Finite Group Databasebeta

← C2×#14541060 #17911202

Subgroups — C2×#14541060 #17911202

Order 4352.

2082 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763530C211yesmaximal, characteristic
2C2×Q8×C22⋊D17C211yesmaximal, characteristic
3#14541060C2116yesmaximal, direct product factor
4C2×#11763158C211yesmaximal, characteristic, complemented
5C2×#11763151C211yesmaximal, characteristic, complemented
6C2×#11763149C211yesmaximal, characteristic, complemented
7C2×#11763092C211yesmaximal, characteristic, complemented
8C2×#11763065C211yesmaximal, characteristic, complemented
9C2×#11763064C211yesmaximal, characteristic, complemented
10C2×#11763017C211yesmaximal, characteristic, complemented
11C2×#11762963C211yesmaximal, characteristic, complemented
12C2×Q16×Dic17C211yesmaximal, characteristic, complemented
13C2×#11762884C211yesmaximal, characteristic
14C2×#11762818C211yesmaximal, characteristic, complemented
15C2×#11762816C211yesmaximal, characteristic, complemented
16C2×C17×#451C211yesmaximal, characteristic, complemented
17C22×Q8×D17C2211yescharacteristic
18C22×#63231C2211yescharacteristic
19C22×#63223C2211yescharacteristic
20C22×#63218C2211yescharacteristic
21#11763530—24no—
22#11763530C2218yes—
23Q8×C22⋊D17—24no—
24Q8×C22⋊D17C2218yes—
25C2×#10587574C2211yescharacteristic
26C2×#10587630—21no—
27C2×#10587630C2211yescharacteristic
28C2×#10587584—21no—
29C2×#10587565—21no—
30C2×#10587571—21no—
31C2×#10587610—21no—
32C2×#10587610C2211yescharacteristic
33C2×#10587632—21no—
34C2×#10587632C2211yescharacteristic
35C2×#10587632C2211yescharacteristic
36C2×Q8×Dic17C2211yescharacteristic
37C2×Q8×Dic17C2211yescharacteristic
38C2×#10587573—21no—
39C2×C4×C22⋊D17—21no—
40C2×C4×C22⋊D17C2211yescharacteristic
41C2×#10587612C2211yescharacteristic
42C2×#10587578C2211yescharacteristic
43#11763158C2218yescomplemented
44#11763151C2218yescomplemented
45#11763149C2218yescomplemented
46#11763092C2218yescomplemented
47#11763065C2218yescomplemented
48#11763064C2218yescomplemented
49#11763017C2218yescomplemented
50#11762963C2218yescomplemented
51Q16×Dic17C2218yescomplemented
52#11762884C2218yes—
53C2×#10587489C2211yescharacteristic
54C2×#10587488C2211yescharacteristic
55C2×#10587479C2211yescharacteristic
56C2×#10587485C2211yescharacteristic
57#11762818C2218yescomplemented
58#11762816C2218yescomplemented
59C2×#10587487C2211yescharacteristic
60C2×#10587487C2211yescharacteristic
61C2×#10587506C2211yescharacteristic
62C2×#10587506C2211yescharacteristic
63C2×#10587506C2211yescharacteristic
64C2×#10587506C2211yescharacteristic
65C2×#10587506C2211yescharacteristic
66C2×#10587481C2211yescharacteristic
67C2×#10587491C2211yescharacteristic
68C2×C8×Dic17C2211yescharacteristic
69C23×Q8×C17C2211yescharacteristic
70C22×Q16×C17C2211yescharacteristic
71C22×Q16×C17C2211yescharacteristic
72C2×C17×C22⋊Q8C2211yescharacteristic
73C17×#451C2218yescomplemented
74C2×C17×#103C2211yescharacteristic
75C2×C17×#103C2211yescharacteristic
76C2×C17×C22⋊C8C2211yescharacteristic
77C22×Q8×C17—22no—
78C22×Q8×C17—21no—
79C22×Q8×C17—24no—
80C22×Q8×C17—42no—
81C22×Q8×C17C2311yescharacteristic
82C22×Q8×C17C2311yescharacteristic
83C22×Q8×C17C2314yes—
84C22×Q8×C17C2311yescharacteristic
85C23×C4×C17—21no—
86C23×C4×C17C2311yescharacteristic
87C22×C22⋊D17D411yescharacteristic
88C2×Q8×D17—22no—
89C2×Q8×D17—24no—
90C2×Q8×D17—42no—
91C2×Q8×D17C2314yes—
92C22×C4×D17—21no—
93C22×C4×D17C2311yescharacteristic
94C22×Dic34—21no—
95C22×Dic34—21no—
96C22×Dic34C2311yescharacteristic
97C2×Q16×C17—24no—
98C2×Q16×C17—42no—
99C2×Q16×C17C2314yes—
100C2×Q16×C17C2314yes—
101C22×C8×C17C2311yescharacteristic
102C22×C8×C17C2311yescharacteristic
103C17×C22⋊Q8—22no—
104C17×C22⋊Q8C2314yes—
105C2×C4⋊C4×C17—21no—
106C2×C4⋊C4×C17C2311yescharacteristic
107C2×C22⋊C4×C17—21no—
108C2×C22⋊Dic17—21no—
109C2×C22⋊Dic17—21no—
110C2×C22⋊Dic17D411yescharacteristic
111#10587632—28no—
112#10587632—22no—
113#10587632—22no—
114#10587632C2314yes—
115#10587632C2314yes—
116Q8×Dic17—22no—
117Q8×Dic17—22no—
118Q8×Dic17C2314yes—
119Q8×Dic17C2314yes—
120#10587630—28no—
121#10587630—22no—
122#10587630C2314yes—
123C2×#63231—42no—
124C2×#63231C2314yes—
125C4×C22⋊D17—28no—
126C4×C22⋊D17D414yes—
127C4×C22⋊D17C2314yes—
128C2×#63227—21no—
129C2×#63227—21no—
130C2×#63227—21no—
131C2×#63227D411yescharacteristic
132#10587612—22no—
133#10587612C2314yes—
134C2×C4⋊Dic17—21no—
135C2×C4⋊Dic17—21no—
136C2×C4⋊Dic17C2311yescharacteristic
137C2×C4⋊Dic17C2311yescharacteristic
138C2×C4⋊Dic17C2311yescharacteristic
139#10587610—22no—
140#10587610—28no—
141#10587610C2314yes—
142C2×#63225—21no—
143C2×#63225—21no—
144C2×#63225—21no—
145C2×#63225—21no—
146C2×#63225—21no—
147C2×#63225—21no—
148C2×#63225D411yescharacteristic
149C2×C4×Dic17—21no—
150C2×C4×Dic17—21no—
151C2×C4×Dic17—21no—
152C2×C4×Dic17—21no—
153C2×C4×Dic17C2311yescharacteristic
154C2×#63223—42no—
155C2×#63223C2314yes—
156C22×#3622C2311yescharacteristic
157C22×#3622C2311yescharacteristic
158C2×#63218—42no—
159C2×#63218C2314yes—
160#10587584—28no—
161#10587578—22no—
162#10587578C2314yes—
163#10587574—22no—
164#10587574C2314yes—
165#10587573—28no—
166#10587571—28no—
167#10587565—28no—
168C17×#103C2314yes—
169C17×#103C2314yes—
170C17×C22⋊C8C2314yes—
171#10587506C2314yes—
172#10587506C2314yes—
173#10587506C2314yes—
174#10587506C2314yes—
175#10587506C2314yes—
176#10587491C2314yes—
177#10587489C2314yes—
178#10587488C2314yes—
179#10587487C2314yes—
180#10587487C2314yes—
181#10587485C2314yes—
182C8×Dic17C2314yes—
183#10587481C2314yes—
184#10587479C2314yes—
185C24×C17C2×D411yescharacteristic
186C23×D17C2×D411yescharacteristic
187C2×Q8×C17—21no—
188C2×Q8×C17—21no—
189C2×Q8×C17—24no—
190C2×Q8×C17—21no—
191C2×Q8×C17—22no—
192C2×Q8×C17—28no—
193C2×Q8×C17—22no—
194C2×Q8×C17—22no—
195C2×Q8×C17—22no—
196C2×Q8×C17—22no—
197C2×Q8×C17—44no—
198C2×Q8×C17—44no—
199C2×Q8×C17—48no—
200C2×Q8×C17#4114yes—
201C2×Q8×C17C2412yes—
202C2×Q8×C17C2412yes—
203C2×Q8×C17C2412yes—
204C22×C4×C17—21no—
205C22×C4×C17—22no—
206C22×C4×C17—22no—
207C22×C4×C17—21no—
208C22×C4×C17—21no—
209C22×C4×C17—24no—
210C22×C4×C17—21no—
211C22×C4×C17—44no—
212C22×C4×C17C2×D412yes—
213C22×C4×C17C2×D411yescharacteristic
214C22×C4×C17C2412yes—
215C22×C4×C17C2411yescharacteristic
216C2×C22⋊D17—24no—
217C2×C22⋊D17C2×D414yes—
218C22×Dic17—21no—
219C22×Dic17—21no—
220C22×Dic17—21no—
221C22×Dic17—21no—
222C22×Dic17C2×D411yescharacteristic
223C22×Dic17C2×D411yescharacteristic
224C22×Dic17C2×D411yescharacteristic
225Q8×D17—28no—
226Q8×D17—44no—
227Q8×D17—48no—
228C2×C4×D17—22no—
229C2×C4×D17—22no—
230C2×C4×D17—24no—
231C2×C4×D17—44no—
232C2×C4×D17C2×D412yes—
233C2×C4×D17C2412yes—
234C2×Dic34—22no—
235C2×Dic34—22no—
236C2×Dic34—21no—
237C2×Dic34—24no—
238C2×Dic34—24no—
239C2×Dic34—44no—
240C2×Dic34—44no—
241C2×Dic34C2412yes—
242Q16×C17—28no—
243Q16×C17—44no—
244C2×C8×C17—22no—
245C2×C8×C17—22no—
246C2×C8×C17C2412yes—
247C2×C8×C17C2412yes—
248C4⋊C4×C17—21no—
249C4⋊C4×C17—24no—
250C4⋊C4×C17C2412yes—
251C22⋊C4×C17—24no—
252C22⋊Dic17—24no—
253C22⋊Dic17—24no—
254C22⋊Dic17C2×D414yes—
255#63231—44no—
256#63227—24no—
257#63227—24no—
258#63227—24no—
259#63227C2×D414yes—
260C4⋊Dic17—21no—
261C4⋊Dic17—21no—
262C4⋊Dic17—21no—
263C4⋊Dic17—24no—
264C4⋊Dic17—24no—
265C4⋊Dic17C2412yes—
266C4⋊Dic17C2412yes—
267C4⋊Dic17C2412yes—
268#63225—24no—
269#63225—24no—
270#63225—24no—
271#63225—24no—
272#63225—24no—
273#63225—24no—
274#63225C2×D414yes—
275C4×Dic17—24no—
276C4×Dic17—24no—
277C4×Dic17—24no—
278C4×Dic17—24no—
279C4×Dic17C2×D412yes—
280C4×Dic17C2412yes—
281#63223—44no—
282C2×#3622—22no—
283C2×#3622—22no—
284C2×#3622C2412yes—
285C2×#3622C2412yes—
286#63218—44no—
287C2×#3328—171nomaximal, Sylow
288C23×C17—22no—
289C23×C17—22no—
290C23×C17—22no—
291C23×C17C22×D412yes—
292C23×C17C22×D411yescharacteristic
293C22×D17—22no—
294C22×D17—22no—
295C22×D17—22no—
296C22×D17C22×D412yes—
297Q8×C17—24no—
298Q8×C17—22no—
299Q8×C17—22no—
300Q8×C17—22no—
301Q8×C17—22no—
302Q8×C17—22no—
303Q8×C17—48no—
304Q8×C17—42no—
305Q8×C17—42no—
306Q8×C17C2×#4114yes—
307C2×C4×C17—24no—
308C2×C4×C17—22no—
309C2×C4×C17—22no—
310C2×C4×C17—24no—
311C2×C4×C17—22no—
312C2×C4×C17—22no—
313C2×C4×C17—22no—
314C2×C4×C17—22no—
315C2×C4×C17—22no—
316C2×C4×C17—48no—
317C2×C4×C17—42no—
318C2×C4×C17—42no—
319C2×C4×C17—42no—
320C2×C4×C17C22×D412yes—
321C2×C4×C17C22×D411yescharacteristic
322C2×C4×C17C2×#4112yes—
323C2×C4×C17H(5,𝔽2)12yes—
324C2×C4×C17C2511yescharacteristic
325C22⋊D17—28no—
326C2×Dic17—22no—
327C2×Dic17—22no—
328C2×Dic17—22no—
329C2×Dic17—22no—
330C2×Dic17—22no—
331C2×Dic17—22no—
332C2×Dic17—42no—
333C2×Dic17—42no—
334C2×Dic17—42no—
335C2×Dic17—42no—
336C2×Dic17#13714yes—
337C2×Dic17C22×D412yes—
338C2×Dic17C22×D412yes—
339C2×Dic17C22×D412yes—
340C4×D17—24no—
341C4×D17—22no—
342C4×D17—22no—
343C4×D17—48no—
344Dic34—22no—
345Dic34—22no—
346Dic34—48no—
347Dic34—42no—
348Dic34—48no—
349C8×C17—22no—
350C8×C17—22no—
351#3622—22no—
352#3622—22no—
353C2×#556—171no—
354C2×D4×Q8—171no—
355#3328—1716no—
356C2×#487—171no—
357C2×#485—171no—
358C2×#485—171no—
359C2×#475—171no—
360C2×#470—171no—
361C2×#470—171no—
362C2×#462—171no—
363C2×#451—171no—
364C2×#451D1711yescharacteristic, complemented
365C2×C4×Q16—171no—
366C2×#436—171no—
367C2×#419—171no—
368C2×#419—171no—
369C22×C17—22no—
370C22×C17—22no—
371C22×C17—22no—
372C22×C17—44no—
373C22×C17#54612yes—
374C22×C17C2×#13712yes—
375C22×C17#57812yes—
376C22×C17C23×D411yescharacteristic
377C2×D17—22no—
378C2×D17—22no—
379C2×D17—22no—
380C2×D17—44no—
381C4×C17—24no—
382C4×C17—22no—
383C4×C17—42no—
384C4×C17—42no—
385C4×C17—42no—
386C4×C17#54612yes—
387C4×C17C22×#4111yescharacteristic
388C4×C17C2×H(5,𝔽2)11yescharacteristic
389Dic17—22no—
390Dic17—22no—
391Dic17—42no—
392Dic17—42no—
393Dic17—42no—
394Dic17—42no—
395Dic17C2×#13714yes—
396C23×Q8—171no—
397C23×Q8C2×D1711yescharacteristic
398C22×Q16—171no—
399C22×Q16C2×D1711yescharacteristic
400C22×Q16C2×D1711yescharacteristic
401C22×M16—171no—
402C22×M16—171no—
403#556—178no—
404#556—344no—
405D4×Q8—178no—
406D4×Q8—344no—
407C2×C4⋊Q8—171no—
408C2×C4⋊Q8—171no—
409C2×C4⋊Q8—341no—
410C2×#126—341no—
411C2×#126—341no—
412C2×#124—341no—
413C2×C22⋊Q8—171no—
414C2×C22⋊Q8—171no—
415C2×C22⋊Q8—171no—
416C2×C22⋊Q8—341no—
417C2×C22⋊Q8—341no—
418C2×C22⋊Q8C2×D1711yescharacteristic
419C2×C4×Q8—171no—
420C2×C4×Q8—171no—
421C2×C4×Q8—341no—
422C2×C4×D4—171no—
423C2×C4×D4—341no—
424C2×#117—171no—
425C2×#117—171no—
426#487—178no—
427#485—178no—
428#485—178no—
429#475—178no—
430#470—178no—
431#470—178no—
432#462—178no—
433#451—178no—
434#451C2×D1718yescomplemented
435C4×Q16—178no—
436#436—178no—
437C2×#107—171no—
438C2×#106—171no—
439C2×#106—171no—
440C2×C4⋊C8—171no—
441#419—178no—
442#419—178no—
443C2×#103—171no—
444C2×#103—171no—
445C2×#103—171no—
446C2×#103—171no—
447C2×#103—171no—
448C2×#103—171no—
449C2×#103—171no—
450C2×#103—171no—
451C2×#103C2×D1711yescharacteristic
452C2×#103C2×D1711yescharacteristic
453C2×C22⋊C8—171no—
454C2×C22⋊C8C2×D1711yescharacteristic
455C2×C4×C8—171no—
456C2×C17—42no—
457C2×C17#332814yescomplemented
458C2×C17C2×#54611yescharacteristic
459C2×C17C22×#13711yescharacteristic
460C2×C17C2×#57811yescharacteristic
461D17—42no—
462C22×Q8—21no—
463C22×Q8—22no—
464C22×Q8—24no—
465C22×Q8—42no—
466C22×Q8—174no—
467C22×Q8—171no—
468C22×Q8—341no—
469C22×Q8—341no—
470C22×Q8—342no—
471C22×Q8—344no—
472C22×Q8—682no—
473C22×Q8C22×D1711yescharacteristic
474C22×Q8C22×D1711yescharacteristic
475C22×Q8C22×D1714yes—
476C22×Q8C22×D1711yescharacteristic
477C22×D4—171no—
478C23×C4—21no—
479C23×C4—171no—
480C23×C4—341no—
481C23×C4C22×D1711yescharacteristic
482C2×Q16—24no—
483C2×Q16—42no—
484C2×Q16—174no—
485C2×Q16—682no—
486C2×Q16C22×D1714yes—
487C2×Q16C22×D1714yes—
488C2×M16—174no—
489C2×M16—174no—
490C2×M16—682no—
491C2×M16—682no—
492C22×C8—171no—
493C22×C8—171no—
494C22×C8C22×D1711yescharacteristic
495C22×C8C22×D1711yescharacteristic
496C4⋊Q8—174no—
497C4⋊Q8—174no—
498C4⋊Q8—342no—
499C4⋊Q8—342no—
500C4⋊Q8—348no—
501#126—348no—
502#126—348no—
503#124—348no—
504C22⋊Q8—22no—
505C22⋊Q8—174no—
506C22⋊Q8—174no—
507C22⋊Q8—174no—
508C22⋊Q8—348no—
509C22⋊Q8—348no—
510C22⋊Q8—342no—
511C22⋊Q8—342no—
512C22⋊Q8—342no—
513C22⋊Q8C22×D1714yes—
514C4×Q8—174no—
515C4×Q8—174no—
516C4×Q8—342no—
517C4×Q8—342no—
518C4×Q8—348no—
519C4×D4—174no—
520C4×D4—174no—
521C4×D4—348no—
522#117—174no—
523#117—174no—
524#117—342no—
525#117—342no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—171no—
528C2×C4⋊C4—171no—
529C2×C4⋊C4—171no—
530C2×C4⋊C4—171no—
531C2×C4⋊C4—341no—
532C2×C4⋊C4—341no—
533C2×C4⋊C4—341no—
534C2×C4⋊C4—341no—
535C2×C4⋊C4—341no—
536C2×C4⋊C4—341no—
537C2×C4⋊C4—341no—
538C2×C4⋊C4—341no—
539C2×C4⋊C4C22×D1711yescharacteristic
540C2×C22⋊C4—21no—
541C2×C22⋊C4—171no—
542C2×C22⋊C4—171no—
543C2×C22⋊C4—341no—
544C2×C22⋊C4—341no—
545C2×C22⋊C4—341no—
546C2×C22⋊C4—341no—
547C2×C22⋊C4—341no—
548C2×C42—171no—
549C2×C42—341no—
550C2×C42—341no—
551C2×C42—341no—
552C2×C42—341no—
553#107—174no—
554#106—174no—
555#106—174no—
556C4⋊C8—174no—
557#103—174no—
558#103—174no—
559#103—174no—
560#103—174no—
561#103—174no—
562#103—174no—
563#103—174no—
564#103—174no—
565#103C22×D1714yes—
566#103C22×D1714yes—
567C22⋊C8—174no—
568C22⋊C8C22×D1714yes—
569C4×C8—174no—
570C17C2×#332811yescharacteristic, complemented, Sylow
571C24—171no—
572C24D4×D1711yescharacteristic
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—24no—
576C2×Q8—21no—
577C2×Q8—22no—
578C2×Q8—28no—
579C2×Q8—22no—
580C2×Q8—22no—
581C2×Q8—22no—
582C2×Q8—22no—
583C2×Q8—44no—
584C2×Q8—44no—
585C2×Q8—48no—
586C2×Q8—172no—
587C2×Q8—344no—
588C2×Q8—344no—
589C2×Q8—341no—
590C2×Q8—348no—
591C2×Q8—342no—
592C2×Q8—342no—
593C2×Q8—684no—
594C2×Q8—684no—
595C2×Q8—684no—
596C2×Q8—688no—
597C2×Q8#6325414yes—
598C2×Q8C23×D1712yes—
599C2×Q8C23×D1712yes—
600C2×Q8C23×D1712yes—
601C2×D4—174no—
602C2×D4—344no—
603C22×C4—21no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—24no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—44no—
611C22×C4—171no—
612C22×C4—171no—
613C22×C4—171no—
614C22×C4—172no—
615C22×C4—172no—
616C22×C4—344no—
617C22×C4—342no—
618C22×C4—342no—
619C22×C4—341no—
620C22×C4—341no—
621C22×C4—341no—
622C22×C4—341no—
623C22×C4—684no—
624C22×C4D4×D1712yes—
625C22×C4D4×D1711yescharacteristic
626C22×C4C23×D1712yes—
627C22×C4C23×D1711yescharacteristic
628Q16—28no—
629Q16—44no—
630Q16—684no—
631M16—684no—
632M16—684no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—172no—
636C2×C8—172no—
637C2×C8—342no—
638C2×C8—342no—
639C2×C8C23×D1712yes—
640C2×C8C23×D1712yes—
641C4⋊C4—24no—
642C4⋊C4—21no—
643C4⋊C4—174no—
644C4⋊C4—172no—
645C4⋊C4—172no—
646C4⋊C4—172no—
647C4⋊C4—344no—
648C4⋊C4—344no—
649C4⋊C4—344no—
650C4⋊C4—344no—
651C4⋊C4—344no—
652C4⋊C4—344no—
653C4⋊C4—344no—
654C4⋊C4—341no—
655C4⋊C4—341no—
656C4⋊C4—341no—
657C4⋊C4—344no—
658C4⋊C4C23×D1712yes—
659C22⋊C4—24no—
660C22⋊C4—174no—
661C22⋊C4—174no—
662C22⋊C4—344no—
663C22⋊C4—344no—
664C22⋊C4—344no—
665C22⋊C4—344no—
666C22⋊C4—344no—
667C42—172no—
668C42—172no—
669C42—344no—
670C42—344no—
671C42—344no—
672C42—344no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—172no—
677C23—342no—
678C23—342no—
679C23—342no—
680C23C2×D4×D1712yes—
681C23C2×D4×D1711yescharacteristic
682Q8—22no—
683Q8—24no—
684Q8—22no—
685Q8—22no—
686Q8—22no—
687Q8—22no—
688Q8—48no—
689Q8—42no—
690Q8—42no—
691Q8—342no—
692Q8—342no—
693Q8—688no—
694Q8—688no—
695Q8—682no—
696Q8C2×#6325414yes—
697D4—348no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—24no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—48no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—174no—
712C2×C4—172no—
713C2×C4—172no—
714C2×C4—172no—
715C2×C4—342no—
716C2×C4—342no—
717C2×C4—342no—
718C2×C4—342no—
719C2×C4—344no—
720C2×C4—342no—
721C2×C4—342no—
722C2×C4—342no—
723C2×C4—342no—
724C2×C4—688no—
725C2×C4—682no—
726C2×C4—682no—
727C2×C4—682no—
728C2×C4—682no—
729C2×C4C2×D4×D1712yes—
730C2×C4C2×D4×D1711yescharacteristic
731C2×C4C2×#6325412yes—
732C2×C4#1058769112yes—
733C2×C4C24×D1711yescharacteristic
734C8—22no—
735C8—22no—
736C8—342no—
737C8—342no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—44no—
742C22—342no—
743C22—342no—
744C22—342no—
745C22—684no—
746C22#1176344612yes—
747C22#137×D1712yes—
748C22#1176362212yes—
749C22C22×D4×D1711yescharacteristic
750C4—22no—
751C4—24no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—174no—
756C4—342no—
757C4—342no—
758C4—682no—
759C4—682no—
760C4—682no—
761C4—682no—
762C4#1176344612yes—
763C4C22×#6325411yescharacteristic
764C4C2×#1058769111yescharacteristic
765C2—42no—
766C2—682no—
767C2#1454106014yesdirect product factor
768C2C2×#1176344611yescharacteristic
769C2C2×#137×D1711yescharacteristic
770C2C2×#1176362211yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#451C2
socleC23×C17C22×D4
prime radicalC22×C22⋊D17D4
hypercenterC2×#451D17
hypocenterC17C2×#3328
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
3. #14541060C2direct (N × H)
4. C2×#11763158C2semidirect
5. C2×#11763151C2semidirect
6. C2×#11763149C2semidirect
7. C2×#11763092C2semidirect
8. C2×#11763065C2semidirect
9. C2×#11763064C2semidirect
10. C2×#11763017C2semidirect
11. C2×#11762963C2semidirect
12. C2×Q16×Dic17C2semidirect
14. C2×#11762818C2semidirect
15. C2×#11762816C2semidirect
16. C2×C17×#451C2semidirect
43. #11763158C22semidirect
44. #11763151C22semidirect
45. #11763149C22semidirect
46. #11763092C22semidirect
47. #11763065C22semidirect
48. #11763064C22semidirect
49. #11763017C22semidirect
50. #11762963C22semidirect
51. Q16×Dic17C22semidirect
57. #11762818C22semidirect
58. #11762816C22semidirect
73. C17×#451C22semidirect
364. C2×#451D17semidirect
434. #451C2×D17semidirect
457. C2×C17#3328semidirect
570. C17C2×#3328semidirect
767. C2#14541060direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117635302
C2×Q8×C22⋊D172
#145410602
C2×#117631582
C2×#117631512
C2×#117631492
C2×#117630922
C2×#117630652
C2×#117630642
C2×#117630172
C2×#117629632
C2×Q16×Dic172
C2×#117628842
C2×#117628182
C2×#117628162
C2×C17×#4512
C2×#332817