Finite Group Databasebeta

← C2×#14545292 #17978972

Subgroups — C2×#14545292 #17978972

Order 4352.

3526 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587677C212yesmaximal
2#14545292C2116yesmaximal, direct product factor
3C2×#11763760C212yesmaximal, complemented
4C2×#11763758C214yesmaximal, complemented
5C2×#11763752C212yesmaximal
6C2×#11763751C211yesmaximal, characteristic
7C2×C4⋊C4×#595C212yesmaximal, complemented
8C2×C4×C22⋊#595C211yesmaximal, characteristic
9C22×C4⋊C4×D17C211yesmaximal, characteristic
10C2×#10587677—216no—
11C2×#10587677C22116yes—
12C22×C4⋊#595C2212yes—
13C22×C4⋊#595C2214yes—
14C22×C22⋊#595C2211yescharacteristic
15C22×C22⋊#595C2212yes—
16C22×C22⋊#595C2211yescharacteristic
17C22×C4×#595C2212yes—
18C22×C4×#595C2214yes—
19#11763760C22116yescomplemented
20#11763758C22132yescomplemented
21#11763752C22116yes—
22#11763751C2218yes—
23C4⋊C4×#595C22116yescomplemented
24C4×C22⋊#595C2218yes—
25C2×(C2×#595)⋊C4C2212yes—
26C2×(C2×#595)⋊C4C2214yes—
27C2×(C2×#595)⋊C4C2212yes—
28C2×(C2×#595)⋊C4C2214yes—
29C23×C4×D17C2211yescharacteristic
30C23×C4×D17C2212yes—
31C22×C4⋊Dic17C411yescharacteristic, complemented
32C22×#63225C412yescomplemented
33C2×C4⋊C4×D17C418yescomplemented
34C2×C4⋊C4×D17C411yescharacteristic, complemented
35C2×C4⋊C4×D17C411yescharacteristic, complemented
36C2×C4⋊C4×D17C412yescomplemented
37C2×C4⋊C4×D17C2211yescharacteristic
38C2×C4⋊C4×D17C2212yes—
39C2×C4⋊C4×D17C2211yescharacteristic
40C2×C4⋊C4×D17C2218yes—
41C22×C4⋊C4×C17C411yescharacteristic, complemented
42C24×D17C2311yescharacteristic
43C23×#595C2312yes—
44C23×#595C2314yes—
45C23×#595C2312yes—
46C23×C4×C17C2×C412yes—
47C23×C4×C17C2×C411yescharacteristic
48C23×Dic17C2×C411yescharacteristic
49C23×Dic17C2×C412yes—
50C22×C4×D17—28no—
51C22×C4×D17—28no—
52C22×C4×D17—28no—
53C22×C4×D17C2×C418yes—
54C22×C4×D17C2×C412yes—
55C22×C4×D17C2×C412yes—
56C22×C4×D17C2×C411yescharacteristic
57C22×C4×D17C2×C411yescharacteristic
58C22×C4×D17C2×C414yes—
59C22×C4×D17C2311yescharacteristic
60C22×C4×D17C2312yes—
61C22×C4×D17C2312yes—
62C22×C4×D17C2314yes—
63C22×C4×D17C2318yes—
64C22×C4×D17C2311yescharacteristic
65C2×C22⋊#595—28no—
66C2×C22⋊#595—24no—
67C2×C22⋊#595D418yes—
68C2×C22⋊#595C2314yes—
69C2×C22⋊#595C2318yes—
70C2×C22⋊#595C2314yes—
71#10587677—264no—
72C2×C4⋊#595—216no—
73C2×C4⋊#595—28no—
74C2×C4⋊#595C2318yes—
75C2×C4⋊#595C23116yes—
76C2×C4×#595—216no—
77C2×C4×#595—28no—
78C2×C4×#595C2318yes—
79C2×C4×#595C23116yes—
80C2×C4⋊C4×C17C2×C412yes—
81C2×C4⋊C4×C17C2×C411yescharacteristic
82C2×C4⋊C4×C17C2×C411yescharacteristic
83C2×C4⋊C4×C17C2×C418yescomplemented
84C2×C4⋊Dic17C2×C412yes—
85C2×C4⋊Dic17C2×C411yescharacteristic
86C2×C4⋊Dic17C2×C411yescharacteristic
87C2×C4⋊Dic17C2×C418yescomplemented
88C2×#63225C2×C412yes—
89C2×#63225C2×C412yes—
90C2×#63225C2×C412yes—
91C2×#63225C2×C412yes—
92C2×#63225C2×C4116yescomplemented
93C4⋊C4×D17C2×C418yes—
94C4⋊C4×D17C2×C414yes—
95C4⋊C4×D17C2×C414yes—
96C4⋊C4×D17C2×C4116yescomplemented
97C4⋊C4×D17C2×C418yescomplemented
98C4⋊C4×D17C2×C418yescomplemented
99C4⋊C4×D17C2314yes—
100C4⋊C4×D17C2318yes—
101C4⋊C4×D17C2314yes—
102(C2×#595)⋊C4C2318yes—
103(C2×#595)⋊C4C23116yes—
104(C2×#595)⋊C4C2318yes—
105(C2×#595)⋊C4C23116yes—
106C24×C17C22×C411yescharacteristic
107C23×D17—24no—
108C23×D17—24no—
109C23×D17C22×C412yes—
110C23×D17C22×C411yescharacteristic
111C23×D17C2×D414yes—
112C23×D17#4114yes—
113C23×D17C2412yes—
114C23×D17C2411yescharacteristic
115C22×#595—24no—
116C22×#595—24no—
117C22×#595—28no—
118C22×#595—24no—
119C22×#595—28no—
120C22×#595—24no—
121C22×#595—28no—
122C22×#595—24no—
123C22×#595C2×D418yes—
124C22×#595C2418yes—
125C22×#595C2414yes—
126C22×#595C2414yes—
127C22×C4×C17—28no—
128C22×C4×C17—24no—
129C22×C4×C17C22×C412yes—
130C22×C4×C17C22×C412yes—
131C22×C4×C17C22×C418yes—
132C22×C4×C17C22×C411yescharacteristic
133C22×C4×C17C22×C414yes—
134C22×C4×C17C22×C411yescharacteristic
135C22×Dic17—28no—
136C22×Dic17—24no—
137C22×Dic17C22×C411yescharacteristic
138C22×Dic17C22×C412yes—
139C22×Dic17C22×C412yes—
140C22×Dic17C22×C414yes—
141C22×Dic17C22×C418yes—
142C22×Dic17C22×C411yescharacteristic
143C2×C4×D17—28no—
144C2×C4×D17—28no—
145C2×C4×D17—232no—
146C2×C4×D17—24no—
147C2×C4×D17—24no—
148C2×C4×D17—216no—
149C2×C4×D17—24no—
150C2×C4×D17—216no—
151C2×C4×D17—24no—
152C2×C4×D17—24no—
153C2×C4×D17—24no—
154C2×C4×D17—24no—
155C2×C4×D17—216no—
156C2×C4×D17—216no—
157C2×C4×D17C22×C412yes—
158C2×C4×D17C22×C414yes—
159C2×C4×D17C22×C414yes—
160C2×C4×D17C22×C418yes—
161C2×C4×D17C22×C418yes—
162C2×C4×D17C22×C414yes—
163C2×C4×D17C22×C414yes—
164C2×C4×D17C22×C412yes—
165C2×C4×D17#4118yes—
166C2×C4×D17C2414yes—
167C2×C4×D17C2414yes—
168C2×C4×D17C2412yes—
169C2×C4×D17C2412yes—
170C22⋊#595—216no—
171C22⋊#595—28no—
172C22⋊#595C2×D4116yes—
173C4⋊#595—232no—
174C4⋊#595—216no—
175C4×#595—232no—
176C4×#595—216no—
177C4⋊C4×C17C22×C418yes—
178C4⋊C4×C17C22×C414yes—
179C4⋊C4×C17C22×C414yes—
180C4⋊Dic17C22×C418yes—
181C4⋊Dic17C22×C414yes—
182C4⋊Dic17C22×C414yes—
183#63225C22×C418yes—
184#63225C22×C418yes—
185#63225C22×C418yes—
186#63225C22×C418yes—
187C2×#2344—171nomaximal, Sylow
188C23×C17—22no—
189C23×C17—22no—
190C23×C17C4×D414yes—
191C23×C17C23×C412yes—
192C23×C17C23×C411yescharacteristic
193C22×D17—22no—
194C22×D17—22no—
195C22×D17—24no—
196C22×D17—24no—
197C22×D17—216no—
198C22×D17—216no—
199C22×D17—24no—
200C22×D17—24no—
201C22×D17C4×D414yes—
202C22×D17C4×D418yes—
203C22×D17C23×C412yes—
204C22×D17C23×C411yescharacteristic
205C22×D17C22×D414yes—
206C22×D17C22×D412yes—
207C22×D17C2×#4114yes—
208C22×D17C2×#4114yes—
209C22×D17C2×#4112yes—
210C22×D172−1+414yes—
211C22×D17C2511yescharacteristic
212C2×#595—216no—
213C2×#595—24no—
214C2×#595—24no—
215C2×#595—28no—
216C2×#595—24no—
217C2×#595—28no—
218C2×#595—24no—
219C2×#595—28no—
220C2×#595—24no—
221C2×#595—416no—
222C2×#595—48no—
223C2×#595C22×D418yes—
224C2×C4×C17—22no—
225C2×C4×C17—216no—
226C2×C4×C17—24no—
227C2×C4×C17—24no—
228C2×C4×C17—28no—
229C2×C4×C17#11714yescomplemented
230C2×C4×C17C23×C414yes—
231C2×C4×C17C23×C414yes—
232C2×C4×C17C23×C412yes—
233C2×C4×C17C23×C412yes—
234C2×Dic17—22no—
235C2×Dic17—216no—
236C2×Dic17—24no—
237C2×Dic17—24no—
238C2×Dic17—28no—
239C2×Dic17#11714yescomplemented
240C2×Dic17C23×C412yes—
241C2×Dic17C23×C414yes—
242C2×Dic17C23×C414yes—
243C2×Dic17C23×C412yes—
244C4×D17—24no—
245C4×D17—216no—
246C4×D17—216no—
247C4×D17—28no—
248C4×D17—28no—
249C4×D17—24no—
250C4×D17—24no—
251C4×D17—24no—
252C4×D17—24no—
253C4×D17—24no—
254C4×D17—28no—
255C4×D17—28no—
256C4×D17#11718yescomplemented
257C4×D17C2×#4118yes—
258C22×#117—172no—
259C23×C4⋊C4—171no—
260#2344—1716no—
261C2×#389—172no—
262C2×#387—174no—
263C2×#381—172no—
264C2×#380—171no—
265C2×C4×C4⋊C4—172no—
266C2×C4×C22⋊C4—171no—
267C22×C17—28no—
268C22×C17—22no—
269C22×C17—22no—
270C22×C17C2×#11712yes—
271C22×C17C2×C4×D414yes—
272C22×C17C2×C4×D412yes—
273C22×C17#51912yes—
274C22×C17C24×C411yescharacteristic
275C2×D17—28no—
276C2×D17—22no—
277C2×D17—22no—
278C2×D17—216no—
279C2×D17—28no—
280C2×D17—28no—
281C2×D17C2×#11712yes—
282C2×D17C2×C4×D414yes—
283C2×D17C2×C4×D412yes—
284C2×D17#51912yes—
285C2×D17#54718yes—
286C2×D17#55218yes—
287C2×D17C23×D411yescharacteristic
288C2×D17C22×#4112yes—
289C2×D17C22×#4111yescharacteristic
290C2×D17C2×2−1+412yes—
291#595—28no—
292#595—48no—
293#595—44no—
294C4×C17—22no—
295C4×C17—24no—
296C4×C17—24no—
297C4×C17C2×#11714yescomplemented
298Dic17—22no—
299Dic17—24no—
300Dic17—24no—
301Dic17C2×#11714yescomplemented
302C24×C4—172no—
303C24×C4—171no—
304C2×#117—1716no—
305C2×#117—3416no—
306C22×C4⋊C4—172no—
307C22×C4⋊C4—171no—
308C22×C4⋊C4—172no—
309C22×C4⋊C4—171no—
310C22×C4⋊C4—171no—
311C22×C4⋊C4—171no—
312C22×C4⋊C4—172no—
313C22×C4⋊C4—171no—
314C22×C4⋊C4—178no—
315C22×C4⋊C4—178no—
316C22×C4⋊C4—174no—
317C22×C4⋊C4—172no—
318C22×C4⋊C4#59511yescharacteristic, complemented
319C22×C22⋊C4—171no—
320C22×C22⋊C4—172no—
321C22×C22⋊C4—171no—
322C22×C42—174no—
323C22×C42—172no—
324#389—1716no—
325#387—1732no—
326#381—1716no—
327#380—178no—
328C4×C4⋊C4—1716no—
329C4×C22⋊C4—178no—
330C2×#95—172no—
331C2×#95—174no—
332C2×#95—172no—
333C2×#95—174no—
334C2×C17—24no—
335C2×C17#234414yescomplemented
336C2×C17C22×#11711yescharacteristic
337C2×C17C22×C4×D411yescharacteristic
338C2×C17C2×#51911yescharacteristic
339D17—24no—
340D17#234414yescomplemented
341D17C2×#54712yes—
342D17C2×#55212yes—
343C25—171no—
344C23×C4—171no—
345C23×C4—172no—
346C23×C4—171no—
347C23×C4—172no—
348C23×C4—172no—
349C23×C4—178no—
350C23×C4—171no—
351C23×C4—174no—
352C23×C4—178no—
353C23×C4—172no—
354C23×C4—172no—
355C23×C4—171no—
356C23×C4—171no—
357C23×C4—172no—
358C23×C4—174no—
359C23×C4—174no—
360C23×C4—172no—
361C23×C4—348no—
362C23×C4—348no—
363C23×C4—348no—
364C23×C4C2×#59512yes—
365C23×C4C2×#59511yescharacteristic
366#117—3464no—
367C2×C4⋊C4—172no—
368C2×C4⋊C4—172no—
369C2×C4⋊C4—172no—
370C2×C4⋊C4—172no—
371C2×C4⋊C4—1716no—
372C2×C4⋊C4—172no—
373C2×C4⋊C4—171no—
374C2×C4⋊C4—171no—
375C2×C4⋊C4—178no—
376C2×C4⋊C4—174no—
377C2×C4⋊C4—178no—
378C2×C4⋊C4—174no—
379C2×C4⋊C4—174no—
380C2×C4⋊C4—174no—
381C2×C4⋊C4—178no—
382C2×C4⋊C4—1716no—
383C2×C4⋊C4—178no—
384C2×C4⋊C4—178no—
385C2×C4⋊C4—1716no—
386C2×C4⋊C4—178no—
387C2×C4⋊C4—3416no—
388C2×C4⋊C4—348no—
389C2×C4⋊C4C2×#59512yes—
390C2×C4⋊C4C2×#59511yescharacteristic
391C2×C4⋊C4C2×#59511yescharacteristic
392C2×C4⋊C4C2×#59518yescomplemented
393C2×C22⋊C4—174no—
394C2×C22⋊C4—178no—
395C2×C22⋊C4—178no—
396C2×C22⋊C4—174no—
397C2×C22⋊C4—348no—
398C2×C22⋊C4—344no—
399C2×C42—1716no—
400C2×C42—178no—
401C2×C42—3416no—
402C2×C42—348no—
403#95—178no—
404#95—1716no—
405#95—178no—
406#95—1716no—
407C17C2×#234411yescharacteristic, complemented, Sylow
408C24—171no—
409C24—174no—
410C24—174no—
411C24—172no—
412C24—172no—
413C24—171no—
414C24—344no—
415C24—344no—
416C24C22×#59511yescharacteristic
417C22×C4—28no—
418C22×C4—24no—
419C22×C4—171no—
420C22×C4—178no—
421C22×C4—172no—
422C22×C4—172no—
423C22×C4—178no—
424C22×C4—174no—
425C22×C4—174no—
426C22×C4—178no—
427C22×C4—171no—
428C22×C4—172no—
429C22×C4—172no—
430C22×C4—174no—
431C22×C4—174no—
432C22×C4—172no—
433C22×C4—174no—
434C22×C4—178no—
435C22×C4—178no—
436C22×C4—174no—
437C22×C4—172no—
438C22×C4—174no—
439C22×C4—174no—
440C22×C4—174no—
441C22×C4—178no—
442C22×C4—344no—
443C22×C4—3416no—
444C22×C4—3416no—
445C22×C4—344no—
446C22×C4—344no—
447C22×C4—3416no—
448C22×C4—344no—
449C22×C4—344no—
450C22×C4—344no—
451C22×C4—3416no—
452C22×C4—3432no—
453C22×C4—348no—
454C22×C4—348no—
455C22×C4—344no—
456C22×C4—344no—
457C22×C4—344no—
458C22×C4—348no—
459C22×C4—344no—
460C22×C4—348no—
461C22×C4—344no—
462C22×C4—344no—
463C22×C4—348no—
464C22×C4—348no—
465C22×C4—344no—
466C22×C4C22×#59518yes—
467C22×C4C22×#59514yes—
468C22×C4C22×#59511yescharacteristic
469C22×C4C22×#59512yes—
470C22×C4C22×#59512yes—
471C22×C4C22×#59511yescharacteristic
472C4⋊C4—178no—
473C4⋊C4—178no—
474C4⋊C4—178no—
475C4⋊C4—178no—
476C4⋊C4—178no—
477C4⋊C4—174no—
478C4⋊C4—174no—
479C4⋊C4—3416no—
480C4⋊C4—3432no—
481C4⋊C4C22×#59518yes—
482C4⋊C4C22×#59514yes—
483C4⋊C4C22×#59514yes—
484C22⋊C4—1716no—
485C22⋊C4—348no—
486C22⋊C4—3416no—
487C42—3416no—
488C42—3432no—
489C23—22no—
490C23—22no—
491C23—174no—
492C23—172no—
493C23—172no—
494C23—174no—
495C23—171no—
496C23—171no—
497C23—174no—
498C23—174no—
499C23—178no—
500C23—174no—
501C23—172no—
502C23—344no—
503C23—344no—
504C23—344no—
505C23—344no—
506C23—3416no—
507C23—3416no—
508C23—342no—
509C23—342no—
510C23D4×#59514yes—
511C23C23×#59512yes—
512C23C23×#59511yescharacteristic
513C2×C4—22no—
514C2×C4—216no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—28no—
518C2×C4—174no—
519C2×C4—172no—
520C2×C4—178no—
521C2×C4—178no—
522C2×C4—178no—
523C2×C4—172no—
524C2×C4—174no—
525C2×C4—174no—
526C2×C4—348no—
527C2×C4—344no—
528C2×C4—344no—
529C2×C4—344no—
530C2×C4—344no—
531C2×C4—344no—
532C2×C4—344no—
533C2×C4—348no—
534C2×C4—348no—
535C2×C4—3416no—
536C2×C4—3416no—
537C2×C4—348no—
538C2×C4—344no—
539C2×C4—344no—
540C2×C4—3416no—
541C2×C4—342no—
542C2×C4—3416no—
543C2×C4—344no—
544C2×C4—344no—
545C2×C4—348no—
546C2×C4—348no—
547C2×C4—344no—
548C2×C4—344no—
549C2×C4—348no—
550C2×C4—344no—
551C2×C4—348no—
552C2×C4—6816no—
553C2×C4—688no—
554C2×C4#1058767714yescomplemented
555C2×C4C23×#59512yes—
556C2×C4C23×#59514yes—
557C2×C4C23×#59514yes—
558C2×C4C23×#59512yes—
559C22—22no—
560C22—22no—
561C22—28no—
562C22—172no—
563C22—172no—
564C22—171no—
565C22—171no—
566C22—172no—
567C22—172no—
568C22—172no—
569C22—178no—
570C22—178no—
571C22—174no—
572C22—348no—
573C22—348no—
574C22—3416no—
575C22—342no—
576C22—342no—
577C22—348no—
578C22C2×#1058767712yes—
579C22C2×D4×#59514yes—
580C22C2×D4×#59512yes—
581C22#1176387712yes—
582C22C24×#59511yescharacteristic
583C4—22no—
584C4—24no—
585C4—24no—
586C4—174no—
587C4—348no—
588C4—342no—
589C4—344no—
590C4—344no—
591C4—688no—
592C4—684no—
593C4C2×#1058767714yescomplemented
594C2—24no—
595C2—172no—
596C2—172no—
597C2—174no—
598C2—344no—
599C2#1454529214yesdirect product factor
600C2C22×#1058767711yescharacteristic
601C2C22×D4×#59511yescharacteristic
602C2C2×#1176387711yescharacteristic
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×#2344
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #14545292C2direct (N × H)
3. C2×#11763760C2semidirect
4. C2×#11763758C2semidirect
7. C2×C4⋊C4×#595C2semidirect
19. #11763760C22semidirect
20. #11763758C22semidirect
23. C4⋊C4×#595C22semidirect
31. C22×C4⋊Dic17C4semidirect
32. C22×#63225C4semidirect
33. C2×C4⋊C4×D17C4semidirect
34. C2×C4⋊C4×D17C4semidirect
35. C2×C4⋊C4×D17C4semidirect
36. C2×C4⋊C4×D17C4semidirect
41. C22×C4⋊C4×C17C4semidirect
83. C2×C4⋊C4×C17C2×C4semidirect
87. C2×C4⋊Dic17C2×C4semidirect
92. C2×#63225C2×C4semidirect
96. C4⋊C4×D17C2×C4semidirect
97. C4⋊C4×D17C2×C4semidirect
98. C4⋊C4×D17C2×C4semidirect
229. C2×C4×C17#117semidirect
239. C2×Dic17#117semidirect
256. C4×D17#117semidirect
297. C4×C17C2×#117semidirect
301. Dic17C2×#117semidirect
318. C22×C4⋊C4#595semidirect
335. C2×C17#2344semidirect
340. D17#2344semidirect
392. C2×C4⋊C4C2×#595semidirect
407. C17C2×#2344semidirect
554. C2×C4#10587677semidirect
593. C4C2×#10587677semidirect
599. C2#14545292direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105876772
#145452922
C2×#117637602
C2×#117637582
C2×#117637522
C2×#117637512
C2×C4⋊C4×#5952
C2×C4×C22⋊#5952
C22×C4⋊C4×D172
C2×#234417