Finite Group Databasebeta

← #17969690

Subgroups — #17969690

Order 4352.

954 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763824C212yesmaximal
2C2×D17⋊#108C211yesmaximal, characteristic
3C22×#10587535C211yesmaximal, characteristic
4#14545427C212yesmaximal
5#14544726C214yesmaximal, complemented
6#14544724C212yesmaximal, complemented
7#14544723C212yesmaximal, complemented
8D17×#405C211yesmaximal, characteristic
9C22×#63243C2212yes—
10C2×D17⋊M16C2212yes—
11#11763824—28no—
12C2×#10587536C2212yes—
13C2×#10587536C2214yes—
14D17⋊#108—24no—
15C2×#10587535—24no—
16C2×#10587535C2212yes—
17C2×#10587535C2212yes—
18C2×#10587535C2211yescharacteristic
19C2×#10587535C2211yescharacteristic
20C2×#10587535C2214yes—
21#11763816—24no—
22#11763815—24no—
23#11763814C2214yes—
24#11763813C2214yes—
25C2×M16×D17C2211yescharacteristic
26C22×C8×D17C2211yescharacteristic
27#117×D17C2211yescharacteristic
28#11762767C411yescharacteristic
29#11762766C412yes—
30#11762765C411yescharacteristic
31#11762764C411yescharacteristic
32#11762763C412yes—
33#97×D17C2212yes—
34C4×C8×D17C2212yes—
35C17×#405C411yescharacteristic
36C22×C4×D17C2311yescharacteristic
37C2×#63247—22no—
38C22×#3624—22no—
39D17⋊M16—24no—
40D17⋊M16—24no—
41C2×#63243—24no—
42C2×#63243—24no—
43C2×#63243—22no—
44C2×#63243C2312yes—
45C2×#63243C2314yes—
46C2×#63243C2312yes—
47C2×#63242—22no—
48C2×M16×C17C2×C411yescharacteristic
49C22×C8×C17C2×C411yescharacteristic
50C17×#117C2×C411yescharacteristic
51#10587612C2×C411yescharacteristic
52C2×#63223C2×C411yescharacteristic
53C22×#3622C2×C411yescharacteristic
54M16×D17D414yes—
55M16×D17Q814yes—
56C2×#63218C2×C412yes—
57C2×C8×D17C2×C411yescharacteristic
58C2×C8×D17C2×C411yescharacteristic
59C2×C8×D17D414yes—
60C2×C8×D17Q814yes—
61C2×C8×D17C2311yescharacteristic
62C2×C8×D17C2312yes—
63C2×C8×D17C2311yescharacteristic
64#10587578D412yes—
65C4⋊C4×D17Q812yes—
66C22⋊C4×D17Q812yes—
67#10587563D412yes—
68#10587558C2×C412yes—
69C42×D17C2312yes—
70#10587544—28no—
71C4⋊#3624—28no—
72#10587536—24no—
73#10587536—28no—
74#10587535—24no—
75#10587535—24no—
76#10587535—22no—
77#10587535—22no—
78#10587535—28no—
79C17×#97C2×C412yes—
80C4×C8×C17C2×C412yes—
81#10587486C2×C412yes—
82#10587486C2×C412yes—
83C8×Dic17C2×C412yes—
84C8×Dic17C2×C412yes—
85#10587474C2×C412yes—
86C4×#3622C2×C412yes—
87C23×D17C2×Q811yescharacteristic
88C22×C4×C17C22×C411yescharacteristic
89C22×Dic17C2×D411yescharacteristic
90C2×C4×D17C22×C411yescharacteristic
91C2×C4×D17C2×D412yes—
92C2×C4×D17C2×D412yes—
93C2×C4×D17C2×D411yescharacteristic
94C2×C4×D17C2×Q814yes—
95C2×C4×D17C2×Q812yes—
96C2×C4×D17C2×Q812yes—
97C2×C4×D17C2×Q811yescharacteristic
98C2×C4×D17C2411yescharacteristic
99#63247—44no—
100C2×#3624—22no—
101C2×#3624—22no—
102C2×#3624—24no—
103C2×#3624—44no—
104#63243—24no—
105#63243—24no—
106#63243—22no—
107#63243—22no—
108#63243—22no—
109#63243—22no—
110#63243—44no—
111#63242—44no—
112M16×C17C4⋊C414yes—
113C2×C8×C17C4⋊C414yes—
114C2×C8×C17C22×C411yescharacteristic
115C2×C8×C17C22×C411yescharacteristic
116C2×C8×C17C22×C412yes—
117C4⋊C4×C17C4⋊C412yes—
118C22⋊C4×C17C4⋊C412yes—
119C42×C17C22×C412yes—
120C22⋊Dic17C4⋊C412yes—
121#63227C4⋊C414yes—
122C4⋊Dic17C4⋊C412yes—
123#63225C4⋊C414yes—
124C4×Dic17C22×C412yes—
125C4×Dic17C2×D414yes—
126#63223C4⋊C414yes—
127C2×#3622C4⋊C414yes—
128C2×#3622C22×C411yescharacteristic
129C2×#3622C22×C412yes—
130C2×#3622C22×C411yescharacteristic
131#63218C4⋊C418yes—
132C8×D17C4⋊C414yes—
133C8×D17C4⋊C414yes—
134C8×D17C2×D412yes—
135C8×D17C2×D412yes—
136C8×D17C2×D414yes—
137C8×D17C2×Q812yes—
138C8×D17C2×Q812yes—
139C8×D17C2×Q814yes—
140#20807—171nomaximal, Sylow
141C23×C17C2×C4⋊C411yescharacteristic
142C22×D17—42no—
143C22×D17C2×C4⋊C411yescharacteristic
144C22×D17C4⋊Q812yes—
145C22×D17C4⋊Q812yes—
146C22×D17C22×Q811yescharacteristic
147C2×C4×C17C2×C4⋊C414yes—
148C2×C4×C17C2×C4⋊C412yes—
149C2×C4×C17C2×C4⋊C412yes—
150C2×C4×C17C2×C4⋊C411yescharacteristic
151C2×C4×C17C23×C411yescharacteristic
152C2×Dic17C2×C4⋊C414yes—
153C2×Dic17C2×C4⋊C411yescharacteristic
154C2×Dic17#12712yes—
155C2×Dic17C4⋊Q812yes—
156C2×Dic17C22×D411yescharacteristic
157C4×D17—44no—
158C4×D17C2×C4⋊C412yes—
159C4×D17C2×C4⋊C412yes—
160C4×D17#12712yes—
161C4×D17C4⋊Q812yes—
162C4×D17C4⋊Q812yes—
163C4×D17C4⋊Q812yes—
164C4×D17C22×D411yescharacteristic
165C4×D17C22×D411yescharacteristic
166C4×D17C22×Q811yescharacteristic
167C4×D17C22×Q811yescharacteristic
168#3624—42no—
169#3624—42no—
170#3624—44no—
171C8×C17C2×C4⋊C412yes—
172C8×C17C2×C4⋊C412yes—
173C8×C17C2×C4⋊C414yes—
174#3622C2×C4⋊C412yes—
175#3622C2×C4⋊C412yes—
176#3622C2×C4⋊C414yes—
177C2×#430—172no—
178C22×#108—171no—
179C22×#108—171no—
180#2905—172no—
181C2×#405—171no—
182#1849—174no—
183#1848—172no—
184#1848—172no—
185C22×C17—22no—
186C22×C17#38412yes—
187C22×C17C22×C4⋊C411yescharacteristic
188C2×D17—22no—
189C2×D17—22no—
190C2×D17—42no—
191C2×D17—42no—
192C2×D17#38412yes—
193C2×D17C2×C4⋊Q811yescharacteristic
194C2×D17C2×C4⋊Q811yescharacteristic
195C4×C17—24no—
196C4×C17#38412yes—
197C4×C17C22×C4⋊C411yescharacteristic
198C4×C17C22×C4⋊C411yescharacteristic
199Dic17—24no—
200Dic17#38412yes—
201Dic17C2×#12711yescharacteristic
202Dic17C2×C4⋊Q811yescharacteristic
203C22×M16—171no—
204C22×M16—172no—
205C22×M16—172no—
206C23×C8—171no—
207C2×#117—171no—
208#430—348no—
209C2×#108—171no—
210C2×#108—172no—
211C2×#108—171no—
212C2×#108—174no—
213C2×#108—174no—
214C2×#108—172no—
215C2×#108—172no—
216C2×#108—344no—
217C2×#108—344no—
218#424—344no—
219#424—344no—
220#423—174no—
221#423—174no—
222#405—171no—
223#405—171no—
224#405—171no—
225#405—172no—
226#405—172no—
227#405#59511yescharacteristic
228C2×#97—172no—
229C2×C4×C8—172no—
230C2×C17—22no—
231C2×C17C2×#38411yescharacteristic
232C2×C17#291612yes—
233D17—21no—
234D17—21no—
235D17—22no—
236C23×C4—171no—
237C2×M16—171no—
238C2×M16—174no—
239C2×M16—174no—
240C2×M16—172no—
241C2×M16—172no—
242C2×M16—174no—
243C2×M16—172no—
244C2×M16—342no—
245C2×M16—342no—
246C2×M16—344no—
247C2×M16—344no—
248C2×M16—344no—
249C2×M16—344no—
250C2×M16C2×#59511yescharacteristic
251C22×C8—171no—
252C22×C8—174no—
253C22×C8—174no—
254C22×C8—171no—
255C22×C8—171no—
256C22×C8—171no—
257C22×C8—171no—
258C22×C8—172no—
259C22×C8—342no—
260C22×C8—342no—
261C22×C8C2×#59511yescharacteristic
262#117—171no—
263#117—172no—
264#117—172no—
265#117—172no—
266#117C2×#59511yescharacteristic
267C2×C4⋊C4—172no—
268C2×C22⋊C4—172no—
269C2×C42—172no—
270#108—344no—
271#108—344no—
272#108—342no—
273#108—342no—
274#108—348no—
275#108—344no—
276#108—348no—
277C4⋊C8—348no—
278C4⋊C8—348no—
279#97—172no—
280#97—172no—
281#97—172no—
282#97C2×#59512yes—
283C4×C8—172no—
284C4×C8—172no—
285C4×C8—172no—
286C4×C8C2×#59512yes—
287C17#2080711yescharacteristic, complemented, Sylow
288C24—171no—
289C22×C4—171no—
290C22×C4—171no—
291C22×C4—172no—
292C22×C4—172no—
293C22×C4—171no—
294C22×C4—172no—
295C22×C4—172no—
296C22×C4—171no—
297C22×C4—171no—
298C22×C4—174no—
299C22×C4C22×#59511yescharacteristic
300M16—174no—
301M16—178no—
302M16—344no—
303M16—344no—
304M16—342no—
305M16—342no—
306M16—342no—
307M16—342no—
308M16—684no—
309M16—684no—
310M16C4⋊#59514yes—
311C2×C8—174no—
312C2×C8—171no—
313C2×C8—172no—
314C2×C8—171no—
315C2×C8—172no—
316C2×C8—172no—
317C2×C8—174no—
318C2×C8—174no—
319C2×C8—174no—
320C2×C8—172no—
321C2×C8—172no—
322C2×C8—174no—
323C2×C8—342no—
324C2×C8—342no—
325C2×C8—344no—
326C2×C8—684no—
327C2×C8—684no—
328C2×C8C4⋊#59514yes—
329C2×C8C22×#59511yescharacteristic
330C2×C8C22×#59512yes—
331C2×C8C22×#59511yescharacteristic
332C4⋊C4—174no—
333C4⋊C4—172no—
334C4⋊C4C4⋊#59512yes—
335C22⋊C4—172no—
336C22⋊C4—174no—
337C22⋊C4C4⋊#59512yes—
338C42—174no—
339C42—172no—
340C42C22×#59512yes—
341C23—171no—
342C23—171no—
343C23—172no—
344C23—172no—
345C23—682no—
346C23C2×C4⋊#59511yescharacteristic
347C2×C4—172no—
348C2×C4—172no—
349C2×C4—171no—
350C2×C4—171no—
351C2×C4—172no—
352C2×C4—172no—
353C2×C4—172no—
354C2×C4—172no—
355C2×C4—171no—
356C2×C4—171no—
357C2×C4—172no—
358C2×C4—171no—
359C2×C4—171no—
360C2×C4—172no—
361C2×C4—174no—
362C2×C4—684no—
363C2×C4C2×C4⋊#59514yes—
364C2×C4C2×C4⋊#59511yescharacteristic
365C2×C4C2×C4⋊#59512yes—
366C2×C4C2×C4⋊#59512yes—
367C2×C4C23×#59511yescharacteristic
368C8—172no—
369C8—172no—
370C8—174no—
371C8—682no—
372C8—682no—
373C8—684no—
374C8C2×C4⋊#59512yes—
375C8C2×C4⋊#59512yes—
376C8C2×C4⋊#59514yes—
377C22—22no—
378C22—171no—
379C22—171no—
380C22—172no—
381C22—342no—
382C22—342no—
383C22—682no—
384C22—682no—
385C22#1176375512yes—
386C22C22×C4⋊#59511yescharacteristic
387C4—24no—
388C4—171no—
389C4—171no—
390C4—172no—
391C4—344no—
392C4#1176375512yes—
393C4C22×C4⋊#59511yescharacteristic
394C4C22×C4⋊#59511yescharacteristic
395C2—22no—
396C2—341no—
397C2—341no—
398C2—342no—
399C2C2×#1176375511yescharacteristic
400C2#1454544512yes—
subgroupG/H
centerC22C22×C4⋊#595
commutatorC2×C4×C17C23×C4
FrattiniC2×C4C23×#595
FittingC17×#405C4
socleC22×C17C22×C4⋊C4
prime radicalC23×D17C2×Q8
cosocleC2×C4×D17C24
hypercenter#405#595
hypocenterC17#20807
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ #117 ◁ #405

Complements

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

NH ≅ G/Ntype
5. #14544726C2semidirect
6. #14544724C2semidirect
7. #14544723C2semidirect
287. C17#20807semidirect

Maximal subgroups

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

subgroupindex
C2×#117638242
C2×D17⋊#1082
C22×#105875352
#145454272
#145447262
#145447242
#145447232
D17×#4052
#2080717