Finite Group Databasebeta

← #17953572

Subgroups — #17953572

Order 4352.

588 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 588 conjugacy classes of subgroups — too many to draw. Only its 108 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#14544676C211yesmaximal, characteristic
2#14543960C211yesmaximal, characteristic
3#14543657C212yesmaximal
4#14543657C212yesmaximal
5#14531188C211yesmaximal, characteristic
6C2×#10587543C2212yes—
7C2×(C2×#595)⋊C4—21no—
8C2×(C2×#595)⋊C4—21no—
9C2×(C2×#595)⋊C4C2212yes—
10#11763675—21no—
11#11763675—21no—
12C2×#10587558—21no—
13C2×C42×D17C2211yescharacteristic
14#11762678C411yescharacteristic, complemented
15#11762678C411yescharacteristic, complemented
16#11762673—21no—
17#11762668—21no—
18#11762666C2211yescharacteristic
19#11762666C2211yescharacteristic
20C4×#63225—21no—
21C4×C4⋊Dic17C411yescharacteristic, complemented
22C4×C4⋊C4×C17C411yescharacteristic, complemented
23C23×#595—22no—
24C22×C4×D17D411yescharacteristic
25C22×C4×D17D411yescharacteristic
26C22×C4×D17C2311yescharacteristic
27C22×#3624—22no—
28C2×C4⋊C4×C17C2×C411yescharacteristic
29C2×C4⋊C4×C17C2×C411yescharacteristic
30C2×C42×C17—21no—
31C2×C42×C17C2×C411yescharacteristic
32C2×#63227—21no—
33C2×#63227—21no—
34C2×C4⋊Dic17C2×C411yescharacteristic
35C2×C4⋊Dic17C2×C411yescharacteristic
36C2×#63225—21no—
37C2×#63225—21no—
38C2×#63225—21no—
39C2×#63225—21no—
40C2×C4×Dic17—21no—
41C2×C4×Dic17C2×C411yescharacteristic
42C2×C4×Dic17D411yescharacteristic
43C2×C4×Dic17D411yescharacteristic
44#10587558—42no—
45#10587558—42no—
46C42×D17—24no—
47(C2×#595)⋊C4—24no—
48(C2×#595)⋊C4—24no—
49(C2×#595)⋊C4—42no—
50#10587543—24no—
51C17×#95—21no—
52#10587502—21no—
53#10587502—21no—
54#10587502—21no—
55C23×D17C2×D411yescharacteristic
56C22×#595—24no—
57C22×#595—42no—
58C22×#595—42no—
59C22×#595—42no—
60C22×#595—42no—
61C22×#595—42no—
62C22×#595—42no—
63C22×C4×C17—21no—
64C22×C4×C17—21no—
65C22×C4×C17C22⋊C411yescharacteristic
66C22×C4×C17C22⋊C411yescharacteristic
67C22×C4×C17C22×C411yescharacteristic
68C22×Dic17—21no—
69C22×Dic17—21no—
70C22×Dic17C22⋊C411yescharacteristic
71C22×Dic17C22⋊C411yescharacteristic
72C22×Dic17C2×D411yescharacteristic
73C2×C4×D17—22no—
74C2×C4×D17—22no—
75C2×C4×D17—22no—
76C2×C4×D17—22no—
77C2×C4×D17—41no—
78C2×C4×D17—41no—
79C2×C4×D17—41no—
80C2×C4×D17D812yes—
81C2×C4×D17SD1612yes—
82C2×C4×D17#4114yes—
83C2×#3624—42no—
84C2×#3624—42no—
85C2×#3624—42no—
86C4⋊C4×C17—41no—
87C4⋊C4×C17—41no—
88C42×C17—22no—
89C42×C17—42no—
90#63227—41no—
91#63227—41no—
92#63227—41no—
93#63227—41no—
94C4⋊Dic17—41no—
95C4⋊Dic17—41no—
96#63225—42no—
97#63225—42no—
98#63225—42no—
99#63225—42no—
100C4×Dic17—22no—
101C4×Dic17—22no—
102C4×Dic17—22no—
103C4×Dic17—42no—
104#8716—171nomaximal, Sylow
105C23×C17C2×C22⋊C411yescharacteristic
106C22×D17—21no—
107C22×D17—21no—
108C22×D17—21no—
109C22×D17—21no—
110C22×D17#12312yes—
111C22×D17C2×D811yescharacteristic
112C22×D17C2×SD1611yescharacteristic
113C22×D17#13712yes—
114C2×#595—44no—
115C2×#595—44no—
116C2×#595—44no—
117C2×#595—82no—
118C2×#595—82no—
119C2×#595—82no—
120C2×#595—82no—
121C2×C4×C17—21no—
122C2×C4×C17—21no—
123C2×C4×C17—21no—
124C2×C4×C17—21no—
125C2×C4×C17—21no—
126C2×C4×C17—21no—
127C2×C4×C17—21no—
128C2×C4×C17—41no—
129C2×C4×C17—41no—
130C2×C4×C17—41no—
131C2×C4×C17—41no—
132C2×C4×C17—41no—
133C2×C4×C17—41no—
134C2×C4×C17#10212yes—
135C2×C4×C17#11712yes—
136C2×Dic17—21no—
137C2×Dic17—21no—
138C2×Dic17—21no—
139C2×Dic17—21no—
140C2×Dic17—21no—
141C2×Dic17—21no—
142C2×Dic17—41no—
143C2×Dic17—41no—
144C2×Dic17—41no—
145C2×Dic17—41no—
146C2×Dic17—41no—
147C2×Dic17—41no—
148C2×Dic17#10212yes—
149C2×Dic17#10412yes—
150C2×Dic17#12312yes—
151C4×D17—24no—
152C4×D17—24no—
153C4×D17—44no—
154C4×D17—44no—
155#3624—82no—
156#2285—171no—
157#1817—171no—
158#1434—171no—
159#1294—172no—
160#1294—172no—
161C22×C17#38111yescharacteristic
162C22×C17#41011yescharacteristic
163C22×C17#41011yescharacteristic
164C22×C17C2×#10211yescharacteristic
165C22×C17#41911yescharacteristic
166C22×C17C2×#10411yescharacteristic
167C22×C17#42111yescharacteristic
168C2×D17—22no—
169C2×D17—22no—
170C2×D17—21no—
171C2×D17—21no—
172C2×D17—22no—
173C2×D17—22no—
174C2×D17—21no—
175C2×D17—21no—
176C2×D17#48012yes—
177C2×D17#48312yes—
178#595—84no—
179C4×C17—22no—
180C4×C17—22no—
181C4×C17—41no—
182C4×C17—81no—
183C4×C17—81no—
184Dic17—22no—
185Dic17—22no—
186Dic17—22no—
187Dic17—81no—
188Dic17—81no—
189C2×#117—341no—
190C22×C42—171no—
191C2×C22⋊C8—172no—
192#384—171no—
193#384—171no—
194#382—341no—
195#380—171no—
196#380—171no—
197#380—341no—
198C4×C4⋊C4—171no—
199C4×C4⋊C4—341no—
200C4×C4⋊C4#59511yescharacteristic, complemented
201C2×#95—172no—
202C2×#95—341no—
203C2×#95—341no—
204#336—341no—
205#336—341no—
206C2×C17#150211yescharacteristic
207C2×C17#150611yescharacteristic
208C2×C17#151511yescharacteristic
209C2×C17#151711yescharacteristic
210C2×C17#182011yescharacteristic
211C2×C17#182311yescharacteristic
212C2×C17#182611yescharacteristic
213D17—22no—
214D17—22no—
215C23×C4—171no—
216C23×C4—171no—
217C23×C4—171no—
218C23×C4—342no—
219C22×C8—342no—
220#117—682no—
221#117—682no—
222C2×C4⋊C4—171no—
223C2×C4⋊C4—171no—
224C2×C4⋊C4—341no—
225C2×C4⋊C4—341no—
226C2×C4⋊C4—341no—
227C2×C4⋊C4—341no—
228C2×C4⋊C4C2×#59511yescharacteristic
229C2×C4⋊C4C2×#59511yescharacteristic
230C2×C22⋊C4—341no—
231C2×C22⋊C4—341no—
232C2×C42—21no—
233C2×C42—171no—
234C2×C42—171no—
235C2×C42—171no—
236C2×C42—344no—
237C2×C42—341no—
238C2×C42C2×#59511yescharacteristic
239C22⋊C8—344no—
240#95—21no—
241#95—341no—
242#95—341no—
243#95—344no—
244#95—344no—
245#95—341no—
246#95—682no—
247C17#871611yescharacteristic, complemented, Sylow
248C24—171no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—171no—
252C22×C4—171no—
253C22×C4—171no—
254C22×C4—172no—
255C22×C4—172no—
256C22×C4—174no—
257C22×C4—342no—
258C22×C4—342no—
259C22×C4—342no—
260C22×C4—342no—
261C22×C4—344no—
262C22×C4—341no—
263C22×C4—341no—
264C22×C4—681no—
265C22×C4—681no—
266C22×C4—681no—
267C22×C4—682no—
268C22×C4—682no—
269C22×C4—682no—
270C22×C4—682no—
271C22×C4—682no—
272C22×C4—682no—
273C22×C4C22⋊#59511yescharacteristic
274C22×C4C22⋊#59511yescharacteristic
275C22×C4C22×#59511yescharacteristic
276C2×C8—682no—
277C2×C8—682no—
278C2×C8—682no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—681no—
282C4⋊C4—681no—
283C4⋊C4—682no—
284C4⋊C4—682no—
285C4⋊C4—682no—
286C4⋊C4—682no—
287C22⋊C4—681no—
288C22⋊C4—681no—
289C22⋊C4—681no—
290C22⋊C4—681no—
291C42—22no—
292C42—42no—
293C42—342no—
294C42—342no—
295C42—342no—
296C42—682no—
297C23—172no—
298C23—171no—
299C23—171no—
300C23—172no—
301C23—341no—
302C23—341no—
303C23—341no—
304C23—341no—
305C23C2×C22⋊#59511yescharacteristic
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—172no—
320C2×C4—172no—
321C2×C4—172no—
322C2×C4—344no—
323C2×C4—344no—
324C2×C4—341no—
325C2×C4—341no—
326C2×C4—341no—
327C2×C4—341no—
328C2×C4—341no—
329C2×C4—341no—
330C2×C4—684no—
331C2×C4—684no—
332C2×C4—684no—
333C2×C4—684no—
334C2×C4—684no—
335C2×C4—681no—
336C2×C4—681no—
337C2×C4—681no—
338C2×C4—681no—
339C2×C4—681no—
340C2×C4—681no—
341C2×C4—1362no—
342C2×C4—1362no—
343C2×C4—1362no—
344C2×C4—1362no—
345C2×C4#1058754712yes—
346C2×C4#1058767712yes—
347C8—1362no—
348C22—172no—
349C22—172no—
350C22—341no—
351C22—341no—
352C22—342no—
353C22—342no—
354C22—342no—
355C22—342no—
356C22—341no—
357C22—341no—
358C22#1176375211yescharacteristic
359C22#1176378811yescharacteristic
360C22#1176378811yescharacteristic
361C22C2×#1058754711yescharacteristic
362C22#1176380211yescharacteristic
363C22D17⋊#10411yescharacteristic
364C22#1176380611yescharacteristic
365C4—22no—
366C4—22no—
367C4—41no—
368C4—81no—
369C4—81no—
370C4—342no—
371C4—342no—
372C4—342no—
373C4—1364no—
374C4—1361no—
375C4—1361no—
376C2—342no—
377C2—342no—
378C2#1454416311yescharacteristic
379C2#1454417711yescharacteristic
380C2#1454420611yescharacteristic
381C2#1454421411yescharacteristic
382C2#1454468111yescharacteristic
383C2#1454468711yescharacteristic
384C2#1454469211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC4×C4⋊C4×C17C4
socleC23×C17C2×C22⋊C4
prime radicalC23×D17C2×D4
cosocleC22×C4×D17C23
hypercenterC4×C4⋊C4#595
hypocenterC17#8716
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
14. #11762678C4semidirect
15. #11762678C4semidirect
21. C4×C4⋊Dic17C4semidirect
22. C4×C4⋊C4×C17C4semidirect
200. C4×C4⋊C4#595semidirect
247. C17#8716semidirect

Maximal subgroups

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

subgroupindex
#145446762
#145439602
#145436572
#145311882
#871617