Finite Group Databasebeta

← #17964278

Subgroups — #17964278

Order 4352.

1246 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14545461C212yesmaximal, complemented
2#14544046C212yesmaximal, complemented
3#14544043C212yesmaximal, complemented
4#14544041C212yesmaximal, complemented
5#14544039C212yesmaximal, complemented
6#14544017C212yesmaximal, complemented
7#14544015C212yesmaximal, complemented
8C2×C4×#63252C211yesmaximal, characteristic
9#11763831—22no—
10#11763830C2214yes—
11#11763828—22no—
12#11763825C2214yes—
13#11763813—22no—
14#11763780C2214yes—
15C4×#63243—22no—
16#11763655C2214yes—
17#11763654C2214yes—
18#11763653C2214yes—
19#11763652C2214yes—
20C22×#63252C411yescharacteristic
21C4×#63252—22no—
22C4×#63252—22no—
23C4×#63252—22no—
24C4×#63252—22no—
25C2×C4×Dic34C411yescharacteristic
26C2×C4×Dic34C2211yescharacteristic
27C2×C4×D68C411yescharacteristic
28C2×C4×D68C2211yescharacteristic
29C2×C4×C22⋊D17C411yescharacteristic
30C2×C4×C22⋊D17C411yescharacteristic
31C2×C4×C22⋊D17C2211yescharacteristic
32C2×C4×C22⋊D17C2211yescharacteristic
33C2×#10587612C2211yescharacteristic
34C2×#10587558C411yescharacteristic
35C2×#10587558C2211yescharacteristic
36C2×C42×D17C411yescharacteristic
37C2×C42×D17C2211yescharacteristic
38C22×C42×C17C411yescharacteristic
39C23×C4×C17C2×C411yescharacteristic
40C23×C4×C17C2×C411yescharacteristic
41C23×C4×C17C2×C411yescharacteristic
42C22×C22⋊D17C2×C411yescharacteristic
43C22×C22⋊D17C2×C411yescharacteristic
44C2×#63252—24no—
45C2×#63252—22no—
46C2×#63252—22no—
47C2×#63252—24no—
48C22×D68C2×C411yescharacteristic
49C22×C4×D17C2×C411yescharacteristic
50C22×C4×D17C2×C411yescharacteristic
51C22×C4×D17C2×C411yescharacteristic
52C22×C4×D17C2×C411yescharacteristic
53C22×C4×D17C2×C411yescharacteristic
54C22×C4×D17C2311yescharacteristic
55C22×Dic34C2×C411yescharacteristic
56C2×#63243—24no—
57C2×C42×C17—21no—
58C2×C42×C17—21no—
59C2×C42×C17—21no—
60C2×C42×C17—21no—
61C2×C42×C17C2×C411yescharacteristic
62C2×C42×C17C2×C411yescharacteristic
63C2×C42×C17C2×C411yescharacteristic
64C2×C42×C17C2×C411yescharacteristic
65C2×C22⋊Dic17C2×C411yescharacteristic
66C2×C22⋊Dic17C2311yescharacteristic
67C4×C22⋊D17—22no—
68C4×C22⋊D17—22no—
69C4×C22⋊D17—22no—
70C4×C22⋊D17—22no—
71C4×C22⋊D17—22no—
72C4×C22⋊D17—22no—
73C4×C22⋊D17—22no—
74C4×C22⋊D17—22no—
75C2×#63227C2×C411yescharacteristic
76C2×#63227C2×C411yescharacteristic
77C2×#63227C2×C411yescharacteristic
78C2×#63227C2311yescharacteristic
79#10587612—22no—
80#10587612—22no—
81C2×C4⋊Dic17C2×C411yescharacteristic
82C2×C4⋊Dic17C2311yescharacteristic
83C2×#63225C2×C411yescharacteristic
84C2×#63225C2×C411yescharacteristic
85C2×#63225C2×C411yescharacteristic
86C2×#63225C2311yescharacteristic
87C2×C4×Dic17C2×C411yescharacteristic
88C2×C4×Dic17C2×C411yescharacteristic
89C2×C4×Dic17C2×C411yescharacteristic
90C2×C4×Dic17C2×C411yescharacteristic
91C2×C4×Dic17C2311yescharacteristic
92C2×C4×Dic17C2311yescharacteristic
93C4×D68—22no—
94C4×D68—22no—
95C4×D68—22no—
96C4×D68—22no—
97#10587558—22no—
98#10587558—22no—
99#10587558—22no—
100#10587558—22no—
101C42×D17—21no—
102C42×D17—21no—
103C42×D17—21no—
104C42×D17—21no—
105C42×D17D412yes—
106C42×D17D412yes—
107C42×D17D412yes—
108C42×D17D412yes—
109C4×Dic34—22no—
110C4×Dic34—22no—
111C4×Dic34—22no—
112C4×Dic34—22no—
113C22⋊#3624C2318yes—
114#10587543—24no—
115#10587542—24no—
116C4⋊#3624—24no—
117C4⋊#3624—24no—
118C4×#3624—24no—
119C24×C17C22×C411yescharacteristic
120C23×D17C22×C411yescharacteristic
121C23×D17C22×C411yescharacteristic
122C22×C4×C17—21no—
123C22×C4×C17—21no—
124C22×C4×C17—22no—
125C22×C4×C17—21no—
126C22×C4×C17—21no—
127C22×C4×C17—21no—
128C22×C4×C17—21no—
129C22×C4×C17—42no—
130C22×C4×C17—42no—
131C22×C4×C17M1614yescomplemented
132C22×C4×C17C22×C411yescharacteristic
133C22×C4×C17C22×C411yescharacteristic
134C22×C4×C17C22×C411yescharacteristic
135C22×C4×C17C22×C411yescharacteristic
136C22×C4×C17C22×C411yescharacteristic
137C22×C4×C17C22×C411yescharacteristic
138C2×C22⋊D17—22no—
139C2×C22⋊D17—22no—
140C2×C22⋊D17—22no—
141C2×C22⋊D17—22no—
142C2×C22⋊D17—22no—
143C2×C22⋊D17—22no—
144C22×Dic17C22×C411yescharacteristic
145C22×Dic17C22×C411yescharacteristic
146C22×Dic17C22×C411yescharacteristic
147C22×Dic17C22×C411yescharacteristic
148C22×Dic17C22×C411yescharacteristic
149C22×Dic17C2411yescharacteristic
150#63252—216no—
151#63252—216no—
152C2×D68—22no—
153C2×D68—22no—
154C2×D68—22no—
155C2×C4×D17—21no—
156C2×C4×D17—21no—
157C2×C4×D17—22no—
158C2×C4×D17—22no—
159C2×C4×D17—22no—
160C2×C4×D17—21no—
161C2×C4×D17—21no—
162C2×C4×D17—21no—
163C2×C4×D17—21no—
164C2×C4×D17—42no—
165C2×C4×D17—42no—
166C2×C4×D17—42no—
167C2×C4×D17—42no—
168C2×C4×D17C22⋊C412yes—
169C2×C4×D17C22⋊C412yes—
170C2×C4×D17C22⋊C412yes—
171C2×C4×D17C22⋊C412yes—
172C2×C4×D17M1614yescomplemented
173C2×C4×D17C2×D412yes—
174C2×C4×D17C2×D412yes—
175C2×Dic34—22no—
176C2×Dic34—22no—
177C2×Dic34—22no—
178C2×#3624—28no—
179#63243—48no—
180C42×C17—21no—
181C42×C17—21no—
182C42×C17—21no—
183C42×C17—21no—
184C42×C17—21no—
185C42×C17—21no—
186C42×C17C22⋊C411yescharacteristic
187C42×C17C22⋊C411yescharacteristic
188C42×C17C22⋊C411yescharacteristic
189C42×C17C22⋊C411yescharacteristic
190C22⋊Dic17—22no—
191C22⋊Dic17—22no—
192#63227—22no—
193#63227—22no—
194#63227—22no—
195#63227—22no—
196C4⋊Dic17—22no—
197C4⋊Dic17—22no—
198#63225—22no—
199#63225—22no—
200#63225—22no—
201#63225—22no—
202C4×Dic17—21no—
203C4×Dic17—21no—
204C4×Dic17—21no—
205C4×Dic17—21no—
206C4×Dic17—21no—
207C4×Dic17—21no—
208C4×Dic17C22⋊C412yes—
209C4×Dic17C22⋊C412yes—
210C4×Dic17C2×D412yes—
211C4×Dic17C2×D412yes—
212C4×Dic17C2×D412yes—
213C4×Dic17C2×D412yes—
214#17361—171nomaximal, Sylow
215C23×C17—21no—
216C23×C17—21no—
217C23×C17—41no—
218C23×C17—41no—
219C23×C17C2×M1612yes—
220C23×C17C23×C411yescharacteristic
221C22×D17—21no—
222C22×D17—21no—
223C22×D17—21no—
224C22×D17—21no—
225C22×D17—41no—
226C22×D17—41no—
227C22×D17—41no—
228C22×D17—41no—
229C22×D17C2×C22⋊C412yes—
230C22×D17C2×M1612yes—
231C2×C4×C17—21no—
232C2×C4×C17—21no—
233C2×C4×C17—24no—
234C2×C4×C17—24no—
235C2×C4×C17—22no—
236C2×C4×C17—22no—
237C2×C4×C17—21no—
238C2×C4×C17—21no—
239C2×C4×C17—42no—
240C2×C4×C17—42no—
241C2×C4×C17—42no—
242C2×C4×C17—42no—
243C2×C4×C17—41no—
244C2×C4×C17—41no—
245C2×C4×C17C2×C22⋊C411yescharacteristic
246C2×C4×C17C2×C22⋊C411yescharacteristic
247C2×C4×C17C2×C22⋊C411yescharacteristic
248C2×C4×C17C2×C22⋊C411yescharacteristic
249C2×C4×C17C2×C22⋊C411yescharacteristic
250C2×C4×C17C2×C22⋊C411yescharacteristic
251C2×C4×C17C2×M1612yes—
252C2×C4×C17C2×M1612yes—
253C2×C4×C17C2×M1612yes—
254C22⋊D17—28no—
255C22⋊D17—28no—
256C2×Dic17—21no—
257C2×Dic17—21no—
258C2×Dic17—21no—
259C2×Dic17—21no—
260C2×Dic17—21no—
261C2×Dic17—21no—
262C2×Dic17—41no—
263C2×Dic17—41no—
264C2×Dic17—41no—
265C2×Dic17—41no—
266C2×Dic17C2×C22⋊C412yes—
267C2×Dic17C2×C22⋊C412yes—
268C2×Dic17C2×M1612yes—
269C2×Dic17C22×D412yes—
270D68—28no—
271C4×D17—24no—
272C4×D17—24no—
273C4×D17—24no—
274C4×D17—24no—
275C4×D17—24no—
276C4×D17—24no—
277C4×D17—42no—
278C4×D17—42no—
279C4×D17—42no—
280C4×D17—42no—
281C4×D17—42no—
282C4×D17—42no—
283Dic34—28no—
284#3624—48no—
285C2×C4×#41—171no—
286#2920—172no—
287#1467—172no—
288#1466—172no—
289#1465—172no—
290#1465—172no—
291#1458—172no—
292#1458—172no—
293C22×C17—21no—
294C22×C17—21no—
295C22×C17—22no—
296C22×C17—42no—
297C22×C17—42no—
298C22×C17—41no—
299C22×C17—41no—
300C22×C17C22×C22⋊C411yescharacteristic
301C22×C17C22×M1611yescharacteristic
302C22×C17C22×M1611yescharacteristic
303C2×D17—22no—
304C2×D17—22no—
305C2×D17—22no—
306C2×D17—22no—
307C2×D17—42no—
308C2×D17—42no—
309C2×D17—42no—
310C2×D17—41no—
311C2×D17—41no—
312C2×D17—42no—
313C4×C17—22no—
314C4×C17—21no—
315C4×C17—21no—
316C4×C17—41no—
317C4×C17—41no—
318C4×C17#40712yes—
319C4×C17#40712yes—
320C4×C17#41012yes—
321C4×C17#41312yes—
322Dic17—22no—
323Dic17—22no—
324Dic17—22no—
325Dic17—22no—
326Dic17—41no—
327Dic17—41no—
328C22×#41—171no—
329C4×#41—342no—
330C4×#41—342no—
331C4×#41—342no—
332C4×#41—342no—
333C2×C4×Q8—171no—
334C2×C4×Q8—171no—
335C2×C4×D4—171no—
336C2×C4×D4—171no—
337C2×C4×D4—171no—
338C2×C4×D4—171no—
339C2×C4×D4—171no—
340C2×C4×D4—171no—
341C2×#117—171no—
342C2×#117—171no—
343C2×#117—171no—
344C22×C42—171no—
345C22×C42—171no—
346C22×C42#59511yescharacteristic
347#432—174no—
348#432—342no—
349#431—174no—
350#431—342no—
351#423—342no—
352#407—174no—
353C4×M16—342no—
354#324—174no—
355#324—174no—
356#323—174no—
357#323—174no—
358C2×C17—21no—
359C2×C17—21no—
360C2×C17—42no—
361C2×C17C2×#40711yescharacteristic
362C2×C17C2×#41011yescharacteristic
363C2×C17C2×#41311yescharacteristic
364D17—42no—
365D17—42no—
366C2×#41—342no—
367C2×#41—342no—
368C2×#41—344no—
369C2×#41—344no—
370C22×Q8—171no—
371C22×D4—171no—
372C22×D4—171no—
373C22×D4—171no—
374C23×C4—171no—
375C23×C4—171no—
376C23×C4—171no—
377C23×C4—171no—
378C23×C4—171no—
379C23×C4—171no—
380C23×C4C2×#59511yescharacteristic
381C23×C4C2×#59511yescharacteristic
382C23×C4C2×#59511yescharacteristic
383C2×M16—344no—
384C4×Q8—342no—
385C4×Q8—342no—
386C4×Q8—342no—
387C4×Q8—342no—
388C4×D4—342no—
389C4×D4—342no—
390C4×D4—342no—
391C4×D4—342no—
392C4×D4—342no—
393C4×D4—342no—
394C4×D4—342no—
395C4×D4—342no—
396C4×D4—342no—
397C4×D4—342no—
398C4×D4—342no—
399C4×D4—342no—
400#117—342no—
401#117—342no—
402#117—342no—
403#117—342no—
404#117—342no—
405#117—342no—
406C2×C4⋊C4—171no—
407C2×C4⋊C4—171no—
408C2×C4⋊C4—171no—
409C2×C4⋊C4—171no—
410C2×C4⋊C4—171no—
411C2×C4⋊C4—171no—
412C2×C22⋊C4—171no—
413C2×C22⋊C4—171no—
414C2×C22⋊C4—171no—
415C2×C22⋊C4—171no—
416C2×C22⋊C4—171no—
417C2×C22⋊C4—171no—
418C2×C42—21no—
419C2×C42—21no—
420C2×C42—21no—
421C2×C42—21no—
422C2×C42—171no—
423C2×C42—171no—
424C2×C42—171no—
425C2×C42—172no—
426C2×C42—172no—
427C2×C42—172no—
428C2×C42—172no—
429C2×C42—171no—
430C2×C42—171no—
431C2×C42—171no—
432C2×C42—341no—
433C2×C42—341no—
434C2×C42—341no—
435C2×C42—341no—
436C2×C42C2×#59511yescharacteristic
437C2×C42C2×#59511yescharacteristic
438C2×C42C2×#59511yescharacteristic
439C2×C42C2×#59511yescharacteristic
440C4⋊C8—344no—
441C4⋊C8—344no—
442C22⋊C8—178no—
443C22⋊C8—344no—
444#97—344no—
445C4×C8—344no—
446C17#1736111yescharacteristic, complemented, Sylow
447C24—171no—
448C24—171no—
449C24C22×#59511yescharacteristic
450#41—3416no—
451#41—3416no—
452C2×Q8—342no—
453C2×Q8—342no—
454C2×Q8—342no—
455C2×D4—342no—
456C2×D4—342no—
457C2×D4—342no—
458C2×D4—342no—
459C2×D4—342no—
460C2×D4—342no—
461C2×D4—342no—
462C2×D4—342no—
463C2×D4—342no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4—171no—
474C22×C4—171no—
475C22×C4—171no—
476C22×C4—171no—
477C22×C4—174no—
478C22×C4—172no—
479C22×C4—172no—
480C22×C4—172no—
481C22×C4—172no—
482C22×C4—172no—
483C22×C4—172no—
484C22×C4—171no—
485C22×C4—171no—
486C22×C4—342no—
487C22×C4—342no—
488C22×C4—342no—
489C22×C4—341no—
490C22×C4—341no—
491C22×C4—341no—
492C22×C4—341no—
493C22×C4—341no—
494C22×C4—341no—
495C22×C4—682no—
496C22×C4—682no—
497C22×C4—682no—
498C22×C4—682no—
499C22×C4#6324314yescomplemented
500C22×C4C22×#59511yescharacteristic
501C22×C4C22×#59511yescharacteristic
502C22×C4C22×#59511yescharacteristic
503C22×C4C22×#59511yescharacteristic
504C22×C4C22×#59511yescharacteristic
505C22×C4C22×#59511yescharacteristic
506M16—688no—
507C2×C8—348no—
508C4⋊C4—342no—
509C4⋊C4—342no—
510C4⋊C4—342no—
511C4⋊C4—342no—
512C4⋊C4—342no—
513C4⋊C4—342no—
514C22⋊C4—342no—
515C22⋊C4—342no—
516C22⋊C4—342no—
517C22⋊C4—342no—
518C22⋊C4—342no—
519C22⋊C4—342no—
520C42—21no—
521C42—21no—
522C42—21no—
523C42—21no—
524C42—21no—
525C42—21no—
526C42—172no—
527C42—172no—
528C42—172no—
529C42—172no—
530C42—172no—
531C42—172no—
532C42—341no—
533C42—341no—
534C42—341no—
535C42—341no—
536C42—341no—
537C42—341no—
538C42C22⋊#59511yescharacteristic
539C42C22⋊#59511yescharacteristic
540C42C22⋊#59511yescharacteristic
541C42C22⋊#59511yescharacteristic
542C23—21no—
543C23—21no—
544C23—41no—
545C23—41no—
546C23—172no—
547C23—172no—
548C23—341no—
549C23—341no—
550C23—341no—
551C23—341no—
552C23—681no—
553C23—681no—
554C23—681no—
555C23—681no—
556C23C2×#6324312yes—
557C23C23×#59511yescharacteristic
558Q8—348no—
559D4—348no—
560D4—348no—
561D4—348no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—172no—
577C2×C4—172no—
578C2×C4—172no—
579C2×C4—172no—
580C2×C4—341no—
581C2×C4—341no—
582C2×C4—341no—
583C2×C4—341no—
584C2×C4—344no—
585C2×C4—344no—
586C2×C4—344no—
587C2×C4—344no—
588C2×C4—344no—
589C2×C4—344no—
590C2×C4—341no—
591C2×C4—341no—
592C2×C4—682no—
593C2×C4—682no—
594C2×C4—682no—
595C2×C4—682no—
596C2×C4—681no—
597C2×C4—681no—
598C2×C4—682no—
599C2×C4—682no—
600C2×C4—681no—
601C2×C4—681no—
602C2×C4C2×#6324312yes—
603C2×C4C2×#6324312yes—
604C2×C4D17⋊M1612yes—
605C2×C4C2×C22⋊#59511yescharacteristic
606C2×C4C2×C22⋊#59511yescharacteristic
607C2×C4C2×C22⋊#59511yescharacteristic
608C2×C4C2×C22⋊#59511yescharacteristic
609C2×C4C2×C22⋊#59511yescharacteristic
610C2×C4C2×C22⋊#59511yescharacteristic
611C8—688no—
612C22—21no—
613C22—21no—
614C22—22no—
615C22—42no—
616C22—42no—
617C22—41no—
618C22—41no—
619C22—342no—
620C22—342no—
621C22—342no—
622C22—342no—
623C22—682no—
624C22—682no—
625C22—682no—
626C22—682no—
627C22—681no—
628C22—681no—
629C22C22×C22⋊#59511yescharacteristic
630C22C2×D17⋊M1611yescharacteristic
631C22C22×#6324311yescharacteristic
632C4—22no—
633C4—21no—
634C4—21no—
635C4—41no—
636C4—41no—
637C4—342no—
638C4—342no—
639C4—342no—
640C4—342no—
641C4—681no—
642C4—681no—
643C4#1176378012yes—
644C4#1176378012yes—
645C4#1176378812yes—
646C4#1176379512yes—
647C2—21no—
648C2—21no—
649C2—42no—
650C2—682no—
651C2—682no—
652C2C2×#1176378011yescharacteristic
653C2C2×#1176378811yescharacteristic
654C2C2×#1176379511yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#595
commutatorC23×C17C23×C4
FrattiniC23C23×#595
FittingC22×C42×C17C4
socleC22×C17C22×C22⋊C4
prime radicalC22×#63252C4
cosocleC22×Dic17C24
hypercenterC22×C42#595
hypocenterC17#17361
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
1. #14545461C2semidirect
2. #14544046C2semidirect
3. #14544043C2semidirect
4. #14544041C2semidirect
5. #14544039C2semidirect
6. #14544017C2semidirect
7. #14544015C2semidirect
131. C22×C4×C17M16semidirect
172. C2×C4×D17M16semidirect
446. C17#17361semidirect
499. C22×C4#63243semidirect

Maximal subgroups

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

subgroupindex
#145454612
#145440462
#145440432
#145440412
#145440392
#145440172
#145440152
C2×C4×#632522
#1736117