Finite Group Databasebeta

← #16944883

Subgroups — #16944883

Order 4352.

544 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 83 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#14533681C211yesmaximal, characteristic
2#14527122C211yesmaximal, characteristic, complemented
3#14526783C212yesmaximal, complemented
4#14526780C212yesmaximal, complemented
5C4×C17×#99C211yesmaximal, characteristic, complemented
6C2×#10587624—21no—
7C2×C4×D68C411yescharacteristic, complemented
8#11762773—21no—
9#11762734C411yescharacteristic, complemented
10#11762734C2211yescharacteristic
11#11762718C411yescharacteristic, complemented
12#11762718C2211yescharacteristic
13#11762688—21no—
14#11762688—21no—
15#11762675C411yescharacteristic, complemented
16#11762666—21no—
17#11762535—21no—
18#11762533C2212yes—
19C2×C4×D4×C17C2211yescharacteristic
20C2×C17×#99—21no—
21C4×C22⋊C4×C17—21no—
22C17×#342C2212yes—
23C22×D4×C17D411yescharacteristic
24C23×C4×C17D411yescharacteristic
25C23×C4×C17D411yescharacteristic
26C22×C22⋊D17—21no—
27C22×C22⋊D17—21no—
28C22×D68C2×C411yescharacteristic
29C22×C4×D17—21no—
30C4×D4×C17—41no—
31C4×D4×C17—41no—
32C2×C4⋊C4×C17D411yescharacteristic
33C2×C22⋊C4×C17—22no—
34C2×C22⋊C4×C17C2×C411yescharacteristic
35C2×C22⋊C4×C17C2311yescharacteristic
36C2×C42×C17—41no—
37C2×C42×C17C2×C411yescharacteristic
38C2×C22⋊Dic17—21no—
39C2×C22⋊Dic17—21no—
40#10587624—44no—
41C2×#63227—21no—
42C2×#63227—21no—
43C2×#63227—21no—
44C2×C4⋊Dic17—21no—
45C2×C4⋊Dic17C2×C411yescharacteristic
46C2×#63223—41no—
47C4×D68—41no—
48C4×D68—41no—
49C17×#99—24no—
50C17×#95—41no—
51#10587502—21no—
52#10587502—21no—
53#10587502—21no—
54#10587502C2×C411yescharacteristic
55#10587502C2×C411yescharacteristic
56C22⋊#3622—22no—
57C22⋊#3622—41no—
58C24×C17C22⋊C411yescharacteristic
59C24×C17C2×D411yescharacteristic
60C23×D17—21no—
61C2×D4×C17—22no—
62C2×D4×C17—22no—
63C2×D4×C17—41no—
64C22×C4×C17—21no—
65C22×C4×C17—21no—
66C22×C4×C17—21no—
67C22×C4×C17—21no—
68C22×C4×C17—42no—
69C22×C4×C17—81no—
70C22×C4×C17—81no—
71C22×C4×C17C22⋊C411yescharacteristic
72C22×C4×C17C22⋊C411yescharacteristic
73C22×C4×C17C22⋊C411yescharacteristic
74C22×C4×C17C22×C411yescharacteristic
75C22×C4×C17C2×D411yescharacteristic
76C2×C22⋊D17—42no—
77C2×C22⋊D17—42no—
78C2×C22⋊D17—42no—
79C2×C22⋊D17—42no—
80C2×C22⋊D17—81no—
81C2×C22⋊D17—81no—
82C22×Dic17—21no—
83C22×Dic17—21no—
84C22×Dic17—21no—
85C2×D68—41no—
86C2×D68—42no—
87C2×C4×D17—42no—
88C2×C4×D17—42no—
89C2×C4×D17—42no—
90C4⋊C4×C17—41no—
91C22⋊C4×C17—24no—
92C22⋊C4×C17—41no—
93C22⋊C4×C17—41no—
94C22⋊C4×C17—42no—
95C42×C17—21no—
96C42×C17—21no—
97C42×C17—82no—
98C22⋊Dic17—42no—
99C22⋊Dic17—42no—
100#63227—41no—
101#63227—41no—
102#63227—81no—
103#63227—81no—
104C4⋊Dic17—42no—
105C4⋊Dic17—41no—
106#63223—82no—
107C2×#3622—42no—
108#11774—171nomaximal, Sylow
109C23×C17—21no—
110C23×C17—21no—
111C23×C17—21no—
112C23×C17—21no—
113C23×C17—21no—
114C23×C17—41no—
115C23×C17—41no—
116C23×C17—41no—
117C23×C17—41no—
118C23×C17C2×C22⋊C411yescharacteristic
119C23×C17AGL(1,ℤ/8)12yes—
120C22×D17—22no—
121C22×D17—41no—
122C22×D17—41no—
123C22×D17—41no—
124C22×D17—41no—
125C22×D17—41no—
126C22×D17—41no—
127D4×C17—44no—
128C2×C4×C17—21no—
129C2×C4×C17—21no—
130C2×C4×C17—21no—
131C2×C4×C17—21no—
132C2×C4×C17—21no—
133C2×C4×C17—41no—
134C2×C4×C17—42no—
135C2×C4×C17—42no—
136C2×C4×C17—41no—
137C2×C4×C17—41no—
138C2×C4×C17—41no—
139C2×C4×C17—44no—
140C2×C4×C17—81no—
141C2×C4×C17—81no—
142C2×C4×C17—82no—
143C2×C4×C17—82no—
144C2×C4×C17#9911yescharacteristic
145C2×C4×C17#9911yescharacteristic
146C2×C4×C17#10412yes—
147C22⋊D17—84no—
148C22⋊D17—84no—
149C2×Dic17—41no—
150C2×Dic17—41no—
151C2×Dic17—41no—
152C2×Dic17—41no—
153C2×Dic17—41no—
154C2×Dic17—41no—
155C2×Dic17—41no—
156C2×Dic17—41no—
157C2×Dic17—41no—
158D68—42no—
159D68—42no—
160C4×D17—84no—
161#3622—82no—
162#2535—171no—
163C4×#99D1711yescharacteristic, complemented
164#1465—171no—
165#1344—172no—
166#1343—172no—
167C22×C17—21no—
168C22×C17—21no—
169C22×C17—22no—
170C22×C17—42no—
171C22×C17—42no—
172C22×C17—41no—
173C22×C17—41no—
174C22×C17—41no—
175C22×C17—41no—
176C22×C17—41no—
177C22×C17—81no—
178C22×C17—81no—
179C22×C17C2×#9911yescharacteristic
180C22×C17#41811yescharacteristic
181C22×C17C2×#10411yescharacteristic
182C2×D17—42no—
183C2×D17—42no—
184C2×D17—42no—
185C2×D17—81no—
186C2×D17—81no—
187C2×D17—81no—
188C2×D17—81no—
189C4×C17—21no—
190C4×C17—21no—
191C4×C17—22no—
192C4×C17—41no—
193C4×C17—41no—
194C4×C17—41no—
195C4×C17—84no—
196Dic17—81no—
197Dic17—81no—
198Dic17—81no—
199C2×#121—341no—
200C2×C4×D4—171no—
201C2×C4×D4C2×D1711yescharacteristic
202C2×#99—21no—
203#407—341no—
204#397—171no—
205#397—171no—
206#392—171no—
207#392—171no—
208#386—341no—
209#386—341no—
210#382—171no—
211#380—341no—
212C4×C22⋊C4—21no—
213#342C2×D1712yes—
214#324—341no—
215#323—172no—
216C2×C17—21no—
217C2×C17—21no—
218C2×C17—42no—
219C2×C17—81no—
220C2×C17#150711yescharacteristic
221C2×C17#212011yescharacteristic
222C2×C17#212711yescharacteristic
223D17—82no—
224C22×D4—171no—
225C22×D4—341no—
226C22×D4—341no—
227C22×D4C22⋊D1711yescharacteristic
228C23×C4—341no—
229C23×C4D6811yescharacteristic
230C23×C4C22⋊D1711yescharacteristic
231C2×M16—681no—
232#121—684no—
233C4×D4—41no—
234C4×D4—41no—
235C4×D4—681no—
236C4×D4—681no—
237C2×C4⋊C4—171no—
238C2×C4⋊C4—341no—
239C2×C4⋊C4D6811yescharacteristic
240C2×C22⋊C4—22no—
241C2×C22⋊C4—341no—
242C2×C22⋊C4—341no—
243C2×C22⋊C4—341no—
244C2×C22⋊C4—341no—
245C2×C22⋊C4—341no—
246C2×C22⋊C4C4×D1711yescharacteristic
247C2×C22⋊C4C22×D1711yescharacteristic
248C2×C42—41no—
249C2×C42C4×D1711yescharacteristic
250#99—24no—
251C22⋊C8—342no—
252C22⋊C8—681no—
253#95—41no—
254#95—171no—
255#95—171no—
256#95—341no—
257#95—341no—
258#95—341no—
259C17#1177411yescharacteristic, complemented, Sylow
260C24—341no—
261C24#6322711yescharacteristic
262C24C2×C22⋊D1711yescharacteristic
263C2×D4—22no—
264C2×D4—22no—
265C2×D4—41no—
266C2×D4—681no—
267C2×D4—682no—
268C2×D4—682no—
269C2×D4—682no—
270C2×D4—682no—
271C2×D4—682no—
272C2×D4—1361no—
273C2×D4—1361no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—42no—
279C22×C4—81no—
280C22×C4—81no—
281C22×C4—341no—
282C22×C4—341no—
283C22×C4—341no—
284C22×C4—682no—
285C22×C4—682no—
286C22×C4—682no—
287C22×C4#6322711yescharacteristic
288C22×C4#6322711yescharacteristic
289C22×C4#6322711yescharacteristic
290C22×C4C2×C4×D1711yescharacteristic
291C22×C4C2×D6811yescharacteristic
292M16—1362no—
293C2×C8—682no—
294C4⋊C4—41no—
295C4⋊C4—681no—
296C4⋊C4—682no—
297C22⋊C4—24no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—42no—
301C22⋊C4—682no—
302C22⋊C4—682no—
303C22⋊C4—681no—
304C22⋊C4—681no—
305C22⋊C4—1361no—
306C22⋊C4—1361no—
307C42—21no—
308C42—21no—
309C42—82no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—342no—
320C23—681no—
321C23—681no—
322C23—681no—
323C23—681no—
324C23—681no—
325C23—681no—
326C23C2×#6322711yescharacteristic
327C23#1058763512yes—
328D4—44no—
329D4—682no—
330D4—682no—
331D4—1364no—
332D4—1364no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—44no—
345C2×C4—81no—
346C2×C4—81no—
347C2×C4—82no—
348C2×C4—82no—
349C2×C4—681no—
350C2×C4—681no—
351C2×C4—681no—
352C2×C4—681no—
353C2×C4—681no—
354C2×C4—681no—
355C2×C4—681no—
356C2×C4—681no—
357C2×C4—681no—
358C2×C4—1364no—
359C2×C4#1058747612yes—
360C2×C4#1058747711yescharacteristic
361C2×C4#1058747711yescharacteristic
362C8—1362no—
363C22—21no—
364C22—21no—
365C22—22no—
366C22—42no—
367C22—42no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—81no—
374C22—81no—
375C22—682no—
376C22—682no—
377C22—682no—
378C22—1361no—
379C22—1361no—
380C22—1361no—
381C22—1361no—
382C22C2×#1058747711yescharacteristic
383C22#1176281311yescharacteristic
384C22C2×#1058747611yescharacteristic
385C4—22no—
386C4—21no—
387C4—21no—
388C4—41no—
389C4—41no—
390C4—41no—
391C4—84no—
392C4—1361no—
393C4—1361no—
394C4—1361no—
395C2—21no—
396C2—21no—
397C2—42no—
398C2—81no—
399C2—1362no—
400C2#1452729911yescharacteristic
401C2#1453042311yescharacteristic
402C2#1453045111yescharacteristic
subgroupG/H
centerC22C2×#10587477
commutatorC22×C4×C17C22×C4
FrattiniC2×C22⋊C4C22×D17
FittingC4×C17×#99C2
socleC22×C17C2×#99
prime radical#14533681C2
cosocleC2×C22⋊C4×C17C23
hypercenterC4×#99D17
hypocenterC17#11774
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
2. #14527122C2semidirect
3. #14526783C2semidirect
4. #14526780C2semidirect
5. C4×C17×#99C2semidirect
7. C2×C4×D68C4semidirect
9. #11762734C4semidirect
11. #11762718C4semidirect
15. #11762675C4semidirect
163. C4×#99D17semidirect
259. C17#11774semidirect

Maximal subgroups

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

subgroupindex
#145336812
#145271222
#145267832
#145267802
C4×C17×#992
#1177417