Finite Group Databasebeta

← C2×#14545896 #17982834

Subgroups — C2×#14545896 #17982834

Order 4352.

1390 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763922C212yesmaximal, complemented
2#14545896C218yesmaximal, direct product factor
3C2×#11763895C212yesmaximal, complemented
4C2×#11763894C212yesmaximal
5C22×#10587677C211yesmaximal, characteristic
6#11763922—24no—
7#11763922C2218yescomplemented
8C2×C4⋊#3633—22no—
9C2×C22⋊#3633C2214yes—
10C2×C4×#3633—22no—
11#11763895C2218yescomplemented
12#11763894C2218yes—
13C2×#10587677—22no—
14C2×#10587677—22no—
15C2×#10587677—24no—
16C2×#10587677C414yes—
17C2×#10587677C2214yes—
18C22×C4⋊#595C411yescharacteristic
19C22×C4⋊#595C2211yescharacteristic
20C22×C22⋊#595C411yescharacteristic
21C22×C22⋊#595C2211yescharacteristic
22C22×C4×#595C411yescharacteristic
23C22×C4×#595C2211yescharacteristic
24C23×C4×D17C411yescharacteristic
25C24×D17C2×C411yescharacteristic
26C23×#595C2×C411yescharacteristic
27C23×#595C2×C411yescharacteristic
28C23×#595C2×C411yescharacteristic
29C23×#595C2311yescharacteristic
30C22×#3633—24no—
31C23×C4×C17C811yescharacteristic, complemented
32C23×Dic17C811yescharacteristic, complemented
33C22×C4×D17—22no—
34C22×C4×D17—21no—
35C22×C4×D17—21no—
36C22×C4×D17—21no—
37C22×C4×D17—22no—
38C22×C4×D17—21no—
39C22×C4×D17C814yescomplemented
40C22×C4×D17C811yescharacteristic, complemented
41C22×C4×D17C811yescharacteristic, complemented
42C22×C4×D17C2×C411yescharacteristic
43C22×C4×D17C2×C414yes—
44C22×C4×D17C2×C411yescharacteristic
45C2×C22⋊#595—22no—
46C2×C22⋊#595—22no—
47C2×C22⋊#595—22no—
48C2×C22⋊#595—22no—
49C2×C22⋊#595C2×C414yes—
50C2×C22⋊#595C2×C412yes—
51C2×C22⋊#595C2312yes—
52#10587677—28no—
53#10587677—28no—
54#10587677—28no—
55#10587677—28no—
56C2×C4⋊#595—22no—
57C2×C4⋊#595—22no—
58C2×C4⋊#595—22no—
59C2×C4⋊#595—22no—
60C2×C4⋊#595C2×C414yes—
61C2×C4⋊#595C2×C412yes—
62C2×C4⋊#595C2312yes—
63C2×C4×#595—22no—
64C2×C4×#595—21no—
65C2×C4×#595—21no—
66C2×C4×#595C2×C414yes—
67C2×C4×#595C2×C412yes—
68C2×C4×#595D412yes—
69C2×C4×#595D412yes—
70C2×C4×#595D414yes—
71C2×C4×#595C2312yes—
72C22⋊#3633—24no—
73C22⋊#3633C2318yes—
74C4⋊#3633—28no—
75C4×#3633—28no—
76C24×C17C2×C811yescharacteristic
77C23×D17—21no—
78C23×D17—21no—
79C23×D17—21no—
80C23×D17—21no—
81C23×D17—42no—
82C23×D17—42no—
83C23×D17C2×C811yescharacteristic
84C23×D17C2×C812yes—
85C23×D17C22×C411yescharacteristic
86C23×D17C22×C412yes—
87C22×#595—21no—
88C22×#595—21no—
89C22×#595—21no—
90C22×#595—21no—
91C22×#595—42no—
92C22×#595—42no—
93C22×#595—42no—
94C22×#595—42no—
95C22×#595C22⋊C412yes—
96C22×#595C22⋊C412yes—
97C22×#595C22×C412yes—
98C22×#595C22×C412yes—
99C22×#595C22×C411yescharacteristic
100C22×#595C22×C412yes—
101C22×#595C2×D412yes—
102C22×#595C2×D412yes—
103C22×#595C2411yescharacteristic
104C2×#3633—28no—
105C2×#3633—48no—
106C22×C4×C17—22no—
107C22×C4×C17—21no—
108C22×C4×C17—21no—
109C22×C4×C17C2×C811yescharacteristic
110C22×C4×C17C2×C811yescharacteristic
111C22×C4×C17C2×C814yescomplemented
112C22×Dic17—22no—
113C22×Dic17—21no—
114C22×Dic17—21no—
115C22×Dic17C2×C811yescharacteristic
116C22×Dic17C2×C811yescharacteristic
117C22×Dic17C2×C814yescomplemented
118C2×C4×D17—21no—
119C2×C4×D17—21no—
120C2×C4×D17—21no—
121C2×C4×D17—21no—
122C2×C4×D17—22no—
123C2×C4×D17—21no—
124C2×C4×D17—21no—
125C2×C4×D17—22no—
126C2×C4×D17—21no—
127C2×C4×D17—21no—
128C2×C4×D17—24no—
129C2×C4×D17—24no—
130C2×C4×D17—24no—
131C2×C4×D17—24no—
132C2×C4×D17—24no—
133C2×C4×D17—24no—
134C2×C4×D17—24no—
135C2×C4×D17—24no—
136C2×C4×D17C22⋊C412yes—
137C2×C4×D17C22⋊C411yescharacteristic
138C2×C4×D17C22⋊C411yescharacteristic
139C2×C4×D17C2×C812yes—
140C2×C4×D17C2×C812yes—
141C2×C4×D17C2×C814yescomplemented
142C2×C4×D17C2×C814yescomplemented
143C2×C4×D17M1611yescharacteristic
144C2×C4×D17M1612yes—
145C2×C4×D17M1611yescharacteristic
146C2×C4×D17C22×C412yes—
147C2×C4×D17C22×C412yes—
148C22⋊#595—24no—
149C22⋊#595—28no—
150C22⋊#595—24no—
151C4⋊#595—24no—
152C4⋊#595—28no—
153C4⋊#595—24no—
154C4×#595—24no—
155C4×#595—24no—
156C4×#595C22⋊C414yes—
157C4×#595C22⋊C414yes—
158C4×#595C2×D414yes—
159C4×#595C2×D414yes—
160C2×#1458—171nomaximal, Sylow
161C23×C17—21no—
162C23×C17—21no—
163C23×C17—42no—
164C23×C17C22×C811yescharacteristic
165C23×C17C22×C812yes—
166C22×D17—22no—
167C22×D17—22no—
168C22×D17—21no—
169C22×D17—21no—
170C22×D17—22no—
171C22×D17—22no—
172C22×D17—22no—
173C22×D17—22no—
174C22×D17—44no—
175C22×D17—42no—
176C22×D17—42no—
177C22×D17—44no—
178C22×D17—44no—
179C22×D17—42no—
180C22×D17—42no—
181C22×D17—42no—
182C22×D17—42no—
183C22×D17—42no—
184C22×D17C2×C22⋊C411yescharacteristic
185C22×D17C2×C22⋊C411yescharacteristic
186C22×D17C22×C811yescharacteristic
187C22×D17C22×C812yes—
188C22×D17C2×M1611yescharacteristic
189C22×D17C2×M1611yescharacteristic
190C22×D17C23×C411yescharacteristic
191C2×#595—24no—
192C2×#595—24no—
193C2×#595—22no—
194C2×#595—22no—
195C2×#595—42no—
196C2×#595—41no—
197C2×#595—42no—
198C2×#595—42no—
199C2×#595—41no—
200C2×#595—42no—
201C2×#595—42no—
202C2×#595—42no—
203C2×#595—42no—
204C2×#595—42no—
205C2×#595—42no—
206C2×#595C2×C22⋊C412yes—
207C2×#595C2×C22⋊C414yes—
208C2×#595C22×D412yes—
209#3633—48no—
210C2×C4×C17—21no—
211C2×C4×C17—21no—
212C2×C4×C17—24no—
213C2×C4×C17—24no—
214C2×C4×C17C22⋊C812yes—
215C2×C4×C17C22⋊C811yescharacteristic
216C2×C4×C17C22⋊C811yescharacteristic
217C2×C4×C17C22×C812yes—
218C2×C4×C17C22×C812yes—
219C2×Dic17—21no—
220C2×Dic17—21no—
221C2×Dic17—24no—
222C2×Dic17—24no—
223C2×Dic17C22⋊C812yes—
224C2×Dic17C22⋊C811yescharacteristic
225C2×Dic17C22⋊C811yescharacteristic
226C2×Dic17C22×C812yes—
227C2×Dic17C22×C812yes—
228C4×D17—22no—
229C4×D17—22no—
230C4×D17—22no—
231C4×D17—22no—
232C4×D17—24no—
233C4×D17—24no—
234C4×D17—24no—
235C4×D17—24no—
236C4×D17C22⋊C812yes—
237C4×D17C22⋊C812yes—
238C4×D17C22⋊C812yes—
239C4×D17C22⋊C812yes—
240C4×D17C2×C22⋊C412yes—
241C4×D17C2×C22⋊C412yes—
242C4×D17C2×M1612yes—
243C4×D17C2×M1612yes—
244C22×#117—171no—
245C2×#431—172no—
246#1458—178no—
247C2×#324—172no—
248C2×#323—172no—
249C22×C17—22no—
250C22×C17—22no—
251C22×C17—42no—
252C22×C17—42no—
253C22×C17—42no—
254C22×C17C2×C22⋊C811yescharacteristic
255C22×C17C2×C22⋊C811yescharacteristic
256C22×C17C23×C811yescharacteristic
257C2×D17—22no—
258C2×D17—21no—
259C2×D17—21no—
260C2×D17—21no—
261C2×D17—21no—
262C2×D17—22no—
263C2×D17—22no—
264C2×D17—22no—
265C2×D17—44no—
266C2×D17—44no—
267C2×D17—42no—
268C2×D17—42no—
269C2×D17—42no—
270C2×D17—42no—
271C2×D17—44no—
272C2×D17—42no—
273C2×D17C2×C22⋊C811yescharacteristic
274C2×D17C2×C22⋊C811yescharacteristic
275C2×D17#41012yes—
276C2×D17#41312yes—
277C2×D17C22×C22⋊C411yescharacteristic
278C2×D17C22×M1611yescharacteristic
279#595—22no—
280#595—22no—
281#595—24no—
282#595—42no—
283#595—42no—
284C4×C17—22no—
285C4×C17C2×C22⋊C812yes—
286C4×C17C2×C22⋊C812yes—
287Dic17—22no—
288Dic17C2×C22⋊C812yes—
289Dic17C2×C22⋊C812yes—
290C24×C4—171no—
291C2×#117—174no—
292C2×#117—174no—
293C2×#117—342no—
294C2×#117—342no—
295C2×#117—344no—
296C22×C4⋊C4—171no—
297C22×C4⋊C4—171no—
298C22×C22⋊C4—171no—
299C22×C22⋊C4—171no—
300C22×C42—171no—
301C22×C42—171no—
302#431—178no—
303#431—344no—
304C2×C4⋊C8—342no—
305C2×C22⋊C8—174no—
306C2×C4×C8—342no—
307#324—178no—
308#323—178no—
309C2×C17—21no—
310C2×C17—21no—
311C2×C17—42no—
312C2×C17#145812yescomplemented
313C2×C17C22×C22⋊C811yescharacteristic
314D17—21no—
315D17—21no—
316D17—42no—
317D17#145812yescomplemented
318D17C2×#41011yescharacteristic
319D17C2×#41311yescharacteristic
320C25—171no—
321C23×C4—171no—
322C23×C4—171no—
323C23×C4—171no—
324C23×C4—171no—
325C23×C4—171no—
326C23×C4—171no—
327C23×C4—171no—
328C23×C4—174no—
329C23×C4—174no—
330C23×C4—171no—
331C23×C4—171no—
332C23×C4—341no—
333C23×C4—342no—
334C23×C4—341no—
335C23×C4—342no—
336C23×C4—341no—
337C23×C4—341no—
338C23×C4#363311yescharacteristic, complemented
339C22×C8—344no—
340#117—348no—
341#117—348no—
342#117—348no—
343#117—348no—
344C2×C4⋊C4—174no—
345C2×C4⋊C4—172no—
346C2×C4⋊C4—172no—
347C2×C4⋊C4—342no—
348C2×C4⋊C4—342no—
349C2×C4⋊C4—342no—
350C2×C4⋊C4—342no—
351C2×C22⋊C4—174no—
352C2×C22⋊C4—172no—
353C2×C22⋊C4—172no—
354C2×C22⋊C4—342no—
355C2×C22⋊C4—342no—
356C2×C22⋊C4—342no—
357C2×C22⋊C4—342no—
358C2×C42—172no—
359C2×C42—172no—
360C2×C42—172no—
361C2×C42—172no—
362C2×C42—174no—
363C2×C42—174no—
364C2×C42—341no—
365C2×C42—342no—
366C2×C42—341no—
367C4⋊C8—348no—
368C22⋊C8—178no—
369C22⋊C8—344no—
370C4×C8—348no—
371C17C2×#145811yescharacteristic, complemented, Sylow
372C24—171no—
373C24—172no—
374C24—171no—
375C24—172no—
376C24—341no—
377C24—341no—
378C24—341no—
379C24—341no—
380C24—682no—
381C24—682no—
382C24C2×#363311yescharacteristic
383C22×C4—22no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—171no—
387C22×C4—171no—
388C22×C4—172no—
389C22×C4—172no—
390C22×C4—171no—
391C22×C4—171no—
392C22×C4—171no—
393C22×C4—172no—
394C22×C4—172no—
395C22×C4—172no—
396C22×C4—172no—
397C22×C4—171no—
398C22×C4—174no—
399C22×C4—172no—
400C22×C4—171no—
401C22×C4—172no—
402C22×C4—172no—
403C22×C4—171no—
404C22×C4—172no—
405C22×C4—174no—
406C22×C4—174no—
407C22×C4—172no—
408C22×C4—172no—
409C22×C4—172no—
410C22×C4—344no—
411C22×C4—344no—
412C22×C4—342no—
413C22×C4—341no—
414C22×C4—341no—
415C22×C4—344no—
416C22×C4—344no—
417C22×C4—344no—
418C22×C4—344no—
419C22×C4—344no—
420C22×C4—344no—
421C22×C4—341no—
422C22×C4—341no—
423C22×C4—341no—
424C22×C4—341no—
425C22×C4—342no—
426C22×C4—341no—
427C22×C4—341no—
428C22×C4—342no—
429C22×C4—341no—
430C22×C4—341no—
431C22×C4—341no—
432C22×C4—341no—
433C22×C4—341no—
434C22×C4—341no—
435C22×C4—682no—
436C22×C4—682no—
437C22×C4—682no—
438C22×C4—682no—
439C22×C4C2×#363311yescharacteristic
440C22×C4C2×#363311yescharacteristic
441C22×C4C2×#363314yescomplemented
442C2×C8—348no—
443C2×C8—688no—
444C4⋊C4—344no—
445C4⋊C4—344no—
446C4⋊C4—348no—
447C22⋊C4—344no—
448C22⋊C4—344no—
449C22⋊C4—348no—
450C42—174no—
451C42—174no—
452C42—174no—
453C42—174no—
454C42—344no—
455C42—344no—
456C23—21no—
457C23—21no—
458C23—42no—
459C23—171no—
460C23—171no—
461C23—171no—
462C23—171no—
463C23—171no—
464C23—171no—
465C23—172no—
466C23—342no—
467C23—342no—
468C23—342no—
469C23—342no—
470C23—342no—
471C23—342no—
472C23—341no—
473C23—341no—
474C23—682no—
475C23—682no—
476C23—682no—
477C23—682no—
478C23—682no—
479C23—684no—
480C23—682no—
481C23—682no—
482C23—684no—
483C23—684no—
484C23C22×#363311yescharacteristic
485C23C22×#363312yes—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—172no—
491C2×C4—171no—
492C2×C4—171no—
493C2×C4—172no—
494C2×C4—172no—
495C2×C4—172no—
496C2×C4—172no—
497C2×C4—172no—
498C2×C4—172no—
499C2×C4—172no—
500C2×C4—172no—
501C2×C4—172no—
502C2×C4—172no—
503C2×C4—172no—
504C2×C4—174no—
505C2×C4—172no—
506C2×C4—344no—
507C2×C4—344no—
508C2×C4—342no—
509C2×C4—342no—
510C2×C4—342no—
511C2×C4—342no—
512C2×C4—344no—
513C2×C4—344no—
514C2×C4—344no—
515C2×C4—344no—
516C2×C4—341no—
517C2×C4—341no—
518C2×C4—344no—
519C2×C4—344no—
520C2×C4—342no—
521C2×C4—342no—
522C2×C4—681no—
523C2×C4—682no—
524C2×C4—682no—
525C2×C4—681no—
526C2×C4—682no—
527C2×C4—682no—
528C2×C4—682no—
529C2×C4—682no—
530C2×C4—682no—
531C2×C4—682no—
532C2×C4—682no—
533C2×C4C22⋊#363311yescharacteristic
534C2×C4C22⋊#363312yes—
535C2×C4C22⋊#363311yescharacteristic
536C2×C4C22×#363312yes—
537C2×C4C22×#363312yes—
538C8—688no—
539C22—22no—
540C22—22no—
541C22—42no—
542C22—42no—
543C22—42no—
544C22—171no—
545C22—171no—
546C22—172no—
547C22—172no—
548C22—171no—
549C22—171no—
550C22—341no—
551C22—341no—
552C22—341no—
553C22—341no—
554C22—342no—
555C22—342no—
556C22—342no—
557C22—342no—
558C22—682no—
559C22—682no—
560C22—682no—
561C22—682no—
562C22—684no—
563C22—684no—
564C22—684no—
565C22—682no—
566C22C2×C22⋊#363311yescharacteristic
567C22C2×C22⋊#363311yescharacteristic
568C22C23×#363311yescharacteristic
569C4—22no—
570C4—172no—
571C4—172no—
572C4—342no—
573C4—342no—
574C4—344no—
575C4—342no—
576C4—682no—
577C4—682no—
578C4C2×C22⋊#363312yes—
579C4C2×C22⋊#363312yes—
580C2—21no—
581C2—21no—
582C2—42no—
583C2—171no—
584C2—171no—
585C2—172no—
586C2—341no—
587C2—341no—
588C2—682no—
589C2#1454589612yesdirect product factor
590C2C22×C22⋊#363311yescharacteristic
subgroupG/H
centerC2×C4C22⋊#3633
commutatorC22×C17C23×C8
FrattiniC22C23×#3633
FittingC23×C4×C17C8
socleC22×C17C2×C22⋊C8
prime radicalC24×D17C2×C4
cosocleC22×#595C24
hypercenterC23×C4#3633
hypocenterC17C2×#1458
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C2×#11763922C2semidirect
2. #14545896C2direct (N × H)
3. C2×#11763895C2semidirect
7. #11763922C22semidirect
11. #11763895C22semidirect
31. C23×C4×C17C8semidirect
32. C23×Dic17C8semidirect
39. C22×C4×D17C8semidirect
40. C22×C4×D17C8semidirect
41. C22×C4×D17C8semidirect
111. C22×C4×C17C2×C8semidirect
117. C22×Dic17C2×C8semidirect
141. C2×C4×D17C2×C8semidirect
142. C2×C4×D17C2×C8semidirect
312. C2×C17#1458semidirect
317. D17#1458semidirect
338. C23×C4#3633semidirect
371. C17C2×#1458semidirect
441. C22×C4C2×#3633semidirect
589. C2#14545896direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117639222
#145458962
C2×#117638952
C2×#117638942
C22×#105876772
C2×#145817