
129C2×C4⋊Dic17C2314yes—
130C2×C4⋊Dic17C2314yes—
131C2×C4⋊Dic17C2311yescharacteristic
132C2×C4⋊Dic17C2311yescharacteristic
133C2×C4⋊Dic17C2311yescharacteristic
134C2×C4⋊Dic17C2311yescharacteristic
135C2×#63225—21no—
136C2×#63225—21no—
137C2×#63225—21no—
138C2×#63225—21no—
139C2×#63225D411yescharacteristic
140C2×C4×Dic17—21no—
141C2×C4×Dic17—21no—
142C2×C4×Dic17C2311yescharacteristic
143C22×#3622C2311yescharacteristic
144C22×#3622C2311yescharacteristic
145C2×#63218—24no—
146C2×#63218C2314yes—
147#10587584—28no—
148#10587578—22no—
149#10587578C2314yes—
150C4⋊C4×D17—22no—
151C4⋊C4×D17C2314yes—
152#10587576—28no—
153#10587576—22no—
154#10587576C2314yes—
155#10587574—22no—
156#10587574C2314yes—
157#10587572—28no—
158#10587569—28no—
159#10587564—28no—
160#10587563—28no—
161C17×#106C2314yes—
162C17×#103C2314yes—
163C17×#102C2314yes—
164#10587506C2314yes—
165#10587506C2314yes—
166#10587503C2314yes—
167#10587503C2314yes—
168C22⋊#3622C2314yes—
169#10587491C2314yes—
170#10587489C2314yes—
171#10587489C2314yes—
172#10587489C2314yes—
173#10587489C2314yes—
174#10587486C2314yes—
175#10587485C2314yes—
176#10587479C2314yes—
177#10587479C2314yes—
178#10587478C2314yes—
179#10587478C2314yes—
180C24×C17—21no—
181C24×C17C2×D411yescharacteristic
182C23×D17C2×D411yescharacteristic
183C2×Q8×C17—21no—
184C2×Q8×C17—22no—
185C2×Q8×C17—22no—
186C2×Q8×C17C2412yes—
187C2×D4×C17—24no—
188C2×D4×C17—21no—
189C2×D4×C17—22no—
190C2×D4×C17—22no—
191C2×D4×C17—44no—
192C2×D4×C17C2412yes—
193C22×C4×C17—22no—
194C22×C4×C17—22no—
195C22×C4×C17—21no—
196C22×C4×C17—21no—
197C22×C4×C17—21no—
198C22×C4×C17C2×D412yes—
199C22×C4×C17C2×D411yescharacteristic
200C22×C4×C17C2412yes—
201C22×C4×C17C2411yescharacteristic
202C2×C22⋊D17—24no—
203C2×C22⋊D17—24no—
204C2×C22⋊D17—44no—
205C2×C22⋊D17C2×D414yes—
206C22×Dic17—21no—
207C22×Dic17—21no—
208C22×Dic17—24no—
209C22×Dic17—24no—
210C22×Dic17—21no—
211C22×Dic17—21no—
212C22×Dic17—24no—
213C22×Dic17—44no—
214C22×Dic17—44no—
215C22×Dic17—44no—
216C22×Dic17C2×D411yescharacteristic
217C22×Dic17C2×D411yescharacteristic
218C22×Dic17C2×D411yescharacteristic
219#63254—432no—
220C2×C4×D17—22no—
221C2×C4×D17—22no—
222C2×C4×D17—24no—
223C2×C4×D17—44no—
224C2×C4×D17C2×D412yes—
225C2×C4×D17C2412yes—
226C2×Dic34—24no—
227C2×Dic34—44no—
228SD16×C17—28no—
229C2×C8×C17—22no—
230C2×C8×C17—28no—
231C2×C8×C17#4114yescomplemented
232C2×C8×C17C2412yes—
233C2×C8×C17C2412yes—
234C4⋊C4×C17—21no—
235C4⋊C4×C17—24no—
236C4⋊C4×C17—21no—
237C4⋊C4×C17C2412yes—
238C4⋊C4×C17C2412yes—
239C22⋊C4×C17—24no—
240C22⋊C4×C17—24no—
241C22⋊Dic17—24no—
242C22⋊Dic17—24no—
243C22⋊Dic17C2×D414yes—
244#63227—24no—
245#63227—24no—
246#63227C2×D414yes—
247C4⋊Dic17—24no—
248C4⋊Dic17—21no—
249C4⋊Dic17—24no—
250C4⋊Dic17—21no—
251C4⋊Dic17—21no—
252C4⋊Dic17—21no—
253C4⋊Dic17—24no—
254C4⋊Dic17—24no—
255C4⋊Dic17C2412yes—
256C4⋊Dic17C2412yes—
257C4⋊Dic17C2412yes—
258C4⋊Dic17C2412yes—
259#63225—24no—
260#63225—24no—
261#63225—24no—
262#63225—24no—
263#63225C2×D414yes—
264C4×Dic17—24no—
265C4×Dic17—24no—
266C4×Dic17C2×D412yes—
267C4×Dic17C2412yes—
268C2×#3622—22no—
269C2×#3622—22no—
270C2×#3622C2412yes—
271C2×#3622C2412yes—
272#63218—28no—
273C2×#3343—171nomaximal, Sylow
274C23×C17—22no—
275C23×C17—22no—
276C23×C17—22no—
277C23×C17—42no—
278C23×C17—42no—
279C23×C17—42no—
280C23×C17AGL(1,ℤ/8)14yes—
281C23×C17C22×D412yes—
282C23×C17C22×D411yescharacteristic
283C22×D17—22no—
284C22×D17—22no—
285C22×D17—22no—
286C22×D17C22×D412yes—
287Q8×C17—22no—
288Q8×C17—22no—
289Q8×C17—42no—
290D4×C17—22no—
291D4×C17—22no—
292D4×C17—48no—
293D4×C17—42no—
294C2×C4×C17—22no—
295C2×C4×C17—24no—
296C2×C4×C17—22no—
297C2×C4×C17—22no—
298C2×C4×C17—22no—
299C2×C4×C17—22no—
300C2×C4×C17—22no—
301C2×C4×C17—42no—
302C2×C4×C17—42no—
303C2×C4×C17—42no—
304C2×C4×C17C22×D412yes—
305C2×C4×C17C22×D411yescharacteristic
306C2×C4×C17C2×#4112yes—
307C2×C4×C172−1+412yes—
308C2×C4×C17C2511yescharacteristic
309C22⋊D17—28no—
310C22⋊D17—48no—
311C2×Dic17—22no—
312C2×Dic17—22no—
313C2×Dic17—22no—
314C2×Dic17—22no—
315C2×Dic17—22no—
316C2×Dic17—22no—
317C2×Dic17—22no—
318C2×Dic17—48no—
319C2×Dic17—42no—
320C2×Dic17—42no—
321C2×Dic17—48no—
322C2×Dic17—48no—
323C2×Dic17—42no—
324C2×Dic17—42no—
325C2×Dic17C22×D412yes—
326C2×Dic17C22×D412yes—
327C2×Dic17C22×D412yes—
328C4×D17—24no—
329C4×D17—22no—
330C4×D17—22no—
331C4×D17—48no—
332Dic34—48no—
333C8×C17—22no—
334C8×C17C2×#4114yescomplemented
335#3622—22no—
336#3622—22no—
337C2×#552—171no—
338C2×#547—171no—
339#3343—1716no—
340C2×#501—171no—
341C2×#484—171no—
342C2×#482—171no—
343C2×#483—171no—
344C2×#480—171no—
345C2×#477—171no—
346C2×#478—171no—
347C2×#468—171no—
348C2×#465D1711yescharacteristic, complemented
349C2×#440—171no—
350C2×#435—171no—
351C2×#428—171no—
352C22×#107—171no—
353C22×C17—28no—
354C22×C17—22no—
355C22×C17—22no—
356C22×C17—42no—
357C22×C17—42no—
358C22×C17—42no—
359C22×C17—84no—
360C22×C17#54712yes—
361C22×C17C2×AGL(1,ℤ/8)14yes—
362C22×C17C2×AGL(1,ℤ/8)12yes—
363C22×C17#57812yes—
364C22×C17C23×D411yescharacteristic
365C2×D17—22no—
366C2×D17—22no—
367C2×D17—22no—
368C2×D17—44no—
369C4×C17—22no—
370C4×C17—42no—
371C4×C17—42no—
372C4×C17—42no—
373C4×C17#54712yes—
374C4×C17C22×#4111yescharacteristic
375C4×C17C2×2−1+411yescharacteristic
376Dic17—22no—
377Dic17—22no—
378Dic17—22no—
379Dic17—42no—
380Dic17—42no—
381Dic17—42no—
382Dic17—42no—
383C22×#41—341no—
384C22×SD16C2×D1711yescharacteristic
385C22×M16—171no—
386C23×C8C2×D1711yescharacteristic
387#552—178no—
388#552—344no—
389#547—178no—
390#547—344no—
391C2×C4⋊Q8—171no—
392C2×#126—341no—
393C2×#125—171no—
394C2×#125—341no—
395C2×#123—341no—
396C2×#123—341no—
397C2×#123—341no—
398C2×C22⋊Q8—171no—
399C2×C22⋊Q8—341no—
400C2×C22⋊Q8C2×D1711yescharacteristic
401C2×#121—171no—
402C2×#121C2×D1711yescharacteristic
403C2×C4×Q8—171no—
404C2×C4×D4—171no—
405C2×C4×D4—171no—
406C2×#117—171no—
407C2×#117—341no—
408C22×C4⋊C4—171no—
409C22×C4⋊C4—171no—
410C22×C4⋊C4—171no—
411#501—178no—
412#484—178no—
413#483—178no—
414#482—178no—
415#480—178no—
416#478—178no—
417#477—178no—
418#468—178no—
419#465C2×D1718yescomplemented
420#440—178no—
421#435—178no—
422#428—178no—
423C2×#107—171no—
424C2×#107—171no—
425C2×#107—178no—
426C2×#107—171no—
427C2×#107—171no—
428C2×#107—171no—
429C2×#107—171no—
430C2×#106—171no—
431C2×#106—171no—
432C2×#106C2×D1711yescharacteristic
433C2×C4⋊C8—171no—
434C2×#103—171no—
435C2×#103—171no—
436C2×#103C2×D1711yescharacteristic
437C2×#102—171no—
438C2×#102—171no—
439C2×#102C2×D1711yescharacteristic
440C2×C22⋊C8—171no—
441C2×C22⋊C8—171no—
442C2×#97—171no—
443C2×C17—24no—
444C2×C17—82no—
445C2×C17#334314yescomplemented
446C2×C17C2×#54711yescharacteristic
447C2×C17C22×AGL(1,ℤ/8)11yescharacteristic
448C2×C17C2×#57811yescharacteristic
449D17—42no—
450C2×#41—348no—
451C2×#41—688no—
452C22×Q8—341no—
453C22×Q8C22×D1711yescharacteristic
454C22×D4—21no—
455C22×D4—171no—
456C22×D4—341no—
457C22×D4C22×D1711yescharacteristic
458C23×C4—171no—
459C23×C4—341no—
460C23×C4—341no—
461C23×C4—341no—
462C23×C4—341no—
463C23×C4C22×D1711yescharacteristic
464C2×SD16—24no—
465C2×SD16C22×D1714yes—
466C2×M16—174no—
467C2×M16—344no—
468C22×C8—24no—
469C22×C8—171no—
470C22×C8—171no—
471C22×C8C22×D1711yescharacteristic
472C22×C8C22×D1714yes—
473C22×C8C22×D1711yescharacteristic
474C4⋊Q8—174no—
475C4⋊Q8—342no—
476#126—348no—
477#125—174no—
478#125—342no—
479#125—348no—
480#123—348no—
481#123—348no—
482#123—348no—
483C22⋊Q8—22no—
484C22⋊Q8—174no—
485C22⋊Q8—348no—
486C22⋊Q8—342no—
487C22⋊Q8C22×D1714yes—
488#121—22no—
489#121—174no—
490#121—342no—
491#121C22×D1714yes—
492C4×Q8—174no—
493C4×Q8—342no—
494C4×D4—174no—
495C4×D4—174no—
496C4×D4—174no—
497C4×D4—342no—
498#117—174no—
499#117—348no—
500#117—342no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—171no—
503C2×C4⋊C4—171no—
504C2×C4⋊C4—171no—
505C2×C4⋊C4—171no—
506C2×C4⋊C4—171no—
507C2×C4⋊C4—174no—
508C2×C4⋊C4—174no—
509C2×C4⋊C4—174no—
510C2×C4⋊C4—342no—
511C2×C4⋊C4—341no—
512C2×C4⋊C4—341no—
513C2×C4⋊C4—341no—
514C2×C4⋊C4—341no—
515C2×C4⋊C4—341no—
516C2×C4⋊C4—341no—
517C2×C4⋊C4—341no—
518C2×C4⋊C4—341no—
519C2×C4⋊C4—342no—
520C2×C4⋊C4—342no—
521C2×C4⋊C4C22×D1711yescharacteristic
522C2×C4⋊C4C22×D1711yescharacteristic
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—171no—
526C2×C22⋊C4—171no—
527C2×C22⋊C4—341no—
528C2×C22⋊C4—341no—
529C2×C22⋊C4—341no—
530C2×C22⋊C4—341no—
531C2×C42—171no—
532C2×C42—341no—
533C2×C42—341no—
534#107—174no—
535#107—174no—
536#107—174no—
537#107—174no—
538#107—174no—
539#107—174no—
540#106—174no—
541#106—174no—
542#106C22×D1714yes—
543C4⋊C8—174no—
544#103—174no—
545#103—174no—
546#103C22×D1714yes—
547#102—174no—
548#102—174no—
549#102C22×D1714yes—
550C22⋊C8—174no—
551C22⋊C8—174no—
552#97—174no—
553C17C2×#334311yescharacteristic, complemented, Sylow
554C24—21no—
555C24—171no—
556C24D4×D1711yescharacteristic
557#41—6832no—
558C2×Q8—21no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—344no—
562C2×Q8—684no—
563C2×Q8C23×D1712yes—
564C2×D4—24no—
565C2×D4—21no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—44no—
569C2×D4—174no—
570C2×D4—344no—
571C2×D4—344no—
572C2×D4—684no—
573C2×D4C23×D1712yes—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—171no—
580C22×C4—171no—
581C22×C4—171no—
582C22×C4—172no—
583C22×C4—172no—
584C22×C4—344no—
585C22×C4—344no—
586C22×C4—342no—
587C22×C4—342no—
588C22×C4—344no—
589C22×C4—344no—
590C22×C4—341no—
591C22×C4—341no—
592C22×C4—341no—
593C22×C4—341no—
594C22×C4—684no—
595C22×C4—684no—
596C22×C4—684no—
597C22×C4—684no—
598C22×C4D4×D1712yes—
599C22×C4D4×D1711yescharacteristic
600C22×C4C23×D1712yes—
601C22×C4C23×D1711yescharacteristic
602SD16—28no—
603M16—348no—
604C2×C8—22no—
605C2×C8—28no—
606C2×C8—172no—
607C2×C8—172no—
608C2×C8—342no—
609C2×C8—342no—
610C2×C8#6325414yescomplemented
611C2×C8C23×D1712yes—
612C2×C8C23×D1712yes—
613C4⋊C4—24no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—174no—
617C4⋊C4—172no—
618C4⋊C4—172no—
619C4⋊C4—172no—
620C4⋊C4—172no—
621C4⋊C4—344no—
622C4⋊C4—344no—
623C4⋊C4—344no—
624C4⋊C4—344no—
625C4⋊C4—344no—
626C4⋊C4—344no—
627C4⋊C4—341no—
628C4⋊C4—341no—
629C4⋊C4—341no—
630C4⋊C4—344no—
631C4⋊C4—341no—
632C4⋊C4—344no—
633C4⋊C4C23×D1712yes—
634C4⋊C4C23×D1712yes—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—174no—
638C22⋊C4—174no—
639C22⋊C4—344no—
640C22⋊C4—344no—
641C22⋊C4—344no—
642C22⋊C4—344no—
643C42—172no—
644C42—172no—
645C42—344no—
646C42—344no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—172no—
654C23—342no—
655C23—342no—
656C23—342no—
657C23#1058760014yes—
658C23C2×D4×D1712yes—
659C23C2×D4×D1711yescharacteristic
660Q8—22no—
661Q8—22no—
662Q8—42no—
663Q8—688no—
664D4—22no—
665D4—22no—
666D4—48no—
667D4—42no—
668D4—348no—
669D4—688no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—172no—
681C2×C4—172no—
682C2×C4—172no—
683C2×C4—342no—
684C2×C4—342no—
685C2×C4—342no—
686C2×C4—344no—
687C2×C4—342no—
688C2×C4—342no—
689C2×C4—342no—
690C2×C4—342no—
691C2×C4—342no—
692C2×C4—342no—
693C2×C4—688no—
694C2×C4—688no—
695C2×C4—682no—
696C2×C4—682no—
697C2×C4—688no—
698C2×C4—688no—
699C2×C4—682no—
700C2×C4—682no—
701C2×C4C2×D4×D1712yes—
702C2×C4C2×D4×D1711yescharacteristic
703C2×C4C2×#6325412yes—
704C2×C4#1058769712yes—
705C2×C4C24×D1711yescharacteristic
706C8—22no—
707C8—342no—
708C8—342no—
709C8C2×#6325414yescomplemented
710C22—22no—
711C22—28no—
712C22—22no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—84no—
717C22—342no—
718C22—342no—
719C22—342no—
720C22—684no—
721C22#1176345912yes—
722C22C2×#1058760014yes—
723C22C2×#1058760012yes—
724C22#1176362312yes—
725C22C22×D4×D1711yescharacteristic
726C4—22no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—342no—
731C4—342no—
732C4—342no—
733C4—682no—
734C4—682no—
735C4—682no—
736C4—682no—
737C4#1176345912yes—
738C4C22×#6325411yescharacteristic
739C4C2×#1058769711yescharacteristic
740C2—24no—
741C2—82no—
742C2—682no—
743C2#1454123014yesdirect product factor
744C2C2×#1176345911yescharacteristic
745C2C22×#1058760011yescharacteristic
746C2C2×#1176362311yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#465C2
socleC23×C17C22×D4
prime radicalC2×#11763459C2
hypercenterC2×#465D17
hypocenterC17C2×#3343
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C2×#11763501C2semidirect
3. #14541230C2direct (N × H)
4. C2×#11763216C2semidirect
5. C2×#11763143C2semidirect
6. C2×#11763131C2semidirect
7. C2×#11763137C2semidirect
8. C2×#11763120C2semidirect
9. C2×#11763102C2semidirect
10. C2×#11763107C2semidirect
11. C2×#11763052C2semidirect
12. C2×#11762910C2semidirect
13. C2×#11762880C2semidirect
14. C2×#11762848C2semidirect
15. C22×#10587489C2semidirect
16. C2×C17×#465C2semidirect
20. #11763501C22semidirect
41. #11763216C22semidirect
42. #11763143C22semidirect
43. #11763137C22semidirect
44. #11763131C22semidirect
45. #11763120C22semidirect
46. #11763107C22semidirect
47. #11763102C22semidirect
48. #11763052C22semidirect
49. #11762910C22semidirect
50. #11762880C22semidirect
51. #11762848C22semidirect
56. C2×#10587489C22semidirect
73. C17×#465C22semidirect
231. C2×C8×C17#41semidirect
334. C8×C17C2×#41semidirect
348. C2×#465D17semidirect
419. #465C2×D17semidirect
445. C2×C17#3343semidirect
553. C17C2×#3343semidirect
610. C2×C8#63254semidirect
709. C8C2×#63254semidirect
743. C2#14541230direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117635012
C2×#117634592
#145412302
C2×#117632162
C2×#117631432
C2×#117631312
C2×#117631372
C2×#117631202
C2×#117631022
C2×#117631072
C2×#117630522
C2×#117629102
C2×#117628802
C2×#117628482
C22×#105874892
C2×C17×#4652
C2×#334317