Finite Group Databasebeta

← #16944801

Subgroups — #16944801

Order 4352.

700 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 700 conjugacy classes of subgroups — too many to draw. Only its 87 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#14533715C211yesmaximal, characteristic
2C2×#11762576C211yesmaximal, characteristic, complemented
3#14526809C212yesmaximal, complemented
4#14526782C212yesmaximal, complemented
5C17×#1462C211yesmaximal, characteristic, complemented
6C2×#10587615—21no—
7C2×#10587616C411yescharacteristic, complemented
8C2×#10587639—21no—
9C22×C22⋊Dic17—21no—
10#11762745C411yescharacteristic, complemented
11#11762745C2211yescharacteristic
12#11762718C411yescharacteristic, complemented
13#11762718C2211yescharacteristic
14#11762709—21no—
15#11762709—21no—
16C4×C22⋊Dic17C411yescharacteristic, complemented
17#11762576—21no—
18#11762576C2212yes—
19C22×C22⋊C4×C17C2211yescharacteristic
20C17×#407—21no—
21C17×#323—21no—
22C17×#323C2212yes—
23C25×C17D411yescharacteristic
24C23×C4×C17C2×C411yescharacteristic
25C23×C4×C17D411yescharacteristic
26C22×C22⋊D17—21no—
27C22×C22⋊D17—21no—
28C22×C22⋊D17—21no—
29C23×Dic17—41no—
30C22×D68C2×C411yescharacteristic, complemented
31C2×M16×C17—41no—
32C2×C22⋊C4×C17—41no—
33C2×C22⋊C4×C17—41no—
34C2×C22⋊C4×C17C2×C411yescharacteristic
35C2×C22⋊C4×C17D411yescharacteristic
36C2×C22⋊C4×C17D411yescharacteristic
37C2×C22⋊C4×C17C2311yescharacteristic
38#10587639—44no—
39C2×C22⋊Dic17—21no—
40C2×C22⋊Dic17—24no—
41C2×C22⋊Dic17—22no—
42C2×C22⋊Dic17—21no—
43C2×C22⋊Dic17—21no—
44C2×C22⋊Dic17—41no—
45C2×C22⋊Dic17—42no—
46#10587616—41no—
47#10587616—41no—
48#10587615—44no—
49C2×#63227—21no—
50C2×#63227—21no—
51C2×#63227—21no—
52C2×C4⋊Dic17C2×C411yescharacteristic, complemented
53C2×#63225—21no—
54C2×#63225—21no—
55C2×C4×Dic17—21no—
56C17×C22⋊C8—22no—
57C17×C22⋊C8—41no—
58#10587502C2×C411yescharacteristic, complemented
59#10587502C2×C411yescharacteristic, complemented
60C24×C17—21no—
61C24×C17—21no—
62C24×C17—22no—
63C24×C17—21no—
64C24×C17—21no—
65C24×C17—42no—
66C24×C17—81no—
67C24×C17C22⋊C411yescharacteristic
68C24×C17C22⋊C411yescharacteristic
69C24×C17C2×D411yescharacteristic
70C23×D17—21no—
71C22×C4×C17—21no—
72C22×C4×C17—21no—
73C22×C4×C17—21no—
74C22×C4×C17—21no—
75C22×C4×C17—42no—
76C22×C4×C17—81no—
77C22×C4×C17C22⋊C411yescharacteristic
78C22×C4×C17C22⋊C411yescharacteristic
79C22×C4×C17C22×C411yescharacteristic
80C22×C4×C17C2×D411yescharacteristic
81C2×C22⋊D17—42no—
82C2×C22⋊D17—42no—
83C2×C22⋊D17—42no—
84C2×C22⋊D17—42no—
85C2×C22⋊D17—41no—
86C2×C22⋊D17—41no—
87C2×C22⋊D17—42no—
88C2×C22⋊D17—41no—
89C2×C22⋊D17—41no—
90C2×C22⋊D17—81no—
91C2×C22⋊D17—81no—
92C22×Dic17—21no—
93C22×Dic17—21no—
94C22×Dic17—21no—
95C22×Dic17—44no—
96C22×Dic17—42no—
97C22×Dic17—82no—
98C22×Dic17—82no—
99C2×D68—41no—
100C2×D68—81no—
101M16×C17—82no—
102C2×C8×C17—42no—
103C22⋊C4×C17—41no—
104C22⋊C4×C17—41no—
105C22⋊C4×C17—41no—
106C22⋊C4×C17—41no—
107C22⋊Dic17—24no—
108C22⋊Dic17—24no—
109C22⋊Dic17—42no—
110C22⋊Dic17—42no—
111C22⋊Dic17—44no—
112C22⋊Dic17—42no—
113#63227—42no—
114#63227—42no—
115#63227—42no—
116C4⋊Dic17—41no—
117#63225—42no—
118#63225—42no—
119C4×Dic17—81no—
120#11757—171nomaximal, Sylow
121C23×C17—22no—
122C23×C17—22no—
123C23×C17—22no—
124C23×C17—22no—
125C23×C17—22no—
126C23×C17—21no—
127C23×C17—21no—
128C23×C17—21no—
129C23×C17—21no—
130C23×C17—21no—
131C23×C17—21no—
132C23×C17—41no—
133C23×C17—42no—
134C23×C17—41no—
135C23×C17—41no—
136C23×C17—41no—
137C23×C17—41no—
138C23×C17—42no—
139C23×C17—81no—
140C23×C17—81no—
141C23×C17—84no—
142C23×C17—82no—
143C23×C17—82no—
144C23×C17#9911yescharacteristic
145C23×C17#9911yescharacteristic
146C23×C17#10412yes—
147C23×C17C2×C22⋊C411yescharacteristic
148C23×C17AGL(1,ℤ/8)11yescharacteristic
149C23×C17#13711yescharacteristic
150C22×D17—41no—
151C22×D17—41no—
152C22×D17—41no—
153C22×D17—41no—
154C22×D17—41no—
155C22×D17—41no—
156C22×D17—41no—
157C2×C4×C17—21no—
158C2×C4×C17—21no—
159C2×C4×C17—21no—
160C2×C4×C17—21no—
161C2×C4×C17—42no—
162C2×C4×C17—41no—
163C2×C4×C17—41no—
164C2×C4×C17—41no—
165C2×C4×C17—41no—
166C2×C4×C17—81no—
167C2×C4×C17—81no—
168C2×C4×C17—81no—
169C22⋊D17—84no—
170C22⋊D17—82no—
171C22⋊D17—82no—
172C22⋊D17—82no—
173C22⋊D17—82no—
174C2×Dic17—22no—
175C2×Dic17—22no—
176C2×Dic17—41no—
177C2×Dic17—41no—
178C2×Dic17—41no—
179C2×Dic17—41no—
180C2×Dic17—44no—
181C2×Dic17—41no—
182C2×Dic17—41no—
183C2×Dic17—41no—
184C2×Dic17—88no—
185C2×Dic17—82no—
186C2×Dic17—82no—
187D68—82no—
188C8×C17—82no—
189#2539—171no—
190C2×#342—171no—
191#1462D1711yescharacteristic, complemented
192#1352—172no—
193#1343—172no—
194C22×C17—21no—
195C22×C17—21no—
196C22×C17—21no—
197C22×C17—21no—
198C22×C17—21no—
199C22×C17—21no—
200C22×C17—21no—
201C22×C17—21no—
202C22×C17—22no—
203C22×C17—21no—
204C22×C17—42no—
205C22×C17—42no—
206C22×C17—42no—
207C22×C17—41no—
208C22×C17—41no—
209C22×C17—44no—
210C22×C17—44no—
211C22×C17—41no—
212C22×C17—41no—
213C22×C17—41no—
214C22×C17—41no—
215C22×C17—81no—
216C22×C17—81no—
217C22×C17—82no—
218C22×C17—82no—
219C22×C17#35312yes—
220C22×C17C2×#9911yescharacteristic
221C22×C17#41711yescharacteristic
222C22×C17C2×#10411yescharacteristic
223C2×D17—81no—
224C2×D17—81no—
225C2×D17—81no—
226C2×D17—81no—
227C2×D17—81no—
228C2×D17—81no—
229C2×D17—81no—
230C4×C17—41no—
231C4×C17—41no—
232C4×C17—41no—
233C4×C17—41no—
234Dic17—42no—
235Dic17—42no—
236Dic17—84no—
237Dic17—81no—
238C2×#123—341no—
239C2×#121—171no—
240C2×#120—341no—
241C22×C22⋊C4—341no—
242C22×C22⋊C4C2×D1711yescharacteristic
243#407—21no—
244#399—171no—
245#399—171no—
246#392—171no—
247#392—171no—
248#390—341no—
249#390—341no—
250C4×C22⋊C4—171no—
251#342—172no—
252#342—341no—
253#323—21no—
254#323C2×D1712yes—
255C2×C17—21no—
256C2×C17—21no—
257C2×C17—22no—
258C2×C17—41no—
259C2×C17—41no—
260C2×C17—42no—
261C2×C17—41no—
262C2×C17#150411yescharacteristic
263C2×C17#212111yescharacteristic
264C2×C17C2×#35311yescharacteristic
265D17—161no—
266C25D6811yescharacteristic
267C22×D4—171no—
268C22×D4—341no—
269C22×D4—341no—
270C22×D4—341no—
271C23×C4—681no—
272C23×C4C4×D1711yescharacteristic
273C23×C4C22⋊D1711yescharacteristic
274C2×M16—41no—
275#123—684no—
276#121—681no—
277#121—681no—
278#120—684no—
279C2×C4⋊C4—171no—
280C2×C4⋊C4—341no—
281C2×C4⋊C4—341no—
282C2×C22⋊C4—41no—
283C2×C22⋊C4—41no—
284C2×C22⋊C4—341no—
285C2×C22⋊C4—344no—
286C2×C22⋊C4—342no—
287C2×C22⋊C4—341no—
288C2×C22⋊C4—341no—
289C2×C22⋊C4—341no—
290C2×C22⋊C4—341no—
291C2×C22⋊C4—341no—
292C2×C22⋊C4—681no—
293C2×C22⋊C4—682no—
294C2×C22⋊C4C4×D1711yescharacteristic
295C2×C22⋊C4D6811yescharacteristic
296C2×C22⋊C4C22⋊D1711yescharacteristic
297C2×C22⋊C4C22×D1711yescharacteristic
298C2×C42—341no—
299C22⋊C8—22no—
300C22⋊C8—41no—
301#95—171no—
302#95—171no—
303C17#1175711yescharacteristic, complemented, Sylow
304C24—21no—
305C24—21no—
306C24—22no—
307C24—21no—
308C24—21no—
309C24—42no—
310C24—81no—
311C24—341no—
312C24#6322711yescharacteristic
313C24#6322711yescharacteristic
314C24C2×D6811yescharacteristic
315C2×D4—681no—
316C2×D4—682no—
317C2×D4—682no—
318C2×D4—682no—
319C2×D4—682no—
320C2×D4—681no—
321C2×D4—681no—
322C2×D4—682no—
323C2×D4—681no—
324C2×D4—681no—
325C2×D4—1361no—
326C2×D4—1361no—
327C2×D4—1361no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—42no—
333C22×C4—81no—
334C22×C4—341no—
335C22×C4—341no—
336C22×C4—341no—
337C22×C4—684no—
338C22×C4—682no—
339C22×C4—1362no—
340C22×C4—1362no—
341C22×C4#6322711yescharacteristic
342C22×C4#6322711yescharacteristic
343C22×C4C2×C4×D1711yescharacteristic
344C22×C4C2×C22⋊D1711yescharacteristic
345M16—82no—
346C2×C8—42no—
347C4⋊C4—681no—
348C4⋊C4—682no—
349C4⋊C4—682no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C22⋊C4—41no—
353C22⋊C4—41no—
354C22⋊C4—344no—
355C22⋊C4—344no—
356C22⋊C4—682no—
357C22⋊C4—682no—
358C22⋊C4—682no—
359C22⋊C4—682no—
360C22⋊C4—682no—
361C22⋊C4—684no—
362C22⋊C4—682no—
363C42—1361no—
364C23—22no—
365C23—22no—
366C23—22no—
367C23—22no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—22no—
373C23—21no—
374C23—21no—
375C23—41no—
376C23—42no—
377C23—41no—
378C23—41no—
379C23—41no—
380C23—41no—
381C23—42no—
382C23—81no—
383C23—81no—
384C23—84no—
385C23—82no—
386C23—82no—
387C23—681no—
388C23—681no—
389C23—681no—
390C23—681no—
391C23—681no—
392C23—681no—
393C23—681no—
394C23#1058747711yescharacteristic
395C23#1058747711yescharacteristic
396C23#1058749612yes—
397C23#1058759411yescharacteristic
398C23#1058759511yescharacteristic
399C23C2×#6322711yescharacteristic
400D4—1362no—
401D4—1364no—
402D4—1362no—
403D4—1362no—
404D4—1362no—
405D4—1362no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—42no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—81no—
416C2×C4—81no—
417C2×C4—81no—
418C2×C4—342no—
419C2×C4—342no—
420C2×C4—681no—
421C2×C4—681no—
422C2×C4—681no—
423C2×C4—681no—
424C2×C4—684no—
425C2×C4—681no—
426C2×C4—681no—
427C2×C4—681no—
428C2×C4—1368no—
429C2×C4—1362no—
430C2×C4—1362no—
431C8—82no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—22no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—42no—
443C22—42no—
444C22—42no—
445C22—41no—
446C22—41no—
447C22—44no—
448C22—44no—
449C22—41no—
450C22—41no—
451C22—41no—
452C22—41no—
453C22—81no—
454C22—81no—
455C22—82no—
456C22—82no—
457C22—1361no—
458C22—1361no—
459C22—1361no—
460C22—1361no—
461C22—1361no—
462C22—1361no—
463C22—1361no—
464C22#1176260112yes—
465C22C2×#1058747711yescharacteristic
466C22#1176281111yescharacteristic
467C22C2×#1058749611yescharacteristic
468C4—41no—
469C4—41no—
470C4—41no—
471C4—41no—
472C4—682no—
473C4—682no—
474C4—1364no—
475C4—1361no—
476C2—21no—
477C2—21no—
478C2—22no—
479C2—41no—
480C2—41no—
481C2—42no—
482C2—41no—
483C2—2721no—
484C2#1452728911yescharacteristic
485C2#1453043111yescharacteristic
486C2C2×#1176260111yescharacteristic
subgroupG/H
centerC22C2×#10587477
commutatorC22×C4×C17C22×C4
FrattiniC2×C22⋊C4C22×D17
FittingC17×#1462C2
socleC22×C17C2×#99
prime radical#14533715C2
cosocleC2×C22⋊C4×C17C23
hypercenter#1462D17
hypocenterC17#11757
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4 ◁ #1462

Complements

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

NH ≅ G/Ntype
2. C2×#11762576C2semidirect
3. #14526809C2semidirect
4. #14526782C2semidirect
5. C17×#1462C2semidirect
7. C2×#10587616C4semidirect
10. #11762745C4semidirect
12. #11762718C4semidirect
16. C4×C22⋊Dic17C4semidirect
30. C22×D68C2×C4semidirect
52. C2×C4⋊Dic17C2×C4semidirect
58. #10587502C2×C4semidirect
59. #10587502C2×C4semidirect
191. #1462D17semidirect
303. C17#11757semidirect

Maximal subgroups

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

subgroupindex
#145337152
C2×#117625762
#145268092
#145267822
C17×#14622
#1175717