Finite Group Databasebeta

← C89×#13023 #36390871

Subgroups — C89×#13023 #36390871

Order 22784.

474 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
1C2×#510×C89C211yesmaximal, characteristic
2C89×#2951C211yesmaximal, characteristic
3C2×#359×C89C211yesmaximal, characteristic
4C2×#358×C89C211yesmaximal, characteristic, complemented
5C89×#1979C211yesmaximal, characteristic, complemented
6C89×#1387C211yesmaximal, characteristic, complemented
7C89×#1379C211yesmaximal, characteristic, complemented
8C2×#135×C89C2211yescharacteristic
9C22×Q16×C89C2211yescharacteristic
10#520×C89—21no—
11#510×C89—22no—
12#510×C89C414yescomplemented
13C2×Q32×C89—21no—
14C2×SD32×C89—21no—
15C2×M32×C89C2211yescharacteristic
16C22×C16×C89C2211yescharacteristic
17#440×C89—22no—
18C4×Q16×C89—21no—
19C4×D8×C89—21no—
20C2×#108×C89C2211yescharacteristic
21C2×#107×C89C2211yescharacteristic
22#419×C89—21no—
23#417×C89—21no—
24C2×#101×C89—21no—
25#405×C89C2211yescharacteristic
26#359×C89—22no—
27#358×C89—22no—
28C2×#41×C89—21no—
29C22×Q8×C89—21no—
30#135×C89—21no—
31#135×C89—21no—
32#135×C89C2×C412yes—
33#135×C89D412yes—
34C2×Q16×C89—21no—
35C2×Q16×C89—21no—
36C2×Q16×C89—21no—
37C2×Q16×C89—21no—
38C2×Q16×C89—21no—
39C2×Q16×C89C2×C412yescomplemented
40C2×Q16×C89D411yescharacteristic
41C2×SD16×C89—21no—
42C2×D8×C89D411yescharacteristic
43C2×M16×C89—21no—
44C2×M16×C89D411yescharacteristic
45C22×C8×C89C2311yescharacteristic
46C4×Q8×C89—22no—
47C4×D4×C89—22no—
48C4×D4×C89—42no—
49#117×C89—41no—
50#117×C89D411yescharacteristic
51C2×C4⋊C4×C89—21no—
52C2×C4⋊C4×C89—41no—
53Q32×C89—24no—
54SD32×C89—24no—
55M32×C89—21no—
56M32×C89C2×C412yescomplemented
57C2×C16×C89—21no—
58C2×C16×C89—21no—
59C2×C16×C89—21no—
60C2×C16×C89—21no—
61#108×C89—21no—
62#108×C89—21no—
63#107×C89—21no—
64#107×C89D412yes—
65#103×C89—22no—
66#103×C89—41no—
67#103×C89—41no—
68#102×C89—22no—
69#101×C89—42no—
70#97×C89—21no—
71C4×C8×C89—21no—
72#41×C89—22no—
73#41×C89—22no—
74#41×C89—41no—
75#41×C89—41no—
76C2×Q8×C89—22no—
77C2×Q8×C89—21no—
78C2×Q8×C89—41no—
79C2×Q8×C89—41no—
80C2×Q8×C89—41no—
81C2×Q8×C89—41no—
82C2×Q8×C89—41no—
83C2×D4×C89—21no—
84C2×D4×C89—41no—
85C22×C4×C89—42no—
86C22×C4×C89—41no—
87C22×C4×C89—41no—
88C22×C4×C89—41no—
89C22×C4×C89C2×D411yescharacteristic
90Q16×C89—22no—
91Q16×C89—22no—
92Q16×C89—21no—
93Q16×C89—41no—
94Q16×C89—41no—
95Q16×C89C22⋊C412yes—
96SD16×C89—22no—
97SD16×C89—22no—
98D8×C89—21no—
99D8×C89C22⋊C412yes—
100M16×C89—21no—
101M16×C89—21no—
102M16×C89—41no—
103M16×C89—41no—
104C2×C8×C89—21no—
105C2×C8×C89—41no—
106C2×C8×C89C22×C411yescharacteristic
107C2×C8×C89C2×D411yescharacteristic
108C2×C8×C89C2×D411yescharacteristic
109C2×C8×C89C2×D411yescharacteristic
110C2×C8×C89#4111yescharacteristic
111C2×C8×C89#4111yescharacteristic
112C4⋊C4×C89—22no—
113C4⋊C4×C89—42no—
114C4⋊C4×C89—41no—
115C4⋊C4×C89D811yescharacteristic
116C4⋊C4×C89D811yescharacteristic
117C22⋊C4×C89—21no—
118C22⋊C4×C89—42no—
119C42×C89—21no—
120C42×C89—42no—
121C16×C89—22no—
122C16×C89—41no—
123C23×C89—41no—
124C23×C89AGL(1,ℤ/8)11yescharacteristic
125Q8×C89—22no—
126Q8×C89—41no—
127Q8×C89—42no—
128Q8×C89—42no—
129Q8×C89—81no—
130Q8×C89—81no—
131D4×C89—22no—
132D4×C89—42no—
133D4×C89—42no—
134D4×C89—41no—
135C2×C4×C89—21no—
136C2×C4×C89—21no—
137C2×C4×C89—41no—
138C2×C4×C89—42no—
139C2×C4×C89—42no—
140C2×C4×C89—42no—
141C2×C4×C89—42no—
142C2×C4×C89—81no—
143C2×C4×C89—81no—
144C2×C4×C89—162no—
145C2×C4×C89—161no—
146C2×C4×C89C4×D411yescharacteristic
147C2×C4×C89#12011yescharacteristic
148C2×C4×C89#12111yescharacteristic
149C2×C4×C89C2×D811yescharacteristic
150C2×C4×C89#13511yescharacteristic
151C2×C4×C89AGL(1,ℤ/8)11yescharacteristic
152C8×C89—41no—
153C8×C89—81no—
154C8×C89C2×C22⋊C411yescharacteristic
155C8×C89C4×D411yescharacteristic
156C8×C89#12111yescharacteristic
157C8×C89#12311yescharacteristic
158C22×C89—21no—
159C22×C89—21no—
160C22×C89—42no—
161C22×C89—81no—
162C22×C89—81no—
163C22×C89#44211yescharacteristic
164C22×C89#44711yescharacteristic
165C22×C89#46311yescharacteristic
166C4×C89—42no—
167C4×C89—41no—
168C4×C89—41no—
169C4×C89—82no—
170C4×C89—82no—
171C4×C89#38611yescharacteristic
172C4×C89C4×D811yescharacteristic
173C4×C89#44911yescharacteristic
174C4×C89#45911yescharacteristic
175#13023C8911yesmaximal, characteristic, direct product factor, Sylow
176C2×C89—21no—
177C2×C89—21no—
178C2×C89—82no—
179C2×C89#187911yescharacteristic
180C2×C89#219411yescharacteristic
181C2×C89#219511yescharacteristic
182C2×#510C2×C8911yescharacteristic
183#2951C2×C8911yescharacteristic
184C2×#359C2×C8911yescharacteristic
185C2×#358C2×C8911yescharacteristic, complemented
186#1979C2×C8911yescharacteristic, complemented
187#1387C2×C8911yescharacteristic, complemented
188#1379C2×C8911yescharacteristic, complemented
189C89#1302311yescharacteristic, direct product factor, Sylow
190C2×#135C22×C8911yescharacteristic
191C22×Q16C22×C8911yescharacteristic
192#520—21no—
193#510—22no—
194#510C4×C8914yescomplemented
195C2×Q32—21no—
196C2×SD32—21no—
197C2×M32C22×C8911yescharacteristic
198C22×C16C22×C8911yescharacteristic
199#440—22no—
200C4×Q16—21no—
201C4×D8—21no—
202C2×#108C22×C8911yescharacteristic
203C2×#107C22×C8911yescharacteristic
204#419—21no—
205#417—21no—
206C2×#101—21no—
207#405C22×C8911yescharacteristic
208#359—22no—
209#358—22no—
210C2×#41—21no—
211C22×Q8—21no—
212#135—21no—
213#135—21no—
214#135C2×C4×C8912yes—
215#135D4×C8912yes—
216C2×Q16—21no—
217C2×Q16—21no—
218C2×Q16—21no—
219C2×Q16—21no—
220C2×Q16—21no—
221C2×Q16C2×C4×C8912yescomplemented
222C2×Q16D4×C8911yescharacteristic
223C2×SD16—21no—
224C2×D8D4×C8911yescharacteristic
225C2×M16—21no—
226C2×M16D4×C8911yescharacteristic
227C22×C8C23×C8911yescharacteristic
228C4×Q8—22no—
229C4×D4—22no—
230C4×D4—42no—
231#117—41no—
232#117D4×C8911yescharacteristic
233C2×C4⋊C4—21no—
234C2×C4⋊C4—41no—
235Q32—24no—
236SD32—24no—
237M32—21no—
238M32C2×C4×C8912yescomplemented
239C2×C16—21no—
240C2×C16—21no—
241C2×C16—21no—
242C2×C16—21no—
243#108—21no—
244#108—21no—
245#107—21no—
246#107D4×C8912yes—
247#103—22no—
248#103—41no—
249#103—41no—
250#102—22no—
251#101—42no—
252#97—21no—
253C4×C8—21no—
254#41—22no—
255#41—22no—
256#41—41no—
257#41—41no—
258C2×Q8—22no—
259C2×Q8—21no—
260C2×Q8—41no—
261C2×Q8—41no—
262C2×Q8—41no—
263C2×Q8—41no—
264C2×Q8—41no—
265C2×D4—21no—
266C2×D4—41no—
267C22×C4—42no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4C2×D4×C8911yescharacteristic
272Q16—22no—
273Q16—22no—
274Q16—21no—
275Q16—41no—
276Q16—41no—
277Q16C22⋊C4×C8912yes—
278SD16—22no—
279SD16—22no—
280D8—21no—
281D8C22⋊C4×C8912yes—
282M16—21no—
283M16—21no—
284M16—41no—
285M16—41no—
286C2×C8—21no—
287C2×C8—41no—
288C2×C8C22×C4×C8911yescharacteristic
289C2×C8C2×D4×C8911yescharacteristic
290C2×C8C2×D4×C8911yescharacteristic
291C2×C8C2×D4×C8911yescharacteristic
292C2×C8#41×C8911yescharacteristic
293C2×C8#41×C8911yescharacteristic
294C4⋊C4—22no—
295C4⋊C4—42no—
296C4⋊C4—41no—
297C4⋊C4D8×C8911yescharacteristic
298C4⋊C4D8×C8911yescharacteristic
299C22⋊C4—21no—
300C22⋊C4—42no—
301C42—21no—
302C42—42no—
303C16—22no—
304C16—41no—
305C23—41no—
306C23AGL(1,ℤ/8)×C8911yescharacteristic
307Q8—22no—
308Q8—41no—
309Q8—42no—
310Q8—42no—
311Q8—81no—
312Q8—81no—
313D4—22no—
314D4—42no—
315D4—42no—
316D4—41no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—41no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—81no—
325C2×C4—81no—
326C2×C4—162no—
327C2×C4—161no—
328C2×C4C4×D4×C8911yescharacteristic
329C2×C4#120×C8911yescharacteristic
330C2×C4#121×C8911yescharacteristic
331C2×C4C2×D8×C8911yescharacteristic
332C2×C4#135×C8911yescharacteristic
333C2×C4AGL(1,ℤ/8)×C8911yescharacteristic
334C8—41no—
335C8—81no—
336C8C2×C22⋊C4×C8911yescharacteristic
337C8C4×D4×C8911yescharacteristic
338C8#121×C8911yescharacteristic
339C8#123×C8911yescharacteristic
340C22—21no—
341C22—21no—
342C22—42no—
343C22—81no—
344C22—81no—
345C22#442×C8911yescharacteristic
346C22#447×C8911yescharacteristic
347C22#463×C8911yescharacteristic
348C4—42no—
349C4—41no—
350C4—41no—
351C4—82no—
352C4—82no—
353C4#386×C8911yescharacteristic
354C4C4×D8×C8911yescharacteristic
355C4#449×C8911yescharacteristic
356C4#459×C8911yescharacteristic
357C2—21no—
358C2—21no—
359C2—82no—
360C2C89×#187911yescharacteristic
361C2C89×#219411yescharacteristic
362C2C89×#219511yescharacteristic
subgroupG/H
center, socleC22×C89#447
commutatorC2×C8C22×C4×C89
Frattini, cosocleC22×C8C23×C89
prime radicalC2×#135×C89C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C89 ◁ C22×C4×C89 ◁ #405×C89 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×#358×C89C2semidirect
5. C89×#1979C2semidirect
6. C89×#1387C2semidirect
7. C89×#1379C2semidirect
12. #510×C89C4semidirect
39. C2×Q16×C89C2×C4semidirect
56. M32×C89C2×C4semidirect
175. #13023C89direct (N × H)
185. C2×#358C2×C89semidirect
186. #1979C2×C89semidirect
187. #1387C2×C89semidirect
188. #1379C2×C89semidirect
189. C89#13023direct (N × H)
194. #510C4×C89semidirect
221. C2×Q16C2×C4×C89semidirect
238. M32C2×C4×C89semidirect

Maximal subgroups

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

subgroupindex
C2×#510×C892
C89×#29512
C2×#359×C892
C2×#358×C892
C89×#19792
C89×#13872
C89×#13792
#1302389