Finite Group Databasebeta

← C4×#11763686 #17956637

Subgroups — C4×#11763686 #17956637

Order 4352.

1482 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C22⋊#595C211yesmaximal, characteristic
2C2×C4×C22⋊#595C211yesmaximal, characteristic
3C2×#11763686C214yesmaximal
4C4×C22⋊C4×D17C211yesmaximal, characteristic
5C22×C22⋊#595C2212yes—
6C22×C22⋊#595C2212yes—
7C22×C4×#595—21no—
8C22×C4×#595C412yescomplemented
9C4×C22⋊#595—21no—
10C4×C22⋊#595—21no—
11C4×C22⋊#595—21no—
12C4×C22⋊#595—21no—
13C4×C22⋊#595—21no—
14C4×C22⋊#595—21no—
15C4×C22⋊#595C412yescomplemented
16C4×C22⋊#595C412yescomplemented
17C2×(C2×#595)⋊C4—21no—
18C2×(C2×#595)⋊C4C412yescomplemented
19#11763686C4116yesdirect product factor
20C23×C4×D17C2211yescharacteristic
21C2×C22⋊C4×D17C2212yes—
22C2×C42×D17—21no—
23C22⋊C4×Dic17C412yescomplemented
24C4×#63227—21no—
25C4×C22⋊Dic17C411yescharacteristic, complemented
26#11762656—21no—
27#95×D17—21no—
28C4×C22⋊C4×C17C411yescharacteristic, complemented
29C24×D17C2311yescharacteristic
30C23×#595—22no—
31C23×#595C2×C414yes—
32C23×C4×C17C2×C411yescharacteristic
33C23×Dic17C2×C411yescharacteristic
34C22×C4×D17—22no—
35C22×C4×D17—44no—
36C22×C4×D17C2×C411yescharacteristic
37C22×C4×D17C2×C411yescharacteristic
38C22×C4×D17C2×C411yescharacteristic
39C22×C4×D17C2×C411yescharacteristic
40C22×C4×D17D411yescharacteristic
41C22×C4×D17D411yescharacteristic
42C22×C4×D17D411yescharacteristic
43C22×C4×D17D411yescharacteristic
44C22×C4×D17D411yescharacteristic
45C22×C4×D17D411yescharacteristic
46C22×C4×D17Q811yescharacteristic
47C22×C4×D17Q811yescharacteristic
48C2×C22⋊#595—22no—
49C2×C22⋊#595—22no—
50C2×C22⋊#595—22no—
51C2×C22⋊#595—24no—
52C2×C22⋊#595—24no—
53C2×C22⋊#595C2×C418yes—
54C2×C22⋊#595C2×C414yes—
55C2×C22⋊#595C2×C418yes—
56C2×C4×#595—22no—
57C2×C4×#595—22no—
58C2×C4×#595—22no—
59C2×C4×#595—22no—
60C2×C4×#595—44no—
61C2×C4×#595—44no—
62C2×C22⋊C4×C17C2×C412yes—
63C2×C42×C17—21no—
64C2×C22⋊Dic17C2×C412yes—
65C2×#63227—22no—
66C2×C4×Dic17—21no—
67C2×C4×Dic17—22no—
68C22⋊C4×D17—24no—
69C22⋊C4×D17C2×C418yes—
70C42×D17—44no—
71(C2×#595)⋊C4—22no—
72(C2×#595)⋊C4—22no—
73(C2×#595)⋊C4—22no—
74(C2×#595)⋊C4—22no—
75C17×#95—21no—
76#10587502—21no—
77#10587502—22no—
78C24×C17C22×C411yescharacteristic
79C23×D17—42no—
80C23×D17—42no—
81C23×D17C22×C411yescharacteristic
82C23×D17C22×C411yescharacteristic
83C23×D17C22×C414yes—
84C23×D17C2×D411yescharacteristic
85C23×D17C2×D411yescharacteristic
86C23×D17C2×D411yescharacteristic
87C23×D17C2×Q811yescharacteristic
88C23×D17#4114yes—
89C22×#595—24no—
90C22×#595—24no—
91C22×#595—24no—
92C22×#595—28no—
93C22×#595—44no—
94C22×#595—44no—
95C22×#595—44no—
96C22×#595—44no—
97C22×#595C4218yescomplemented
98C22×C4×C17—22no—
99C22×C4×C17—42no—
100C22×C4×C17C4211yescharacteristic
101C22×C4×C17C4211yescharacteristic
102C22×C4×C17C22⋊C411yescharacteristic
103C22×C4×C17C22⋊C411yescharacteristic
104C22×C4×C17C4⋊C411yescharacteristic
105C22×C4×C17C4⋊C411yescharacteristic
106C22×Dic17—22no—
107C22×Dic17—42no—
108C22×Dic17C4211yescharacteristic
109C22×Dic17C4211yescharacteristic
110C22×Dic17C22⋊C411yescharacteristic
111C22×Dic17C22⋊C411yescharacteristic
112C22×Dic17C4⋊C411yescharacteristic
113C22×Dic17C4⋊C411yescharacteristic
114C2×C4×D17—24no—
115C2×C4×D17—24no—
116C2×C4×D17—24no—
117C2×C4×D17—28no—
118C2×C4×D17—42no—
119C2×C4×D17—42no—
120C2×C4×D17—42no—
121C2×C4×D17—42no—
122C2×C4×D17—42no—
123C2×C4×D17—42no—
124C2×C4×D17—42no—
125C2×C4×D17—42no—
126C2×C4×D17—42no—
127C2×C4×D17—44no—
128C2×C4×D17—44no—
129C2×C4×D17C22⋊C411yescharacteristic
130C2×C4×D17C22⋊C411yescharacteristic
131C2×C4×D17C22⋊C411yescharacteristic
132C2×C4×D17C22⋊C411yescharacteristic
133C2×C4×D17C22⋊C411yescharacteristic
134C2×C4×D17C22⋊C411yescharacteristic
135C2×C4×D17C22⋊C411yescharacteristic
136C2×C4×D17C22⋊C411yescharacteristic
137C2×C4×D17C4⋊C411yescharacteristic
138C2×C4×D17C4⋊C411yescharacteristic
139C2×C4×D17C4⋊C411yescharacteristic
140C2×C4×D17C4⋊C411yescharacteristic
141C2×C4×D17C4⋊C411yescharacteristic
142C2×C4×D17C4⋊C411yescharacteristic
143C2×C4×D17C4⋊C411yescharacteristic
144C2×C4×D17C4⋊C411yescharacteristic
145C22⋊#595—24no—
146C22⋊#595—28no—
147C22⋊#595—28no—
148C22⋊#595—28no—
149C22⋊#595C4218yescomplemented
150C4×#595—44no—
151C4×#595—44no—
152C4×#595—44no—
153C4×#595—44no—
154C22⋊C4×C17—22no—
155C22⋊C4×C17C4214yescomplemented
156C42×C17—42no—
157C22⋊Dic17—22no—
158C22⋊Dic17C4214yescomplemented
159#63227—28no—
160C4×Dic17—44no—
161C4×Dic17—42no—
162C4×#342—171nomaximal, Sylow
163C23×C17—41no—
164C23×C17—41no—
165C23×C17C2×C4211yescharacteristic
166C23×C17C2×C4212yes—
167C23×C17C2×C22⋊C411yescharacteristic
168C23×C17C2×C4⋊C411yescharacteristic
169C23×C17#11712yes—
170C22×D17—22no—
171C22×D17—22no—
172C22×D17—22no—
173C22×D17—22no—
174C22×D17—22no—
175C22×D17—22no—
176C22×D17—48no—
177C22×D17—48no—
178C22×D17—41no—
179C22×D17—41no—
180C22×D17—41no—
181C22×D17—41no—
182C22×D17—41no—
183C22×D17—41no—
184C22×D17C2×C4212yes—
185C22×D17C2×C4212yes—
186C22×D17C2×C22⋊C411yescharacteristic
187C22×D17C2×C22⋊C411yescharacteristic
188C22×D17C2×C4⋊C411yescharacteristic
189C22×D17C2×C4⋊C411yescharacteristic
190C22×D17#11712yes—
191C22×D17#11712yes—
192C22×D17C4×D414yes—
193C22×D17C4×D414yes—
194C22×D17C4×D414yes—
195C22×D17C4×Q814yes—
196C2×#595—28no—
197C2×#595—28no—
198C2×#595—44no—
199C2×#595—44no—
200C2×#595—416no—
201C2×#595—48no—
202C2×#595—44no—
203C2×#595—44no—
204C2×#595—48no—
205C2×C4×C17—22no—
206C2×C4×C17—22no—
207C2×C4×C17—22no—
208C2×C4×C17—24no—
209C2×C4×C17—41no—
210C2×C4×C17—41no—
211C2×C4×C17—41no—
212C2×C4×C17—42no—
213C2×C4×C17—42no—
214C2×C4×C17#9511yescharacteristic
215C2×C4×C17#9511yescharacteristic
216C2×C4×C17#9511yescharacteristic
217C2×C4×C17#9511yescharacteristic
218C2×Dic17—22no—
219C2×Dic17—22no—
220C2×Dic17—22no—
221C2×Dic17—24no—
222C2×Dic17—41no—
223C2×Dic17—41no—
224C2×Dic17—41no—
225C2×Dic17—42no—
226C2×Dic17—42no—
227C2×Dic17#9511yescharacteristic
228C2×Dic17#9511yescharacteristic
229C2×Dic17#9511yescharacteristic
230C2×Dic17#9511yescharacteristic
231C4×D17—22no—
232C4×D17—22no—
233C4×D17—22no—
234C4×D17—22no—
235C4×D17—22no—
236C4×D17—22no—
237C4×D17—22no—
238C4×D17—22no—
239C4×D17—22no—
240C4×D17—41no—
241C4×D17—41no—
242C4×D17—41no—
243C4×D17—41no—
244C4×D17—41no—
245C4×D17—41no—
246C4×D17—416no—
247C4×D17#9914yes—
248C2×C4×C22⋊C4—171no—
249C2×C4×C22⋊C4—171no—
250C2×C4×C22⋊C4—171no—
251C2×#342—174no—
252C22×C17—21no—
253C22×C17—21no—
254C22×C17—21no—
255C22×C17—21no—
256C22×C17—21no—
257C22×C17—21no—
258C22×C17—42no—
259C22×C17—42no—
260C22×C17C4311yescharacteristic
261C22×C17C2×#9511yescharacteristic
262C22×C17#37611yescharacteristic
263C22×C17C4×C22⋊C412yes—
264C22×C17C4×C4⋊C412yes—
265C2×D17—21no—
266C2×D17—21no—
267C2×D17—21no—
268C2×D17—21no—
269C2×D17—21no—
270C2×D17—21no—
271C2×D17—28no—
272C2×D17—24no—
273C2×D17—24no—
274C2×D17—28no—
275C2×D17—42no—
276C2×D17—42no—
277C2×D17—44no—
278C2×D17—44no—
279C2×D17C4×C22⋊C412yes—
280C2×D17C4×C22⋊C412yes—
281C2×D17C4×C4⋊C412yes—
282C2×D17C4×C4⋊C412yes—
283C2×D17C2×#9912yes—
284C2×D17#41012yes—
285#595—48no—
286#595—48no—
287C4×C17—21no—
288C4×C17—21no—
289C4×C17—21no—
290C4×C17—44no—
291C4×C17#34212yescomplemented
292Dic17—21no—
293Dic17—21no—
294Dic17—21no—
295Dic17—44no—
296Dic17#34212yescomplemented
297C24×C4—171no—
298C22×C22⋊C4—172no—
299C22×C22⋊C4—172no—
300C22×C22⋊C4—172no—
301C22×C42—172no—
302C22×C42—341no—
303C22×C42—341no—
304C4×C22⋊C4—172no—
305C4×C22⋊C4—172no—
306C4×C22⋊C4—171no—
307C4×C22⋊C4—172no—
308C4×C22⋊C4—341no—
309C4×C22⋊C4—341no—
310C4×C22⋊C4—341no—
311C4×C22⋊C4—341no—
312C4×C22⋊C4—341no—
313C4×C22⋊C4—341no—
314C4×C22⋊C4—341no—
315C4×C22⋊C4—341no—
316C4×C22⋊C4#59511yescharacteristic, complemented
317C2×#95—172no—
318C2×#95—341no—
319C2×#95—341no—
320#342—1716no—
321C2×C17—22no—
322C2×C17—21no—
323C2×C17—21no—
324C2×C17—22no—
325C2×C17C4×#9511yescharacteristic
326C2×C17C2×#34211yescharacteristic
327C2×C17#174011yescharacteristic
328D17—22no—
329D17—22no—
330D17—22no—
331D17C4×#9914yes—
332C25—171no—
333C23×C4—171no—
334C23×C4—171no—
335C23×C4—171no—
336C23×C4—171no—
337C23×C4—171no—
338C23×C4—171no—
339C23×C4—171no—
340C23×C4—171no—
341C23×C4—171no—
342C23×C4—171no—
343C23×C4—171no—
344C23×C4—171no—
345C23×C4—171no—
346C23×C4—174no—
347C23×C4—342no—
348C23×C4—342no—
349C23×C4—684no—
350C23×C4C2×#59511yescharacteristic
351C2×C22⋊C4—178no—
352C2×C22⋊C4—174no—
353C2×C22⋊C4—172no—
354C2×C22⋊C4—178no—
355C2×C22⋊C4—178no—
356C2×C22⋊C4—344no—
357C2×C22⋊C4—342no—
358C2×C22⋊C4—344no—
359C2×C22⋊C4—344no—
360C2×C22⋊C4—342no—
361C2×C22⋊C4—342no—
362C2×C22⋊C4—342no—
363C2×C22⋊C4C2×#59512yes—
364C2×C42—21no—
365C2×C42—342no—
366C2×C42—342no—
367C2×C42—342no—
368C2×C42—342no—
369C2×C42—342no—
370C2×C42—341no—
371C2×C42—684no—
372C2×C42—684no—
373C2×C42—684no—
374#95—21no—
375#95—342no—
376#95—342no—
377#95—342no—
378#95—342no—
379#95—342no—
380#95—341no—
381C17C4×#34211yescharacteristic, complemented, Sylow
382C24—171no—
383C24—171no—
384C24—171no—
385C24—174no—
386C24—171no—
387C24—171no—
388C24—174no—
389C24—171no—
390C24—682no—
391C24—682no—
392C24C22×#59511yescharacteristic
393C22×C4—22no—
394C22×C4—42no—
395C22×C4—171no—
396C22×C4—171no—
397C22×C4—171no—
398C22×C4—171no—
399C22×C4—171no—
400C22×C4—171no—
401C22×C4—171no—
402C22×C4—171no—
403C22×C4—171no—
404C22×C4—171no—
405C22×C4—171no—
406C22×C4—171no—
407C22×C4—171no—
408C22×C4—171no—
409C22×C4—171no—
410C22×C4—171no—
411C22×C4—171no—
412C22×C4—171no—
413C22×C4—171no—
414C22×C4—171no—
415C22×C4—171no—
416C22×C4—171no—
417C22×C4—178no—
418C22×C4—344no—
419C22×C4—344no—
420C22×C4—344no—
421C22×C4—348no—
422C22×C4—344no—
423C22×C4—344no—
424C22×C4—348no—
425C22×C4—344no—
426C22×C4—342no—
427C22×C4—682no—
428C22×C4—682no—
429C22×C4—682no—
430C22×C4—682no—
431C22×C4—682no—
432C22×C4—682no—
433C22×C4—682no—
434C22×C4—682no—
435C22×C4—682no—
436C22×C4—684no—
437C22×C4—684no—
438C22×C4—682no—
439C22×C4—684no—
440C22×C4—684no—
441C22×C4—684no—
442C22×C4—684no—
443C22×C4C4×#59511yescharacteristic
444C22×C4C4×#59511yescharacteristic
445C22×C4C4⋊#59511yescharacteristic
446C22×C4C4⋊#59511yescharacteristic
447C22×C4C22⋊#59511yescharacteristic
448C22×C4C22⋊#59511yescharacteristic
449C22⋊C4—22no—
450C22⋊C4—178no—
451C22⋊C4—174no—
452C22⋊C4—348no—
453C22⋊C4—344no—
454C22⋊C4—348no—
455C22⋊C4—348no—
456C22⋊C4—348no—
457C22⋊C4—342no—
458C22⋊C4C4×#59514yescomplemented
459C42—42no—
460C42—682no—
461C42—684no—
462C42—684no—
463C42—684no—
464C42—684no—
465C42—684no—
466C23—41no—
467C23—41no—
468C23—171no—
469C23—172no—
470C23—171no—
471C23—171no—
472C23—171no—
473C23—172no—
474C23—174no—
475C23—174no—
476C23—172no—
477C23—172no—
478C23—174no—
479C23—174no—
480C23—342no—
481C23—342no—
482C23—342no—
483C23—342no—
484C23—342no—
485C23—342no—
486C23—681no—
487C23—681no—
488C23—681no—
489C23—681no—
490C23—681no—
491C23—681no—
492C23—688no—
493C23—688no—
494C23C2×C4×#59511yescharacteristic
495C23C2×C4×#59512yes—
496C23C2×C4⋊#59511yescharacteristic
497C23#1058767712yes—
498C23C2×C22⋊#59511yescharacteristic
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—24no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—171no—
509C2×C4—174no—
510C2×C4—171no—
511C2×C4—171no—
512C2×C4—171no—
513C2×C4—342no—
514C2×C4—342no—
515C2×C4—342no—
516C2×C4—342no—
517C2×C4—342no—
518C2×C4—342no—
519C2×C4—342no—
520C2×C4—342no—
521C2×C4—342no—
522C2×C4—342no—
523C2×C4—342no—
524C2×C4—342no—
525C2×C4—348no—
526C2×C4—348no—
527C2×C4—344no—
528C2×C4—681no—
529C2×C4—681no—
530C2×C4—681no—
531C2×C4—681no—
532C2×C4—681no—
533C2×C4—681no—
534C2×C4—6816no—
535C2×C4—681no—
536C2×C4—681no—
537C2×C4—681no—
538C2×C4—682no—
539C2×C4—682no—
540C2×C4—684no—
541C2×C4—684no—
542C2×C4—684no—
543C2×C4—688no—
544C2×C4—6816no—
545C2×C4—684no—
546C2×C4—688no—
547C2×C4(C2×#595)⋊C411yescharacteristic
548C2×C4(C2×#595)⋊C411yescharacteristic
549C2×C4(C2×#595)⋊C411yescharacteristic
550C2×C4(C2×#595)⋊C411yescharacteristic
551C22—21no—
552C22—21no—
553C22—21no—
554C22—21no—
555C22—21no—
556C22—21no—
557C22—42no—
558C22—42no—
559C22—172no—
560C22—172no—
561C22—172no—
562C22—172no—
563C22—172no—
564C22—172no—
565C22—348no—
566C22—344no—
567C22—344no—
568C22—348no—
569C22—341no—
570C22—341no—
571C22—341no—
572C22—341no—
573C22—341no—
574C22—341no—
575C22—684no—
576C22—682no—
577C22—682no—
578C22—684no—
579C22C42×#59511yescharacteristic
580C22C2×(C2×#595)⋊C411yescharacteristic
581C22#1176374511yescharacteristic
582C22C4×C22⋊#59512yes—
583C22C4×C4⋊#59512yes—
584C4—21no—
585C4—21no—
586C4—21no—
587C4—44no—
588C4—172no—
589C4—341no—
590C4—341no—
591C4—341no—
592C4—684no—
593C4—688no—
594C4—688no—
595C4#1176368612yesdirect product factor
596C2—22no—
597C2—21no—
598C2—21no—
599C2—22no—
600C2—174no—
601C2—342no—
602C2—342no—
603C2—342no—
604C2C4×(C2×#595)⋊C411yescharacteristic
605C2C2×#1176368611yescharacteristic
606C2#1454448211yescharacteristic
subgroupG/H
centerC2×C4(C2×#595)⋊C4
commutatorC22×C17C43
FrattiniC24C22×#595
FittingC4×C22⋊C4×C17C4
socleC22×C17C2×#95
prime radical, cosocleC24×D17C23
hypercenterC4×C22⋊C4#595
hypocenterC17C4×#342
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
8. C22×C4×#595C4semidirect
15. C4×C22⋊#595C4semidirect
16. C4×C22⋊#595C4semidirect
18. C2×(C2×#595)⋊C4C4semidirect
19. #11763686C4direct (N × H)
23. C22⋊C4×Dic17C4semidirect
25. C4×C22⋊Dic17C4semidirect
28. C4×C22⋊C4×C17C4semidirect
97. C22×#595C42semidirect
149. C22⋊#595C42semidirect
155. C22⋊C4×C17C42semidirect
158. C22⋊Dic17C42semidirect
291. C4×C17#342semidirect
296. Dic17#342semidirect
316. C4×C22⋊C4#595semidirect
381. C17C4×#342semidirect
458. C22⋊C4C4×#595semidirect
595. C4#11763686direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊#5952
C2×#117636862
C4×C22⋊C4×D172
C4×#34217