Finite Group Databasebeta

← C2×#14538999 #17902588

Subgroups — C2×#14538999 #17902588

Order 4352.

2070 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763419C211yesmaximal, characteristic, complemented
2C2×#11763292C211yesmaximal, characteristic
3#14538999C2116yesmaximal, direct product factor
4C2×#11763145C211yesmaximal, characteristic, complemented
5C2×#11763137C211yesmaximal, characteristic, complemented
6C2×#11763118C211yesmaximal, characteristic, complemented
7C2×#11763107C211yesmaximal, characteristic, complemented
8C2×#11763017C211yesmaximal, characteristic, complemented
9C2×#11763012C211yesmaximal, characteristic, complemented
10C2×#11762971C211yesmaximal, characteristic
11C2×#11762913C211yesmaximal, characteristic, complemented
12C2×#11762910C211yesmaximal, characteristic, complemented
13C2×Q16×Dic17C211yesmaximal, characteristic, complemented
14C2×#11762900C211yesmaximal, characteristic, complemented
15C2×#11762867C211yesmaximal, characteristic, complemented
16C2×C17×#452C211yesmaximal, characteristic
17C22×#63231C2211yescharacteristic
18C22×#63229C2211yescharacteristic
19#11763419—24no—
20#11763419C2218yescomplemented
21C2×#10587630C2211yescharacteristic
22C2×#10587565—21no—
23C2×#10587565—21no—
24C2×#10587576—21no—
25C2×#10587576C2211yescharacteristic
26C2×#10587575—21no—
27C2×#10587610C2211yescharacteristic
28#11763292—24no—
29#11763292C2218yes—
30C2×Q8×Dic17C2211yescharacteristic
31C2×Q8×Dic17C2211yescharacteristic
32C2×Q8×Dic17C2211yescharacteristic
33C2×#10587573C2211yescharacteristic
34C2×D4×Dic17—21no—
35C2×D4×Dic17—21no—
36C2×D4×Dic17C2211yescharacteristic
37C2×D4×Dic17C2211yescharacteristic
38C2×#10587612—21no—
39C2×#10587612C2211yescharacteristic
40C22×C4⋊Dic17—21no—
41C22×C4⋊Dic17C2211yescharacteristic
42#11763145C2218yescomplemented
43#11763137C2218yescomplemented
44#11763118C2218yescomplemented
45#11763107C2218yescomplemented
46#11763017C2218yescomplemented
47#11763012C2218yescomplemented
48#11762971C2218yes—
49#11762913C2218yescomplemented
50#11762910C2218yescomplemented
51Q16×Dic17C2218yescomplemented
52#11762900C2218yescomplemented
53#11762867C2218yescomplemented
54C2×#10587489C2211yescharacteristic
55C2×#10587489C2211yescharacteristic
56C2×#10587479C2211yescharacteristic
57C2×#10587479C2211yescharacteristic
58C2×#10587485C2211yescharacteristic
59C2×#10587485C2211yescharacteristic
60C2×#10587487C2211yescharacteristic
61C2×#10587487C2211yescharacteristic
62C2×#10587506C2211yescharacteristic
63C2×#10587506C2211yescharacteristic
64C2×#10587506C2211yescharacteristic
65C2×#10587503C2211yescharacteristic
66C2×C22⋊#3622C2211yescharacteristic
67C2×#10587486C2211yescharacteristic
68C2×C8×Dic17C2211yescharacteristic
69C22×#41×C17C2211yescharacteristic
70C22×Q16×C17C2211yescharacteristic
71C22×SD16×C17C2211yescharacteristic
72C2×C17×C22⋊Q8C2211yescharacteristic
73C17×#452C2218yes—
74C2×C17×#103C2211yescharacteristic
75C2×C17×#102C2211yescharacteristic
76C2×C17×C22⋊C8C2211yescharacteristic
77C2×#41×C17—24no—
78C2×#41×C17—24no—
79C2×#41×C17—22no—
80C2×#41×C17C2314yes—
81C22×Q8×C17C2311yescharacteristic
82C22×Q8×C17C2311yescharacteristic
83C22×D4×C17—21no—
84C22×D4×C17C2311yescharacteristic
85C23×C4×C17—21no—
86C23×C4×C17C2311yescharacteristic
87C23×Dic17—21no—
88C23×Dic17—21no—
89C23×Dic17—21no—
90C22×Dic34C2311yescharacteristic
91C2×Q16×C17—24no—
92C2×Q16×C17C2314yes—
93C2×SD16×C17—24no—
94C2×SD16×C17C2314yes—
95C22×C8×C17C2311yescharacteristic
96C22×C8×C17C2311yescharacteristic
97C17×C22⋊Q8—22no—
98C17×C22⋊Q8C2314yes—
99C2×C4⋊C4×C17—21no—
100C2×C4⋊C4×C17C2311yescharacteristic
101C2×C22⋊C4×C17—21no—
102C2×C22⋊Dic17—21no—
103C2×C22⋊Dic17—21no—
104C2×C22⋊Dic17—21no—
105C2×C22⋊Dic17D411yescharacteristic
106C2×C22⋊Dic17D411yescharacteristic
107Q8×Dic17—22no—
108Q8×Dic17—22no—
109Q8×Dic17—22no—
110Q8×Dic17C2314yes—
111Q8×Dic17C2314yes—
112Q8×Dic17C2314yes—
113#10587630—22no—
114#10587630C2314yes—
115C2×#63231—24no—
116C2×#63231C2314yes—
117D4×Dic17—22no—
118D4×Dic17—22no—
119D4×Dic17—28no—
120D4×Dic17—28no—
121D4×Dic17C2314yes—
122D4×Dic17C2314yes—
123C2×#63229—24no—
124C2×#63229C2314yes—
125#10587612—28no—
126#10587612D414yes—
127#10587612C2314yes—
128C2×C4⋊Dic17—28no—
129C2×C4⋊Dic17—21no—
130C2×C4⋊Dic17—22no—
131C2×C4⋊Dic17—21no—
132C2×C4⋊Dic17—21no—
133C2×C4⋊Dic17—21no—
134C2×C4⋊Dic17—21no—
135C2×C4⋊Dic17D411yescharacteristic
136C2×C4⋊Dic17D411yescharacteristic
137C2×C4⋊Dic17C2311yescharacteristic
138C2×C4⋊Dic17C2311yescharacteristic
139C2×C4⋊Dic17C2314yes—
140C2×C4⋊Dic17C2311yescharacteristic
141#10587610—22no—
142#10587610C2314yes—
143C2×#63225—21no—
144C2×#63225—21no—
145C2×#63225—21no—
146C2×#63225—21no—
147C2×#63225—21no—
148C2×C4×Dic17—21no—
149C2×C4×Dic17—21no—
150C2×C4×Dic17—21no—
151C2×C4×Dic17—21no—
152C2×C4×Dic17C2311yescharacteristic
153C2×C4×Dic17C2311yescharacteristic
154C22×#3622C2311yescharacteristic
155C22×#3622C2311yescharacteristic
156#10587576—28no—
157#10587576—22no—
158#10587576C2314yes—
159#10587575—28no—
160#10587573—22no—
161#10587573C2314yes—
162#10587565—28no—
163#10587565—28no—
164C17×#103C2314yes—
165C17×#102C2314yes—
166C17×C22⋊C8C2314yes—
167#10587506C2314yes—
168#10587506C2314yes—
169#10587506C2314yes—
170#10587503C2314yes—
171C22⋊#3622C2314yes—
172#10587489C2314yes—
173#10587489C2314yes—
174#10587487C2314yes—
175#10587487C2314yes—
176#10587486C2314yes—
177#10587485C2314yes—
178#10587485C2314yes—
179C8×Dic17C2314yes—
180#10587479C2314yes—
181#10587479C2314yes—
182C24×C17—21no—
183C24×C17C2×D411yescharacteristic
184#41×C17—216no—
185#41×C17—28no—
186#41×C17—28no—
187C2×Q8×C17—21no—
188C2×Q8×C17—21no—
189C2×Q8×C17—22no—
190C2×Q8×C17—22no—
191C2×Q8×C17—22no—
192C2×Q8×C17#4114yes—
193C2×Q8×C17C2412yes—
194C2×Q8×C17C2412yes—
195C2×D4×C17—28no—
196C2×D4×C17—24no—
197C2×D4×C17—21no—
198C2×D4×C17—22no—
199C2×D4×C17#4114yes—
200C2×D4×C17C2412yes—
201C22×C4×C17—28no—
202C22×C4×C17—21no—
203C22×C4×C17—24no—
204C22×C4×C17—22no—
205C22×C4×C17—22no—
206C22×C4×C17—21no—
207C22×C4×C17—21no—
208C22×C4×C17C2×D412yes—
209C22×C4×C17C2×D411yescharacteristic
210C22×C4×C17C2412yes—
211C22×C4×C17C2411yescharacteristic
212C22×Dic17—21no—
213C22×Dic17—21no—
214C22×Dic17—21no—
215C22×Dic17—21no—
216C22×Dic17—24no—
217C22×Dic17—24no—
218C22×Dic17—24no—
219C22×Dic17—82no—
220C22×Dic17—82no—
221C22×Dic17—82no—
222C22×Dic17C2×D411yescharacteristic
223C22×Dic17C2×D411yescharacteristic
224C22×Dic17C2×D411yescharacteristic
225C22×Dic17C2×D411yescharacteristic
226C2×Dic34—22no—
227C2×Dic34—22no—
228C2×Dic34—21no—
229C2×Dic34C2412yes—
230Q16×C17—28no—
231SD16×C17—28no—
232C2×C8×C17—22no—
233C2×C8×C17—22no—
234C2×C8×C17C2412yes—
235C2×C8×C17C2412yes—
236C4⋊C4×C17—21no—
237C4⋊C4×C17—24no—
238C4⋊C4×C17C2412yes—
239C22⋊C4×C17—24no—
240C22⋊Dic17—24no—
241C22⋊Dic17—24no—
242C22⋊Dic17—24no—
243C22⋊Dic17C2×D414yes—
244C22⋊Dic17C2×D414yes—
245#63231—28no—
246#63229—28no—
247C4⋊Dic17—21no—
248C4⋊Dic17—24no—
249C4⋊Dic17—21no—
250C4⋊Dic17—21no—
251C4⋊Dic17—24no—
252C4⋊Dic17—24no—
253C4⋊Dic17—24no—
254C4⋊Dic17—24no—
255C4⋊Dic17C2×D414yes—
256C4⋊Dic17C2×D414yes—
257C4⋊Dic17C2412yes—
258C4⋊Dic17C2412yes—
259C4⋊Dic17C2412yes—
260#63225—24no—
261#63225—24no—
262#63225—24no—
263#63225—24no—
264#63225—24no—
265C4×Dic17—24no—
266C4×Dic17—24no—
267C4×Dic17—24no—
268C4×Dic17—24no—
269C4×Dic17C2×D412yes—
270C4×Dic17C2×D412yes—
271C4×Dic17C2412yes—
272C4×Dic17C2412yes—
273C2×#3622—22no—
274C2×#3622—22no—
275C2×#3622C2412yes—
276C2×#3622C2412yes—
277C2×#3120—171nomaximal, Sylow
278C23×C17—22no—
279C23×C17—24no—
280C23×C17—22no—
281C23×C17—22no—
282C23×C17—22no—
283C23×C17—42no—
284C23×C17—42no—
285C23×C17C22×D412yes—
286C23×C17C22×D411yescharacteristic
287Q8×C17—24no—
288Q8×C17—22no—
289Q8×C17—22no—
290Q8×C17—22no—
291Q8×C17—42no—
292Q8×C17C2×#4114yes—
293D4×C17—216no—
294D4×C17—24no—
295D4×C17—22no—
296D4×C17C2×#4114yes—
297C2×C4×C17—216no—
298C2×C4×C17—22no—
299C2×C4×C17—24no—
300C2×C4×C17—22no—
301C2×C4×C17—24no—
302C2×C4×C17—22no—
303C2×C4×C17—22no—
304C2×C4×C17—22no—
305C2×C4×C17—22no—
306C2×C4×C17—42no—
307C2×C4×C17—42no—
308C2×C4×C17C22×D412yes—
309C2×C4×C17C22×D411yescharacteristic
310C2×C4×C17C2×#4112yes—
311C2×C4×C17C2×#4112yes—
312C2×C4×C17C2511yescharacteristic
313C2×Dic17—22no—
314C2×Dic17—22no—
315C2×Dic17—22no—
316C2×Dic17—22no—
317C2×Dic17—22no—
318C2×Dic17—22no—
319C2×Dic17—22no—
320C2×Dic17—22no—
321C2×Dic17—42no—
322C2×Dic17—42no—
323C2×Dic17—42no—
324C2×Dic17—42no—
325C2×Dic17—84no—
326C2×Dic17—84no—
327C2×Dic17—84no—
328C2×Dic17C22×D412yes—
329C2×Dic17C22×D412yes—
330C2×Dic17C22×D412yes—
331C2×Dic17C22×D412yes—
332Dic34—22no—
333Dic34—22no—
334Dic34—42no—
335C8×C17—22no—
336C8×C17—22no—
337#3622—22no—
338#3622—22no—
339C2×#541—171no—
340C2×#520—171no—
341#3120—1716no—
342C2×#484—171no—
343C2×#483—171no—
344C2×#479—171no—
345C2×#478—171no—
346C2×#462—171no—
347C2×#461—171no—
348C2×#452—171no—
349C2×#452D1711yescharacteristic
350C2×#441—171no—
351C2×#440—171no—
352C2×C4×Q16—171no—
353C2×C4×SD16—171no—
354C2×#433—171no—
355C22×C17—22no—
356C22×C17—24no—
357C22×C17—22no—
358C22×C17—22no—
359C22×C17—44no—
360C22×C17—48no—
361C22×C17—42no—
362C22×C17—42no—
363C22×C17#52512yes—
364C22×C17#57712yes—
365C22×C17#57812yes—
366C22×C17C23×D411yescharacteristic
367C4×C17—22no—
368C4×C17—24no—
369C4×C17—42no—
370C4×C17—42no—
371C4×C17#52512yes—
372C4×C17C22×#4111yescharacteristic
373C4×C17C22×#4111yescharacteristic
374Dic17—22no—
375Dic17—22no—
376Dic17—22no—
377Dic17—22no—
378Dic17—42no—
379Dic17—42no—
380Dic17—42no—
381Dic17—42no—
382C22×#41C2×D1711yescharacteristic
383C22×Q16—171no—
384C22×Q16C2×D1711yescharacteristic
385C22×SD16—171no—
386C22×SD16C2×D1711yescharacteristic
387#541—178no—
388#541—344no—
389C2×C4⋊Q8—171no—
390C2×#126—341no—
391C2×#126—341no—
392C2×#125—171no—
393C2×#125—341no—
394C2×#125—341no—
395C2×C22⋊Q8—171no—
396C2×C22⋊Q8C2×D1711yescharacteristic
397#520—178no—
398#520—344no—
399C2×C4×Q8—171no—
400C2×C4×Q8—171no—
401C2×C4×Q8—171no—
402C2×C4×Q8—171no—
403C2×C4×D4—171no—
404C2×C4×D4—171no—
405C2×C4×D4—341no—
406C2×C4×D4—341no—
407C2×#117—171no—
408C2×#117—341no—
409C22×C4⋊C4—171no—
410C22×C4⋊C4—341no—
411#484—178no—
412#483—178no—
413#479—178no—
414#478—178no—
415#462—178no—
416#461—178no—
417#452—178no—
418#452C2×D1718yes—
419#441—178no—
420#440—178no—
421C4×Q16—178no—
422C4×SD16—178no—
423#433—178no—
424C2×#107—171no—
425C2×#107—171no—
426C2×#106—171no—
427C2×#106—171no—
428C2×C4⋊C8—171no—
429C2×C4⋊C8—171no—
430C2×#103—171no—
431C2×#103—171no—
432C2×#103—171no—
433C2×#103—171no—
434C2×#103—171no—
435C2×#103C2×D1711yescharacteristic
436C2×#102—171no—
437C2×#102C2×D1711yescharacteristic
438C2×C22⋊C8—171no—
439C2×C22⋊C8C2×D1711yescharacteristic
440C2×#97—171no—
441C2×C4×C8—171no—
442C2×C17—42no—
443C2×C17—44no—
444C2×C17#312014yescomplemented
445C2×C17C2×#52511yescharacteristic
446C2×C17C2×#57711yescharacteristic
447C2×C17C2×#57811yescharacteristic
448C2×#41—24no—
449C2×#41—24no—
450C2×#41—22no—
451C2×#41C22×D1714yes—
452C22×Q8—171no—
453C22×Q8C22×D1711yescharacteristic
454C22×Q8C22×D1711yescharacteristic
455C22×D4—21no—
456C22×D4C22×D1711yescharacteristic
457C23×C4—21no—
458C23×C4—341no—
459C23×C4—341no—
460C23×C4—341no—
461C23×C4C22×D1711yescharacteristic
462C2×Q16—24no—
463C2×Q16—174no—
464C2×Q16—344no—
465C2×Q16C22×D1714yes—
466C2×SD16—24no—
467C2×SD16—174no—
468C2×SD16—344no—
469C2×SD16C22×D1714yes—
470C22×C8—171no—
471C22×C8—171no—
472C22×C8C22×D1711yescharacteristic
473C22×C8C22×D1711yescharacteristic
474C4⋊Q8—174no—
475C4⋊Q8—342no—
476#126—348no—
477#126—348no—
478#125—174no—
479#125—342no—
480#125—348no—
481#125—348no—
482C22⋊Q8—22no—
483C22⋊Q8—174no—
484C22⋊Q8—342no—
485C22⋊Q8C22×D1714yes—
486C4×Q8—174no—
487C4×Q8—174no—
488C4×Q8—174no—
489C4×Q8—174no—
490C4×Q8—342no—
491C4×Q8—342no—
492C4×Q8—342no—
493C4×Q8—342no—
494C4×D4—174no—
495C4×D4—174no—
496C4×D4—342no—
497C4×D4—342no—
498C4×D4—348no—
499C4×D4—348no—
500#117—174no—
501#117—174no—
502#117—348no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—171no—
505C2×C4⋊C4—171no—
506C2×C4⋊C4—171no—
507C2×C4⋊C4—171no—
508C2×C4⋊C4—174no—
509C2×C4⋊C4—171no—
510C2×C4⋊C4—348no—
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—341no—
520C2×C4⋊C4—342no—
521C2×C4⋊C4—341no—
522C2×C4⋊C4C22×D1711yescharacteristic
523C2×C22⋊C4—21no—
524C2×C22⋊C4—171no—
525C2×C22⋊C4—171no—
526C2×C22⋊C4—341no—
527C2×C22⋊C4—341no—
528C2×C22⋊C4—341no—
529C2×C42—171no—
530C2×C42—171no—
531C2×C42—341no—
532C2×C42—341no—
533C2×C42—341no—
534C2×C42—341no—
535#107—174no—
536#107—174no—
537#106—174no—
538#106—174no—
539C4⋊C8—174no—
540C4⋊C8—174no—
541#103—174no—
542#103—174no—
543#103—174no—
544#103—174no—
545#103—174no—
546#103C22×D1714yes—
547#102—174no—
548#102C22×D1714yes—
549C22⋊C8—174no—
550C22⋊C8C22×D1714yes—
551#97—174no—
552C4×C8—174no—
553C17C2×#312011yescharacteristic, complemented, Sylow
554C24—21no—
555C24D4×D1711yescharacteristic
556#41—216no—
557#41—28no—
558#41—28no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—22no—
562C2×Q8—22no—
563C2×Q8—22no—
564C2×Q8—172no—
565C2×Q8—341no—
566C2×Q8—342no—
567C2×Q8—342no—
568C2×Q8#6325414yes—
569C2×Q8C23×D1712yes—
570C2×Q8C23×D1712yes—
571C2×D4—28no—
572C2×D4—24no—
573C2×D4—21no—
574C2×D4—22no—
575C2×D4#6325414yes—
576C2×D4C23×D1712yes—
577C22×C4—28no—
578C22×C4—21no—
579C22×C4—24no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—171no—
585C22×C4—171no—
586C22×C4—171no—
587C22×C4—171no—
588C22×C4—344no—
589C22×C4—344no—
590C22×C4—341no—
591C22×C4—341no—
592C22×C4—341no—
593C22×C4—341no—
594C22×C4—344no—
595C22×C4—1362no—
596C22×C4—1362no—
597C22×C4—1362no—
598C22×C4D4×D1712yes—
599C22×C4D4×D1711yescharacteristic
600C22×C4C23×D1712yes—
601C22×C4C23×D1711yescharacteristic
602Q16—28no—
603Q16—348no—
604SD16—28no—
605SD16—348no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—172no—
609C2×C8—172no—
610C2×C8—342no—
611C2×C8—342no—
612C2×C8C23×D1712yes—
613C2×C8C23×D1712yes—
614C4⋊C4—24no—
615C4⋊C4—21no—
616C4⋊C4—174no—
617C4⋊C4—174no—
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—344no—
628C4⋊C4—344no—
629C4⋊C4—344no—
630C4⋊C4—341no—
631C4⋊C4—341no—
632C4⋊C4—341no—
633C4⋊C4—344no—
634C4⋊C4C23×D1712yes—
635C22⋊C4—24no—
636C22⋊C4—174no—
637C22⋊C4—174no—
638C22⋊C4—344no—
639C22⋊C4—344no—
640C22⋊C4—344no—
641C42—172no—
642C42—172no—
643C42—172no—
644C42—172no—
645C42—344no—
646C42—344no—
647C42—344no—
648C42—344no—
649C23—22no—
650C23—24no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—42no—
655C23—42no—
656C23C2×D4×D1712yes—
657C23C2×D4×D1711yescharacteristic
658Q8—24no—
659Q8—22no—
660Q8—22no—
661Q8—22no—
662Q8—42no—
663Q8—342no—
664Q8—342no—
665Q8—682no—
666Q8C2×#6325414yes—
667D4—216no—
668D4—24no—
669D4—22no—
670D4C2×#6325414yes—
671C2×C4—216no—
672C2×C4—22no—
673C2×C4—24no—
674C2×C4—22no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—172no—
683C2×C4—172no—
684C2×C4—172no—
685C2×C4—172no—
686C2×C4—342no—
687C2×C4—342no—
688C2×C4—342no—
689C2×C4—342no—
690C2×C4—342no—
691C2×C4—342no—
692C2×C4—342no—
693C2×C4—342no—
694C2×C4—682no—
695C2×C4—682no—
696C2×C4—682no—
697C2×C4—682no—
698C2×C4—1364no—
699C2×C4—1364no—
700C2×C4—1364no—
701C2×C4C2×D4×D1712yes—
702C2×C4C2×D4×D1711yescharacteristic
703C2×C4C2×#6325412yes—
704C2×C4C2×#6325412yes—
705C2×C4C24×D1711yescharacteristic
706C8—22no—
707C8—22no—
708C8—342no—
709C8—342no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—24no—
714C22—42no—
715C22—42no—
716C22—44no—
717C22—48no—
718C22#1176331512yes—
719C22#1176361812yes—
720C22#1176362312yes—
721C22C22×D4×D1711yescharacteristic
722C4—22no—
723C4—24no—
724C4—42no—
725C4—42no—
726C4—342no—
727C4—342no—
728C4—342no—
729C4—342no—
730C4—682no—
731C4—682no—
732C4—682no—
733C4—682no—
734C4#1176331512yes—
735C4C22×#6325411yescharacteristic
736C4C22×#6325411yescharacteristic
737C2—42no—
738C2—44no—
739C2#1453899914yesdirect product factor
740C2C2×#1176331511yescharacteristic
741C2C2×#1176361811yescharacteristic
742C2C2×#1176362311yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#452C2
socleC23×C17C22×D4
prime radicalC22×#41×C17C22
hypercenterC2×#452D17
hypocenterC17C2×#3120
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C2×#11763419C2semidirect
3. #14538999C2direct (N × H)
4. C2×#11763145C2semidirect
5. C2×#11763137C2semidirect
6. C2×#11763118C2semidirect
7. C2×#11763107C2semidirect
8. C2×#11763017C2semidirect
9. C2×#11763012C2semidirect
11. C2×#11762913C2semidirect
12. C2×#11762910C2semidirect
13. C2×Q16×Dic17C2semidirect
14. C2×#11762900C2semidirect
15. C2×#11762867C2semidirect
20. #11763419C22semidirect
42. #11763145C22semidirect
43. #11763137C22semidirect
44. #11763118C22semidirect
45. #11763107C22semidirect
46. #11763017C22semidirect
47. #11763012C22semidirect
49. #11762913C22semidirect
50. #11762910C22semidirect
51. Q16×Dic17C22semidirect
52. #11762900C22semidirect
53. #11762867C22semidirect
444. C2×C17#3120semidirect
553. C17C2×#3120semidirect
739. C2#14538999direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117634192
C2×#117632922
#145389992
C2×#117631452
C2×#117631372
C2×#117631182
C2×#117631072
C2×#117630172
C2×#117630122
C2×#117629712
C2×#117629132
C2×#117629102
C2×Q16×Dic172
C2×#117629002
C2×#117628672
C2×C17×#4522
C2×#312017