Finite Group Databasebeta

← #595⋊#324 #17981603

Subgroups — #595⋊#324 #17981603

Order 4352.

730 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C22⋊#3633C212yesmaximal
2C2×#11763895C212yesmaximal
3#14545793C212yesmaximal
4C2×C4⋊C4×#595C211yesmaximal, characteristic
5C2×C22⋊#3633C2214yes—
6C2×C4×#3633—22no—
7(C2×#3633)⋊C4—22no—
8#11763895C418yescomplemented
9C22×C4⋊#595C2211yescharacteristic
10C22×C4×#595C411yescharacteristic
11C22×C4×#595C411yescharacteristic
12C22×C4×#595C2211yescharacteristic
13C4⋊C4×#595—22no—
14C4⋊C4×#595—22no—
15C2×(C2×#595)⋊C4C411yescharacteristic
16C2×(C2×#595)⋊C4C2211yescharacteristic
17C2×C4⋊C4×D17C411yescharacteristic
18C23×#595C2×C411yescharacteristic
19C23×#595C2×C411yescharacteristic
20C23×#595C2×C411yescharacteristic
21C23×#595C2311yescharacteristic
22C22×#3633—24no—
23C22×C4×D17C2×C411yescharacteristic
24C22×C4×D17C2×C411yescharacteristic
25C22×C4×D17C2×C411yescharacteristic
26C2×C4⋊#595—22no—
27C2×C4⋊#595—22no—
28C2×C4⋊#595C2×C414yes—
29C2×C4×#595—21no—
30C2×C4×#595—21no—
31C2×C4×#595—22no—
32C2×C4×#595—21no—
33C2×C4×#595—21no—
34C2×C4×#595—42no—
35C2×C4×#595—42no—
36C2×C4×#595C814yescomplemented
37C2×C4×#595D412yes—
38C2×C4×#595D412yes—
39C22⋊#3633—24no—
40C22⋊#3633C2×C418yes—
41C4×#3633—44no—
42C2×C4⋊C4×C17C811yescharacteristic, complemented
43C2×C4⋊Dic17C811yescharacteristic, complemented
44C2×#63225C811yescharacteristic, complemented
45C2×#63225C811yescharacteristic, complemented
46C4⋊C4×D17—22no—
47C4⋊C4×D17—22no—
48(C2×#595)⋊C4—22no—
49(C2×#595)⋊C4—22no—
50C23×D17C22×C411yescharacteristic
51C22×#595—22no—
52C22×#595—22no—
53C22×#595—21no—
54C22×#595—21no—
55C22×#595—21no—
56C22×#595—21no—
57C22×#595—41no—
58C22×#595—41no—
59C22×#595—41no—
60C22×#595—41no—
61C22×#595—41no—
62C22×#595—41no—
63C22×#595C4212yes—
64C22×#595C22⋊C411yescharacteristic
65C22×#595C22⋊C411yescharacteristic
66C22×#595C2×C812yes—
67C22×#595C2×C812yes—
68C22×#595M1612yes—
69C22×#595C22×C412yes—
70C22×#595C2×D412yes—
71C22×#595#4112yes—
72C2×#3633—28no—
73C2×#3633—44no—
74C2×#3633—44no—
75C22×C4×C17C2×C811yescharacteristic
76C22×C4×C17C2×C811yescharacteristic
77C22×C4×C17C2×C811yescharacteristic
78C22×Dic17C2×C811yescharacteristic
79C22×Dic17C2×C811yescharacteristic
80C22×Dic17C2×C811yescharacteristic
81C2×C4×D17—21no—
82C2×C4×D17—21no—
83C2×C4×D17—21no—
84C2×C4×D17—21no—
85C2×C4×D17—21no—
86C2×C4×D17—21no—
87C2×C4×D17—41no—
88C2×C4×D17—41no—
89C2×C4×D17—41no—
90C2×C4×D17—41no—
91C2×C4×D17C4212yes—
92C2×C4×D17C22⋊C412yes—
93C2×C4×D17C2×C812yes—
94C2×C4×D17M1612yes—
95C4⋊#595—28no—
96C4×#595—24no—
97C4×#595—24no—
98C4×#595—24no—
99C4×#595—42no—
100C4×#595—42no—
101C4×#595—42no—
102C4⋊C4×C17—22no—
103C4⋊Dic17—22no—
104#63225—22no—
105#63225—22no—
106C4×#324—171nomaximal, Sylow
107C23×C17C22×C811yescharacteristic
108C22×D17—21no—
109C22×D17—21no—
110C22×D17—21no—
111C22×D17—21no—
112C22×D17C2×C4211yescharacteristic
113C22×D17C2×C22⋊C411yescharacteristic
114C22×D17#11711yescharacteristic
115C22×D17C22×C811yescharacteristic
116C22×D17C2×M1611yescharacteristic
117C22×D17C2×M1611yescharacteristic
118C2×#595—22no—
119C2×#595—21no—
120C2×#595—22no—
121C2×#595—21no—
122C2×#595—24no—
123C2×#595—24no—
124C2×#595—22no—
125C2×#595—22no—
126C2×#595—42no—
127C2×#595—42no—
128C2×#595—42no—
129C2×#595—42no—
130C2×#595—41no—
131C2×#595—41no—
132C2×#595—41no—
133C2×#595—41no—
134C2×#595—42no—
135C2×#595—42no—
136C2×#595C22⋊C812yes—
137C2×#595C22⋊C812yes—
138C2×#595#9912yes—
139C2×#595#10112yes—
140C2×#595C4×D414yes—
141#3633—48no—
142C2×C4×C17—21no—
143C2×C4×C17—21no—
144C2×C4×C17—21no—
145C2×C4×C17—41no—
146C2×C4×C17—41no—
147C2×C4×C17C4×C812yescomplemented
148C2×C4×C17C22⋊C812yes—
149C2×Dic17—21no—
150C2×Dic17—21no—
151C2×Dic17—21no—
152C2×Dic17—41no—
153C2×Dic17—41no—
154C2×Dic17C4×C812yescomplemented
155C2×Dic17C22⋊C812yes—
156C4×D17—22no—
157C4×D17—22no—
158C4×D17—22no—
159C4×D17—22no—
160C4×D17—22no—
161C4×D17—22no—
162C4×D17—42no—
163C4×D17—42no—
164C4×D17—41no—
165C4×D17—41no—
166C2×C4×C4⋊C4—171no—
167C4×C22⋊C8—172no—
168C2×#324—172no—
169#1280—172no—
170C22×C17—21no—
171C22×C17—21no—
172C22×C17C2×C4×C811yescharacteristic
173C22×C17C2×C22⋊C811yescharacteristic
174C22×C17#43111yescharacteristic
175C2×D17—21no—
176C2×D17—21no—
177C2×D17—21no—
178C2×D17—21no—
179C2×D17—21no—
180C2×D17—21no—
181C2×D17—21no—
182C2×D17—21no—
183C2×D17—21no—
184C2×D17—21no—
185C2×D17C4×C22⋊C411yescharacteristic
186C2×D17C4×M1611yescharacteristic
187C2×D17C2×C22⋊C811yescharacteristic
188C2×D17C2×#9911yescharacteristic
189C2×D17#41011yescharacteristic
190C2×D17C2×#10111yescharacteristic
191C2×D17#41311yescharacteristic
192C2×D17#43111yescharacteristic
193#595—22no—
194#595—24no—
195#595—42no—
196#595—42no—
197#595#32414yescomplemented
198C4×C17—22no—
199C4×C17—22no—
200C4×C17—41no—
201Dic17—22no—
202Dic17—22no—
203Dic17—41no—
204C22×C4⋊C4—171no—
205C22×C4⋊C4—171no—
206C22×C42—171no—
207C22×C42—171no—
208C22×C42—171no—
209C2×C22⋊C8—174no—
210C2×C4×C8—342no—
211C4×C4⋊C4—342no—
212C4×C4⋊C4—342no—
213C2×#95—171no—
214C2×#95—171no—
215#336—342no—
216#324—178no—
217C2×C17—21no—
218C2×C17—21no—
219C2×C17#145911yescharacteristic
220C2×C17#146111yescharacteristic
221C2×C17C4×C22⋊C811yescharacteristic
222D17—21no—
223D17—21no—
224D17C2×#32411yescharacteristic
225D17#145811yescharacteristic
226D17C4×#9911yescharacteristic
227D17C4×#10111yescharacteristic
228C23×C4—171no—
229C23×C4—171no—
230C23×C4—171no—
231C23×C4—171no—
232C23×C4—171no—
233C23×C4—171no—
234C23×C4—171no—
235C22×C8—344no—
236C2×C4⋊C4—174no—
237C2×C4⋊C4—171no—
238C2×C4⋊C4—171no—
239C2×C4⋊C4—171no—
240C2×C4⋊C4—342no—
241C2×C4⋊C4—342no—
242C2×C4⋊C4—342no—
243C2×C4⋊C4—342no—
244C2×C4⋊C4#363311yescharacteristic, complemented
245C2×C42—174no—
246C2×C42—172no—
247C2×C42—172no—
248C2×C42—341no—
249C2×C42—341no—
250C2×C42—342no—
251C2×C42—341no—
252C2×C42—341no—
253C2×C42—682no—
254C2×C42—682no—
255C22⋊C8—178no—
256C22⋊C8—344no—
257C4×C8—684no—
258#95—342no—
259#95—342no—
260C17C4×#32411yescharacteristic, complemented, Sylow
261C24—171no—
262C22×C4—171no—
263C22×C4—171no—
264C22×C4—172no—
265C22×C4—172no—
266C22×C4—172no—
267C22×C4—171no—
268C22×C4—172no—
269C22×C4—172no—
270C22×C4—171no—
271C22×C4—172no—
272C22×C4—172no—
273C22×C4—172no—
274C22×C4—172no—
275C22×C4—172no—
276C22×C4—172no—
277C22×C4—171no—
278C22×C4—341no—
279C22×C4—341no—
280C22×C4—341no—
281C22×C4—341no—
282C22×C4—341no—
283C22×C4—341no—
284C22×C4—342no—
285C22×C4—342no—
286C22×C4—341no—
287C22×C4—341no—
288C22×C4—341no—
289C22×C4—341no—
290C22×C4—681no—
291C22×C4—681no—
292C22×C4—681no—
293C22×C4—681no—
294C22×C4—681no—
295C22×C4—681no—
296C22×C4—681no—
297C22×C4—681no—
298C22×C4—681no—
299C22×C4—681no—
300C22×C4C2×#363311yescharacteristic
301C22×C4C2×#363311yescharacteristic
302C22×C4C2×#363311yescharacteristic
303C2×C8—348no—
304C2×C8—684no—
305C2×C8—684no—
306C4⋊C4—22no—
307C4⋊C4—342no—
308C4⋊C4—342no—
309C4⋊C4—348no—
310C4⋊C4—342no—
311C42—344no—
312C42—344no—
313C42—344no—
314C42—682no—
315C42—682no—
316C42—682no—
317C23—171no—
318C23—171no—
319C23—171no—
320C23—171no—
321C23—171no—
322C23—171no—
323C23—341no—
324C23—341no—
325C23—341no—
326C23—341no—
327C23C22×#363311yescharacteristic
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—172no—
334C2×C4—172no—
335C2×C4—172no—
336C2×C4—172no—
337C2×C4—174no—
338C2×C4—172no—
339C2×C4—172no—
340C2×C4—342no—
341C2×C4—342no—
342C2×C4—342no—
343C2×C4—342no—
344C2×C4—342no—
345C2×C4—342no—
346C2×C4—344no—
347C2×C4—344no—
348C2×C4—342no—
349C2×C4—341no—
350C2×C4—342no—
351C2×C4—341no—
352C2×C4—341no—
353C2×C4—341no—
354C2×C4—342no—
355C2×C4—342no—
356C2×C4—341no—
357C2×C4—682no—
358C2×C4—681no—
359C2×C4—681no—
360C2×C4—682no—
361C2×C4—681no—
362C2×C4—682no—
363C2×C4—682no—
364C2×C4—681no—
365C2×C4—681no—
366C2×C4—681no—
367C2×C4—681no—
368C2×C4—682no—
369C2×C4—682no—
370C2×C4—681no—
371C2×C4—682no—
372C2×C4—682no—
373C2×C4C4×#363312yescomplemented
374C2×C4C22⋊#363312yes—
375C8—688no—
376C22—21no—
377C22—21no—
378C22—171no—
379C22—171no—
380C22—171no—
381C22—171no—
382C22—171no—
383C22—171no—
384C22—171no—
385C22—171no—
386C22—341no—
387C22—341no—
388C22—341no—
389C22—341no—
390C22—341no—
391C22—341no—
392C22—341no—
393C22—341no—
394C22—341no—
395C22—341no—
396C22C2×C4×#363311yescharacteristic
397C22C2×C22⋊#363311yescharacteristic
398C22#1176392211yescharacteristic
399C4—22no—
400C4—22no—
401C4—41no—
402C4—174no—
403C4—344no—
404C4—342no—
405C4—342no—
406C4—342no—
407C4—682no—
408C4—682no—
409C4—681no—
410C2—21no—
411C2—21no—
412C2—171no—
413C2—171no—
414C2—171no—
415C2—171no—
416C2—341no—
417C2—341no—
418C2#1454589711yescharacteristic
419C2#1454589911yescharacteristic
420C2C4×C22⋊#363311yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3633
commutatorC22×C17C2×C4×C8
FrattiniC23C22×#3633
FittingC2×C4⋊C4×C17C8
socleC22×C17C2×C22⋊C8
prime radicalC23×D17C22×C4
cosocleC23×#595C23
hypercenterC2×C4⋊C4#3633
hypocenterC17C4×#324
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
8. #11763895C4semidirect
36. C2×C4×#595C8semidirect
42. C2×C4⋊C4×C17C8semidirect
43. C2×C4⋊Dic17C8semidirect
44. C2×#63225C8semidirect
45. C2×#63225C8semidirect
147. C2×C4×C17C4×C8semidirect
154. C2×Dic17C4×C8semidirect
197. #595#324semidirect
244. C2×C4⋊C4#3633semidirect
260. C17C4×#324semidirect
373. C2×C4C4×#3633semidirect

Maximal subgroups

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

subgroupindex
C4×C22⋊#36332
C2×#117638952
#145457932
C2×C4⋊C4×#5952
C4×#32417