Finite Group Databasebeta

← C2×#14538707 #17902102

Subgroups — C2×#14538707 #17902102

Order 4352.

2650 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763320C211yesmaximal, characteristic
2#14538707C2116yesmaximal, direct product factor
3C2×#11763144C212yesmaximal, complemented
4C2×#11763127C212yesmaximal, complemented
5C2×#11763139C212yesmaximal, complemented
6C2×#11763122C212yesmaximal, complemented
7C2×#11762849C212yesmaximal, complemented
8C2×#11762808C212yesmaximal, complemented
9C2×#11762773C211yesmaximal, characteristic, complemented
10C23×C4⋊C4×C17C211yesmaximal, characteristic, complemented
11C22×#63252C2211yescharacteristic
12C22×#63223C2212yes—
13#11763320—24no—
14#11763320C2218yes—
15C2×#10587615—21no—
16C2×#10587610C2211yescharacteristic
17C2×#10587610C2211yescharacteristic
18C2×#10587616C2211yescharacteristic
19C2×#10587616C2211yescharacteristic
20C2×#10587639—21no—
21C2×C4×C22⋊D17—21no—
22C2×C4×C22⋊D17—21no—
23C2×#10587612C2211yescharacteristic
24#11763144C22116yescomplemented
25#11763139C22116yescomplemented
26#11763127C22116yescomplemented
27#11763122C22116yescomplemented
28#11762849C22116yescomplemented
29C2×#10587478C2214yescomplemented
30C2×#10587479C2214yescomplemented
31#11762808C22116yescomplemented
32C2×#10587481C2214yescomplemented
33C2×#10587480C2214yescomplemented
34#11762773C2218yescomplemented
35C2×C22⋊#3622C2212yes—
36C2×C22⋊#3622C2212yes—
37C24×C4×C17—21no—
38C24×C4×C17C2211yescharacteristic
39C22×C4⋊C4×C17—21no—
40C22×C4⋊C4×C17—21no—
41C22×C4⋊C4×C17—21no—
42C22×C4⋊C4×C17—24no—
43C22×C4⋊C4×C17C2212yes—
44C22×C4⋊C4×C17C2212yes—
45C22×C4⋊C4×C17C2212yes—
46C22×C4⋊C4×C17C2218yescomplemented
47C25×C17D411yescharacteristic
48C23×C4×C17—28no—
49C23×C4×C17—22no—
50C23×C4×C17—22no—
51C23×C4×C17—22no—
52C23×C4×C17—28no—
53C23×C4×C17—48no—
54C23×C4×C17D411yescharacteristic
55C23×C4×C17D411yescharacteristic
56C23×C4×C17D411yescharacteristic
57C23×C4×C17D414yes—
58C23×C4×C17C2311yescharacteristic
59C23×C4×C17C2311yescharacteristic
60C23×C4×C17C2314yes—
61C23×C4×C17C2311yescharacteristic
62C22×C22⋊D17—21no—
63C22×C22⋊D17—21no—
64C22×C22⋊D17—21no—
65C2×#63252—22no—
66C2×#63252—28no—
67C2×#63252C2314yes—
68C22×D68C2311yescharacteristic
69C22×C4×D17—21no—
70C22×Dic34C2311yescharacteristic
71C2×C4⋊C4×C17—22no—
72C2×C4⋊C4×C17—22no—
73C2×C4⋊C4×C17—24no—
74C2×C4⋊C4×C17—24no—
75C2×C4⋊C4×C17—22no—
76C2×C4⋊C4×C17—24no—
77C2×C4⋊C4×C17—28no—
78C2×C4⋊C4×C17—28no—
79C2×C4⋊C4×C17—28no—
80C2×C4⋊C4×C17C2314yes—
81C2×C4⋊C4×C17C2318yes—
82C2×C4⋊C4×C17C2318yes—
83C2×C4⋊C4×C17C2318yes—
84#10587639—28no—
85C2×C22⋊Dic17—21no—
86C2×C22⋊Dic17—21no—
87C2×C22⋊Dic17—21no—
88#10587616—22no—
89#10587616—22no—
90#10587616C2314yes—
91#10587616C2314yes—
92#10587615—28no—
93C4×C22⋊D17—28no—
94C4×C22⋊D17—28no—
95C2×#63227—21no—
96C2×#63227—21no—
97#10587612—22no—
98#10587612C2314yes—
99C2×C4⋊Dic17C2311yescharacteristic
100C2×C4⋊Dic17C2311yescharacteristic
101#10587610—22no—
102#10587610—22no—
103#10587610C2314yes—
104#10587610C2314yes—
105C2×#63225—21no—
106C2×#63225—21no—
107C2×C4×Dic17—21no—
108C2×#63223—28no—
109C2×#63223C2318yes—
110C22×#3622C2314yes—
111C22⋊#3622C2318yes—
112C22⋊#3622C2318yes—
113#10587481C23116yescomplemented
114#10587480C23116yescomplemented
115#10587479C23116yescomplemented
116#10587478C23116yescomplemented
117C24×C17—24no—
118C24×C17—24no—
119C24×C17—24no—
120C24×C17C2×D414yes—
121C24×C17C2×D411yescharacteristic
122C24×C17C2×D411yescharacteristic
123C24×C17C2×D411yescharacteristic
124C23×D17—21no—
125C22×C4×C17—24no—
126C22×C4×C17—24no—
127C22×C4×C17—24no—
128C22×C4×C17—216no—
129C22×C4×C17—24no—
130C22×C4×C17—24no—
131C22×C4×C17—216no—
132C22×C4×C17—28no—
133C22×C4×C17—28no—
134C22×C4×C17—28no—
135C22×C4×C17—24no—
136C22×C4×C17—48no—
137C22×C4×C17—48no—
138C22×C4×C17—432no—
139C22×C4×C17—48no—
140C22×C4×C17C2×D411yescharacteristic
141C22×C4×C17C2×D411yescharacteristic
142C22×C4×C17C2×D412yes—
143C22×C4×C17C2×D412yes—
144C22×C4×C17C2×D414yes—
145C22×C4×C17C2×D414yes—
146C22×C4×C17C2×D414yes—
147C22×C4×C17C2×D411yescharacteristic
148C22×C4×C17C2×D412yes—
149C22×C4×C17#4118yes—
150C22×C4×C17C2412yes—
151C22×C4×C17C2412yes—
152C22×C4×C17C2411yescharacteristic
153C22×C4×C17C2412yes—
154C2×C22⋊D17—24no—
155C2×C22⋊D17—24no—
156C2×C22⋊D17—24no—
157C2×C22⋊D17—44no—
158C2×C22⋊D17—44no—
159C2×C22⋊D17—44no—
160C22×Dic17—21no—
161C22×Dic17—21no—
162C22×Dic17—21no—
163#63252—216no—
164#63252—48no—
165C2×D68—24no—
166C2×D68—21no—
167C2×D68C2412yes—
168C2×C4×D17—24no—
169C2×C4×D17—44no—
170C2×Dic34—24no—
171C2×Dic34—21no—
172C2×Dic34C2412yes—
173C4⋊C4×C17—28no—
174C4⋊C4×C17—28no—
175C4⋊C4×C17—24no—
176C4⋊C4×C17—28no—
177C4⋊C4×C17C2418yes—
178C22⋊Dic17—24no—
179C22⋊Dic17—24no—
180C22⋊Dic17—24no—
181#63227—24no—
182#63227—24no—
183C4⋊Dic17—21no—
184C4⋊Dic17—21no—
185C4⋊Dic17C2412yes—
186C4⋊Dic17C2412yes—
187#63225—24no—
188#63225—24no—
189C4×Dic17—24no—
190#63223—216no—
191C2×#3622—28no—
192C2×#3622C2418yes—
193C2×#3092—171nomaximal, Sylow
194C23×C17—232no—
195C23×C17—28no—
196C23×C17—22no—
197C23×C17—22no—
198C23×C17—28no—
199C23×C17—22no—
200C23×C17—22no—
201C23×C17—28no—
202C23×C17—22no—
203C23×C17—22no—
204C23×C17#12314yes—
205C23×C17AGL(1,ℤ/8)14yes—
206C23×C17#13714yes—
207C23×C17C22×D412yes—
208C23×C17C22×D412yes—
209C23×C17C22×D412yes—
210C23×C17C22×D411yescharacteristic
211C22×D17—22no—
212C22×D17—42no—
213C22×D17—42no—
214C22×D17—42no—
215C2×C4×C17—28no—
216C2×C4×C17—22no—
217C2×C4×C17—22no—
218C2×C4×C17—24no—
219C2×C4×C17—24no—
220C2×C4×C17—28no—
221C2×C4×C17—28no—
222C2×C4×C17—24no—
223C2×C4×C17—24no—
224C2×C4×C17—28no—
225C2×C4×C17—416no—
226C2×C4×C17—416no—
227C2×C4×C17—416no—
228C2×C4×C17—48no—
229C2×C4×C17#12314yes—
230C2×C4×C17#12318yes—
231C2×C4×C17C22×D412yes—
232C2×C4×C17C22×D412yes—
233C2×C4×C17C22×D411yescharacteristic
234C2×C4×C17C22×D412yes—
235C2×C4×C17C2×#4114yes—
236C2×C4×C17C2×#4118yes—
237C2×C4×C17C2511yescharacteristic
238C22⋊D17—48no—
239C22⋊D17—48no—
240C22⋊D17—48no—
241C2×Dic17—22no—
242C2×Dic17—22no—
243C2×Dic17—22no—
244C2×Dic17—42no—
245C2×Dic17—42no—
246C2×Dic17—42no—
247D68—24no—
248D68—42no—
249C4×D17—48no—
250Dic34—24no—
251Dic34—42no—
252#3622—28no—
253C2×#525—171no—
254C23×C4⋊C4D1711yescharacteristic, complemented
255#3092—1716no—
256C2×#484—172no—
257C2×#481—172no—
258C2×#483—172no—
259C2×#480—172no—
260C2×#428—172no—
261C2×#417—172no—
262C2×#407—171no—
263C22×C17—232no—
264C22×C17—28no—
265C22×C17—28no—
266C22×C17—28no—
267C22×C17—22no—
268C22×C17—22no—
269C22×C17—22no—
270C22×C17—22no—
271C22×C17—22no—
272C22×C17—22no—
273C22×C17C2×#12314yes—
274C22×C17C2×#12312yes—
275C22×C17C2×AGL(1,ℤ/8)14yes—
276C22×C17C2×AGL(1,ℤ/8)12yes—
277C22×C17C2×#13714yes—
278C22×C17C2×#13712yes—
279C22×C17C23×D411yescharacteristic
280C2×D17—42no—
281C2×D17—42no—
282C2×D17—42no—
283C2×D17—84no—
284C4×C17—22no—
285C4×C17—22no—
286C4×C17—48no—
287C4×C17C2×#12312yes—
288C4×C17C2×#12314yes—
289C4×C17C22×#4112yes—
290Dic17—42no—
291Dic17—42no—
292Dic17—42no—
293C22×#41—171no—
294C24×C4—21no—
295C24×C4C2×D1711yescharacteristic
296C22×M16—172no—
297#525—178no—
298#525—344no—
299C2×#123—341no—
300C2×C22⋊Q8—171no—
301C2×C22⋊Q8—171no—
302C2×#121—171no—
303C2×#121—171no—
304C2×#120—341no—
305C2×C4×D4—341no—
306C2×C4×D4—341no—
307C2×#117—171no—
308C22×C4⋊C4—24no—
309C22×C4⋊C4—21no—
310C22×C4⋊C4—21no—
311C22×C4⋊C4—21no—
312C22×C4⋊C4C2×D1712yes—
313C22×C4⋊C4C2×D1712yes—
314C22×C4⋊C4C2×D1712yes—
315C22×C4⋊C4C2×D1718yescomplemented
316#484—1716no—
317#483—1716no—
318#481—1716no—
319#480—1716no—
320#428—1716no—
321C2×#107—174no—
322C2×#106—174no—
323#417—1716no—
324C2×#103—174no—
325C2×#102—174no—
326#407—178no—
327C2×C22⋊C8—172no—
328C2×C22⋊C8—172no—
329C2×C17—24no—
330C2×C17—24no—
331C2×C17—24no—
332C2×C17#309214yescomplemented
333C2×C17C22×#12311yescharacteristic
334C2×C17C22×AGL(1,ℤ/8)11yescharacteristic
335C2×C17C22×#13711yescharacteristic
336D17—82no—
337C25C22⋊D1711yescharacteristic
338C2×#41—174no—
339C2×#41—342no—
340C2×#41—348no—
341C22×Q8—171no—
342C22×D4—171no—
343C22×D4—341no—
344C22×D4—341no—
345C22×D4—341no—
346C23×C4—28no—
347C23×C4—22no—
348C23×C4—22no—
349C23×C4—22no—
350C23×C4—28no—
351C23×C4—48no—
352C23×C4—341no—
353C23×C4C22⋊D1711yescharacteristic
354C23×C4C22⋊D1711yescharacteristic
355C23×C4C22⋊D1711yescharacteristic
356C23×C4C22⋊D1714yes—
357C23×C4C22×D1711yescharacteristic
358C23×C4C22×D1711yescharacteristic
359C23×C4C22×D1714yes—
360C23×C4C22×D1711yescharacteristic
361C2×M16—178no—
362C2×M16—348no—
363C22×C8—174no—
364#123—348no—
365C22⋊Q8—174no—
366C22⋊Q8—174no—
367C22⋊Q8—342no—
368C22⋊Q8—342no—
369#121—174no—
370#121—174no—
371#121—342no—
372#121—342no—
373#120—348no—
374C4×D4—348no—
375C4×D4—348no—
376#117—174no—
377#117—342no—
378C2×C4⋊C4—24no—
379C2×C4⋊C4—24no—
380C2×C4⋊C4—24no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—28no—
385C2×C4⋊C4—28no—
386C2×C4⋊C4—28no—
387C2×C4⋊C4—171no—
388C2×C4⋊C4—171no—
389C2×C4⋊C4—341no—
390C2×C4⋊C4—341no—
391C2×C4⋊C4C22×D1714yes—
392C2×C4⋊C4C22×D1718yes—
393C2×C4⋊C4C22×D1718yes—
394C2×C4⋊C4C22×D1718yes—
395C2×C22⋊C4—341no—
396C2×C22⋊C4—341no—
397C2×C22⋊C4—341no—
398C2×C22⋊C4—341no—
399C2×C22⋊C4—341no—
400C2×C42—341no—
401#107—1716no—
402#106—1716no—
403#103—1716no—
404#102—1716no—
405C22⋊C8—178no—
406C22⋊C8—178no—
407C17C2×#309211yescharacteristic, complemented, Sylow
408C24—24no—
409C24—24no—
410C24—24no—
411C24—341no—
412C24C2×C22⋊D1714yes—
413C24C2×C22⋊D1711yescharacteristic
414C24C2×C22⋊D1711yescharacteristic
415C24C2×C22⋊D1711yescharacteristic
416#41—3416no—
417#41—688no—
418C2×Q8—172no—
419C2×Q8—341no—
420C2×Q8—344no—
421C2×D4—172no—
422C2×D4—344no—
423C2×D4—344no—
424C2×D4—344no—
425C2×D4—344no—
426C2×D4—341no—
427C2×D4—684no—
428C2×D4—684no—
429C2×D4—684no—
430C22×C4—24no—
431C22×C4—24no—
432C22×C4—24no—
433C22×C4—216no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—216no—
437C22×C4—28no—
438C22×C4—28no—
439C22×C4—28no—
440C22×C4—24no—
441C22×C4—48no—
442C22×C4—48no—
443C22×C4—432no—
444C22×C4—48no—
445C22×C4—341no—
446C22×C4—341no—
447C22×C4—341no—
448C22×C4—344no—
449C22×C4—684no—
450C22×C4#6325218yes—
451C22×C4C2×C22⋊D1714yes—
452C22×C4C2×C22⋊D1714yes—
453C22×C4C2×C22⋊D1712yes—
454C22×C4C2×C22⋊D1712yes—
455C22×C4C2×C22⋊D1714yes—
456C22×C4C2×C22⋊D1711yescharacteristic
457C22×C4C2×C22⋊D1711yescharacteristic
458C22×C4C2×C22⋊D1712yes—
459C22×C4C2×C22⋊D1711yescharacteristic
460C22×C4C23×D1712yes—
461C22×C4C23×D1712yes—
462C22×C4C23×D1712yes—
463C22×C4C23×D1711yescharacteristic
464M16—3416no—
465C2×C8—178no—
466C2×C8—348no—
467C4⋊C4—28no—
468C4⋊C4—28no—
469C4⋊C4—28no—
470C4⋊C4—24no—
471C4⋊C4—172no—
472C4⋊C4—172no—
473C4⋊C4—341no—
474C4⋊C4—341no—
475C4⋊C4—344no—
476C4⋊C4—344no—
477C4⋊C4C23×D1718yes—
478C22⋊C4—344no—
479C22⋊C4—344no—
480C22⋊C4—344no—
481C22⋊C4—344no—
482C22⋊C4—344no—
483C42—344no—
484C23—232no—
485C23—28no—
486C23—22no—
487C23—22no—
488C23—28no—
489C23—22no—
490C23—22no—
491C23—28no—
492C23—22no—
493C23—22no—
494C23—342no—
495C23—682no—
496C23—682no—
497C23—682no—
498C23#1058761514yes—
499C23#1058761814yes—
500C23#1058762814yes—
501C23C22×C22⋊D1712yes—
502C23C22×C22⋊D1712yes—
503C23C22×C22⋊D1712yes—
504C23C22×C22⋊D1711yescharacteristic
505Q8—344no—
506Q8—682no—
507D4—344no—
508D4—688no—
509D4—688no—
510D4—688no—
511D4—682no—
512C2×C4—28no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—28no—
516C2×C4—28no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—24no—
521C2×C4—28no—
522C2×C4—416no—
523C2×C4—416no—
524C2×C4—416no—
525C2×C4—48no—
526C2×C4—342no—
527C2×C4—342no—
528C2×C4—342no—
529C2×C4—682no—
530C2×C4—682no—
531C2×C4—682no—
532C2×C4—688no—
533C2×C4#1058761514yes—
534C2×C4#1058761518yes—
535C2×C4C2×#6325214yes—
536C2×C4C2×#6325218yes—
537C2×C4C22×C22⋊D1712yes—
538C2×C4C22×C22⋊D1712yes—
539C2×C4C22×C22⋊D1712yes—
540C2×C4C22×C22⋊D1711yescharacteristic
541C2×C4C24×D1711yescharacteristic
542C8—348no—
543C22—232no—
544C22—22no—
545C22—22no—
546C22—22no—
547C22—22no—
548C22—22no—
549C22—22no—
550C22—28no—
551C22—28no—
552C22—28no—
553C22—682no—
554C22—682no—
555C22—682no—
556C22—1364no—
557C22C2×#1058761514yes—
558C22C2×#1058761512yes—
559C22C2×#1058761814yes—
560C22C2×#1058761812yes—
561C22C2×#1058762814yes—
562C22C2×#1058762812yes—
563C22C23×C22⋊D1711yescharacteristic
564C4—22no—
565C4—22no—
566C4—48no—
567C4—682no—
568C4—682no—
569C4—682no—
570C4C2×#1058761514yes—
571C4C2×#1058761512yes—
572C4C22×#6325212yes—
573C2—24no—
574C2—24no—
575C2—24no—
576C2—1362no—
577C2#1453870714yesdirect product factor
578C2C22×#1058761511yescharacteristic
579C2C22×#1058761811yescharacteristic
580C2C22×#1058762811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC23×C4⋊C4×C17C2
socleC23×C17C22×D4
prime radicalC2×#11763320C2
hypercenterC23×C4⋊C4D17
hypocenterC17C2×#3092
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C24×C4 ◁ C23×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #14538707C2direct (N × H)
3. C2×#11763144C2semidirect
4. C2×#11763127C2semidirect
5. C2×#11763139C2semidirect
6. C2×#11763122C2semidirect
7. C2×#11762849C2semidirect
8. C2×#11762808C2semidirect
9. C2×#11762773C2semidirect
10. C23×C4⋊C4×C17C2semidirect
24. #11763144C22semidirect
25. #11763139C22semidirect
26. #11763127C22semidirect
27. #11763122C22semidirect
28. #11762849C22semidirect
29. C2×#10587478C22semidirect
30. C2×#10587479C22semidirect
31. #11762808C22semidirect
32. C2×#10587481C22semidirect
33. C2×#10587480C22semidirect
34. #11762773C22semidirect
46. C22×C4⋊C4×C17C22semidirect
113. #10587481C23semidirect
114. #10587480C23semidirect
115. #10587479C23semidirect
116. #10587478C23semidirect
254. C23×C4⋊C4D17semidirect
315. C22×C4⋊C4C2×D17semidirect
332. C2×C17#3092semidirect
407. C17C2×#3092semidirect
577. C2#14538707direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117633202
#145387072
C2×#117631442
C2×#117631272
C2×#117631392
C2×#117631222
C2×#117628492
C2×#117628082
C2×#117627732
C23×C4⋊C4×C172
C2×#309217