Finite Group Databasebeta

← #16922929

Subgroups — #16922929

Order 4352.

526 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 101 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#14537114C211yesmaximal, characteristic
2#14528763C211yesmaximal, characteristic, complemented
3#14528763C211yesmaximal, characteristic, complemented
4#14526608C211yesmaximal, characteristic, complemented
5#14526606C211yesmaximal, characteristic, complemented
6#14526605C211yesmaximal, characteristic, complemented
7C17×#1270C211yesmaximal, characteristic, complemented
8C2×#10587569—21no—
9C2×#10587624C411yescharacteristic
10C2×C42×D17C2211yescharacteristic
11C2×#10587485—21no—
12C2×#10587485—21no—
13C2×#10587491—21no—
14C2×#10587491—21no—
15#11762712C411yescharacteristic
16#11762708C411yescharacteristic
17#11762707C2211yescharacteristic
18#11762703—21no—
19#11762702—21no—
20#11762685—21no—
21#11762666C411yescharacteristic
22#11762564C2211yescharacteristic
23#11762564C2211yescharacteristic
24C17×#390C2211yescharacteristic
25C17×#336C2211yescharacteristic
26C17×#336C2211yescharacteristic
27C22×D4×C17C2×C411yescharacteristic
28C22×C22⋊D17—21no—
29C22×C4×D17C2×C411yescharacteristic
30C22×C4×D17D411yescharacteristic
31C22×C4×D17D411yescharacteristic
32C22×C8×C17—21no—
33C22×C8×C17—21no—
34C2×C4⋊C4×C17C2×C411yescharacteristic
35C2×C22⋊C4×C17—21no—
36C2×C22⋊C4×C17—21no—
37C2×C42×C17C2311yescharacteristic
38C2×C22⋊Dic17—21no—
39C2×C22⋊Dic17—21no—
40C2×C22⋊Dic17—21no—
41#10587624—42no—
42C2×#63227—21no—
43C2×C4⋊Dic17—21no—
44C2×C4⋊Dic17C2×C411yescharacteristic
45C2×C4⋊Dic17C2×C411yescharacteristic
46C2×#63225—21no—
47C2×C4×Dic17C2×C411yescharacteristic
48C2×C4×Dic17D411yescharacteristic
49C2×C4×Dic17D411yescharacteristic
50C22×#3622—21no—
51C22×#3622—21no—
52#10587569—42no—
53#10587569—42no—
54C42×D17—42no—
55#10587502—21no—
56#10587502—21no—
57#10587502—21no—
58#10587491—42no—
59#10587491—42no—
60#10587485—42no—
61#10587485—42no—
62C24×C17—21no—
63C23×D17C22⋊C411yescharacteristic
64C2×D4×C17—21no—
65C2×D4×C17—21no—
66C2×D4×C17—41no—
67C2×D4×C17—41no—
68C22×C4×C17—21no—
69C22×C4×C17C22×C411yescharacteristic
70C22×C4×C17C2×D411yescharacteristic
71C22×C4×C17C2×D411yescharacteristic
72C2×C22⋊D17—42no—
73C2×C22⋊D17—42no—
74C2×C22⋊D17—42no—
75C22×Dic17—21no—
76C22×Dic17—21no—
77C22×Dic17C22⋊C411yescharacteristic
78C22×Dic17C22⋊C411yescharacteristic
79C22×Dic17C22⋊C411yescharacteristic
80C2×C4×D17—21no—
81C2×C4×D17—21no—
82C2×C4×D17—21no—
83C2×C4×D17—21no—
84C2×C4×D17—22no—
85C2×C4×D17—41no—
86C2×C4×D17—41no—
87C2×C4×D17—41no—
88C2×C4×D17—41no—
89C2×C4×D17—41no—
90C2×C4×D17D812yes—
91C2×C4×D17SD1612yes—
92C2×C8×C17—41no—
93C2×C8×C17—41no—
94C2×C8×C17—41no—
95C2×C8×C17—41no—
96C2×C8×C17—41no—
97C2×C8×C17—41no—
98C4⋊C4×C17—41no—
99C22⋊C4×C17—41no—
100C22⋊C4×C17—41no—
101C22⋊C4×C17—41no—
102C22⋊C4×C17—41no—
103C42×C17—41no—
104C22⋊Dic17—42no—
105C22⋊Dic17—42no—
106C22⋊Dic17—42no—
107#63227—42no—
108C4⋊Dic17—21no—
109C4⋊Dic17—21no—
110C4⋊Dic17—42no—
111C4⋊Dic17—41no—
112#63225—41no—
113#63225—41no—
114C4×Dic17—22no—
115C4×Dic17—22no—
116C4×Dic17—41no—
117C2×#3622—41no—
118C2×#3622—41no—
119C2×#3622—41no—
120C2×#3622—41no—
121C2×#3622—41no—
122C2×#3622—41no—
123#7714—171nomaximal, Sylow
124C23×C17—41no—
125C23×C17—41no—
126C23×C17—41no—
127C23×C17—41no—
128C23×C17—41no—
129C23×C17—41no—
130C23×C17—41no—
131C23×C17C2×C22⋊C411yescharacteristic
132C22×D17—21no—
133C22×D17—21no—
134C22×D17—21no—
135C22×D17—21no—
136C22×D17—21no—
137C22×D17—21no—
138C22×D17#10212yes—
139D4×C17—81no—
140D4×C17—81no—
141C2×C4×C17—21no—
142C2×C4×C17—21no—
143C2×C4×C17—21no—
144C2×C4×C17—21no—
145C2×C4×C17—21no—
146C2×C4×C17—21no—
147C2×C4×C17—41no—
148C2×C4×C17—41no—
149C2×C4×C17—41no—
150C2×C4×C17#13111yescharacteristic
151C2×C4×C17#13111yescharacteristic
152C2×C4×C17C2×D811yescharacteristic
153C2×C4×C17C2×SD1611yescharacteristic
154C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C17#13711yescharacteristic
156C22⋊D17—84no—
157C2×Dic17—21no—
158C2×Dic17—21no—
159C2×Dic17—21no—
160C2×Dic17—21no—
161C2×Dic17—21no—
162C2×Dic17—21no—
163C2×Dic17—21no—
164C2×Dic17—41no—
165C2×Dic17—41no—
166C2×Dic17—41no—
167C2×Dic17—41no—
168C2×Dic17—41no—
169C2×Dic17—41no—
170C2×Dic17#9912yes—
171C2×Dic17#10212yes—
172C4×D17—42no—
173C4×D17—42no—
174C4×D17—42no—
175C4×D17—42no—
176C4×D17—42no—
177C4×D17—42no—
178C8×C17—81no—
179C8×C17—81no—
180#3622—81no—
181#3622—81no—
182#2854—171no—
183#1797—171no—
184#1797—171no—
185#1271—171no—
186#1271—171no—
187#1270—171no—
188#1270D1711yescharacteristic, complemented
189C22×C17—81no—
190C22×C17—81no—
191C22×C17—81no—
192C22×C17—81no—
193C22×C17—81no—
194C22×C17—81no—
195C22×C17—81no—
196C22×C17#40811yescharacteristic
197C22×C17C2×#9911yescharacteristic
198C22×C17#41311yescharacteristic
199C22×C17C2×#10211yescharacteristic
200C22×C17#41711yescharacteristic
201C22×C17#42111yescharacteristic
202C22×C17#42111yescharacteristic
203C2×D17—22no—
204C2×D17—22no—
205C2×D17—22no—
206C2×D17—41no—
207C2×D17—41no—
208C2×D17—41no—
209C2×D17—41no—
210C4×C17—21no—
211C4×C17—21no—
212C4×C17—21no—
213C4×C17—21no—
214C4×C17—21no—
215C4×C17—21no—
216C4×C17—81no—
217Dic17—22no—
218Dic17—22no—
219Dic17—41no—
220Dic17—81no—
221Dic17—81no—
222C2×#123—341no—
223C2×#121—171no—
224C22×C42—171no—
225C2×C4⋊C8—341no—
226C2×C4⋊C8—341no—
227C2×C22⋊C8—341no—
228C2×C22⋊C8—341no—
229#390—171no—
230#390C2×D1711yescharacteristic
231#389—171no—
232#389—171no—
233#388—341no—
234#388—341no—
235#386—341no—
236#380—171no—
237#336—171no—
238#336—171no—
239#336C2×D1711yescharacteristic
240#336C2×D1711yescharacteristic
241C2×C17—161no—
242C2×C17#146811yescharacteristic
243C2×C17#148011yescharacteristic
244C2×C17#149511yescharacteristic
245C2×C17#151311yescharacteristic
246C2×C17#151911yescharacteristic
247C2×C17#153511yescharacteristic
248C2×C17#154711yescharacteristic
249D17—42no—
250C22×D4—341no—
251C22×D4C4×D1711yescharacteristic
252C23×C4—171no—
253C23×C4—171no—
254C23×C4—171no—
255C22×C8—21no—
256C22×C8—21no—
257C22×C8—341no—
258C22×C8—341no—
259#123—682no—
260#123—682no—
261#121—682no—
262C2×C4⋊C4—171no—
263C2×C4⋊C4—171no—
264C2×C4⋊C4—341no—
265C2×C4⋊C4—341no—
266C2×C4⋊C4C4×D1711yescharacteristic
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—341no—
270C2×C22⋊C4—341no—
271C2×C22⋊C4—341no—
272C2×C22⋊C4—341no—
273C2×C42—171no—
274C2×C42—171no—
275C2×C42—171no—
276C2×C42—682no—
277C2×C42C22×D1711yescharacteristic
278C4⋊C8—682no—
279C4⋊C8—682no—
280C22⋊C8—682no—
281C22⋊C8—682no—
282#95—341no—
283#95—341no—
284#95—341no—
285C17#771411yescharacteristic, complemented, Sylow
286C24—21no—
287C24—171no—
288C2×D4—21no—
289C2×D4—21no—
290C2×D4—41no—
291C2×D4—41no—
292C2×D4—682no—
293C2×D4—682no—
294C2×D4—682no—
295C22×C4—21no—
296C22×C4—171no—
297C22×C4—171no—
298C22×C4—172no—
299C22×C4—172no—
300C22×C4—171no—
301C22×C4—342no—
302C22×C4—341no—
303C22×C4—341no—
304C22×C4—341no—
305C22×C4—341no—
306C22×C4—341no—
307C22×C4—341no—
308C22×C4—681no—
309C22×C4—681no—
310C22×C4—681no—
311C22×C4—681no—
312C22×C4—681no—
313C22×C4C2×C4×D1711yescharacteristic
314C22×C4D4×D1711yescharacteristic
315C22×C4D4×D1711yescharacteristic
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—681no—
323C2×C8—681no—
324C2×C8—681no—
325C2×C8—681no—
326C2×C8—681no—
327C2×C8—681no—
328C4⋊C4—41no—
329C4⋊C4—341no—
330C4⋊C4—341no—
331C4⋊C4—681no—
332C4⋊C4—682no—
333C4⋊C4—681no—
334C4⋊C4—681no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—682no—
340C22⋊C4—682no—
341C22⋊C4—682no—
342C22⋊C4—682no—
343C42—41no—
344C42—342no—
345C42—342no—
346C42—681no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23—172no—
355C23—341no—
356C23—341no—
357C23—341no—
358C23—341no—
359C23—341no—
360C23—341no—
361C23C22⋊C4×D1711yescharacteristic
362D4—81no—
363D4—81no—
364D4—1364no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—172no—
375C2×C4—172no—
376C2×C4—341no—
377C2×C4—341no—
378C2×C4—341no—
379C2×C4—341no—
380C2×C4—341no—
381C2×C4—341no—
382C2×C4—341no—
383C2×C4—682no—
384C2×C4—682no—
385C2×C4—682no—
386C2×C4—682no—
387C2×C4—682no—
388C2×C4—682no—
389C2×C4—681no—
390C2×C4—681no—
391C2×C4—681no—
392C2×C4—681no—
393C2×C4—681no—
394C2×C4—681no—
395C2×C4#1058758711yescharacteristic
396C2×C4#1058759311yescharacteristic
397C2×C4D8×D1711yescharacteristic
398C2×C4#1058759711yescharacteristic
399C2×C4SD16×D1711yescharacteristic
400C2×C4#1058760111yescharacteristic
401C8—81no—
402C8—81no—
403C8—1361no—
404C8—1361no—
405C22—81no—
406C22—81no—
407C22—81no—
408C22—81no—
409C22—81no—
410C22—81no—
411C22—81no—
412C22—342no—
413C22—342no—
414C22—342no—
415C22—681no—
416C22—681no—
417C22—681no—
418C22—681no—
419C22#1176277411yescharacteristic
420C22#99×D1711yescharacteristic
421C22#1176279011yescharacteristic
422C22#102×D1711yescharacteristic
423C22#1176280711yescharacteristic
424C22#1176282411yescharacteristic
425C22#1176282411yescharacteristic
426C4—21no—
427C4—21no—
428C4—21no—
429C4—21no—
430C4—21no—
431C4—21no—
432C4—81no—
433C4—342no—
434C4—342no—
435C4—681no—
436C4—1361no—
437C4—1361no—
438C2—161no—
439C2—682no—
440C2#1452712911yescharacteristic
441C2#1452718111yescharacteristic
442C2#1452724611yescharacteristic
443C2#1452732411yescharacteristic
444C2#1452735011yescharacteristic
445C2#1452741211yescharacteristic
446C2#1452745811yescharacteristic
subgroupG/H
centerC23C22⋊C4×D17
commutatorC22×C4×C17C22×C4
FrattiniC2×C42C22×D17
FittingC17×#1270C2
socleC23×C17C2×C22⋊C4
prime radicalC2×#10587624C4
cosocleC2×C42×C17C23
hypercenter#1270D17
hypocenterC17#7714
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
2. #14528763C2semidirect
3. #14528763C2semidirect
4. #14526608C2semidirect
5. #14526606C2semidirect
6. #14526605C2semidirect
7. C17×#1270C2semidirect
188. #1270D17semidirect
285. C17#7714semidirect

Maximal subgroups

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

subgroupindex
#145371142
#145287632
#145266082
#145266062
#145266052
C17×#12702
#771417