Finite Group Databasebeta

← #17969447

Subgroups — #17969447

Order 4352.

2038 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763828C212yesmaximal, complemented
2#14544676C212yesmaximal, complemented
3#14544639C212yesmaximal, complemented
4#14544638C212yesmaximal, complemented
5#14544607C212yesmaximal
6C4×#10587543C212yesmaximal, complemented
7C4×C22⋊#3624C212yesmaximal, complemented
8C22×C42×D17C211yesmaximal, characteristic
9#11763828—28no—
10C2×C4⋊#3624C2214yescomplemented
11C2×#10587543C2214yes—
12C2×#10587543C2214yes—
13C2×C22⋊#3624C2214yes—
14C2×C4×#3624C2214yescomplemented
15#11763675C2214yescomplemented
16#11763675C2214yescomplemented
17C23×C4×D17C411yescharacteristic
18C23×C4×D17C411yescharacteristic
19C23×C4×D17C2211yescharacteristic
20C22×C4×Dic17C411yescharacteristic
21C22×C4×Dic17C2211yescharacteristic
22C22×C4×Dic17C2211yescharacteristic
23C2×C42×D17—28no—
24C2×C42×D17C411yescharacteristic
25C2×C42×D17C411yescharacteristic
26C2×C42×D17C411yescharacteristic
27C2×C42×D17C411yescharacteristic
28C2×C42×D17C2211yescharacteristic
29C2×C42×D17C2211yescharacteristic
30C2×C42×D17C2211yescharacteristic
31C2×C42×D17C2211yescharacteristic
32C22×C42×C17C411yescharacteristic
33C24×D17C2×C411yescharacteristic
34C23×C4×C17C2×C411yescharacteristic
35C23×C4×C17C2×C411yescharacteristic
36C23×C4×C17C2×C411yescharacteristic
37C23×Dic17C2×C411yescharacteristic
38C23×Dic17C2×C411yescharacteristic
39C23×Dic17C2311yescharacteristic
40C22×C4×D17—24no—
41C22×C4×D17—24no—
42C22×C4×D17—24no—
43C22×C4×D17—24no—
44C22×C4×D17—24no—
45C22×C4×D17—24no—
46C22×C4×D17—24no—
47C22×C4×D17—24no—
48C22×C4×D17C818yescomplemented
49C22×C4×D17C2×C411yescharacteristic
50C22×C4×D17C2×C411yescharacteristic
51C22×C4×D17C2×C411yescharacteristic
52C22×C4×D17C2×C411yescharacteristic
53C22×C4×D17C2×C411yescharacteristic
54C22×C4×D17C2×C411yescharacteristic
55C22×C4×D17C2×C411yescharacteristic
56C22×C4×D17C2×C411yescharacteristic
57C22×C4×D17C2×C411yescharacteristic
58C22×C4×D17C2×C411yescharacteristic
59C22×C4×D17C2311yescharacteristic
60C22×C4×D17C2311yescharacteristic
61C22×#3624C2318yes—
62C2×C42×C17—24no—
63C2×C42×C17C2×C411yescharacteristic
64C2×C42×C17C2×C411yescharacteristic
65C2×C42×C17C2×C411yescharacteristic
66C2×C42×C17C2×C411yescharacteristic
67C2×C4×Dic17—24no—
68C2×C4×Dic17—24no—
69C2×C4×Dic17—24no—
70C2×C4×Dic17C2×C411yescharacteristic
71C2×C4×Dic17C2×C411yescharacteristic
72C2×C4×Dic17C2×C411yescharacteristic
73C2×C4×Dic17C2×C411yescharacteristic
74C2×C4×Dic17C2×C411yescharacteristic
75C2×C4×Dic17C2×C411yescharacteristic
76C2×C4×Dic17C2×C411yescharacteristic
77C2×C4×Dic17C2×C411yescharacteristic
78C2×C4×Dic17C2311yescharacteristic
79C2×C4×Dic17C2311yescharacteristic
80C2×C4×Dic17C2311yescharacteristic
81C2×C4×Dic17C2311yescharacteristic
82C42×D17—24no—
83C42×D17—24no—
84C42×D17—24no—
85C42×D17—24no—
86C42×D17—24no—
87C42×D17—24no—
88C42×D17—24no—
89C42×D17D418yes—
90C22⋊#3624—28no—
91#10587543—28no—
92#10587543—28no—
93C4⋊#3624—28no—
94C4×#3624—28no—
95C24×C17C22×C411yescharacteristic
96C23×D17—22no—
97C23×D17—22no—
98C23×D17—22no—
99C23×D17—22no—
100C23×D17—22no—
101C23×D17—22no—
102C23×D17C2×C814yes—
103C23×D17C22×C411yescharacteristic
104C23×D17C22×C411yescharacteristic
105C22×C4×C17—22no—
106C22×C4×C17—22no—
107C22×C4×C17—22no—
108C22×C4×C17—22no—
109C22×C4×C17—22no—
110C22×C4×C17—22no—
111C22×C4×C17—22no—
112C22×C4×C17C2×C814yes—
113C22×C4×C17M1614yes—
114C22×C4×C17C22×C411yescharacteristic
115C22×C4×C17C22×C411yescharacteristic
116C22×C4×C17C22×C411yescharacteristic
117C22×C4×C17C22×C411yescharacteristic
118C22×C4×C17C22×C411yescharacteristic
119C22×C4×C17C22×C411yescharacteristic
120C22×Dic17—22no—
121C22×Dic17—22no—
122C22×Dic17—22no—
123C22×Dic17—22no—
124C22×Dic17—22no—
125C22×Dic17—22no—
126C22×Dic17—22no—
127C22×Dic17C2×C814yes—
128C22×Dic17C22×C411yescharacteristic
129C22×Dic17C22×C411yescharacteristic
130C22×Dic17C22×C411yescharacteristic
131C22×Dic17C22×C411yescharacteristic
132C22×Dic17C22×C411yescharacteristic
133C22×Dic17#4114yes—
134C22×Dic17C2411yescharacteristic
135C2×C4×D17—232no—
136C2×C4×D17—232no—
137C2×C4×D17—22no—
138C2×C4×D17—22no—
139C2×C4×D17—22no—
140C2×C4×D17—22no—
141C2×C4×D17—22no—
142C2×C4×D17—22no—
143C2×C4×D17—22no—
144C2×C4×D17—22no—
145C2×C4×D17—22no—
146C2×C4×D17—22no—
147C2×C4×D17—22no—
148C2×C4×D17—22no—
149C2×C4×D17—22no—
150C2×C4×D17—22no—
151C2×C4×D17—22no—
152C2×C4×D17—22no—
153C2×C4×D17—22no—
154C2×C4×D17—22no—
155C2×C4×D17—22no—
156C2×C4×D17—22no—
157C2×C4×D17—22no—
158C2×C4×D17—22no—
159C2×C4×D17—22no—
160C2×C4×D17—22no—
161C2×C4×D17—22no—
162C2×C4×D17—22no—
163C2×C4×D17—232no—
164C2×C4×D17C22⋊C414yes—
165C2×C4×D17C22⋊C414yes—
166C2×C4×D17C2×C814yes—
167C2×C4×D17C2×C814yes—
168C2×C4×D17C2×C814yes—
169C2×C4×D17C2×C814yes—
170C2×C4×D17M1614yes—
171C2×C4×D17M1614yes—
172C2×C4×D17C2×D414yes—
173C2×C4×D17#4114yes—
174C2×#3624—28no—
175C2×#3624—28no—
176C2×#3624—28no—
177C42×C17—22no—
178C42×C17—22no—
179C42×C17—22no—
180C42×C17C22⋊C414yes—
181C4×Dic17—22no—
182C4×Dic17—22no—
183C4×Dic17—22no—
184C4×Dic17—22no—
185C4×Dic17—22no—
186C4×Dic17—22no—
187C4×Dic17—22no—
188C4×Dic17—22no—
189C4×Dic17—22no—
190C4×Dic17C22⋊C414yes—
191C4×Dic17C2×D414yes—
192C4×Dic17C2×D414yes—
193#20714—171nomaximal, Sylow
194C23×C17—21no—
195C23×C17—21no—
196C23×C17—21no—
197C23×C17—21no—
198C23×C17#11712yes—
199C23×C17C22×C812yes—
200C23×C17C2×M1612yes—
201C23×C17C23×C411yescharacteristic
202C22×D17—28no—
203C22×D17—28no—
204C22×D17—28no—
205C22×D17—28no—
206C22×D17—21no—
207C22×D17—21no—
208C22×D17—21no—
209C22×D17—21no—
210C22×D17—21no—
211C22×D17—21no—
212C22×D17—21no—
213C22×D17—21no—
214C22×D17—28no—
215C22×D17—28no—
216C22×D17—28no—
217C22×D17C2×C22⋊C412yes—
218C22×D17#11712yes—
219C22×D17C22×C812yes—
220C22×D17C22×C812yes—
221C22×D17C2×M1612yes—
222C22×D17C2×M1612yes—
223C2×C4×C17—28no—
224C2×C4×C17—21no—
225C2×C4×C17—21no—
226C2×C4×C17—21no—
227C2×C4×C17—21no—
228C2×C4×C17—21no—
229C2×C4×C17—21no—
230C2×C4×C17—21no—
231C2×C4×C17—21no—
232C2×C4×C17—28no—
233C2×C4×C17—28no—
234C2×C4×C17C2×C22⋊C412yes—
235C2×C4×C17C2×C22⋊C412yes—
236C2×C4×C17C2×C22⋊C412yes—
237C2×C4×C17#11712yes—
238C2×C4×C17C22×C812yes—
239C2×C4×C17C22×C812yes—
240C2×C4×C17C2×M1612yes—
241C2×C4×C17C2×M1612yes—
242C2×C4×C17C2×M1612yes—
243C2×C4×C17C2×M1612yes—
244C2×Dic17—28no—
245C2×Dic17—21no—
246C2×Dic17—21no—
247C2×Dic17—21no—
248C2×Dic17—21no—
249C2×Dic17—21no—
250C2×Dic17—21no—
251C2×Dic17—21no—
252C2×Dic17—21no—
253C2×Dic17—28no—
254C2×Dic17—28no—
255C2×Dic17C2×C22⋊C412yes—
256C2×Dic17C2×C22⋊C412yes—
257C2×Dic17#11712yes—
258C2×Dic17C22×C812yes—
259C2×Dic17C22×C812yes—
260C2×Dic17C2×M1612yes—
261C2×Dic17C2×M1612yes—
262C2×Dic17C22×D412yes—
263C2×Dic17C2×#4112yes—
264C2×Dic17C2×#4112yes—
265C4×D17—28no—
266C4×D17—28no—
267C4×D17—28no—
268C4×D17—28no—
269C4×D17—28no—
270C4×D17—28no—
271C4×D17—28no—
272C4×D17—28no—
273C4×D17—28no—
274C4×D17—28no—
275C4×D17—28no—
276C4×D17C22⋊C8116yescomplemented
277#3624—48no—
278C23×C42—171no—
279C2×#431—172no—
280#1817—172no—
281#1797—172no—
282#1797—172no—
283#1779—172no—
284C4×C22⋊C8—172no—
285C4×C22⋊C8—172no—
286C22×C17—22no—
287C22×C17—22no—
288C22×C17—22no—
289C22×C17—22no—
290C22×C17—22no—
291C22×C17—22no—
292C22×C17#43114yescomplemented
293C22×C17C22×C22⋊C411yescharacteristic
294C22×C17C2×#11711yescharacteristic
295C22×C17C2×#11711yescharacteristic
296C22×C17C23×C811yescharacteristic
297C22×C17C22×M1611yescharacteristic
298C22×C17C22×M1611yescharacteristic
299C22×C17C22×M1611yescharacteristic
300C2×D17—232no—
301C2×D17—22no—
302C2×D17—22no—
303C2×D17—22no—
304C2×D17—22no—
305C2×D17—22no—
306C2×D17—22no—
307C2×D17—22no—
308C2×D17—22no—
309C2×D17—22no—
310C2×D17—22no—
311C2×D17—22no—
312C2×D17—22no—
313C2×D17C2×C22⋊C814yes—
314C2×D17#43114yescomplemented
315C4×C17—22no—
316C4×C17—22no—
317C4×C17—22no—
318C4×C17—22no—
319C4×C17C2×C22⋊C814yes—
320C4×C17#40714yes—
321Dic17—22no—
322Dic17—22no—
323Dic17—22no—
324Dic17—22no—
325Dic17C2×C22⋊C814yes—
326Dic17#52514yes—
327C24×C4—171no—
328C24×C4—171no—
329C24×C4—171no—
330C22×C42—171no—
331C22×C42—171no—
332C22×C42—171no—
333C22×C42—171no—
334C22×C42—171no—
335C22×C42—171no—
336C22×C42—171no—
337C22×C42—171no—
338C22×C42—171no—
339C22×C42—171no—
340C22×C42—171no—
341C22×C42—348no—
342C22×C42#59511yescharacteristic
343#431—348no—
344C2×C4⋊C8—174no—
345C2×C22⋊C8—174no—
346C2×C22⋊C8—174no—
347C2×C22⋊C8—174no—
348C2×C4×C8—174no—
349#336—174no—
350#336—174no—
351C2×C17—24no—
352C2×C17#228011yescharacteristic
353C2×C17C22×C22⋊C811yescharacteristic
354C2×C17C2×#40711yescharacteristic
355C2×C17C2×#43111yescharacteristic
356C2×C17C2×#43111yescharacteristic
357C2×C17#292011yescharacteristic
358C2×C17#292011yescharacteristic
359D17—24no—
360D17—24no—
361C25—171no—
362C23×C4—171no—
363C23×C4—171no—
364C23×C4—171no—
365C23×C4—178no—
366C23×C4—171no—
367C23×C4—171no—
368C23×C4—171no—
369C23×C4—171no—
370C23×C4—171no—
371C23×C4—171no—
372C23×C4—171no—
373C23×C4—171no—
374C23×C4—171no—
375C23×C4—171no—
376C23×C4—171no—
377C23×C4—171no—
378C23×C4—344no—
379C23×C4—344no—
380C23×C4—344no—
381C23×C4—344no—
382C23×C4—344no—
383C23×C4—344no—
384C23×C4—344no—
385C23×C4—344no—
386C23×C4C2×#59511yescharacteristic
387C23×C4C2×#59511yescharacteristic
388C23×C4C2×#59511yescharacteristic
389C22×C8—178no—
390C2×C42—24no—
391C2×C42—171no—
392C2×C42—171no—
393C2×C42—171no—
394C2×C42—178no—
395C2×C42—171no—
396C2×C42—171no—
397C2×C42—171no—
398C2×C42—171no—
399C2×C42—171no—
400C2×C42—171no—
401C2×C42—171no—
402C2×C42—171no—
403C2×C42—171no—
404C2×C42—344no—
405C2×C42—344no—
406C2×C42—344no—
407C2×C42—344no—
408C2×C42—344no—
409C2×C42—344no—
410C2×C42—344no—
411C2×C42—344no—
412C2×C42—344no—
413C2×C42—344no—
414C2×C42C2×#59511yescharacteristic
415C2×C42C2×#59511yescharacteristic
416C2×C42C2×#59511yescharacteristic
417C2×C42C2×#59511yescharacteristic
418C4⋊C8—348no—
419C22⋊C8—348no—
420C22⋊C8—348no—
421C22⋊C8—348no—
422C4×C8—348no—
423C17#2071411yescharacteristic, complemented, Sylow
424C24—171no—
425C24—171no—
426C24—174no—
427C24—342no—
428C24—342no—
429C24—342no—
430C24—342no—
431C24—342no—
432C24—342no—
433C24C22×#59511yescharacteristic
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—171no—
442C22×C4—171no—
443C22×C4—174no—
444C22×C4—174no—
445C22×C4—174no—
446C22×C4—174no—
447C22×C4—174no—
448C22×C4—171no—
449C22×C4—171no—
450C22×C4—171no—
451C22×C4—171no—
452C22×C4—174no—
453C22×C4—174no—
454C22×C4—174no—
455C22×C4—174no—
456C22×C4—174no—
457C22×C4—174no—
458C22×C4—174no—
459C22×C4—342no—
460C22×C4—342no—
461C22×C4—342no—
462C22×C4—342no—
463C22×C4—342no—
464C22×C4—342no—
465C22×C4—342no—
466C22×C4—342no—
467C22×C4—342no—
468C22×C4—342no—
469C22×C4—3432no—
470C22×C4—342no—
471C22×C4—342no—
472C22×C4—342no—
473C22×C4—342no—
474C22×C4—342no—
475C22×C4—342no—
476C22×C4—3432no—
477C22×C4—3432no—
478C22×C4—342no—
479C22×C4—342no—
480C22×C4—342no—
481C22×C4—342no—
482C22×C4—342no—
483C22×C4—342no—
484C22×C4—342no—
485C22×C4—342no—
486C22×C4—342no—
487C22×C4—342no—
488C22×C4—342no—
489C22×C4—342no—
490C22×C4—342no—
491C22×C4—342no—
492C22×C4—342no—
493C22×C4—342no—
494C22×C4—342no—
495C22×C4#6324214yes—
496C22×C4#6324314yes—
497C22×C4C22×#59511yescharacteristic
498C22×C4C22×#59511yescharacteristic
499C22×C4C22×#59511yescharacteristic
500C22×C4C22×#59511yescharacteristic
501C22×C4C22×#59511yescharacteristic
502C22×C4C22×#59511yescharacteristic
503C2×C8—348no—
504C2×C8—348no—
505C2×C8—348no—
506C42—22no—
507C42—22no—
508C42—22no—
509C42—174no—
510C42—174no—
511C42—174no—
512C42—342no—
513C42—342no—
514C42—342no—
515C42—342no—
516C42—342no—
517C42—342no—
518C42—342no—
519C42—342no—
520C42—342no—
521C42C22⋊#59514yes—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—172no—
527C23—172no—
528C23—172no—
529C23—172no—
530C23—172no—
531C23—172no—
532C23—348no—
533C23—348no—
534C23—348no—
535C23—348no—
536C23—348no—
537C23—348no—
538C23—348no—
539C23—341no—
540C23—341no—
541C23—341no—
542C23—341no—
543C23—341no—
544C23—341no—
545C23—341no—
546C23—341no—
547C23C2×#6324212yes—
548C23C2×#6324312yes—
549C23#1058767712yes—
550C23C23×#59511yescharacteristic
551C2×C4—28no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—28no—
561C2×C4—28no—
562C2×C4—172no—
563C2×C4—172no—
564C2×C4—172no—
565C2×C4—172no—
566C2×C4—172no—
567C2×C4—172no—
568C2×C4—1716no—
569C2×C4—172no—
570C2×C4—172no—
571C2×C4—172no—
572C2×C4—172no—
573C2×C4—348no—
574C2×C4—348no—
575C2×C4—348no—
576C2×C4—348no—
577C2×C4—348no—
578C2×C4—348no—
579C2×C4—348no—
580C2×C4—348no—
581C2×C4—348no—
582C2×C4—348no—
583C2×C4—348no—
584C2×C4—341no—
585C2×C4—341no—
586C2×C4—341no—
587C2×C4—341no—
588C2×C4—341no—
589C2×C4—341no—
590C2×C4—341no—
591C2×C4—341no—
592C2×C4—348no—
593C2×C4—348no—
594C2×C4—348no—
595C2×C4C2×#6324212yes—
596C2×C4C2×#6324212yes—
597C2×C4C2×#6324312yes—
598C2×C4C2×#6324312yes—
599C2×C4D17⋊M1612yes—
600C2×C4D17⋊M1612yes—
601C2×C4#1058767712yes—
602C2×C4C2×C22⋊#59512yes—
603C2×C4C2×C22⋊#59512yes—
604C2×C4C2×C22⋊#59512yes—
605C8—688no—
606C22—22no—
607C22—22no—
608C22—22no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—174no—
613C22—174no—
614C22—3432no—
615C22—342no—
616C22—342no—
617C22—342no—
618C22—342no—
619C22—342no—
620C22—342no—
621C22—342no—
622C22—342no—
623C22—342no—
624C22—342no—
625C22—342no—
626C22—342no—
627C22#1176382814yescomplemented
628C22C22×C22⋊#59511yescharacteristic
629C22C2×#1058767711yescharacteristic
630C22C2×#1058767711yescharacteristic
631C22C22×#6324211yescharacteristic
632C22C2×D17⋊M1611yescharacteristic
633C22C2×D17⋊M1611yescharacteristic
634C22C22×#6324311yescharacteristic
635C4—22no—
636C4—22no—
637C4—22no—
638C4—22no—
639C4—174no—
640C4—174no—
641C4—342no—
642C4—342no—
643C4—342no—
644C4—342no—
645C4#1176377714yes—
646C4#1176378014yes—
647C2—24no—
648C2—344no—
649C2—344no—
650C2#1454522811yescharacteristic
651C2C2×#1176377711yescharacteristic
652C2C2×#1176378011yescharacteristic
653C2#1454544811yescharacteristic
654C2C2×#1176382811yescharacteristic
655C2#1454546111yescharacteristic
656C2#1454546211yescharacteristic
subgroupG/H
centerC22×C4C22×#595
commutatorC22×C17C23×C8
FrattiniC23C23×#595
FittingC22×C42×C17C4
socleC23×C17C23×C4
prime radicalC24×D17C2×C4
cosocleC22×Dic17C24
hypercenterC22×C42#595
hypocenterC17#20714
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
1. C2×#11763828C2semidirect
2. #14544676C2semidirect
3. #14544639C2semidirect
4. #14544638C2semidirect
6. C4×#10587543C2semidirect
7. C4×C22⋊#3624C2semidirect
10. C2×C4⋊#3624C22semidirect
14. C2×C4×#3624C22semidirect
15. #11763675C22semidirect
16. #11763675C22semidirect
48. C22×C4×D17C8semidirect
276. C4×D17C22⋊C8semidirect
292. C22×C17#431semidirect
314. C2×D17#431semidirect
423. C17#20714semidirect
627. C22#11763828semidirect

Maximal subgroups

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

subgroupindex
C2×#117638282
#145446762
#145446392
#145446382
#145446072
C4×#105875432
C4×C22⋊#36242
C22×C42×D172
#2071417