Finite Group Databasebeta

← #16922949

Subgroups — #16922949

Order 4352.

506 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 506 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14537114C211yesmaximal, characteristic
2#14528851C211yesmaximal, characteristic, complemented
3#14528851C211yesmaximal, characteristic, complemented
4#14526608C211yesmaximal, characteristic, complemented
5#14526606C211yesmaximal, characteristic, complemented
6#14526605C211yesmaximal, characteristic, complemented
7C17×#1270C211yesmaximal, characteristic, complemented
8C2×#10587569—21no—
9C2×#10587624C411yescharacteristic
10C2×C42×D17C2211yescharacteristic
11C2×#10587491—21no—
12C2×#10587491—21no—
13#11762712C411yescharacteristic
14#11762708C411yescharacteristic
15#11762707C2211yescharacteristic
16#11762703—21no—
17#11762702—21no—
18#11762685—21no—
19#11762666C411yescharacteristic
20#11762564C2211yescharacteristic
21#11762564C2211yescharacteristic
22#11762563—21no—
23#11762563—21no—
24C17×#390C2211yescharacteristic
25C17×#336C2211yescharacteristic
26C17×#336C2211yescharacteristic
27C22×D4×C17C2×C411yescharacteristic
28C22×C22⋊D17—21no—
29C22×C4×D17C2×C411yescharacteristic
30C22×C4×D17D411yescharacteristic
31C22×C4×D17D411yescharacteristic
32C22×C8×C17—21no—
33C22×C8×C17—21no—
34C2×C4⋊C4×C17C2×C411yescharacteristic
35C2×C22⋊C4×C17—21no—
36C2×C22⋊C4×C17—21no—
37C2×C42×C17C2311yescharacteristic
38C2×C22⋊Dic17—21no—
39C2×C22⋊Dic17—21no—
40C2×C22⋊Dic17—21no—
41#10587624—42no—
42C2×#63227—21no—
43C2×C4⋊Dic17—21no—
44C2×C4⋊Dic17C2×C411yescharacteristic
45C2×C4⋊Dic17C2×C411yescharacteristic
46C2×#63225—21no—
47C2×C4×Dic17C2×C411yescharacteristic
48C2×C4×Dic17D411yescharacteristic
49C2×C4×Dic17D411yescharacteristic
50C22×#3622—21no—
51C22×#3622—21no—
52#10587569—42no—
53#10587569—42no—
54C42×D17—42no—
55#10587502—21no—
56#10587502—21no—
57#10587502—21no—
58#10587491—42no—
59#10587491—42no—
60C24×C17—21no—
61C23×D17C22⋊C411yescharacteristic
62C2×D4×C17—21no—
63C2×D4×C17—21no—
64C2×D4×C17—41no—
65C2×D4×C17—41no—
66C22×C4×C17—21no—
67C22×C4×C17C22×C411yescharacteristic
68C22×C4×C17C2×D411yescharacteristic
69C22×C4×C17C2×D411yescharacteristic
70C2×C22⋊D17—42no—
71C2×C22⋊D17—42no—
72C2×C22⋊D17—42no—
73C22×Dic17—21no—
74C22×Dic17—21no—
75C22×Dic17C22⋊C411yescharacteristic
76C22×Dic17C22⋊C411yescharacteristic
77C22×Dic17C22⋊C411yescharacteristic
78C2×C4×D17—22no—
79C2×C4×D17—22no—
80C2×C4×D17—22no—
81C2×C4×D17—21no—
82C2×C4×D17—21no—
83C2×C4×D17—21no—
84C2×C4×D17—21no—
85C2×C4×D17—21no—
86C2×C4×D17—21no—
87C2×C4×D17—41no—
88C2×C4×D17—41no—
89C2×C4×D17—41no—
90C2×C8×C17—41no—
91C2×C8×C17—41no—
92C2×C8×C17—41no—
93C2×C8×C17—41no—
94C2×C8×C17—41no—
95C2×C8×C17—41no—
96C4⋊C4×C17—41no—
97C22⋊C4×C17—41no—
98C22⋊C4×C17—41no—
99C22⋊C4×C17—41no—
100C22⋊C4×C17—41no—
101C42×C17—41no—
102C22⋊Dic17—42no—
103C22⋊Dic17—42no—
104C22⋊Dic17—42no—
105#63227—42no—
106C4⋊Dic17—21no—
107C4⋊Dic17—21no—
108C4⋊Dic17—42no—
109C4⋊Dic17—41no—
110#63225—41no—
111#63225—41no—
112C4×Dic17—41no—
113C4×Dic17—41no—
114C4×Dic17—41no—
115C2×#3622—41no—
116C2×#3622—41no—
117C2×#3622—41no—
118C2×#3622—41no—
119C2×#3622—41no—
120C2×#3622—41no—
121#7718—171nomaximal, Sylow
122C23×C17—41no—
123C23×C17—41no—
124C23×C17—41no—
125C23×C17—41no—
126C23×C17—41no—
127C23×C17—41no—
128C23×C17—41no—
129C23×C17C2×C22⋊C411yescharacteristic
130C22×D17—21no—
131C22×D17—21no—
132C22×D17—21no—
133C22×D17—21no—
134C22×D17—21no—
135C22×D17—21no—
136C22×D17#9912yes—
137D4×C17—81no—
138D4×C17—81no—
139C2×C4×C17—21no—
140C2×C4×C17—21no—
141C2×C4×C17—21no—
142C2×C4×C17—21no—
143C2×C4×C17—21no—
144C2×C4×C17—21no—
145C2×C4×C17—41no—
146C2×C4×C17—41no—
147C2×C4×C17—41no—
148C2×C4×C17#13111yescharacteristic
149C2×C4×C17#13111yescharacteristic
150C2×C4×C17#13511yescharacteristic
151C2×C4×C17#13511yescharacteristic
152C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
154C22⋊D17—84no—
155C2×Dic17—21no—
156C2×Dic17—21no—
157C2×Dic17—21no—
158C2×Dic17—21no—
159C2×Dic17—21no—
160C2×Dic17—21no—
161C2×Dic17—21no—
162C2×Dic17—21no—
163C2×Dic17—21no—
164C2×Dic17—41no—
165C2×Dic17—41no—
166C2×Dic17—41no—
167C2×Dic17—41no—
168C2×Dic17—41no—
169C2×Dic17—41no—
170C4×D17—42no—
171C4×D17—42no—
172C4×D17—42no—
173C4×D17—42no—
174C4×D17—42no—
175C4×D17—42no—
176C8×C17—81no—
177C8×C17—81no—
178#3622—81no—
179#3622—81no—
180#2854—171no—
181#1817—171no—
182#1817—171no—
183#1271—171no—
184#1271—171no—
185#1270—171no—
186#1270D1711yescharacteristic, complemented
187C22×C17—81no—
188C22×C17—81no—
189C22×C17—81no—
190C22×C17—81no—
191C22×C17—81no—
192C22×C17—81no—
193C22×C17—81no—
194C22×C17#40811yescharacteristic
195C22×C17C2×#9911yescharacteristic
196C22×C17#41311yescharacteristic
197C22×C17#41611yescharacteristic
198C22×C17#41811yescharacteristic
199C22×C17#42111yescharacteristic
200C22×C17#42111yescharacteristic
201C2×D17—22no—
202C2×D17—22no—
203C2×D17—22no—
204C2×D17—41no—
205C2×D17—41no—
206C2×D17—41no—
207C2×D17—41no—
208C4×C17—21no—
209C4×C17—21no—
210C4×C17—21no—
211C4×C17—21no—
212C4×C17—21no—
213C4×C17—21no—
214C4×C17—81no—
215Dic17—41no—
216Dic17—41no—
217Dic17—41no—
218Dic17—81no—
219Dic17—81no—
220C2×#123—341no—
221C2×#121—171no—
222C22×C42—171no—
223C2×C22⋊C8—341no—
224C2×C22⋊C8—341no—
225#390—171no—
226#390C2×D1711yescharacteristic
227#389—171no—
228#389—171no—
229#388—341no—
230#388—341no—
231#386—341no—
232#380—171no—
233#336—171no—
234#336—171no—
235#336—341no—
236#336—341no—
237#336C2×D1711yescharacteristic
238#336C2×D1711yescharacteristic
239C2×C17—161no—
240C2×C17#146811yescharacteristic
241C2×C17#148211yescharacteristic
242C2×C17#149611yescharacteristic
243C2×C17#151011yescharacteristic
244C2×C17#151611yescharacteristic
245C2×C17#153511yescharacteristic
246C2×C17#155311yescharacteristic
247D17—42no—
248C22×D4—341no—
249C22×D4C4×D1711yescharacteristic
250C23×C4—171no—
251C23×C4—171no—
252C23×C4—171no—
253C22×C8—21no—
254C22×C8—21no—
255C22×C8—341no—
256C22×C8—341no—
257#123—682no—
258#123—682no—
259#121—682no—
260C2×C4⋊C4—171no—
261C2×C4⋊C4—171no—
262C2×C4⋊C4—341no—
263C2×C4⋊C4—341no—
264C2×C4⋊C4C4×D1711yescharacteristic
265C2×C22⋊C4—21no—
266C2×C22⋊C4—21no—
267C2×C22⋊C4—341no—
268C2×C22⋊C4—341no—
269C2×C22⋊C4—341no—
270C2×C22⋊C4—341no—
271C2×C42—171no—
272C2×C42—171no—
273C2×C42—171no—
274C2×C42—682no—
275C2×C42C22×D1711yescharacteristic
276C22⋊C8—682no—
277C22⋊C8—682no—
278#95—341no—
279#95—341no—
280#95—341no—
281C17#771811yescharacteristic, complemented, Sylow
282C24—21no—
283C24—171no—
284C2×D4—21no—
285C2×D4—21no—
286C2×D4—41no—
287C2×D4—41no—
288C2×D4—682no—
289C2×D4—682no—
290C2×D4—682no—
291C22×C4—21no—
292C22×C4—171no—
293C22×C4—171no—
294C22×C4—171no—
295C22×C4—342no—
296C22×C4—342no—
297C22×C4—342no—
298C22×C4—341no—
299C22×C4—341no—
300C22×C4—341no—
301C22×C4—341no—
302C22×C4—341no—
303C22×C4—341no—
304C22×C4—341no—
305C22×C4—341no—
306C22×C4—681no—
307C22×C4—681no—
308C22×C4—681no—
309C22×C4C2×C4×D1711yescharacteristic
310C22×C4D4×D1711yescharacteristic
311C22×C4D4×D1711yescharacteristic
312C2×C8—41no—
313C2×C8—41no—
314C2×C8—41no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—681no—
319C2×C8—681no—
320C2×C8—681no—
321C2×C8—681no—
322C2×C8—681no—
323C2×C8—681no—
324C4⋊C4—41no—
325C4⋊C4—341no—
326C4⋊C4—341no—
327C4⋊C4—681no—
328C4⋊C4—682no—
329C4⋊C4—681no—
330C4⋊C4—681no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C22⋊C4—682no—
336C22⋊C4—682no—
337C22⋊C4—682no—
338C22⋊C4—682no—
339C42—41no—
340C42—681no—
341C42—681no—
342C42—681no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23—172no—
351C23—341no—
352C23—341no—
353C23—341no—
354C23—341no—
355C23—341no—
356C23—341no—
357C23C22⋊C4×D1711yescharacteristic
358D4—81no—
359D4—81no—
360D4—1364no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—341no—
371C2×C4—341no—
372C2×C4—341no—
373C2×C4—341no—
374C2×C4—341no—
375C2×C4—341no—
376C2×C4—341no—
377C2×C4—341no—
378C2×C4—341no—
379C2×C4—682no—
380C2×C4—682no—
381C2×C4—682no—
382C2×C4—682no—
383C2×C4—682no—
384C2×C4—682no—
385C2×C4—681no—
386C2×C4—681no—
387C2×C4—681no—
388C2×C4—681no—
389C2×C4—681no—
390C2×C4—681no—
391C2×C4#1058758711yescharacteristic
392C2×C4#1058759311yescharacteristic
393C2×C4#1058759711yescharacteristic
394C2×C4#1058759811yescharacteristic
395C2×C4#1058760011yescharacteristic
396C2×C4#1058760211yescharacteristic
397C8—81no—
398C8—81no—
399C8—1361no—
400C8—1361no—
401C22—81no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22—81no—
406C22—81no—
407C22—81no—
408C22—342no—
409C22—342no—
410C22—342no—
411C22—681no—
412C22—681no—
413C22—681no—
414C22—681no—
415C22#1176277411yescharacteristic
416C22#99×D1711yescharacteristic
417C22#1176279011yescharacteristic
418C22#1176280211yescharacteristic
419C22#1176281211yescharacteristic
420C22#1176282411yescharacteristic
421C22#1176282411yescharacteristic
422C4—21no—
423C4—21no—
424C4—21no—
425C4—21no—
426C4—21no—
427C4—21no—
428C4—81no—
429C4—681no—
430C4—681no—
431C4—681no—
432C4—1361no—
433C4—1361no—
434C2—161no—
435C2—682no—
436C2#1452712911yescharacteristic
437C2#1452718911yescharacteristic
438C2#1452725111yescharacteristic
439C2#1452731111yescharacteristic
440C2#1452733711yescharacteristic
441C2#1452741211yescharacteristic
442C2#1452748611yescharacteristic
subgroupG/H
centerC23C22⋊C4×D17
commutatorC22×C4×C17C22×C4
FrattiniC2×C42C22×D17
FittingC17×#1270C2
socleC23×C17C2×C22⋊C4
prime radicalC2×#10587624C4
cosocleC2×C42×C17C23
hypercenter#1270D17
hypocenterC17#7718
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
2. #14528851C2semidirect
3. #14528851C2semidirect
4. #14526608C2semidirect
5. #14526606C2semidirect
6. #14526605C2semidirect
7. C17×#1270C2semidirect
186. #1270D17semidirect
281. C17#7718semidirect

Maximal subgroups

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

subgroupindex
#145371142
#145288512
#145266082
#145266062
#145266052
C17×#12702
#771817