Finite Group Databasebeta

← #16936639

Subgroups — #16936639

Order 4352.

728 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763089C211yesmaximal, characteristic, complemented
2C2×#11763014C211yesmaximal, characteristic, complemented
3#14529744C211yesmaximal, characteristic, complemented
4C2×D4⋊#3622C211yesmaximal, characteristic, complemented
5C2×D4⋊#3622C211yesmaximal, characteristic, complemented
6#14526667C211yesmaximal, characteristic, complemented
7C17×#2537C211yesmaximal, characteristic
8C22×#63229—21no—
9C2×#10587555C2211yescharacteristic
10#11763089—22no—
11#11763089—22no—
12#11763014—22no—
13#11763014—22no—
14C2×#10587478—21no—
15C2×C4⋊#3622C2211yescharacteristic
16C2×C4⋊#3622C2211yescharacteristic
17C2×#10587481—21no—
18C2×#10587503—21no—
19C2×C4×#3622C2211yescharacteristic
20#11762571—22no—
21D4⋊#3622—22no—
22D4⋊#3622—22no—
23C2×C17×#121—21no—
24C2×C17×#121—21no—
25C2×C4×D4×C17C2211yescharacteristic
26C2×C4×D4×C17C2211yescharacteristic
27C17×#394—22no—
28C17×#384C2211yescharacteristic
29C17×#380—21no—
30C17×#380—21no—
31C22×D4×C17—22no—
32C22×D4×C17D411yescharacteristic
33C22×D4×C17D411yescharacteristic
34C23×C4×C17—21no—
35C23×C4×C17—21no—
36C22×Dic34—21no—
37C17×#121—42no—
38C17×#121—42no—
39C17×#121—42no—
40C17×#121—42no—
41C4×D4×C17—21no—
42C4×D4×C17—21no—
43C4×D4×C17—21no—
44C4×D4×C17—21no—
45C4×D4×C17—21no—
46C4×D4×C17—21no—
47C4×D4×C17—21no—
48C4×D4×C17—21no—
49C2×C4⋊C4×C17—21no—
50C2×C4⋊C4×C17—21no—
51C2×C4⋊C4×C17D411yescharacteristic
52C2×C4⋊C4×C17D411yescharacteristic
53C2×C4⋊C4×C17D412yes—
54C2×C22⋊C4×C17—22no—
55C2×C22⋊C4×C17—22no—
56C2×C22⋊C4×C17—21no—
57C2×C22⋊C4×C17—21no—
58C2×C42×C17C2311yescharacteristic
59C2×#63229—24no—
60C2×#63229—42no—
61C2×#63229—42no—
62C2×C4⋊Dic17—21no—
63C2×C4⋊Dic17—21no—
64C22×#3622—21no—
65C22×#3622—21no—
66C22×#3622—21no—
67#10587555—21no—
68#10587555—21no—
69#10587555—21no—
70#10587555D412yescomplemented
71C17×#95—22no—
72#10587503—24no—
73#10587481—24no—
74#10587478—24no—
75C4⋊#3622—21no—
76C4⋊#3622—21no—
77C4⋊#3622D412yescomplemented
78C4⋊#3622D412yescomplemented
79C4×#3622—21no—
80C4×#3622—21no—
81C24×C17—21no—
82C24×C17—21no—
83C2×D4×C17—21no—
84C2×D4×C17—21no—
85C2×D4×C17—21no—
86C2×D4×C17—21no—
87C2×D4×C17—21no—
88C2×D4×C17—21no—
89C2×D4×C17—21no—
90C2×D4×C17—21no—
91C2×D4×C17—21no—
92C2×D4×C17—21no—
93C2×D4×C17—44no—
94C2×D4×C17—44no—
95C2×D4×C17—82no—
96C2×D4×C17D812yes—
97C2×D4×C17SD1612yescomplemented
98C22×C4×C17—21no—
99C22×C4×C17—21no—
100C22×C4×C17—22no—
101C22×C4×C17—41no—
102C22×C4×C17—41no—
103C22×C4×C17—41no—
104C22×C4×C17—41no—
105C22×C4×C17—41no—
106C22×C4×C17—41no—
107C22×C4×C17—41no—
108C22×C4×C17—41no—
109C22×C4×C17—41no—
110C22×C4×C17—41no—
111C22×C4×C17—41no—
112C22×C4×C17—41no—
113C22×C4×C17C2×D411yescharacteristic
114C22×C4×C17C2×D411yescharacteristic
115C22×C4×C17C2×D411yescharacteristic
116C22×Dic17—41no—
117C2×Dic34—22no—
118C2×Dic34—41no—
119C2×Dic34—41no—
120C2×Dic34—41no—
121C2×Dic34—41no—
122C2×Dic34—41no—
123C4⋊C4×C17—21no—
124C4⋊C4×C17—21no—
125C4⋊C4×C17—21no—
126C4⋊C4×C17—21no—
127C4⋊C4×C17—42no—
128C4⋊C4×C17—41no—
129C4⋊C4×C17—41no—
130C4⋊C4×C17—41no—
131C4⋊C4×C17—41no—
132C22⋊C4×C17—44no—
133C22⋊C4×C17—44no—
134C22⋊C4×C17—41no—
135C22⋊C4×C17—41no—
136C22⋊C4×C17—41no—
137C22⋊C4×C17—41no—
138C42×C17C2×D411yescharacteristic
139C42×C17C2×D411yescharacteristic
140C42×C17C2×D411yescharacteristic
141C42×C17#4111yescharacteristic
142#63229—48no—
143C4⋊Dic17—22no—
144C4⋊Dic17—22no—
145C4⋊Dic17—41no—
146C4⋊Dic17—41no—
147C2×#3622—22no—
148C2×#3622—22no—
149C2×#3622—22no—
150C2×#3622—41no—
151C2×#3622—41no—
152C2×#3622—41no—
153C2×#3622—41no—
154C2×#3622—41no—
155C2×#3622—41no—
156#10231—171nomaximal, Sylow
157C23×C17—22no—
158C23×C17—22no—
159C23×C17—41no—
160C23×C17—41no—
161C23×C17—41no—
162C23×C17—41no—
163C23×C17—41no—
164C23×C17—41no—
165C23×C17—41no—
166C23×C17—41no—
167C23×C17—41no—
168C23×C17—41no—
169C23×C17—41no—
170C23×C17—41no—
171C23×C17#12011yescharacteristic
172D4×C17—22no—
173D4×C17—22no—
174D4×C17—22no—
175D4×C17—22no—
176D4×C17—41no—
177D4×C17—41no—
178D4×C17—41no—
179D4×C17—41no—
180D4×C17—88no—
181C2×C4×C17—21no—
182C2×C4×C17—21no—
183C2×C4×C17—41no—
184C2×C4×C17—41no—
185C2×C4×C17—41no—
186C2×C4×C17—42no—
187C2×C4×C17—41no—
188C2×C4×C17—41no—
189C2×C4×C17—42no—
190C2×C4×C17—41no—
191C2×C4×C17—42no—
192C2×C4×C17—81no—
193C2×C4×C17—81no—
194C2×C4×C17—81no—
195C2×C4×C17—81no—
196C2×C4×C17—81no—
197C2×C4×C17—81no—
198C2×C4×C17—81no—
199C2×C4×C17—81no—
200C2×C4×C17#12011yescharacteristic
201C2×C4×C17#12011yescharacteristic
202C2×C4×C17#12111yescharacteristic
203C2×C4×C17#12111yescharacteristic
204C2×C4×C17#12111yescharacteristic
205C2×C4×C17#12711yescharacteristic
206C2×C4×C17C2×D811yescharacteristic
207C2×C4×C17C2×SD1611yescharacteristic
208C2×C4×C17#13511yescharacteristic
209C2×C4×C17#13511yescharacteristic
210C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
211C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
212C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
213C2×C4×C17#13711yescharacteristic
214C2×Dic17—42no—
215C2×Dic17—81no—
216C2×Dic17—81no—
217Dic34—42no—
218Dic34—42no—
219Dic34—81no—
220Dic34—81no—
221#3622—42no—
222#3622—42no—
223#3622—42no—
224C2×#474—171no—
225C2×#461—171no—
226#2537D1711yescharacteristic
227#1990—171no—
228C2×D4⋊C8—171no—
229C2×D4⋊C8—171no—
230#1296—171no—
231C22×C17—42no—
232C22×C17—42no—
233C22×C17—42no—
234C22×C17—42no—
235C22×C17—42no—
236C22×C17—42no—
237C22×C17—81no—
238C22×C17—81no—
239C22×C17—81no—
240C22×C17—81no—
241C22×C17—81no—
242C22×C17—81no—
243C22×C17—81no—
244C22×C17—81no—
245C22×C17#39211yescharacteristic
246C22×C17#44711yescharacteristic
247C22×C17#44911yescharacteristic
248C22×C17#45011yescharacteristic
249C22×C17#45211yescharacteristic
250C22×C17#45511yescharacteristic
251C22×C17#45611yescharacteristic
252C4×C17—21no—
253C4×C17—21no—
254C4×C17—82no—
255C4×C17—81no—
256C4×C17—81no—
257C4×C17#44711yescharacteristic
258C4×C17#44811yescharacteristic
259C4×C17#44911yescharacteristic
260C4×C17#44911yescharacteristic
261C4×C17#46511yescharacteristic
262C4×C17#46611yescharacteristic
263C4×C17#46811yescharacteristic
264C4×C17#46911yescharacteristic
265Dic17—82no—
266C22×SD16—341no—
267C2×C4⋊Q8—171no—
268C2×#121—21no—
269C2×#121—21no—
270C2×C4×D4C2×D1711yescharacteristic
271C2×C4×D4C2×D1711yescharacteristic
272#474—342no—
273#474—342no—
274#461—342no—
275#461—342no—
276C2×#107—341no—
277C2×C4⋊C8—171no—
278C2×C4⋊C8—171no—
279C2×#103—341no—
280C2×#102—341no—
281C2×C4×C8—171no—
282#394—22no—
283#384C2×D1711yescharacteristic
284#380—21no—
285#380—21no—
286#340—342no—
287D4⋊C8—342no—
288D4⋊C8—342no—
289C2×C17—82no—
290C2×C17—82no—
291C2×C17#163911yescharacteristic
292C2×C17#164611yescharacteristic
293C2×C17#164711yescharacteristic
294C2×C17#165411yescharacteristic
295C2×C17#199911yescharacteristic
296C2×C17#200011yescharacteristic
297C2×C17#200711yescharacteristic
298C22×Q8—341no—
299C22×D4—22no—
300C22×D4C22⋊D1711yescharacteristic
301C22×D4C22⋊D1711yescharacteristic
302C23×C4—21no—
303C23×C4—21no—
304C2×SD16—344no—
305C2×SD16—682no—
306C2×SD16—682no—
307C22×C8—341no—
308C22×C8—341no—
309C22×C8—341no—
310C4⋊Q8—172no—
311C4⋊Q8—341no—
312C4⋊Q8—341no—
313C4⋊Q8—341no—
314#121—42no—
315#121—42no—
316#121—42no—
317#121—42no—
318C4×D4—21no—
319C4×D4—21no—
320C4×D4—21no—
321C4×D4—21no—
322C4×D4—21no—
323C4×D4—21no—
324C4×D4—21no—
325C4×D4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—341no—
329C2×C4⋊C4—341no—
330C2×C4⋊C4C22⋊D1711yescharacteristic
331C2×C4⋊C4C22⋊D1711yescharacteristic
332C2×C4⋊C4C22⋊D1712yes—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—21no—
336C2×C22⋊C4—21no—
337C2×C42C22×D1711yescharacteristic
338#107—344no—
339C4⋊C8—172no—
340C4⋊C8—172no—
341C4⋊C8—341no—
342C4⋊C8—341no—
343#103—344no—
344#102—344no—
345C4×C8—341no—
346C4×C8—341no—
347#95—22no—
348C17#1023111yescharacteristic, complemented, Sylow
349C24—21no—
350C24—21no—
351C2×Q8—342no—
352C2×Q8—681no—
353C2×Q8—681no—
354C2×Q8—681no—
355C2×Q8—681no—
356C2×Q8—681no—
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—21no—
360C2×D4—21no—
361C2×D4—21no—
362C2×D4—21no—
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4—44no—
368C2×D4—44no—
369C2×D4—82no—
370C2×D4#6322812yes—
371C2×D4#6322912yescomplemented
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—22no—
375C22×C4—41no—
376C22×C4—41no—
377C22×C4—41no—
378C22×C4—41no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—41no—
384C22×C4—41no—
385C22×C4—41no—
386C22×C4—41no—
387C22×C4—681no—
388C22×C4C2×C22⋊D1711yescharacteristic
389C22×C4C2×C22⋊D1711yescharacteristic
390C22×C4C2×C22⋊D1711yescharacteristic
391SD16—688no—
392C2×C8—342no—
393C2×C8—342no—
394C2×C8—342no—
395C2×C8—681no—
396C2×C8—681no—
397C2×C8—681no—
398C2×C8—681no—
399C2×C8—681no—
400C2×C8—681no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—42no—
406C4⋊C4—41no—
407C4⋊C4—41no—
408C4⋊C4—41no—
409C4⋊C4—41no—
410C4⋊C4—342no—
411C4⋊C4—342no—
412C4⋊C4—681no—
413C4⋊C4—681no—
414C22⋊C4—44no—
415C22⋊C4—44no—
416C22⋊C4—41no—
417C22⋊C4—41no—
418C22⋊C4—41no—
419C22⋊C4—41no—
420C42D4×D1711yescharacteristic
421C42D4×D1711yescharacteristic
422C42D4×D1711yescharacteristic
423C42#6325411yescharacteristic
424C23—22no—
425C23—22no—
426C23—41no—
427C23—41no—
428C23—41no—
429C23—41no—
430C23—41no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23—41no—
435C23—41no—
436C23—41no—
437C23—41no—
438C23#1058763911yescharacteristic
439Q8—682no—
440Q8—682no—
441Q8—1361no—
442Q8—1361no—
443D4—22no—
444D4—22no—
445D4—22no—
446D4—22no—
447D4—41no—
448D4—41no—
449D4—41no—
450D4—41no—
451D4—88no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—42no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—42no—
461C2×C4—41no—
462C2×C4—42no—
463C2×C4—81no—
464C2×C4—81no—
465C2×C4—81no—
466C2×C4—81no—
467C2×C4—81no—
468C2×C4—81no—
469C2×C4—81no—
470C2×C4—81no—
471C2×C4—682no—
472C2×C4—1361no—
473C2×C4—1361no—
474C2×C4C2×#6322811yescharacteristic
475C2×C4#1058761811yescharacteristic
476C2×C4#1058761811yescharacteristic
477C2×C4C2×#6322911yescharacteristic
478C2×C4#1058762311yescharacteristic
479C2×C4#1058762311yescharacteristic
480C2×C4#1058762411yescharacteristic
481C2×C4#1058762511yescharacteristic
482C2×C4#1058762511yescharacteristic
483C2×C4#1058762611yescharacteristic
484C2×C4#1058763511yescharacteristic
485C2×C4#1058763611yescharacteristic
486C2×C4#1058763611yescharacteristic
487C2×C4#1058763711yescharacteristic
488C8—682no—
489C8—682no—
490C8—682no—
491C22—42no—
492C22—42no—
493C22—42no—
494C22—42no—
495C22—42no—
496C22—42no—
497C22—81no—
498C22—81no—
499C22—81no—
500C22—81no—
501C22—81no—
502C22—81no—
503C22—81no—
504C22—81no—
505C22#1176271711yescharacteristic
506C22#1176294311yescharacteristic
507C22#1176295411yescharacteristic
508C22#1176296011yescharacteristic
509C22#1176297111yescharacteristic
510C22#1176298711yescharacteristic
511C22#1176299211yescharacteristic
512C4—21no—
513C4—21no—
514C4—82no—
515C4—81no—
516C4—81no—
517C4—1362no—
518C4#1176294211yescharacteristic
519C4#1176294711yescharacteristic
520C4#1176295211yescharacteristic
521C4#1176295211yescharacteristic
522C4#1176303611yescharacteristic
523C4#1176304311yescharacteristic
524C4#1176305311yescharacteristic
525C4#1176306011yescharacteristic
526C2—82no—
527C2—82no—
528C2#1452796311yescharacteristic
529C2#1452801211yescharacteristic
530C2#1452801911yescharacteristic
531C2#1452806811yescharacteristic
532C2#1452978011yescharacteristic
533C2#1452978711yescharacteristic
534C2#1452983111yescharacteristic
subgroupG/H
centerC23#10587639
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
Fitting, prime radicalC17×#2537C2
socleC23×C17#120
hypercenter#2537D17
hypocenterC17#10231
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2537

Complements

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

NH ≅ G/Ntype
1. C2×#11763089C2semidirect
2. C2×#11763014C2semidirect
3. #14529744C2semidirect
4. C2×D4⋊#3622C2semidirect
5. C2×D4⋊#3622C2semidirect
6. #14526667C2semidirect
70. #10587555D4semidirect
77. C4⋊#3622D4semidirect
78. C4⋊#3622D4semidirect
97. C2×D4×C17SD16semidirect
348. C17#10231semidirect
371. C2×D4#63229semidirect

Maximal subgroups

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

subgroupindex
C2×#117630892
C2×#117630142
#145297442
C2×D4⋊#36222
#145266672
C17×#25372
#1023117