Finite Group Databasebeta

← #37543453

Subgroups — #37543453

Order 23168.

446 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26042075C211yesmaximal, characteristic
2C2×#19153845C211yesmaximal, characteristic, complemented
3#137×D181C211yesmaximal, characteristic, complemented
4#26042044C211yesmaximal, characteristic, complemented
5#26041555C211yesmaximal, characteristic, complemented
6#26041554C211yesmaximal, characteristic, complemented
7#26041553C211yesmaximal, characteristic, complemented
8#26041552C211yesmaximal, characteristic, complemented
9#26041541C211yesmaximal, characteristic, complemented
10#26041540C211yesmaximal, characteristic, complemented
11#26041539C211yesmaximal, characteristic, complemented
12#26041326C211yesmaximal, characteristic, complemented
13#26041260C211yesmaximal, characteristic, complemented
14#101×D181C211yesmaximal, characteristic, complemented
15#471×C181C211yesmaximal, characteristic, complemented
16C2×#15668448C2211yescharacteristic
17#41×D181C2211yescharacteristic
18C2×Q8×D181C2211yescharacteristic
19#19153849C2211yescharacteristic
20#19153849C2211yescharacteristic
21#19153848—21no—
22#19153847C2211yescharacteristic
23#19153846C2211yescharacteristic
24#19153846C2211yescharacteristic
25#19153845—21no—
26#19153845—21no—
27#19153845—21no—
28#19153845—21no—
29#19153845—21no—
30#19153845—21no—
31#19153842C2211yescharacteristic
32#19153840—21no—
33#19153837—21no—
34#19153835—21no—
35C2×Dic724C2211yescharacteristic, complemented
36C2×#15668439C2211yescharacteristic, complemented
37Q16×D181—21no—
38C2×#15668437C2211yescharacteristic, complemented
39SD16×D181—21no—
40#19153824—21no—
41#19153824C2211yescharacteristic
42#19153823C2211yescharacteristic
43#19153822—21no—
44#19153822C2211yescharacteristic
45C2×#15668432—21no—
46C2×#15668432C2211yescharacteristic
47M16×D181—21no—
48M16×D181C2211yescharacteristic
49M16×D181C2211yescharacteristic
50M16×D181C2211yescharacteristic
51#19153752C2211yescharacteristic, complemented
52#19153751C2211yescharacteristic, complemented
53#19153751C2211yescharacteristic, complemented
54#19153735C2211yescharacteristic, complemented
55#19153734C2211yescharacteristic, complemented
56#19153734C2211yescharacteristic, complemented
57#19153734C2211yescharacteristic, complemented
58#19153734C2211yescharacteristic, complemented
59#19153733C2211yescharacteristic, complemented
60#137×C181C2211yescharacteristic
61AGL(1,ℤ/8)×C181C2211yescharacteristic
62C2×SD16×C181C2211yescharacteristic, complemented
63#131×C181C2211yescharacteristic
64#108×C181C2211yescharacteristic, complemented
65#101×C181C2211yescharacteristic, complemented
66#100×C181C2211yescharacteristic, complemented
67#15668450D411yescharacteristic
68#15668449—21no—
69#15668449C2311yescharacteristic
70#15668448—21no—
71#15668448—21no—
72#15668448—21no—
73#15668448—21no—
74#15668448—21no—
75#15668448D411yescharacteristic
76C2×Dic362—21no—
77C2×Dic362C2311yescharacteristic
78C2×Dic362C2311yescharacteristic
79Q8×D181—21no—
80Q8×D181—21no—
81Q8×D181—21no—
82Q8×D181—21no—
83Q8×D181D411yescharacteristic
84C2×C22⋊D181—21no—
85D4×D181—21no—
86D4×D181D411yescharacteristic
87C22×Dic181—21no—
88C2×C4×D181—21no—
89C2×C4×D181—21no—
90C2×C4×D181C2311yescharacteristic
91Dic724—21no—
92Dic724—21no—
93Dic724—21no—
94Dic724—21no—
95#15668439—21no—
96#15668439—21no—
97#15668439—21no—
98#15668439—21no—
99#15668439—21no—
100#15668438—21no—
101#15668438—21no—
102#15668437—21no—
103#15668437—21no—
104#15668437—21no—
105#15668437—21no—
106#15668437—21no—
107#15668436—21no—
108#15668434—21no—
109#15668433—21no—
110#15668433C2311yescharacteristic
111#15668433C2311yescharacteristic
112#15668433C2311yescharacteristic
113#15668432—21no—
114#15668432—21no—
115#15668432—21no—
116#15668432—21no—
117#15668432—21no—
118#15668432D411yescharacteristic
119#15668432D411yescharacteristic
120#15668432D411yescharacteristic
121#15668432D411yescharacteristic
122C2×#13089678—21no—
123C2×#13089678C2311yescharacteristic
124C8×D181—21no—
125C8×D181—21no—
126C8×D181—21no—
127C8×D181—21no—
128C8×D181—21no—
129#41×C181C2311yescharacteristic
130C2×Q8×C181C2311yescharacteristic
131C2×D4×C181C2311yescharacteristic
132Q16×C181—21no—
133SD16×C181—21no—
134SD16×C181—21no—
135SD16×C181—21no—
136SD16×C181—21no—
137D8×C181—21no—
138M16×C181—21no—
139M16×C181C2311yescharacteristic
140M16×C181C2311yescharacteristic
141M16×C181C2311yescharacteristic
142C2×C8×C181—21no—
143C2×C8×C181C2311yescharacteristic
144C22×D181—21no—
145C22×D181#4111yescharacteristic
146Dic362—21no—
147Dic362—21no—
148Dic362—21no—
149Dic362—21no—
150Dic362—21no—
151Dic362—41no—
152Dic362—41no—
153Dic362C2×D411yescharacteristic
154D724—21no—
155D724C2×D411yescharacteristic
156C22⋊D181—21no—
157C22⋊D181—21no—
158C22⋊D181—21no—
159C22⋊D181—41no—
160C22⋊D181—41no—
161C2×Dic181—21no—
162C2×Dic181—21no—
163C2×Dic181—21no—
164C2×Dic181—41no—
165C2×Dic181—41no—
166C2×Dic181#4111yescharacteristic
167C4×D181—21no—
168C4×D181—21no—
169C4×D181—21no—
170C4×D181—41no—
171C4×D181—41no—
172C4×D181C2×D411yescharacteristic
173C4×D181C2×D411yescharacteristic
174C4×D181C2×D411yescharacteristic
175C4×D181C2×D411yescharacteristic
176#13089678—21no—
177#13089678—21no—
178#13089678—21no—
179#13089678C2×D411yescharacteristic
180#13089678C2×D411yescharacteristic
181C23×C181—21no—
182Q8×C181—21no—
183Q8×C181—21no—
184Q8×C181C2×D411yescharacteristic
185D4×C181—21no—
186D4×C181—21no—
187D4×C181—21no—
188D4×C181C2×D411yescharacteristic
189C2×C4×C181—21no—
190C2×C4×C181—21no—
191C2×C4×C181C2411yescharacteristic
192C8×C181—21no—
193C8×C181—21no—
194C8×C181—21no—
195C8×C181C2×D411yescharacteristic
196C8×C181C2×D411yescharacteristic
197C22×C181—21no—
198C22×C181—41no—
199C22×C181—81no—
200C22×C181C2×#4111yescharacteristic
201C2×D181—21no—
202C2×D181—41no—
203C2×D181—81no—
204C2×D181#12111yescharacteristic
205C2×D181#12111yescharacteristic
206C4×C181—21no—
207C4×C181—41no—
208C4×C181C22×D411yescharacteristic
209C4×C181C22×D411yescharacteristic
210Dic181—21no—
211Dic181—41no—
212Dic181—41no—
213Dic181#12111yescharacteristic
214Dic181#12111yescharacteristic
215C2×C181—21no—
216C2×C181—41no—
217C2×C181—81no—
218C2×C181C2×#12111yescharacteristic
219D181—21no—
220D181—21no—
221D181—41no—
222C181#306911yescharacteristic, complemented, Sylow
223#3069—1811nomaximal, Sylow
224#575—1811no—
225C2×#137—1811no—
226C2×#137—1811no—
227#568—1811no—
228#473—1811no—
229#473—1811no—
230#473—1811no—
231#473—1811no—
232#471—1811no—
233#471—1811no—
234#471—1811no—
235#471D18111yescharacteristic, complemented
236#430—1811no—
237#413—1811no—
238C2×#101—1811no—
239C2×#41—1811no—
240C2×#41—1811no—
241C22×Q8—1811no—
242#137—3621no—
243#137—3621no—
244#137—3621no—
245#137—3621no—
246#137—3621no—
247#137—3621no—
248#137—3621no—
249#137—1811no—
250#137—1811no—
251#137—1811no—
252#137—1811no—
253#137—1811no—
254#137C2×D18111yescharacteristic
255AGL(1,ℤ/8)—3621no—
256AGL(1,ℤ/8)—1811no—
257AGL(1,ℤ/8)C2×D18111yescharacteristic
258#135—3621no—
259#135—3621no—
260C2×Q16—3621no—
261C2×Q16—1811no—
262C2×Q16—1811no—
263C2×SD16—3621no—
264C2×SD16—1811no—
265C2×SD16C2×D18111yescharacteristic, complemented
266#131—3621no—
267#131—3621no—
268#131—1811no—
269#131—1811no—
270#131—1811no—
271#131C2×D18111yescharacteristic
272C2×M16—3621no—
273C2×M16—3621no—
274C2×M16—1811no—
275C2×M16—1811no—
276C2×M16—1811no—
277C2×M16—1811no—
278#108—1811no—
279#108—1811no—
280#108—1811no—
281#108C2×D18111yescharacteristic, complemented
282#101—1811no—
283#101—1811no—
284#101—1811no—
285#101—1811no—
286#101—1811no—
287#101C2×D18111yescharacteristic, complemented
288#100—1811no—
289#100C2×D18111yescharacteristic, complemented
290#41—3621no—
291#41—3621no—
292#41—3621no—
293#41—3621no—
294#41—3621no—
295#41—3621no—
296#41—1811no—
297#41—1811no—
298#41—1811no—
299#41C22×D18111yescharacteristic
300C2×Q8—3621no—
301C2×Q8—3621no—
302C2×Q8—3621no—
303C2×Q8—3621no—
304C2×Q8—3621no—
305C2×Q8—1811no—
306C2×Q8—1811no—
307C2×Q8—1811no—
308C2×Q8C22×D18111yescharacteristic
309C2×D4—3621no—
310C2×D4—3621no—
311C2×D4—1811no—
312C2×D4C22×D18111yescharacteristic
313C22×C4—3621no—
314C22×C4—3621no—
315C22×C4—3621no—
316C22×C4—1811no—
317Q16—21no—
318Q16—3621no—
319Q16—3621no—
320Q16—3621no—
321Q16—3621no—
322Q16—3621no—
323Q16—3621no—
324Q16—3621no—
325Q16—3621no—
326Q16—3621no—
327SD16—21no—
328SD16—21no—
329SD16—21no—
330SD16—21no—
331SD16—3621no—
332SD16—3621no—
333SD16—3621no—
334SD16—3621no—
335SD16—3621no—
336SD16—3621no—
337SD16—3621no—
338SD16—3621no—
339D8—21no—
340D8—3621no—
341M16—21no—
342M16—3621no—
343M16—3621no—
344M16—3621no—
345M16—3621no—
346M16—3621no—
347M16—3621no—
348M16—1811no—
349M16—1811no—
350M16—1811no—
351M16—1811no—
352M16—1811no—
353M16—1811no—
354M16—1811no—
355M16C22×D18111yescharacteristic
356M16C22×D18111yescharacteristic
357M16C22×D18111yescharacteristic
358C2×C8—21no—
359C2×C8—3621no—
360C2×C8—3621no—
361C2×C8—3621no—
362C2×C8—3621no—
363C2×C8—3621no—
364C2×C8—3621no—
365C2×C8—1811no—
366C2×C8C22×D18111yescharacteristic
367C23—21no—
368C23—3621no—
369C23—1811no—
370Q8—21no—
371Q8—21no—
372Q8—3621no—
373Q8—3621no—
374Q8—3621no—
375Q8—3621no—
376Q8—3621no—
377Q8—1811no—
378Q8—7241no—
379Q8—7241no—
380Q8D4×D18111yescharacteristic
381D4—21no—
382D4—21no—
383D4—21no—
384D4—3621no—
385D4—3621no—
386D4—3621no—
387D4—3621no—
388D4—1811no—
389D4—7241no—
390D4—7241no—
391D4D4×D18111yescharacteristic
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—3621no—
395C2×C4—3621no—
396C2×C4—3621no—
397C2×C4—3621no—
398C2×C4—3621no—
399C2×C4—3621no—
400C2×C4—1811no—
401C2×C4—1811no—
402C2×C4—1811no—
403C2×C4—1811no—
404C2×C4—1811no—
405C2×C4—7241no—
406C2×C4—7241no—
407C2×C4—7241no—
408C2×C4—7241no—
409C2×C4C23×D18111yescharacteristic
410C8—21no—
411C8—21no—
412C8—21no—
413C8—3621no—
414C8—3621no—
415C8—3621no—
416C8—1811no—
417C8—1811no—
418C8D4×D18111yescharacteristic
419C8D4×D18111yescharacteristic
420C22—21no—
421C22—41no—
422C22—81no—
423C22—3621no—
424C22—14481no—
425C22—1811no—
426C22—1811no—
427C22—7241no—
428C22#41×D18111yescharacteristic
429C4—21no—
430C4—41no—
431C4—3621no—
432C4—1811no—
433C4—1811no—
434C4—7241no—
435C4—7241no—
436C4C2×D4×D18111yescharacteristic
437C4C2×D4×D18111yescharacteristic
438C2—21no—
439C2—41no—
440C2—81no—
441C2—3621no—
442C2—3621no—
443C2—7241no—
444C2#121×D18111yescharacteristic
subgroupG/H
centerC2#121×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#471×C181C2
socleC2×C181C2×#121
prime radical#26042075C2
hypercenter#471D181
hypocenterC181#3069
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C2 ◁ C2×C4 ◁ #471

Complements

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

NH ≅ G/Ntype
2. C2×#19153845C2semidirect
3. #137×D181C2semidirect
4. #26042044C2semidirect
5. #26041555C2semidirect
6. #26041554C2semidirect
7. #26041553C2semidirect
8. #26041552C2semidirect
9. #26041541C2semidirect
10. #26041540C2semidirect
11. #26041539C2semidirect
12. #26041326C2semidirect
13. #26041260C2semidirect
14. #101×D181C2semidirect
15. #471×C181C2semidirect
35. C2×Dic724C22semidirect
36. C2×#15668439C22semidirect
38. C2×#15668437C22semidirect
51. #19153752C22semidirect
52. #19153751C22semidirect
53. #19153751C22semidirect
54. #19153735C22semidirect
55. #19153734C22semidirect
56. #19153734C22semidirect
57. #19153734C22semidirect
58. #19153734C22semidirect
59. #19153733C22semidirect
62. C2×SD16×C181C22semidirect
64. #108×C181C22semidirect
65. #101×C181C22semidirect
66. #100×C181C22semidirect
222. C181#3069semidirect
235. #471D181semidirect
265. C2×SD16C2×D181semidirect
281. #108C2×D181semidirect
287. #101C2×D181semidirect
289. #100C2×D181semidirect

Maximal subgroups

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

subgroupindex
#260420752
C2×#191538452
#137×D1812
#260420442
#260415552
#260415542
#260415532
#260415522
#260415412
#260415402
#260415392
#260413262
#260412602
#101×D1812
#471×C1812
#3069181