Finite Group Databasebeta

← #36470490

Subgroups — #36470490

Order 22784.

422 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#15668034C211yesmaximal, characteristic
2C2×#19151406C212yesmaximal
3#26020424C211yesmaximal, characteristic, complemented
4#26018348C212yesmaximal, complemented
5C2×C4⋊C16×C89C211yesmaximal, characteristic, complemented
6C2×#15668034C2211yescharacteristic
7C4×#13083574—21no—
8C4×Dic356C411yescharacteristic
9C4×Dic356C411yescharacteristic
10C4×#13083563—21no—
11C4×#13083563—21no—
12C4×D712C411yescharacteristic
13C4×D712C411yescharacteristic
14C2×#15667948—21no—
15C2×#15667948C2212yes—
16#19151636C2211yescharacteristic
17#19151622—21no—
18#19151595—21no—
19#19151406—24no—
20C22×C16×C89C2212yes—
21C2×C4×C8×C89C2211yescharacteristic
22C4⋊C16×C89—21no—
23C4⋊C16×C89—21no—
24C2×#13083574—21no—
25#15668034—21no—
26#15668034—21no—
27#15668034D412yes—
28#15668034Q812yes—
29C2×Dic356C2×C411yescharacteristic
30C2×#13083563—21no—
31C2×D712C2×C411yescharacteristic
32C2×#13083558—22no—
33C4×Dic178—21no—
34C4×Dic178—21no—
35C4×D356—21no—
36C4×D356—21no—
37C4×C22⋊D89—41no—
38C4×C22⋊D89—41no—
39#15667971—21no—
40#15667969—41no—
41C42×D89—41no—
42#15667948—22no—
43#15667948—22no—
44#15667948—42no—
45#15667946C2×C411yescharacteristic
46#15667946C2×C411yescharacteristic
47#15667944—21no—
48C4⋊#10623494—41no—
49C4⋊#10623494—41no—
50#15667937—21no—
51#15667937—21no—
52#15667934—21no—
53#15667934—21no—
54C22×C8×C89D411yescharacteristic
55C22×C8×C89C2311yescharacteristic
56C2×C42×C89D411yescharacteristic
57C2×C16×C89—22no—
58C2×C16×C89—22no—
59C2×C16×C89—22no—
60C4×C8×C89C2×C411yescharacteristic
61C4×C8×C89C2×C411yescharacteristic
62C4×C8×C89D411yescharacteristic
63C4×C8×C89D411yescharacteristic
64#13083574—22no—
65#13083574—22no—
66#13083574—41no—
67#13083574—41no—
68C2×Dic178—21no—
69C2×D356—21no—
70C2×C22⋊D89—41no—
71C2×C4×D89—41no—
72C2×C4×D89—41no—
73C2×C4×D89—41no—
74Dic356—21no—
75Dic356C4⋊C412yes—
76#13083563—22no—
77#13083563—22no—
78D712—21no—
79D712C4⋊C412yes—
80#13083558—42no—
81#13083558—42no—
82C2×#10623494—42no—
83C4⋊Dic89—21no—
84C4⋊Dic89—21no—
85#13083553—41no—
86#13083553—41no—
87C22⋊Dic89—41no—
88#13083551—41no—
89#13083551—41no—
90C4×Dic89—41no—
91C4×Dic89—41no—
92C4×Dic89—41no—
93C22×C4×C89SD1611yescharacteristic
94C22×C4×C89SD1611yescharacteristic
95C22×C4×C89C2×D411yescharacteristic
96C2×C8×C89—21no—
97C2×C8×C89—21no—
98C2×C8×C89C22⋊C411yescharacteristic
99C2×C8×C89C22⋊C411yescharacteristic
100C2×C8×C89C22×C411yescharacteristic
101C2×C8×C89C2×D411yescharacteristic
102C2×C8×C89C2×D411yescharacteristic
103C2×C8×C89C2×Q811yescharacteristic
104C2×C8×C89#4111yescharacteristic
105C2×C8×C89#4111yescharacteristic
106C42×C89C22⋊C411yescharacteristic
107C42×C89C22⋊C411yescharacteristic
108C42×C89D811yescharacteristic
109C42×C89D811yescharacteristic
110C16×C89—42no—
111C23×C89C2×SD1611yescharacteristic
112C22×D89—41no—
113C2×C4×C89—22no—
114C2×C4×C89—41no—
115C2×C4×C89#10211yescharacteristic
116C2×C4×C89#10211yescharacteristic
117C2×C4×C89#10211yescharacteristic
118C2×C4×C89#10211yescharacteristic
119C2×C4×C89C2×C22⋊C411yescharacteristic
120C2×C4×C89#12111yescharacteristic
121C2×C4×C89C22⋊Q811yescharacteristic
122C2×C4×C89C2×D811yescharacteristic
123C2×C4×C89AGL(1,ℤ/8)11yescharacteristic
124C2×C4×C89#13711yescharacteristic
125C22⋊D89—42no—
126C22⋊D89—42no—
127C2×Dic89—41no—
128C2×Dic89—41no—
129C2×Dic89—41no—
130D356—22no—
131D356—41no—
132C4×D89—42no—
133C4×D89—42no—
134C4×D89—82no—
135C4×D89—82no—
136Dic178—22no—
137Dic178—41no—
138C8×C89—21no—
139C8×C89—21no—
140C8×C89C2×C4⋊C411yescharacteristic
141C8×C89#11711yescharacteristic
142C8×C89#12111yescharacteristic
143C8×C89C22⋊Q811yescharacteristic
144#10623494—82no—
145C22×C89—21no—
146C22×C89—21no—
147C22×C89C2×#10211yescharacteristic
148C22×C89#46111yescharacteristic
149C22×C89#47611yescharacteristic
150C2×D89—42no—
151C2×D89—81no—
152C2×D89—81no—
153C4×C89—21no—
154C4×C89—21no—
155C4×C89—21no—
156C4×C89#35912yescomplemented
157C4×C89#38011yescharacteristic
158C4×C89#41711yescharacteristic
159C4×C89#45911yescharacteristic
160C4×C89#47411yescharacteristic
161Dic89—42no—
162Dic89—81no—
163Dic89—81no—
164#12815—891nomaximal, Sylow
165C2×C89—21no—
166C2×C89—21no—
167C2×C89#180211yescharacteristic
168C2×C89C2×#35911yescharacteristic
169C2×C89#214311yescharacteristic
170D89—82no—
171C4×#135—891no—
172C2×C4⋊C16D8911yescharacteristic, complemented
173C2×#359—892no—
174#1848—891no—
175#1382—892no—
176C89#1281511yescharacteristic, complemented, Sylow
177C2×#135—891no—
178C4×#41—1781no—
179C22×C16C2×D8912yes—
180C4×Q16—891no—
181C4×Q16—891no—
182C4×SD16—1781no—
183C4×SD16—1781no—
184C4×D8—891no—
185C4×D8—891no—
186C2×#108—892no—
187C2×#108—1781no—
188#427—891no—
189#423—1781no—
190#416—1781no—
191C2×C4×C8C2×D8911yescharacteristic
192C4⋊C16—21no—
193C4⋊C16—21no—
194#359—1784no—
195C2×#41—1781no—
196#135—892no—
197#135—892no—
198#135—1781no—
199#135—1781no—
200C2×Q16—891no—
201C2×SD16—1781no—
202C2×D8—891no—
203C2×M16—1782no—
204C22×C8D35611yescharacteristic
205C22×C8C22×D8911yescharacteristic
206C4×Q8—1781no—
207C4×Q8—1781no—
208C4×D4—3561no—
209C4×D4—3561no—
210C4×D4—1781no—
211C4×D4—1781no—
212#117—3561no—
213#117—1781no—
214C2×C42—3561no—
215C2×C42D35611yescharacteristic
216C2×C16—22no—
217C2×C16—22no—
218C2×C16—22no—
219#108—3562no—
220#108—1782no—
221#108—1782no—
222#107—891no—
223#107—891no—
224#106—1781no—
225C4⋊C8—3561no—
226C4⋊C8—3561no—
227#103—1781no—
228#103—1781no—
229#102—1781no—
230#102—1781no—
231C4×C8C4×D8911yescharacteristic
232C4×C8C4×D8911yescharacteristic
233C4×C8C22⋊D8911yescharacteristic
234C4×C8C22⋊D8911yescharacteristic
235#41—3561no—
236#41—3561no—
237#41—1782no—
238#41—1782no—
239C2×Q8—1781no—
240C2×D4—3561no—
241C2×D4—1781no—
242C22×C4—3561no—
243C22×C4—3561no—
244C22×C4—3561no—
245C22×C4#1308356311yescharacteristic
246C22×C4#1308356311yescharacteristic
247C22×C4C2×D35611yescharacteristic
248Q16—892no—
249Q16—1781no—
250SD16—1782no—
251SD16—1782no—
252D8—892no—
253D8—1781no—
254M16—3562no—
255M16—3562no—
256C2×C8—21no—
257C2×C8—21no—
258C2×C8—3562no—
259C2×C8#1308355111yescharacteristic
260C2×C8#1308355111yescharacteristic
261C2×C8C2×C4×D8911yescharacteristic
262C2×C8D4×D8911yescharacteristic
263C2×C8C2×C22⋊D8911yescharacteristic
264C2×C8Q8×D8911yescharacteristic
265C2×C8#1308357311yescharacteristic
266C2×C8#1308357511yescharacteristic
267C4⋊C4—3561no—
268C4⋊C4—3561no—
269C4⋊C4—1781no—
270C4⋊C4—1781no—
271C22⋊C4—3561no—
272C22⋊C4—3561no—
273C22⋊C4—3561no—
274C42—3561no—
275C42—3561no—
276C42—3561no—
277C42#1308355111yescharacteristic
278C42#1308355111yescharacteristic
279C42D71211yescharacteristic
280C42D71211yescharacteristic
281C16—42no—
282C23—3561no—
283C23C2×#1308356311yescharacteristic
284Q8—3561no—
285Q8—1782no—
286D4—3562no—
287D4—3562no—
288D4—3561no—
289D4—1782no—
290C2×C4—22no—
291C2×C4—41no—
292C2×C4—3561no—
293C2×C4—3562no—
294C2×C4—3562no—
295C2×C4—3561no—
296C2×C4—3561no—
297C2×C4—7122no—
298C2×C4—7122no—
299C2×C4#1566793411yescharacteristic
300C2×C4#1566793411yescharacteristic
301C2×C4#1566793411yescharacteristic
302C2×C4#1566793411yescharacteristic
303C2×C4C2×#1308355111yescharacteristic
304C2×C4#1566798711yescharacteristic
305C2×C4#1566799211yescharacteristic
306C2×C4C2×D71211yescharacteristic
307C2×C4#1566804011yescharacteristic
308C2×C4#1566804511yescharacteristic
309C8—21no—
310C8—21no—
311C8—7122no—
312C8C4⋊C4×D8911yescharacteristic
313C8#1566797011yescharacteristic
314C8#1566798311yescharacteristic
315C8#1566798811yescharacteristic
316C22—21no—
317C22—21no—
318C22—3562no—
319C22—7121no—
320C22—7121no—
321C22C2×#1566793411yescharacteristic
322C22#1915180411yescharacteristic
323C22#1915188911yescharacteristic
324C4—21no—
325C4—21no—
326C4—21no—
327C4—3562no—
328C4—7121no—
329C4—7121no—
330C4#1915140612yescomplemented
331C4#1915145511yescharacteristic
332C4#1915160011yescharacteristic
333C4#1915179411yescharacteristic
334C4#1915187911yescharacteristic
335C2—21no—
336C2—21no—
337C2—7122no—
338C2#2602025311yescharacteristic
339C2C2×#1915140611yescharacteristic
340C2#2602198111yescharacteristic
subgroupG/H
centerC2×C4C2×D712
commutatorC2×C8×C89C22×C4
FrattiniC22×C8C22×D89
FittingC2×C4⋊C16×C89C2
socleC22×C89C2×#102
prime radicalC2×#15668034C22
cosocleC22×C8×C89C23
hypercenterC2×C4⋊C16D89
hypocenterC89#12815
LCSG ▷ C2×C8×C89 ▷ C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×C4⋊C16

Complements

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

NH ≅ G/Ntype
3. #26020424C2semidirect
4. #26018348C2semidirect
5. C2×C4⋊C16×C89C2semidirect
156. C4×C89#359semidirect
172. C2×C4⋊C16D89semidirect
176. C89#12815semidirect
330. C4#19151406semidirect

Maximal subgroups

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

subgroupindex
C4×#156680342
C2×#191514062
#260204242
#260183482
C2×C4⋊C16×C892
#1281589