Finite Group Databasebeta

← C2×#14538802 #17902339

Subgroups — C2×#14538802 #17902339

Order 4352.

2202 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763343C211yesmaximal, characteristic, complemented
2#14538802C2116yesmaximal, direct product factor
3C2×#11763150C211yesmaximal, characteristic, complemented
4C2×#11763133C211yesmaximal, characteristic, complemented
5C2×#11763116C211yesmaximal, characteristic, complemented
6C2×#11763109C211yesmaximal, characteristic, complemented
7C2×#11763031C211yesmaximal, characteristic, complemented
8C2×#11763024C211yesmaximal, characteristic, complemented
9C2×#11762971C211yesmaximal, characteristic, complemented
10C2×#11762954C211yesmaximal, characteristic
11C2×C4×#63231C211yesmaximal, characteristic, complemented
12C2×C4×#63230C211yesmaximal, characteristic, complemented
13C2×C4×#63229C211yesmaximal, characteristic, complemented
14C2×C4×#63228C211yesmaximal, characteristic, complemented
15C2×#11762862C211yesmaximal, characteristic, complemented
16C2×C4×#41×C17C211yesmaximal, characteristic, complemented
17C22×#63231C2211yescharacteristic
18C22×#63229C2211yescharacteristic
19C22×#63230C2211yescharacteristic
20C22×#63228C2211yescharacteristic
21#11763343—24no—
22#11763343C2218yescomplemented
23C2×#10587562—21no—
24C2×#10587556C2211yescharacteristic
25C2×#10587561C2211yescharacteristic
26C2×#10587615—21no—
27C2×#10587610C2211yescharacteristic
28C2×#10587616C2211yescharacteristic
29C2×C4×Dic34C2211yescharacteristic
30C2×C4×D68C2211yescharacteristic
31C2×C4×C22⋊D17—21no—
32C2×#10587558—21no—
33#11763150C2218yescomplemented
34#11763133C2218yescomplemented
35#11763116C2218yescomplemented
36#11763109C2218yescomplemented
37#11763031C2218yescomplemented
38#11763024C2218yescomplemented
39#11762971C2218yescomplemented
40#11762954C2218yes—
41C4×#63231C2218yescomplemented
42C4×#63230C2218yescomplemented
43C4×#63229C2218yescomplemented
44C4×#63228C2218yescomplemented
45#11762862C2218yescomplemented
46C2×#10587478C2211yescharacteristic
47C2×#10587478C2211yescharacteristic
48C2×#10587479C2211yescharacteristic
49C2×#10587479C2211yescharacteristic
50C2×C4⋊#3622C2211yescharacteristic
51C2×C4⋊#3622C2211yescharacteristic
52C2×#10587506C2211yescharacteristic
53C2×#10587506C2211yescharacteristic
54C2×#10587481C2211yescharacteristic
55C2×#10587481C2211yescharacteristic
56C2×#10587503C2211yescharacteristic
57C2×#10587503C2211yescharacteristic
58C2×#10587480C2211yescharacteristic
59C2×#10587480C2211yescharacteristic
60C2×C22⋊#3622C2211yescharacteristic
61C2×C22⋊#3622C2211yescharacteristic
62C2×C4×#3622C2211yescharacteristic
63C2×C4×#3622C2211yescharacteristic
64C22×#41×C17C2211yescharacteristic
65C4×#41×C17—24no—
66C4×#41×C17C2218yescomplemented
67C2×C4×Q8×C17C2211yescharacteristic
68C2×C4×Q8×C17C2211yescharacteristic
69C2×C4×D4×C17—21no—
70C2×C4×D4×C17—21no—
71C2×C4×D4×C17C2211yescharacteristic
72C2×C4×D4×C17C2211yescharacteristic
73C2×C17×#117—21no—
74C2×C17×#117C2211yescharacteristic
75C22×C42×C17—21no—
76C22×C42×C17C2211yescharacteristic
77C2×#41×C17—24no—
78C2×#41×C17—24no—
79C2×#41×C17—22no—
80C2×#41×C17C2314yes—
81C22×Q8×C17C2311yescharacteristic
82C22×D4×C17—21no—
83C22×D4×C17C2311yescharacteristic
84C23×C4×C17—21no—
85C23×C4×C17—21no—
86C23×C4×C17—21no—
87C23×C4×C17D411yescharacteristic
88C23×C4×C17D411yescharacteristic
89C23×C4×C17C2311yescharacteristic
90C22×C22⋊D17—21no—
91C22×D68C2311yescharacteristic
92C22×C4×D17—21no—
93C22×Dic34C2311yescharacteristic
94C4×Q8×C17—22no—
95C4×Q8×C17—22no—
96C4×Q8×C17C2314yes—
97C4×Q8×C17C2314yes—
98C4×D4×C17—28no—
99C4×D4×C17—28no—
100C4×D4×C17—22no—
101C4×D4×C17—22no—
102C4×D4×C17C2314yes—
103C4×D4×C17C2314yes—
104C17×#117—22no—
105C17×#117—28no—
106C17×#117C2314yes—
107C2×C4⋊C4×C17—21no—
108C2×C4⋊C4×C17—21no—
109C2×C4⋊C4×C17C2311yescharacteristic
110C2×C4⋊C4×C17C2311yescharacteristic
111C2×C22⋊C4×C17—21no—
112C2×C22⋊C4×C17—21no—
113C2×C22⋊C4×C17—21no—
114C2×C42×C17—21no—
115C2×C42×C17—21no—
116C2×C42×C17—21no—
117C2×C42×C17—28no—
118C2×C42×C17D411yescharacteristic
119C2×C42×C17D411yescharacteristic
120C2×C42×C17D414yes—
121C2×C42×C17C2311yescharacteristic
122C2×C42×C17C2311yescharacteristic
123C2×C42×C17C2314yes—
124C2×C22⋊Dic17—21no—
125C2×#63231—24no—
126C2×#63231C2314yes—
127C2×#63230—24no—
128C2×#63230C2314yes—
129C2×#63229—24no—
130C2×#63229C2314yes—
131C2×#63228—24no—
132C2×#63228C2314yes—
133#10587616—22no—
134#10587616C2314yes—
135#10587615—28no—
136C4×C22⋊D17—28no—
137C2×#63227—21no—
138C2×#63227—21no—
139C2×#63227—21no—
140C2×#63227—21no—
141C2×C4⋊Dic17C2311yescharacteristic
142C2×C4⋊Dic17C2311yescharacteristic
143#10587610—22no—
144#10587610C2314yes—
145C2×#63225—21no—
146C2×#63225—21no—
147C2×#63225—21no—
148C2×#63225—21no—
149C2×C4×Dic17—21no—
150C22×#3622C2311yescharacteristic
151C22×#3622C2311yescharacteristic
152C22×#3622C2311yescharacteristic
153C22×#3622C2311yescharacteristic
154#10587562—28no—
155#10587561—22no—
156#10587561C2314yes—
157C4×D68—22no—
158C4×D68C2314yes—
159#10587558—28no—
160#10587556—22no—
161#10587556C2314yes—
162C4×Dic34—22no—
163C4×Dic34C2314yes—
164#10587506C2314yes—
165#10587506C2314yes—
166#10587503C2314yes—
167#10587503C2314yes—
168C22⋊#3622C2314yes—
169C22⋊#3622C2314yes—
170#10587481C2314yes—
171#10587481C2314yes—
172#10587480C2314yes—
173#10587480C2314yes—
174#10587479C2314yes—
175#10587479C2314yes—
176#10587478C2314yes—
177#10587478C2314yes—
178C4⋊#3622C2314yes—
179C4⋊#3622C2314yes—
180C4×#3622C2314yes—
181C4×#3622C2314yes—
182C24×C17—21no—
183C24×C17C2×D411yescharacteristic
184C23×D17—21no—
185#41×C17—216no—
186#41×C17—28no—
187#41×C17—28no—
188C2×Q8×C17—21no—
189C2×Q8×C17—22no—
190C2×Q8×C17#4114yes—
191C2×Q8×C17C2412yes—
192C2×D4×C17—28no—
193C2×D4×C17—24no—
194C2×D4×C17—21no—
195C2×D4×C17—22no—
196C2×D4×C17#4114yes—
197C2×D4×C17C2412yes—
198C22×C4×C17—28no—
199C22×C4×C17—21no—
200C22×C4×C17—24no—
201C22×C4×C17—24no—
202C22×C4×C17—22no—
203C22×C4×C17—22no—
204C22×C4×C17—21no—
205C22×C4×C17—21no—
206C22×C4×C17—24no—
207C22×C4×C17—24no—
208C22×C4×C17—42no—
209C22×C4×C17—44no—
210C22×C4×C17—44no—
211C22×C4×C17C2×D411yescharacteristic
212C22×C4×C17C2×D411yescharacteristic
213C22×C4×C17C2×D411yescharacteristic
214C22×C4×C17C2×D411yescharacteristic
215C22×C4×C17C2×D414yes—
216C22×C4×C17C2×D412yes—
217C22×C4×C17C2×D414yes—
218C22×C4×C17C2×D411yescharacteristic
219C22×C4×C17C2412yes—
220C22×C4×C17C2411yescharacteristic
221C2×C22⋊D17—24no—
222C2×C22⋊D17—44no—
223C22×Dic17—21no—
224C22×Dic17—21no—
225C22×Dic17—21no—
226C2×D68—22no—
227C2×D68—22no—
228C2×D68—21no—
229C2×D68C2412yes—
230C2×C4×D17—24no—
231C2×C4×D17—44no—
232C2×Dic34—22no—
233C2×Dic34—22no—
234C2×Dic34—21no—
235C2×Dic34C2412yes—
236C4⋊C4×C17—24no—
237C4⋊C4×C17—24no—
238C4⋊C4×C17—21no—
239C4⋊C4×C17—21no—
240C4⋊C4×C17C2412yes—
241C4⋊C4×C17C2412yes—
242C22⋊C4×C17—24no—
243C22⋊C4×C17—24no—
244C22⋊C4×C17—24no—
245C42×C17—24no—
246C42×C17—24no—
247C42×C17—24no—
248C42×C17C2×D412yes—
249C42×C17C2×D412yes—
250C42×C17C2×D414yes—
251C42×C17C2×D414yes—
252C42×C17C2412yes—
253C42×C17C2412yes—
254C22⋊Dic17—24no—
255#63231—28no—
256#63230—28no—
257#63229—28no—
258#63228—28no—
259#63227—24no—
260#63227—24no—
261#63227—24no—
262#63227—24no—
263C4⋊Dic17—21no—
264C4⋊Dic17—21no—
265C4⋊Dic17C2412yes—
266C4⋊Dic17C2412yes—
267#63225—24no—
268#63225—24no—
269#63225—24no—
270#63225—24no—
271C4×Dic17—24no—
272C2×#3622—22no—
273C2×#3622—22no—
274C2×#3622—22no—
275C2×#3622—22no—
276C2×#3622C2412yes—
277C2×#3622C2412yes—
278C2×#3622C2412yes—
279C2×#3622C2412yes—
280C2×#3102—171nomaximal, Sylow
281C23×C17—22no—
282C23×C17—24no—
283C23×C17—22no—
284C23×C17—22no—
285C23×C17—22no—
286C23×C17—42no—
287C23×C17—42no—
288C23×C17C22×D412yes—
289C23×C17C22×D411yescharacteristic
290C22×D17—22no—
291C22×D17—42no—
292C22×D17—42no—
293C22×D17—42no—
294Q8×C17—24no—
295Q8×C17—22no—
296Q8×C17C2×#4114yes—
297D4×C17—216no—
298D4×C17—24no—
299D4×C17—22no—
300D4×C17C2×#4114yes—
301C2×C4×C17—216no—
302C2×C4×C17—22no—
303C2×C4×C17—24no—
304C2×C4×C17—22no—
305C2×C4×C17—22no—
306C2×C4×C17—22no—
307C2×C4×C17—22no—
308C2×C4×C17—24no—
309C2×C4×C17—28no—
310C2×C4×C17—22no—
311C2×C4×C17—22no—
312C2×C4×C17—22no—
313C2×C4×C17—22no—
314C2×C4×C17—44no—
315C2×C4×C17—48no—
316C2×C4×C17—42no—
317C2×C4×C17—42no—
318C2×C4×C17—48no—
319C2×C4×C17#13514yes—
320C2×C4×C17C22×D412yes—
321C2×C4×C17C22×D412yes—
322C2×C4×C17C22×D412yes—
323C2×C4×C17C22×D412yes—
324C2×C4×C17C22×D411yescharacteristic
325C2×C4×C17C22×D412yes—
326C2×C4×C17C2×#4112yes—
327C2×C4×C17C2×#4112yes—
328C2×C4×C17C2511yescharacteristic
329C22⋊D17—48no—
330C2×Dic17—22no—
331C2×Dic17—22no—
332C2×Dic17—22no—
333C2×Dic17—42no—
334C2×Dic17—42no—
335C2×Dic17—42no—
336D68—22no—
337D68—22no—
338D68—42no—
339C4×D17—48no—
340Dic34—22no—
341Dic34—22no—
342Dic34—42no—
343#3622—22no—
344#3622—22no—
345#3622—22no—
346#3622—22no—
347C2×#529—171no—
348C2×C4×#41D1711yescharacteristic, complemented
349#3102—1716no—
350C2×#485—171no—
351C2×#482—171no—
352C2×#479—171no—
353C2×#478—171no—
354C2×#464—171no—
355C2×#463—171no—
356C2×#452—171no—
357C2×#449—171no—
358C2×C4×Q16—171no—
359C2×C4×SD16—171no—
360C2×C4×SD16—171no—
361C2×C4×D8—171no—
362C2×#431—171no—
363C22×C17—22no—
364C22×C17—24no—
365C22×C17—22no—
366C22×C17—22no—
367C22×C17—44no—
368C22×C17—48no—
369C22×C17—42no—
370C22×C17—42no—
371C22×C17#52512yes—
372C22×C17C2×#13512yes—
373C22×C17#57512yes—
374C22×C17C23×D411yescharacteristic
375C2×D17—42no—
376C2×D17—42no—
377C2×D17—42no—
378C2×D17—84no—
379C4×C17—22no—
380C4×C17—24no—
381C4×C17—22no—
382C4×C17—22no—
383C4×C17—22no—
384C4×C17—42no—
385C4×C17—42no—
386C4×C17#52512yes—
387C4×C17C2×#13514yes—
388C4×C17C22×#4111yescharacteristic
389C4×C17C22×#4111yescharacteristic
390Dic17—42no—
391Dic17—42no—
392Dic17—42no—
393C22×#41C2×D1711yescharacteristic
394C22×Q16—171no—
395C22×SD16—171no—
396C22×SD16—171no—
397C22×D8—171no—
398#529—178no—
399#529—344no—
400C2×#126—341no—
401C2×#125—171no—
402C2×#124—171no—
403C2×#123—341no—
404C2×C22⋊Q8—171no—
405C2×#121—171no—
406C4×#41—24no—
407C4×#41C2×D1718yescomplemented
408C2×C4×Q8—171no—
409C2×C4×Q8C2×D1711yescharacteristic
410C2×C4×Q8C2×D1711yescharacteristic
411C2×C4×D4—21no—
412C2×C4×D4—21no—
413C2×C4×D4—171no—
414C2×C4×D4—341no—
415C2×C4×D4C2×D1711yescharacteristic
416C2×C4×D4C2×D1711yescharacteristic
417C2×#117—21no—
418C2×#117—341no—
419C2×#117C2×D1711yescharacteristic
420C22×C42—21no—
421C22×C42C2×D1711yescharacteristic
422#485—178no—
423#482—178no—
424#479—178no—
425#478—178no—
426#464—178no—
427#463—178no—
428#452—178no—
429#449—178no—
430C4×Q16—178no—
431C4×SD16—178no—
432C4×SD16—178no—
433C4×D8—178no—
434#431—178no—
435C2×#107—171no—
436C2×#107—171no—
437C2×#106—171no—
438C2×#106—171no—
439C2×C4⋊C8—171no—
440C2×C4⋊C8—171no—
441C2×#103—171no—
442C2×#103—171no—
443C2×#103—171no—
444C2×#103—171no—
445C2×#102—171no—
446C2×#102—171no—
447C2×#102—171no—
448C2×#102—171no—
449C2×C22⋊C8—171no—
450C2×C22⋊C8—171no—
451C2×C4×C8—171no—
452C2×C4×C8—171no—
453C2×C17—42no—
454C2×C17—44no—
455C2×C17#310214yescomplemented
456C2×C17C2×#52511yescharacteristic
457C2×C17C22×#13511yescharacteristic
458C2×C17C2×#57511yescharacteristic
459D17—82no—
460C2×#41—24no—
461C2×#41—24no—
462C2×#41—22no—
463C2×#41C22×D1714yes—
464C22×Q8—171no—
465C22×Q8C22×D1711yescharacteristic
466C22×D4—21no—
467C22×D4—171no—
468C22×D4—341no—
469C22×D4C22×D1711yescharacteristic
470C23×C4—21no—
471C23×C4—21no—
472C23×C4—21no—
473C23×C4—341no—
474C23×C4C22⋊D1711yescharacteristic
475C23×C4C22⋊D1711yescharacteristic
476C23×C4C22×D1711yescharacteristic
477C2×Q16—174no—
478C2×Q16—344no—
479C2×SD16—174no—
480C2×SD16—174no—
481C2×SD16—344no—
482C2×SD16—344no—
483C2×D8—174no—
484C2×D8—344no—
485C22×C8—171no—
486C22×C8—171no—
487C22×C8—171no—
488C22×C8—171no—
489#126—348no—
490#125—174no—
491#125—342no—
492#124—174no—
493#124—342no—
494#123—348no—
495C22⋊Q8—174no—
496C22⋊Q8—342no—
497#121—174no—
498#121—342no—
499C4×Q8—22no—
500C4×Q8—22no—
501C4×Q8—174no—
502C4×Q8—342no—
503C4×Q8C22×D1714yes—
504C4×Q8C22×D1714yes—
505C4×D4—28no—
506C4×D4—28no—
507C4×D4—22no—
508C4×D4—22no—
509C4×D4—174no—
510C4×D4—348no—
511C4×D4—342no—
512C4×D4C22×D1714yes—
513C4×D4C22×D1714yes—
514#117—22no—
515#117—28no—
516#117—348no—
517#117C22×D1714yes—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—171no—
521C2×C4⋊C4—171no—
522C2×C4⋊C4—341no—
523C2×C4⋊C4—341no—
524C2×C4⋊C4—341no—
525C2×C4⋊C4—341no—
526C2×C4⋊C4C22×D1711yescharacteristic
527C2×C4⋊C4C22×D1711yescharacteristic
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—341no—
532C2×C22⋊C4—341no—
533C2×C22⋊C4—341no—
534C2×C22⋊C4—341no—
535C2×C22⋊C4—341no—
536C2×C42—21no—
537C2×C42—21no—
538C2×C42—21no—
539C2×C42—28no—
540C2×C42—341no—
541C2×C42C22⋊D1711yescharacteristic
542C2×C42C22⋊D1714yes—
543C2×C42C22⋊D1711yescharacteristic
544C2×C42C22×D1711yescharacteristic
545C2×C42C22×D1714yes—
546C2×C42C22×D1711yescharacteristic
547#107—174no—
548#107—174no—
549#106—174no—
550#106—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#102—174no—
560#102—174no—
561C22⋊C8—174no—
562C22⋊C8—174no—
563C4×C8—174no—
564C4×C8—174no—
565C17C2×#310211yescharacteristic, complemented, Sylow
566C24—21no—
567C24—341no—
568C24C2×C22⋊D1711yescharacteristic
569#41—216no—
570#41—28no—
571#41—28no—
572C2×Q8—22no—
573C2×Q8—21no—
574C2×Q8—172no—
575C2×Q8—341no—
576C2×Q8—342no—
577C2×Q8—342no—
578C2×Q8#6325214yes—
579C2×Q8C23×D1712yes—
580C2×D4—28no—
581C2×D4—24no—
582C2×D4—22no—
583C2×D4—21no—
584C2×D4—172no—
585C2×D4—344no—
586C2×D4—342no—
587C2×D4—342no—
588C2×D4—341no—
589C2×D4—684no—
590C2×D4#6325214yes—
591C2×D4C23×D1712yes—
592C22×C4—28no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—24no—
597C22×C4—24no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—24no—
601C22×C4—24no—
602C22×C4—42no—
603C22×C4—44no—
604C22×C4—44no—
605C22×C4—341no—
606C22×C4—341no—
607C22×C4—341no—
608C22×C4—344no—
609C22×C4—684no—
610C22×C4C2×C22⋊D1711yescharacteristic
611C22×C4C2×C22⋊D1711yescharacteristic
612C22×C4C2×C22⋊D1712yes—
613C22×C4C2×C22⋊D1711yescharacteristic
614C22×C4C2×C22⋊D1711yescharacteristic
615C22×C4C2×C22⋊D1714yes—
616C22×C4C2×C22⋊D1714yes—
617C22×C4C2×C22⋊D1711yescharacteristic
618C22×C4C23×D1712yes—
619C22×C4C23×D1711yescharacteristic
620Q16—348no—
621SD16—348no—
622SD16—348no—
623D8—348no—
624C2×C8—172no—
625C2×C8—172no—
626C2×C8—172no—
627C2×C8—172no—
628C2×C8—342no—
629C2×C8—342no—
630C2×C8—342no—
631C2×C8—342no—
632C4⋊C4—24no—
633C4⋊C4—24no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—172no—
637C4⋊C4—172no—
638C4⋊C4—341no—
639C4⋊C4—341no—
640C4⋊C4—344no—
641C4⋊C4—344no—
642C4⋊C4—344no—
643C4⋊C4—344no—
644C4⋊C4C23×D1712yes—
645C4⋊C4C23×D1712yes—
646C22⋊C4—24no—
647C22⋊C4—24no—
648C22⋊C4—24no—
649C22⋊C4—344no—
650C22⋊C4—344no—
651C22⋊C4—344no—
652C22⋊C4—344no—
653C22⋊C4—344no—
654C42—24no—
655C42—24no—
656C42—24no—
657C42—344no—
658C42C2×C22⋊D1714yes—
659C42C2×C22⋊D1714yes—
660C42C2×C22⋊D1712yes—
661C42C2×C22⋊D1712yes—
662C42C23×D1712yes—
663C42C23×D1712yes—
664C23—22no—
665C23—24no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—42no—
670C23—42no—
671C23—342no—
672C23—682no—
673C23—682no—
674C23—682no—
675C23C22×C22⋊D1712yes—
676C23C22×C22⋊D1711yescharacteristic
677Q8—24no—
678Q8—22no—
679Q8—342no—
680Q8—342no—
681Q8—682no—
682Q8C2×#6325214yes—
683D4—216no—
684D4—24no—
685D4—22no—
686D4—342no—
687D4—342no—
688D4—688no—
689D4—682no—
690D4C2×#6325214yes—
691C2×C4—216no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—28no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—44no—
705C2×C4—48no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—48no—
709C2×C4—342no—
710C2×C4—342no—
711C2×C4—342no—
712C2×C4—682no—
713C2×C4—682no—
714C2×C4—682no—
715C2×C4—688no—
716C2×C4#1058763614yes—
717C2×C4C2×#6325212yes—
718C2×C4C2×#6325212yes—
719C2×C4C22×C22⋊D1712yes—
720C2×C4C22×C22⋊D1712yes—
721C2×C4C22×C22⋊D1712yes—
722C2×C4C22×C22⋊D1712yes—
723C2×C4C22×C22⋊D1711yescharacteristic
724C2×C4C22×C22⋊D1712yes—
725C2×C4C24×D1711yescharacteristic
726C8—342no—
727C8—342no—
728C8—342no—
729C8—342no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—24no—
734C22—44no—
735C22—48no—
736C22—42no—
737C22—42no—
738C22—682no—
739C22—682no—
740C22—682no—
741C22—1364no—
742C22#1176332012yes—
743C22C2×#1058763612yes—
744C22#1176360712yes—
745C22C23×C22⋊D1711yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—22no—
750C4—24no—
751C4—42no—
752C4—42no—
753C4—682no—
754C4—682no—
755C4—682no—
756C4#1176332012yes—
757C4C2×#1058763614yes—
758C4C22×#6325211yescharacteristic
759C4C22×#6325211yescharacteristic
760C2—42no—
761C2—44no—
762C2—1362no—
763C2#1453880214yesdirect product factor
764C2C2×#1176332011yescharacteristic
765C2C22×#1058763611yescharacteristic
766C2C2×#1176360711yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C4×#41×C17C2
socleC23×C17C22×D4
prime radicalC2×#11762954C2
hypercenterC2×C4×#41D17
hypocenterC17C2×#3102
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. C2×#11763343C2semidirect
2. #14538802C2direct (N × H)
3. C2×#11763150C2semidirect
4. C2×#11763133C2semidirect
5. C2×#11763116C2semidirect
6. C2×#11763109C2semidirect
7. C2×#11763031C2semidirect
8. C2×#11763024C2semidirect
9. C2×#11762971C2semidirect
11. C2×C4×#63231C2semidirect
12. C2×C4×#63230C2semidirect
13. C2×C4×#63229C2semidirect
14. C2×C4×#63228C2semidirect
15. C2×#11762862C2semidirect
16. C2×C4×#41×C17C2semidirect
22. #11763343C22semidirect
33. #11763150C22semidirect
34. #11763133C22semidirect
35. #11763116C22semidirect
36. #11763109C22semidirect
37. #11763031C22semidirect
38. #11763024C22semidirect
39. #11762971C22semidirect
41. C4×#63231C22semidirect
42. C4×#63230C22semidirect
43. C4×#63229C22semidirect
44. C4×#63228C22semidirect
45. #11762862C22semidirect
66. C4×#41×C17C22semidirect
348. C2×C4×#41D17semidirect
407. C4×#41C2×D17semidirect
455. C2×C17#3102semidirect
565. C17C2×#3102semidirect
763. C2#14538802direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117633432
#145388022
C2×#117631502
C2×#117631332
C2×#117631162
C2×#117631092
C2×#117630312
C2×#117630242
C2×#117629712
C2×#117629542
C2×C4×#632312
C2×C4×#632302
C2×C4×#632292
C2×C4×#632282
C2×#117628622
C2×C4×#41×C172
C2×#310217