Finite Group Databasebeta

← #36452602

Subgroups — #36452602

Order 22784.

460 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26021046C211yesmaximal, characteristic
2C8×C4⋊Dic89C211yesmaximal, characteristic, complemented
3C4×#15667934C211yesmaximal, characteristic
4C2×#19151351C211yesmaximal, characteristic, complemented
5C2×#19151327C211yesmaximal, characteristic
6#26018092C211yesmaximal, characteristic, complemented
7C89×#1273C211yesmaximal, characteristic, complemented
8C2×C4×D356C2211yescharacteristic
9C2×C4⋊#10623494C2211yescharacteristic
10C2×C4⋊#10623494C2211yescharacteristic
11C2×#15667934C411yescharacteristic
12C2×#15667934C411yescharacteristic
13C2×#15667924—21no—
14C2×#15667924—21no—
15C2×C8×Dic89—21no—
16C4×C4⋊Dic89C2211yescharacteristic
17#19151361C411yescharacteristic
18#19151361C411yescharacteristic
19#19151352—21no—
20#19151351—22no—
21#19151327—22no—
22C2×C4×C8×C89C2211yescharacteristic
23C2×C4×C8×C89C2211yescharacteristic
24C2×C4×C8×C89C2211yescharacteristic
25C22×D356C2×C411yescharacteristic
26C22×C4×D89—21no—
27C22×#10623494—21no—
28C22×#10623494—21no—
29C4×D356—21no—
30C4×D356—21no—
31C4×D356—21no—
32C4×D356—21no—
33C2×C4⋊Dic89C2×C411yescharacteristic
34C2×C4⋊Dic89C2×C411yescharacteristic
35C2×C4⋊Dic89C2×C411yescharacteristic
36C2×#13083551—21no—
37C2×C4×Dic89—21no—
38C4⋊#10623494—21no—
39C4⋊#10623494—21no—
40C4⋊#10623494—21no—
41C4⋊#10623494D412yes—
42#15667934—22no—
43#15667934C814yescomplemented
44#15667924—42no—
45#15667924—42no—
46C8×Dic89—42no—
47#15667919—21no—
48C22×C8×C89—21no—
49C22×C8×C89C2×C411yescharacteristic
50C22×C8×C89C2×C411yescharacteristic
51C22×C8×C89D411yescharacteristic
52C22×C8×C89D411yescharacteristic
53C2×C42×C89C2311yescharacteristic
54C4×C8×C89—21no—
55C4×C8×C89—21no—
56C4×C8×C89—21no—
57C4×C8×C89—21no—
58C4×C8×C89—21no—
59C4×C8×C89—21no—
60C23×D89—21no—
61C2×D356—21no—
62C2×D356—21no—
63C2×D356—21no—
64C2×D356—21no—
65C2×D356—21no—
66C2×D356C2×C812yes—
67C22×Dic89—21no—
68C22×Dic89—21no—
69C22×Dic89—21no—
70C2×C4×D89—41no—
71C2×C4×D89—41no—
72C2×C4×D89—41no—
73C2×C4×D89—41no—
74C2×C4×D89—41no—
75C2×C4×D89—41no—
76C2×#10623494—22no—
77C2×#10623494—41no—
78C2×#10623494—41no—
79C2×#10623494—41no—
80C2×#10623494—41no—
81C2×#10623494—41no—
82C4⋊Dic89—21no—
83C4⋊Dic89—21no—
84C4⋊Dic89—21no—
85C4⋊Dic89—21no—
86C4⋊Dic89C2×C812yes—
87C4⋊Dic89M1612yes—
88#13083551—41no—
89#13083551—41no—
90C4×Dic89—41no—
91C4×Dic89—41no—
92C22×C4×C89C22×C411yescharacteristic
93C22×C4×C89C2×D411yescharacteristic
94C22×C4×C89#4111yescharacteristic
95C2×C8×C89—21no—
96C2×C8×C89—21no—
97C2×C8×C89—21no—
98C2×C8×C89—21no—
99C2×C8×C89—22no—
100C2×C8×C89—21no—
101C2×C8×C89—21no—
102C2×C8×C89—21no—
103C2×C8×C89—21no—
104C2×C8×C89—21no—
105C2×C8×C89—21no—
106C2×C8×C89—41no—
107C2×C8×C89—41no—
108C2×C8×C89C2×C812yes—
109C2×C8×C89D812yes—
110C42×C89C2×D411yescharacteristic
111C42×C89#4111yescharacteristic
112C42×C89#4111yescharacteristic
113C42×C89#4111yescharacteristic
114C23×C89C4×D411yescharacteristic
115C22×D89—22no—
116C22×D89—41no—
117C22×D89—41no—
118C22×D89—41no—
119C22×D89—41no—
120C22×D89—41no—
121C22×D89—41no—
122C2×C4×C89—21no—
123C2×C4×C89—21no—
124C2×C4×C89#11711yescharacteristic
125C2×C4×C89C4×D411yescharacteristic
126C2×C4×C89#12111yescharacteristic
127C2×C4×C89#12311yescharacteristic
128C2×C4×C89#12411yescharacteristic
129C2×C4×C89#12611yescharacteristic
130C2×C4×C89C22×C811yescharacteristic
131C2×C4×C89C2×M1611yescharacteristic
132C2×C4×C89#13111yescharacteristic
133C2×C4×C89#13111yescharacteristic
134C2×C4×C89C2×D811yescharacteristic
135C2×C4×C89#13511yescharacteristic
136C2×C4×C89AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C89#13711yescharacteristic
138C2×Dic89—22no—
139C2×Dic89—22no—
140C2×Dic89—41no—
141C2×Dic89—41no—
142C2×Dic89—41no—
143C2×Dic89—41no—
144C2×Dic89—41no—
145C2×Dic89—41no—
146C2×Dic89—41no—
147D356—22no—
148D356—22no—
149D356—41no—
150D356—41no—
151C4×D89—81no—
152C4×D89—81no—
153C4×D89—81no—
154C4×D89—81no—
155C8×C89—22no—
156C8×C89—22no—
157C8×C89—42no—
158C8×C89—41no—
159C8×C89—41no—
160#10623494—42no—
161#10623494—81no—
162C22×C89#38811yescharacteristic
163C22×C89C8×D411yescharacteristic
164C22×C89#43511yescharacteristic
165C22×C89C4×D811yescharacteristic
166C22×C89#44011yescharacteristic
167C22×C89#44311yescharacteristic
168C22×C89#44411yescharacteristic
169C2×D89—42no—
170C2×D89—42no—
171C2×D89—42no—
172C2×D89—81no—
173C2×D89—81no—
174C2×D89—81no—
175C2×D89—81no—
176C4×C89—21no—
177C4×C89—21no—
178C4×C89#43111yescharacteristic
179C4×C89#43311yescharacteristic
180C4×C89C8×D411yescharacteristic
181C4×C89#43611yescharacteristic
182C4×C89#45911yescharacteristic
183C4×C89#46411yescharacteristic
184C4×C89#48011yescharacteristic
185C4×C89#48211yescharacteristic
186Dic89—42no—
187Dic89—42no—
188Dic89—81no—
189#9541—891nomaximal, Sylow
190C2×C89C8×D811yescharacteristic
191C2×C89SD16⋊C811yescharacteristic
192C2×C89#158111yescharacteristic
193C2×C89#158811yescharacteristic
194C2×C89#192311yescharacteristic
195C2×C89#192511yescharacteristic
196C2×C89#192911yescharacteristic
197D89—82no—
198#1954—891no—
199C8×C4⋊C4—891no—
200C4×#102—891no—
201C2×#335—891no—
202C2×D4⋊C8—891no—
203#1279—891no—
204#1273D8911yescharacteristic, complemented
205C89#954111yescharacteristic, complemented, Sylow
206C2×C4×D4—891no—
207C2×C4⋊C8—891no—
208C2×C4⋊C8—891no—
209C2×#102—891no—
210C2×#102—891no—
211C2×C22⋊C8—1781no—
212C2×C22⋊C8—1781no—
213C2×C4×C8—1781no—
214C2×C4×C8C2×D8911yescharacteristic
215C2×C4×C8C2×D8911yescharacteristic
216C2×C4×C8C2×D8911yescharacteristic
217C4×C4⋊C4—891no—
218#340—891no—
219#340—891no—
220#336—1781no—
221#335—1782no—
222D4⋊C8—1782no—
223C22×D4—891no—
224C23×C4—1781no—
225C22×C8—21no—
226C22×C8—1781no—
227C22×C8—1781no—
228C22×C8C4×D8911yescharacteristic
229C22×C8C4×D8911yescharacteristic
230C22×C8D35611yescharacteristic
231C22×C8D35611yescharacteristic
232C4×D4—1781no—
233C4×D4—1781no—
234C4×D4—1781no—
235C4×D4—1781no—
236C2×C4⋊C4—891no—
237C2×C4⋊C4—891no—
238C2×C4⋊C4—891no—
239C2×C22⋊C4—1781no—
240C2×C42—1781no—
241C2×C42C22×D8911yescharacteristic
242C4⋊C8—892no—
243C4⋊C8—1781no—
244C4⋊C8—1781no—
245C4⋊C8—1781no—
246#102—894no—
247#102—1782no—
248C22⋊C8—3562no—
249C22⋊C8—3562no—
250C4×C8—21no—
251C4×C8—21no—
252C4×C8—21no—
253C4×C8—21no—
254C4×C8—21no—
255C4×C8—21no—
256C4×C8—3562no—
257#95—1781no—
258C24—1781no—
259C2×D4—892no—
260C2×D4—1781no—
261C2×D4—1781no—
262C2×D4—1781no—
263C2×D4—1781no—
264C2×D4—1781no—
265C22×C4—3561no—
266C22×C4—3561no—
267C22×C4—3561no—
268C22×C4—3561no—
269C22×C4—3561no—
270C22×C4—3561no—
271C22×C4—1781no—
272C22×C4—1781no—
273C22×C4—1781no—
274C22×C4C2×C4×D8911yescharacteristic
275C22×C4C2×D35611yescharacteristic
276C22×C4#1308357411yescharacteristic
277C2×C8—21no—
278C2×C8—21no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—22no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8—21no—
285C2×C8—21no—
286C2×C8—21no—
287C2×C8—21no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8—3561no—
291C2×C8—3561no—
292C2×C8—3561no—
293C2×C8—3561no—
294C2×C8—3561no—
295C2×C8—1782no—
296C2×C8C8×D8912yes—
297C2×C8D71212yes—
298C4⋊C4—892no—
299C4⋊C4—892no—
300C4⋊C4—1781no—
301C4⋊C4—1781no—
302C4⋊C4—1781no—
303C4⋊C4—1781no—
304C22⋊C4—3561no—
305C22⋊C4—3561no—
306C42—3561no—
307C42—3561no—
308C42D4×D8911yescharacteristic
309C42#1308357311yescharacteristic
310C42#1308357311yescharacteristic
311C42#1308357511yescharacteristic
312C23—3561no—
313C23—3561no—
314C23—3561no—
315C23—3561no—
316C23—3561no—
317C23—3561no—
318C23—1782no—
319C23C4×D35611yescharacteristic
320D4—3561no—
321D4—3561no—
322D4—1782no—
323D4—1782no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—3561no—
327C2×C4—3561no—
328C2×C4—3561no—
329C2×C4—3561no—
330C2×C4—3561no—
331C2×C4—3561no—
332C2×C4—3561no—
333C2×C4—1782no—
334C2×C4—1782no—
335C2×C4—7121no—
336C2×C4—7121no—
337C2×C4—7121no—
338C2×C4—7121no—
339C2×C4#1566797011yescharacteristic
340C2×C4#1566797211yescharacteristic
341C2×C4#1566798711yescharacteristic
342C2×C4#1566799611yescharacteristic
343C2×C4#1566799811yescharacteristic
344C2×C4#1566800711yescharacteristic
345C2×C4C2×C8×D8911yescharacteristic
346C2×C4M16×D8911yescharacteristic
347C2×C4#1566801811yescharacteristic
348C2×C4#1566802011yescharacteristic
349C2×C4C2×D71211yescharacteristic
350C2×C4#1566803411yescharacteristic
351C2×C4#1566804011yescharacteristic
352C2×C4#1566804511yescharacteristic
353C8—22no—
354C8—22no—
355C8—42no—
356C8—41no—
357C8—41no—
358C8—3562no—
359C8—7121no—
360C22—3562no—
361C22—3562no—
362C22—3562no—
363C22—7121no—
364C22—7121no—
365C22—7121no—
366C22—7121no—
367C22#1915149011yescharacteristic
368C22C8×D35611yescharacteristic
369C22#1915167111yescharacteristic
370C22C4×D71211yescharacteristic
371C22#1915170011yescharacteristic
372C22#1915171611yescharacteristic
373C22#1915172111yescharacteristic
374C4—21no—
375C4—21no—
376C4—3562no—
377C4—3562no—
378C4—7121no—
379C4#1915165011yescharacteristic
380C4#1915165811yescharacteristic
381C4#1915166111yescharacteristic
382C4#1915167311yescharacteristic
383C4#1915179411yescharacteristic
384C4#1915182111yescharacteristic
385C4#1915191211yescharacteristic
386C4#1915192311yescharacteristic
387C2—7122no—
388C2C8×D71211yescharacteristic
389C2#2601906611yescharacteristic
390C2#2601908311yescharacteristic
391C2#2601913211yescharacteristic
392C2#2602085911yescharacteristic
393C2#2602087311yescharacteristic
394C2#2602090111yescharacteristic
subgroupG/H
centerC22×C4C2×D356
commutatorC2×C4×C89C22×C8
FrattiniC2×C42C22×D89
FittingC89×#1273C2
socleC23×C89C4×D4
prime radicalC22×D356C2×C4
cosocleC2×C42×C89C23
hypercenter#1273D89
hypocenterC89#9541
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22×C4 ◁ C2×C4×C8 ◁ #1273

Complements

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

NH ≅ G/Ntype
2. C8×C4⋊Dic89C2semidirect
4. C2×#19151351C2semidirect
6. #26018092C2semidirect
7. C89×#1273C2semidirect
43. #15667934C8semidirect
204. #1273D89semidirect
205. C89#9541semidirect

Maximal subgroups

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

subgroupindex
#260210462
C8×C4⋊Dic892
C4×#156679342
C2×#191513512
C2×#191513272
#260180922
C89×#12732
#954189