Finite Group Databasebeta

← #17951157

Subgroups — #17951157

Order 4352.

1130 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763777C211yesmaximal, characteristic
2C2×#11763751C211yesmaximal, characteristic
3#14543657C214yesmaximal, complemented
4C2×#11762666C211yesmaximal, characteristic
5C22×#63242—21no—
6C22×C4⋊#595—21no—
7C22×C22⋊#595—21no—
8C2×#10587543C2212yes—
9#11763777—22no—
10#11763777C414yescomplemented
11C2×C22⋊#3624—21no—
12#11763751—22no—
13#11763751C414yescomplemented
14C2×(C2×#595)⋊C4C2212yes—
15C23×C4×D17C2211yescharacteristic
16C22×C4⋊Dic17C411yescharacteristic, complemented
17C22×#63227—21no—
18#11762666—21no—
19#11762666—21no—
20#11762666C412yescomplemented
21#11762666C2212yes—
22C2×#10587502—21no—
23C22×C4⋊C4×C17C411yescharacteristic, complemented
24C24×D17D411yescharacteristic
25C23×#595—22no—
26C23×C4×C17—21no—
27C23×C4×C17C2×C411yescharacteristic
28C23×Dic17—21no—
29C23×Dic17D411yescharacteristic
30C22×C4×D17—42no—
31C22×C4×D17—42no—
32C22×C4×D17C2×C411yescharacteristic
33C22×C4×D17C2×C412yes—
34C22×C4×D17C2×C412yes—
35C22×C4×D17D411yescharacteristic
36C22×C4×D17D411yescharacteristic
37C22×C4×D17D412yes—
38C22×C4×D17Q812yes—
39C22×C4×D17C2311yescharacteristic
40C2×C22⋊#595—24no—
41C2×C22⋊#595—42no—
42C2×C22⋊#595—42no—
43C22×#3624—22no—
44C2×C4⋊#595—24no—
45C2×C4⋊#595—42no—
46C2×C4⋊#595—42no—
47C2×#63242—24no—
48C2×#63242—42no—
49C2×#63242—42no—
50C2×C4⋊C4×C17—21no—
51C2×C4⋊C4×C17—42no—
52C2×C4⋊C4×C17C2×C412yes—
53C2×#63227—22no—
54C2×#63227—22no—
55C2×#63227—42no—
56C2×#63227—42no—
57C2×C4⋊Dic17—21no—
58C2×C4⋊Dic17—42no—
59C2×C4⋊Dic17C2×C412yes—
60C22⋊#3624—24no—
61(C2×#595)⋊C4—22no—
62(C2×#595)⋊C4C2×C414yescomplemented
63#10587543—22no—
64#10587543C2×C414yescomplemented
65#10587502—22no—
66#10587502—22no—
67C24×C17C22⋊C411yescharacteristic
68C23×D17—41no—
69C23×D17—41no—
70C23×D17—41no—
71C23×D17—41no—
72C23×D17C22⋊C411yescharacteristic
73C23×D17C22⋊C412yes—
74C23×D17C4⋊C412yes—
75C23×D17D812yes—
76C23×D17SD1612yes—
77C23×D17SD1612yes—
78C23×D17Q1612yes—
79C23×D17C2×D411yescharacteristic
80C22×#595—24no—
81C22×#595—42no—
82C22×#595—42no—
83C22×#595—42no—
84C22×#595—42no—
85C22×#595—42no—
86C22×#595—42no—
87C22×C4×C17—22no—
88C22×C4×C17—22no—
89C22×C4×C17—22no—
90C22×C4×C17—42no—
91C22×C4×C17—42no—
92C22×C4×C17—42no—
93C22×C4×C17C4212yes—
94C22×C4×C17C22⋊C411yescharacteristic
95C22×C4×C17C4⋊C412yes—
96C22×C4×C17C22×C411yescharacteristic
97C22×Dic17—22no—
98C22×Dic17—41no—
99C22×Dic17—41no—
100C22×Dic17—42no—
101C22×Dic17—42no—
102C22×Dic17—42no—
103C22×Dic17C22⋊C411yescharacteristic
104C22×Dic17C22⋊C412yes—
105C22×Dic17C4⋊C412yes—
106C22×Dic17C2×D411yescharacteristic
107C2×C4×D17—22no—
108C2×C4×D17—22no—
109C2×C4×D17—22no—
110C2×C4×D17—22no—
111C2×C4×D17—44no—
112C2×C4×D17—44no—
113C2×C4×D17—44no—
114C2×C4×D17—44no—
115C2×C4×D17—41no—
116C2×C4×D17—41no—
117C2×C4×D17—41no—
118C2×C4×D17—41no—
119C2×C4×D17C4212yes—
120C2×C4×D17C22⋊C412yes—
121C2×C4×D17C22⋊C412yes—
122C2×C4×D17C4⋊C412yes—
123C2×C4×D17C4⋊C412yes—
124C2×C4×D17C4⋊C412yes—
125C2×C4×D17C22×C411yescharacteristic
126C2×C4×D17C22×C411yescharacteristic
127C2×C4×D17C2×D411yescharacteristic
128C2×C4×D17C2×Q811yescharacteristic
129C22⋊#595—48no—
130C2×#3624—24no—
131C2×#3624—42no—
132C2×#3624—42no—
133C4⋊#595—48no—
134#63242—48no—
135C4⋊C4×C17—42no—
136C4⋊C4×C17—42no—
137#63227—44no—
138#63227—42no—
139#63227—42no—
140C4⋊Dic17—42no—
141C4⋊Dic17—42no—
142#8023—171nomaximal, Sylow
143C23×C17—21no—
144C23×C17—21no—
145C23×C17—21no—
146C23×C17—21no—
147C23×C17#9512yes—
148C23×C17#10212yes—
149C23×C17#10312yes—
150C23×C17C2×C22⋊C411yescharacteristic
151C22×D17—21no—
152C22×D17—21no—
153C22×D17—21no—
154C22×D17—21no—
155C22×D17—21no—
156C22×D17—21no—
157C22×D17—21no—
158C22×D17—21no—
159C22×D17—42no—
160C22×D17—42no—
161C22×D17—42no—
162C22×D17—42no—
163C22×D17—42no—
164C22×D17—42no—
165C22×D17—42no—
166C22×D17—42no—
167C22×D17—42no—
168C22×D17—42no—
169C22×D17—42no—
170C22×D17—42no—
171C22×D17#9512yes—
172C22×D17#10212yes—
173C22×D17#10214yes—
174C22×D17#10312yes—
175C22×D17#10314yes—
176C22×D17#10614yes—
177C22×D17#10714yes—
178C22×D17C2×C22⋊C411yescharacteristic
179C22×D17C2×C4⋊C411yescharacteristic
180C22×D17C2×D811yescharacteristic
181C22×D17C2×SD1611yescharacteristic
182C22×D17C2×SD1611yescharacteristic
183C22×D17C2×Q1611yescharacteristic
184C2×#595—44no—
185C2×#595—44no—
186C2×#595—44no—
187C2×#595—82no—
188C2×#595—82no—
189C2×#595—82no—
190C2×#595—82no—
191C2×C4×C17—21no—
192C2×C4×C17—21no—
193C2×C4×C17—24no—
194C2×C4×C17—24no—
195C2×C4×C17—42no—
196C2×C4×C17—42no—
197C2×C4×C17—42no—
198C2×C4×C17—84no—
199C2×C4×C17#9512yes—
200C2×C4×C17#9912yes—
201C2×C4×C17#9912yes—
202C2×C4×C17C2×C4211yescharacteristic
203C2×C4×C17C2×C4⋊C411yescharacteristic
204C2×Dic17—21no—
205C2×Dic17—21no—
206C2×Dic17—21no—
207C2×Dic17—21no—
208C2×Dic17—42no—
209C2×Dic17—42no—
210C2×Dic17—42no—
211C2×Dic17—42no—
212C2×Dic17—42no—
213C2×Dic17—84no—
214C2×Dic17#9512yes—
215C2×Dic17C2×C22⋊C411yescharacteristic
216C2×Dic17C2×C4⋊C411yescharacteristic
217C4×D17—24no—
218C4×D17—24no—
219C4×D17—24no—
220C4×D17—24no—
221C4×D17—42no—
222C4×D17—42no—
223C4×D17—41no—
224C4×D17—41no—
225C4×D17—41no—
226C4×D17—41no—
227#3624—44no—
228C22×C22⋊C8—171no—
229C2×#380—171no—
230C2×#380—171no—
231#1294—174no—
232C22×C17—22no—
233C22×C17—22no—
234C22×C17—22no—
235C22×C17—22no—
236C22×C17—22no—
237C22×C17—22no—
238C22×C17#34014yes—
239C22×C17C2×#9511yescharacteristic
240C22×C17C2×#9911yescharacteristic
241C22×C17C2×#9911yescharacteristic
242C22×C17C2×#10211yescharacteristic
243C22×C17C2×#10311yescharacteristic
244C22×C17#42111yescharacteristic
245C22×C17#42111yescharacteristic
246C2×D17—21no—
247C2×D17—22no—
248C2×D17—21no—
249C2×D17—21no—
250C2×D17—22no—
251C2×D17—21no—
252C2×D17—21no—
253C2×D17—21no—
254C2×D17—22no—
255C2×D17—22no—
256C2×D17—21no—
257C2×D17—21no—
258C2×D17—21no—
259C2×D17—21no—
260C2×D17—22no—
261C2×D17—22no—
262C2×D17—21no—
263C2×D17—21no—
264C2×D17—44no—
265C2×D17—44no—
266C2×D17—44no—
267C2×D17—44no—
268C2×D17#34014yes—
269C2×D17C2×#10211yescharacteristic
270C2×D17C2×#10311yescharacteristic
271C2×D17C2×#10611yescharacteristic
272C2×D17C2×#10711yescharacteristic
273#595—84no—
274C4×C17—21no—
275C4×C17—21no—
276C4×C17—82no—
277C4×C17#34214yes—
278Dic17—21no—
279Dic17—22no—
280Dic17—21no—
281Dic17—82no—
282C24×C4—171no—
283C23×C8—341no—
284C22×C4⋊C4—171no—
285C22×C4⋊C4—341no—
286C22×C4⋊C4#59511yescharacteristic, complemented
287C22×C22⋊C4—341no—
288C22×C22⋊C4—341no—
289C2×C22⋊C8—172no—
290C2×C22⋊C8—174no—
291C2×C22⋊C8—341no—
292C2×C22⋊C8—342no—
293#380—174no—
294#380—172no—
295#380—172no—
296#380—341no—
297#380—341no—
298#380—342no—
299C2×#95—172no—
300C2×#95—341no—
301C2×C17—24no—
302C2×C17#151911yescharacteristic
303C2×C17#151911yescharacteristic
304C2×C17#152011yescharacteristic
305C2×C17#152011yescharacteristic
306C2×C17#173311yescharacteristic
307C2×C17C2×#34011yescharacteristic
308C2×C17C2×#34211yescharacteristic
309D17—21no—
310D17—24no—
311D17—21no—
312D17—21no—
313D17—21no—
314C25—171no—
315C23×C4—21no—
316C23×C4—171no—
317C23×C4—171no—
318C23×C4—171no—
319C23×C4—172no—
320C23×C4—172no—
321C23×C4—172no—
322C23×C4—172no—
323C23×C4—171no—
324C23×C4—171no—
325C23×C4—342no—
326C23×C4—341no—
327C23×C4—682no—
328C23×C4—682no—
329C23×C4C2×#59511yescharacteristic
330C22×C8—344no—
331C22×C8—342no—
332C22×C8—682no—
333C22×C8—682no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—42no—
336C2×C4⋊C4—172no—
337C2×C4⋊C4—344no—
338C2×C4⋊C4—341no—
339C2×C4⋊C4—682no—
340C2×C4⋊C4—682no—
341C2×C4⋊C4—682no—
342C2×C4⋊C4C2×#59512yes—
343C2×C22⋊C4—342no—
344C2×C22⋊C4—342no—
345C2×C22⋊C4—344no—
346C2×C22⋊C4—682no—
347C2×C22⋊C4—682no—
348C2×C22⋊C4—682no—
349C2×C22⋊C4—682no—
350C22⋊C8—174no—
351C22⋊C8—342no—
352C22⋊C8—344no—
353#95—174no—
354#95—342no—
355#95—342no—
356#95—342no—
357C17#802311yescharacteristic, complemented, Sylow
358C24—171no—
359C24—171no—
360C24—172no—
361C24—172no—
362C24—172no—
363C24—172no—
364C24—172no—
365C24—172no—
366C24—681no—
367C24—681no—
368C24—681no—
369C24—681no—
370C24C22⋊#59511yescharacteristic
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—42no—
375C22×C4—42no—
376C22×C4—42no—
377C22×C4—171no—
378C22×C4—171no—
379C22×C4—172no—
380C22×C4—172no—
381C22×C4—172no—
382C22×C4—172no—
383C22×C4—172no—
384C22×C4—172no—
385C22×C4—172no—
386C22×C4—171no—
387C22×C4—171no—
388C22×C4—172no—
389C22×C4—171no—
390C22×C4—171no—
391C22×C4—342no—
392C22×C4—342no—
393C22×C4—342no—
394C22×C4—342no—
395C22×C4—344no—
396C22×C4—342no—
397C22×C4—684no—
398C22×C4—684no—
399C22×C4—684no—
400C22×C4—684no—
401C22×C4—681no—
402C22×C4—681no—
403C22×C4—681no—
404C22×C4—681no—
405C22×C4—681no—
406C22×C4—681no—
407C22×C4—682no—
408C22×C4—682no—
409C22×C4—682no—
410C22×C4—682no—
411C22×C4—682no—
412C22×C4—682no—
413C22×C4—682no—
414C22×C4—682no—
415C22×C4—682no—
416C22×C4C4×#59512yes—
417C22×C4C4⋊#59512yes—
418C22×C4C22⋊#59511yescharacteristic
419C22×C4C22×#59511yescharacteristic
420C2×C8—344no—
421C2×C8—688no—
422C2×C8—682no—
423C2×C8—682no—
424C4⋊C4—42no—
425C4⋊C4—42no—
426C4⋊C4—682no—
427C4⋊C4—688no—
428C4⋊C4—682no—
429C22⋊C4—682no—
430C22⋊C4—684no—
431C22⋊C4—682no—
432C22⋊C4—688no—
433C23—21no—
434C23—21no—
435C23—21no—
436C23—21no—
437C23—171no—
438C23—172no—
439C23—171no—
440C23—171no—
441C23—172no—
442C23—171no—
443C23—171no—
444C23—172no—
445C23—171no—
446C23—174no—
447C23—174no—
448C23—174no—
449C23—174no—
450C23—341no—
451C23—341no—
452C23—341no—
453C23—341no—
454C23—341no—
455C23—341no—
456C23—341no—
457C23—341no—
458C23—682no—
459C23—682no—
460C23—682no—
461C23—682no—
462C23—682no—
463C23—682no—
464C23—682no—
465C23—682no—
466C23—682no—
467C23—682no—
468C23—682no—
469C23—682no—
470C23(C2×#595)⋊C412yes—
471C23#1058754712yes—
472C23#1058754912yes—
473C23C2×C22⋊#59511yescharacteristic
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—84no—
482C2×C4—171no—
483C2×C4—172no—
484C2×C4—171no—
485C2×C4—341no—
486C2×C4—341no—
487C2×C4—341no—
488C2×C4—341no—
489C2×C4—344no—
490C2×C4—344no—
491C2×C4—344no—
492C2×C4—344no—
493C2×C4—681no—
494C2×C4—681no—
495C2×C4—682no—
496C2×C4—681no—
497C2×C4—682no—
498C2×C4—681no—
499C2×C4—682no—
500C2×C4—682no—
501C2×C4—684no—
502C2×C4—684no—
503C2×C4—684no—
504C2×C4—682no—
505C2×C4—682no—
506C2×C4—682no—
507C2×C4—1364no—
508C2×C4—1362no—
509C2×C4—1362no—
510C2×C4—1362no—
511C2×C4—1362no—
512C2×C4#1058753912yes—
513C2×C4(C2×#595)⋊C412yes—
514C2×C4#1058755112yes—
515C2×C4C2×C4×#59511yescharacteristic
516C2×C4C2×C4⋊#59511yescharacteristic
517C8—684no—
518C22—22no—
519C22—22no—
520C22—22no—
521C22—22no—
522C22—22no—
523C22—22no—
524C22—171no—
525C22—174no—
526C22—171no—
527C22—171no—
528C22—171no—
529C22—341no—
530C22—342no—
531C22—341no—
532C22—341no—
533C22—342no—
534C22—341no—
535C22—341no—
536C22—342no—
537C22—341no—
538C22—341no—
539C22—342no—
540C22—341no—
541C22—341no—
542C22—342no—
543C22—341no—
544C22—341no—
545C22—342no—
546C22—341no—
547C22—684no—
548C22—684no—
549C22—684no—
550C22—684no—
551C22#1176368214yes—
552C22C2×(C2×#595)⋊C411yescharacteristic
553C22C2×#1058755111yescharacteristic
554C22C2×#1058753911yescharacteristic
555C22C2×#1058754711yescharacteristic
556C22C2×#1058754911yescharacteristic
557C22#1176380711yescharacteristic
558C22#1176380811yescharacteristic
559C4—21no—
560C4—21no—
561C4—82no—
562C4—341no—
563C4—342no—
564C4—341no—
565C4—1364no—
566C4—1362no—
567C4#1176368714yes—
568C2—24no—
569C2—341no—
570C2—344no—
571C2—341no—
572C2—341no—
573C2—341no—
574C2#1454422011yescharacteristic
575C2#1454422111yescharacteristic
576C2#1454422311yescharacteristic
577C2#1454422411yescharacteristic
578C2#1454446311yescharacteristic
579C2C2×#1176368211yescharacteristic
580C2C2×#1176368711yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC2×C4×C17C2×C42
FrattiniC22×C4C22×#595
FittingC22×C4⋊C4×C17C4
socleC23×C17C2×C22⋊C4
prime radicalC24×D17D4
cosocleC22×C4×D17C23
hypercenterC22×C4⋊C4#595
hypocenterC17#8023
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #14543657C2semidirect
10. #11763777C4semidirect
13. #11763751C4semidirect
16. C22×C4⋊Dic17C4semidirect
20. #11762666C4semidirect
23. C22×C4⋊C4×C17C4semidirect
62. (C2×#595)⋊C4C2×C4semidirect
64. #10587543C2×C4semidirect
286. C22×C4⋊C4#595semidirect
357. C17#8023semidirect

Maximal subgroups

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

subgroupindex
C2×#117637772
C2×#117637512
#145436572
C2×#117626662
#802317