Finite Group Databasebeta

← #17964015

Subgroups — #17964015

Order 4352.

902 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14545448C211yesmaximal, characteristic
2C2×C4×#63242C211yesmaximal, characteristic
3#14544000C214yesmaximal, complemented
4#14543999C214yesmaximal, complemented
5#14543980C212yesmaximal, complemented
6#14543978C212yesmaximal, complemented
7D17×#431C211yesmaximal, characteristic
8C22×#63242C412yes—
9#11763828C2212yes—
10#11763827C412yes—
11#11763826C2212yes—
12#11763825C412yes—
13#11763810C412yes—
14#11763777C412yes—
15C4×#63242C412yes—
16C4×#63242C412yes—
17C4×#63242C2212yes—
18C4×#63242C2211yescharacteristic
19C4×#63242C2211yescharacteristic
20C4×#63242C2212yes—
21C2×C4×#3624C412yes—
22C2×C4×#3624C2212yes—
23#11763651C2218yescomplemented
24#11763650C2218yescomplemented
25C2×C42×D17C2211yescharacteristic
26#11762862C411yescharacteristic
27#11762861C2212yes—
28#11762860C412yes—
29#11762859C2212yes—
30C4⋊C8×D17C412yes—
31C22⋊C8×D17C412yes—
32C4×C8×D17C2212yes—
33C17×#431C411yescharacteristic
34C22×C4×D17C2×C411yescharacteristic
35C22×C4×D17C2×C411yescharacteristic
36C22×C4×D17C2×C411yescharacteristic
37C22×#3624C2×C414yes—
38C2×#63242—28no—
39C2×#63242C2×C412yes—
40C2×#63242C2×C412yes—
41C2×#63242C2×C414yes—
42C2×#63242C2×C414yes—
43C2×C42×C17C2×C411yescharacteristic
44C2×C4×Dic17C2×C411yescharacteristic
45C2×C4×Dic17C2×C411yescharacteristic
46C2×C4×Dic17C2311yescharacteristic
47C2×C8×D17C2×C414yes—
48C42×D17C2×C411yescharacteristic
49C42×D17C2×C411yescharacteristic
50C42×D17C2×C411yescharacteristic
51C42×D17C2×C411yescharacteristic
52C42×D17C2×C411yescharacteristic
53C42×D17C2×C411yescharacteristic
54C42×D17C2311yescharacteristic
55C42×D17C2311yescharacteristic
56C22⋊#3624C2×C414yes—
57#10587544C2×C414yes—
58#10587543C2×C414yes—
59C4⋊#3624C2×C414yes—
60C4×#3624C2×C412yes—
61C4×#3624C2×C412yes—
62C4×#3624C2×C414yes—
63C4×#3624C2×C414yes—
64C4×#3624C2×C414yes—
65C4×#3624C2312yes—
66C4×#3624C2312yes—
67C4×#3624C2314yes—
68C17×C4⋊C8C2×C412yes—
69C17×C22⋊C8C2×C412yes—
70C4×C8×C17C2×C412yes—
71C22⋊#3622C2×C412yes—
72#10587491C2×C414yes—
73#10587485C2×C414yes—
74C8×Dic17C2314yes—
75C4⋊#3622C2×C412yes—
76C4×#3622C2×C412yes—
77C23×D17C4211yescharacteristic
78C22×C4×C17C4211yescharacteristic
79C22×C4×C17C4211yescharacteristic
80C22×C4×C17C22×C411yescharacteristic
81C22×Dic17C4211yescharacteristic
82C22×Dic17C22×C411yescharacteristic
83C22×Dic17C22×C411yescharacteristic
84C2×C4×D17—24no—
85C2×C4×D17—24no—
86C2×C4×D17C4211yescharacteristic
87C2×C4×D17C4211yescharacteristic
88C2×C4×D17C4211yescharacteristic
89C2×C4×D17C4211yescharacteristic
90C2×C4×D17C4211yescharacteristic
91C2×C4×D17C4211yescharacteristic
92C2×C4×D17M1618yes—
93C2×C4×D17C22×C411yescharacteristic
94C2×C4×D17C22×C411yescharacteristic
95C2×C4×D17C22×C411yescharacteristic
96C2×C4×D17C22×C411yescharacteristic
97C2×C4×D17C22×C411yescharacteristic
98C2×C4×D17C22×C411yescharacteristic
99C2×#3624—28no—
100C2×#3624C22×C414yes—
101C2×#3624C22×C414yes—
102C2×#3624C22×C418yes—
103#63242—28no—
104#63242—24no—
105#63242—24no—
106#63242—28no—
107C2×C8×C17C22×C414yes—
108C42×C17C4211yescharacteristic
109C42×C17C4211yescharacteristic
110C42×C17C22×C411yescharacteristic
111C42×C17C22×C411yescharacteristic
112C4×Dic17C4211yescharacteristic
113C4×Dic17C4211yescharacteristic
114C4×Dic17C4211yescharacteristic
115C4×Dic17C4211yescharacteristic
116C4×Dic17C22×C411yescharacteristic
117C4×Dic17C22×C411yescharacteristic
118C4×Dic17C22×C411yescharacteristic
119C4×Dic17C22×C411yescharacteristic
120C4×Dic17C22×C411yescharacteristic
121C4×Dic17C22×C411yescharacteristic
122C4×Dic17C22×C411yescharacteristic
123C4×Dic17C2411yescharacteristic
124C2×#3622C22×C414yes—
125C8×D17—28no—
126C2×#1452—171nomaximal, Sylow
127C23×C17C2×C4211yescharacteristic
128C22×D17—22no—
129C22×D17—22no—
130C22×D17#9714yes—
131C22×D17C2×C4211yescharacteristic
132C22×D17C2×C4211yescharacteristic
133C2×C4×C17—22no—
134C2×C4×C17—22no—
135C2×C4×C17#9714yes—
136C2×C4×C17C2×C4211yescharacteristic
137C2×C4×C17C2×C4211yescharacteristic
138C2×C4×C17C2×C4211yescharacteristic
139C2×C4×C17C2×C4211yescharacteristic
140C2×C4×C17C2×C4211yescharacteristic
141C2×C4×C17C23×C411yescharacteristic
142C2×Dic17—22no—
143C2×Dic17—22no—
144C2×Dic17C2×C4211yescharacteristic
145C2×Dic17C2×C4211yescharacteristic
146C2×Dic17C2×C4211yescharacteristic
147C2×Dic17C2×C4211yescharacteristic
148C2×Dic17C2×M1614yes—
149C2×Dic17C23×C411yescharacteristic
150C2×Dic17C23×C411yescharacteristic
151C4×D17—22no—
152C4×D17—22no—
153C4×D17—22no—
154C4×D17—22no—
155C4×D17—22no—
156C4×D17—22no—
157C4×D17#9714yes—
158C4×D17#9714yes—
159C4×D17C2×M1614yes—
160C4×D17C2×M1614yes—
161C4×D17#13114yes—
162C4×D17#13114yes—
163#3624—24no—
164#3624—24no—
165#3624—28no—
166C8×C17—24no—
167#3622—24no—
168C2×#431—171no—
169C2×#431—171no—
170C22×C4×C8—171no—
171#1452—174no—
172#1452—174no—
173C2×#322—172no—
174C2×#322—172no—
175C22×C17—21no—
176C22×C17—21no—
177C22×C17C2×#9712yes—
178C22×C17C22×C4211yescharacteristic
179C2×D17—21no—
180C2×D17—21no—
181C2×D17—28no—
182C2×D17C2×#9712yes—
183C2×D17C2×#9712yes—
184C2×D17#40512yes—
185C2×D17#40512yes—
186C4×C17—21no—
187C4×C17—21no—
188C4×C17C2×#9712yes—
189C4×C17C2×#9712yes—
190C4×C17#40512yes—
191C4×C17C2×#13112yes—
192Dic17—21no—
193Dic17—21no—
194Dic17C2×#9712yes—
195Dic17#40512yes—
196Dic17C22×M1612yes—
197Dic17C2×#13112yes—
198C23×C8—172no—
199C22×C42—171no—
200#431—172no—
201#431—172no—
202#431—172no—
203#431—172no—
204#431—171no—
205#431—172no—
206#431—172no—
207#431—172no—
208#431#59511yescharacteristic
209C2×C4⋊C8—172no—
210C2×C4⋊C8—172no—
211C2×C22⋊C8—172no—
212C2×C22⋊C8—172no—
213C2×C4×C8—172no—
214C2×C4×C8—172no—
215C2×C4×C8—172no—
216C2×C4×C8—172no—
217C2×C4×C8—171no—
218C2×C4×C8—171no—
219C2×C4×C8—172no—
220C2×C4×C8—172no—
221C2×C4×C8—172no—
222#322—178no—
223#322—178no—
224C2×C17—22no—
225C2×C17C22×#9711yescharacteristic
226C2×C17C2×#40511yescharacteristic
227C2×C17C2×#40511yescharacteristic
228D17—22no—
229D17#145214yescomplemented
230C23×C4—171no—
231C23×C4—171no—
232C23×C4—171no—
233C22×C8—172no—
234C22×C8—172no—
235C22×C8—174no—
236C22×C8—174no—
237C22×C8—174no—
238C22×C8—174no—
239C22×C8—348no—
240C2×C42—171no—
241C2×C42—171no—
242C2×C42—171no—
243C2×C42—171no—
244C2×C42—171no—
245C2×C42—171no—
246C2×C42—171no—
247C2×C42—171no—
248C2×C42—171no—
249C2×C42—171no—
250C2×C42—171no—
251C2×C42C2×#59511yescharacteristic
252C4⋊C8—174no—
253C4⋊C8—174no—
254C4⋊C8—174no—
255C4⋊C8—172no—
256C4⋊C8C2×#59512yes—
257C22⋊C8—174no—
258C22⋊C8—174no—
259C22⋊C8—172no—
260C22⋊C8—174no—
261C22⋊C8C2×#59512yes—
262C4×C8—172no—
263C4×C8—172no—
264C4×C8—174no—
265C4×C8—172no—
266C4×C8—172no—
267C4×C8—174no—
268C4×C8—174no—
269C4×C8—174no—
270C4×C8—174no—
271C4×C8—172no—
272C4×C8C2×#59512yes—
273C17C2×#145211yescharacteristic, complemented, Sylow
274C24—171no—
275C22×C4—171no—
276C22×C4—171no—
277C22×C4—171no—
278C22×C4—171no—
279C22×C4—171no—
280C22×C4—171no—
281C22×C4—171no—
282C22×C4—178no—
283C22×C4—171no—
284C22×C4—171no—
285C22×C4—171no—
286C22×C4—171no—
287C22×C4—171no—
288C22×C4—171no—
289C22×C4—171no—
290C22×C4—171no—
291C22×C4—344no—
292C22×C4—344no—
293C22×C4C4×#59511yescharacteristic
294C22×C4C4×#59511yescharacteristic
295C22×C4C22×#59511yescharacteristic
296C2×C8—174no—
297C2×C8—174no—
298C2×C8—178no—
299C2×C8—174no—
300C2×C8—348no—
301C2×C8—348no—
302C2×C8—344no—
303C2×C8—344no—
304C2×C8—348no—
305C2×C8—348no—
306C2×C8C22×#59514yes—
307C42—171no—
308C42—171no—
309C42—171no—
310C42—171no—
311C42—171no—
312C42—171no—
313C42—171no—
314C42—171no—
315C42—171no—
316C42—171no—
317C42—171no—
318C42—171no—
319C42C4×#59511yescharacteristic
320C42C4×#59511yescharacteristic
321C42C22×#59511yescharacteristic
322C42C22×#59511yescharacteristic
323C23—171no—
324C23—174no—
325C23—171no—
326C23—342no—
327C23—342no—
328C23C2×C4×#59511yescharacteristic
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—174no—
332C2×C4—171no—
333C2×C4—171no—
334C2×C4—171no—
335C2×C4—171no—
336C2×C4—174no—
337C2×C4—174no—
338C2×C4—174no—
339C2×C4—174no—
340C2×C4—174no—
341C2×C4—174no—
342C2×C4—171no—
343C2×C4—171no—
344C2×C4—342no—
345C2×C4—342no—
346C2×C4—342no—
347C2×C4—342no—
348C2×C4—342no—
349C2×C4—342no—
350C2×C4—342no—
351C2×C4—342no—
352C2×C4#1058753214yes—
353C2×C4C2×C4×#59511yescharacteristic
354C2×C4C2×C4×#59511yescharacteristic
355C2×C4C2×C4×#59511yescharacteristic
356C2×C4C2×C4×#59511yescharacteristic
357C2×C4C2×C4×#59511yescharacteristic
358C2×C4C23×#59511yescharacteristic
359C8—24no—
360C8—344no—
361C8—344no—
362C8—348no—
363C8—344no—
364C22—21no—
365C22—21no—
366C22—172no—
367C22—172no—
368C22—172no—
369C22—172no—
370C22—348no—
371C22—341no—
372C22—341no—
373C22C2×#1058753212yes—
374C22C22×C4×#59511yescharacteristic
375C4—21no—
376C4—21no—
377C4—172no—
378C4—172no—
379C4—172no—
380C4—172no—
381C4—341no—
382C4—341no—
383C4C2×#1058753212yes—
384C4C2×#1058753212yes—
385C4#1176377512yes—
386C4D17⋊#13112yes—
387C2—22no—
388C2—174no—
389C2—342no—
390C2C22×#1058753211yescharacteristic
391C2#1454534411yescharacteristic
392C2C2×#1176377511yescharacteristic
subgroupG/H
centerC42C22×#595
commutator, socleC22×C17C22×C42
FrattiniC2×C4C23×#595
FittingC17×#431C4
prime radicalC23×D17C42
cosocleC4×Dic17C24
hypercenter#431#595
hypocenterC17C2×#1452
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C42 ◁ #431

Complements

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

NH ≅ G/Ntype
3. #14544000C2semidirect
4. #14543999C2semidirect
5. #14543980C2semidirect
6. #14543978C2semidirect
23. #11763651C22semidirect
24. #11763650C22semidirect
229. D17#1452semidirect
273. C17C2×#1452semidirect

Maximal subgroups

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

subgroupindex
#145454482
C2×C4×#632422
#145440002
#145439992
#145439802
#145439782
D17×#4312
C2×#145217