Finite Group Databasebeta

← #16945085

Subgroups — #16945085

Order 4352.

626 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 626 conjugacy classes of subgroups — too many to draw. Only its 91 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#14528772C211yesmaximal, characteristic, complemented
2#14527125C211yesmaximal, characteristic, complemented
3#14526805C212yesmaximal, complemented
4#14526781C212yesmaximal, complemented
5C17×#2388C211yesmaximal, characteristic
6#11762866—21no—
7C2×#10587505—21no—
8#11762669—21no—
9#11762576C2212yes—
10#11762533—21no—
11#11762533C2212yes—
12C22×#41×C17C411yescharacteristic, complemented
13C2×C4×D4×C17—21no—
14C2×C4×D4×C17C2211yescharacteristic
15C17×#395C411yescharacteristic, complemented
16C17×#394—21no—
17C17×#394C411yescharacteristic, complemented
18C17×#393C2211yescharacteristic
19C17×#392—21no—
20C17×#392C2211yescharacteristic
21C4×C22⋊C4×C17—21no—
22C4×C22⋊C4×C17C411yescharacteristic, complemented
23C2×#41×C17—44no—
24C2×#41×C17—41no—
25C2×#41×C17—41no—
26C22×Q8×C17C2×C411yescharacteristic
27C22×D4×C17—21no—
28C22×D4×C17—21no—
29C22×D4×C17C2×C411yescharacteristic
30C22×D4×C17D411yescharacteristic
31C23×C4×C17—21no—
32C23×C4×C17C2×C411yescharacteristic
33C23×C4×C17D411yescharacteristic
34C4×D4×C17—41no—
35C4×D4×C17—41no—
36C4×D4×C17—44no—
37C2×C4⋊C4×C17—21no—
38C2×C4⋊C4×C17C2×C411yescharacteristic
39C2×C22⋊C4×C17—21no—
40C2×C22⋊C4×C17—21no—
41C2×C22⋊C4×C17—21no—
42C2×C22⋊C4×C17—21no—
43C2×C22⋊C4×C17—21no—
44C2×C22⋊C4×C17D411yescharacteristic
45C2×C22⋊C4×C17C2311yescharacteristic
46C2×C42×C17—21no—
47C2×C42×C17D411yescharacteristic
48C2×C22⋊Dic17—22no—
49C2×C4⋊Dic17—41no—
50C17×#95—21no—
51C17×#95—21no—
52C17×#95C2×C411yescharacteristic
53C17×#95C2×C411yescharacteristic
54#10587505—42no—
55#10587502—41no—
56C22⋊#3622—22no—
57C4⋊#3622—41no—
58#10587474—41no—
59C24×C17—21no—
60C24×C17C22⋊C411yescharacteristic
61C24×C17C2×D411yescharacteristic
62#41×C17—44no—
63#41×C17—44no—
64#41×C17—44no—
65#41×C17—44no—
66C2×Q8×C17—42no—
67C2×Q8×C17—41no—
68C2×D4×C17—21no—
69C2×D4×C17—21no—
70C2×D4×C17—41no—
71C2×D4×C17—41no—
72C2×D4×C17—41no—
73C2×D4×C17—42no—
74C2×D4×C17—42no—
75C2×D4×C17—42no—
76C2×D4×C17—42no—
77C2×D4×C17—42no—
78C2×D4×C17—41no—
79C2×D4×C17—41no—
80C2×D4×C17—42no—
81C22×C4×C17—24no—
82C22×C4×C17—21no—
83C22×C4×C17—21no—
84C22×C4×C17—21no—
85C22×C4×C17—21no—
86C22×C4×C17—21no—
87C22×C4×C17—21no—
88C22×C4×C17—21no—
89C22×C4×C17—42no—
90C22×C4×C17—42no—
91C22×C4×C17—42no—
92C22×C4×C17—41no—
93C22×C4×C17—41no—
94C22×C4×C17C22⋊C411yescharacteristic
95C22×C4×C17C22⋊C411yescharacteristic
96C22×C4×C17C22⋊C411yescharacteristic
97C22×C4×C17C22×C411yescharacteristic
98C22×C4×C17C2×D411yescharacteristic
99C22×Dic17—42no—
100C4⋊C4×C17—41no—
101C4⋊C4×C17—42no—
102C22⋊C4×C17—41no—
103C22⋊C4×C17—41no—
104C22⋊C4×C17—42no—
105C22⋊C4×C17—42no—
106C22⋊C4×C17—42no—
107C22⋊C4×C17—42no—
108C22⋊C4×C17—42no—
109C42×C17—21no—
110C42×C17—21no—
111C42×C17—42no—
112C22⋊Dic17—42no—
113C22⋊Dic17—42no—
114C4⋊Dic17—82no—
115C2×#3622—42no—
116#11820—171nomaximal, Sylow
117C23×C17—21no—
118C23×C17—21no—
119C23×C17—22no—
120C23×C17—21no—
121C23×C17—21no—
122C23×C17—21no—
123C23×C17—41no—
124C23×C17—41no—
125C23×C17—41no—
126C23×C17—41no—
127C23×C17—41no—
128C23×C17—41no—
129C23×C17—41no—
130C23×C17—41no—
131C23×C17—41no—
132C23×C17—41no—
133C23×C17C2×C22⋊C411yescharacteristic
134C23×C17AGL(1,ℤ/8)11yescharacteristic
135C23×C17#13711yescharacteristic
136Q8×C17—42no—
137Q8×C17—42no—
138D4×C17—42no—
139D4×C17—42no—
140D4×C17—42no—
141D4×C17—44no—
142D4×C17—44no—
143D4×C17—48no—
144D4×C17—42no—
145C2×C4×C17—22no—
146C2×C4×C17—22no—
147C2×C4×C17—22no—
148C2×C4×C17—21no—
149C2×C4×C17—21no—
150C2×C4×C17—21no—
151C2×C4×C17—21no—
152C2×C4×C17—21no—
153C2×C4×C17—21no—
154C2×C4×C17—44no—
155C2×C4×C17—42no—
156C2×C4×C17—41no—
157C2×C4×C17—41no—
158C2×C4×C17—41no—
159C2×C4×C17—41no—
160C2×C4×C17—44no—
161C2×C4×C17—42no—
162C2×C4×C17—42no—
163C2×C4×C17—41no—
164C2×C4×C17—41no—
165C2×C4×C17—41no—
166C2×C4×C17—41no—
167C2×C4×C17—41no—
168C2×C4×C17—41no—
169C2×C4×C17—81no—
170C2×C4×C17#9911yescharacteristic
171C2×C4×C17#9911yescharacteristic
172C2×Dic17—82no—
173C2×Dic17—82no—
174C2×Dic17—82no—
175#3622—82no—
176#2388D1711yescharacteristic
177#1799—171no—
178#1466—171no—
179#1351—172no—
180#1343—172no—
181C22×C17—21no—
182C22×C17—21no—
183C22×C17—21no—
184C22×C17—21no—
185C22×C17—41no—
186C22×C17—41no—
187C22×C17—42no—
188C22×C17—42no—
189C22×C17—41no—
190C22×C17—41no—
191C22×C17—41no—
192C22×C17—42no—
193C22×C17—41no—
194C22×C17—41no—
195C22×C17—81no—
196C22×C17—81no—
197C22×C17—81no—
198C22×C17—81no—
199C22×C17—81no—
200C22×C17—81no—
201C22×C17—81no—
202C22×C17C2×#9911yescharacteristic
203C22×C17#41711yescharacteristic
204C22×C17#42111yescharacteristic
205C4×C17—21no—
206C4×C17—42no—
207C4×C17—42no—
208C4×C17—41no—
209C4×C17—41no—
210C4×C17—41no—
211C4×C17—41no—
212C4×C17—81no—
213C4×C17AΣL(1,𝔽16)12yes—
214Dic17—162no—
215C22×#41Dic1711yescharacteristic, complemented
216C2×C4×D4—21no—
217C2×C4×D4C2×D1711yescharacteristic
218#432—341no—
219C2×#99—341no—
220#395Dic1711yescharacteristic, complemented
221#394—21no—
222#394Dic1711yescharacteristic, complemented
223#393C2×D1711yescharacteristic
224#392—21no—
225#392C2×D1711yescharacteristic
226#380—341no—
227C4×C22⋊C4—21no—
228C4×C22⋊C4Dic1711yescharacteristic, complemented
229#342—172no—
230#323—172no—
231#323—341no—
232C2×C17—21no—
233C2×C17—21no—
234C2×C17—41no—
235C2×C17—41no—
236C2×C17—81no—
237C2×C17—82no—
238C2×C17#151311yescharacteristic
239C2×C17C2×AΣL(1,𝔽16)11yescharacteristic
240C2×C17#212611yescharacteristic
241C2×#41—44no—
242C2×#41—41no—
243C2×#41—41no—
244C22×Q8C2×Dic1711yescharacteristic
245C22×D4—21no—
246C22×D4—21no—
247C22×D4C2×Dic1711yescharacteristic
248C22×D4C22⋊D1711yescharacteristic
249C23×C4—21no—
250C23×C4C2×Dic1711yescharacteristic
251C23×C4C22⋊D1711yescharacteristic
252C4×D4—41no—
253C4×D4—41no—
254C4×D4—44no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—681no—
257C2×C4⋊C4C2×Dic1711yescharacteristic
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—21no—
261C2×C22⋊C4—21no—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—342no—
264C2×C22⋊C4C22⋊D1711yescharacteristic
265C2×C22⋊C4C22×D1711yescharacteristic
266C2×C42—21no—
267C2×C42C22⋊D1711yescharacteristic
268C4⋊C8—681no—
269#99—682no—
270C22⋊C8—342no—
271#97—681no—
272#95—21no—
273#95—21no—
274#95—681no—
275#95C2×Dic1711yescharacteristic
276#95C2×Dic1711yescharacteristic
277C17#1182011yescharacteristic, complemented, Sylow
278C24—21no—
279C24C22⋊Dic1711yescharacteristic
280C24C2×C22⋊D1711yescharacteristic
281#41—44no—
282#41—44no—
283#41—44no—
284#41—44no—
285C2×Q8—42no—
286C2×Q8—41no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—41no—
290C2×D4—41no—
291C2×D4—41no—
292C2×D4—42no—
293C2×D4—42no—
294C2×D4—42no—
295C2×D4—42no—
296C2×D4—42no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—42no—
300C22×C4—24no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—42no—
309C22×C4—42no—
310C22×C4—42no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—682no—
314C22×C4C22⋊Dic1711yescharacteristic
315C22×C4C22⋊Dic1711yescharacteristic
316C22×C4C22⋊Dic1711yescharacteristic
317C22×C4C22×Dic1711yescharacteristic
318C22×C4C2×C22⋊D1711yescharacteristic
319C2×C8—682no—
320C4⋊C4—41no—
321C4⋊C4—42no—
322C4⋊C4—1362no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C22⋊C4—42no—
326C22⋊C4—42no—
327C22⋊C4—42no—
328C22⋊C4—42no—
329C22⋊C4—42no—
330C22⋊C4—682no—
331C22⋊C4—682no—
332C42—21no—
333C42—21no—
334C42—42no—
335C23—21no—
336C23—21no—
337C23—22no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23#1058763511yescharacteristic
352C23#1058763711yescharacteristic
353C23C2×C22⋊Dic1711yescharacteristic
354Q8—42no—
355Q8—42no—
356D4—42no—
357D4—42no—
358D4—42no—
359D4—48no—
360D4—42no—
361D4—44no—
362D4—44no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—44no—
373C2×C4—42no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—42no—
379C2×C4—44no—
380C2×C4—42no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—81no—
388C2×C4—1362no—
389C2×C4—1362no—
390C2×C4—1362no—
391C2×C4#1058750511yescharacteristic
392C2×C4#1058750511yescharacteristic
393C8—1362no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—41no—
399C22—41no—
400C22—42no—
401C22—42no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—42no—
407C22—41no—
408C22—81no—
409C22—81no—
410C22—81no—
411C22—81no—
412C22—81no—
413C22—81no—
414C22—81no—
415C22C2×#1058750511yescharacteristic
416C22#1176281011yescharacteristic
417C22#1176282611yescharacteristic
418C4—21no—
419C4—42no—
420C4—41no—
421C4—42no—
422C4—41no—
423C4—41no—
424C4—41no—
425C4—81no—
426C4—2722no—
427C4#1176259612yes—
428C2—21no—
429C2—21no—
430C2—41no—
431C2—41no—
432C2—82no—
433C2—81no—
434C2#1452732711yescharacteristic
435C2C2×#1176259611yescharacteristic
436C2#1453044911yescharacteristic
subgroupG/H
centerC22C2×#10587505
commutatorC22×C4×C17C22×C4
FrattiniC2×C22⋊C4C22×D17
Fitting, prime radicalC17×#2388C2
socleC22×C17C2×#99
cosocleC2×C22⋊C4×C17C23
hypercenter#2388D17
hypocenterC17#11820
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2388

Complements

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

NH ≅ G/Ntype
1. #14528772C2semidirect
2. #14527125C2semidirect
3. #14526805C2semidirect
4. #14526781C2semidirect
12. C22×#41×C17C4semidirect
15. C17×#395C4semidirect
17. C17×#394C4semidirect
22. C4×C22⋊C4×C17C4semidirect
215. C22×#41Dic17semidirect
220. #395Dic17semidirect
222. #394Dic17semidirect
228. C4×C22⋊C4Dic17semidirect
277. C17#11820semidirect

Maximal subgroups

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

subgroupindex
#145287722
#145271252
#145268052
#145267812
C17×#23882
#1182017