Finite Group Databasebeta

← #16928418

Subgroups — #16928418

Order 4352.

702 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14531484C211yesmaximal, characteristic
2#14529101C211yesmaximal, characteristic
3C2×#11762544C211yesmaximal, characteristic
4#14527047C211yesmaximal, characteristic, complemented
5#14526662C211yesmaximal, characteristic, complemented
6#14526626C211yesmaximal, characteristic, complemented
7C17×#1853C211yesmaximal, characteristic, complemented
8C2×#10587616C2211yescharacteristic
9C2×#10587567—21no—
10C22×#63225—21no—
11C2×#10587480—21no—
12C2×C22⋊#3622C2211yescharacteristic
13#11762699—21no—
14#11762692—21no—
15#11762687—21no—
16#11762686—21no—
17#11762680—21no—
18C2×#10587502—21no—
19C2×#10587502C2211yescharacteristic
20C2×#10587502C2211yescharacteristic
21#11762571—21no—
22#11762544C414yescomplemented
23C22×C4⋊C4×C17C2211yescharacteristic
24C2×C17×#106—21no—
25C2×C17×C22⋊C8C2211yescharacteristic
26C17×#380C2211yescharacteristic
27C17×#340—21no—
28C23×C4×C17—21no—
29C23×C4×C17C2311yescharacteristic
30C22×C22⋊D17—21no—
31C23×Dic17—21no—
32C23×Dic17D411yescharacteristic
33C23×Dic17D411yescharacteristic
34C22×D68D411yescharacteristic
35C22×C4×D17—21no—
36C22×C8×C17—21no—
37C2×C4⋊C4×C17—21no—
38C2×C4⋊C4×C17—21no—
39C2×C4⋊C4×C17—42no—
40C2×C4⋊C4×C17D411yescharacteristic
41C2×C4⋊C4×C17D411yescharacteristic
42C2×C22⋊C4×C17—21no—
43#10587616—21no—
44#10587616—21no—
45#10587616C2×C412yes—
46#10587616Q812yes—
47C2×#63227—21no—
48C2×#63227—21no—
49C2×#63227—21no—
50C2×#63227—21no—
51C2×C4⋊Dic17D411yescharacteristic
52C2×#63225—21no—
53C2×#63225—42no—
54C2×#63225—42no—
55C2×#63225—42no—
56C2×C4×Dic17—21no—
57C22×#3622—21no—
58#10587567—42no—
59#10587567—42no—
60C17×#106—42no—
61C17×C22⋊C8—21no—
62C17×C22⋊C8C2×C412yescomplemented
63C17×#95—21no—
64#10587502—21no—
65#10587502—21no—
66#10587502—21no—
67#10587502—21no—
68#10587502—21no—
69#10587502—42no—
70#10587502C2×C412yescomplemented
71C22⋊#3622—21no—
72C22⋊#3622—21no—
73#10587480—42no—
74C24×C17C2×D411yescharacteristic
75C23×D17—21no—
76C22×C4×C17—22no—
77C22×C4×C17—21no—
78C22×C4×C17—21no—
79C22×C4×C17—41no—
80C22×C4×C17—41no—
81C22×C4×C17—41no—
82C22×C4×C17—41no—
83C22×C4×C17—41no—
84C22×C4×C17—41no—
85C22×C4×C17—41no—
86C22×C4×C17—41no—
87C22×C4×C17C22×C411yescharacteristic
88C22×C4×C17C2×D411yescharacteristic
89C22×C4×C17C2×D411yescharacteristic
90C22×C4×C17C2×Q811yescharacteristic
91C22×C4×C17#4111yescharacteristic
92C22×C4×C17#4111yescharacteristic
93C2×C22⋊D17—22no—
94C2×C22⋊D17—22no—
95C2×C22⋊D17—41no—
96C2×C22⋊D17—41no—
97C2×C22⋊D17—41no—
98C2×C22⋊D17—41no—
99C22×Dic17—22no—
100C22×Dic17—22no—
101C22×Dic17—22no—
102C22×Dic17—21no—
103C22×Dic17—21no—
104C22×Dic17—21no—
105C22×Dic17—21no—
106C22×Dic17—21no—
107C22×Dic17—21no—
108C22×Dic17—41no—
109C22×Dic17—41no—
110C22×Dic17—41no—
111C22×Dic17—41no—
112C22×Dic17—41no—
113C22×Dic17—41no—
114C22×Dic17—41no—
115C22×Dic17—41no—
116C22×Dic17SD1612yes—
117C2×D68—21no—
118C2×D68—41no—
119C2×D68—41no—
120C2×D68C4⋊C412yescomplemented
121C2×C4×D17—42no—
122C2×C4×D17—81no—
123C2×C4×D17—81no—
124C2×C8×C17—22no—
125C2×C8×C17—41no—
126C2×C8×C17—41no—
127C4⋊C4×C17—22no—
128C4⋊C4×C17—22no—
129C4⋊C4×C17—41no—
130C4⋊C4×C17—41no—
131C4⋊C4×C17—41no—
132C4⋊C4×C17—41no—
133C22⋊C4×C17—41no—
134C22⋊C4×C17—41no—
135#63227—22no—
136#63227—22no—
137#63227—42no—
138#63227—81no—
139#63227—81no—
140C4⋊Dic17—21no—
141C4⋊Dic17C4⋊C412yescomplemented
142#63225—42no—
143#63225—48no—
144C4×Dic17—42no—
145C2×#3622—41no—
146C2×#3622—41no—
147C2×#3622—41no—
148#8873—171nomaximal, Sylow
149C23×C17—21no—
150C23×C17—21no—
151C23×C17—21no—
152C23×C17—21no—
153C23×C17C4×D411yescharacteristic
154C23×C17#12011yescharacteristic
155C23×C17C22⋊Q811yescharacteristic
156C23×C17C2×SD1611yescharacteristic
157C23×C17#13511yescharacteristic
158C23×C17AGL(1,ℤ/8)11yescharacteristic
159C23×C17AGL(1,ℤ/8)11yescharacteristic
160C22×D17—22no—
161C22×D17—41no—
162C22×D17—41no—
163C22×D17—41no—
164C22×D17—41no—
165C22×D17—41no—
166C22×D17—41no—
167C2×C4×C17—21no—
168C2×C4×C17—21no—
169C2×C4×C17—21no—
170C2×C4×C17—21no—
171C2×C4×C17—41no—
172C2×C4×C17—41no—
173C2×C4×C17—41no—
174C2×C4×C17—41no—
175C2×C4×C17—42no—
176C2×C4×C17—42no—
177C2×C4×C17—41no—
178C2×C4×C17—41no—
179C2×C4×C17—41no—
180C2×C4×C17—41no—
181C2×C4×C17—42no—
182C2×C4×C17—41no—
183C2×C4×C17—41no—
184C2×C4×C17—81no—
185C2×C4×C17—81no—
186C2×C4×C17—81no—
187C2×C4×C17—81no—
188C2×C4×C17C2×C4⋊C411yescharacteristic
189C2×C4×C17C4×D411yescharacteristic
190C2×C4×C17C22⋊Q811yescharacteristic
191C2×C4×C17#12311yescharacteristic
192C22⋊D17—42no—
193C22⋊D17—42no—
194C22⋊D17—42no—
195C22⋊D17—42no—
196C2×Dic17—24no—
197C2×Dic17—22no—
198C2×Dic17—22no—
199C2×Dic17—42no—
200C2×Dic17—42no—
201C2×Dic17—42no—
202C2×Dic17—42no—
203C2×Dic17—42no—
204C2×Dic17—42no—
205C2×Dic17—41no—
206C2×Dic17—41no—
207C2×Dic17—41no—
208C2×Dic17—41no—
209C2×Dic17—42no—
210C2×Dic17—42no—
211C2×Dic17—41no—
212C2×Dic17—41no—
213C2×Dic17—41no—
214C2×Dic17—81no—
215C2×Dic17—81no—
216D68—42no—
217D68—81no—
218C4×D17—84no—
219C8×C17—42no—
220#3622—81no—
221#2325—171no—
222#1874—171no—
223#1853D1711yescharacteristic, complemented
224C2×#327—171no—
225#1444—171no—
226#1294—171no—
227#1280—171no—
228C22×C17—21no—
229C22×C17—21no—
230C22×C17—21no—
231C22×C17—21no—
232C22×C17—21no—
233C22×C17—21no—
234C22×C17—21no—
235C22×C17—21no—
236C22×C17—21no—
237C22×C17—21no—
238C22×C17—21no—
239C22×C17—21no—
240C22×C17#38511yescharacteristic
241C22×C17C4×SD1611yescharacteristic
242C22×C17#44211yescharacteristic
243C22×C17#44911yescharacteristic
244C22×C17#45011yescharacteristic
245C22×C17#45311yescharacteristic
246C22×C17#45611yescharacteristic
247C22×C17B(4,𝔽2)11yescharacteristic
248C22×C17#45811yescharacteristic
249C22×C17#47611yescharacteristic
250C22×C17#47811yescharacteristic
251C2×D17—42no—
252C2×D17—42no—
253C2×D17—42no—
254C2×D17—81no—
255C2×D17—81no—
256C2×D17—81no—
257C2×D17—81no—
258C4×C17—21no—
259C4×C17—21no—
260C4×C17—21no—
261C4×C17—21no—
262C4×C17—82no—
263C4×C17—81no—
264C4×C17—81no—
265Dic17—44no—
266Dic17—42no—
267Dic17—42no—
268Dic17—81no—
269C2×#121—171no—
270C2×C4×D4—341no—
271C22×C4⋊C4—341no—
272C22×C4⋊C4C2×D1711yescharacteristic
273C2×#106—21no—
274C2×#102—341no—
275C2×C22⋊C8—171no—
276C2×C22⋊C8C2×D1711yescharacteristic
277#388—341no—
278#387—341no—
279#386—341no—
280#386—341no—
281#385—341no—
282#380C2×D1711yescharacteristic
283C2×#95—171no—
284C2×#95—171no—
285C2×#95—341no—
286#340—21no—
287#340—341no—
288#327—174no—
289C2×C17—21no—
290C2×C17—21no—
291C2×C17—21no—
292C2×C17—21no—
293C2×C17#160011yescharacteristic
294C2×C17#160411yescharacteristic
295C2×C17#160911yescharacteristic
296C2×C17#161311yescharacteristic
297C2×C17#185911yescharacteristic
298C2×C17#186411yescharacteristic
299C2×C17#186711yescharacteristic
300D17—82no—
301C22×D4—171no—
302C22×D4—341no—
303C23×C4—21no—
304C23×C4—171no—
305C23×C4—171no—
306C23×C4—341no—
307C23×C4—341no—
308C23×C4C22×D1711yescharacteristic
309C22×C8—21no—
310C22×C8—341no—
311#121—172no—
312#121—172no—
313#121—341no—
314#121—341no—
315C4×D4—682no—
316C4×D4—682no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4—171no—
321C2×C4⋊C4—341no—
322C2×C4⋊C4—682no—
323C2×C4⋊C4—682no—
324C2×C4⋊C4—682no—
325C2×C4⋊C4C22⋊D1711yescharacteristic
326C2×C4⋊C4C22⋊D1711yescharacteristic
327C2×C22⋊C4—21no—
328C2×C22⋊C4—341no—
329C2×C22⋊C4—341no—
330C2×C22⋊C4—341no—
331C2×C22⋊C4—341no—
332C2×C42—341no—
333#106—42no—
334#102—682no—
335C22⋊C8—21no—
336C22⋊C8—341no—
337C22⋊C8—341no—
338C22⋊C8C4×D1712yescomplemented
339#95—21no—
340#95—172no—
341#95—341no—
342#95—341no—
343#95—341no—
344#95—341no—
345#95—341no—
346#95—682no—
347C17#887311yescharacteristic, complemented, Sylow
348C24—341no—
349C24D4×D1711yescharacteristic
350C2×D4—172no—
351C2×D4—342no—
352C2×D4—342no—
353C2×D4—341no—
354C2×D4—681no—
355C2×D4—681no—
356C2×D4—681no—
357C2×D4—681no—
358C2×D4—681no—
359C2×D4—681no—
360C22×C4—22no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—41no—
364C22×C4—41no—
365C22×C4—41no—
366C22×C4—41no—
367C22×C4—41no—
368C22×C4—41no—
369C22×C4—41no—
370C22×C4—41no—
371C22×C4—172no—
372C22×C4—342no—
373C22×C4—342no—
374C22×C4—342no—
375C22×C4—341no—
376C22×C4—341no—
377C22×C4—341no—
378C22×C4—341no—
379C22×C4—341no—
380C22×C4—341no—
381C22×C4—682no—
382C22×C4—681no—
383C22×C4—681no—
384C22×C4—681no—
385C22×C4—681no—
386C22×C4—681no—
387C22×C4—681no—
388C22×C4—681no—
389C22×C4—681no—
390C22×C4—1361no—
391C22×C4—1361no—
392C22×C4C2×C4×D1711yescharacteristic
393C22×C4#6325211yescharacteristic
394C22×C4D4×D1711yescharacteristic
395C22×C4Q8×D1711yescharacteristic
396C22×C4#6325611yescharacteristic
397C22×C4C2×C22⋊D1711yescharacteristic
398C2×C8—22no—
399C2×C8—41no—
400C2×C8—41no—
401C2×C8—681no—
402C2×C8—681no—
403C2×C8—681no—
404C4⋊C4—22no—
405C4⋊C4—22no—
406C4⋊C4—41no—
407C4⋊C4—41no—
408C4⋊C4—41no—
409C4⋊C4—41no—
410C4⋊C4—172no—
411C4⋊C4—341no—
412C4⋊C4—682no—
413C4⋊C4—688no—
414C22⋊C4—41no—
415C22⋊C4—41no—
416C22⋊C4—342no—
417C22⋊C4—342no—
418C22⋊C4—682no—
419C22⋊C4—1361no—
420C22⋊C4—1361no—
421C42—682no—
422C23—21no—
423C23—21no—
424C23—21no—
425C23—21no—
426C23—342no—
427C23—681no—
428C23—681no—
429C23—681no—
430C23—681no—
431C23—681no—
432C23—681no—
433C23#1058757911yescharacteristic
434C23#1058758211yescharacteristic
435C23SD16×D1711yescharacteristic
436C23#1058760011yescharacteristic
437C23#1058760011yescharacteristic
438C23#1058760211yescharacteristic
439C23#1058762311yescharacteristic
440D4—682no—
441D4—682no—
442D4—682no—
443D4—682no—
444D4—682no—
445D4—1361no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—42no—
462C2×C4—41no—
463C2×C4—81no—
464C2×C4—81no—
465C2×C4—81no—
466C2×C4—81no—
467C2×C4—344no—
468C2×C4—342no—
469C2×C4—342no—
470C2×C4—682no—
471C2×C4—682no—
472C2×C4—682no—
473C2×C4—682no—
474C2×C4—682no—
475C2×C4—681no—
476C2×C4—681no—
477C2×C4—681no—
478C2×C4—681no—
479C2×C4—682no—
480C2×C4—682no—
481C2×C4—682no—
482C2×C4—681no—
483C2×C4—681no—
484C2×C4—681no—
485C2×C4—1364no—
486C2×C4—1361no—
487C2×C4—1361no—
488C2×C4C4⋊C4×D1711yescharacteristic
489C2×C4#1058758011yescharacteristic
490C2×C4C4×C22⋊D1711yescharacteristic
491C2×C4#1058763211yescharacteristic
492C8—42no—
493C8—1361no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—682no—
507C22—682no—
508C22—682no—
509C22—1361no—
510C22—1361no—
511C22—1361no—
512C22—1361no—
513C22#1176268011yescharacteristic
514C22#1176289611yescharacteristic
515C22#1176292011yescharacteristic
516C22#1176295311yescharacteristic
517C22#1176295811yescharacteristic
518C22#1176297511yescharacteristic
519C22#1176299011yescharacteristic
520C22#1176299511yescharacteristic
521C22#1176299811yescharacteristic
522C22#1176309811yescharacteristic
523C22#1176310811yescharacteristic
524C4—21no—
525C4—21no—
526C4—21no—
527C4—21no—
528C4—81no—
529C4—81no—
530C4—82no—
531C4—684no—
532C4—682no—
533C4—682no—
534C4—1361no—
535C2—21no—
536C2—21no—
537C2—21no—
538C2—21no—
539C2—1362no—
540C2#1452772911yescharacteristic
541C2#1452775111yescharacteristic
542C2#1452778011yescharacteristic
543C2#1452780211yescharacteristic
544C2#1452900711yescharacteristic
545C2#1452904211yescharacteristic
546C2#1452906311yescharacteristic
subgroupG/H
centerC23#10587623
commutatorC22×C4×C17C22×C4
FrattiniC23×C4C22×D17
FittingC17×#1853C2
socleC23×C17#120
prime radicalC2×#10587616C22
cosocleC23×C4×C17C23
hypercenter#1853D17
hypocenterC17#8873
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1853

Complements

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

NH ≅ G/Ntype
4. #14527047C2semidirect
5. #14526662C2semidirect
6. #14526626C2semidirect
7. C17×#1853C2semidirect
22. #11762544C4semidirect
62. C17×C22⋊C8C2×C4semidirect
70. #10587502C2×C4semidirect
120. C2×D68C4⋊C4semidirect
141. C4⋊Dic17C4⋊C4semidirect
223. #1853D17semidirect
338. C22⋊C8C4×D17semidirect
347. C17#8873semidirect

Maximal subgroups

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

subgroupindex
#145314842
#145291012
C2×#117625442
#145270472
#145266622
#145266262
C17×#18532
#887317