Finite Group Databasebeta

← C2×#14541235 #17912867

Subgroups — C2×#14541235 #17912867

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×#11763514C211yesmaximal, characteristic
2C2×#11763494C211yesmaximal, characteristic
3#14541235C2116yesmaximal, direct product factor
4C2×#11763216C211yesmaximal, characteristic, complemented
5C2×#11763144C211yesmaximal, characteristic, complemented
6C2×#11763153C211yesmaximal, characteristic, complemented
7C2×#11763141C211yesmaximal, characteristic, complemented
8C2×#11763139C211yesmaximal, characteristic, complemented
9C2×#11763119C211yesmaximal, characteristic, complemented
10C2×#11763093C211yesmaximal, characteristic, complemented
11C2×#11763068C211yesmaximal, characteristic, complemented
12C2×#11763050C211yesmaximal, characteristic, complemented
13C2×#11762915C211yesmaximal, characteristic, complemented
14C2×#11762880C211yesmaximal, characteristic
15C2×#11762848C211yesmaximal, characteristic, complemented
16C22×C17×#106C211yesmaximal, characteristic, complemented
17C22×Dic68C2211yescharacteristic
18C22×#63218C2211yescharacteristic
19#11763514—24no—
20#11763514C2218yes—
21#11763494—24no—
22#11763494C2218yes—
23C2×#10587574C2211yescharacteristic
24C2×#10587584—21no—
25C2×#10587576C2211yescharacteristic
26C2×#10587575—21no—
27C2×#10587575—21no—
28C2×#10587615—21no—
29C2×#10587583C2211yescharacteristic
30C2×#10587583C2211yescharacteristic
31C2×#10587610—21no—
32C2×#10587610C2211yescharacteristic
33C2×#10587610C2211yescharacteristic
34C2×#10587582—21no—
35C2×#10587573C2211yescharacteristic
36C2×#10587573C2211yescharacteristic
37C2×C4×C22⋊D17—21no—
38C2×C4×C22⋊D17C2211yescharacteristic
39C2×#10587612—21no—
40C2×#10587578C2211yescharacteristic
41C2×C4⋊C4×D17C2211yescharacteristic
42#11763216C2218yescomplemented
43#11763153C2218yescomplemented
44#11763144C2218yescomplemented
45#11763141C2218yescomplemented
46#11763139C2218yescomplemented
47#11763119C2218yescomplemented
48#11763093C2218yescomplemented
49#11763068C2218yescomplemented
50#11763050C2218yescomplemented
51#11762915C2218yescomplemented
52#11762880C2218yes—
53#11762848C2218yescomplemented
54C2×#10587489C2211yescharacteristic
55C2×#10587478C2211yescharacteristic
56C2×#10587478C2211yescharacteristic
57C2×#10587479C2211yescharacteristic
58C2×#10587479C2211yescharacteristic
59C2×#10587485C2211yescharacteristic
60C2×#10587487C2211yescharacteristic
61C2×#10587487C2211yescharacteristic
62C2×#10587481C2211yescharacteristic
63C2×#10587481C2211yescharacteristic
64C2×#10587481C2211yescharacteristic
65C2×#10587481C2211yescharacteristic
66C2×C22⋊#3622C2211yescharacteristic
67C2×#10587491C2211yescharacteristic
68C2×#10587486C2211yescharacteristic
69C23×C8×C17C2211yescharacteristic
70C22×C4⋊C4×C17C2211yescharacteristic
71C22×C4⋊C4×C17C2211yescharacteristic
72C2×C17×#106C2211yescharacteristic
73C2×C17×#106C2211yescharacteristic
74C2×C17×#106C2211yescharacteristic
75C2×C17×#106C2211yescharacteristic
76C2×C17×#106C2218yescomplemented
77C23×C4×C17—21no—
78C23×C4×C17—21no—
79C23×C4×C17C2311yescharacteristic
80C22×C22⋊D17D411yescharacteristic
81C22×C4×D17—21no—
82C22×C4×D17C2311yescharacteristic
83C22×Dic34—21no—
84C22×Dic34C2311yescharacteristic
85C22×Dic34C2311yescharacteristic
86C22×C8×C17—24no—
87C22×C8×C17C2311yescharacteristic
88C22×C8×C17C2314yes—
89C22×C8×C17C2311yescharacteristic
90C2×C4⋊C4×C17—22no—
91C2×C4⋊C4×C17—22no—
92C2×C4⋊C4×C17—21no—
93C2×C4⋊C4×C17—21no—
94C2×C4⋊C4×C17C2314yes—
95C2×C4⋊C4×C17C2311yescharacteristic
96C2×C4⋊C4×C17C2314yes—
97C2×C4⋊C4×C17C2311yescharacteristic
98C2×C4⋊C4×C17C2311yescharacteristic
99C2×C4⋊C4×C17C2311yescharacteristic
100C2×C22⋊Dic17—21no—
101C2×C22⋊Dic17—21no—
102C2×C22⋊Dic17D411yescharacteristic
103#10587615—28no—
104C4×C22⋊D17—28no—
105C4×C22⋊D17D414yes—
106C4×C22⋊D17C2314yes—
107C2×#63227—21no—
108C2×#63227—21no—
109C2×#63227—21no—
110C2×#63227D411yescharacteristic
111#10587612—28no—
112C2×C4⋊Dic17—21no—
113C2×C4⋊Dic17—21no—
114C2×C4⋊Dic17—21no—
115C2×C4⋊Dic17C2311yescharacteristic
116C2×C4⋊Dic17C2311yescharacteristic
117#10587610—22no—
118#10587610—22no—
119#10587610—28no—
120#10587610C2314yes—
121#10587610C2314yes—
122C2×#63225—21no—
123C2×#63225—21no—
124C2×#63225—21no—
125C2×#63225—21no—
126C2×#63225—21no—
127C2×#63225—21no—
128C2×#63225—21no—
129C2×#63225D411yescharacteristic
130C2×C4×Dic17—21no—
131C2×C4×Dic17—21no—
132C2×C4×Dic17—21no—
133C2×C4×Dic17C2311yescharacteristic
134C22×#3622C2311yescharacteristic
135C22×#3622C2311yescharacteristic
136C2×Dic68—24no—
137C2×Dic68C2314yes—
138C2×#63218—24no—
139C2×#63218C2314yes—
140#10587584—28no—
141#10587583—22no—
142#10587583—22no—
143#10587583C2314yes—
144#10587583C2314yes—
145#10587582—28no—
146#10587578—22no—
147#10587578C2314yes—
148C4⋊C4×D17—22no—
149C4⋊C4×D17C2314yes—
150#10587576—22no—
151#10587576C2314yes—
152#10587575—28no—
153#10587575—28no—
154#10587574—22no—
155#10587574C2314yes—
156#10587573—22no—
157#10587573—22no—
158#10587573C2314yes—
159#10587573C2314yes—
160C17×#106C2314yes—
161C17×#106C2314yes—
162C17×#106C2314yes—
163C17×#106C2314yes—
164C22⋊#3622C2314yes—
165#10587491C2314yes—
166#10587489C2314yes—
167#10587487C2314yes—
168#10587487C2314yes—
169#10587486C2314yes—
170#10587485C2314yes—
171#10587481C2314yes—
172#10587481C2314yes—
173#10587481C2314yes—
174#10587481C2314yes—
175#10587479C2314yes—
176#10587479C2314yes—
177#10587478C2314yes—
178#10587478C2314yes—
179C24×C17C2×D411yescharacteristic
180C23×D17C2×D411yescharacteristic
181C22×C4×C17—22no—
182C22×C4×C17—22no—
183C22×C4×C17—21no—
184C22×C4×C17—21no—
185C22×C4×C17—21no—
186C22×C4×C17—21no—
187C22×C4×C17—24no—
188C22×C4×C17—24no—
189C22×C4×C17—44no—
190C22×C4×C17—82no—
191C22×C4×C17C2×D411yescharacteristic
192C22×C4×C17C2×D412yes—
193C22×C4×C17C2412yes—
194C22×C4×C17C2411yescharacteristic
195C2×C22⋊D17—24no—
196C2×C22⋊D17C2×D414yes—
197C22×Dic17—21no—
198C22×Dic17—21no—
199C22×Dic17—21no—
200C22×Dic17—21no—
201C22×Dic17C2×D411yescharacteristic
202C22×Dic17C2×D411yescharacteristic
203C22×Dic17C2×D411yescharacteristic
204C2×C4×D17—22no—
205C2×C4×D17—22no—
206C2×C4×D17—24no—
207C2×C4×D17—82no—
208C2×C4×D17C2×D412yes—
209C2×C4×D17C2412yes—
210C2×Dic34—22no—
211C2×Dic34—22no—
212C2×Dic34—22no—
213C2×Dic34—22no—
214C2×Dic34—21no—
215C2×Dic34—21no—
216C2×Dic34—24no—
217C2×Dic34—82no—
218C2×Dic34C2412yes—
219C2×Dic34C2412yes—
220C2×C8×C17—22no—
221C2×C8×C17—28no—
222C2×C8×C17#4114yes—
223C2×C8×C17C2412yes—
224C2×C8×C17C2412yes—
225C4⋊C4×C17—21no—
226C4⋊C4×C17—21no—
227C4⋊C4×C17—21no—
228C4⋊C4×C17—24no—
229C4⋊C4×C17—24no—
230C4⋊C4×C17—21no—
231C4⋊C4×C17C2412yes—
232C4⋊C4×C17C2412yes—
233C4⋊C4×C17C2412yes—
234C4⋊C4×C17C2412yes—
235C22⋊Dic17—24no—
236C22⋊Dic17—24no—
237C22⋊Dic17C2×D414yes—
238#63227—24no—
239#63227—24no—
240#63227—24no—
241#63227C2×D414yes—
242C4⋊Dic17—21no—
243C4⋊Dic17—21no—
244C4⋊Dic17—24no—
245C4⋊Dic17—24no—
246C4⋊Dic17—24no—
247C4⋊Dic17C2412yes—
248C4⋊Dic17C2412yes—
249#63225—24no—
250#63225—24no—
251#63225—24no—
252#63225—24no—
253#63225—24no—
254#63225—24no—
255#63225—24no—
256#63225C2×D414yes—
257C4×Dic17—24no—
258C4×Dic17—24no—
259C4×Dic17—24no—
260C4×Dic17C2×D412yes—
261C4×Dic17C2412yes—
262C2×#3622—22no—
263C2×#3622—22no—
264C2×#3622C2412yes—
265C2×#3622C2412yes—
266Dic68—28no—
267#63218—28no—
268C2×#3344—171nomaximal, Sylow
269C23×C17—22no—
270C23×C17—22no—
271C23×C17#13714yes—
272C23×C17C22×D412yes—
273C23×C17C22×D411yescharacteristic
274C22×D17—22no—
275C22×D17—22no—
276C22×D17—22no—
277C22×D17C22×D412yes—
278C2×C4×C17—22no—
279C2×C4×C17—24no—
280C2×C4×C17—22no—
281C2×C4×C17—22no—
282C2×C4×C17—22no—
283C2×C4×C17—22no—
284C2×C4×C17—22no—
285C2×C4×C17—22no—
286C2×C4×C17—48no—
287C2×C4×C17—42no—
288C2×C4×C17—42no—
289C2×C4×C17—42no—
290C2×C4×C17—42no—
291C2×C4×C17—84no—
292C2×C4×C17C22×D412yes—
293C2×C4×C17C22×D411yescharacteristic
294C2×C4×C17C2×#4112yes—
295C2×C4×C172−1+412yes—
296C2×C4×C17C2511yescharacteristic
297C22⋊D17—28no—
298C2×Dic17—22no—
299C2×Dic17—22no—
300C2×Dic17—22no—
301C2×Dic17—22no—
302C2×Dic17—22no—
303C2×Dic17—22no—
304C2×Dic17—22no—
305C2×Dic17—42no—
306C2×Dic17—42no—
307C2×Dic17—42no—
308C2×Dic17—42no—
309C2×Dic17C22×D412yes—
310C2×Dic17C22×D412yes—
311C2×Dic17C22×D412yes—
312C4×D17—24no—
313C4×D17—22no—
314C4×D17—22no—
315C4×D17—84no—
316Dic34—22no—
317Dic34—22no—
318Dic34—22no—
319Dic34—22no—
320Dic34—42no—
321Dic34—42no—
322Dic34—84no—
323C8×C17—22no—
324C8×C17C2×#4114yes—
325#3622—22no—
326#3622—22no—
327C2×#554—171no—
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×#106D1711yescharacteristic, complemented
343C22×C17—28no—
344C22×C17—22no—
345C22×C17—22no—
346C22×C17#54712yes—
347C22×C17C2×#13714yes—
348C22×C17C2×#13712yes—
349C22×C17#57712yes—
350C22×C17C23×D411yescharacteristic
351C2×D17—22no—
352C2×D17—22no—
353C2×D17—22no—
354C2×D17—44no—
355C4×C17—22no—
356C4×C17—42no—
357C4×C17—42no—
358C4×C17—42no—
359C4×C17—42no—
360C4×C17#54712yes—
361C4×C17C22×#4111yescharacteristic
362C4×C17C2×2−1+411yescharacteristic
363Dic17—22no—
364Dic17—22no—
365Dic17—22no—
366Dic17—42no—
367Dic17—42no—
368Dic17—42no—
369Dic17—42no—
370C22×Q16—171no—
371C22×M16—171no—
372C23×C8C2×D1711yescharacteristic
373#554—178no—
374#554—344no—
375#552—178no—
376#552—344no—
377C2×C4⋊Q8—171no—
378C2×#126—341no—
379C2×#125—171no—
380C2×#125—341no—
381C2×#125—341no—
382C2×#123—341no—
383C2×C22⋊Q8—171no—
384C2×C22⋊Q8—171no—
385C2×C22⋊Q8—171no—
386C2×C22⋊Q8—171no—
387C2×C22⋊Q8—341no—
388C2×C22⋊Q8—341no—
389C2×C4×Q8—171no—
390C2×C4×Q8—171no—
391C2×C4×D4—171no—
392C2×C4×D4—341no—
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×#106C2×D1711yescharacteristic
416C2×#106C2×D1711yescharacteristic
417C2×#106C2×D1711yescharacteristic
418C2×#106C2×D1711yescharacteristic
419C2×#106C2×D1718yescomplemented
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#334414yescomplemented
432C2×C17C2×#54711yescharacteristic
433C2×C17C22×#13711yescharacteristic
434C2×C17C2×#57711yescharacteristic
435D17—42no—
436C22×Q8—171no—
437C22×Q8—171no—
438C22×Q8—341no—
439C22×D4—171no—
440C23×C4—21no—
441C23×C4—21no—
442C23×C4—171no—
443C23×C4—341no—
444C23×C4C22×D1711yescharacteristic
445C2×Q16—174no—
446C2×Q16—344no—
447C2×M16—174no—
448C2×M16—344no—
449C22×C8—24no—
450C22×C8—171no—
451C22×C8—171no—
452C22×C8C22×D1711yescharacteristic
453C22×C8C22×D1714yes—
454C22×C8C22×D1711yescharacteristic
455C4⋊Q8—174no—
456C4⋊Q8—342no—
457#126—348no—
458#125—174no—
459#125—342no—
460#125—348no—
461#125—348no—
462#123—348no—
463C22⋊Q8—174no—
464C22⋊Q8—174no—
465C22⋊Q8—174no—
466C22⋊Q8—174no—
467C22⋊Q8—348no—
468C22⋊Q8—348no—
469C22⋊Q8—342no—
470C22⋊Q8—342no—
471C22⋊Q8—342no—
472C22⋊Q8—342no—
473C4×Q8—174no—
474C4×Q8—174no—
475C4×Q8—342no—
476C4×Q8—342no—
477C4×D4—174no—
478C4×D4—174no—
479C4×D4—348no—
480#117—174no—
481#117—348no—
482#117—342no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—22no—
486C2×C4⋊C4—22no—
487C2×C4⋊C4—171no—
488C2×C4⋊C4—171no—
489C2×C4⋊C4—171no—
490C2×C4⋊C4—174no—
491C2×C4⋊C4—342no—
492C2×C4⋊C4—341no—
493C2×C4⋊C4—341no—
494C2×C4⋊C4—341no—
495C2×C4⋊C4—341no—
496C2×C4⋊C4—341no—
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—171no—
509C2×C22⋊C4—171no—
510C2×C22⋊C4—341no—
511C2×C22⋊C4—341no—
512C2×C22⋊C4—341no—
513C2×C22⋊C4—341no—
514C2×C22⋊C4—341no—
515C2×C42—171no—
516C2×C42—341no—
517C2×C42—341no—
518C2×C42—341no—
519#107—174no—
520#107—174no—
521#107—174no—
522#106—174no—
523#106—174no—
524#106C22×D1714yes—
525#106C22×D1714yes—
526#106C22×D1714yes—
527#106C22×D1714yes—
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
539C24—171no—
540C24D4×D1711yescharacteristic
541C2×Q8—172no—
542C2×Q8—172no—
543C2×Q8—344no—
544C2×Q8—341no—
545C2×Q8—341no—
546C2×Q8—342no—
547C2×Q8—342no—
548C2×Q8—342no—
549C2×Q8—342no—
550C2×Q8—1362no—
551C2×D4—174no—
552C2×D4—344no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—24no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—24no—
561C22×C4—44no—
562C22×C4—82no—
563C22×C4—171no—
564C22×C4—171no—
565C22×C4—171no—
566C22×C4—172no—
567C22×C4—172no—
568C22×C4—344no—
569C22×C4—342no—
570C22×C4—342no—
571C22×C4—341no—
572C22×C4—341no—
573C22×C4—341no—
574C22×C4—341no—
575C22×C4—1362no—
576C22×C4D4×D1712yes—
577C22×C4D4×D1711yescharacteristic
578C22×C4C23×D1712yes—
579C22×C4C23×D1711yescharacteristic
580Q16—348no—
581M16—348no—
582C2×C8—22no—
583C2×C8—28no—
584C2×C8—172no—
585C2×C8—172no—
586C2×C8—342no—
587C2×C8—342no—
588C2×C8#6325214yes—
589C2×C8C23×D1712yes—
590C2×C8C23×D1712yes—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—24no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—24no—
597C4⋊C4—174no—
598C4⋊C4—172no—
599C4⋊C4—172no—
600C4⋊C4—344no—
601C4⋊C4—344no—
602C4⋊C4—344no—
603C4⋊C4—344no—
604C4⋊C4—344no—
605C4⋊C4—344no—
606C4⋊C4—344no—
607C4⋊C4—344no—
608C4⋊C4—341no—
609C4⋊C4—341no—
610C4⋊C4—344no—
611C4⋊C4—344no—
612C4⋊C4C23×D1712yes—
613C4⋊C4C23×D1712yes—
614C4⋊C4C23×D1712yes—
615C4⋊C4C23×D1712yes—
616C22⋊C4—174no—
617C22⋊C4—174no—
618C22⋊C4—344no—
619C22⋊C4—344no—
620C22⋊C4—344no—
621C22⋊C4—344no—
622C22⋊C4—344no—
623C42—172no—
624C42—172no—
625C42—344no—
626C42—344no—
627C42—344no—
628C23—22no—
629C23—22no—
630C23—172no—
631C23—342no—
632C23—342no—
633C23—342no—
634C23#1058760114yes—
635C23C2×D4×D1712yes—
636C23C2×D4×D1711yescharacteristic
637Q8—342no—
638Q8—342no—
639Q8—342no—
640Q8—342no—
641Q8—682no—
642Q8—682no—
643Q8—1364no—
644D4—348no—
645C2×C4—22no—
646C2×C4—24no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—48no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—84no—
659C2×C4—172no—
660C2×C4—172no—
661C2×C4—172no—
662C2×C4—342no—
663C2×C4—342no—
664C2×C4—342no—
665C2×C4—344no—
666C2×C4—342no—
667C2×C4—342no—
668C2×C4—342no—
669C2×C4—342no—
670C2×C4—342no—
671C2×C4—342no—
672C2×C4—682no—
673C2×C4—682no—
674C2×C4—682no—
675C2×C4—682no—
676C2×C4—1364no—
677C2×C4C2×#6325212yes—
678C2×C4C2×D4×D1712yes—
679C2×C4C2×D4×D1711yescharacteristic
680C2×C4#1058769412yes—
681C2×C4C24×D1711yescharacteristic
682C8—22no—
683C8—342no—
684C8—342no—
685C8C2×#6325214yes—
686C22—22no—
687C22—28no—
688C22—22no—
689C22—342no—
690C22—342no—
691C22—342no—
692C22—684no—
693C22#1176346012yes—
694C22C2×#1058760114yes—
695C22C2×#1058760112yes—
696C22#1176361512yes—
697C22C22×D4×D1711yescharacteristic
698C4—22no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—342no—
704C4—342no—
705C4—342no—
706C4—682no—
707C4—682no—
708C4—682no—
709C4—682no—
710C4#1176346012yes—
711C4C22×#6325211yescharacteristic
712C4C2×#1058769411yescharacteristic
713C2—24no—
714C2—682no—
715C2#1454123514yesdirect product factor
716C2C2×#1176346011yescharacteristic
717C2C22×#1058760111yescharacteristic
718C2C2×#1176361511yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC22×C17×#106C2
socleC23×C17C22×D4
prime radicalC22×C22⋊D17D4
hypercenterC22×#106D17
hypocenterC17C2×#3344
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#106

Complements

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

NH ≅ G/Ntype
3. #14541235C2direct (N × H)
4. C2×#11763216C2semidirect
5. C2×#11763144C2semidirect
6. C2×#11763153C2semidirect
7. C2×#11763141C2semidirect
8. C2×#11763139C2semidirect
9. C2×#11763119C2semidirect
10. C2×#11763093C2semidirect
11. C2×#11763068C2semidirect
12. C2×#11763050C2semidirect
13. C2×#11762915C2semidirect
15. C2×#11762848C2semidirect
16. C22×C17×#106C2semidirect
42. #11763216C22semidirect
43. #11763153C22semidirect
44. #11763144C22semidirect
45. #11763141C22semidirect
46. #11763139C22semidirect
47. #11763119C22semidirect
48. #11763093C22semidirect
49. #11763068C22semidirect
50. #11763050C22semidirect
51. #11762915C22semidirect
53. #11762848C22semidirect
76. C2×C17×#106C22semidirect
342. C22×#106D17semidirect
419. C2×#106C2×D17semidirect
431. C2×C17#3344semidirect
538. C17C2×#3344semidirect
715. C2#14541235direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117635142
C2×#117634942
#145412352
C2×#117632162
C2×#117631442
C2×#117631532
C2×#117631412
C2×#117631392
C2×#117631192
C2×#117630932
C2×#117630682
C2×#117630502
C2×#117629152
C2×#117628802
C2×#117628482
C22×C17×#1062
C2×#334417