Finite Group Databasebeta

← C2×#14543658 #17951111

Subgroups — C2×#14543658 #17951111

Order 4352.

1454 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763777C211yesmaximal, characteristic
2C2×#11763751C211yesmaximal, characteristic
3#14543658C214yesmaximal, direct product factor
4C2×#95×D17C211yesmaximal, characteristic
5C22×#63242—21no—
6C22×C4⋊#595C412yescomplemented
7C22×C22⋊#595—21no—
8C2×#10587543C412yescomplemented
9#11763777—21no—
10#11763777—21no—
11#11763777C412yescomplemented
12#11763777C2212yes—
13C2×C22⋊#3624—21no—
14#11763751—21no—
15#11763751—21no—
16#11763751C412yescomplemented
17#11763751C2212yes—
18C2×(C2×#595)⋊C4—21no—
19C23×C4×D17—21no—
20C23×C4×D17C2211yescharacteristic
21C2×#10587502—21no—
22C2×#10587502C411yescharacteristic, complemented
23#95×D17—21no—
24#95×D17—21no—
25#95×D17C412yescomplemented
26#95×D17C2212yes—
27C2×C17×#95C411yescharacteristic, complemented
28C24×D17D411yescharacteristic
29C23×#595—22no—
30C23×C4×C17—21no—
31C23×C4×C17C2×C411yescharacteristic
32C23×Dic17—21no—
33C23×Dic17D411yescharacteristic
34C22×C4×D17—28no—
35C22×C4×D17—22no—
36C22×C4×D17—22no—
37C22×C4×D17—44no—
38C22×C4×D17—44no—
39C22×C4×D17—42no—
40C22×C4×D17—42no—
41C22×C4×D17C2×C411yescharacteristic
42C22×C4×D17C2×C411yescharacteristic
43C22×C4×D17C2×C411yescharacteristic
44C22×C4×D17C2×C411yescharacteristic
45C22×C4×D17C2×C411yescharacteristic
46C22×C4×D17D411yescharacteristic
47C22×C4×D17D411yescharacteristic
48C22×C4×D17D411yescharacteristic
49C22×C4×D17D411yescharacteristic
50C22×C4×D17Q811yescharacteristic
51C22×C4×D17Q811yescharacteristic
52C22×C4×D17C2311yescharacteristic
53C2×C22⋊#595—22no—
54C2×C22⋊#595—22no—
55C2×C22⋊#595—42no—
56C2×C22⋊#595—42no—
57C22×#3624—22no—
58C2×C4⋊#595—22no—
59C2×C4⋊#595—44no—
60C2×C4⋊#595C2×C414yescomplemented
61C2×#63242—22no—
62C2×#63242—22no—
63C2×#63242—44no—
64C22⋊#3624—22no—
65C22⋊#3624—22no—
66(C2×#595)⋊C4—22no—
67(C2×#595)⋊C4—22no—
68#10587543—22no—
69#10587543C2×C414yescomplemented
70C17×#95—21no—
71C17×#95C2×C412yescomplemented
72#10587502—21no—
73#10587502—22no—
74#10587502—22no—
75#10587502C2×C412yescomplemented
76C24×C17C22⋊C411yescharacteristic
77C23×D17—24no—
78C23×D17—24no—
79C23×D17C22⋊C411yescharacteristic
80C23×D17C22⋊C411yescharacteristic
81C23×D17C22⋊C411yescharacteristic
82C23×D17C4⋊C411yescharacteristic
83C23×D17C4⋊C411yescharacteristic
84C23×D17D812yes—
85C23×D17SD1612yes—
86C23×D17SD1612yes—
87C23×D17Q1612yes—
88C23×D17C2×D411yescharacteristic
89C22×#595—24no—
90C22×#595—44no—
91C22×#595—44no—
92C22×#595—44no—
93C22×C4×C17—24no—
94C22×C4×C17—22no—
95C22×C4×C17—42no—
96C22×C4×C17—42no—
97C22×C4×C17—42no—
98C22×C4×C17C4211yescharacteristic
99C22×C4×C17C4211yescharacteristic
100C22×C4×C17C22⋊C411yescharacteristic
101C22×C4×C17C4⋊C411yescharacteristic
102C22×C4×C17C4⋊C411yescharacteristic
103C22×C4×C17C22×C411yescharacteristic
104C22×Dic17—24no—
105C22×Dic17—22no—
106C22×Dic17—42no—
107C22×Dic17—42no—
108C22×Dic17—42no—
109C22×Dic17C22⋊C411yescharacteristic
110C22×Dic17C22⋊C411yescharacteristic
111C22×Dic17C22⋊C411yescharacteristic
112C22×Dic17C4⋊C411yescharacteristic
113C22×Dic17C4⋊C411yescharacteristic
114C22×Dic17C2×D411yescharacteristic
115C2×C4×D17—24no—
116C2×C4×D17—24no—
117C2×C4×D17—28no—
118C2×C4×D17—28no—
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—42no—
128C2×C4×D17—42no—
129C2×C4×D17—416no—
130C2×C4×D17—416no—
131C2×C4×D17—44no—
132C2×C4×D17—44no—
133C2×C4×D17—44no—
134C2×C4×D17—42no—
135C2×C4×D17—42no—
136C2×C4×D17C4211yescharacteristic
137C2×C4×D17C4211yescharacteristic
138C2×C4×D17C22⋊C411yescharacteristic
139C2×C4×D17C22⋊C411yescharacteristic
140C2×C4×D17C22⋊C411yescharacteristic
141C2×C4×D17C22⋊C411yescharacteristic
142C2×C4×D17C4⋊C411yescharacteristic
143C2×C4×D17C4⋊C411yescharacteristic
144C2×C4×D17C4⋊C411yescharacteristic
145C2×C4×D17C4⋊C411yescharacteristic
146C2×C4×D17C4⋊C411yescharacteristic
147C2×C4×D17C4⋊C411yescharacteristic
148C2×C4×D17C22×C411yescharacteristic
149C2×C4×D17C22×C411yescharacteristic
150C2×C4×D17C2×D411yescharacteristic
151C2×C4×D17C2×Q811yescharacteristic
152C22⋊#595—44no—
153C22⋊#595—42no—
154C22⋊#595—42no—
155C2×#3624—24no—
156C2×#3624—44no—
157C4⋊#595—44no—
158C4⋊#595—44no—
159#63242—44no—
160#63242—44no—
161C2×#1294—171nomaximal, Sylow
162C23×C17—22no—
163C23×C17—22no—
164C23×C17#9511yescharacteristic
165C23×C17#9511yescharacteristic
166C23×C17#10212yes—
167C23×C17#10312yes—
168C23×C17C2×C22⋊C411yescharacteristic
169C22×D17—22no—
170C22×D17—22no—
171C22×D17—28no—
172C22×D17—28no—
173C22×D17—28no—
174C22×D17—28no—
175C22×D17—22no—
176C22×D17—22no—
177C22×D17—22no—
178C22×D17—22no—
179C22×D17—22no—
180C22×D17—22no—
181C22×D17—22no—
182C22×D17—22no—
183C22×D17#9511yescharacteristic
184C22×D17#9511yescharacteristic
185C22×D17#9914yes—
186C22×D17#10212yes—
187C22×D17#10212yes—
188C22×D17#10212yes—
189C22×D17#10312yes—
190C22×D17#10312yes—
191C22×D17#10312yes—
192C22×D17#10414yes—
193C22×D17#10612yes—
194C22×D17#10612yes—
195C22×D17#10712yes—
196C22×D17#10712yes—
197C22×D17C2×C22⋊C411yescharacteristic
198C22×D17C2×C4⋊C411yescharacteristic
199C22×D17C2×D811yescharacteristic
200C22×D17C2×SD1611yescharacteristic
201C22×D17C2×SD1611yescharacteristic
202C22×D17C2×Q1611yescharacteristic
203C2×#595—44no—
204C2×#595—44no—
205C2×#595—44no—
206C2×#595—88no—
207C2×C4×C17—22no—
208C2×C4×C17—22no—
209C2×C4×C17—24no—
210C2×C4×C17—41no—
211C2×C4×C17—41no—
212C2×C4×C17—41no—
213C2×C4×C17—41no—
214C2×C4×C17—48no—
215C2×C4×C17—42no—
216C2×C4×C17—42no—
217C2×C4×C17#9511yescharacteristic
218C2×C4×C17#9511yescharacteristic
219C2×C4×C17C2×C4211yescharacteristic
220C2×C4×C17C2×C4⋊C411yescharacteristic
221C2×Dic17—22no—
222C2×Dic17—22no—
223C2×Dic17—24no—
224C2×Dic17—41no—
225C2×Dic17—41no—
226C2×Dic17—41no—
227C2×Dic17—41no—
228C2×Dic17—48no—
229C2×Dic17—42no—
230C2×Dic17—42no—
231C2×Dic17#9511yescharacteristic
232C2×Dic17#9511yescharacteristic
233C2×Dic17C2×C22⋊C411yescharacteristic
234C2×Dic17C2×C4⋊C411yescharacteristic
235C4×D17—22no—
236C4×D17—22no—
237C4×D17—22no—
238C4×D17—22no—
239C4×D17—22no—
240C4×D17—22no—
241C4×D17—22no—
242C4×D17—22no—
243C4×D17—41no—
244C4×D17—41no—
245C4×D17—41no—
246C4×D17—41no—
247C4×D17—41no—
248C4×D17—41no—
249C4×D17—41no—
250C4×D17—41no—
251C4×D17—416no—
252C4×D17—48no—
253C4×D17—48no—
254#3624—44no—
255C22×C22⋊C8—171no—
256C2×#380—171no—
257C22×#95—171no—
258#1294—174no—
259C22×C17—24no—
260C22×C17—24no—
261C22×C17—21no—
262C22×C17—21no—
263C22×C17—21no—
264C22×C17—21no—
265C22×C17#33912yes—
266C22×C17#34012yes—
267C22×C17#34012yes—
268C22×C17#34212yes—
269C22×C17C2×#9511yescharacteristic
270C22×C17C2×#10211yescharacteristic
271C22×C17C2×#10311yescharacteristic
272C2×D17—24no—
273C2×D17—24no—
274C2×D17—21no—
275C2×D17—21no—
276C2×D17—21no—
277C2×D17—21no—
278C2×D17—24no—
279C2×D17—24no—
280C2×D17—24no—
281C2×D17—24no—
282C2×D17—22no—
283C2×D17—24no—
284C2×D17—22no—
285C2×D17—22no—
286C2×D17—24no—
287C2×D17—22no—
288C2×D17#32718yes—
289C2×D17#32818yes—
290C2×D17#33912yes—
291C2×D17#34012yes—
292C2×D17#34012yes—
293C2×D17#34212yes—
294C2×D17C2×#9912yes—
295C2×D17C2×#10211yescharacteristic
296C2×D17C2×#10311yescharacteristic
297C2×D17C2×#10412yes—
298C2×D17C2×#10611yescharacteristic
299C2×D17C2×#10711yescharacteristic
300#595—84no—
301C4×C17—21no—
302C4×C17—21no—
303C4×C17—21no—
304C4×C17—21no—
305C4×C17—44no—
306Dic17—21no—
307Dic17—21no—
308Dic17—21no—
309Dic17—21no—
310Dic17—44no—
311C24×C4—171no—
312C24×C4—341no—
313C23×C8—341no—
314C22×C4⋊C4—172no—
315C22×C22⋊C4—341no—
316C2×C22⋊C8—172no—
317C2×C22⋊C8—172no—
318C2×C22⋊C8—172no—
319C2×C22⋊C8—341no—
320C2×C22⋊C8—341no—
321C2×C22⋊C8—341no—
322#380—172no—
323#380—172no—
324#380—341no—
325#380—341no—
326C2×#95—171no—
327C2×#95—172no—
328C2×#95—172no—
329C2×#95—341no—
330C2×#95—341no—
331C2×#95—341no—
332C2×#95—341no—
333C2×#95#59511yescharacteristic, complemented
334C2×C17—21no—
335C2×C17—22no—
336C2×C17—21no—
337C2×C17#129414yescomplemented
338C2×C17C2×#33911yescharacteristic
339C2×C17C2×#34011yescharacteristic
340C2×C17C2×#34211yescharacteristic
341D17—22no—
342D17—21no—
343D17—21no—
344D17#129414yescomplemented
345D17C2×#32712yes—
346D17C2×#32812yes—
347C25—171no—
348C23×C4—21no—
349C23×C4—171no—
350C23×C4—171no—
351C23×C4—171no—
352C23×C4—171no—
353C23×C4—171no—
354C23×C4—171no—
355C23×C4—171no—
356C23×C4—171no—
357C23×C4—171no—
358C23×C4—171no—
359C23×C4—171no—
360C23×C4—171no—
361C23×C4—171no—
362C23×C4—342no—
363C23×C4—342no—
364C23×C4—348no—
365C23×C4—341no—
366C23×C4—342no—
367C23×C4—684no—
368C23×C4—682no—
369C23×C4—682no—
370C23×C4—684no—
371C23×C4C2×#59511yescharacteristic
372C22×C8—342no—
373C22×C8—342no—
374C22×C8—342no—
375C22×C8—684no—
376C2×C4⋊C4—174no—
377C2×C4⋊C4—342no—
378C2×C4⋊C4—684no—
379C2×C22⋊C4—342no—
380C2×C22⋊C4—342no—
381C2×C22⋊C4—682no—
382C2×C22⋊C4—682no—
383C22⋊C8—174no—
384C22⋊C8—342no—
385C22⋊C8—342no—
386C22⋊C8—342no—
387#95—21no—
388#95—172no—
389#95—342no—
390#95—342no—
391#95—342no—
392#95—342no—
393#95—341no—
394#95C2×#59512yescomplemented
395C17C2×#129411yescharacteristic, complemented, Sylow
396C24—171no—
397C24—171no—
398C24—171no—
399C24—171no—
400C24—171no—
401C24—171no—
402C24—172no—
403C24—172no—
404C24—172no—
405C24—172no—
406C24—344no—
407C24—344no—
408C24C22⋊#59511yescharacteristic
409C22×C4—24no—
410C22×C4—22no—
411C22×C4—42no—
412C22×C4—42no—
413C22×C4—42no—
414C22×C4—171no—
415C22×C4—171no—
416C22×C4—171no—
417C22×C4—171no—
418C22×C4—171no—
419C22×C4—171no—
420C22×C4—171no—
421C22×C4—171no—
422C22×C4—171no—
423C22×C4—171no—
424C22×C4—171no—
425C22×C4—171no—
426C22×C4—171no—
427C22×C4—171no—
428C22×C4—171no—
429C22×C4—171no—
430C22×C4—171no—
431C22×C4—171no—
432C22×C4—171no—
433C22×C4—171no—
434C22×C4—171no—
435C22×C4—171no—
436C22×C4—344no—
437C22×C4—344no—
438C22×C4—348no—
439C22×C4—348no—
440C22×C4—344no—
441C22×C4—342no—
442C22×C4—344no—
443C22×C4—682no—
444C22×C4—682no—
445C22×C4—682no—
446C22×C4—682no—
447C22×C4—682no—
448C22×C4—682no—
449C22×C4—682no—
450C22×C4—682no—
451C22×C4—682no—
452C22×C4—682no—
453C22×C4—682no—
454C22×C4—684no—
455C22×C4—682no—
456C22×C4—684no—
457C22×C4—684no—
458C22×C4—6816no—
459C22×C4—6816no—
460C22×C4—682no—
461C22×C4—682no—
462C22×C4—682no—
463C22×C4—684no—
464C22×C4—684no—
465C22×C4—684no—
466C22×C4C4×#59511yescharacteristic
467C22×C4C4×#59511yescharacteristic
468C22×C4C4⋊#59511yescharacteristic
469C22×C4C4⋊#59511yescharacteristic
470C22×C4C22⋊#59511yescharacteristic
471C22×C4C22×#59511yescharacteristic
472C2×C8—344no—
473C2×C8—684no—
474C2×C8—684no—
475C2×C8—684no—
476C4⋊C4—684no—
477C4⋊C4—684no—
478C22⋊C4—682no—
479C22⋊C4—682no—
480C22⋊C4—684no—
481C23—22no—
482C23—22no—
483C23—171no—
484C23—171no—
485C23—174no—
486C23—172no—
487C23—172no—
488C23—174no—
489C23—171no—
490C23—171no—
491C23—171no—
492C23—172no—
493C23—171no—
494C23—171no—
495C23—172no—
496C23—171no—
497C23—172no—
498C23—172no—
499C23—172no—
500C23—172no—
501C23—172no—
502C23—172no—
503C23—342no—
504C23—342no—
505C23—342no—
506C23—342no—
507C23—348no—
508C23—348no—
509C23—342no—
510C23—342no—
511C23—348no—
512C23—348no—
513C23—342no—
514C23—342no—
515C23—342no—
516C23—342no—
517C23(C2×#595)⋊C411yescharacteristic
518C23(C2×#595)⋊C411yescharacteristic
519C23#1058754712yes—
520C23#1058754912yes—
521C23C2×C22⋊#59511yescharacteristic
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—24no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—48no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—171no—
533C2×C4—171no—
534C2×C4—171no—
535C2×C4—171no—
536C2×C4—342no—
537C2×C4—342no—
538C2×C4—342no—
539C2×C4—342no—
540C2×C4—342no—
541C2×C4—342no—
542C2×C4—342no—
543C2×C4—342no—
544C2×C4—342no—
545C2×C4—342no—
546C2×C4—344no—
547C2×C4—681no—
548C2×C4—681no—
549C2×C4—681no—
550C2×C4—681no—
551C2×C4—681no—
552C2×C4—681no—
553C2×C4—681no—
554C2×C4—681no—
555C2×C4—688no—
556C2×C4—6816no—
557C2×C4—688no—
558C2×C4—681no—
559C2×C4—681no—
560C2×C4—681no—
561C2×C4—681no—
562C2×C4—688no—
563C2×C4—682no—
564C2×C4—682no—
565C2×C4—684no—
566C2×C4—684no—
567C2×C4—684no—
568C2×C4—1368no—
569C2×C4(C2×#595)⋊C411yescharacteristic
570C2×C4(C2×#595)⋊C411yescharacteristic
571C2×C4C2×C4×#59511yescharacteristic
572C2×C4C2×C4⋊#59511yescharacteristic
573C8—684no—
574C22—24no—
575C22—24no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—178no—
581C22—178no—
582C22—172no—
583C22—172no—
584C22—171no—
585C22—172no—
586C22—171no—
587C22—172no—
588C22—172no—
589C22—172no—
590C22—171no—
591C22—171no—
592C22—342no—
593C22—344no—
594C22—342no—
595C22—342no—
596C22—344no—
597C22—342no—
598C22—344no—
599C22—344no—
600C22—344no—
601C22—344no—
602C22—344no—
603C22—344no—
604C22—341no—
605C22—341no—
606C22—341no—
607C22—341no—
608C22#1176368012yes—
609C22#1176368212yes—
610C22#1176368212yes—
611C22#1176368612yes—
612C22C2×(C2×#595)⋊C411yescharacteristic
613C22C2×#1058754711yescharacteristic
614C22C2×#1058754911yescharacteristic
615C4—21no—
616C4—21no—
617C4—21no—
618C4—21no—
619C4—44no—
620C4—341no—
621C4—341no—
622C4—341no—
623C4—341no—
624C4—684no—
625C4—1364no—
626C2—21no—
627C2—21no—
628C2—22no—
629C2—172no—
630C2—174no—
631C2—172no—
632C2—342no—
633C2—341no—
634C2—341no—
635C2#1454365814yesdirect product factor
636C2C2×#1176368011yescharacteristic
637C2C2×#1176368211yescharacteristic
638C2C2×#1176368611yescharacteristic
subgroupG/H
centerC23(C2×#595)⋊C4
commutatorC2×C4×C17C2×C42
FrattiniC22×C4C22×#595
FittingC2×C17×#95C4
socleC23×C17#95
prime radicalC24×D17D4
cosocleC22×C4×D17C23
hypercenterC2×#95#595
hypocenterC17C2×#1294
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
3. #14543658C2direct (N × H)
6. C22×C4⋊#595C4semidirect
8. C2×#10587543C4semidirect
11. #11763777C4semidirect
16. #11763751C4semidirect
22. C2×#10587502C4semidirect
25. #95×D17C4semidirect
27. C2×C17×#95C4semidirect
60. C2×C4⋊#595C2×C4semidirect
69. #10587543C2×C4semidirect
71. C17×#95C2×C4semidirect
75. #10587502C2×C4semidirect
333. C2×#95#595semidirect
337. C2×C17#1294semidirect
344. D17#1294semidirect
394. #95C2×#595semidirect
395. C17C2×#1294semidirect
635. C2#14543658direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117637772
C2×#117637512
#145436582
C2×#95×D172
C2×#129417