Finite Group Databasebeta

← #17955974

Subgroups — #17955974

Order 4352.

640 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 640 conjugacy classes of subgroups — too many to draw. Only its 122 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#14544638C211yesmaximal, characteristic
2#14544510C211yesmaximal, characteristic
3C2×#11763655C212yesmaximal
4C2×#11763654C212yesmaximal
5C2×#11762706C211yesmaximal, characteristic
6C2×C4⋊#3624—21no—
7C2×C22⋊#3624C2212yes—
8C2×C22⋊#3624C2212yes—
9C2×#10587542—21no—
10#11763675—21no—
11#11763675—21no—
12#11763655—24no—
13#11763654—24no—
14C22×C4⋊Dic17C2211yescharacteristic
15C22×#63225C411yescharacteristic
16C22×#63225C411yescharacteristic
17C22×#63225C2211yescharacteristic
18C22×C4×Dic17C2211yescharacteristic
19#11762706—21no—
20#11762706—21no—
21#11762706—21no—
22#11762706—21no—
23C2×#10587502C411yescharacteristic
24C2×C17×#95C411yescharacteristic
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⋊Dic17—21no—
35C2×C4⋊Dic17—21no—
36C2×C4⋊Dic17—22no—
37C2×C4⋊Dic17—22no—
38C2×#63225—22no—
39C2×#63225—21no—
40C2×#63225—21no—
41C2×#63225—21no—
42C2×#63225—21no—
43C2×#63225—22no—
44C2×#63225—21no—
45C2×#63225—21no—
46C2×#63225—22no—
47C2×#63225—22no—
48C2×#63225—42no—
49C2×C4×Dic17—42no—
50C2×C4×Dic17D411yescharacteristic
51C2×C4×Dic17D411yescharacteristic
52C2×C4×Dic17D411yescharacteristic
53C2×C4×Dic17D411yescharacteristic
54C22⋊#3624—22no—
55C22⋊#3624—22no—
56C22⋊#3624—22no—
57C22⋊#3624D414yes—
58#10587542—42no—
59C4⋊#3624—42no—
60C17×#95—21no—
61C17×#95—21no—
62#10587502—21no—
63#10587502—21no—
64C24×C17C22×C411yescharacteristic
65C22×C4×C17—21no—
66C22×C4×C17—22no—
67C22×C4×C17—21no—
68C22×C4×C17—22no—
69C22×C4×C17—22no—
70C22×C4×C17—22no—
71C22×C4×C17—21no—
72C22×C4×C17—22no—
73C22×C4×C17—41no—
74C22×C4×C17—41no—
75C22×C4×C17—41no—
76C22×C4×C17C22⋊C411yescharacteristic
77C22×C4×C17C22⋊C411yescharacteristic
78C22×C4×C17M1612yes—
79C22×Dic17—21no—
80C22×Dic17—21no—
81C22×Dic17—22no—
82C22×Dic17—22no—
83C22×Dic17—21no—
84C22×Dic17—22no—
85C22×Dic17—21no—
86C22×Dic17—22no—
87C22×Dic17—21no—
88C22×Dic17—22no—
89C22×Dic17—41no—
90C22×Dic17—41no—
91C22×Dic17—41no—
92C22×Dic17—41no—
93C22×Dic17C22⋊C411yescharacteristic
94C22×Dic17C22⋊C411yescharacteristic
95C22×Dic17M1612yes—
96C22×Dic17C2×D411yescharacteristic
97C22×Dic17C2×D411yescharacteristic
98C22×Dic17C2×D412yes—
99C22×Dic17#4112yes—
100C2×#3624—24no—
101C2×#3624—42no—
102C2×#3624—42no—
103C2×#3624—42no—
104C2×#3624—42no—
105C2×#3624—42no—
106C4⋊Dic17—42no—
107C4⋊Dic17—41no—
108C4⋊Dic17—41no—
109#63225—24no—
110#63225—24no—
111#63225—42no—
112#63225—42no—
113#63225—42no—
114#63225—41no—
115#63225—41no—
116C4×Dic17—22no—
117C4×Dic17—22no—
118C4×Dic17—41no—
119C4×Dic17—41no—
120#9654—171nomaximal, Sylow
121C23×C17—21no—
122C23×C17—21no—
123C23×C17—21no—
124C23×C17—21no—
125C23×C17C2×C22⋊C411yescharacteristic
126C23×C17C4×D412yes—
127C23×C17C2×M1611yescharacteristic
128C23×C17C2×M1611yescharacteristic
129C23×C17#13112yes—
130C2×C4×C17—21no—
131C2×C4×C17—21no—
132C2×C4×C17—22no—
133C2×C4×C17—21no—
134C2×C4×C17—21no—
135C2×C4×C17—21no—
136C2×C4×C17—24no—
137C2×C4×C17—44no—
138C2×C4×C17—41no—
139C2×C4×C17—41no—
140C2×C4×C17—42no—
141C2×C4×C17—41no—
142C2×C4×C17—41no—
143C2×C4×C17—41no—
144C2×C4×C17—82no—
145C2×C4×C17#10112yes—
146C2×Dic17—24no—
147C2×Dic17—24no—
148C2×Dic17—21no—
149C2×Dic17—21no—
150C2×Dic17—21no—
151C2×Dic17—21no—
152C2×Dic17—21no—
153C2×Dic17—21no—
154C2×Dic17—21no—
155C2×Dic17—21no—
156C2×Dic17—22no—
157C2×Dic17—24no—
158C2×Dic17—42no—
159C2×Dic17—42no—
160C2×Dic17—41no—
161C2×Dic17—41no—
162C2×Dic17—42no—
163C2×Dic17—41no—
164C2×Dic17—41no—
165C2×Dic17—41no—
166C2×Dic17—82no—
167C2×Dic17#9912yes—
168C2×Dic17#10112yes—
169C2×Dic17#12112yes—
170C2×Dic17#12411yescharacteristic
171C2×Dic17#12711yescharacteristic
172#3624—44no—
173#3624—82no—
174C2×#389—171no—
175#1797—171no—
176#1749—171no—
177C2×#324—172no—
178C2×#324—172no—
179C22×C17—22no—
180C22×C17—22no—
181C22×C17—21no—
182C22×C17—21no—
183C22×C17—21no—
184C22×C17—21no—
185C22×C17—22no—
186C22×C17—22no—
187C22×C17#39011yescharacteristic
188C22×C17#40711yescharacteristic
189C22×C17#40811yescharacteristic
190C22×C17C2×#9911yescharacteristic
191C22×C17#41011yescharacteristic
192C22×C17C2×#10111yescharacteristic
193C22×C17C2×#10111yescharacteristic
194C22×C17#43512yes—
195C22×C17#43512yes—
196C4×C17—22no—
197C4×C17—42no—
198C4×C17—41no—
199C4×C17—81no—
200Dic17—22no—
201Dic17—21no—
202Dic17—21no—
203Dic17—22no—
204Dic17—22no—
205Dic17—42no—
206Dic17—81no—
207C22×C4⋊C4—171no—
208C22×C4⋊C4—171no—
209C22×C4⋊C4—171no—
210C22×C4⋊C4—171no—
211C22×C42—171no—
212C2×C4⋊C8—341no—
213C2×C22⋊C8—172no—
214C2×C22⋊C8—172no—
215C2×#97—341no—
216#389—341no—
217#389—341no—
218#389—341no—
219#389—341no—
220C2×#95—171no—
221C2×#95#59511yescharacteristic
222#336—341no—
223#336—341no—
224#324—344no—
225#324—344no—
226C2×C17—22no—
227C2×C17—22no—
228C2×C17#146311yescharacteristic
229C2×C17#146711yescharacteristic
230C2×C17#147011yescharacteristic
231C2×C17#147211yescharacteristic
232C2×C17#195511yescharacteristic
233C2×C17#196411yescharacteristic
234C2×C17#196611yescharacteristic
235C23×C4—171no—
236C23×C4—171no—
237C23×C4—171no—
238C23×C4—171no—
239C23×C4C2×#59511yescharacteristic
240C23×C4C2×#59511yescharacteristic
241C23×C4C2×#59511yescharacteristic
242C22×C8—342no—
243C22×C8—342no—
244C2×C4⋊C4—341no—
245C2×C4⋊C4—341no—
246C2×C4⋊C4—342no—
247C2×C4⋊C4—342no—
248C2×C4⋊C4—342no—
249C2×C4⋊C4—342no—
250C2×C4⋊C4—341no—
251C2×C4⋊C4—341no—
252C2×C4⋊C4—341no—
253C2×C4⋊C4—341no—
254C2×C4⋊C4—341no—
255C2×C4⋊C4—341no—
256C2×C4⋊C4—342no—
257C2×C4⋊C4—342no—
258C2×C4⋊C4—682no—
259C2×C42—171no—
260C2×C42—171no—
261C2×C42—171no—
262C2×C42—171no—
263C2×C42—682no—
264C4⋊C8—682no—
265C22⋊C8—174no—
266C22⋊C8—342no—
267C22⋊C8—342no—
268C22⋊C8—342no—
269#97—682no—
270#95—21no—
271#95—21no—
272#95—341no—
273#95—341no—
274C17#965411yescharacteristic, complemented, Sylow
275C24C22×#59511yescharacteristic
276C22×C4—21no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—21no—
281C22×C4—22no—
282C22×C4—21no—
283C22×C4—22no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—171no—
288C22×C4—171no—
289C22×C4—171no—
290C22×C4—171no—
291C22×C4—172no—
292C22×C4—172no—
293C22×C4—172no—
294C22×C4—342no—
295C22×C4—342no—
296C22×C4—341no—
297C22×C4—341no—
298C22×C4—341no—
299C22×C4—342no—
300C22×C4—342no—
301C22×C4—341no—
302C22×C4—341no—
303C22×C4—342no—
304C22×C4—681no—
305C22×C4—681no—
306C22×C4—681no—
307C22×C4—681no—
308C22×C4#6324312yes—
309C22×C4C22⋊#59511yescharacteristic
310C22×C4C22⋊#59511yescharacteristic
311C2×C8—344no—
312C2×C8—682no—
313C2×C8—682no—
314C2×C8—682no—
315C2×C8—682no—
316C2×C8—682no—
317C4⋊C4—344no—
318C4⋊C4—344no—
319C4⋊C4—682no—
320C4⋊C4—681no—
321C4⋊C4—681no—
322C4⋊C4—682no—
323C4⋊C4—681no—
324C4⋊C4—681no—
325C4⋊C4—682no—
326C4⋊C4—682no—
327C42—342no—
328C42—342no—
329C42—681no—
330C42—681no—
331C23—21no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23C2×#6324311yescharacteristic
336C23D17⋊M1611yescharacteristic
337C23#1058767812yes—
338C23D4×#59512yes—
339C23C2×C22⋊#59511yescharacteristic
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—22no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—24no—
347C2×C4—44no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—42no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—82no—
355C2×C4—172no—
356C2×C4—171no—
357C2×C4—171no—
358C2×C4—172no—
359C2×C4—172no—
360C2×C4—344no—
361C2×C4—344no—
362C2×C4—341no—
363C2×C4—341no—
364C2×C4—341no—
365C2×C4—341no—
366C2×C4—341no—
367C2×C4—341no—
368C2×C4—341no—
369C2×C4—341no—
370C2×C4—342no—
371C2×C4—344no—
372C2×C4—682no—
373C2×C4—682no—
374C2×C4—681no—
375C2×C4—681no—
376C2×C4—682no—
377C2×C4—681no—
378C2×C4—681no—
379C2×C4—681no—
380C2×C4—1362no—
381C2×C4#1058754512yes—
382C8—684no—
383C8—1362no—
384C22—22no—
385C22—22no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—22no—
391C22—22no—
392C22#1176376111yescharacteristic
393C22#1176378011yescharacteristic
394C22#1176378211yescharacteristic
395C22D17⋊#9911yescharacteristic
396C22#1176378811yescharacteristic
397C22C2×#1058754511yescharacteristic
398C22D17⋊#10111yescharacteristic
399C22#1176383812yes—
400C22#1176384112yes—
401C4—22no—
402C4—42no—
403C4—41no—
404C4—81no—
405C4—342no—
406C4—341no—
407C4—341no—
408C4—342no—
409C4—342no—
410C4—682no—
411C4—1361no—
412C2—22no—
413C2—22no—
414C2#1454403311yescharacteristic
415C2#1454404611yescharacteristic
416C2#1454405611yescharacteristic
417C2#1454406311yescharacteristic
418C2#1454490911yescharacteristic
419C2#1454492511yescharacteristic
420C2#1454492711yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutator, prime radicalC24×C17C22×C4
FrattiniC24C22×#595
FittingC2×C17×#95C4
socleC23×C17C2×C22⋊C4
cosocleC23×Dic17C23
hypercenterC2×#95#595
hypocenterC17#9654
LCSG ▷ C24×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
274. C17#9654semidirect

Maximal subgroups

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

subgroupindex
#145446382
#145445102
C2×#117636552
C2×#117636542
C2×#117627062
#965417