Finite Group Databasebeta

← C2×#14544063 #17964377

Subgroups — C2×#14544063 #17964377

Order 4352.

1426 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763779C211yesmaximal, characteristic
2C22×C22⋊#3624C211yesmaximal, characteristic
3#14544063C218yesmaximal, direct product factor
4C2×#11763655C212yesmaximal, complemented
5C2×#11763654C212yesmaximal, complemented
6C22×#10587564C211yesmaximal, characteristic
7C22×#63247—21no—
8C23×#3624—21no—
9#11763779—22no—
10#11763779C2214yes—
11C2×C22⋊#3624—22no—
12C2×C22⋊#3624—21no—
13C2×C22⋊#3624—21no—
14C2×C22⋊#3624C2212yes—
15C2×C22⋊#3624C2212yes—
16C2×C22⋊#3624C2214yes—
17#11763655C2218yescomplemented
18#11763654C2218yescomplemented
19C23×Dic34C411yescharacteristic
20C24×Dic17C2211yescharacteristic
21C2×#10587564—21no—
22C2×#10587564—21no—
23C2×#10587564—22no—
24C2×#10587564—21no—
25C2×#10587564—21no—
26C2×#10587564—22no—
27C2×#10587564C414yes—
28C2×#10587564C2214yes—
29C22×C4⋊Dic17C2211yescharacteristic
30C22×#63225C411yescharacteristic
31C22×#63225C2211yescharacteristic
32C22×C22⋊Dic17C411yescharacteristic
33C22×C22⋊C4×C17C411yescharacteristic
34C25×C17C2×C411yescharacteristic
35C23×C4×C17C2×C411yescharacteristic
36C23×C4×C17C2×C411yescharacteristic
37C23×Dic17—44no—
38C23×Dic17C2×C411yescharacteristic
39C23×Dic17C2×C411yescharacteristic
40C23×Dic17C2×C411yescharacteristic
41C23×Dic17C2×C412yes—
42C23×Dic17D411yescharacteristic
43C23×Dic17D411yescharacteristic
44C23×Dic17D412yes—
45C23×Dic17D411yescharacteristic
46C23×Dic17D411yescharacteristic
47C23×Dic17D412yes—
48C23×Dic17C2311yescharacteristic
49C23×Dic17C2312yes—
50C22×Dic34—21no—
51C22×Dic34—22no—
52C22×Dic34—21no—
53C22×Dic34—44no—
54C22×Dic34C2×C414yes—
55C2×#63247—24no—
56C2×#63247—44no—
57C22×#3624—24no—
58C22×#3624—22no—
59C22×#3624—22no—
60C22×#3624—44no—
61C2×C22⋊C4×C17—21no—
62C2×C22⋊C4×C17—22no—
63C2×C22⋊C4×C17—21no—
64C2×C22⋊C4×C17C2×C414yes—
65C2×C22⋊Dic17—21no—
66C2×C22⋊Dic17—22no—
67C2×C22⋊Dic17—21no—
68C2×C22⋊Dic17C2×C414yes—
69C2×C4⋊Dic17—21no—
70C2×C4⋊Dic17—21no—
71C2×C4⋊Dic17—21no—
72C2×C4⋊Dic17—21no—
73C2×C4⋊Dic17C2×C412yes—
74C2×C4⋊Dic17C2312yes—
75C2×#63225—22no—
76C2×#63225—21no—
77C2×#63225—21no—
78C2×#63225—21no—
79C2×#63225—21no—
80C2×#63225—21no—
81C2×#63225—21no—
82C2×#63225C2×C414yes—
83C2×#63225C2×C412yes—
84C2×#63225C2312yes—
85#10587564—24no—
86#10587564—24no—
87#10587564—24no—
88#10587564—24no—
89#10587564—24no—
90#10587564—24no—
91#10587564—24no—
92#10587564—24no—
93C22⋊#3624—24no—
94C22⋊#3624—22no—
95C22⋊#3624—24no—
96C22⋊#3624—22no—
97C22⋊#3624C2314yes—
98C22⋊#3624C2314yes—
99C24×C17—24no—
100C24×C17—24no—
101C24×C17—42no—
102C24×C17C22⋊C411yescharacteristic
103C24×C17C22⋊C412yes—
104C24×C17C22⋊C411yescharacteristic
105C24×C17C22×C412yes—
106C24×C17C22×C411yescharacteristic
107C22×C4×C17—21no—
108C22×C4×C17—21no—
109C22×C4×C17—21no—
110C22×C4×C17—21no—
111C22×C4×C17—24no—
112C22×C4×C17—42no—
113C22×C4×C17C22×C412yes—
114C22×C4×C17C22×C412yes—
115C22×Dic17—24no—
116C22×Dic17—24no—
117C22×Dic17—24no—
118C22×Dic17—21no—
119C22×Dic17—21no—
120C22×Dic17—21no—
121C22×Dic17—21no—
122C22×Dic17—24no—
123C22×Dic17—44no—
124C22×Dic17—44no—
125C22×Dic17—44no—
126C22×Dic17—44no—
127C22×Dic17—42no—
128C22×Dic17—42no—
129C22×Dic17—42no—
130C22×Dic17—42no—
131C22×Dic17C22⋊C412yes—
132C22×Dic17C22⋊C411yescharacteristic
133C22×Dic17C22⋊C412yes—
134C22×Dic17C22⋊C412yes—
135C22×Dic17C22⋊C412yes—
136C22×Dic17C22⋊C412yes—
137C22×Dic17C22⋊C411yescharacteristic
138C22×Dic17C22×C412yes—
139C22×Dic17C22×C412yes—
140C22×Dic17C22×C412yes—
141C22×Dic17C22×C411yescharacteristic
142C22×Dic17C2×D412yes—
143C22×Dic17C2×D411yescharacteristic
144C22×Dic17C2×D411yescharacteristic
145C22×Dic17C2×D412yes—
146C22×Dic17C2×D412yes—
147C22×Dic17C2×D412yes—
148C22×Dic17C2×D411yescharacteristic
149C22×Dic17C2×D411yescharacteristic
150C22×Dic17C2411yescharacteristic
151C2×Dic34—24no—
152C2×Dic34—24no—
153C2×Dic34—44no—
154C2×Dic34—48no—
155C2×Dic34—44no—
156C2×Dic34—48no—
157#63247—48no—
158C2×#3624—24no—
159C2×#3624—24no—
160C2×#3624—44no—
161C2×#3624—48no—
162C2×#3624—44no—
163C22⋊C4×C17—24no—
164C22⋊C4×C17—24no—
165C22⋊Dic17—24no—
166C22⋊Dic17—24no—
167C4⋊Dic17—22no—
168C4⋊Dic17—22no—
169C4⋊Dic17—22no—
170C4⋊Dic17—22no—
171#63225—24no—
172#63225—22no—
173#63225—22no—
174#63225—24no—
175#63225—22no—
176#63225—22no—
177C2×#1472—171nomaximal, Sylow
178C23×C17—22no—
179C23×C17—22no—
180C23×C17—22no—
181C23×C17—22no—
182C23×C17—24no—
183C23×C17—24no—
184C23×C17—22no—
185C23×C17—22no—
186C23×C17—24no—
187C23×C17—22no—
188C23×C17—24no—
189C23×C17—42no—
190C23×C17—42no—
191C23×C17—416no—
192C23×C17#10114yes—
193C23×C17C2×C22⋊C412yes—
194C23×C17C2×C22⋊C411yescharacteristic
195C23×C17C2×C22⋊C412yes—
196C23×C17C2×C22⋊C411yescharacteristic
197C23×C17#13114yes—
198C23×C17C23×C411yescharacteristic
199C2×C4×C17—22no—
200C2×C4×C17—22no—
201C2×C4×C17—24no—
202C2×C4×C17—42no—
203C2×C4×C17—42no—
204C2×C4×C17—42no—
205C2×C4×C17—42no—
206C2×C4×C17—42no—
207C2×Dic17—22no—
208C2×Dic17—22no—
209C2×Dic17—22no—
210C2×Dic17—24no—
211C2×Dic17—24no—
212C2×Dic17—24no—
213C2×Dic17—24no—
214C2×Dic17—24no—
215C2×Dic17—24no—
216C2×Dic17—22no—
217C2×Dic17—22no—
218C2×Dic17—24no—
219C2×Dic17—42no—
220C2×Dic17—42no—
221C2×Dic17—41no—
222C2×Dic17—42no—
223C2×Dic17—42no—
224C2×Dic17—41no—
225C2×Dic17—41no—
226C2×Dic17—41no—
227C2×Dic17—42no—
228C2×Dic17—42no—
229C2×Dic17—42no—
230C2×Dic17—42no—
231C2×Dic17—42no—
232C2×Dic17#9914yes—
233C2×Dic17C2×C22⋊C412yes—
234C2×Dic17C2×C22⋊C411yescharacteristic
235C2×Dic17C2×C22⋊C411yescharacteristic
236C2×Dic17C2×C22⋊C412yes—
237C2×Dic17C22×D411yescharacteristic
238C2×Dic17C22×D411yescharacteristic
239Dic34—48no—
240Dic34—48no—
241#3624—44no—
242#3624—44no—
243C22×C22⋊Q8—171no—
244C2×#407—171no—
245C22×C22⋊C8—171no—
246#1472—178no—
247C2×#324—172no—
248C2×#324—172no—
249C22×C17—22no—
250C22×C17—21no—
251C22×C17—21no—
252C22×C17—22no—
253C22×C17—21no—
254C22×C17—21no—
255C22×C17—28no—
256C22×C17—28no—
257C22×C17—22no—
258C22×C17—22no—
259C22×C17—22no—
260C22×C17—48no—
261C22×C17—48no—
262C22×C17—44no—
263C22×C17#40812yes—
264C22×C17#40812yes—
265C22×C17C2×#9912yes—
266C22×C17C2×#10114yes—
267C22×C17C2×#10112yes—
268C22×C17C22×C22⋊C411yescharacteristic
269C22×C17C2×#13112yes—
270C4×C17—42no—
271C4×C17—42no—
272Dic17—21no—
273Dic17—21no—
274Dic17—22no—
275Dic17—21no—
276Dic17—21no—
277Dic17—42no—
278Dic17—42no—
279Dic17C2×#9914yes—
280C23×Q8—171no—
281C24×C4—171no—
282C22×M16—341no—
283C23×C8—341no—
284C2×C22⋊Q8—174no—
285C2×C22⋊Q8—174no—
286C2×C22⋊Q8—341no—
287C2×C22⋊Q8—341no—
288C2×C22⋊Q8—342no—
289C2×C22⋊Q8—341no—
290C2×C22⋊Q8—341no—
291C2×C22⋊Q8—342no—
292C22×C4⋊C4—171no—
293C22×C4⋊C4—171no—
294C22×C4⋊C4—171no—
295C22×C22⋊C4—171no—
296C22×C22⋊C4#59511yescharacteristic
297#407—174no—
298#407—342no—
299C2×C22⋊C8—172no—
300C2×C22⋊C8—174no—
301C2×C22⋊C8—172no—
302C2×C22⋊C8—342no—
303C2×C22⋊C8—341no—
304C2×C22⋊C8—341no—
305#324—178no—
306#324—178no—
307C2×C17—22no—
308C2×C17—22no—
309C2×C17—24no—
310C2×C17—42no—
311C2×C17#147214yescomplemented
312C2×C17C2×#40811yescharacteristic
313C2×C17C22×#9911yescharacteristic
314C2×C17C22×#10111yescharacteristic
315C25C2×#59511yescharacteristic
316C22×Q8—174no—
317C22×Q8—342no—
318C22×Q8—341no—
319C22×Q8—341no—
320C22×Q8—684no—
321C23×C4—171no—
322C23×C4—171no—
323C23×C4—171no—
324C23×C4—172no—
325C23×C4—171no—
326C23×C4—171no—
327C23×C4—172no—
328C23×C4—171no—
329C23×C4—172no—
330C23×C4—172no—
331C23×C4—171no—
332C23×C4—171no—
333C23×C4—684no—
334C23×C4C2×#59511yescharacteristic
335C23×C4C2×#59511yescharacteristic
336C2×M16—344no—
337C2×M16—684no—
338C22×C8—344no—
339C22×C8—342no—
340C22×C8—342no—
341C22×C8—684no—
342C22⋊Q8—344no—
343C22⋊Q8—344no—
344C22⋊Q8—344no—
345C22⋊Q8—344no—
346C22⋊Q8—344no—
347C22⋊Q8—344no—
348C22⋊Q8—344no—
349C22⋊Q8—344no—
350C2×C4⋊C4—172no—
351C2×C4⋊C4—172no—
352C2×C4⋊C4—174no—
353C2×C4⋊C4—172no—
354C2×C4⋊C4—172no—
355C2×C4⋊C4—342no—
356C2×C4⋊C4—341no—
357C2×C4⋊C4—341no—
358C2×C4⋊C4—341no—
359C2×C4⋊C4—341no—
360C2×C4⋊C4—341no—
361C2×C4⋊C4—341no—
362C2×C4⋊C4—341no—
363C2×C4⋊C4—341no—
364C2×C4⋊C4—341no—
365C2×C4⋊C4—341no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—174no—
370C2×C22⋊C4—342no—
371C2×C22⋊C4—341no—
372C2×C22⋊C4—341no—
373C2×C22⋊C4C2×#59514yes—
374C22⋊C8—174no—
375C22⋊C8—174no—
376C22⋊C8—342no—
377C22⋊C8—344no—
378C22⋊C8—342no—
379C22⋊C8—344no—
380C17C2×#147211yescharacteristic, complemented, Sylow
381C24—24no—
382C24—24no—
383C24—42no—
384C24C22⋊#59511yescharacteristic
385C24C22⋊#59512yes—
386C24C22⋊#59511yescharacteristic
387C24C22×#59512yes—
388C24C22×#59511yescharacteristic
389C2×Q8—344no—
390C2×Q8—344no—
391C2×Q8—684no—
392C2×Q8—688no—
393C2×Q8—688no—
394C2×Q8—684no—
395C22×C4—24no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—42no—
401C22×C4—171no—
402C22×C4—172no—
403C22×C4—172no—
404C22×C4—172no—
405C22×C4—172no—
406C22×C4—172no—
407C22×C4—171no—
408C22×C4—171no—
409C22×C4—171no—
410C22×C4—172no—
411C22×C4—172no—
412C22×C4—172no—
413C22×C4—171no—
414C22×C4—171no—
415C22×C4—172no—
416C22×C4—172no—
417C22×C4—171no—
418C22×C4—171no—
419C22×C4—172no—
420C22×C4—172no—
421C22×C4—344no—
422C22×C4—344no—
423C22×C4—344no—
424C22×C4—344no—
425C22×C4—341no—
426C22×C4—341no—
427C22×C4—341no—
428C22×C4—341no—
429C22×C4—684no—
430C22×C4—684no—
431C22×C4—684no—
432C22×C4—684no—
433C22×C4—682no—
434C22×C4—682no—
435C22×C4—682no—
436C22×C4—682no—
437C22×C4C22×#59512yes—
438C22×C4C22×#59512yes—
439M16—688no—
440C2×C8—344no—
441C2×C8—344no—
442C2×C8—688no—
443C2×C8—684no—
444C2×C8—684no—
445C4⋊C4—344no—
446C4⋊C4—344no—
447C4⋊C4—342no—
448C4⋊C4—342no—
449C4⋊C4—342no—
450C4⋊C4—342no—
451C4⋊C4—342no—
452C4⋊C4—342no—
453C4⋊C4—342no—
454C4⋊C4—342no—
455C22⋊C4—24no—
456C22⋊C4—24no—
457C22⋊C4—344no—
458C22⋊C4—344no—
459C23—22no—
460C23—22no—
461C23—22no—
462C23—22no—
463C23—24no—
464C23—22no—
465C23—22no—
466C23—24no—
467C23—22no—
468C23—24no—
469C23—24no—
470C23—42no—
471C23—42no—
472C23—416no—
473C23#1058754514yes—
474C23#1058767814yes—
475C23C2×C22⋊#59512yes—
476C23C2×C22⋊#59511yescharacteristic
477C23C2×C22⋊#59512yes—
478C23C2×C22⋊#59511yescharacteristic
479C23C23×#59511yescharacteristic
480Q8—688no—
481Q8—688no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—24no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—174no—
491C2×C4—172no—
492C2×C4—171no—
493C2×C4—171no—
494C2×C4—171no—
495C2×C4—171no—
496C2×C4—172no—
497C2×C4—344no—
498C2×C4—344no—
499C2×C4—344no—
500C2×C4—344no—
501C2×C4—344no—
502C2×C4—344no—
503C2×C4—342no—
504C2×C4—342no—
505C2×C4—342no—
506C2×C4—342no—
507C2×C4—342no—
508C2×C4—344no—
509C2×C4—681no—
510C2×C4—682no—
511C2×C4—682no—
512C2×C4—681no—
513C2×C4—681no—
514C2×C4—682no—
515C2×C4—682no—
516C2×C4—681no—
517C2×C4—682no—
518C2×C4—682no—
519C2×C4—682no—
520C2×C4—682no—
521C2×C4—682no—
522C8—684no—
523C8—684no—
524C22—28no—
525C22—28no—
526C22—22no—
527C22—21no—
528C22—21no—
529C22—22no—
530C22—21no—
531C22—21no—
532C22—22no—
533C22—22no—
534C22—22no—
535C22—48no—
536C22—48no—
537C22—44no—
538C22#1176378212yes—
539C22#1176378212yes—
540C22D17⋊#9912yes—
541C22C2×#1058754514yes—
542C22C2×#1058754512yes—
543C22C22×C22⋊#59511yescharacteristic
544C22C2×#1058767812yes—
545C4—42no—
546C4—42no—
547C4—174no—
548C4—341no—
549C4—341no—
550C4—342no—
551C4—341no—
552C4—341no—
553C4—682no—
554C4—682no—
555C2—22no—
556C2—24no—
557C2—22no—
558C2—42no—
559C2#1454406314yesdirect product factor
560C2C2×#1176378211yescharacteristic
561C2C2×D17⋊#9911yescharacteristic
562C2C22×#1058754511yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC23×C17C23×C4
FrattiniC23C23×#595
FittingC22×C22⋊C4×C17C4
socleC23×C17C2×C22⋊C4
prime radicalC25×C17C2×C4
cosocleC22×Dic17C24
hypercenterC22×C22⋊C4#595
hypocenterC17C2×#1472
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C25 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #14544063C2direct (N × H)
4. C2×#11763655C2semidirect
5. C2×#11763654C2semidirect
17. #11763655C22semidirect
18. #11763654C22semidirect
311. C2×C17#1472semidirect
380. C17C2×#1472semidirect
559. C2#14544063direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117637792
C22×C22⋊#36242
#145440632
C2×#117636552
C2×#117636542
C22×#105875642
C2×#147217