Finite Group Databasebeta

← #16950297

Subgroups — #16950297

Order 4352.

600 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
1C2×#11762596C212yesmaximal
2#14528776C211yesmaximal, characteristic, complemented
3#14528772C211yesmaximal, characteristic, complemented
4#14526902C212yesmaximal, complemented
5C17×#2321C211yesmaximal, characteristic
6#11762833—21no—
7C2×#10587504C2212yes—
8C2×#10587505C2212yes—
9#11762669—21no—
10#11762596—24no—
11#11762578—21no—
12#11762576—21no—
13C2×C17×#120C2211yescharacteristic
14C2×C4×D4×C17C2211yescharacteristic
15C22×C22⋊C4×C17C411yescharacteristic, complemented
16C17×#390—21no—
17C17×#388—21no—
18C17×#388—21no—
19C17×#386—21no—
20C17×#386C2211yescharacteristic
21C17×#385C411yescharacteristic, complemented
22C17×#379C411yescharacteristic, complemented
23C4×C22⋊C4×C17C411yescharacteristic, complemented
24C25×C17C2×C411yescharacteristic
25C22×D4×C17—21no—
26C22×D4×C17C2311yescharacteristic
27C23×C4×C17C2×C411yescharacteristic
28C23×C4×C17C2×C411yescharacteristic
29C23×C4×C17D411yescharacteristic
30C17×#120—21no—
31C17×#120—21no—
32C17×#120D412yes—
33C17×#120Q812yes—
34C4×D4×C17—41no—
35C4×D4×C17—41no—
36C2×C4⋊C4×C17—21no—
37C2×C4⋊C4×C17D411yescharacteristic
38C2×C22⋊C4×C17—21no—
39C2×C22⋊C4×C17—21no—
40C2×C22⋊C4×C17—21no—
41C2×C22⋊C4×C17—21no—
42C2×C22⋊C4×C17—21no—
43C2×C22⋊C4×C17—21no—
44C2×C22⋊C4×C17—41no—
45C2×C22⋊C4×C17—41no—
46C2×C22⋊C4×C17C2×C411yescharacteristic
47C2×C22⋊C4×C17C2×C411yescharacteristic
48C2×C22⋊C4×C17C2×C411yescharacteristic
49C2×C22⋊C4×C17D411yescharacteristic
50C2×C42×C17—21no—
51C2×C42×C17D411yescharacteristic
52C2×C22⋊Dic17—22no—
53C2×C4⋊Dic17—41no—
54C2×#63223—22no—
55C17×#95—21no—
56C17×#95—21no—
57C17×#95—21no—
58#10587505—22no—
59#10587505—22no—
60#10587504—22no—
61#10587504—22no—
62#10587502—41no—
63C4⋊#3622—41no—
64C4⋊#3622—41no—
65C24×C17—21no—
66C24×C17—21no—
67C24×C17—41no—
68C24×C17—41no—
69C24×C17—81no—
70C24×C17—81no—
71C24×C17C4⋊C412yescomplemented
72C24×C17C22×C411yescharacteristic
73C24×C17C2×D411yescharacteristic
74C2×D4×C17—22no—
75C2×D4×C17—22no—
76C2×D4×C17—41no—
77C2×D4×C17—41no—
78C2×D4×C17—81no—
79C2×D4×C17—81no—
80C2×D4×C17C2×D411yescharacteristic
81C2×D4×C17C2×Q811yescharacteristic
82C2×D4×C17#4111yescharacteristic
83C2×D4×C17#4111yescharacteristic
84C22×C4×C17—21no—
85C22×C4×C17—21no—
86C22×C4×C17—21no—
87C22×C4×C17—21no—
88C22×C4×C17—21no—
89C22×C4×C17—21no—
90C22×C4×C17—21no—
91C22×C4×C17—41no—
92C22×C4×C17—81no—
93C22×C4×C17—81no—
94C22×C4×C17—81no—
95C22×C4×C17C22⋊C411yescharacteristic
96C22×C4×C17C22⋊C411yescharacteristic
97C22×C4×C17C22⋊C411yescharacteristic
98C22×C4×C17C22⋊C411yescharacteristic
99C22×C4×C17C2×D411yescharacteristic
100C22×Dic17—42no—
101C4⋊C4×C17—41no—
102C4⋊C4×C17—81no—
103C22⋊C4×C17—21no—
104C22⋊C4×C17—22no—
105C22⋊C4×C17—22no—
106C22⋊C4×C17—41no—
107C22⋊C4×C17—41no—
108C22⋊C4×C17—42no—
109C22⋊C4×C17—41no—
110C22⋊C4×C17—41no—
111C22⋊C4×C17—41no—
112C22⋊C4×C17—81no—
113C22⋊C4×C17—81no—
114C22⋊C4×C17—81no—
115C22⋊C4×C17C4⋊C412yescomplemented
116C42×C17—21no—
117C42×C17—21no—
118C42×C17—81no—
119C22⋊Dic17—42no—
120C22⋊Dic17—42no—
121C4⋊Dic17—82no—
122#63223—42no—
123#63223—42no—
124C2×#3622—42no—
125#12795—171nomaximal, Sylow
126C23×C17—21no—
127C23×C17—21no—
128C23×C17—21no—
129C23×C17—21no—
130C23×C17—22no—
131C23×C17—41no—
132C23×C17—41no—
133C23×C17—41no—
134C23×C17—41no—
135C23×C17—41no—
136C23×C17—41no—
137C23×C17—41no—
138C23×C17—41no—
139C23×C17—42no—
140C23×C17—42no—
141C23×C17—41no—
142C23×C17—41no—
143C23×C17—82no—
144C23×C17—82no—
145C23×C17—82no—
146C23×C17—82no—
147C23×C17—84no—
148C23×C17C2×C22⋊C411yescharacteristic
149C23×C17C2×C4⋊C411yescharacteristic
150C23×C17#11711yescharacteristic
151C23×C17#12111yescharacteristic
152C23×C17C22⋊Q811yescharacteristic
153D4×C17—41no—
154D4×C17—41no—
155D4×C17—41no—
156D4×C17—41no—
157D4×C17—82no—
158D4×C17—82no—
159C2×C4×C17—21no—
160C2×C4×C17—21no—
161C2×C4×C17—22no—
162C2×C4×C17—21no—
163C2×C4×C17—21no—
164C2×C4×C17—21no—
165C2×C4×C17—41no—
166C2×C4×C17—42no—
167C2×C4×C17—41no—
168C2×C4×C17—41no—
169C2×C4×C17—41no—
170C2×C4×C17—41no—
171C2×C4×C17—41no—
172C2×C4×C17—41no—
173C2×C4×C17—41no—
174C2×C4×C17—41no—
175C2×C4×C17—41no—
176C2×C4×C17—41no—
177C2×C4×C17—41no—
178C2×C4×C17—81no—
179C2×C4×C17—81no—
180C2×C4×C17—81no—
181C2×C4×C17—82no—
182C2×C4×C17#9911yescharacteristic
183C2×C4×C17#9911yescharacteristic
184C2×C4×C17#12111yescharacteristic
185C2×C4×C17C22⋊Q811yescharacteristic
186C2×Dic17—82no—
187C2×Dic17—82no—
188C2×Dic17—82no—
189#3622—82no—
190#2321D1711yescharacteristic
191C2×AΣL(1,𝔽16)—172no—
192#1800—171no—
193#1799—171no—
194#1390—172no—
195C22×C17—21no—
196C22×C17—21no—
197C22×C17—21no—
198C22×C17—21no—
199C22×C17—21no—
200C22×C17—21no—
201C22×C17—41no—
202C22×C17—41no—
203C22×C17—41no—
204C22×C17—41no—
205C22×C17—42no—
206C22×C17—42no—
207C22×C17—42no—
208C22×C17—41no—
209C22×C17—41no—
210C22×C17—41no—
211C22×C17—41no—
212C22×C17—42no—
213C22×C17—81no—
214C22×C17—81no—
215C22×C17—81no—
216C22×C17—84no—
217C22×C17—84no—
218C22×C17—81no—
219C22×C17—81no—
220C22×C17#38011yescharacteristic
221C22×C17C2×#9911yescharacteristic
222C22×C17#41011yescharacteristic
223C4×C17—21no—
224C4×C17—21no—
225C4×C17—21no—
226C4×C17—21no—
227C4×C17—42no—
228C4×C17—41no—
229C4×C17—41no—
230C4×C17—41no—
231C4×C17—81no—
232C4×C17—81no—
233Dic17—162no—
234C2×#120C2×D1711yescharacteristic
235C2×C4×D4C2×D1711yescharacteristic
236C22×C22⋊C4Dic1711yescharacteristic, complemented
237#423—341no—
238C2×#100—172no—
239C2×#99—172no—
240#390—21no—
241#388—21no—
242#388—21no—
243#386—21no—
244#386C2×D1711yescharacteristic
245#385Dic1711yescharacteristic, complemented
246#380—341no—
247#379Dic1711yescharacteristic, complemented
248C4×C22⋊C4Dic1711yescharacteristic, complemented
249AΣL(1,𝔽16)—344no—
250#343—341no—
251#342—341no—
252C2×C17—21no—
253C2×C17—21no—
254C2×C17—41no—
255C2×C17—41no—
256C2×C17—41no—
257C2×C17—41no—
258C2×C17—82no—
259C2×C17#179911yescharacteristic
260C2×C17#212111yescharacteristic
261C2×C17#212211yescharacteristic
262C25C2×Dic1711yescharacteristic
263C22×D4—21no—
264C22×D4C22×D1711yescharacteristic
265C23×C4C2×Dic1711yescharacteristic
266C23×C4C2×Dic1711yescharacteristic
267C23×C4C22⋊D1711yescharacteristic
268C2×M16—342no—
269#120—21no—
270#120—21no—
271#120Dic3412yes—
272#120D6812yes—
273C4×D4—41no—
274C4×D4—41no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—681no—
277C2×C4⋊C4C22⋊D1711yescharacteristic
278C2×C22⋊C4—21no—
279C2×C22⋊C4—21no—
280C2×C22⋊C4—21no—
281C2×C22⋊C4—21no—
282C2×C22⋊C4—21no—
283C2×C22⋊C4—21no—
284C2×C22⋊C4—41no—
285C2×C22⋊C4—41no—
286C2×C22⋊C4—342no—
287C2×C22⋊C4C2×Dic1711yescharacteristic
288C2×C22⋊C4C2×Dic1711yescharacteristic
289C2×C22⋊C4C2×Dic1711yescharacteristic
290C2×C22⋊C4C22⋊D1711yescharacteristic
291C2×C42—21no—
292C2×C42C22⋊D1711yescharacteristic
293C4⋊C8—681no—
294C4⋊C8—681no—
295#100—342no—
296#100—342no—
297#99—342no—
298#99—342no—
299#95—21no—
300#95—21no—
301#95—21no—
302#95—681no—
303C17#1279511yescharacteristic, complemented, Sylow
304C24—21no—
305C24—21no—
306C24—41no—
307C24—41no—
308C24—81no—
309C24—81no—
310C24C4⋊Dic1712yescomplemented
311C24C22×Dic1711yescharacteristic
312C24C2×C22⋊D1711yescharacteristic
313C2×D4—22no—
314C2×D4—22no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—81no—
318C2×D4—81no—
319C2×D4C2×Dic3411yescharacteristic
320C2×D4C2×D6811yescharacteristic
321C2×D4#6325211yescharacteristic
322C2×D4#6325211yescharacteristic
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—41no—
331C22×C4—81no—
332C22×C4—81no—
333C22×C4—81no—
334C22×C4—682no—
335C22×C4C22⋊Dic1711yescharacteristic
336C22×C4C22⋊Dic1711yescharacteristic
337C22×C4C22⋊Dic1711yescharacteristic
338C22×C4C22⋊Dic1711yescharacteristic
339C22×C4C2×C22⋊D1711yescharacteristic
340M16—682no—
341M16—682no—
342C2×C8—682no—
343C4⋊C4—41no—
344C4⋊C4—81no—
345C4⋊C4—1362no—
346C22⋊C4—21no—
347C22⋊C4—22no—
348C22⋊C4—22no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C22⋊C4—42no—
352C22⋊C4—41no—
353C22⋊C4—41no—
354C22⋊C4—41no—
355C22⋊C4—81no—
356C22⋊C4—81no—
357C22⋊C4—81no—
358C22⋊C4—682no—
359C22⋊C4—682no—
360C22⋊C4C4⋊Dic1712yescomplemented
361C42—21no—
362C42—21no—
363C42—81no—
364C23—21no—
365C23—21no—
366C23—21no—
367C23—21no—
368C23—22no—
369C23—41no—
370C23—41no—
371C23—41no—
372C23—41no—
373C23—41no—
374C23—41no—
375C23—41no—
376C23—41no—
377C23—42no—
378C23—42no—
379C23—41no—
380C23—41no—
381C23—82no—
382C23—82no—
383C23—82no—
384C23—82no—
385C23—84no—
386C23#1058761011yescharacteristic
387C23C2×C4⋊Dic1711yescharacteristic
388C23#1058761211yescharacteristic
389C23#1058761611yescharacteristic
390C23C2×C22⋊Dic1711yescharacteristic
391D4—41no—
392D4—41no—
393D4—41no—
394D4—41no—
395D4—82no—
396D4—82no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—22no—
403C2×C4—41no—
404C2×C4—42no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—81no—
417C2×C4—81no—
418C2×C4—81no—
419C2×C4—82no—
420C2×C4—1362no—
421C2×C4—1362no—
422C2×C4—1362no—
423C2×C4#1058750511yescharacteristic
424C2×C4#1058750511yescharacteristic
425C2×C4#1058761011yescharacteristic
426C2×C4#1058761611yescharacteristic
427C8—1362no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—41no—
435C22—41no—
436C22—41no—
437C22—41no—
438C22—42no—
439C22—42no—
440C22—42no—
441C22—41no—
442C22—41no—
443C22—41no—
444C22—41no—
445C22—42no—
446C22—81no—
447C22—81no—
448C22—81no—
449C22—84no—
450C22—84no—
451C22—81no—
452C22—81no—
453C22#1176266911yescharacteristic
454C22C2×#1058750511yescharacteristic
455C22#1176278311yescharacteristic
456C4—21no—
457C4—21no—
458C4—21no—
459C4—21no—
460C4—42no—
461C4—41no—
462C4—41no—
463C4—41no—
464C4—81no—
465C4—81no—
466C4—2722no—
467C2—21no—
468C2—21no—
469C2—41no—
470C2—41no—
471C2—41no—
472C2—41no—
473C2—82no—
474C2#1452877211yescharacteristic
475C2#1453043011yescharacteristic
476C2#1453043411yescharacteristic
subgroupG/H
centerC22C2×#10587505
commutatorC24×C17C22×C4
FrattiniC22×D4C22×D17
FittingC17×#2321C2
socleC22×C17C2×#99
prime radicalC2×C17×#120C22
cosocleC22×D4×C17C23
hypercenter#2321D17
hypocenterC17#12795
LCSG ▷ C24×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2321

Complements

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

NH ≅ G/Ntype
2. #14528776C2semidirect
3. #14528772C2semidirect
4. #14526902C2semidirect
15. C22×C22⋊C4×C17C4semidirect
21. C17×#385C4semidirect
22. C17×#379C4semidirect
23. C4×C22⋊C4×C17C4semidirect
71. C24×C17C4⋊C4semidirect
115. C22⋊C4×C17C4⋊C4semidirect
236. C22×C22⋊C4Dic17semidirect
245. #385Dic17semidirect
247. #379Dic17semidirect
248. C4×C22⋊C4Dic17semidirect
303. C17#12795semidirect
310. C24C4⋊Dic17semidirect
360. C22⋊C4C4⋊Dic17semidirect

Maximal subgroups

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

subgroupindex
C2×#117625962
#145287762
#145287722
#145269022
C17×#23212
#1279517