Finite Group Databasebeta

← C2×#14541233 #17912865

Subgroups — C2×#14541233 #17912865

Order 4352.

1878 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763499C211yesmaximal, characteristic
2#14541233C2116yesmaximal, direct product factor
3C2×#11763215C211yesmaximal, characteristic, complemented
4C2×#11763144C211yesmaximal, characteristic, complemented
5C2×#11763147C211yesmaximal, characteristic, complemented
6C2×#11763139C211yesmaximal, characteristic, complemented
7C2×#11763137C211yesmaximal, characteristic, complemented
8C2×#11763116C211yesmaximal, characteristic, complemented
9C2×#11763091C211yesmaximal, characteristic, complemented
10C2×#11763065C211yesmaximal, characteristic, complemented
11C2×#11763048C211yesmaximal, characteristic, complemented
12C2×#11762914C211yesmaximal, characteristic, complemented
13C2×#11762881C211yesmaximal, characteristic
14C2×#11762849C211yesmaximal, characteristic, complemented
15C22×#10587479C211yesmaximal, characteristic, complemented
16C2×C17×#554C211yesmaximal, characteristic
17C22×#63231C2211yescharacteristic
18C22×#63223C2211yescharacteristic
19C23×#3622C2211yescharacteristic
20#11763499—24no—
21#11763499C2218yes—
22C2×#10587565—21no—
23C2×#10587556C2211yescharacteristic
24C2×#10587575—21no—
25C2×#10587621—21no—
26C2×#10587610C2211yescharacteristic
27C2×#10587610C2211yescharacteristic
28C2×C4×Dic34C2211yescharacteristic
29C2×#10587612C2211yescharacteristic
30C2×#10587563—21no—
31C22×C4⋊Dic17C2211yescharacteristic
32#11763215C2218yescomplemented
33#11763147C2218yescomplemented
34#11763144C2218yescomplemented
35#11763139C2218yescomplemented
36#11763137C2218yescomplemented
37#11763116C2218yescomplemented
38#11763091C2218yescomplemented
39#11763065C2218yescomplemented
40#11763048C2218yescomplemented
41#11762914C2218yescomplemented
42#11762881C2218yes—
43#11762849C2218yescomplemented
44C2×#10587478C2211yescharacteristic
45C2×#10587478C2211yescharacteristic
46C2×#10587478C2211yescharacteristic
47C2×#10587479C2211yescharacteristic
48C2×#10587479C2211yescharacteristic
49C2×#10587479C2211yescharacteristic
50C2×#10587479C2211yescharacteristic
51C2×#10587479C2211yescharacteristic
52C2×#10587479C2211yescharacteristic
53C2×#10587479C2218yescomplemented
54C2×C4⋊#3622C2211yescharacteristic
55C2×#10587506C2211yescharacteristic
56C2×#10587506C2211yescharacteristic
57C2×#10587506C2211yescharacteristic
58C2×#10587481C2211yescharacteristic
59C2×#10587481C2211yescharacteristic
60C2×#10587481C2211yescharacteristic
61C2×C22⋊#3622C2211yescharacteristic
62C2×C22⋊#3622C2211yescharacteristic
63C2×#10587474C2211yescharacteristic
64C17×#554—24no—
65C17×#554C2218yes—
66C2×C17×C4⋊Q8C2211yescharacteristic
67C2×C17×#125—21no—
68C2×C17×C22⋊Q8—21no—
69C2×C17×C22⋊Q8—21no—
70C2×C17×C22⋊Q8C2211yescharacteristic
71C2×C17×C22⋊Q8C2211yescharacteristic
72C2×C4×Q8×C17C2211yescharacteristic
73C2×C4×D4×C17—21no—
74C2×C4×D4×C17C2211yescharacteristic
75C22×C4⋊C4×C17C2211yescharacteristic
76C22×C4⋊C4×C17C2211yescharacteristic
77C22×Q8×C17—21no—
78C22×Q8×C17C2311yescharacteristic
79C22×D4×C17D411yescharacteristic
80C23×C4×C17—21no—
81C23×C4×C17—21no—
82C23×C4×C17C2311yescharacteristic
83C23×C4×C17C2311yescharacteristic
84C23×Dic17—21no—
85C22×Dic34C2311yescharacteristic
86C17×C4⋊Q8—22no—
87C17×C4⋊Q8C2314yes—
88C17×#125—28no—
89C17×C22⋊Q8—22no—
90C17×C22⋊Q8—22no—
91C17×C22⋊Q8—28no—
92C17×C22⋊Q8—28no—
93C17×C22⋊Q8C2314yes—
94C17×C22⋊Q8C2314yes—
95C4×Q8×C17—22no—
96C4×Q8×C17C2314yes—
97C4×D4×C17—28no—
98C4×D4×C17D414yes—
99C4×D4×C17C2314yes—
100C2×C4⋊C4×C17—21no—
101C2×C4⋊C4×C17—21no—
102C2×C4⋊C4×C17—22no—
103C2×C4⋊C4×C17—22no—
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×C17C2311yescharacteristic
110C2×C4⋊C4×C17C2311yescharacteristic
111C2×C4⋊C4×C17C2311yescharacteristic
112C2×C4⋊C4×C17C2314yes—
113C2×C4⋊C4×C17C2314yes—
114C2×C22⋊C4×C17—21no—
115C2×C22⋊C4×C17—21no—
116C2×C22⋊C4×C17D411yescharacteristic
117C2×C22⋊C4×C17D411yescharacteristic
118C2×C42×C17—21no—
119C2×C42×C17C2311yescharacteristic
120C2×C22⋊Dic17—21no—
121C2×C22⋊Dic17—21no—
122C2×C22⋊Dic17—21no—
123C2×#63231—24no—
124C2×#63231C2314yes—
125#10587621—28no—
126#10587612—22no—
127#10587612C2314yes—
128C2×C4⋊Dic17—22no—
129C2×C4⋊Dic17—21no—
130C2×C4⋊Dic17C2314yes—
131C2×C4⋊Dic17C2311yescharacteristic
132C2×C4⋊Dic17C2311yescharacteristic
133C2×C4⋊Dic17C2311yescharacteristic
134#10587610—22no—
135#10587610—22no—
136#10587610C2314yes—
137#10587610C2314yes—
138C2×#63225—21no—
139C2×#63225—21no—
140C2×#63225—21no—
141C2×#63225—21no—
142C2×#63225—21no—
143C2×C4×Dic17—21no—
144C2×C4×Dic17—21no—
145C2×#63223—24no—
146C2×#63223C2314yes—
147C22×#3622—24no—
148C22×#3622C2311yescharacteristic
149C22×#3622C2311yescharacteristic
150C22×#3622C2311yescharacteristic
151C22×#3622C2314yes—
152C22×#3622C2311yescharacteristic
153#10587575—28no—
154#10587565—28no—
155#10587563—28no—
156#10587556—22no—
157#10587556C2314yes—
158C4×Dic34—22no—
159C4×Dic34C2314yes—
160#10587506C2314yes—
161#10587506C2314yes—
162#10587506C2314yes—
163C22⋊#3622C2314yes—
164C22⋊#3622C2314yes—
165#10587481C2314yes—
166#10587481C2314yes—
167#10587481C2314yes—
168#10587479C2314yes—
169#10587479C2314yes—
170#10587479C2314yes—
171#10587479C2314yes—
172#10587479C2314yes—
173#10587479C2314yes—
174#10587478C2314yes—
175#10587478C2314yes—
176#10587478C2314yes—
177C4⋊#3622C2314yes—
178#10587474C2314yes—
179C24×C17C2×D411yescharacteristic
180C24×C17C2×D411yescharacteristic
181C2×Q8×C17—21no—
182C2×Q8×C17—24no—
183C2×Q8×C17—22no—
184C2×Q8×C17—22no—
185C2×Q8×C17—82no—
186C2×Q8×C17C2412yes—
187C2×D4×C17—24no—
188C2×D4×C17C2×D414yes—
189C22×C4×C17—22no—
190C22×C4×C17—22no—
191C22×C4×C17—22no—
192C22×C4×C17—22no—
193C22×C4×C17—21no—
194C22×C4×C17—21no—
195C22×C4×C17—21no—
196C22×C4×C17—21no—
197C22×C4×C17—24no—
198C22×C4×C17—24no—
199C22×C4×C17—82no—
200C22×C4×C17—82no—
201C22×C4×C17C2×D412yes—
202C22×C4×C17C2×D412yes—
203C22×C4×C17C2×D411yescharacteristic
204C22×C4×C17C2×D411yescharacteristic
205C22×C4×C17C2×D411yescharacteristic
206C22×C4×C17C2×D411yescharacteristic
207C22×C4×C17C2412yes—
208C22×C4×C17C2412yes—
209C22×C4×C17C2411yescharacteristic
210C22×Dic17—21no—
211C22×Dic17—24no—
212C22×Dic17—21no—
213C22×Dic17—21no—
214C22×Dic17—21no—
215C22×Dic17—44no—
216C2×Dic34—22no—
217C2×Dic34—22no—
218C2×Dic34—21no—
219C2×Dic34C2412yes—
220C4⋊C4×C17—24no—
221C4⋊C4×C17—24no—
222C4⋊C4×C17—24no—
223C4⋊C4×C17—24no—
224C4⋊C4×C17—24no—
225C4⋊C4×C17—21no—
226C4⋊C4×C17—21no—
227C4⋊C4×C17—24no—
228C4⋊C4×C17—21no—
229C4⋊C4×C17C2×D414yes—
230C4⋊C4×C17C2412yes—
231C4⋊C4×C17C2412yes—
232C4⋊C4×C17C2412yes—
233C22⋊C4×C17—24no—
234C22⋊C4×C17—24no—
235C22⋊C4×C17C2×D414yes—
236C22⋊C4×C17C2×D414yes—
237C42×C17—24no—
238C42×C17C2×D412yes—
239C42×C17C2412yes—
240C22⋊Dic17—24no—
241C22⋊Dic17—24no—
242C22⋊Dic17—24no—
243#63231—28no—
244C4⋊Dic17—21no—
245C4⋊Dic17—21no—
246C4⋊Dic17—21no—
247C4⋊Dic17—24no—
248C4⋊Dic17C2412yes—
249C4⋊Dic17C2412yes—
250C4⋊Dic17C2412yes—
251#63225—24no—
252#63225—24no—
253#63225—24no—
254#63225—24no—
255#63225—24no—
256C4×Dic17—24no—
257C4×Dic17—24no—
258#63223—28no—
259C2×#3622—22no—
260C2×#3622—22no—
261C2×#3622—22no—
262C2×#3622—28no—
263C2×#3622#4114yes—
264C2×#3622C2412yes—
265C2×#3622C2412yes—
266C2×#3622C2412yes—
267C2×#3622C2412yes—
268C2×#3344—171nomaximal, Sylow
269C23×C17—22no—
270C23×C17—22no—
271C23×C17—22no—
272C23×C17—22no—
273C23×C17—22no—
274C23×C17#13714yes—
275C23×C17C22×D412yes—
276C23×C17C22×D412yes—
277C23×C17C22×D411yescharacteristic
278Q8×C17—22no—
279Q8×C17—22no—
280Q8×C17—42no—
281Q8×C17—84no—
282D4×C17—28no—
283C2×C4×C17—22no—
284C2×C4×C17—22no—
285C2×C4×C17—22no—
286C2×C4×C17—22no—
287C2×C4×C17—24no—
288C2×C4×C17—24no—
289C2×C4×C17—22no—
290C2×C4×C17—22no—
291C2×C4×C17—22no—
292C2×C4×C17—22no—
293C2×C4×C17—22no—
294C2×C4×C17—22no—
295C2×C4×C17—22no—
296C2×C4×C17—22no—
297C2×C4×C17—42no—
298C2×C4×C17—42no—
299C2×C4×C17—42no—
300C2×C4×C17—42no—
301C2×C4×C17—84no—
302C2×C4×C17—84no—
303C2×C4×C17C22×D412yes—
304C2×C4×C17C22×D412yes—
305C2×C4×C17C22×D412yes—
306C2×C4×C17C22×D412yes—
307C2×C4×C17C22×D411yescharacteristic
308C2×C4×C17C2×#4112yes—
309C2×C4×C172−1+412yes—
310C2×C4×C17C2511yescharacteristic
311C2×Dic17—22no—
312C2×Dic17—22no—
313C2×Dic17—22no—
314C2×Dic17—22no—
315C2×Dic17—42no—
316C2×Dic17—48no—
317C2×Dic17—42no—
318C2×Dic17—42no—
319C2×Dic17—42no—
320Dic34—22no—
321Dic34—22no—
322Dic34—42no—
323#3622—22no—
324#3622—22no—
325#3622—22no—
326#3622C2×#4114yes—
327C2×#554D1711yescharacteristic
328C2×#552—171no—
329#3344—1716no—
330C2×#501—171no—
331C2×#484—171no—
332C2×#485—171no—
333C2×#483—171no—
334C2×#483—171no—
335C2×#479—171no—
336C2×#475—171no—
337C2×#470—171no—
338C2×#467—171no—
339C2×#441—171no—
340C2×#435—171no—
341C2×#428—171no—
342C22×#106—171no—
343C22×C17—28no—
344C22×C17—22no—
345C22×C17—22no—
346C22×C17—22no—
347C22×C17—22no—
348C22×C17—22no—
349C22×C17—44no—
350C22×C17#54712yes—
351C22×C17C2×#13714yes—
352C22×C17C2×#13712yes—
353C22×C17#57712yes—
354C22×C17C23×D411yescharacteristic
355C4×C17—22no—
356C4×C17—22no—
357C4×C17—22no—
358C4×C17—22no—
359C4×C17—42no—
360C4×C17—42no—
361C4×C17—42no—
362C4×C17—42no—
363C4×C17#54712yes—
364C4×C17C22×#4111yescharacteristic
365C4×C17C2×2−1+411yescharacteristic
366Dic17—42no—
367Dic17—42no—
368Dic17—42no—
369Dic17—42no—
370C22×Q16—171no—
371C22×M16—171no—
372C23×C8—171no—
373#554—24no—
374#554C2×D1718yes—
375#552—178no—
376#552—344no—
377C2×C4⋊Q8C2×D1711yescharacteristic
378C2×#126—341no—
379C2×#125—21no—
380C2×#125—171no—
381C2×#125—341no—
382C2×#123—341no—
383C2×C22⋊Q8—21no—
384C2×C22⋊Q8—21no—
385C2×C22⋊Q8—171no—
386C2×C22⋊Q8—171no—
387C2×C22⋊Q8C2×D1711yescharacteristic
388C2×C22⋊Q8C2×D1711yescharacteristic
389C2×C4×Q8—171no—
390C2×C4×Q8C2×D1711yescharacteristic
391C2×C4×D4—21no—
392C2×C4×D4C2×D1711yescharacteristic
393C2×#117—171no—
394C2×#117—341no—
395C22×C4⋊C4—171no—
396C22×C4⋊C4C2×D1711yescharacteristic
397C22×C4⋊C4C2×D1711yescharacteristic
398#501—178no—
399#485—178no—
400#484—178no—
401#483—178no—
402#483—178no—
403#479—178no—
404#475—178no—
405#470—178no—
406#467—178no—
407#441—178no—
408#435—178no—
409#428—178no—
410C2×#107—171no—
411C2×#107—171no—
412C2×#107—171no—
413C2×#106—171no—
414C2×#106—171no—
415C2×#106—171no—
416C2×#106—171no—
417C2×#106—178no—
418C2×#106—171no—
419C2×#106—171no—
420C2×C4⋊C8—171no—
421C2×#103—171no—
422C2×#103—171no—
423C2×#103—171no—
424C2×#103—171no—
425C2×#103—171no—
426C2×#103—171no—
427C2×C22⋊C8—171no—
428C2×C22⋊C8—171no—
429C2×#97—171no—
430C2×C17—24no—
431C2×C17—42no—
432C2×C17#334414yescomplemented
433C2×C17C2×#54711yescharacteristic
434C2×C17C22×#13711yescharacteristic
435C2×C17C2×#57711yescharacteristic
436C22×Q8—21no—
437C22×Q8—171no—
438C22×Q8C22×D1711yescharacteristic
439C22×D4C22⋊D1711yescharacteristic
440C23×C4—21no—
441C23×C4—21no—
442C23×C4—341no—
443C23×C4C22×D1711yescharacteristic
444C23×C4C22×D1711yescharacteristic
445C2×Q16—174no—
446C2×Q16—344no—
447C2×M16—174no—
448C2×M16—344no—
449C22×C8—171no—
450C22×C8—171no—
451C22×C8—174no—
452C22×C8—171no—
453C22×C8—171no—
454C22×C8—344no—
455C4⋊Q8—22no—
456C4⋊Q8C22×D1714yes—
457#126—348no—
458#125—28no—
459#125—174no—
460#125—348no—
461#125—342no—
462#123—348no—
463C22⋊Q8—22no—
464C22⋊Q8—22no—
465C22⋊Q8—28no—
466C22⋊Q8—28no—
467C22⋊Q8—174no—
468C22⋊Q8—174no—
469C22⋊Q8—342no—
470C22⋊Q8—342no—
471C22⋊Q8C22×D1714yes—
472C22⋊Q8C22×D1714yes—
473C4×Q8—22no—
474C4×Q8—174no—
475C4×Q8—342no—
476C4×Q8C22×D1714yes—
477C4×D4—28no—
478C4×D4C22⋊D1714yes—
479C4×D4C22×D1714yes—
480#117—174no—
481#117—342no—
482#117—348no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—22no—
486C2×C4⋊C4—22no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—171no—
492C2×C4⋊C4—171no—
493C2×C4⋊C4—174no—
494C2×C4⋊C4—171no—
495C2×C4⋊C4—341no—
496C2×C4⋊C4—342no—
497C2×C4⋊C4—341no—
498C2×C4⋊C4—341no—
499C2×C4⋊C4—341no—
500C2×C4⋊C4—341no—
501C2×C4⋊C4—341no—
502C2×C4⋊C4C22⋊D1711yescharacteristic
503C2×C4⋊C4C22×D1711yescharacteristic
504C2×C4⋊C4C22×D1711yescharacteristic
505C2×C4⋊C4C22×D1711yescharacteristic
506C2×C4⋊C4C22×D1714yes—
507C2×C4⋊C4C22×D1714yes—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—341no—
511C2×C22⋊C4—341no—
512C2×C22⋊C4—341no—
513C2×C22⋊C4C22⋊D1711yescharacteristic
514C2×C22⋊C4C22⋊D1711yescharacteristic
515C2×C42—21no—
516C2×C42—341no—
517C2×C42—341no—
518C2×C42C22×D1711yescharacteristic
519#107—174no—
520#107—174no—
521#107—174no—
522#106—174no—
523#106—174no—
524#106—174no—
525#106—174no—
526#106—174no—
527#106—174no—
528C4⋊C8—174no—
529#103—174no—
530#103—174no—
531#103—174no—
532#103—174no—
533#103—174no—
534#103—174no—
535C22⋊C8—174no—
536C22⋊C8—174no—
537#97—174no—
538C17C2×#334411yescharacteristic, complemented, Sylow
539C24C2×C22⋊D1711yescharacteristic
540C24C2×C22⋊D1711yescharacteristic
541C2×Q8—21no—
542C2×Q8—24no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8—82no—
546C2×Q8—172no—
547C2×Q8—341no—
548C2×Q8—342no—
549C2×Q8—342no—
550C2×Q8C23×D1712yes—
551C2×D4—24no—
552C2×D4C2×C22⋊D1714yes—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—82no—
564C22×C4—82no—
565C22×C4—344no—
566C22×C4—341no—
567C22×C4—341no—
568C22×C4—341no—
569C22×C4—341no—
570C22×C4—684no—
571C22×C4C2×C22⋊D1712yes—
572C22×C4C2×C22⋊D1712yes—
573C22×C4C2×C22⋊D1711yescharacteristic
574C22×C4C2×C22⋊D1711yescharacteristic
575C22×C4C2×C22⋊D1711yescharacteristic
576C22×C4C2×C22⋊D1711yescharacteristic
577C22×C4C23×D1712yes—
578C22×C4C23×D1712yes—
579C22×C4C23×D1711yescharacteristic
580Q16—348no—
581M16—348no—
582C2×C8—174no—
583C2×C8—172no—
584C2×C8—172no—
585C2×C8—172no—
586C2×C8—172no—
587C2×C8—348no—
588C2×C8—342no—
589C2×C8—342no—
590C2×C8—342no—
591C4⋊C4—21no—
592C4⋊C4—24no—
593C4⋊C4—24no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—24no—
599C4⋊C4—24no—
600C4⋊C4—172no—
601C4⋊C4—172no—
602C4⋊C4—172no—
603C4⋊C4—341no—
604C4⋊C4—341no—
605C4⋊C4—344no—
606C4⋊C4—341no—
607C4⋊C4—344no—
608C4⋊C4—344no—
609C4⋊C4—344no—
610C4⋊C4—344no—
611C4⋊C4—344no—
612C4⋊C4C2×C22⋊D1714yes—
613C4⋊C4C23×D1712yes—
614C4⋊C4C23×D1712yes—
615C4⋊C4C23×D1712yes—
616C22⋊C4—24no—
617C22⋊C4—24no—
618C22⋊C4—344no—
619C22⋊C4—344no—
620C22⋊C4—344no—
621C22⋊C4C2×C22⋊D1714yes—
622C22⋊C4C2×C22⋊D1714yes—
623C42—24no—
624C42—344no—
625C42—344no—
626C42C2×C22⋊D1712yes—
627C42C23×D1712yes—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23#1058762814yes—
634C23C22×C22⋊D1712yes—
635C23C22×C22⋊D1712yes—
636C23C22×C22⋊D1711yescharacteristic
637Q8—22no—
638Q8—22no—
639Q8—42no—
640Q8—84no—
641Q8—342no—
642Q8—342no—
643Q8—682no—
644D4—28no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—84no—
664C2×C4—84no—
665C2×C4—342no—
666C2×C4—342no—
667C2×C4—342no—
668C2×C4—342no—
669C2×C4—682no—
670C2×C4—688no—
671C2×C4—682no—
672C2×C4—682no—
673C2×C4—682no—
674C2×C4#41×D1712yes—
675C2×C4#1058769712yes—
676C2×C4C22×C22⋊D1712yes—
677C2×C4C22×C22⋊D1712yes—
678C2×C4C22×C22⋊D1712yes—
679C2×C4C22×C22⋊D1712yes—
680C2×C4C22×C22⋊D1711yescharacteristic
681C2×C4C24×D1711yescharacteristic
682C8—174no—
683C8—342no—
684C8—342no—
685C8—342no—
686C22—22no—
687C22—28no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—44no—
693C22#1176345812yes—
694C22C2×#1058762814yes—
695C22C2×#1058762812yes—
696C22#1176362012yes—
697C22C23×C22⋊D1711yescharacteristic
698C4—22no—
699C4—22no—
700C4—22no—
701C4—22no—
702C4—42no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—682no—
707C4—682no—
708C4—682no—
709C4—682no—
710C4#1176345812yes—
711C4C2×#41×D1711yescharacteristic
712C4C2×#1058769711yescharacteristic
713C2—24no—
714C2—42no—
715C2#1454123314yesdirect product factor
716C2C2×#1176345811yescharacteristic
717C2C22×#1058762811yescharacteristic
718C2C2×#1176362011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#554C2
socleC23×C17C22×D4
prime radicalC22×D4×C17D4
hypercenterC2×#554D17
hypocenterC17C2×#3344
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
2. #14541233C2direct (N × H)
3. C2×#11763215C2semidirect
4. C2×#11763144C2semidirect
5. C2×#11763147C2semidirect
6. C2×#11763139C2semidirect
7. C2×#11763137C2semidirect
8. C2×#11763116C2semidirect
9. C2×#11763091C2semidirect
10. C2×#11763065C2semidirect
11. C2×#11763048C2semidirect
12. C2×#11762914C2semidirect
14. C2×#11762849C2semidirect
15. C22×#10587479C2semidirect
32. #11763215C22semidirect
33. #11763147C22semidirect
34. #11763144C22semidirect
35. #11763139C22semidirect
36. #11763137C22semidirect
37. #11763116C22semidirect
38. #11763091C22semidirect
39. #11763065C22semidirect
40. #11763048C22semidirect
41. #11762914C22semidirect
43. #11762849C22semidirect
53. C2×#10587479C22semidirect
432. C2×C17#3344semidirect
538. C17C2×#3344semidirect
715. C2#14541233direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117634992
#145412332
C2×#117632152
C2×#117631442
C2×#117631472
C2×#117631392
C2×#117631372
C2×#117631162
C2×#117630912
C2×#117630652
C2×#117630482
C2×#117629142
C2×#117628812
C2×#117628492
C22×#105874792
C2×C17×#5542
C2×#334417