Finite Group Databasebeta

← #16930381

Subgroups — #16930381

Order 4352.

516 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 105 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#14534600C211yesmaximal, characteristic
2#14531386C211yesmaximal, characteristic
3#14527357C211yesmaximal, characteristic
4#14527355C211yesmaximal, characteristic
5C2×#11762534C211yesmaximal, characteristic
6#14526651C211yesmaximal, characteristic
7C17×#1289C211yesmaximal, characteristic
8C2×#10587610C2211yescharacteristic
9C22×#63225C2211yescharacteristic
10C2×C22⋊#3622C2211yescharacteristic
11#11762749C412yescomplemented
12#11762739—22no—
13#11762730C412yescomplemented
14#11762696—22no—
15#11762690—22no—
16#11762684—21no—
17#11762670—21no—
18#11762670—21no—
19#11762669C2211yescharacteristic
20C22⋊C4×Dic17—21no—
21#11762547—22no—
22#11762545—22no—
23#11762534—22no—
24C2×C17×C22⋊C8C2211yescharacteristic
25C17×#380C2211yescharacteristic
26C17×#380C2211yescharacteristic
27C23×C4×C17C2311yescharacteristic
28C23×Dic17D411yescharacteristic
29C23×Dic17D411yescharacteristic
30C22×Dic34C2×C411yescharacteristic
31C22×C8×C17—21no—
32C2×C4⋊C4×C17—21no—
33C2×C4⋊C4×C17—21no—
34C2×C22⋊C4×C17—21no—
35C2×C22⋊C4×C17—21no—
36C2×C22⋊Dic17—21no—
37C2×C22⋊Dic17—21no—
38C2×C4⋊Dic17—21no—
39C2×C4⋊Dic17—22no—
40C2×C4⋊Dic17C2×C411yescharacteristic
41#10587610—21no—
42#10587610—21no—
43#10587610—21no—
44#10587610—21no—
45C2×#63225—21no—
46C2×#63225—21no—
47C2×#63225—21no—
48C2×#63225—21no—
49C2×#63225—21no—
50C2×#63225C2×C412yes—
51C2×#63225D412yes—
52C2×C4×Dic17—22no—
53C22×#3622—21no—
54C17×C22⋊C8—21no—
55C17×C22⋊C8—21no—
56C17×#95C2×C412yes—
57C17×#95D412yes—
58#10587502—22no—
59#10587502—24no—
60#10587502—22no—
61#10587502—22no—
62#10587502—22no—
63#10587502D412yes—
64C22⋊#3622—21no—
65C22⋊#3622—21no—
66C24×C17C2×D411yescharacteristic
67C22×C4×C17—22no—
68C22×C4×C17—22no—
69C22×C4×C17—81no—
70C22×C4×C17C22×C411yescharacteristic
71C22×C4×C17C2×D411yescharacteristic
72C22×C4×C17C2×D411yescharacteristic
73C22×C4×C17C2×D411yescharacteristic
74C22×C4×C17#4111yescharacteristic
75C22×C4×C17#4111yescharacteristic
76C22×Dic17—21no—
77C22×Dic17—21no—
78C22×Dic17—21no—
79C22×Dic17—21no—
80C22×Dic17—21no—
81C22×Dic17—21no—
82C22×Dic17—21no—
83C22×Dic17—21no—
84C22×Dic17—21no—
85C22×Dic17—21no—
86C22×Dic17—22no—
87C22×Dic17—81no—
88C22×Dic17C22⋊C412yes—
89C22×Dic17C22⋊C412yes—
90C2×Dic34—21no—
91C2×Dic34—21no—
92C2×Dic34—81no—
93C2×C8×C17—41no—
94C2×C8×C17—81no—
95C4⋊C4×C17—81no—
96C4⋊C4×C17—81no—
97C22⋊C4×C17—41no—
98C22⋊C4×C17—41no—
99C22⋊C4×C17—41no—
100C22⋊C4×C17—41no—
101C22⋊Dic17—41no—
102C22⋊Dic17—41no—
103C22⋊Dic17—41no—
104C22⋊Dic17—41no—
105C4⋊Dic17—21no—
106C4⋊Dic17—21no—
107C4⋊Dic17—82no—
108C4⋊Dic17—81no—
109#63225—22no—
110#63225—22no—
111#63225—22no—
112#63225—22no—
113#63225—41no—
114#63225—41no—
115C4×Dic17—82no—
116C2×#3622—41no—
117C2×#3622—81no—
118#9202—171nomaximal, Sylow
119C23×C17—41no—
120C23×C17—41no—
121C23×C17C2×C22⋊C411yescharacteristic
122C23×C17#12011yescharacteristic
123C23×C17#12311yescharacteristic
124C23×C17#13511yescharacteristic
125C23×C17#13511yescharacteristic
126C23×C17#13711yescharacteristic
127C23×C17#13711yescharacteristic
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—42no—
135C2×C4×C17—42no—
136C2×C4×C17—42no—
137C2×C4×C17—42no—
138C2×C4×C17—42no—
139C2×C4×C17—42no—
140C2×C4×C17C4×D411yescharacteristic
141C2×C4×C17C4×D411yescharacteristic
142C2×C4×C17#12111yescharacteristic
143C2×C4×C17#12111yescharacteristic
144C2×Dic17—22no—
145C2×Dic17—22no—
146C2×Dic17—22no—
147C2×Dic17—22no—
148C2×Dic17—42no—
149C2×Dic17—41no—
150C2×Dic17—41no—
151C2×Dic17—41no—
152C2×Dic17—41no—
153C2×Dic17—42no—
154C2×Dic17—42no—
155C2×Dic17—42no—
156C2×Dic17—42no—
157C2×Dic17—42no—
158C2×Dic17—41no—
159C2×Dic17—41no—
160C2×Dic17—42no—
161C2×Dic17—81no—
162Dic34—81no—
163Dic34—81no—
164C8×C17—81no—
165#3622—81no—
166#2627—171no—
167#2313—171no—
168#1520—171no—
169#1520—171no—
170C2×#324—171no—
171#1289—171no—
172#1289D1711yescharacteristic
173C22×C17—21no—
174C22×C17—21no—
175C22×C17—21no—
176C22×C17—21no—
177C22×C17—21no—
178C22×C17—21no—
179C22×C17—41no—
180C22×C17—41no—
181C22×C17—41no—
182C22×C17—41no—
183C22×C17#38611yescharacteristic
184C22×C17#41611yescharacteristic
185C22×C17#41911yescharacteristic
186C22×C17#45211yescharacteristic
187C22×C17#45211yescharacteristic
188C22×C17#48511yescharacteristic
189C22×C17#48511yescharacteristic
190C4×C17—21no—
191C4×C17—21no—
192C4×C17—21no—
193C4×C17—21no—
194C4×C17—82no—
195C4×C17—82no—
196Dic17—42no—
197Dic17—42no—
198Dic17—82no—
199Dic17—81no—
200Dic17—81no—
201C2×C22⋊Q8—171no—
202C22×C4⋊C4—171no—
203C2×C22⋊C8—171no—
204C2×C22⋊C8C2×D1711yescharacteristic
205#400—172no—
206#398—342no—
207#395—172no—
208#387—342no—
209#387—342no—
210#385—341no—
211#381—341no—
212#381—341no—
213#380—171no—
214#380C2×D1711yescharacteristic
215#380C2×D1711yescharacteristic
216C4×C22⋊C4—341no—
217#328—342no—
218#328—342no—
219#324—342no—
220C2×C17—21no—
221C2×C17—21no—
222C2×C17—21no—
223C2×C17—21no—
224C2×C17—21no—
225C2×C17—21no—
226C2×C17#187311yescharacteristic
227C2×C17#191211yescharacteristic
228C2×C17#191311yescharacteristic
229C22×Q8—171no—
230C23×C4—171no—
231C23×C4—171no—
232C23×C4C22×D1711yescharacteristic
233C22×C8—21no—
234C22×C8—341no—
235C22⋊Q8—341no—
236C22⋊Q8—341no—
237C22⋊Q8—341no—
238C22⋊Q8—341no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—172no—
242C2×C4⋊C4—172no—
243C2×C4⋊C4—171no—
244C2×C4⋊C4—341no—
245C2×C4⋊C4—341no—
246C2×C4⋊C4—341no—
247C2×C4⋊C4—341no—
248C2×C4⋊C4—341no—
249C2×C4⋊C4—342no—
250C2×C4⋊C4—341no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—341no—
254C2×C22⋊C4—341no—
255C2×C42—342no—
256C22⋊C8—21no—
257C22⋊C8—21no—
258C22⋊C8—341no—
259C22⋊C8—341no—
260#95—172no—
261#95—342no—
262#95—342no—
263#95—342no—
264#95—342no—
265#95—344no—
266#95C4×D1712yes—
267#95D6812yes—
268C17#920211yescharacteristic, complemented, Sylow
269C24D4×D1711yescharacteristic
270C2×Q8—341no—
271C2×Q8—341no—
272C2×Q8—1361no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—81no—
276C22×C4—172no—
277C22×C4—172no—
278C22×C4—341no—
279C22×C4—341no—
280C22×C4—341no—
281C22×C4—341no—
282C22×C4—341no—
283C22×C4—341no—
284C22×C4—341no—
285C22×C4—341no—
286C22×C4—341no—
287C22×C4—341no—
288C22×C4—342no—
289C22×C4—1361no—
290C22×C4C2×C4×D1711yescharacteristic
291C22×C4C2×D6811yescharacteristic
292C22×C4#6325211yescharacteristic
293C22×C4D4×D1711yescharacteristic
294C22×C4D4×D1711yescharacteristic
295C22×C4#6325611yescharacteristic
296C2×C8—41no—
297C2×C8—81no—
298C2×C8—681no—
299C2×C8—1361no—
300C4⋊C4—81no—
301C4⋊C4—81no—
302C4⋊C4—342no—
303C4⋊C4—342no—
304C4⋊C4—342no—
305C4⋊C4—342no—
306C4⋊C4—341no—
307C4⋊C4—341no—
308C4⋊C4—681no—
309C4⋊C4—681no—
310C4⋊C4—1361no—
311C4⋊C4—1362no—
312C22⋊C4—41no—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C22⋊C4—681no—
317C22⋊C4—681no—
318C22⋊C4—681no—
319C22⋊C4—681no—
320C42—1362no—
321C23—41no—
322C23—41no—
323C23C22⋊C4×D1711yescharacteristic
324C23#1058756811yescharacteristic
325C23#1058758011yescharacteristic
326C23#1058759811yescharacteristic
327C23#1058760111yescharacteristic
328C23#1058760211yescharacteristic
329C23#1058760411yescharacteristic
330Q8—1361no—
331Q8—1361no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—342no—
345C2×C4—342no—
346C2×C4—342no—
347C2×C4—342no—
348C2×C4—682no—
349C2×C4—681no—
350C2×C4—681no—
351C2×C4—681no—
352C2×C4—681no—
353C2×C4—682no—
354C2×C4—682no—
355C2×C4—682no—
356C2×C4—682no—
357C2×C4—682no—
358C2×C4—682no—
359C2×C4—681no—
360C2×C4—681no—
361C2×C4—1361no—
362C2×C4C4×D6811yescharacteristic
363C2×C4#1058757011yescharacteristic
364C2×C4#1058757911yescharacteristic
365C2×C4#1058758111yescharacteristic
366C8—81no—
367C8—1361no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22#1176268711yescharacteristic
379C22#1176280211yescharacteristic
380C22#1176281611yescharacteristic
381C22#1176297211yescharacteristic
382C22#1176297411yescharacteristic
383C22#1176315211yescharacteristic
384C22#1176315311yescharacteristic
385C4—21no—
386C4—21no—
387C4—21no—
388C4—21no—
389C4—82no—
390C4—82no—
391C4—682no—
392C4—682no—
393C4—1362no—
394C4—1361no—
395C4—1361no—
396C2—21no—
397C2—21no—
398C2—21no—
399C2—21no—
400C2—21no—
401C2—21no—
402C2#1452909511yescharacteristic
403C2#1452932011yescharacteristic
404C2#1452932511yescharacteristic
subgroupG/H
centerC22#11762687
commutatorC22×C4×C17C22×C4
FrattiniC23×C4C22×D17
FittingC17×#1289C2
socleC22×C17#386
prime radicalC24×C17C2×D4
cosocleC23×C4×C17C23
hypercenter#1289D17
hypocenterC17#9202
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1289

Complements

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

NH ≅ G/Ntype
11. #11762749C4semidirect
13. #11762730C4semidirect
268. C17#9202semidirect

Maximal subgroups

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

subgroupindex
#145346002
#145313862
#145273572
#145273552
C2×#117625342
#145266512
C17×#12892
#920217