Finite Group Databasebeta

← C2×#14545293 #17978973

Subgroups — C2×#14545293 #17978973

Order 4352.

3094 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14545293C2116yesmaximal, direct product factor
2C2×#11763760C212yesmaximal, complemented
3C2×#11763758C214yesmaximal, complemented
4C2×#11763751C212yesmaximal
5C2×#11763751C211yesmaximal, characteristic
6C2×C4⋊C4×#595C212yesmaximal, complemented
7C2×C4×C22⋊#595C211yesmaximal, characteristic
8C2×C4×C22⋊#595C212yesmaximal
9C22×C4⋊C4×D17C211yesmaximal, characteristic
10C22×C4⋊#595C2212yes—
11C22×C4⋊#595C2214yes—
12C22×C22⋊#595C2211yescharacteristic
13C22×C22⋊#595C2212yes—
14C22×C22⋊#595C2211yescharacteristic
15C22×C4×#595C2212yes—
16C22×C4×#595C2214yes—
17#11763760C22116yescomplemented
18#11763758C22132yescomplemented
19#11763751C2218yes—
20#11763751C22116yes—
21C4⋊C4×#595C22116yescomplemented
22C4×C22⋊#595C2218yes—
23C4×C22⋊#595C22116yes—
24C2×(C2×#595)⋊C4C2212yes—
25C2×(C2×#595)⋊C4C2214yes—
26C2×(C2×#595)⋊C4C2214yes—
27C2×(C2×#595)⋊C4C2212yes—
28C23×C4×D17C2211yescharacteristic
29C23×C4×D17C2212yes—
30C22×C4⋊Dic17C411yescharacteristic, complemented
31C22×#63225C412yescomplemented
32C2×C4⋊C4×D17C418yescomplemented
33C2×C4⋊C4×D17C411yescharacteristic, complemented
34C2×C4⋊C4×D17C411yescharacteristic, complemented
35C2×C4⋊C4×D17C412yescomplemented
36C2×C4⋊C4×D17C2211yescharacteristic
37C2×C4⋊C4×D17C2212yes—
38C2×C4⋊C4×D17C2211yescharacteristic
39C2×C4⋊C4×D17C2218yes—
40C22×C4⋊C4×C17C411yescharacteristic, complemented
41C24×D17C2311yescharacteristic
42C23×#595C2312yes—
43C23×#595C2314yes—
44C23×#595C2312yes—
45C23×C4×C17C2×C411yescharacteristic
46C23×C4×C17C2×C412yes—
47C23×Dic17C2×C411yescharacteristic
48C23×Dic17C2×C412yes—
49C22×C4×D17—28no—
50C22×C4×D17—48no—
51C22×C4×D17C2×C411yescharacteristic
52C22×C4×D17C2×C411yescharacteristic
53C22×C4×D17C2×C414yes—
54C22×C4×D17C2×C418yes—
55C22×C4×D17C2×C412yes—
56C22×C4×D17C2×C412yes—
57C22×C4×D17C2311yescharacteristic
58C22×C4×D17C2312yes—
59C22×C4×D17C2312yes—
60C22×C4×D17C2314yes—
61C22×C4×D17C2318yes—
62C22×C4×D17C2311yescharacteristic
63C2×C22⋊#595—24no—
64C2×C22⋊#595—28no—
65C2×C22⋊#595Q818yes—
66C2×C22⋊#595C2314yes—
67C2×C22⋊#595C2318yes—
68C2×C22⋊#595C2314yes—
69C2×C4⋊#595—28no—
70C2×C4⋊#595—48no—
71C2×C4⋊#595C2318yes—
72C2×C4⋊#595C23116yes—
73C2×C4×#595—28no—
74C2×C4×#595—48no—
75C2×C4×#595C2318yes—
76C2×C4×#595C23116yes—
77C2×C4⋊C4×C17C2×C412yes—
78C2×C4⋊C4×C17C2×C411yescharacteristic
79C2×C4⋊C4×C17C2×C411yescharacteristic
80C2×C4⋊C4×C17C2×C418yescomplemented
81C2×C4⋊Dic17C2×C412yes—
82C2×C4⋊Dic17C2×C411yescharacteristic
83C2×C4⋊Dic17C2×C411yescharacteristic
84C2×C4⋊Dic17C2×C418yescomplemented
85C2×#63225C2×C412yes—
86C2×#63225C2×C412yes—
87C2×#63225C2×C412yes—
88C2×#63225C2×C412yes—
89C2×#63225C2×C4116yescomplemented
90C4⋊C4×D17C2×C418yes—
91C4⋊C4×D17C2×C414yes—
92C4⋊C4×D17C2×C414yes—
93C4⋊C4×D17C2×C4116yescomplemented
94C4⋊C4×D17C2×C418yescomplemented
95C4⋊C4×D17C2×C418yescomplemented
96C4⋊C4×D17C2314yes—
97C4⋊C4×D17C2318yes—
98C4⋊C4×D17C2314yes—
99(C2×#595)⋊C4C2318yes—
100(C2×#595)⋊C4C23116yes—
101(C2×#595)⋊C4C23116yes—
102(C2×#595)⋊C4C2318yes—
103C24×C17C22×C411yescharacteristic
104C23×D17—24no—
105C23×D17—24no—
106C23×D17C22×C412yes—
107C23×D17C22×C411yescharacteristic
108C23×D17C2×Q814yes—
109C23×D17#4114yes—
110C23×D17C2412yes—
111C23×D17C2411yescharacteristic
112C22×#595—24no—
113C22×#595—24no—
114C22×#595—24no—
115C22×#595—28no—
116C22×#595—24no—
117C22×#595—28no—
118C22×#595—28no—
119C22×#595—24no—
120C22×#595C2×Q818yes—
121C22×#595C2414yes—
122C22×#595C2418yes—
123C22×#595C2414yes—
124C22×C4×C17—24no—
125C22×C4×C17—44no—
126C22×C4×C17C22×C412yes—
127C22×C4×C17C22×C412yes—
128C22×C4×C17C22×C411yescharacteristic
129C22×C4×C17C22×C414yes—
130C22×C4×C17C22×C418yes—
131C22×C4×C17C22×C411yescharacteristic
132C22×Dic17—24no—
133C22×Dic17—44no—
134C22×Dic17C22×C411yescharacteristic
135C22×Dic17C22×C412yes—
136C22×Dic17C22×C412yes—
137C22×Dic17C22×C414yes—
138C22×Dic17C22×C418yes—
139C22×Dic17C22×C411yescharacteristic
140C2×C4×D17—24no—
141C2×C4×D17—28no—
142C2×C4×D17—28no—
143C2×C4×D17—24no—
144C2×C4×D17—24no—
145C2×C4×D17—216no—
146C2×C4×D17—216no—
147C2×C4×D17—416no—
148C2×C4×D17—416no—
149C2×C4×D17—44no—
150C2×C4×D17—44no—
151C2×C4×D17C22×C412yes—
152C2×C4×D17C22×C414yes—
153C2×C4×D17C22×C414yes—
154C2×C4×D17C22×C414yes—
155C2×C4×D17C22×C414yes—
156C2×C4×D17C22×C418yes—
157C2×C4×D17C22×C418yes—
158C2×C4×D17C22×C412yes—
159C2×C4×D17#4118yes—
160C2×C4×D17C2414yes—
161C2×C4×D17C2414yes—
162C2×C4×D17C2412yes—
163C2×C4×D17C2412yes—
164C22⋊#595—28no—
165C22⋊#595—216no—
166C22⋊#595C2×Q8116yes—
167C4⋊#595—216no—
168C4⋊#595—416no—
169C4×#595—216no—
170C4×#595—416no—
171C4⋊C4×C17C22×C418yes—
172C4⋊C4×C17C22×C414yes—
173C4⋊C4×C17C22×C414yes—
174C4⋊Dic17C22×C418yes—
175C4⋊Dic17C22×C414yes—
176C4⋊Dic17C22×C414yes—
177#63225C22×C418yes—
178#63225C22×C418yes—
179#63225C22×C418yes—
180#63225C22×C418yes—
181C2×#2345—171nomaximal, Sylow
182C23×C17—22no—
183C23×C17—22no—
184C23×C17C4×Q814yes—
185C23×C17C23×C412yes—
186C23×C17C23×C411yescharacteristic
187C22×D17—22no—
188C22×D17—22no—
189C22×D17—24no—
190C22×D17—24no—
191C22×D17—216no—
192C22×D17—216no—
193C22×D17—24no—
194C22×D17—24no—
195C22×D17C4×Q814yes—
196C22×D17C4×Q818yes—
197C22×D17C23×C412yes—
198C22×D17C23×C411yescharacteristic
199C22×D17C22×Q814yes—
200C22×D17C22×Q812yes—
201C22×D17C2×#4114yes—
202C22×D17C2×#4114yes—
203C22×D17C2×#4112yes—
204C22×D17H(5,𝔽2)14yes—
205C22×D17C2511yescharacteristic
206C2×#595—216no—
207C2×#595—24no—
208C2×#595—24no—
209C2×#595—24no—
210C2×#595—28no—
211C2×#595—24no—
212C2×#595—28no—
213C2×#595—28no—
214C2×#595—24no—
215C2×#595—48no—
216C2×#595—416no—
217C2×#595C22×Q818yes—
218C2×C4×C17—22no—
219C2×C4×C17—24no—
220C2×C4×C17—24no—
221C2×C4×C17—28no—
222C2×C4×C17—48no—
223C2×C4×C17#11714yes—
224C2×C4×C17C23×C414yes—
225C2×C4×C17C23×C414yes—
226C2×C4×C17C23×C412yes—
227C2×C4×C17C23×C412yes—
228C2×Dic17—22no—
229C2×Dic17—24no—
230C2×Dic17—24no—
231C2×Dic17—28no—
232C2×Dic17—48no—
233C2×Dic17#11714yes—
234C2×Dic17C23×C412yes—
235C2×Dic17C23×C414yes—
236C2×Dic17C23×C414yes—
237C2×Dic17C23×C412yes—
238C4×D17—24no—
239C4×D17—28no—
240C4×D17—28no—
241C4×D17—24no—
242C4×D17—28no—
243C4×D17—28no—
244C4×D17—28no—
245C4×D17—28no—
246C4×D17—48no—
247C4×D17—48no—
248C4×D17#11718yes—
249C4×D17C2×#4118yes—
250C23×C4⋊C4—171no—
251#2345—1716no—
252C2×#389—172no—
253C2×#387—174no—
254C2×#380—171no—
255C2×#380—172no—
256C2×C4×C4⋊C4—172no—
257C2×C4×C22⋊C4—171no—
258C2×C4×C22⋊C4—172no—
259C22×C17—28no—
260C22×C17—22no—
261C22×C17—22no—
262C22×C17C2×#11712yes—
263C22×C17C2×C4×Q814yes—
264C22×C17C2×C4×Q812yes—
265C22×C17#51812yes—
266C22×C17C24×C411yescharacteristic
267C2×D17—28no—
268C2×D17—22no—
269C2×D17—22no—
270C2×D17—216no—
271C2×D17—28no—
272C2×D17—28no—
273C2×D17C2×#11712yes—
274C2×D17C2×C4×Q814yes—
275C2×D17C2×C4×Q812yes—
276C2×D17#51812yes—
277C2×D17#55318yes—
278C2×D17#55418yes—
279C2×D17C23×Q811yescharacteristic
280C2×D17C22×#4111yescharacteristic
281C2×D17C22×#4112yes—
282C2×D17C2×H(5,𝔽2)12yes—
283#595—28no—
284#595—44no—
285#595—48no—
286C4×C17—22no—
287C4×C17—24no—
288C4×C17—24no—
289C4×C17C2×#11714yes—
290Dic17—22no—
291Dic17—24no—
292Dic17—24no—
293Dic17C2×#11714yes—
294C24×C4—171no—
295C24×C4—172no—
296C22×C4⋊C4—172no—
297C22×C4⋊C4—171no—
298C22×C4⋊C4—172no—
299C22×C4⋊C4—171no—
300C22×C4⋊C4—171no—
301C22×C4⋊C4—171no—
302C22×C4⋊C4—172no—
303C22×C4⋊C4—171no—
304C22×C4⋊C4—178no—
305C22×C4⋊C4—178no—
306C22×C4⋊C4—172no—
307C22×C4⋊C4—174no—
308C22×C4⋊C4#59511yescharacteristic, complemented
309C22×C22⋊C4—171no—
310C22×C22⋊C4—171no—
311C22×C22⋊C4—172no—
312C22×C42—172no—
313C22×C42—174no—
314#389—1716no—
315#387—1732no—
316#380—1716no—
317#380—178no—
318C4×C4⋊C4—1716no—
319C4×C22⋊C4—178no—
320C4×C22⋊C4—1716no—
321C2×#95—172no—
322C2×#95—174no—
323C2×#95—174no—
324C2×#95—172no—
325C2×C17—24no—
326C2×C17#234514yescomplemented
327C2×C17C22×#11711yescharacteristic
328C2×C17C22×C4×Q811yescharacteristic
329C2×C17C2×#51811yescharacteristic
330D17—24no—
331D17#234514yescomplemented
332D17C2×#55312yes—
333D17C2×#55412yes—
334C25—171no—
335C23×C4—171no—
336C23×C4—172no—
337C23×C4—171no—
338C23×C4—172no—
339C23×C4—172no—
340C23×C4—171no—
341C23×C4—174no—
342C23×C4—171no—
343C23×C4—171no—
344C23×C4—172no—
345C23×C4—174no—
346C23×C4—172no—
347C23×C4—172no—
348C23×C4—178no—
349C23×C4—178no—
350C23×C4—172no—
351C23×C4—174no—
352C23×C4—348no—
353C23×C4—688no—
354C23×C4C2×#59511yescharacteristic
355C23×C4C2×#59512yes—
356C2×C4⋊C4—172no—
357C2×C4⋊C4—172no—
358C2×C4⋊C4—172no—
359C2×C4⋊C4—172no—
360C2×C4⋊C4—1716no—
361C2×C4⋊C4—172no—
362C2×C4⋊C4—171no—
363C2×C4⋊C4—171no—
364C2×C4⋊C4—178no—
365C2×C4⋊C4—174no—
366C2×C4⋊C4—178no—
367C2×C4⋊C4—174no—
368C2×C4⋊C4—174no—
369C2×C4⋊C4—174no—
370C2×C4⋊C4—178no—
371C2×C4⋊C4—1716no—
372C2×C4⋊C4—178no—
373C2×C4⋊C4—178no—
374C2×C4⋊C4—178no—
375C2×C4⋊C4—1716no—
376C2×C4⋊C4—348no—
377C2×C4⋊C4—688no—
378C2×C4⋊C4C2×#59512yes—
379C2×C4⋊C4C2×#59511yescharacteristic
380C2×C4⋊C4C2×#59511yescharacteristic
381C2×C4⋊C4C2×#59518yescomplemented
382C2×C22⋊C4—178no—
383C2×C22⋊C4—174no—
384C2×C22⋊C4—174no—
385C2×C22⋊C4—178no—
386C2×C22⋊C4—344no—
387C2×C22⋊C4—348no—
388C2×C42—178no—
389C2×C42—1716no—
390C2×C42—348no—
391C2×C42—688no—
392#95—178no—
393#95—1716no—
394#95—1716no—
395#95—178no—
396C17C2×#234511yescharacteristic, complemented, Sylow
397C24—171no—
398C24—174no—
399C24—174no—
400C24—172no—
401C24—172no—
402C24—171no—
403C24—344no—
404C24—344no—
405C24C22×#59511yescharacteristic
406C22×C4—24no—
407C22×C4—44no—
408C22×C4—171no—
409C22×C4—178no—
410C22×C4—172no—
411C22×C4—172no—
412C22×C4—178no—
413C22×C4—174no—
414C22×C4—174no—
415C22×C4—171no—
416C22×C4—172no—
417C22×C4—172no—
418C22×C4—178no—
419C22×C4—174no—
420C22×C4—172no—
421C22×C4—174no—
422C22×C4—174no—
423C22×C4—174no—
424C22×C4—172no—
425C22×C4—174no—
426C22×C4—174no—
427C22×C4—178no—
428C22×C4—178no—
429C22×C4—174no—
430C22×C4—178no—
431C22×C4—344no—
432C22×C4—3416no—
433C22×C4—3416no—
434C22×C4—348no—
435C22×C4—348no—
436C22×C4—344no—
437C22×C4—344no—
438C22×C4—344no—
439C22×C4—344no—
440C22×C4—344no—
441C22×C4—344no—
442C22×C4—348no—
443C22×C4—344no—
444C22×C4—348no—
445C22×C4—348no—
446C22×C4—344no—
447C22×C4—684no—
448C22×C4—684no—
449C22×C4—6816no—
450C22×C4—6816no—
451C22×C4—684no—
452C22×C4C22×#59514yes—
453C22×C4C22×#59511yescharacteristic
454C22×C4C22×#59512yes—
455C22×C4C22×#59512yes—
456C22×C4C22×#59518yes—
457C22×C4C22×#59511yescharacteristic
458C4⋊C4—178no—
459C4⋊C4—178no—
460C4⋊C4—178no—
461C4⋊C4—178no—
462C4⋊C4—178no—
463C4⋊C4—174no—
464C4⋊C4—174no—
465C4⋊C4—3416no—
466C4⋊C4—6816no—
467C4⋊C4C22×#59518yes—
468C4⋊C4C22×#59514yes—
469C4⋊C4C22×#59514yes—
470C22⋊C4—1716no—
471C22⋊C4—348no—
472C22⋊C4—3416no—
473C42—3416no—
474C42—6816no—
475C23—22no—
476C23—22no—
477C23—174no—
478C23—172no—
479C23—172no—
480C23—174no—
481C23—171no—
482C23—171no—
483C23—174no—
484C23—174no—
485C23—178no—
486C23—174no—
487C23—172no—
488C23—344no—
489C23—344no—
490C23—344no—
491C23—344no—
492C23—3416no—
493C23—3416no—
494C23—342no—
495C23—342no—
496C23Q8×#59514yes—
497C23C23×#59512yes—
498C23C23×#59511yescharacteristic
499C2×C4—22no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—28no—
503C2×C4—48no—
504C2×C4—174no—
505C2×C4—172no—
506C2×C4—178no—
507C2×C4—178no—
508C2×C4—178no—
509C2×C4—172no—
510C2×C4—174no—
511C2×C4—174no—
512C2×C4—348no—
513C2×C4—348no—
514C2×C4—348no—
515C2×C4—344no—
516C2×C4—344no—
517C2×C4—348no—
518C2×C4—348no—
519C2×C4—348no—
520C2×C4—344no—
521C2×C4—344no—
522C2×C4—3416no—
523C2×C4—342no—
524C2×C4—344no—
525C2×C4—344no—
526C2×C4—348no—
527C2×C4—344no—
528C2×C4—348no—
529C2×C4—344no—
530C2×C4—348no—
531C2×C4—348no—
532C2×C4—344no—
533C2×C4—688no—
534C2×C4—688no—
535C2×C4—688no—
536C2×C4—688no—
537C2×C4—6816no—
538C2×C4#1058767714yes—
539C2×C4C23×#59512yes—
540C2×C4C23×#59514yes—
541C2×C4C23×#59514yes—
542C2×C4C23×#59512yes—
543C22—22no—
544C22—22no—
545C22—28no—
546C22—172no—
547C22—172no—
548C22—171no—
549C22—171no—
550C22—172no—
551C22—172no—
552C22—172no—
553C22—178no—
554C22—178no—
555C22—174no—
556C22—348no—
557C22—348no—
558C22—3416no—
559C22—342no—
560C22—342no—
561C22—348no—
562C22C2×#1058767712yes—
563C22C2×Q8×#59514yes—
564C22C2×Q8×#59512yes—
565C22#1176387612yes—
566C22C24×#59511yescharacteristic
567C4—22no—
568C4—24no—
569C4—24no—
570C4—174no—
571C4—348no—
572C4—342no—
573C4—344no—
574C4—344no—
575C4—684no—
576C4—688no—
577C4C2×#1058767714yes—
578C2—24no—
579C2—172no—
580C2—172no—
581C2—174no—
582C2—344no—
583C2#1454529314yesdirect product factor
584C2C22×#1058767711yescharacteristic
585C2C22×Q8×#59511yescharacteristic
586C2C2×#1176387611yescharacteristic
subgroupG/H
centerC23C23×#595
commutatorC22×C17C24×C4
FrattiniC22C24×#595
FittingC22×C4⋊C4×C17C4
socleC23×C17C23×C4
prime radicalC24×D17C23
cosocleC22×D17C25
hypercenterC22×C4⋊C4#595
hypocenterC17C2×#2345
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #14545293C2direct (N × H)
2. C2×#11763760C2semidirect
3. C2×#11763758C2semidirect
6. C2×C4⋊C4×#595C2semidirect
17. #11763760C22semidirect
18. #11763758C22semidirect
21. C4⋊C4×#595C22semidirect
30. C22×C4⋊Dic17C4semidirect
31. C22×#63225C4semidirect
32. C2×C4⋊C4×D17C4semidirect
33. C2×C4⋊C4×D17C4semidirect
34. C2×C4⋊C4×D17C4semidirect
35. C2×C4⋊C4×D17C4semidirect
40. C22×C4⋊C4×C17C4semidirect
80. C2×C4⋊C4×C17C2×C4semidirect
84. C2×C4⋊Dic17C2×C4semidirect
89. C2×#63225C2×C4semidirect
93. C4⋊C4×D17C2×C4semidirect
94. C4⋊C4×D17C2×C4semidirect
95. C4⋊C4×D17C2×C4semidirect
308. C22×C4⋊C4#595semidirect
326. C2×C17#2345semidirect
331. D17#2345semidirect
381. C2×C4⋊C4C2×#595semidirect
396. C17C2×#2345semidirect
583. C2#14545293direct (N × H)

Maximal subgroups

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

subgroupindex
#145452932
C2×#117637602
C2×#117637582
C2×#117637512
C2×C4⋊C4×#5952
C2×C4×C22⋊#5952
C22×C4⋊C4×D172
C2×#234517