Finite Group Databasebeta

← #17953144

Subgroups — #17953144

Order 4352.

678 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14544640C211yesmaximal, characteristic, complemented
2#14544638C211yesmaximal, characteristic, complemented
3C2×#11763652C212yesmaximal
4#14543622C212yesmaximal, complemented
5C2×#11762703C211yesmaximal, characteristic
6C2×#10587544—21no—
7C2×C4⋊#3624—21no—
8C2×C22⋊#3624C2212yes—
9C2×C22⋊#3624C2212yes—
10#11763675—21no—
11#11763675—21no—
12#11763652—24no—
13C22×#63225C411yescharacteristic
14C22×C22⋊Dic17C411yescharacteristic
15C22×C22⋊Dic17C2211yescharacteristic
16C22×C4×Dic17C2211yescharacteristic
17#11762703—21no—
18#11762703—21no—
19#11762703—21no—
20#11762703—21no—
21C2×#10587502C411yescharacteristic
22C2×#10587502C2211yescharacteristic
23C22×C22⋊C4×C17C411yescharacteristic
24C25×C17C2×C411yescharacteristic
25C23×C4×C17C2×C411yescharacteristic
26C23×C4×C17C2×C411yescharacteristic
27C23×Dic17C2×C411yescharacteristic
28C23×Dic17C2×C411yescharacteristic
29C23×Dic17C2×C411yescharacteristic
30C23×Dic17C2311yescharacteristic
31C22×#3624—22no—
32C22×#3624—22no—
33C2×C22⋊C4×C17—21no—
34C2×C22⋊C4×C17—21no—
35C2×C22⋊C4×C17—42no—
36C2×C22⋊Dic17—21no—
37C2×C22⋊Dic17—21no—
38C2×C22⋊Dic17—21no—
39C2×C22⋊Dic17—21no—
40C2×C22⋊Dic17—21no—
41C2×C22⋊Dic17—21no—
42C2×C22⋊Dic17—42no—
43C2×C22⋊Dic17D412yes—
44C2×C22⋊Dic17Q812yes—
45C2×#63225—21no—
46C2×#63225—21no—
47C2×#63225—42no—
48C2×C4×Dic17—42no—
49C2×C4×Dic17D411yescharacteristic
50C2×C4×Dic17D411yescharacteristic
51C2×C4×Dic17D411yescharacteristic
52C2×C4×Dic17D411yescharacteristic
53C22⋊#3624—22no—
54C22⋊#3624—22no—
55C22⋊#3624—22no—
56C22⋊#3624—22no—
57#10587544—42no—
58C4⋊#3624—42no—
59#10587502—21no—
60#10587502—21no—
61#10587502—21no—
62#10587502—21no—
63C24×C17—21no—
64C24×C17—21no—
65C24×C17—22no—
66C24×C17—22no—
67C24×C17—41no—
68C24×C17—41no—
69C24×C17—41no—
70C24×C17—41no—
71C24×C17C4⋊C412yes—
72C24×C17C22×C411yescharacteristic
73C22×C4×C17—22no—
74C22×C4×C17—22no—
75C22×C4×C17—21no—
76C22×C4×C17—22no—
77C22×C4×C17—41no—
78C22×C4×C17—41no—
79C22×C4×C17—41no—
80C22×C4×C17C22⋊C411yescharacteristic
81C22×C4×C17C22⋊C411yescharacteristic
82C22×Dic17—21no—
83C22×Dic17—21no—
84C22×Dic17—22no—
85C22×Dic17—22no—
86C22×Dic17—21no—
87C22×Dic17—22no—
88C22×Dic17—41no—
89C22×Dic17—41no—
90C22×Dic17—41no—
91C22×Dic17—41no—
92C22×Dic17—41no—
93C22×Dic17—41no—
94C22×Dic17—41no—
95C22×Dic17C22⋊C411yescharacteristic
96C22×Dic17C22⋊C411yescharacteristic
97C22×Dic17C4⋊C412yes—
98C22×Dic17C2×D411yescharacteristic
99C22×Dic17C2×D411yescharacteristic
100C22×Dic17C2×D411yescharacteristic
101C22×Dic17C2×Q811yescharacteristic
102C22×Dic17#4111yescharacteristic
103C22×Dic17#4111yescharacteristic
104C2×#3624—42no—
105C2×#3624—42no—
106C2×#3624—42no—
107C2×#3624—42no—
108C2×#3624—42no—
109C2×#3624—42no—
110C22⋊C4×C17—42no—
111C22⋊C4×C17—42no—
112C22⋊Dic17—22no—
113C22⋊Dic17—22no—
114C22⋊Dic17—22no—
115C22⋊Dic17—22no—
116C22⋊Dic17—42no—
117C22⋊Dic17—42no—
118#63225—42no—
119#63225—42no—
120C4×Dic17—22no—
121C4×Dic17—22no—
122C4×Dic17—41no—
123C4×Dic17—41no—
124#8561—171nomaximal, Sylow
125C23×C17—21no—
126C23×C17—21no—
127C23×C17—21no—
128C23×C17—21no—
129C23×C17—22no—
130C23×C17—24no—
131C23×C17—42no—
132C23×C17—42no—
133C23×C17—42no—
134C23×C17—42no—
135C23×C17—41no—
136C23×C17—41no—
137C23×C17—41no—
138C23×C17—41no—
139C23×C17—41no—
140C23×C17—41no—
141C23×C17—42no—
142C23×C17—82no—
143C23×C17—82no—
144C23×C17—82no—
145C23×C17—82no—
146C23×C17C2×C22⋊C411yescharacteristic
147C23×C17C2×C4⋊C411yescharacteristic
148C23×C17#11711yescharacteristic
149C23×C17#13112yes—
150C23×C17#13112yes—
151C2×C4×C17—21no—
152C2×C4×C17—21no—
153C2×C4×C17—21no—
154C2×C4×C17—21no—
155C2×C4×C17—21no—
156C2×C4×C17—44no—
157C2×C4×C17—41no—
158C2×C4×C17—41no—
159C2×C4×C17—41no—
160C2×C4×C17—82no—
161C2×C4×C17#10012yes—
162C2×Dic17—21no—
163C2×Dic17—21no—
164C2×Dic17—21no—
165C2×Dic17—21no—
166C2×Dic17—21no—
167C2×Dic17—21no—
168C2×Dic17—22no—
169C2×Dic17—21no—
170C2×Dic17—21no—
171C2×Dic17—21no—
172C2×Dic17—41no—
173C2×Dic17—41no—
174C2×Dic17—41no—
175C2×Dic17—41no—
176C2×Dic17—44no—
177C2×Dic17—42no—
178C2×Dic17—41no—
179C2×Dic17—41no—
180C2×Dic17—42no—
181C2×Dic17—41no—
182C2×Dic17—41no—
183C2×Dic17—41no—
184C2×Dic17—82no—
185C2×Dic17#9912yes—
186C2×Dic17#12111yescharacteristic
187C2×Dic17#12111yescharacteristic
188C2×Dic17C22⋊Q811yescharacteristic
189C2×Dic17C22⋊Q811yescharacteristic
190#3624—82no—
191#3624—82no—
192C2×#388—171no—
193#1797—171no—
194#1797—171no—
195C2×#323—172no—
196#1280—172no—
197C22×C17—21no—
198C22×C17—21no—
199C22×C17—21no—
200C22×C17—21no—
201C22×C17—22no—
202C22×C17—22no—
203C22×C17—22no—
204C22×C17—22no—
205C22×C17—42no—
206C22×C17—42no—
207C22×C17—42no—
208C22×C17—84no—
209C22×C17—84no—
210C22×C17—81no—
211C22×C17—81no—
212C22×C17—81no—
213C22×C17—81no—
214C22×C17#38011yescharacteristic
215C22×C17#40811yescharacteristic
216C22×C17#40811yescharacteristic
217C22×C17C2×#9911yescharacteristic
218C22×C17#41011yescharacteristic
219C22×C17C2×#10011yescharacteristic
220C22×C17#41311yescharacteristic
221C22×C17#42412yes—
222C22×C17#43312yes—
223C4×C17—22no—
224C4×C17—41no—
225C4×C17—81no—
226Dic17—21no—
227Dic17—21no—
228Dic17—21no—
229Dic17—21no—
230Dic17—22no—
231Dic17—42no—
232Dic17—41no—
233Dic17—81no—
234C22×C4⋊C4—171no—
235C22×C22⋊C4—171no—
236C22×C22⋊C4—171no—
237C22×C22⋊C4#59511yescharacteristic
238C22×C42—171no—
239C2×C4⋊C8—341no—
240C2×C4⋊C8—341no—
241C2×C22⋊C8—172no—
242C2×C22⋊C8—172no—
243#388—341no—
244#388—341no—
245#388—341no—
246#388—341no—
247C2×#95—171no—
248C2×#95—171no—
249#336—341no—
250#336—341no—
251#323—344no—
252C2×C17—22no—
253C2×C17—22no—
254C2×C17—82no—
255C2×C17#146811yescharacteristic
256C2×C17#146911yescharacteristic
257C2×C17#147111yescharacteristic
258C2×C17#147311yescharacteristic
259C2×C17#179811yescharacteristic
260C2×C17#179911yescharacteristic
261C2×C17#180011yescharacteristic
262C25C2×#59511yescharacteristic
263C23×C4—171no—
264C23×C4—171no—
265C23×C4—171no—
266C23×C4—171no—
267C23×C4C2×#59511yescharacteristic
268C23×C4C2×#59511yescharacteristic
269C22×C8—342no—
270C22×C8—342no—
271C2×C4⋊C4—341no—
272C2×C4⋊C4—341no—
273C2×C4⋊C4—682no—
274C2×C22⋊C4—21no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—42no—
277C2×C22⋊C4—172no—
278C2×C22⋊C4—172no—
279C2×C22⋊C4—341no—
280C2×C22⋊C4—341no—
281C2×C22⋊C4—341no—
282C2×C22⋊C4—341no—
283C2×C22⋊C4—341no—
284C2×C22⋊C4—341no—
285C2×C22⋊C4—682no—
286C2×C42—171no—
287C2×C42—171no—
288C2×C42—171no—
289C2×C42—171no—
290C2×C42—682no—
291C4⋊C8—682no—
292C4⋊C8—682no—
293C22⋊C8—342no—
294C22⋊C8—342no—
295C22⋊C8—342no—
296C22⋊C8—342no—
297#95—341no—
298#95—341no—
299#95—341no—
300#95—341no—
301C17#856111yescharacteristic, complemented, Sylow
302C24—21no—
303C24—21no—
304C24—22no—
305C24—22no—
306C24—41no—
307C24—41no—
308C24—41no—
309C24—41no—
310C24C4⋊#59512yes—
311C24C22×#59511yescharacteristic
312C22×C4—22no—
313C22×C4—22no—
314C22×C4—21no—
315C22×C4—22no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4—171no—
320C22×C4—171no—
321C22×C4—171no—
322C22×C4—171no—
323C22×C4—171no—
324C22×C4—171no—
325C22×C4—171no—
326C22×C4—171no—
327C22×C4—172no—
328C22×C4—342no—
329C22×C4—341no—
330C22×C4—342no—
331C22×C4—341no—
332C22×C4—341no—
333C22×C4—342no—
334C22×C4—681no—
335C22×C4—681no—
336C22×C4—681no—
337C22×C4—681no—
338C22×C4—681no—
339C22×C4—681no—
340C22×C4—681no—
341C22×C4C22⋊#59511yescharacteristic
342C22×C4C22⋊#59511yescharacteristic
343C2×C8—682no—
344C2×C8—682no—
345C2×C8—682no—
346C2×C8—682no—
347C2×C8—682no—
348C2×C8—682no—
349C4⋊C4—682no—
350C4⋊C4—682no—
351C22⋊C4—42no—
352C22⋊C4—42no—
353C22⋊C4—342no—
354C22⋊C4—342no—
355C22⋊C4—342no—
356C22⋊C4—342no—
357C22⋊C4—682no—
358C22⋊C4—682no—
359C42—342no—
360C42—342no—
361C42—681no—
362C42—681no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23—21no—
367C23—22no—
368C23—24no—
369C23—42no—
370C23—42no—
371C23—42no—
372C23—42no—
373C23—41no—
374C23—41no—
375C23—41no—
376C23—41no—
377C23—41no—
378C23—41no—
379C23—42no—
380C23—82no—
381C23—82no—
382C23—82no—
383C23—82no—
384C23C2×C4⋊#59511yescharacteristic
385C23#1058767711yescharacteristic
386C23#1058767812yes—
387C23#1058767812yes—
388C23C2×C22⋊#59511yescharacteristic
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—44no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—82no—
399C2×C4—171no—
400C2×C4—171no—
401C2×C4—171no—
402C2×C4—171no—
403C2×C4—172no—
404C2×C4—341no—
405C2×C4—341no—
406C2×C4—341no—
407C2×C4—341no—
408C2×C4—341no—
409C2×C4—341no—
410C2×C4—342no—
411C2×C4—341no—
412C2×C4—341no—
413C2×C4—341no—
414C2×C4—681no—
415C2×C4—681no—
416C2×C4—681no—
417C2×C4—681no—
418C2×C4—684no—
419C2×C4—682no—
420C2×C4—681no—
421C2×C4—681no—
422C2×C4—682no—
423C2×C4—681no—
424C2×C4—681no—
425C2×C4—681no—
426C2×C4—1362no—
427C2×C4#1058755312yes—
428C8—1362no—
429C8—1362no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—22no—
435C22—22no—
436C22—22no—
437C22—22no—
438C22—42no—
439C22—42no—
440C22—42no—
441C22—84no—
442C22—84no—
443C22—81no—
444C22—81no—
445C22—81no—
446C22—81no—
447C22#1176375111yescharacteristic
448C22#1176378211yescharacteristic
449C22#1176378311yescharacteristic
450C22D17⋊#9911yescharacteristic
451C22#1176378911yescharacteristic
452C22C2×#1058755311yescharacteristic
453C22#1176379511yescharacteristic
454C22#1176381512yes—
455C22#1176383312yes—
456C4—22no—
457C4—41no—
458C4—81no—
459C4—341no—
460C4—341no—
461C4—341no—
462C4—341no—
463C4—342no—
464C4—682no—
465C4—681no—
466C4—1361no—
467C2—22no—
468C2—22no—
469C2—82no—
470C2#1454405011yescharacteristic
471C2#1454405411yescharacteristic
472C2#1454406011yescharacteristic
473C2#1454406611yescharacteristic
474C2#1454464211yescharacteristic
475C2#1454464611yescharacteristic
476C2#1454464811yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC24×C17C22×C4
FrattiniC24C22×#595
FittingC22×C22⋊C4×C17C4
socleC23×C17C2×C22⋊C4
prime radicalC25×C17C2×C4
cosocleC23×Dic17C23
hypercenterC22×C22⋊C4#595
hypocenterC17#8561
LCSG ▷ C24×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #14544640C2semidirect
2. #14544638C2semidirect
4. #14543622C2semidirect
301. C17#8561semidirect

Maximal subgroups

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

subgroupindex
#145446402
#145446382
C2×#117636522
#145436222
C2×#117627032
#856117