Finite Group Databasebeta

← #17949990

Subgroups — #17949990

Order 4352.

544 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 100 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#14544640C211yesmaximal, characteristic, complemented
2C4×C22⋊#3624C211yesmaximal, characteristic, complemented
3#14543602C212yesmaximal, complemented
4#14543601C212yesmaximal, complemented
5#14537116C211yesmaximal, characteristic
6C2×#10587544—21no—
7C2×C22⋊#3624—21no—
8C2×C22⋊#3624—21no—
9C2×C4×#3624—21no—
10#11763675C2212yes—
11#11763675C2212yes—
12C2×#10587572—21no—
13C2×#10587616C411yescharacteristic
14C22×C4×Dic17C2211yescharacteristic
15#11762710C411yescharacteristic
16#11762710C2211yescharacteristic
17#11762708C411yescharacteristic
18#11762708C2211yescharacteristic
19#11762701—21no—
20#11762701—21no—
21#11762686—21no—
22C17×#380C411yescharacteristic
23C23×C4×C17C2×C411yescharacteristic
24C22×C22⋊D17—21no—
25C23×Dic17D411yescharacteristic
26C23×Dic17D411yescharacteristic
27C22×D68C2×C411yescharacteristic
28C22×#3624—22no—
29C22×#3624—22no—
30C2×C4⋊C4×C17C2×C411yescharacteristic
31C2×C4⋊C4×C17C2×C411yescharacteristic
32C2×C22⋊C4×C17—21no—
33#10587616—42no—
34C2×#63227—21no—
35C2×#63227—21no—
36C2×#63227—21no—
37C2×#63227—21no—
38C2×#63227—21no—
39C2×C4⋊Dic17—21no—
40C2×C4⋊Dic17—21no—
41C2×C4⋊Dic17C2×C411yescharacteristic
42C2×C4×Dic17—42no—
43C2×C4×Dic17C2×C411yescharacteristic
44C2×C4×Dic17D411yescharacteristic
45C2×C4×Dic17D411yescharacteristic
46C2×C4×Dic17C2311yescharacteristic
47#10587572—42no—
48#10587572—42no—
49C22⋊#3624—24no—
50C22⋊#3624—42no—
51#10587544—42no—
52C4×#3624—42no—
53C17×#95—21no—
54#10587502—21no—
55#10587502—21no—
56C24×C17C22⋊C411yescharacteristic
57C23×D17—21no—
58C22×C4×C17—22no—
59C22×C4×C17—22no—
60C22×C4×C17—21no—
61C22×C4×C17—21no—
62C22×C4×C17—41no—
63C22×C4×C17C22⋊C411yescharacteristic
64C22×C4×C17C22×C411yescharacteristic
65C2×C22⋊D17—42no—
66C2×C22⋊D17—42no—
67C2×C22⋊D17—42no—
68C22×Dic17—22no—
69C22×Dic17—22no—
70C22×Dic17—21no—
71C22×Dic17—41no—
72C22×Dic17—41no—
73C22×Dic17—41no—
74C22×Dic17C22⋊C411yescharacteristic
75C22×Dic17C22⋊C411yescharacteristic
76C22×Dic17D812yes—
77C22×Dic17SD1612yes—
78C22×Dic17C2×D411yescharacteristic
79C22×Dic17C2×D411yescharacteristic
80C2×D68—22no—
81C2×D68—41no—
82C2×D68—41no—
83C2×#3624—24no—
84C2×#3624—42no—
85C2×#3624—42no—
86C2×#3624—42no—
87C2×#3624—42no—
88C2×#3624—42no—
89C4⋊C4×C17—22no—
90C4⋊C4×C17—41no—
91C22⋊C4×C17—42no—
92#63227—42no—
93#63227—42no—
94#63227—42no—
95#63227—41no—
96#63227—41no—
97#63227—42no—
98C4⋊Dic17—42no—
99C4⋊Dic17—41no—
100C4⋊Dic17—41no—
101C4⋊Dic17—41no—
102C4×Dic17—22no—
103C4×Dic17—22no—
104C4×Dic17—41no—
105C4×Dic17—41no—
106#7658—171nomaximal, Sylow
107C23×C17—21no—
108C23×C17—21no—
109C23×C17—21no—
110C23×C17—21no—
111C23×C17—21no—
112C23×C17—21no—
113C23×C17#10212yes—
114C23×C17C2×C22⋊C411yescharacteristic
115C22×D17—41no—
116C22×D17—41no—
117C22×D17—41no—
118C22×D17—41no—
119C22×D17—41no—
120C22×D17—41no—
121C22×D17—41no—
122C2×C4×C17—21no—
123C2×C4×C17—21no—
124C2×C4×C17—21no—
125C2×C4×C17—21no—
126C2×C4×C17—44no—
127C2×C4×C17—41no—
128C2×C4×C17—41no—
129C2×C4×C17—41no—
130C2×C4×C17—41no—
131C2×C4×C17—41no—
132C2×C4×C17—41no—
133C2×C4×C17#9912yes—
134C2×C4×C17#13112yes—
135C22⋊D17—84no—
136C2×Dic17—21no—
137C2×Dic17—21no—
138C2×Dic17—21no—
139C2×Dic17—21no—
140C2×Dic17—21no—
141C2×Dic17—21no—
142C2×Dic17—21no—
143C2×Dic17—21no—
144C2×Dic17—42no—
145C2×Dic17—42no—
146C2×Dic17—44no—
147C2×Dic17—41no—
148C2×Dic17—41no—
149C2×Dic17—41no—
150C2×Dic17#10212yes—
151C2×Dic17#10412yes—
152C2×Dic17C2×D811yescharacteristic
153C2×Dic17C2×SD1611yescharacteristic
154C2×Dic17#13512yes—
155D68—82no—
156#3624—44no—
157#3624—82no—
158#2854—171no—
159#1797—171no—
160C4×C22⋊C8—171no—
161#1271—172no—
162#1270—172no—
163C22×C17—22no—
164C22×C17—22no—
165C22×C17—22no—
166C22×C17—41no—
167C22×C17—41no—
168C22×C17—41no—
169C22×C17—41no—
170C22×C17#40811yescharacteristic
171C22×C17C2×#9911yescharacteristic
172C22×C17#41311yescharacteristic
173C22×C17C2×#10211yescharacteristic
174C22×C17#41611yescharacteristic
175C22×C17C2×#10411yescharacteristic
176C22×C17#42111yescharacteristic
177C2×D17—81no—
178C2×D17—81no—
179C2×D17—81no—
180C2×D17—81no—
181C2×D17—81no—
182C2×D17—81no—
183C2×D17—81no—
184C4×C17—22no—
185C4×C17—22no—
186C4×C17—81no—
187C4×C17—81no—
188Dic17—22no—
189Dic17—22no—
190Dic17—21no—
191Dic17—22no—
192Dic17—21no—
193Dic17—81no—
194C2×#123—341no—
195C2×#121—171no—
196C22×C42—171no—
197C2×C4⋊C8—341no—
198C2×C22⋊C8—341no—
199C2×C22⋊C8—341no—
200C2×C4×C8—341no—
201#390—171no—
202#390—171no—
203#389—171no—
204#389—171no—
205#388—341no—
206#388—341no—
207#386—341no—
208#380#59511yescharacteristic
209#336—172no—
210#336—172no—
211C2×C17—42no—
212C2×C17#146811yescharacteristic
213C2×C17#148211yescharacteristic
214C2×C17#149211yescharacteristic
215C2×C17#150111yescharacteristic
216C2×C17#151911yescharacteristic
217C2×C17#152911yescharacteristic
218C2×C17#154011yescharacteristic
219D17—161no—
220C22×D4—171no—
221C22×D4—341no—
222C23×C4—171no—
223C23×C4—171no—
224C23×C4C2×#59511yescharacteristic
225C22×C8—342no—
226C22×C8—342no—
227#123—682no—
228#123—682no—
229#121—682no—
230C2×C4⋊C4—171no—
231C2×C4⋊C4—341no—
232C2×C4⋊C4—341no—
233C2×C4⋊C4C2×#59511yescharacteristic
234C2×C4⋊C4C2×#59511yescharacteristic
235C2×C22⋊C4—21no—
236C2×C22⋊C4—341no—
237C2×C22⋊C4—341no—
238C2×C22⋊C4—341no—
239C2×C22⋊C4—341no—
240C2×C22⋊C4—341no—
241C2×C42—171no—
242C2×C42—171no—
243C2×C42—171no—
244C2×C42—171no—
245C2×C42—682no—
246C4⋊C8—682no—
247C22⋊C8—344no—
248C22⋊C8—682no—
249C4×C8—682no—
250#95—21no—
251#95—341no—
252#95—341no—
253C17#765811yescharacteristic, complemented, Sylow
254C24—341no—
255C24C22⋊#59511yescharacteristic
256C2×D4—342no—
257C2×D4—681no—
258C2×D4—681no—
259C2×D4—682no—
260C2×D4—682no—
261C2×D4—682no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—41no—
267C22×C4—171no—
268C22×C4—171no—
269C22×C4—171no—
270C22×C4—171no—
271C22×C4—172no—
272C22×C4—172no—
273C22×C4—342no—
274C22×C4—342no—
275C22×C4—341no—
276C22×C4—681no—
277C22×C4—681no—
278C22×C4—681no—
279C22×C4C22⋊#59511yescharacteristic
280C22×C4C22×#59511yescharacteristic
281C2×C8—344no—
282C2×C8—682no—
283C2×C8—682no—
284C2×C8—682no—
285C2×C8—682no—
286C2×C8—682no—
287C4⋊C4—22no—
288C4⋊C4—41no—
289C4⋊C4—681no—
290C4⋊C4—681no—
291C4⋊C4—682no—
292C4⋊C4—681no—
293C22⋊C4—42no—
294C22⋊C4—681no—
295C22⋊C4—682no—
296C22⋊C4—681no—
297C22⋊C4—682no—
298C22⋊C4—682no—
299C22⋊C4—682no—
300C42—342no—
301C42—342no—
302C42—681no—
303C42—681no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—681no—
311C23—681no—
312C23—681no—
313C23—681no—
314C23—681no—
315C23—681no—
316C23—681no—
317C23#1058754712yes—
318C23C2×C22⋊#59511yescharacteristic
319D4—1362no—
320D4—1364no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—44no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—171no—
333C2×C4—172no—
334C2×C4—171no—
335C2×C4—172no—
336C2×C4—172no—
337C2×C4—341no—
338C2×C4—341no—
339C2×C4—341no—
340C2×C4—341no—
341C2×C4—341no—
342C2×C4—341no—
343C2×C4—341no—
344C2×C4—341no—
345C2×C4—682no—
346C2×C4—682no—
347C2×C4—684no—
348C2×C4—681no—
349C2×C4—681no—
350C2×C4—681no—
351C2×C4#1058753912yes—
352C2×C4#1058767812yes—
353C8—684no—
354C8—1362no—
355C22—22no—
356C22—22no—
357C22—22no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—1361no—
363C22—1361no—
364C22—1361no—
365C22—1361no—
366C22—1361no—
367C22—1361no—
368C22—1361no—
369C22#1176378211yescharacteristic
370C22C2×#1058753911yescharacteristic
371C22#1176379611yescharacteristic
372C22C2×#1058754711yescharacteristic
373C22#1176379911yescharacteristic
374C22D17⋊#10411yescharacteristic
375C22#1176380811yescharacteristic
376C4—22no—
377C4—22no—
378C4—81no—
379C4—81no—
380C4—342no—
381C4—342no—
382C4—341no—
383C4—342no—
384C4—341no—
385C4—1361no—
386C2—42no—
387C2—2721no—
388C2#1454405111yescharacteristic
389C2#1454409711yescharacteristic
390C2#1454412911yescharacteristic
391C2#1454416111yescharacteristic
392C2#1454422111yescharacteristic
393C2#1454425211yescharacteristic
394C2#1454428211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC17×#380C4
socleC23×C17C2×C22⋊C4
prime radicalC2×#10587616C4
cosocleC2×C4×Dic17C23
hypercenter#380#595
hypocenterC17#7658
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
1. #14544640C2semidirect
2. C4×C22⋊#3624C2semidirect
3. #14543602C2semidirect
4. #14543601C2semidirect
253. C17#7658semidirect

Maximal subgroups

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

subgroupindex
#145446402
C4×C22⋊#36242
#145436022
#145436012
#145371162
#765817