Finite Group Databasebeta

← #17949780

Subgroups — #17949780

Order 4352.

588 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 588 conjugacy classes of subgroups — too many to draw. Only its 106 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, complemented
2#14544641C211yesmaximal, characteristic, complemented
3#14543603C212yesmaximal, complemented
4#14543600C212yesmaximal, complemented
5C4×#10587624C211yesmaximal, characteristic
6C2×#10587544—21no—
7C2×#10587543—21no—
8C2×#10587543—21no—
9#11763675—21no—
10#11763675C2212yes—
11#11763675C2212yes—
12C2×#10587624C411yescharacteristic
13C2×C4×C22⋊D17—21no—
14C2×C42×D17C2211yescharacteristic
15#11762712C2211yescharacteristic
16#11762705C2211yescharacteristic
17#11762697—21no—
18#11762685—21no—
19#11762666C411yescharacteristic
20C4×C4⋊Dic17C411yescharacteristic
21C4×C22⋊Dic17—21no—
22C2×C4×D4×C17C411yescharacteristic
23C22×D4×C17C2×C411yescharacteristic
24C23×C4×C17—21no—
25C22×C22⋊D17—21no—
26C22×C4×D17C2×C411yescharacteristic
27C22×C4×D17D411yescharacteristic
28C22×C4×D17D411yescharacteristic
29C22×#3624—22no—
30C22×#3624—22no—
31C4×D4×C17—42no—
32C2×C4⋊C4×C17C2×C411yescharacteristic
33C2×C22⋊C4×C17—21no—
34C2×C42×C17C2×C411yescharacteristic
35C2×C22⋊Dic17—21no—
36C2×C22⋊Dic17—21no—
37C2×C22⋊Dic17—21no—
38#10587624—22no—
39#10587624C814yescomplemented
40C4×C22⋊D17—44no—
41C2×#63227—21no—
42C2×C4⋊Dic17C2×C411yescharacteristic
43C2×C4⋊Dic17C2×C411yescharacteristic
44C2×#63225—21no—
45C2×C4×Dic17—21no—
46C2×C4×Dic17D411yescharacteristic
47C2×C4×Dic17D411yescharacteristic
48C2×C4×Dic17C2311yescharacteristic
49C42×D17—42no—
50#10587544—42no—
51#10587543—42no—
52#10587543—42no—
53#10587502—21no—
54#10587502—21no—
55#10587502—21no—
56C24×C17—21no—
57C23×D17C22⋊C411yescharacteristic
58C2×D4×C17—21no—
59C2×D4×C17—41no—
60C2×D4×C17—41no—
61C2×D4×C17C2×C812yes—
62C22×C4×C17—21no—
63C22×C4×C17—42no—
64C22×C4×C17—42no—
65C22×C4×C17—42no—
66C22×C4×C17C22⋊C411yescharacteristic
67C22×C4×C17C22⋊C411yescharacteristic
68C22×C4×C17C22×C411yescharacteristic
69C2×C22⋊D17—24no—
70C2×C22⋊D17—42no—
71C2×C22⋊D17—42no—
72C22×Dic17—21no—
73C22×Dic17—21no—
74C22×Dic17C22⋊C411yescharacteristic
75C22×Dic17C2×D411yescharacteristic
76C22×Dic17C2×D411yescharacteristic
77C2×C4×D17—22no—
78C2×C4×D17—21no—
79C2×C4×D17—22no—
80C2×C4×D17—21no—
81C2×C4×D17—41no—
82C2×C4×D17—41no—
83C2×C4×D17—41no—
84C2×C4×D17—41no—
85C2×C4×D17—41no—
86C2×C4×D17C2×C812yes—
87C2×C4×D17M1612yes—
88C2×#3624—42no—
89C2×#3624—42no—
90C2×#3624—42no—
91C2×#3624—42no—
92C2×#3624—42no—
93C2×#3624—42no—
94C4⋊C4×C17—41no—
95C22⋊C4×C17—42no—
96C42×C17—22no—
97C22⋊Dic17—24no—
98C22⋊Dic17—42no—
99C22⋊Dic17—41no—
100C22⋊Dic17—41no—
101#63227—42no—
102C4⋊Dic17—21no—
103C4⋊Dic17—41no—
104C4⋊Dic17C2×C812yes—
105#63225—42no—
106C4×Dic17—22no—
107C4×Dic17—41no—
108C4×Dic17—41no—
109C4×Dic17—42no—
110#7599—171nomaximal, Sylow
111C23×C17—22no—
112C23×C17—41no—
113C23×C17—41no—
114C23×C17—41no—
115C23×C17—41no—
116C23×C17—41no—
117C23×C17—41no—
118C23×C17C2×C22⋊C411yescharacteristic
119C22×D17—21no—
120C22×D17—21no—
121C22×D17—21no—
122C22×D17—21no—
123C22×D17—21no—
124C22×D17—21no—
125C22×D17C22⋊C812yes—
126D4×C17—42no—
127D4×C17—42no—
128C2×C4×C17—21no—
129C2×C4×C17—21no—
130C2×C4×C17—21no—
131C2×C4×C17—21no—
132C2×C4×C17—21no—
133C2×C4×C17—21no—
134C2×C4×C17—21no—
135C2×C4×C17—41no—
136C2×C4×C17—41no—
137C2×C4×C17—41no—
138C2×C4×C17—84no—
139C2×C4×C17#9912yes—
140C2×C4×C17C22×C811yescharacteristic
141C2×C4×C17C2×M1611yescharacteristic
142C22⋊D17—48no—
143C2×Dic17—21no—
144C2×Dic17—21no—
145C2×Dic17—21no—
146C2×Dic17—21no—
147C2×Dic17—21no—
148C2×Dic17—21no—
149C2×Dic17—22no—
150C2×Dic17—41no—
151C2×Dic17—41no—
152C2×Dic17—41no—
153C2×Dic17—41no—
154C2×Dic17—41no—
155C2×Dic17C22⋊C812yes—
156C2×Dic17AGL(1,ℤ/8)11yescharacteristic
157C2×Dic17AGL(1,ℤ/8)12yes—
158C2×Dic17#13711yescharacteristic
159C4×D17—42no—
160C4×D17—42no—
161C4×D17—44no—
162C4×D17—42no—
163C4×D17—42no—
164#3624—82no—
165#3624—82no—
166C4×#121—171no—
167#1817—171no—
168#1797—171no—
169#1271—172no—
170#1270—172no—
171C22×C17—42no—
172C22×C17—42no—
173C22×C17—42no—
174C22×C17—81no—
175C22×C17—81no—
176C22×C17—81no—
177C22×C17—81no—
178C22×C17C2×C22⋊C811yescharacteristic
179C22×C17C2×#9911yescharacteristic
180C22×C17#41311yescharacteristic
181C22×C17#41711yescharacteristic
182C22×C17#41811yescharacteristic
183C22×C17#42111yescharacteristic
184C22×C17#42111yescharacteristic
185C2×D17—22no—
186C2×D17—22no—
187C2×D17—22no—
188C2×D17—41no—
189C2×D17—41no—
190C2×D17—41no—
191C2×D17—41no—
192C4×C17—21no—
193C4×C17—21no—
194C4×C17—22no—
195C4×C17—41no—
196C4×C17—81no—
197Dic17—22no—
198Dic17—22no—
199Dic17—21no—
200Dic17—21no—
201Dic17—42no—
202Dic17—81no—
203C2×#121—171no—
204C2×C4×D4—341no—
205C2×C4×D4#59511yescharacteristic
206C22×C42—171no—
207C2×C4⋊C8—341no—
208C2×C22⋊C8—341no—
209C2×C22⋊C8—341no—
210#390—171no—
211#389—171no—
212#388—341no—
213#386—341no—
214#380—171no—
215C4×C4⋊C4—171no—
216C4×C22⋊C4—341no—
217#336—172no—
218#336—172no—
219#336—341no—
220C2×C17—82no—
221C2×C17#145911yescharacteristic
222C2×C17#147711yescharacteristic
223C2×C17#147811yescharacteristic
224C2×C17#151011yescharacteristic
225C2×C17#151311yescharacteristic
226C2×C17#153511yescharacteristic
227C2×C17#155711yescharacteristic
228D17—42no—
229C22×D4—341no—
230C22×D4C2×#59511yescharacteristic
231C23×C4—21no—
232C23×C4—171no—
233C23×C4—171no—
234C23×C4—171no—
235C22×C8—342no—
236C22×C8—342no—
237#121—174no—
238#121—342no—
239C4×D4—42no—
240C4×D4—684no—
241C2×C4⋊C4—171no—
242C2×C4⋊C4—171no—
243C2×C4⋊C4—341no—
244C2×C4⋊C4C2×#59511yescharacteristic
245C2×C22⋊C4—21no—
246C2×C22⋊C4—341no—
247C2×C22⋊C4—341no—
248C2×C22⋊C4—341no—
249C2×C22⋊C4—341no—
250C2×C42—171no—
251C2×C42—171no—
252C2×C42—171no—
253C2×C42—341no—
254C2×C42—682no—
255C2×C42C2×#59511yescharacteristic
256C4⋊C8—682no—
257C22⋊C8—682no—
258C22⋊C8—682no—
259#95—341no—
260#95—341no—
261#95—341no—
262C17#759911yescharacteristic, complemented, Sylow
263C24—21no—
264C24—171no—
265C2×D4—21no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—344no—
269C2×D4—682no—
270C2×D4—682no—
271C2×D4#6324212yes—
272C22×C4—21no—
273C22×C4—42no—
274C22×C4—42no—
275C22×C4—42no—
276C22×C4—171no—
277C22×C4—171no—
278C22×C4—171no—
279C22×C4—172no—
280C22×C4—172no—
281C22×C4—341no—
282C22×C4—342no—
283C22×C4—341no—
284C22×C4—341no—
285C22×C4—342no—
286C22×C4—341no—
287C22×C4—681no—
288C22×C4—681no—
289C22×C4—681no—
290C22×C4—681no—
291C22×C4—681no—
292C22×C4C22⋊#59511yescharacteristic
293C22×C4C22⋊#59511yescharacteristic
294C22×C4C22×#59511yescharacteristic
295C2×C8—682no—
296C2×C8—682no—
297C2×C8—682no—
298C2×C8—682no—
299C2×C8—682no—
300C2×C8—682no—
301C4⋊C4—41no—
302C4⋊C4—172no—
303C4⋊C4—341no—
304C4⋊C4—681no—
305C4⋊C4—682no—
306C22⋊C4—42no—
307C22⋊C4—344no—
308C22⋊C4—682no—
309C22⋊C4—681no—
310C22⋊C4—681no—
311C22⋊C4—682no—
312C42—22no—
313C42—342no—
314C42—681no—
315C42—681no—
316C42—682no—
317C23—22no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23—172no—
325C23—341no—
326C23—341no—
327C23—341no—
328C23—341no—
329C23—341no—
330C23—341no—
331C23C2×C22⋊#59511yescharacteristic
332D4—42no—
333D4—42no—
334D4—688no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—84no—
346C2×C4—172no—
347C2×C4—171no—
348C2×C4—171no—
349C2×C4—172no—
350C2×C4—341no—
351C2×C4—341no—
352C2×C4—341no—
353C2×C4—341no—
354C2×C4—341no—
355C2×C4—341no—
356C2×C4—342no—
357C2×C4—682no—
358C2×C4—682no—
359C2×C4—684no—
360C2×C4—682no—
361C2×C4—682no—
362C2×C4—681no—
363C2×C4—681no—
364C2×C4—681no—
365C2×C4—681no—
366C2×C4—681no—
367C2×C4#1058755112yes—
368C2×C4C2×#6324211yescharacteristic
369C2×C4D17⋊M1611yescharacteristic
370C8—1362no—
371C8—1362no—
372C22—42no—
373C22—42no—
374C22—42no—
375C22—81no—
376C22—81no—
377C22—81no—
378C22—81no—
379C22—342no—
380C22—342no—
381C22—342no—
382C22—681no—
383C22—681no—
384C22—681no—
385C22—681no—
386C22#1176377711yescharacteristic
387C22C2×#1058755111yescharacteristic
388C22#1176379511yescharacteristic
389C22#1176380011yescharacteristic
390C22#1176380111yescharacteristic
391C22#1176380611yescharacteristic
392C22#1176380711yescharacteristic
393C4—22no—
394C4—21no—
395C4—21no—
396C4—41no—
397C4—81no—
398C4—342no—
399C4—341no—
400C4—341no—
401C4—342no—
402C4—682no—
403C4—1361no—
404C2—82no—
405C2—682no—
406C2#1454401911yescharacteristic
407C2#1454408011yescharacteristic
408C2#1454408411yescharacteristic
409C2#1454418911yescharacteristic
410C2#1454419911yescharacteristic
411C2#1454426811yescharacteristic
412C2#1454431511yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC2×C4×C17C22×C8
FrattiniC22×C4C22×#595
FittingC2×C4×D4×C17C4
socleC23×C17C2×C22⋊C4
prime radicalC2×#10587624C4
cosocleC2×C4×Dic17C23
hypercenterC2×C4×D4#595
hypocenterC17#7599
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #14544676C2semidirect
2. #14544641C2semidirect
3. #14543603C2semidirect
4. #14543600C2semidirect
39. #10587624C8semidirect
262. C17#7599semidirect

Maximal subgroups

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

subgroupindex
#145446762
#145446412
#145436032
#145436002
C4×#105876242
#759917