Finite Group Databasebeta

← #17954520

Subgroups — #17954520

Order 4352.

604 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 118 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
1C2×#11763829C211yesmaximal, characteristic
2#14544674C211yesmaximal, characteristic
3C2×#11763654C212yesmaximal
4#14543622C212yesmaximal
5C2×#11762695C211yesmaximal, characteristic
6#11763829—24no—
7C2×#10587544—21no—
8C2×C22⋊#3624C2212yes—
9C2×C22⋊#3624C2212yes—
10C2×#10587542—21no—
11#11763675—21no—
12#11763675—21no—
13#11763654—24no—
14C22×C4⋊Dic17C2211yescharacteristic
15C22×C4×Dic17C2211yescharacteristic
16#11762695—21no—
17#11762695—21no—
18#11762695—21no—
19#11762695—21no—
20C2×#10587502C411yescharacteristic
21C2×#10587502C411yescharacteristic
22C2×#10587502C411yescharacteristic
23C2×#10587502C2211yescharacteristic
24C22×C4⋊C4×C17C411yescharacteristic
25C23×C4×C17C2×C411yescharacteristic
26C23×C4×C17C2×C411yescharacteristic
27C23×C4×C17C2×C411yescharacteristic
28C23×Dic17C2×C411yescharacteristic
29C23×Dic17C2×C411yescharacteristic
30C23×Dic17C2×C411yescharacteristic
31C23×Dic17C2311yescharacteristic
32C22×#3624—22no—
33C22×#3624—22no—
34C2×C4⋊C4×C17—21no—
35C2×C4⋊C4×C17—21no—
36C2×C4⋊C4×C17—22no—
37C2×C4⋊C4×C17—22no—
38C2×C4⋊Dic17—21no—
39C2×C4⋊Dic17—21no—
40C2×C4⋊Dic17—22no—
41C2×C4⋊Dic17—22no—
42C2×C4×Dic17—22no—
43C2×C4×Dic17—22no—
44C2×C4×Dic17D411yescharacteristic
45C2×C4×Dic17D411yescharacteristic
46C2×C4×Dic17D411yescharacteristic
47C2×C4×Dic17D411yescharacteristic
48C22⋊#3624—22no—
49C22⋊#3624—22no—
50C22⋊#3624—22no—
51C22⋊#3624D414yes—
52#10587544—24no—
53#10587542—24no—
54#10587502—21no—
55#10587502—21no—
56#10587502—21no—
57#10587502—21no—
58#10587502—21no—
59#10587502—21no—
60#10587502—21no—
61#10587502—21no—
62C24×C17C22×C411yescharacteristic
63C22×C4×C17—21no—
64C22×C4×C17—21no—
65C22×C4×C17—22no—
66C22×C4×C17—22no—
67C22×C4×C17—21no—
68C22×C4×C17—21no—
69C22×C4×C17—21no—
70C22×C4×C17—21no—
71C22×C4×C17—22no—
72C22×C4×C17—22no—
73C22×C4×C17—41no—
74C22×C4×C17—41no—
75C22×C4×C17C22⋊C411yescharacteristic
76C22×C4×C17C22⋊C411yescharacteristic
77C22×C4×C17M1612yes—
78C22×C4×C17M1612yes—
79C22×Dic17—22no—
80C22×Dic17—22no—
81C22×Dic17—21no—
82C22×Dic17—21no—
83C22×Dic17—22no—
84C22×Dic17—22no—
85C22×Dic17—41no—
86C22×Dic17—41no—
87C22×Dic17—41no—
88C22×Dic17—41no—
89C22×Dic17—41no—
90C22×Dic17—41no—
91C22×Dic17—41no—
92C22×Dic17C22⋊C411yescharacteristic
93C22×Dic17C22⋊C411yescharacteristic
94C22×Dic17C2×D411yescharacteristic
95C22×Dic17C2×D411yescharacteristic
96C22×Dic17C2×D412yes—
97C22×Dic17#4112yes—
98C2×#3624—24no—
99C2×#3624—42no—
100C2×#3624—42no—
101C2×#3624—42no—
102C2×#3624—42no—
103C2×#3624—42no—
104C4⋊C4×C17—24no—
105C4⋊C4×C17—24no—
106C4⋊Dic17—41no—
107C4⋊Dic17—42no—
108C4⋊Dic17—41no—
109C4×Dic17—21no—
110C4×Dic17—21no—
111C4×Dic17—22no—
112C4×Dic17—22no—
113C4×Dic17—21no—
114C4×Dic17—21no—
115#9086—171nomaximal, Sylow
116C23×C17—21no—
117C23×C17—21no—
118C23×C17—21no—
119C23×C17—21no—
120C23×C17C2×C22⋊C411yescharacteristic
121C23×C17C4×D412yes—
122C23×C17C2×M1611yescharacteristic
123C23×C17C2×M1611yescharacteristic
124C23×C17#13112yes—
125C2×C4×C17—21no—
126C2×C4×C17—21no—
127C2×C4×C17—21no—
128C2×C4×C17—21no—
129C2×C4×C17—22no—
130C2×C4×C17—22no—
131C2×C4×C17—21no—
132C2×C4×C17—21no—
133C2×C4×C17—24no—
134C2×C4×C17—42no—
135C2×C4×C17—41no—
136C2×C4×C17—41no—
137C2×C4×C17—41no—
138C2×C4×C17—41no—
139C2×C4×C17—42no—
140C2×C4×C17—42no—
141C2×C4×C17—42no—
142C2×C4×C17—42no—
143C2×Dic17—21no—
144C2×Dic17—21no—
145C2×Dic17—21no—
146C2×Dic17—21no—
147C2×Dic17—21no—
148C2×Dic17—21no—
149C2×Dic17—21no—
150C2×Dic17—21no—
151C2×Dic17—21no—
152C2×Dic17—42no—
153C2×Dic17—42no—
154C2×Dic17—44no—
155C2×Dic17—41no—
156C2×Dic17—41no—
157C2×Dic17—41no—
158C2×Dic17—41no—
159C2×Dic17—41no—
160C2×Dic17—41no—
161C2×Dic17—82no—
162C2×Dic17—82no—
163C2×Dic17#10112yes—
164C2×Dic17#12011yescharacteristic
165C2×Dic17#12112yes—
166C2×Dic17#12311yescharacteristic
167#3624—44no—
168#3624—82no—
169C2×#432—171no—
170C2×#387—171no—
171#1817—171no—
172C2×#324—172no—
173#1280—172no—
174C22×C17—22no—
175C22×C17—22no—
176C22×C17—21no—
177C22×C17—21no—
178C22×C17—21no—
179C22×C17—21no—
180C22×C17—22no—
181C22×C17—22no—
182C22×C17#38611yescharacteristic
183C22×C17#40711yescharacteristic
184C22×C17#40811yescharacteristic
185C22×C17#41011yescharacteristic
186C22×C17#41011yescharacteristic
187C22×C17C2×#10111yescharacteristic
188C22×C17#41311yescharacteristic
189C22×C17#43512yes—
190C22×C17#43612yes—
191C4×C17—41no—
192C4×C17—41no—
193C4×C17—42no—
194C4×C17—42no—
195Dic17—21no—
196Dic17—22no—
197Dic17—21no—
198Dic17—22no—
199Dic17—41no—
200Dic17—81no—
201Dic17—81no—
202C22×C4⋊C4—171no—
203C22×C4⋊C4#59511yescharacteristic
204C22×C42—171no—
205#432—344no—
206C2×C4⋊C8—341no—
207C2×C22⋊C8—172no—
208C2×C22⋊C8—172no—
209C2×#97—341no—
210#387—341no—
211#387—341no—
212#387—341no—
213#387—341no—
214C2×#95—171no—
215C2×#95—171no—
216C2×#95—171no—
217C2×#95—171no—
218#336—341no—
219#336—341no—
220#324—344no—
221C2×C17—22no—
222C2×C17—22no—
223C2×C17#146411yescharacteristic
224C2×C17#146711yescharacteristic
225C2×C17#147011yescharacteristic
226C2×C17#147311yescharacteristic
227C2×C17#187011yescharacteristic
228C2×C17#189911yescharacteristic
229C2×C17#190111yescharacteristic
230C23×C4—171no—
231C23×C4—171no—
232C23×C4—171no—
233C23×C4—171no—
234C23×C4C2×#59511yescharacteristic
235C23×C4C2×#59511yescharacteristic
236C23×C4C2×#59511yescharacteristic
237C22×C8—342no—
238C22×C8—342no—
239C2×C4⋊C4—22no—
240C2×C4⋊C4—22no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—342no—
244C2×C4⋊C4—341no—
245C2×C4⋊C4—341no—
246C2×C4⋊C4—342no—
247C2×C42—171no—
248C2×C42—171no—
249C2×C42—171no—
250C2×C42—171no—
251C2×C42—342no—
252C2×C42—342no—
253C4⋊C8—344no—
254C22⋊C8—174no—
255C22⋊C8—342no—
256C22⋊C8—342no—
257C22⋊C8—342no—
258#97—344no—
259#95—341no—
260#95—341no—
261#95—341no—
262#95—341no—
263#95—341no—
264#95—341no—
265#95—341no—
266#95—341no—
267C17#908611yescharacteristic, complemented, Sylow
268C24C22×#59511yescharacteristic
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—171no—
282C22×C4—171no—
283C22×C4—171no—
284C22×C4—172no—
285C22×C4—172no—
286C22×C4—171no—
287C22×C4—342no—
288C22×C4—342no—
289C22×C4—341no—
290C22×C4—341no—
291C22×C4—342no—
292C22×C4—342no—
293C22×C4—681no—
294C22×C4—681no—
295C22×C4—681no—
296C22×C4—681no—
297C22×C4—681no—
298C22×C4—681no—
299C22×C4—681no—
300C22×C4#6324712yes—
301C22×C4#6324712yes—
302C22×C4C22⋊#59511yescharacteristic
303C22×C4C22⋊#59511yescharacteristic
304C2×C8—344no—
305C2×C8—682no—
306C2×C8—682no—
307C2×C8—682no—
308C2×C8—682no—
309C2×C8—682no—
310C4⋊C4—24no—
311C4⋊C4—24no—
312C4⋊C4—681no—
313C4⋊C4—682no—
314C4⋊C4—681no—
315C42—341no—
316C42—341no—
317C42—342no—
318C42—342no—
319C42—341no—
320C42—341no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23#1058767812yes—
326C23D4×#59512yes—
327C23C2×#6324711yescharacteristic
328C23C2×#6324711yescharacteristic
329C23C2×C22⋊#59511yescharacteristic
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—24no—
339C2×C4—42no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—171no—
349C2×C4—172no—
350C2×C4—171no—
351C2×C4—172no—
352C2×C4—341no—
353C2×C4—341no—
354C2×C4—341no—
355C2×C4—341no—
356C2×C4—341no—
357C2×C4—341no—
358C2×C4—341no—
359C2×C4—341no—
360C2×C4—341no—
361C2×C4—682no—
362C2×C4—682no—
363C2×C4—684no—
364C2×C4—681no—
365C2×C4—681no—
366C2×C4—681no—
367C2×C4—681no—
368C2×C4—681no—
369C2×C4—681no—
370C2×C4—1362no—
371C2×C4—1362no—
372C8—684no—
373C8—1362no—
374C22—21no—
375C22—21no—
376C22—22no—
377C22—22no—
378C22—21no—
379C22—21no—
380C22—22no—
381C22—22no—
382C22#1176375711yescharacteristic
383C22#1176377911yescharacteristic
384C22#1176378211yescharacteristic
385C22#1176378811yescharacteristic
386C22#1176379011yescharacteristic
387C22D17⋊#10111yescharacteristic
388C22#1176379511yescharacteristic
389C22#1176384012yes—
390C22#1176384412yes—
391C4—41no—
392C4—41no—
393C4—42no—
394C4—42no—
395C4—341no—
396C4—342no—
397C4—341no—
398C4—342no—
399C4—681no—
400C4—1361no—
401C4—1361no—
402C2—22no—
403C2—22no—
404C2#1454403511yescharacteristic
405C2#1454404711yescharacteristic
406C2#1454405611yescharacteristic
407C2#1454406811yescharacteristic
408C2#1454476111yescharacteristic
409C2#1454480811yescharacteristic
410C2#1454481211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutator, prime radicalC24×C17C22×C4
FrattiniC24C22×#595
FittingC22×C4⋊C4×C17C4
socleC23×C17C2×C22⋊C4
cosocleC23×Dic17C23
hypercenterC22×C4⋊C4#595
hypocenterC17#9086
LCSG ▷ C24×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
267. C17#9086semidirect

Maximal subgroups

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

subgroupindex
C2×#117638292
#145446742
C2×#117636542
#145436222
C2×#117626952
#908617