Finite Group Databasebeta

← #36471339

Subgroups — #36471339

Order 22784.

456 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26033355C211yesmaximal, characteristic, complemented
2#26021880C211yesmaximal, characteristic, complemented
3#26021880C211yesmaximal, characteristic, complemented
4#26021873C211yesmaximal, characteristic, complemented
5#26018336C211yesmaximal, characteristic, complemented
6#26018332C211yesmaximal, characteristic, complemented
7C2×#444×C89C211yesmaximal, characteristic
8#19152015—22no—
9#19152015—22no—
10C2×#15667952—22no—
11C2×#15667952C2211yescharacteristic
12C2×#15667952C2211yescharacteristic
13C2×#15667952C2211yescharacteristic
14C2×#15667952C2211yescharacteristic
15#19151382—22no—
16#19151382—22no—
17#19151380—22no—
18C2×#135×C89C411yescharacteristic
19C2×#131×C89C2211yescharacteristic
20C2×#131×C89C2211yescharacteristic
21#444×C89—22no—
22#444×C89—22no—
23C2×#108×C89C411yescharacteristic
24C2×#104×C89C411yescharacteristic
25C2×#104×C89C411yescharacteristic
26C2×#97×C89C2211yescharacteristic
27#15667952—24no—
28#15667952—21no—
29#15667952—21no—
30#15667952—21no—
31#15667952—21no—
32#15667952—21no—
33#15667952—21no—
34#15667952—21no—
35#15667952D412yes—
36C2×#13083549—24no—
37C2×#13083549—21no—
38C2×#13083549—21no—
39C2×#13083549—21no—
40C2×#13083549D412yes—
41C2×#41×C89C2×C411yescharacteristic
42C2×#41×C89C2×C411yescharacteristic
43#135×C89—22no—
44#135×C89—22no—
45C2×Q16×C89C811yescharacteristic
46C2×SD16×C89C811yescharacteristic
47C2×SD16×C89C811yescharacteristic
48C2×D8×C89C811yescharacteristic
49#131×C89—21no—
50#131×C89—21no—
51#131×C89—21no—
52#131×C89—21no—
53#131×C89—21no—
54#131×C89—21no—
55#131×C89D412yes—
56#131×C89D412yes—
57C2×M16×C89—21no—
58C2×M16×C89—21no—
59C2×M16×C89C2×C411yescharacteristic
60C2×M16×C89C2×C411yescharacteristic
61C22×C8×C89—21no—
62C22×C8×C89—21no—
63C22×C8×C89C2×C411yescharacteristic
64C22×C8×C89C2311yescharacteristic
65C2×C42×C89C2×C411yescharacteristic
66#108×C89—22no—
67#104×C89—22no—
68#104×C89—22no—
69#97×C89—21no—
70#97×C89—21no—
71#13083549—22no—
72#13083549—22no—
73#13083549—41no—
74#13083549—41no—
75#41×C89—21no—
76#41×C89—21no—
77#41×C89—21no—
78#41×C89—21no—
79#41×C89—21no—
80#41×C89—21no—
81#41×C89C22⋊C412yes—
82#41×C89M1612yes—
83C2×Q8×C89C2×C811yescharacteristic
84C2×Q8×C89C2×C811yescharacteristic
85C2×D4×C89—21no—
86C2×D4×C89—21no—
87C2×D4×C89C2×C811yescharacteristic
88C2×D4×C89C2×C811yescharacteristic
89C22×C4×C89—21no—
90C22×C4×C89—21no—
91C22×C4×C89—21no—
92C22×C4×C89C22×C411yescharacteristic
93Q16×C89—22no—
94SD16×C89—22no—
95SD16×C89—22no—
96D8×C89—22no—
97M16×C89—21no—
98M16×C89—22no—
99M16×C89—22no—
100M16×C89—21no—
101M16×C89—21no—
102M16×C89—41no—
103M16×C89—41no—
104M16×C89C22⋊C412yes—
105C2×C8×C89—21no—
106C2×C8×C89—21no—
107C2×C8×C89—21no—
108C2×C8×C89—22no—
109C2×C8×C89—22no—
110C2×C8×C89—21no—
111C2×C8×C89—41no—
112C2×C8×C89—41no—
113C2×C8×C89C2×C811yescharacteristic
114C2×C8×C89C2×C811yescharacteristic
115C2×C8×C89C2×D411yescharacteristic
116C2×C8×C89C2×D411yescharacteristic
117C2×C8×C89C2×D411yescharacteristic
118C2×C8×C89C2×D411yescharacteristic
119C2×C8×C89#4111yescharacteristic
120C2×C8×C89#4111yescharacteristic
121C42×C89—21no—
122C42×C89—21no—
123C23×C89—21no—
124C23×C89—21no—
125C23×C89#13111yescharacteristic
126Q8×C89—21no—
127Q8×C89—21no—
128Q8×C89—21no—
129Q8×C89C22⋊C812yes—
130D4×C89—22no—
131D4×C89—22no—
132D4×C89—21no—
133D4×C89—21no—
134D4×C89—21no—
135D4×C89—41no—
136D4×C89—41no—
137D4×C89C22⋊C812yes—
138C2×C4×C89—21no—
139C2×C4×C89—22no—
140C2×C4×C89—22no—
141C2×C4×C89—21no—
142C2×C4×C89—41no—
143C2×C4×C89—41no—
144C2×C4×C89—41no—
145C2×C4×C89—81no—
146C2×C4×C89C2×C22⋊C411yescharacteristic
147C2×C4×C89C4×D411yescharacteristic
148C2×C4×C89C4×D411yescharacteristic
149C2×C4×C89C22×C811yescharacteristic
150C2×C4×C89C2×M1611yescharacteristic
151C2×C4×C89#13111yescharacteristic
152C8×C89—22no—
153C8×C89—21no—
154C8×C89—21no—
155C8×C89—41no—
156C8×C89#12011yescharacteristic
157C8×C89#12111yescharacteristic
158C8×C89#12111yescharacteristic
159C8×C89#12311yescharacteristic
160C22×C89—22no—
161C22×C89—41no—
162C22×C89—41no—
163C22×C89—81no—
164C22×C89—81no—
165C22×C89#40811yescharacteristic
166C22×C89C8×D411yescharacteristic
167C22×C89#43511yescharacteristic
168C4×C89—22no—
169C4×C89—41no—
170C4×C89—81no—
171C4×C89#38611yescharacteristic
172C4×C89C2×C22⋊C811yescharacteristic
173C4×C89C8×D411yescharacteristic
174C4×C89#43511yescharacteristic
175#12986—891nomaximal, Sylow
176C2×C89—21no—
177C2×C89—21no—
178C2×C89—21no—
179C2×C89—42no—
180C2×C89—81no—
181C2×C89#186911yescharacteristic
182#3407—891no—
183C2×#444D8911yescharacteristic
184#2117—891no—
185#2117—891no—
186#2115—891no—
187#1377—891no—
188#1375—891no—
189C89#1298611yescharacteristic, complemented, Sylow
190C2×#135Dic8911yescharacteristic
191C2×#131C2×D8911yescharacteristic
192C2×#131C2×D8911yescharacteristic
193#504—1782no—
194#504—1782no—
195C2×M32—891no—
196C2×M32—891no—
197C2×M32—891no—
198C2×M32—891no—
199C2×M32—1782no—
200#444—22no—
201#444—22no—
202C2×#108Dic8911yescharacteristic
203C2×#104Dic8911yescharacteristic
204C2×#104Dic8911yescharacteristic
205C2×#97C2×D8911yescharacteristic
206#350—1782no—
207#350—1782no—
208#349—1782no—
209C2×#41C2×Dic8911yescharacteristic
210C2×#41C2×Dic8911yescharacteristic
211#135—22no—
212#135—22no—
213C2×Q16#1062349411yescharacteristic
214C2×SD16#1062349411yescharacteristic
215C2×SD16#1062349411yescharacteristic
216C2×D8#1062349411yescharacteristic
217#131—21no—
218#131—21no—
219#131—21no—
220#131—21no—
221#131—21no—
222#131—21no—
223#131C22⋊D8912yes—
224#131C22⋊D8912yes—
225C2×M16—21no—
226C2×M16—21no—
227C2×M16C2×Dic8911yescharacteristic
228C2×M16C2×Dic8911yescharacteristic
229C22×C8—21no—
230C22×C8—21no—
231C22×C8C2×Dic8911yescharacteristic
232C22×C8C22×D8911yescharacteristic
233C2×C42C2×Dic8911yescharacteristic
234M32—892no—
235M32—1781no—
236M32—1781no—
237M32—1781no—
238M32—1781no—
239M32—1784no—
240M32—1781no—
241M32—1781no—
242M32—1781no—
243C2×C16—892no—
244C2×C16—1781no—
245C2×C16—1781no—
246C2×C16—1784no—
247C2×C16—1781no—
248#108—22no—
249#104—22no—
250#104—22no—
251#97—21no—
252#97—21no—
253#41—21no—
254#41—21no—
255#41—21no—
256#41—21no—
257#41—21no—
258#41—21no—
259#41C22⋊Dic8912yes—
260#41#1308355812yes—
261C2×Q8C2×#1062349411yescharacteristic
262C2×Q8C2×#1062349411yescharacteristic
263C2×D4—21no—
264C2×D4—21no—
265C2×D4C2×#1062349411yescharacteristic
266C2×D4C2×#1062349411yescharacteristic
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4C22×Dic8911yescharacteristic
271Q16—22no—
272SD16—22no—
273SD16—22no—
274D8—22no—
275M16—21no—
276M16—22no—
277M16—22no—
278M16—21no—
279M16—21no—
280M16—41no—
281M16—41no—
282M16C22⋊Dic8912yes—
283C2×C8—21no—
284C2×C8—21no—
285C2×C8—21no—
286C2×C8—22no—
287C2×C8—22no—
288C2×C8—21no—
289C2×C8—41no—
290C2×C8—41no—
291C2×C8C2×#1062349411yescharacteristic
292C2×C8C2×#1062349411yescharacteristic
293C2×C8D4×D8911yescharacteristic
294C2×C8D4×D8911yescharacteristic
295C2×C8C2×C22⋊D8911yescharacteristic
296C2×C8C2×C22⋊D8911yescharacteristic
297C2×C8#1308357311yescharacteristic
298C2×C8#1308357311yescharacteristic
299C42—21no—
300C42—21no—
301C16—3561no—
302C16—3561no—
303C16—1782no—
304C16—1782no—
305C23—21no—
306C23—21no—
307C23#1566801911yescharacteristic
308Q8—21no—
309Q8—21no—
310Q8—21no—
311Q8C22⋊#1062349412yes—
312D4—22no—
313D4—22no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—41no—
318D4—41no—
319D4C22⋊#1062349412yes—
320C2×C4—21no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—21no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—81no—
328C2×C4C2×C22⋊Dic8911yescharacteristic
329C2×C4D4×Dic8911yescharacteristic
330C2×C4D4×Dic8911yescharacteristic
331C2×C4C22×#1062349411yescharacteristic
332C2×C4C2×#1308355811yescharacteristic
333C2×C4#1566801911yescharacteristic
334C8—22no—
335C8—21no—
336C8—21no—
337C8—41no—
338C8#1566798011yescharacteristic
339C8#1566798411yescharacteristic
340C8#1566798411yescharacteristic
341C8#1566799311yescharacteristic
342C22—22no—
343C22—41no—
344C22—41no—
345C22—81no—
346C22—81no—
347C22#1915156511yescharacteristic
348C22D4×#1062349411yescharacteristic
349C22#1915167011yescharacteristic
350C4—22no—
351C4—41no—
352C4—81no—
353C4#1915147811yescharacteristic
354C4C2×C22⋊#1062349411yescharacteristic
355C4D4×#1062349411yescharacteristic
356C4#1915167011yescharacteristic
357C2—21no—
358C2—21no—
359C2—21no—
360C2—42no—
361C2—81no—
362C2#2602054511yescharacteristic
subgroupG/H
centerC4#19151478
commutatorC2×C4×C89C22×C8
FrattiniC22×C8C22×D89
FittingC2×#444×C89C2
socleC2×C89#1869
prime radicalC2×#135×C89C4
cosocleC22×C8×C89C23
hypercenterC2×#444D89
hypocenterC89#12986
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C4 ◁ C22×C8 ◁ C2×#444

Complements

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

NH ≅ G/Ntype
1. #26033355C2semidirect
2. #26021880C2semidirect
3. #26021880C2semidirect
4. #26021873C2semidirect
5. #26018336C2semidirect
6. #26018332C2semidirect
189. C89#12986semidirect

Maximal subgroups

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

subgroupindex
#260333552
#260218802
#260218732
#260183362
#260183322
C2×#444×C892
#1298689