Finite Group Databasebeta

← #17953558

Subgroups — #17953558

Order 4352.

940 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 940 conjugacy classes of subgroups — too many to draw. Only its 126 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#14544607C211yesmaximal, characteristic
2#14543958C211yesmaximal, characteristic
3#14543657C214yesmaximal, complemented
4C2×#11762666C211yesmaximal, characteristic
5C22×C22⋊#595—21no—
6C2×#10587543—21no—
7C2×#10587543C2212yes—
8C2×C22⋊#3624—21no—
9C2×(C2×#595)⋊C4—21no—
10C2×(C2×#595)⋊C4C2212yes—
11C23×C4×D17C2211yescharacteristic
12C22×C4⋊Dic17C411yescharacteristic, complemented
13C22×#63227—21no—
14#11762666—21no—
15#11762666—21no—
16#11762666C412yescomplemented
17#11762666C2212yes—
18C2×#10587502—21no—
19C22×C4⋊C4×C17C411yescharacteristic, complemented
20C24×D17D411yescharacteristic
21C23×#595—22no—
22C23×C4×C17—21no—
23C23×C4×C17C2×C411yescharacteristic
24C23×Dic17—21no—
25C23×Dic17D411yescharacteristic
26C22×C4×D17—24no—
27C22×C4×D17—42no—
28C22×C4×D17—42no—
29C22×C4×D17C2×C411yescharacteristic
30C22×C4×D17D411yescharacteristic
31C22×C4×D17D411yescharacteristic
32C22×C4×D17C2311yescharacteristic
33C2×C22⋊#595—24no—
34C2×C22⋊#595—42no—
35C2×C22⋊#595—42no—
36C22×#3624—22no—
37C2×C4⋊C4×C17—21no—
38C2×C4⋊C4×C17—42no—
39C2×C4⋊C4×C17C2×C412yes—
40C2×#63227—22no—
41C2×#63227—22no—
42C2×#63227—42no—
43C2×#63227—42no—
44C2×C4⋊Dic17—21no—
45C2×C4⋊Dic17—42no—
46C2×C4⋊Dic17C2×C412yes—
47C22⋊#3624—42no—
48(C2×#595)⋊C4—24no—
49(C2×#595)⋊C4—42no—
50#10587543—24no—
51#10587543—42no—
52#10587502—22no—
53#10587502—22no—
54C24×C17C22⋊C411yescharacteristic
55C23×D17—22no—
56C23×D17—22no—
57C23×D17—22no—
58C23×D17—22no—
59C23×D17—41no—
60C23×D17—41no—
61C23×D17C22⋊C411yescharacteristic
62C23×D17D812yes—
63C23×D17SD1612yes—
64C23×D17C2×D411yescharacteristic
65C22×#595—24no—
66C22×#595—42no—
67C22×#595—42no—
68C22×#595—42no—
69C22×#595—42no—
70C22×#595—42no—
71C22×#595—42no—
72C22×C4×C17—22no—
73C22×C4×C17—22no—
74C22×C4×C17—22no—
75C22×C4×C17—22no—
76C22×C4×C17—42no—
77C22×C4×C17—42no—
78C22×C4×C17—42no—
79C22×C4×C17C22⋊C411yescharacteristic
80C22×C4×C17C22×C411yescharacteristic
81C22×Dic17—22no—
82C22×Dic17—22no—
83C22×Dic17—22no—
84C22×Dic17—41no—
85C22×Dic17—42no—
86C22×Dic17—42no—
87C22×Dic17—42no—
88C22×Dic17C22⋊C411yescharacteristic
89C22×Dic17C2×D411yescharacteristic
90C2×C4×D17—22no—
91C2×C4×D17—22no—
92C2×C4×D17—22no—
93C2×C4×D17—22no—
94C2×C4×D17—22no—
95C2×C4×D17—41no—
96C2×C4×D17—41no—
97C2×C4×D17—41no—
98C2×C4×D17—41no—
99C2×C4×D17—41no—
100C2×C4×D17—41no—
101C2×C4×D17—416no—
102C2×C4×D17#4114yes—
103C22⋊#595—48no—
104C2×#3624—42no—
105C2×#3624—42no—
106C2×#3624—42no—
107C4⋊C4×C17—42no—
108C4⋊C4×C17—42no—
109#63227—44no—
110#63227—42no—
111#63227—42no—
112C4⋊Dic17—42no—
113C4⋊Dic17—42no—
114#8712—171nomaximal, Sylow
115C23×C17—21no—
116C23×C17—21no—
117C23×C17—21no—
118C23×C17—21no—
119C23×C17#9912yes—
120C23×C17#10212yes—
121C23×C17#10412yes—
122C23×C17C2×C22⋊C411yescharacteristic
123C22×D17—21no—
124C22×D17—21no—
125C22×D17—21no—
126C22×D17—21no—
127C22×D17—24no—
128C22×D17—24no—
129C22×D17—21no—
130C22×D17—21no—
131C22×D17—21no—
132C22×D17—21no—
133C22×D17—21no—
134C22×D17—21no—
135C22×D17—24no—
136C22×D17—24no—
137C22×D17—42no—
138C22×D17—42no—
139C22×D17—44no—
140C22×D17—44no—
141C22×D17—44no—
142C22×D17—44no—
143C22×D17#10212yes—
144C22×D17#12312yes—
145C22×D17C2×D811yescharacteristic
146C22×D17C2×SD1611yescharacteristic
147C22×D17#13712yes—
148C2×#595—44no—
149C2×#595—44no—
150C2×#595—44no—
151C2×#595—82no—
152C2×#595—82no—
153C2×#595—82no—
154C2×#595—82no—
155C2×C4×C17—28no—
156C2×C4×C17—21no—
157C2×C4×C17—21no—
158C2×C4×C17—21no—
159C2×C4×C17—21no—
160C2×C4×C17—42no—
161C2×C4×C17—42no—
162C2×C4×C17—42no—
163C2×C4×C17—84no—
164C2×C4×C17#9912yes—
165C2×C4×C17#11712yes—
166C2×Dic17—21no—
167C2×Dic17—21no—
168C2×Dic17—21no—
169C2×Dic17—21no—
170C2×Dic17—21no—
171C2×Dic17—44no—
172C2×Dic17—42no—
173C2×Dic17—42no—
174C2×Dic17—42no—
175C2×Dic17—84no—
176C2×Dic17#12312yes—
177C4×D17—44no—
178C4×D17—44no—
179C4×D17—44no—
180C4×D17—44no—
181#3624—82no—
182C2×#380—171no—
183#1779—171no—
184C22⋊#95—171no—
185#1294—174no—
186C22×C17—22no—
187C22×C17—22no—
188C22×C17—22no—
189C22×C17—22no—
190C22×C17—22no—
191C22×C17—22no—
192C22×C17#32714yes—
193C22×C17#38111yescharacteristic
194C22×C17C2×#9911yescharacteristic
195C22×C17C2×#9911yescharacteristic
196C22×C17C2×#10211yescharacteristic
197C22×C17#41911yescharacteristic
198C22×C17C2×#10411yescharacteristic
199C22×C17#42111yescharacteristic
200C2×D17—22no—
201C2×D17—22no—
202C2×D17—21no—
203C2×D17—21no—
204C2×D17—22no—
205C2×D17—22no—
206C2×D17—21no—
207C2×D17—21no—
208C2×D17—22no—
209C2×D17—22no—
210C2×D17—22no—
211C2×D17—48no—
212C2×D17—48no—
213C2×D17—41no—
214C2×D17—41no—
215C2×D17—41no—
216C2×D17—41no—
217C2×D17#48012yes—
218C2×D17#48312yes—
219#595—84no—
220C4×C17—22no—
221C4×C17—22no—
222C4×C17—82no—
223Dic17—22no—
224Dic17—41no—
225Dic17—82no—
226C24×C4—171no—
227C22×C4⋊C4—171no—
228C22×C4⋊C4#59511yescharacteristic, complemented
229C22×C22⋊C4—341no—
230C22×C22⋊C4—341no—
231C2×C22⋊C8—172no—
232C2×C22⋊C8—341no—
233C2×C22⋊C8—341no—
234#380—172no—
235#380—172no—
236#380—341no—
237#380—341no—
238C2×#95—172no—
239C2×#95—341no—
240C2×#95—341no—
241C2×C17—24no—
242C2×C17C2×#32711yescharacteristic
243C2×C17#150811yescharacteristic
244C2×C17#151111yescharacteristic
245C2×C17#151911yescharacteristic
246C2×C17#181911yescharacteristic
247C2×C17#182311yescharacteristic
248C2×C17#182611yescharacteristic
249D17—22no—
250D17—22no—
251D17—42no—
252C25—171no—
253C23×C4—21no—
254C23×C4—171no—
255C23×C4—171no—
256C23×C4—171no—
257C23×C4—171no—
258C23×C4—171no—
259C23×C4—344no—
260C23×C4—342no—
261C23×C4—341no—
262C23×C4—682no—
263C23×C4—682no—
264C23×C4C2×#59511yescharacteristic
265C22×C8—342no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—42no—
268C2×C4⋊C4—172no—
269C2×C4⋊C4—341no—
270C2×C4⋊C4—682no—
271C2×C4⋊C4C2×#59512yes—
272C2×C22⋊C4—342no—
273C2×C22⋊C4—342no—
274C2×C22⋊C4—344no—
275C2×C22⋊C4—682no—
276C2×C22⋊C4—682no—
277C2×C22⋊C4—682no—
278C2×C22⋊C4—682no—
279C22⋊C8—344no—
280C22⋊C8—682no—
281C22⋊C8—682no—
282#95—342no—
283#95—342no—
284#95—344no—
285#95—682no—
286C17#871211yescharacteristic, complemented, Sylow
287C24—171no—
288C24—171no—
289C24—172no—
290C24—172no—
291C24—342no—
292C24—342no—
293C24—342no—
294C24—342no—
295C24—681no—
296C24—681no—
297C24C22⋊#59511yescharacteristic
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—42no—
303C22×C4—42no—
304C22×C4—42no—
305C22×C4—171no—
306C22×C4—174no—
307C22×C4—171no—
308C22×C4—342no—
309C22×C4—342no—
310C22×C4—342no—
311C22×C4—342no—
312C22×C4—342no—
313C22×C4—342no—
314C22×C4—342no—
315C22×C4—344no—
316C22×C4—342no—
317C22×C4—681no—
318C22×C4—681no—
319C22×C4—681no—
320C22×C4—681no—
321C22×C4—681no—
322C22×C4—681no—
323C22×C4—6816no—
324C22×C4—681no—
325C22×C4—682no—
326C22×C4—682no—
327C22×C4—682no—
328C22×C4—682no—
329C22×C4—682no—
330C22×C4—682no—
331C22×C4—682no—
332C22×C4—682no—
333C22×C4—682no—
334C22×C4C22⋊#59511yescharacteristic
335C22×C4C22×#59511yescharacteristic
336C2×C8—682no—
337C2×C8—682no—
338C2×C8—682no—
339C4⋊C4—42no—
340C4⋊C4—42no—
341C4⋊C4—682no—
342C4⋊C4—682no—
343C22⋊C4—682no—
344C22⋊C4—682no—
345C22⋊C4—684no—
346C22⋊C4—688no—
347C23—21no—
348C23—21no—
349C23—21no—
350C23—21no—
351C23—172no—
352C23—171no—
353C23—171no—
354C23—172no—
355C23—172no—
356C23—344no—
357C23—344no—
358C23—341no—
359C23—341no—
360C23—341no—
361C23—341no—
362C23—341no—
363C23—341no—
364C23—341no—
365C23—341no—
366C23—341no—
367C23—341no—
368C23—344no—
369C23—344no—
370C23—682no—
371C23—682no—
372C23—684no—
373C23—684no—
374C23—684no—
375C23—684no—
376C23#1058754712yes—
377C23#1058754812yes—
378C23#1058755112yes—
379C23C2×C22⋊#59511yescharacteristic
380C2×C4—28no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—84no—
389C2×C4—172no—
390C2×C4—341no—
391C2×C4—341no—
392C2×C4—341no—
393C2×C4—341no—
394C2×C4—341no—
395C2×C4—684no—
396C2×C4—684no—
397C2×C4—684no—
398C2×C4—684no—
399C2×C4—684no—
400C2×C4—684no—
401C2×C4—684no—
402C2×C4—684no—
403C2×C4—682no—
404C2×C4—682no—
405C2×C4—682no—
406C2×C4—1364no—
407C2×C4—1362no—
408C2×C4—1362no—
409C2×C4—1362no—
410C2×C4—1362no—
411C2×C4#1058753912yes—
412C2×C4#1058767712yes—
413C8—1362no—
414C22—22no—
415C22—22no—
416C22—22no—
417C22—22no—
418C22—22no—
419C22—22no—
420C22—172no—
421C22—172no—
422C22—341no—
423C22—341no—
424C22—342no—
425C22—342no—
426C22—342no—
427C22—342no—
428C22—341no—
429C22—341no—
430C22—342no—
431C22—342no—
432C22—342no—
433C22—688no—
434C22—688no—
435C22—681no—
436C22—681no—
437C22—681no—
438C22—681no—
439C22#1176366014yes—
440C22#1176375211yescharacteristic
441C22C2×#1058755111yescharacteristic
442C22C2×#1058753911yescharacteristic
443C22C2×#1058754711yescharacteristic
444C22#1176380211yescharacteristic
445C22C2×#1058754811yescharacteristic
446C22#1176380811yescharacteristic
447C4—22no—
448C4—22no—
449C4—82no—
450C4—342no—
451C4—681no—
452C4—1364no—
453C4—1362no—
454C2—24no—
455C2—342no—
456C2—342no—
457C2—682no—
458C2C2×#1176366011yescharacteristic
459C2#1454418311yescharacteristic
460C2#1454419411yescharacteristic
461C2#1454422111yescharacteristic
462C2#1454467911yescharacteristic
463C2#1454468711yescharacteristic
464C2#1454469011yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC22×C4⋊C4×C17C4
socleC23×C17C2×C22⋊C4
prime radicalC24×D17D4
cosocleC22×C4×D17C23
hypercenterC22×C4⋊C4#595
hypocenterC17#8712
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #14543657C2semidirect
12. C22×C4⋊Dic17C4semidirect
16. #11762666C4semidirect
19. C22×C4⋊C4×C17C4semidirect
228. C22×C4⋊C4#595semidirect
286. C17#8712semidirect

Maximal subgroups

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

subgroupindex
#145446072
#145439582
#145436572
C2×#117626662
#871217