Finite Group Databasebeta

← C89×#10550 #36388398

Subgroups — C89×#10550 #36388398

Order 22784.

450 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C89×#3152C211yesmaximal, characteristic
2C89×#1950C211yesmaximal, characteristic, complemented
3C89×#1547C211yesmaximal, characteristic
4C89×#1546C211yesmaximal, characteristic, complemented
5C2×#332×C89C211yesmaximal, characteristic, complemented
6C89×#1480C211yesmaximal, characteristic
7C89×#1283C211yesmaximal, characteristic, complemented
8C2×#137×C89—21no—
9C2×#137×C89—21no—
10#532×C89C2211yescharacteristic
11C2×C4⋊Q8×C89C2211yescharacteristic
12#497×C89—22no—
13#494×C89—21no—
14#492×C89—21no—
15#431×C89C2211yescharacteristic
16C2×#108×C89—21no—
17#423×C89C2211yescharacteristic
18C2×C4⋊C8×C89C2211yescharacteristic
19C2×C4⋊C8×C89C2211yescharacteristic
20C4×M16×C89C2211yescharacteristic
21#341×C89—21no—
22#332×C89—22no—
23#332×C89—21no—
24#332×C89—22no—
25#331×C89—21no—
26D4⋊C8×C89—22no—
27C2×#41×C89—21no—
28C22×Q8×C89—21no—
29#137×C89—42no—
30#137×C89—42no—
31#137×C89—42no—
32#137×C89—42no—
33C2×Q16×C89—22no—
34C2×Q16×C89—22no—
35C2×SD16×C89—22no—
36C2×SD16×C89—22no—
37C2×M16×C89—21no—
38C2×M16×C89D411yescharacteristic
39C2×M16×C89D411yescharacteristic
40C22×C8×C89—21no—
41C22×C8×C89—21no—
42C4⋊Q8×C89—21no—
43C4⋊Q8×C89—21no—
44C4⋊Q8×C89—21no—
45C4⋊Q8×C89D411yescharacteristic
46C4⋊Q8×C89D412yes—
47#127×C89D411yescharacteristic
48#124×C89—21no—
49#121×C89—21no—
50#121×C89—21no—
51C4×D4×C89—21no—
52C4×D4×C89—21no—
53C2×C4⋊C4×C89—21no—
54C2×C4⋊C4×C89—21no—
55C2×C42×C89C2311yescharacteristic
56#108×C89—42no—
57C4⋊C8×C89—21no—
58C4⋊C8×C89—21no—
59C4⋊C8×C89—21no—
60C4⋊C8×C89—21no—
61C4⋊C8×C89—21no—
62C4⋊C8×C89—21no—
63C4⋊C8×C89D412yes—
64C22⋊C8×C89—21no—
65#97×C89—21no—
66C4×C8×C89—21no—
67C4×C8×C89—21no—
68#41×C89—41no—
69#41×C89—41no—
70#41×C89—41no—
71#41×C89—41no—
72C2×Q8×C89—21no—
73C2×Q8×C89—22no—
74C2×Q8×C89—41no—
75C2×Q8×C89—41no—
76C2×Q8×C89—41no—
77C2×Q8×C89—41no—
78C2×Q8×C89—41no—
79C2×D4×C89—21no—
80C2×D4×C89—21no—
81C2×D4×C89—21no—
82C2×D4×C89—41no—
83C22×C4×C89—41no—
84C22×C4×C89—41no—
85C22×C4×C89C2×D411yescharacteristic
86C22×C4×C89#4111yescharacteristic
87C22×C4×C89#4111yescharacteristic
88Q16×C89—44no—
89Q16×C89—44no—
90SD16×C89—44no—
91SD16×C89—44no—
92M16×C89—21no—
93M16×C89—21no—
94M16×C89—41no—
95M16×C89—41no—
96M16×C89D812yes—
97M16×C89SD1612yes—
98C2×C8×C89—21no—
99C2×C8×C89—21no—
100C2×C8×C89—22no—
101C2×C8×C89—41no—
102C2×C8×C89—41no—
103C2×C8×C89—41no—
104C2×C8×C89—41no—
105C2×C8×C89—41no—
106C2×C8×C89—81no—
107C4⋊C4×C89—22no—
108C4⋊C4×C89—21no—
109C4⋊C4×C89—22no—
110C4⋊C4×C89—21no—
111C4⋊C4×C89—41no—
112C4⋊C4×C89—41no—
113C22⋊C4×C89—41no—
114C22⋊C4×C89—41no—
115C42×C89C2×D411yescharacteristic
116C42×C89C2×D411yescharacteristic
117C42×C89C2×D411yescharacteristic
118C42×C89#4111yescharacteristic
119C23×C89—41no—
120C23×C89#12411yescharacteristic
121Q8×C89—42no—
122Q8×C89—41no—
123Q8×C89—42no—
124Q8×C89—41no—
125Q8×C89—81no—
126Q8×C89—81no—
127D4×C89—41no—
128D4×C89—41no—
129D4×C89—41no—
130D4×C89—41no—
131D4×C89—81no—
132D4×C89—81no—
133D4×C89—81no—
134C2×C4×C89—21no—
135C2×C4×C89—21no—
136C2×C4×C89—41no—
137C2×C4×C89—41no—
138C2×C4×C89—42no—
139C2×C4×C89—81no—
140C2×C4×C89—81no—
141C2×C4×C89—81no—
142C2×C4×C89—81no—
143C2×C4×C89#12011yescharacteristic
144C2×C4×C89#12111yescharacteristic
145C2×C4×C89#12111yescharacteristic
146C2×C4×C89#12111yescharacteristic
147C2×C4×C89#12311yescharacteristic
148C2×C4×C89#12311yescharacteristic
149C2×C4×C89C2×D811yescharacteristic
150C2×C4×C89C2×SD1611yescharacteristic
151C2×C4×C89AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C89AGL(1,ℤ/8)11yescharacteristic
153C8×C89—22no—
154C8×C89—22no—
155C8×C89—42no—
156C8×C89—81no—
157C8×C89—81no—
158C8×C89—81no—
159C22×C89—21no—
160C22×C89—21no—
161C22×C89—81no—
162C22×C89—81no—
163C22×C89—81no—
164C22×C89#39411yescharacteristic
165C22×C89#48611yescharacteristic
166C22×C89#49011yescharacteristic
167C4×C89—21no—
168C4×C89—21no—
169C4×C89—21no—
170C4×C89—81no—
171C4×C89—82no—
172C4×C89#44711yescharacteristic
173C4×C89#45011yescharacteristic
174C4×C89#45911yescharacteristic
175C4×C89#46011yescharacteristic
176C4×C89#47111yescharacteristic
177C4×C89#47311yescharacteristic
178#10550C8911yesmaximal, characteristic, direct product factor, Sylow
179C2×C89—21no—
180C2×C89—21no—
181C2×C89—161no—
182C2×C89#204111yescharacteristic
183C2×C89#204911yescharacteristic
184C2×C89#205211yescharacteristic
185#3152C2×C8911yescharacteristic
186#1950C2×C8911yescharacteristic, complemented
187#1547C2×C8911yescharacteristic
188#1546C2×C8911yescharacteristic, complemented
189C2×#332C2×C8911yescharacteristic, complemented
190#1480C2×C8911yescharacteristic
191#1283C2×C8911yescharacteristic, complemented
192C89#1055011yescharacteristic, direct product factor, Sylow
193C2×#137—21no—
194C2×#137—21no—
195#532C22×C8911yescharacteristic
196C2×C4⋊Q8C22×C8911yescharacteristic
197#497—22no—
198#494—21no—
199#492—21no—
200#431C22×C8911yescharacteristic
201C2×#108—21no—
202#423C22×C8911yescharacteristic
203C2×C4⋊C8C22×C8911yescharacteristic
204C2×C4⋊C8C22×C8911yescharacteristic
205C4×M16C22×C8911yescharacteristic
206#341—21no—
207#332—22no—
208#332—21no—
209#332—22no—
210#331—21no—
211D4⋊C8—22no—
212C2×#41—21no—
213C22×Q8—21no—
214#137—42no—
215#137—42no—
216#137—42no—
217#137—42no—
218C2×Q16—22no—
219C2×Q16—22no—
220C2×SD16—22no—
221C2×SD16—22no—
222C2×M16—21no—
223C2×M16D4×C8911yescharacteristic
224C2×M16D4×C8911yescharacteristic
225C22×C8—21no—
226C22×C8—21no—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8—21no—
230C4⋊Q8D4×C8912yes—
231C4⋊Q8D4×C8911yescharacteristic
232#127D4×C8911yescharacteristic
233#124—21no—
234#121—21no—
235#121—21no—
236C4×D4—21no—
237C4×D4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C42C23×C8911yescharacteristic
241#108—42no—
242C4⋊C8—21no—
243C4⋊C8—21no—
244C4⋊C8—21no—
245C4⋊C8—21no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8D4×C8912yes—
249C22⋊C8—21no—
250#97—21no—
251C4×C8—21no—
252C4×C8—21no—
253#41—41no—
254#41—41no—
255#41—41no—
256#41—41no—
257C2×Q8—21no—
258C2×Q8—22no—
259C2×Q8—41no—
260C2×Q8—41no—
261C2×Q8—41no—
262C2×Q8—41no—
263C2×Q8—41no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—41no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4C2×D4×C8911yescharacteristic
271C22×C4#41×C8911yescharacteristic
272C22×C4#41×C8911yescharacteristic
273Q16—44no—
274Q16—44no—
275SD16—44no—
276SD16—44no—
277M16—21no—
278M16—21no—
279M16—41no—
280M16—41no—
281M16D8×C8912yes—
282M16SD16×C8912yes—
283C2×C8—21no—
284C2×C8—21no—
285C2×C8—22no—
286C2×C8—41no—
287C2×C8—41no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8—41no—
291C2×C8—81no—
292C4⋊C4—22no—
293C4⋊C4—21no—
294C4⋊C4—22no—
295C4⋊C4—21no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C42C2×D4×C8911yescharacteristic
301C42C2×D4×C8911yescharacteristic
302C42C2×D4×C8911yescharacteristic
303C42#41×C8911yescharacteristic
304C23—41no—
305C23#124×C8911yescharacteristic
306Q8—42no—
307Q8—41no—
308Q8—42no—
309Q8—41no—
310Q8—81no—
311Q8—81no—
312D4—41no—
313D4—41no—
314D4—41no—
315D4—41no—
316D4—81no—
317D4—81no—
318D4—81no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—42no—
324C2×C4—81no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4#120×C8911yescharacteristic
329C2×C4#121×C8911yescharacteristic
330C2×C4#121×C8911yescharacteristic
331C2×C4#121×C8911yescharacteristic
332C2×C4#123×C8911yescharacteristic
333C2×C4#123×C8911yescharacteristic
334C2×C4C2×D8×C8911yescharacteristic
335C2×C4C2×SD16×C8911yescharacteristic
336C2×C4AGL(1,ℤ/8)×C8911yescharacteristic
337C2×C4AGL(1,ℤ/8)×C8911yescharacteristic
338C8—22no—
339C8—22no—
340C8—42no—
341C8—81no—
342C8—81no—
343C8—81no—
344C22—21no—
345C22—21no—
346C22—81no—
347C22—81no—
348C22—81no—
349C22#394×C8911yescharacteristic
350C22#486×C8911yescharacteristic
351C22#490×C8911yescharacteristic
352C4—21no—
353C4—21no—
354C4—21no—
355C4—81no—
356C4—82no—
357C4#447×C8911yescharacteristic
358C4#450×C8911yescharacteristic
359C4#459×C8911yescharacteristic
360C4#460×C8911yescharacteristic
361C4#471×C8911yescharacteristic
362C4#473×C8911yescharacteristic
363C2—21no—
364C2—21no—
365C2—161no—
366C2C89×#204111yescharacteristic
367C2C89×#204911yescharacteristic
368C2C89×#205211yescharacteristic
subgroupG/H
center, socleC22×C89#394
commutator, Frattini, cosocleC2×C42C23×C89
prime radical#532×C89C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C89 ◁ C2×C42×C89 ◁ G

Complements

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

NH ≅ G/Ntype
2. C89×#1950C2semidirect
4. C89×#1546C2semidirect
5. C2×#332×C89C2semidirect
7. C89×#1283C2semidirect
178. #10550C89direct (N × H)
186. #1950C2×C89semidirect
188. #1546C2×C89semidirect
189. C2×#332C2×C89semidirect
191. #1283C2×C89semidirect
192. C89#10550direct (N × H)

Maximal subgroups

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

subgroupindex
C89×#31522
C89×#19502
C89×#15472
C89×#15462
C2×#332×C892
C89×#14802
C89×#12832
#1055089